Advances in Physical Organic Chemistry, Volume 44

Advances in Physical Organic Chemistry Volume 44

Editor JOHN P. RICHARD Department of Chemistry University at Buffalo, SUNY Buffalo, NY, USA

Amsterdam – Boston – Heidelberg – London – New York – Oxford Paris – San Diego – San Francisco – Singapore – Sydney – Tokyo Academic Press is an imprint of Elsevier

Contributors to Volume 44 Claude F. Bernasconi Department of Chemistry and Biochemistry, University of California, Santa Cruz, CA 95064, USA W.W. Cleland Department of Biochemistry and Institute for Enzyme Research, University of Wisconsin-Madison, Madison WI 53726, USA Ronald Kluger Davenport Chemistry Laboratories, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada Scott O.C. Mundle Davenport Chemistry Laboratories, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada Rory More O’Ferrall School of Chemistry and Chemical Biology, University College Dublin, Belfield, Dublin 4, Ireland Charles L. Perrin Department of Chemistry & Biochemistry, University of California—San Diego, La Jolla, CA 92093-0358, USA Jakob Wirz Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland Hiroshi Yamataka Department of Chemistry, College of Science and Research Institute for Future Molecules, Rikkyo University, Tokyo, Japan

xi

The low-barrier hydrogen bond in enzymic catalysis W.W. CLELAND Department of Biochemistry and Institute for Enzyme Research, University of Wisconsin-Madison, Madison, WI 53726, USA 1 Introduction 1 2 Properties of hydrogen bonds 1 3 Role of low-barrier hydrogen bonds in enzymatic reactions 3 Enolization reactions 3 Facilitated tetrahedral intermediate formation 6 Facilitated proton ionization 10 Aspartic proteases 12 Miscellaneous enzymes 13 Acid–Base catalysis 14 4 Conclusion 15 References 15

1

Introduction

The term ‘‘low-barrier hydrogen bond’’ was introduced by me in 1992 to describe hydrogen bonds between groups of equal pK that showed low deuterium fractionation factors (as low as 0.3).1 It was not until an Enzyme Mechanisms conference in Key Largo, however, that a number of us finally realized how such bonds can help catalyze enzymic reactions and papers describing this appeared in 1993 and 1994.2–5 Since then such bonds have been shown to play a role in many enzymic reactions and a Google search under ‘‘low-barrier hydrogen bond’’ turns up over 5000 hits. In this review I shall describe the properties of low-barrier hydrogen bonds and then give a number of examples. I have not tried to cover the entire literature and apologize to those whose works are not mentioned.

2

Properties of hydrogen bonds

Hydrogen bonds come in a continuum of bond lengths and strengths. Those in water which hold it together as a liquid are
2.8 A˚ between oxygens and are weak (only a few kcal mol1). Since the pK of water as an acid is above 15 and its pK as a base is less than –1, the pK’s of the two 1 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44001-7

Ó 2010 Elsevier Ltd. All rights reserved

2

W.W. CLELAND

oxygens in the hydrogen bond are drastically different and the hydrogen is covalently bound to one oxygen with a bond distance of 1 A˚ and weakly bonded electrostatically to the other oxygen. When the pK’s of the two groups are the same, as in a hydrogen bond between formic acid and formate ion, the bond is shorter (2.5–2.6 A˚) and the zero point energy level of the hydrogen is at or above the barrier (thus ‘‘low-barrier hydrogen bond,’’ Fig. 1).6–8 Neutron diffraction of crystals containing such bonds show a diffuse distribution centered between the two heavy atoms.9 In certain cases where the bond is especially short, there is no barrier as in the F–H–F or HO–H–OH ions which are only 2.3 A˚ long.10,11 Low-barrier hydrogen bonds are quite strong (as much as 27 kcal mol1 in the gas phase and perhaps 12 in aqueous solution7), but in a medium with a dielectric constant of
7 (similar to what occurs in an enzyme active site) the strength decreases by
1 kcal mol1 per pH unit mismatch in the pK’s of the groups involved.12 Thus there is a continuum between the very strong ones with matched pK’s and the weak ones with very different pK’s and the distances similarly differ as well. Low-barrier hydrogen bonds have considerable covalent character,6,13 which decreases as the bonds weaken and lengthen, so that the weak ones are only electrostatic in nature. As noted in 1992, low-barrier hydrogen bonds show low fractionation factors, with up to threefold discrimination against deuterium. They show downfield chemical shifts in proton nuclear magnetic resonance (NMR) of 18–20 ppm. At first it was thought that they only occur in the gas phase or organic solvents, but it is now clear that they can occur in solutions containing a high mole fraction of water, even at room temperature.14,15 What limits their determination in aqueous solution is rapid exchange with solvent protons. Hydrogen bonds can occur between two oxygens, two nitrogens, or one of each. We will show examples of O–O and O–N bonds in the discussion below.

(a)

O O

(b)

H H

O O

O

(c)

H

O

O

H

O

Fig. 1 Energy diagrams for hydrogen bonds between groups of equal pK. (a) Weak hydrogen bond; O–O distance 2.8 A˚. (b) Low-barrier hydrogen bond (2.55 A˚); the hydrogen diffusely distributed. (c) Single-well hydrogen bond (2.29 A˚). Horizontal lines are zero point energy levels for hydrogen (upper) and deuterium (lower).

THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

3

3

Role of low-barrier hydrogen bonds in enzymatic reactions

ENOLIZATION REACTIONS

The first examples of enzymatic reactions where low-barrier hydrogen bonds played a role involved enolization of the substrate to change the pK of a key group in the reaction. Mandelate racemase enolizes R or S mandelate to convert the carboxyl group into an aci-carboxylate which can be protonated on opposite sides to give the R or S forms. In the ground state, one oxygen of the carboxyl group of mandelate is coordinated to Mg2þ and the other oxygen is hydrogen bonded to Glu317 which is protonated.16 The pK of a CTO group is low, so this is a weak hydrogen bond. In the aci-carboxylate intermediate, however, the pK of its oxygen will be similar to that of Glu317 and the hydrogen bond becomes a low-barrier one (Fig. 2). The energy liberated by formation of the strong hydrogen bond lowers the activation for formation of the intermediate. The 105 reduction in kcat for the E317Q mutant supports this model.17 A similar situation occurs with triose-P isomerase, where Glu165 abstracts a proton from either glyceraldehyde-3-P or dihydroxyacetone-P to give an enediolate intermediate. The carbonyl group of the substrate is hydrogen bonded to a neutral imidazole in the active site; this will be a weak hydrogen bond because of the huge mismatch in pK’s.18 The pK of both the imidazole and the enediol intermediate, however will be
11, and thus this hydrogen bond becomes a low-barrier one in the intermediate Fig. 3). An isoenergetic shift of the imidazole from one OH to the other shifts the strong hydrogen bond to the oxygen destined to become a carbonyl group when the intermediate is protonated by Glu165 to complete the reaction. Ketosteroid isomerase is another enzyme in which enolization of the substrate changes the pK of a key atom so that a low-barrier hydrogen bond forms and helps stabilize the intermediate. Asp38 is the general base that removes a proton from the substrate, and Tyr14 is hydrogen bonded to the carbonyl oxygen of the substrate. The pK’s of a ketone and of tyrosine are

Mg

Mg

HO

HO O

C H

O

C

C O

Lys166 (bases) His297

C

H Glu

O

H

Glu

H-base

Fig. 2 Mechanism of mandelate racemase.16,17 Lys166 and His297 are the two general bases and are on opposite sides of mandelate.

4

W.W. CLELAND H Glu– HC

H OH

C

OH

C

O

GluH C

O

HN

N

H

CH2OPO32–

CH2OPO32–

H

H

C

O

HN

N

C

O

C

OH

H

N

N

N

N

GluH Glu– HC

OH

CH2OPO32–

CH2OPO32–

Fig. 3 Mechanism of triose-P isomerase.4 Note the isoenergetic shift of the histidine between the two OH groups of the enediolate intermediate; a low-barrier hydrogen bond is present in both structures.

drastically different, but in the dienolate intermediate, the pK’s become more similar. An analog aromatic in the A ring and containing a phenolic hydroxyl in place of the ketone bound at least 1000-fold tighter to the D38N mutant than to wild-type isomerase.19 The neutral Asn38 mimics the protonated state of Asp38 after the formation of the intermediate dienolate. In the inhibitor complex proton NMR peaks were at 18.15 and 11.6, with the proton at 18.15 having a deuterium fractionation factor of 0.34 and the hydrogen bond having a strength of 7.1 kcal mol1 more than one between inhibitor and water. This increase in hydrogen bond strength corresponds to over 5 orders of magnitude rate acceleration and matches the decrease in rate of 4.7 orders of magnitude in the Y14F mutant. Subsequent work has shown that Asp99 is involved in the hydrogen bond network in this enzyme and the 18.15 ppm NMR peak is from a hydrogen bond between it and Tyr14.20 The 11.6 ppm peak comes from the hydrogen bond between the intermediate and Tyr14. Despite this complexity, it is still true that formation of a strong hydrogen bond in the presence of the intermediate decreases the activation energy of the reaction and thus provides catalysis. Aconitase contains a 4Fe–4S center with citrate or isocitrate binding with one of their carboxyl groups and the OH group coordinated to the Fe at one corner of the Fe–S cluster.21,22 A water molecule is also coordinated to this

THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

5

Fe and is hydrogen bonded to a free carboxyl group. The general base for the elimination reaction is Ser642, which donated its proton to the Fe-bound hydroxide when the substrate bound. Proton removal by Ser642 produces an aci-carboxylate from the carboxyl next to the carbon from which the proton was removed, and the pK of the aci-carboxylate now is a close match to the pK of the Fe-bound water to which it is hydrogen bonded. This hydrogen bond thus becomes a low-barrier one, its formation providing part of the energy needed to form the aci-carboxylate (Fig. 4). His101 then protonates the Fe-coordinated OH of the substrate to allow it to be eliminated to give cis-aconitate. In the E-isocitrate X-ray structure the hydrogen bond between the Fe-bound water and the carboxyl of isocitrate is 2.7 A˚ long, while in a similar structure with the nitro analog of isocitrate bound as an aci-nitronate the distance is 2.5 A˚.21 Citrate synthase catalyzes the enolization of acetyl-CoA and attack of the enolate on oxaloacetate to form citryl-CoA, which is then hydrolyzed. Asp375 takes the proton from the methyl group of acetyl-CoA and neutral His274 hydrogen bonds to the carbonyl oxygen to stabilize the enolate.23 X-ray structures of carboxyl or amide analogs of acetyl-CoA showed 2.4–2.5 A˚ hydrogen bonds between the carboxyl or amide group of the inhibitor (replacing the methyl of acetyl-CoA) and Asp375.24 The Ki of the amide inhibitor was pH independent, while that of the carboxylate decreased as the pH decreased, showing that the protonated form was the inhibitor. The carboxyl inhibitor binds 4 orders of magnitude tighter than acetyl-CoA and thus the low-barrier hydrogen bond (chemical shift 20 ppm25) contributes at least this much to binding. During the catalytic reaction, the low-barrier hydrogen bond should be between His274 and the enolate oxygen, since their pK’s will be similar, and the energy from formation of the stronger hydrogen bond will help catalyze the enolization (Fig. 5). Vitamin K-dependent carboxylase uses vitamin K epoxidation to drive the carboxylation of glutamate groups in Gla domains. It is thought that reaction of oxygen with reduced vitamin K produces a strongly basic form of an

H

H

OH Fe

O

Fe

O

O HO C

O

C H

H His C

C CH2

H – – O Ser

O HO

O

C COO–

O

C

H H

H His C

OH Fe

O C CH2

H HO–Ser

O–

COO–

O

O

O HOH

His

C

C

C

C CH2

H

O

COO–

HO–Ser

Fig. 4 Mechanism of aconitase.4 The aci-carboxylate intermediate shares a low-barrier hydrogen bond with the Fe–OH group.

6

W.W. CLELAND COO–

O

HN

N

Arg

COO–

O

C

C SCoA

H

N

N

Arg O

C

CH3

O

C SCoA

His

CH2

His CH2

CH2

Asp–

COO–

AspH

COO–

COO–

O

HN

N

Arg

COO–

O

C

C SCoA

HN

N

Arg HO

C

CH2

HO

C SCoA

His

CH2

His CH2

Asp–

COO–

COO–

O

H

Arg

N

N

CH2

O

H

COO–

H

Asp

COO–

O

HN

C

C

N

Arg HO

C

CH2

HO

C SCoA

His

CH2

His CH2

O –

COO

H Asp

H

CH2 COO

H + HSCoA

O –

Asp

–

Fig. 5 Putative mechanism of citrate synthase.4 A low-barrier hydrogen bond helps to stabilize the enol and tetrahedral intermediates.

epoxide that removes a proton from a glutamate residue to give a carbanion intermediate that reacts with CO2. It was recently found that a H160A mutant carried out epoxidation readily, but carboxylation very poorly.26 It was postulated that His160 forms a hydrogen bond to one oxygen of the carboxyl group of glutamate. This will be a weak hydrogen bond before enolization, but proton removal will give an aci-carboxylate whose pK is a close match to that of neutral histidine. Thus the authors proposed that a low-barrier hydrogen bond between aci-carboxylate and His160 helped to stabilize the intermediate. As yet there is no structural evidence in support of this attractive hypothesis.

FACILITATED TETRAHEDRAL INTERMEDIATE FORMATION

A low-barrier hydrogen bond forms between Asp102 and His57 in the tetrahedral intermediate of the reaction catalyzed by chymotrypsin and similar serine proteases. In the free enzyme the pK of Asp102 and the neutral form of His57 are quite different, but when the Ser195 proton is transferred to His57 during formation of the tetrahedral intermediate, the pK’s of Asp102 and protonated His57 now become matched and the hydrogen bond between

THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

7

them becomes a low-barrier one, thus providing the energy for formation of the unstable intermediate (Fig. 6).5 Transfer of the proton from His57 to the leaving amino group gives an acyl enzyme and dissipates the strength of the His57 O Ser195

:N

OH

N H

C

Asp102

C

Asp102

O

O C Peptidyl

NHR

O C Peptidyl Ser195

His57 O

NHR :N

OH

N H

O

O–

Peptidyl C

His57 O

NHR

y–

Ser195

O

HN

y+

N

H

C

Asp102

O

H2NR

O

Peptidyl

His57 O

C

C Ser195

O

:N

N H

Asp102

O

Fig. 6 Mechanism of chymotrypsin.5 A low-barrier hydrogen bond between Asp102 and His57 helps stabilize the tetrahedral intermediate.

8

W.W. CLELAND

low-barrier hydrogen bond. Clear evidence for this mechanism is provided by observation of tetrahedral adducts of trifluoromethyl ketone inhibitors with the enzyme. In these complexes the proton chemical shift of the proton in the Asp102–His57 hydrogen bond is 18–19 ppm and the fractionation factor is 0.3–0.4. The exchange rate of the proton with the solvent ranges from 282 s1 for N–AcF–CF3 with a Ki of 26 mM to 12.4 s1 for N–AcLF–CF3 with a Ki of 1.8 mM. The pK of His57 in these complexes is 10.7 or 12.1. The pK of 12.1 is 5 pH units higher than that in free enzyme, corresponding to 5 orders of magnitude rate acceleration.27,28 This situation was mimicked by observing complexes of N-alkylimidazoles with carboxylic acids in chloroform.29 As the pK of the acid increased, the chemical shift of the proton in the hydrogen bond moved downfield to 18 ppm and then moved back upfield. With 2,2-dichloropropionate the chemical shift of 18 ppm did not change with dilution, suggesting a strong hydrogen bond between the two molecules. The chemical shifts of complexes with more upfield protons moved further upfield on dilution, showing that they were weaker. Calorimetric measurements of complexes between 2,2-dichloropropionate and N-methyl or N-t-butylimidazole gave values of 12 or 15 kcal mol1 for the enthalpy of formation.30 The IR spectrum of a complex with 2,2-dichloropropionate showed two peaks for the CTO stretch at 1700 cm1 for the low-barrier hydrogen bond (
2/3 of the complex) and 1647 cm1 for the edge-on ion pair where the carboxyl group is perpendicular to the ring of the imidazole and both oxygens are in contact with the positively charged nitrogens (
1/3 of the complex). The NMR shift of 18 ppm is an average for the two species, which are in rapid equilibrium on the NMR timescale. An 0.78 A˚ structure of subtilisin resolved the proton between His64 and Asp32 of the catalytic triad.31 The distance of the hydrogen bond was 2.62 A˚ with the proton 1.2 A˚ from His64 and 1.5 A˚ from Asp32. The authors felt that this was not a low-barrier hydrogen bond because His64 was not protonated, but the short distance suggests that when His64 does become protonated during formation of the tetrahedral intermediate, it will become a low-barrier one. For the reaction catalyzed by cytidine deaminase, an analog of cytidine where the 3–4 bond is a single one and there is a hydroxy group at C4 (zebularine 3,4-hydrate) is a competitive inhibitor with a Ki of 1012 M.32 An X-ray structure of this inhibitor bound to the enzyme shows a 2.45 A˚ hydrogen bond between the OH group at C4 and the carboxylate of Glu104.33 The OH group is also coordinated to a Zn2þ ion and the other oxygen of Glu104 is hydrogen bonded to N3 (2.74 A˚). This structure corresponds to the putative tetrahedral intermediate formed by attack of the Zn-bound hydroxyl group on C4 of the pyrimidine ring, but with the amino group at C4 replaced with hydrogen (Fig. 7). It appears that the formation of a low-barrier hydrogen bond between the OH group and Glu104 may provide some of the energy

THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

9

His102 Cys132

S Zn

S

C C

Glu104

2.49Å O H O H

C

Cys129

HN

O HN O

NH

N

Ala103

Ribose

Fig. 7 Structure of cytidine deaminase with zebularine 3,4-hydrate bound.33 The lowbarrier hydrogen bond between Glu104 and the Zn–OH would help stabilize the tetrahedral intermediate, which would have an NH2 in place of the H at C4 of the ring in this structure.

needed to form the tetrahedral intermediate. Transfer of the proton in this bond to the amino group then permits it to leave as ammonia to complete the reaction. However, the proton NMR spectrum of the bound inhibitor did not show any downfield peaks that could be assigned to a low-barrier hydrogen bond, so its importance in the reaction is uncertain. Thermolysin and carboxypeptidase use Zn2þ to polarize the carbonyl group of the amide substrate to permit attack by Zn-bound water. A glutamate residue (143 in thermolysin and 270 in carboxypeptidase) acts as a general base and is hydrogen bonded to the Zn-bound water. A proton is transferred to the leaving nitrogen, which permits the tetrahedral intermediate that is bidentately coordinated to Zn to decompose to the final products of the reaction (Fig. 8). The tetrahedral intermediate has been mimicked by several phosphonates with Ki values as low as 10 fM. X-ray structures show these inhibitors as bidentate ligands of Zn and the hydrogen bond between the catalytic glutamate and one Zn-coordinated oxygen of the phosphono group is 2.3–2.5 A˚ in the three structures of each of the two enzymes.34–37 These short

R–NH

Glu

H

R–NH

R C

H O

O Zn

Glu

H

R

R–NH

C

H

O

O Zn

Glu

H

R

R–NH

C

H O

O Zn

Glu

H

R C

H

O

O Zn

Fig. 8 Mechanism of thermolysin and carboxypeptidase based on X-ray structures of enzymes with bound phosphonate inhibitors.34–37

10

W.W. CLELAND 18.00 ppm 12.67 ppm (normal H-bond) (strong H-bond) His48

Asp99

CH2–(CH2)5–CH3 O

O–

H

N

N

H

Oδ–

P

Oδ– O

O H3C–(CH2)7 –S–CH2

C H

H2C

O

P

O

+

(CH2)2 –NH3

O–

Fig. 9 Structure of phospholipase A2 with bound phosphonate inhibitor mimicking the tetrahedral intermediate.38

distances suggest that this hydrogen bond in the tetrahedral intermediate is a low-barrier one, with the energy released by its formation helping to form the high-energy intermediate. Phospholipase A2 catalyzes the hydrolysis of phospholipids at the sn-2 bond, using a water molecule coordinated to Ca2þ. Enzymes from bovine pancreas and bee venom are similar in many respects and both contain an aspartate and histidine as catalytic groups. In the presence of phosphonate inhibitors that mimic a tetrahedral intermediate, a low-barrier hydrogen bond exists between the histidine and a phosphonate oxygen, while the hydrogen bond between the histidine and aspartate is a normal one (Fig. 9).38 The proton NMR chemical shifts for the protons in the low-barrier hydrogen bond is
18 ppm, while the other proton has a chemical shift of
13 ppm. The lowfield proton has a fractionation factor of 0.6 and the pK of the histidine is shifted from 5.7 in free enzyme to 9 in the presence of the inhibitor. This suggests a minimum of 4.5 kcal mol1 extra energy made available for catalysis by the low-barrier hydrogen (the actual value is probably higher, as the inhibitor dissociates when the histidine is deprotonated).

FACILITATED PROTON IONIZATION

In the liver alcohol dehydrogenase reaction the alcohol substrate is bound to a Zn2þ ion in the active site. The proton of the OH group is transferred via a hydrogen bond network involving Ser48 and the ribose 20 -OH of NAD to His51. Hydride transfer from the alkoxide intermediate then completes the reaction. In a structure with NAD and pentafluorobenzyl alcohol bound, the distance between the oxygens of the alcohol and Ser48 is 2.5 A˚.39 In D2O solvent isotope effects on single turnover reactions of benzyl alcohol with

THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

11

E-NAD, the fractionation factor of the proton between the alcohol and Ser48 was 0.37 and that in the transition state was 0.73, partway to
1.0, the value expected for the weak hydrogen bond between Ser48 and the aldehyde product.40 It thus appears that in the alkoxide intermediate the hydrogen bond between the alcohol substrate and Ser48 is a low-barrier one, with the energy released by its formation driving the proton movement to His51, which would otherwise not be energetically favorable (Fig. 10). UDP-galactose 4-epimerase contains bound NAD and catalyzes the interconversion of UDP-glucose and UDP-galactose via a 40 -keto intermediate. Two residues, Ser132 and Tyr157 are in close proximity of the 40 -OH of the substrate, with Ser132 only 2.5 A˚ from the 40 -OH. It was postulated that Tyr147 is the general base for proton removal from the 40 -OH during hydride transfer to give the 40 -keto intermediate, but that a low-barrier hydrogen bond between Ser132 and the 40 -OH provided the energy to help drive the process.41 This situation is reminiscent of that with liver alcohol dehydrogenase discussed above. Yeast pyrophosphatase uses a water molecule bound between two Mg2þ ions as the nucleophile to attack bound Mg-pyrophosphate. Asp117 acts as a general base to deprotonate this bound water, whose pK is 5.85.42 It was suggested on the basis of X-ray structures and the similar pK’s that the hydrogen bond between Asp117 and the nucleophilic water was a low-barrier one.43 Coordination to both Mg2þ ions as well as formation of a low-barrier hydrogen bond should certainly be sufficient to lower the pK of the bound water to the observed value. Pyruvate decarboxylase binds thiamine diphosphate as its cofactor, and the pK of the pyrimidine ring of the cofactor is 5.0. N10 of the ring can form a hydrogen bond to Glu50 when the ring is in the 10 ,40 -imino tautomer and it has been suggested that a low-barrier hydrogen bond forms between N10 and Glu50 in order to enhance the proportion of imino tautomer, with the N40 NH group then removing the proton to give the active ylide form of the cofactor (Fig. 11).44

Zn O H

C

S48 H

Zn δ

O

H NAD

H

O

H

C

H

S48

Zn

O

O δ

NAD

H

C

R

R

R

ΦR = 0.37

ΦT = 0.73

ΦP = 1.0

S48 H

O NADH

Fig. 10 Changes in the hydrogen bond between Zn–OH and Ser48 during hydride transfer to NAD in the liver alcohol reaction.40 The  values are deuterium fractionation factors.

12

W.W. CLELAND O Glu

C O

CH2 N N

N

NH2 H

S

OPP ThDP

O Glu

C O

H

CH2 N N

N

NH H

S

OPP 1′,4′-imino tautomer of ThDP

O Glu

C O

H

CH2 N N

NH2

N S

OPP ThDP ylide

Substrate

Fig. 11 Possible formation of a low-barrier hydrogen bond between Glu50 and bound thiamin-PP to enhance the proportion of ylide in the pyruvate decarboxylase reaction.44

ASPARTIC PROTEASES

Aspartic proteases have two aspartates hydrogen bonded to each other and sharing a water molecule between their other oxygens. This water then becomes the nucleophile for attack on the substrate. Ab initio calculations on human immunodeficiency virus (HIV)-1 protease found that the most stable form is one where there is a low-barrier hydrogen bond (2.5  0.1 A˚) between the aspartates and a net negative charge to the cluster (Fig. 12).45 Northrop then formulated a mechanism for the protease in which the lowbarrier hydrogen bond becomes a normal one as protons shift during attack on the substrate to form a tetrahedral intermediate.46 The central proton then

THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

13

O H

H

O

O C

C Asp25

O

H

O

Asp25′

Fig. 12 Low-barrier hydrogen bond between aspartates of HIV protease to generate nucleophilic water.45 The overall cluster has a negative charge.

shifts back to the other aspartate as the leaving group is protonated and the tetrahedral intermediate falls apart. Product release, replacement with water, and deprotonation then reform the low-barrier hydrogen bond and the enzyme is cocked for the next catalytic cycle. In contrast to this proposal, X-ray and neutron diffraction studies of complexes of aspartic proteases with bound inhibitors have found hydrogen bonds other than that between the two aspartates to be short and likely low-barrier ones. The 1.03 A˚ structure of a complex with a phenylnorstatine inhibitor shows a 2.97 A˚ hydrogen bond between the aspartates with the proton visible midway between the two oxygens.47 By contrast, the hydrogen bonds from the other oxygens of the aspartates to a hydroxyl and ketone of the inhibitor are 2.61 and 2.55 A˚. A 1.65 A˚ structure with the products bound showed the hydrogen bond between the two aspartates to be 2.30 A˚ long, certainly a low-barrier hydrogen bond.48 In a neutron diffraction structure of endothiapepsin with an inhibitor thought to mimic the tetrahedral intermediate, hydrogen bonds from the aspartates to the hydroxyl of the inhibitor were
2.6 A˚, and a hydrogen bond was not seen between the aspartates.49 A neutron diffraction structure of endothiapepsin with an inhibitor with a gem-diol in the active site showed hydrogen bonds of 2.54 and 2.65 A˚ between the gem-diol oxygens and oxygens of the aspartates, while the other aspartate oxygens were 2.93 A˚ apart.50 A 1.6 A˚ X-ray structure of HIV-1 protease with bound products shows 2.4 and 2.45 A˚ hydrogen bonds from the aspartates to the carboxyl of one product, with the distance between the other oxygens of the aspartate being 2.95 A˚.51 It is clear from these structures that a number of possible hydrogen bond orientations are possible, depending on what is bound. Whether Northrop’s mechanism is correct in all of its details is not yet clear, but it appears that low-barrier hydrogen bonds do play a role in aspartic proteases.

MISCELLANEOUS ENZYMES

A low-field resonance at 19.1 ppm is seen in the proton NMR spectrum of 2-amino-3-ketobutryate-CoA ligase. The signal is present only when the cofactor pyridoxal-P is bound and it was assigned to the proton between the

14

W.W. CLELAND

pyridinium nitrogen and a putative aspartate.52 The pK of this signal was 6, which is consistent with a low-barrier hydrogen bond. Such a bond would in this case stabilize and help bind the cofactor in the proper position. A structure of the N-terminal half of hen ovotransferrin has a 2.3 A˚ distance between the terminal nitrogen atoms of Lys209 and Lys301 which are in separate domains.53 It was proposed that this was a low-barrier hydrogen bond holding the two domains together and that when the transferrin entered an acidic endosome, the protonation of this lysine pair would cause the lysines to move apart, thus allowing release of the bound Fe3þ. This lysine pair would thus be a pH-sensitive trigger for Fe3þ release. A recent neutron crystallography study of photoactive yellow protein discovered a low-barrier hydrogen bond between the phenolic oxygen of the 4-hydroxycinnamic acid chromophore and Glu46 in the ground state.54 The deuterium atom in the structure was 1.37 A˚ from the phenolic oxygen and 1.21 A˚ from the oxygen of Glu46. The role of the low-barrier hydrogen bond is postulated to be stabilization of the negative charge on the chromophore and Glu46 system. Upon photoactivation the chromophore is isomerized and the hydrogen bond is no longer a low-barrier one, with the proton transferred to Glu46. In H148D mutants of green fluorescent protein it appears that a low-barrier hydrogen bond is present between Asp148 and the phenolic oxygen of the chromophore (2.4 A˚ in a S65T/H148D mutant).55 Despite the change in hydrogen bonding in the active site, the Asp148 mutants permit fluorescence in S65T and E222Q mutants, which do not fluoresce if His148 is still present. A recent sub-A˚ngstrom X-ray structure of a phosphate-binding protein showed that there are 11 hydrogen bonds to the phosphate oxygens from OH or NH groups, and the proton on one oxygen of the phosphate dianion forms a 2.5 A˚ low-barrier hydrogen bond with an aspartate.56 Formation of this strong bond ensures that even at pH 4.5 the protein binds phosphate as the dianion.

ACID–BASE CATALYSIS

Low-barrier hydrogen bonds are likely to form during general acid and general base catalysis. In the lactate dehydrogenase reaction, for example, the hydroxyl group of lactate is weakly hydrogen bonded to His195 before catalysis and weakly hydrogen bonded to the carbonyl oxygen of pyruvate after reaction. As the hydride ion is transferred from lactate to NAD the pK of the oxygen on lactate changes from
14 in lactate to
–5 in pyruvate. At the point where the pK of this oxygen is
6, the pK’s of it and His195 will be matched and the hydrogen bond will become a low-barrier one. As the pK’s diverge the bond will weaken and the proton will transfer to His195. The transition state for the reaction should be close to the point where the pK’s match and thus

THE LOW-BARRIER HYDROGEN BOND IN ENZYMIC CATALYSIS

15

the energy released by forming the low-barrier hydrogen bond will lower the activation barrier for the reaction. General acid–base catalysis provides as much as 5 orders of magnitude rate acceleration in enzymatic reactions, which is consistent with the energy provided by forming a low-barrier hydrogen bond in the transition state.57

4

Conclusion

It should be clear from this brief review that low-barrier hydrogen bonds play an important role in many enzymatic reactions, in many cases contributing the energy of their formation to provide catalysis. I have not reviewed the extensive computational literature on low-barrier hydrogen bonds, but an early review will provide more information.10 Other short reviews on their role in enzymatic reactions have been published.4,15,58,59 I have not included references to early critics of the role of low-barrier hydrogen bonds, as I think their criticisms have been shown to be invalid. References to those articles are available in the reviews noted above.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Cleland WW. Biochemistry 1992;31:317–9. Gerlt JA, Gassman PG. J Am Chem Soc 1993;115:11552–68. Gerlt JA, Gassman PG. Biochemistry 1993;32:11943–52. Cleland WW, Kreevoy MM. Science 1994;264:1887–90. Frey PA, Whitt SA, Tobin JB. Science 1994;264:1927–30. Gilli P, Bertolasi V, Ferretti V, Gilli G. J Am Chem Soc 1994;116:909–15. Pan Y, McAllister MA. J Am Chem Soc 1998;120:166–9. Kumar GA, Pan Y, Smallwood CJ, McAllister MA. J Comput Chem 1998;19:1345–52. Steiner T, Saenger W. Acta Chrystallogr Sect B Struct Sci 1994;50:348–7. Hibbert F, Emsley J. Adv Phys Org Chem 1990;26:255–379. Abu-Dari K, Raymond KN, Freyberg DP. J Am Chem Soc 1979;101:3688–9. Shan S-ou, Loh S, Herschlag D. Science 1996;272:97–101. Schiott B, Iverson BB, Madsen GKH, Larsen FK, Bruice TC. Proc Natl Acad Sci USA 1998;95:12799–802. Frey PA, Cleland WW. Bioorg Chem 1998;26:175–92. Cleland WW. Arch Biochem Biophys 2000;382:1–5. Landro JA, Gerlt JA, Kozarich JW, Koo CW, Shah VJ, Kenyon GL, et al. Biochemistry 1994;33:635–43. Mitra B, Kallarakal AT, Kozarich JW, Gerlt JA, Clifton JR, Petsko GA, et al. Biochemistry 1995;34:2777–87. Lodi PJ, Knowles JR. Biochemistry 1991;30:6948–56. Zhao Q, Abeygunawardana C, Talalay P, Mildvan AS. Proc Natl Acad Sci USA 1996;93:8220–4. Zhao Q, Abeygunawardana C, Gittis AG, Mildvan AS. Biochemistry 1997;36:14616–26.

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21. 22. 23. 24.

Lauble H, Kennedy MC, Beinert H, Stout CD. Biochemistry 1992;31:2735–48. Werst MM, Kennedy MC, Beinert H, Hoffman BM. Biochemistry 1990;29:10526–32. Remington SJ. Curr Opin Struct Biol 1992;2:730–5. Usher KC, Remington SJ, Martin DP, Drueckammer DG. Biochemistry 1994;33:7753–9. Gu Z, Drueckhammer DG, Kurz L, Liu K, Martin DP, McDermott A. Biochemistry 1999;38:8022–31. Rishavy MA, Berkner KL. Biochemistry 2008;47:9836–46. Cassidy CS, Lin J, Frey PA. Biochemistry 1997;36:4576–84. Lin J, Westler WM, Cleland WW, Markley JL, Frey PA. Proc Natl Acad Sci USA 1998;95:14664–8. Tobin JB, Whitt SA, Cassidy CS, Frey PA. Biochemistry 1995;34:6919–24. Reinhardt LA, Sacksteder KA, Cleland WW. J Am Chem Soc 1998;120:13366–9. Kuhn P, Knapp M, Soltis SM, Ganshow G, Thoene M, Bott R. Biochemistry 1998;37:13446–52. Frick L, Yang C, Marquez VE, Wolfenden RV. Biochemistry 1989;28:9423–30. Xiang S, Short SA, Wolfenden R, Carter CW Jr., Biochemistry 1995;34:4516–23. Tronrud DE, Monzingo AF, Matthews BW. Eur J Biochem 1986;157:261–8. Holden HM, Tronrud DE, Monzingo AF, Weaver LH, Matthews BW. Biochemistry 1987;26:8542–53. Kim H, Lipscomb WN. Biochemistry 1990;29:5546–55. Kim H, Lipscomb WN. Biochemistry 1991;30:8171–80. Poi MJ, Tomaszewski JW, Yuan C, Dunlap CA, Andersen NH, Gelb MH, et al. J Mol Biol 2003;329:997–1009. Ramaswamy S, Park D-H, Plapp BV. Biochemistry 1999;38:13951–9. Sekhar VC, Plapp BV. Biochemistry 1990;29:4289–95. Thoden JB, Wohlers TM, Fridovich-Keil JL, Holden HM. Biochemistry 2000;39:5691–701. Belogurov GA, Fabrichniy IP, Pohjanjoki P, Kasho VN, Lehtihuhta E, Turkina MV, et al. Biochemistry 2000;39:13931–8. Heikinheimo P, Tuominen V, Ahonen A-K, Teplyakov A, Cooperman BS, Baykov AA, et al. Proc Natl Acad Sci USA 2001;98:3121–6. Tittmann K, Neef H, Golbik R, Hubner G, Kern D. Biochemistry 2005;44:8697–700. Piana S, Carloni P. Proteins: Struct Funct Genet 2000;39:26–36. Northrop DB. Acc Chem Res 2001;34:790–7. Brynda J, Rezacova P, Fabry M, Horejsi M, Stouracova R, Sedlacek J, et al. J Med Chem 2004;47:2030–6. Das A, Prashar V, Mahale S, Serre L, Ferrer J-L, Hosur MV. Proc Natl Acad Sci USA 2006;103:18464–9. Coates L, Erskine PT, Wood SP, Myles AA, Cooper JB. Biochemistry 2001;40:13149–57. Coates L, Tuan H-F, Tomanicek S, Kovalevsky A, Mustyakimov M, Erskine P, et al. J Am Chem Soc 2008;130:7235–7. Tyndall JDA, Pattenden LK, Reid RC, Hu S-H, Alewood D, Alewood PF, et al. Biochemistry 2008;47:3736–44. Tong H, Davis L. Biochemistry 1995;34:3362–7. Dewan JC, Mikami B, Hirose M, Sacchettini JC. Biochemistry 1993;32:11963–8. Yamaguchi S, Kamikubo H, Kurihara K, Duroki R, Nimura N, Shimizu N, et al. Proc Natl Acad Sci USA 2009;106:440–4. Stoner-Ma D, Jaye AA, Ronayne KL, Nappa J, Meech SR, Tonge PJ. J Am Chem Soc 2008;130:1227–35.

25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.

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56. Liebschner D, Elias M, Moniot S, Fournier B, Scott K, Jelsch, C, et al. J Am Chem Soc 2009;131:7879–86. 57. Meloche HP, O’Connell EL. J Protein Chem 1983;2:399–410. 58. Gerlt JA, Kreevoy MM, Cleland WW, Frey PA. Chem Biol 1997;4:259–67. 59. Cleland WW, Frey PA, Gerlt JA. J Biol Chem 1998;273:25529–32.

Stabilities and Reactivities of Carbocations RORY MORE O’FERRALL School of Chemistry and Chemical Biology, University College Dublin, Belfield, Dublin 4, Ireland 1 Introduction 19 2 Stabilities of carbocations 21 Measures of stability 21 Equilibrium measurements of pKR 28 Kinetic methods for determining pKR 30 Arenonium ions 37 Alkyl cations 46 Vinyl cations 48 The methyl cation: a correlation between solution and the gas phase Oxygen-Substituted carbocations 51 Metal-Coordinated carbocations 64 Carbocations as protonated carbenes 68 Halide and azide ion equilibria 71 3 Reactivity of carbocations 76 Nucleophilic reactions with water 77 Reactions with water as a base 87 Reactions of nucleophiles other than water 90 Reactivity, selectivity, and transition state structure 105 Hard and soft nucleophiles 110 Summary and conclusions 112 Acknowledgments 114 References 114

1

49

Introduction

There have been a number of reviews of carbocation chemistry in the past 10 years,1–11 including a volume of essays marking the 100th anniversary of the subject.1 That volume illustrates the variety of structures and reactions that characterize carbocations. It is this variety which suggests scope for a further study, namely of the stability and reactivity of carbocations in (mainly) aqueous solution. Dedication to AJ Kresge is appropriate. He has pioneered the quantitative characterization of reactive intermediates in water as solvent. If he is best known for his work on enolic species, his steady referencing throughout this chapter reflects the breadth of his influence in physical organic chemistry.

19 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44002-9


2010 Elsevier Ltd. All rights reserved

20

R. MORE O’FERRALL

Attempts to measure the stabilities of carbocations are not new. Hughes and Ingold established the essential features of solvolysis reactions in the 1930s.12 They identified the SN1 mechanism as involving the formation of a carbocation intermediate and recognized that the rate of solvolysis reflects the stability of that carbocation. For more than 80 years, rate constants of solvolyses have provided measures of stability (with allowance for variations in the stability of reactants).13 Only recently have the stabilities of more than mildly reactive carbocations, accessible by direct equilibrium measurements,14–16 been determined. Indeed the emergence of gas-phase ion chemistry and new techniques of mass spectrometry in the 1980s led to a wider knowledge of the stabilities of carbocations in the gas phase than in solution.2,17 The extension of equilibrium measurements to normally reactive carbocations in solution followed two experimental developments. One was the stoichiometric generation of cations by flash photolysis or radiolysis under conditions that their subsequent reactions could be monitored by rapid recording spectroscopic techniques.3,4,18–20 The second was the identification of nucleophiles reacting with carbocations under diffusion control, which could be used as clocks for competing reactions in analogy with similar measurements of the lifetimes of radicals.21,22 The combination of rate constants for reactions of carbocations determined by these methods with rate constants for their formation in the reverse solvolytic (or other) reactions furnished the desired equilibrium constants. Important contributors to these developments were McClelland and Richard, who have published reviews of their own and related studies.3–8 The present chapter will focus on recent work therefore and present earlier results mainly for comparison with new measurements. It will consider two further methods for deriving equilibrium constants: (a) from kinetic measurements where the reverse reaction of the carbocation is controlled by diffusion or relaxation of solvent molecules23–25 and (b) from a correlation of solution measurements with the more extensive measurements of stabilities of carbocations in the gas phase.26 It will also show that stabilities of highly reactive carbocations can be determined from measurements of protonation and hydration of carbon–carbon double bonds. The existence of equilibrium measurements today usually implies access to a rate constant for direct reaction of the carbocation with a nucleophile or base. The chapter will also consider reactivity and selectivity for these reactions. This area too has been well studied and reviewed,3–8 especially by Mayr’s group in Munich, who have made extensive recent contributions to the field.27–31 It should be admitted that the author’s own work25,26,32 will be a further focus for the chapter, which in part will be an ‘‘account of research,’’ and indeed an update of an earlier multiauthored review.9 The chapter begins, however, with a digression on the significance of different measures of the stabilities of carbocations. This is followed by a discussion of the use of a solvent free energy relationship to extrapolate equilibrium and kinetic measurements in concentrated solutions of strong acids to a purely aqueous medium. Some readers may

STABILITIES AND REACTIVITIES OF CARBOCATIONS

21

wish to omit these sections. However, throughout the first third of the chapter experimental results are presented in the context of methods used for measurements. The emphasis on methods is followed by discussions of oxygen substituent effects, coordination of metal ions, protonations of carbenes, and equilibria for the reactions of carbocations with halide or azide ions. The discussion of reactivity concludes the chapter.

2

Stabilities of carbocations

MEASURES OF STABILITY

The choice of equilibrium constant for measuring the stability of a carbocation depends partly on experimental accessibility and partly on the choice of solvent. A desire to relate measurements to the majority of existing equilibrium constants implies the use of water as solvent. Water has the advantage and disadvantage that it reacts with carbocations. It follows that the most widely used equilibrium constant is that for the hydration reaction shown in Equation (1), which is denoted KR (or pKR). A simple interpretation of KR is that it measures the ratio of concentrations of unionized alcohol to carbocation in an (ideal) solution of aqueous acid of concentration 1 M. Rþ þ 2H2 O ¼ ROH7 þ H3 Oþ KR ¼

ð1Þ

½R  OH½H3 Oþ  ½Rþ 

Nucleophile affinities As pointed out by Mayr,28 Ritchie,15 and Hine33,34 KR also measures the relative affinities of Rþ and H3Oþ for the hydroxide ion. It can be regarded as providing a general affinity scale applicable to electrophiles other than carbocations.33,35 It can also be factored into independent affinities of Rþ and H3Oþ as shown in Equations (2) and (3). Such equilibrium constants have been denoted Kc by Hine.33 KR corresponds to the ratio of constants for reactions (2) and (3) and, in so far as Kc for H3Oþ is the inverse of Kw the autoprotolysis constant for water, KR = KcKw Rþþ HO  ¼ ROH Kc ¼

½ROH ½Rþ ½HO  

ð2Þ

22

H3 Oþ þ HO  ¼ 2H2 O

R. MORE O’FERRALL

ð3Þ

A distinction between the reactions of Rþ and H3Oþ is that while Rþ reacts with hydroxide ion in an associative process, H3Oþ reacts by transfer of a proton. The difference corresponds to that between the product-forming step of an SN1 mechanism and an SN2 reaction. Many carbocations are capable of existing in solution independently of a nucleophile, but this is not true of highly reactive electrophiles such as Hþ (or, e.g., CHþ 3 ) reactions of which involve breaking as well as making a bond to a nucleophile. If we focus on Hþ rather than H3Oþ, affinities for nucleophiles (bases) must be expressed relative to a suitable reference. In principle, the familiar equilibrium constants Ka and Kb measure affinities relative to water and hydroxide ion, respectively [Equations (4) and (5)]. AH þ H2 O ¼ A  þ H3 Oþ

ð4Þ

A  þ H2 O ¼ AH þ HO 

ð5Þ

In practice, it is perhaps unfortunate that the complementary character of the KR and Ka scales is somewhat obscured by the formulation of Ka as a measure of acidity, so that the appropriate measure of affinity (in this case basicity) is 1/ K a. For carbocations, an electrophilicity (Lewis acidity) scale can be based on ions other than the hydroxide ion as is shown in general for X in Equation (6), for which the equilibrium constant can be denoted K X R . Scales based on chloride ion, for example, have been used in the gas phase2,17,36 and are also appropriate for nonaqueous solvents. Rþ þ X  ¼ RX

ð6Þ

A further popular scale in the gas phase is hydride ion affinity (HIA)2,37 for which X = H. To avoid dealing explicitly with H, this scale is conveniently referenced to a particular ion such as CHþ 3 as in Equation (7). Commonly HIAs are expressed as free energies rather than pK’s. Rþ þ CH4 ¼ R  H þ CH3þ

ð7Þ

The hydride affinity scale is also applicable to aqueous solution. In analogy with KR we can take H3Oþ as reference as in Equation (8). Rþ þ H2 þ H2 O ¼ RH þ H3 Oþ

ð8Þ

STABILITIES AND REACTIVITIES OF CARBOCATIONS

23


 The two scales are readily interconverted and a ratio of KR values K H R =K R is given by Equation (9). KH ½R  H½H2 O R ¼ KR ½ROH½H2 

ð9Þ

The right-hand side of this equation is evaluated in terms of free energies of formation in aqueous solution at 25C of R–H, R–OH, H2O, and H2.38 Free energies of formation, hydride ion affinities, and pKR: Is there an optimum measure of carbocation stability? The problem arises, which equilibrium constant offers the most effective measure of carbocation stability? A good discussion of this question has been provided by Mayr and Ofial,29 who point out that a rigorous comparison of stabilities is possible only for isomeric cations. Comparisons between nonisomeric cations depend on the equilibrium chosen for the measurements. They argue that the appropriate choice depends on the context and imply that it is not possible to identify a ‘‘best’’ measure of carbocation stability. While this is certainly true it is worthwhile pursuing further the likelihood that some equilibria provide better measures of stability than others, and to assess their effectiveness and limitations. For carbocations possessing a b-hydrogen atom, an alternative to nucleophilic affinities is provided by the pKa for dissociation of a proton to form an alkene. It is rather easy to recognize that a pKa is not always a good measure of carbocation stability. This is evident from an example chosen by Mayr and Ofial, namely, the cyclohexadienyl cation, for which the conjugate base is benzene [Equation (10)]. Thus, if we seek to compare stabilities of the cyclohexadienyl cation and t-butyl cation [Equation (11)] in terms of pKas, the difference will strongly reflect the different stabilities of the carbon–carbon double bonds of their conjugate bases. In this case comparing values of pKR provides a better measure of stability because a contribution from the difference between the corresponding alcohols is smaller. C6 H7 þ ¼ C6 H6 þHþ

ð10Þ

ðCH3 Þ3 Cþ ¼ ðCH3 Þ2 C¼CH2 þ Hþ

ð11Þ

Of course, to speak of the stability of a double bond implies further equilibria or reference structures with which the energy of the unsaturated molecule itself is compared. An obvious reference is the saturated hydrocarbon, with respect to which stability is measured, for example, by a heat of hydrogenation.

24

R. MORE O’FERRALL

Perhaps less obviously, the hydrocarbon also provides a reference for the carbocation. It is worthwhile examining the implications of such a reference, by considering briefly ‘‘thermodynamic’’ measurements of carbocation stabilities in terms of heats (enthalpies) or free energies of formation. Mayr and Ofial contrast our ability to measure the relative energies of tertiary and secondary butyl cations with the significant differences in relative stabilities of secondary butyl and isopropyl cations derived from different equilibrium measurements, namely, hydride, chloride, or hydroxide ion affinities. It is convenient to focus on this example and to assess the effectiveness of hydride affinities for comparing the stabilities of these three ions. Extensive measurements of heats of formation of carbocations in the gas phase exist and there have been more limited measurements in solution for nonhydroxylic solvents.39 For comparison with equilibrium measurements in water, however, the most appropriate measurement would appear to be free energies of formation in aqueous solution. It is fortunate therefore that a convenient compilation of values of DGf (aq) at 25C has been provided by Guthrie.38 This allows us for example to derive a value of DGf (aq) for a carbocation from a measurement of its pKR value, provided that the free energy of formation of the corresponding alcohol [R–OH in Equation (1)] is known. Heats or free energies of formation can be used to compare directly the energies of isomeric carbocations. Such a comparison is similar to the more familiar comparisons of energies of isomeric olefins, such as cis- and trans-butene. It depends on the energies of formation of isomeric molecules or ions being based on the same combination of elements. Energies of isomerization can also be measured directly, and Bittener, Arnett, and Saunders have measured the enthalpy of isomerization of secondary to tertiary butyl cations in CH2Cl2 as solvent.39 It is possible to compare direct measurements of relative stabilities of isomeric ions with comparisons of nonisomeric ions by use of a ‘‘group additivity’’ scheme. Group additivity schemes have been developed by Benson for heats of formation (and other thermodynamic properties) of organic molecules in the gas phase,40 and by Guthrie to represent free energies of formation in aqueous solution.38 In both cases, energies of unstrained hydrocarbons accurately correspond to a sum of contributions from primary, secondary, tertiary, and quaternary carbons CH3, CH2, CH, and C. Such a scheme can be extended to carbons bearing functional groups (X) by assigning contributions for CH2X, CHX, and CX. In principle, carbocations can be included, with the positively charged carbon considered as a functional group, with characteristic contributions for primary, secondary, and tertiary cation centers. For strict additivity, a group scheme implies that the influence of a functional group does not extend beyond the carbon atoms adjacent to the functionalized atom, that is, in our case the carbon bearing the positive charge.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

25

This can be tested by drawing on extensive information on carbocation stabilities in the gas phase. Heats of formation of ethyl, isopropyl, sec-butyl and tbutyl cations2 are shown below. From these values it is evident that the t-butyl cation is more stable than the sec-butyl cation by 13 kcal mol1. This corresponds to the direct comparison of (isomeric) ion stabilities noted above by Arnett and Mayr.

DHf (g)

1

(kcal mol )

(CH3)3Cþ

CH3CH2CHþCH3

(CH3)2CHþ

CH3 CH2

170

183

193

215

It can also be seen that the heat of formation of the iso-butyl cation is 10 kcal mol1 less than that of the isopropyl cation. Based on this difference, we may assess the effectiveness of group additivity by comparing the changes in energy for inserting a methylene group into the isopropyl cation to give a sec-butyl cation with the same change in propane to give butane or in propanol to give sec-butyl alcohol. For an effective additivity scheme these changes should be the same because the methylene group is two carbons removed from the charge center of the cation. In practice, whereas converting the isopropyl cation to a sec-butyl cation reduces the heat of formation by 10 kcal mol1, the corresponding conversion for propane and isopropyl alcohol reduces it by 5.0 and 4.8 kcal mol1, respectively. While this implies that to a good approximation an OH functional group is well accommodated by the additivity scheme the carbocation center certainly is not. The situation in solution is quite different. The difficulty of stabilizing charge in the gas phase is well known and in solution smaller differences between structures are expected. There should also be less dependence on the size of the ion, which is a well-recognized feature of gas-phase ion stabilization, but does not appear to be significant in solution.41 Shown in Table 1 are free energies of formation of the same ions in aqueous solution at 25C. The measurements of pKa from which they are derived are described later in the chapter (p. 47). Suffice to say here that the relative values for isopropyl and secondary butyl cations are based on the inference from measurements of equal rate constants for protonation of propene and 1-butene42 that the pKas of the conjugate acids of these alkenes are the same. It can be seen that the differences in energies of formation between the cations are significantly less than in the gas phase. Thus the difference between the t-butyl and ethyl cations is reduced from 45 kcal mol1 to less than 20 kcal mol1. On the other hand, the difference between the t-butyl and sec-butyl cations shows a much smaller reduction, from 13 to 10.2 kcal mol1. Moreover, instead of the energy of the isopropyl cation being 10 kcal mol1 greater than the sec-butyl cation it is now 2.3 kcal mol1 less. In the gas phase the extra CH2

26

R. MORE O’FERRALL

provides important stabilization. In aqueous solution this is overridden by an unfavorable effect on solvation (recall that the standard state remains the gas phase).43 If as above we compare the value of this ‘‘group contribution’’ for CH2 with values based on increases in free energies of formation between propane and butane (2.0 kcal mol1) and isopropyl alcohol and sec-butanol (1.6 kcal mol1), it is apparent that there is a much better cancellation, and thus better prospect that energies of alkyl carbocations can be approximated by an additivity scheme in solution than in the gas phase. Calculated group contributions to free energies of formation for tertiary, secondary, and primary carbocations in aqueous soloution based on the above data are shown below and are compared with Guthrie’s values for hydrocarbons (which were also used for remote methyl groups in deriving the carbocation group contributions). As expected the cations have large positive values. Indeed the values are substantially larger than for alkyne carbons, which fall in the range 27–29 kcal mol1 and currently represent the largest carbon group contributions. CH2þ CHþ Cþ

57.9 50.7 45.7

CH3 CH2 CH C

3.93 2.16 6.43 10.40

The group contributions apply only to alkyl cations and are of limited practical value. However, apart from illustrating the application of group additivity contributions to energies of formation of carbocations, they offer a significant insight into comparisons of stability based on hydride ion affinities (HIAs) and pKR values. HIAs of the carbocations are listed in Table 1 as differences in values from the t-butyl cation (DHIA in free energies mol1). Returning to the comparison of isopropyl and sec-butyl cations it can be seen that the difference in their

Table 1 Free energies of formation, HIAs, and pKR values for alkyl cations in aqueous solution

DGf (aq) (kcal mol1) DHIAa 1.364pKRb 1.364DpKRc

(CH3)3Cþ

CH3CH2CHþCH3

(CH3)2CHþ

CH3 CH2

33.9 9.8 –22.4

45.6 9.7 –30.6 8.2

43.3 23.3 –30.1 7.7

54.0

HIAs relative to (CH3)3Cþ. pKR converted to free energy mol1. c Relative to (CH3)3Cþ. a

b

–40.8 18.4

STABILITIES AND REACTIVITIES OF CARBOCATIONS

27

HIAs is only 0.1 kcal mol1. This reflects almost complete cancellation of contributions from the extra CH2 group in the butyl structure between the cation and hydrocarbon. It indicates that HIAs provide a good approximation to differences in stability between a carbocation center and the corresponding group contribution from a hydrocarbon, independently of structural variations at carbon atoms not attached to the carbocation center. Moreover, a comparison between two secondary carbocations leads to almost complete cancellation of the contributions from the parent hydrocarbons and from alkyl groups of the carbocations too far removed from the charge center to influence stability. One is very close therefore to a comparison of stabilities comparable to that between isomeric cations. It should be noted that such ‘‘intrinsic’’ stabilities are not expressed in heats of formation of carbocations because they include uncanceled contributions from more remote portions of the structure. Also shown in Table 1 are differences in pKR. These are multiplied by 1.364 to give free energies for easier comparison with HIAs. They correspond to ‘‘intrinsic’’ differences between tertiary, secondary, and primary carbocation centers (CHþ, CH2þ, and CH3þ ) and the corresponding values for the carbon bound to an OH functional group (C–OH, CH–OH, and CH2–OH). In principle, carbocation stabilities may be expressed relative to any functional group, but clearly the convenience and prevalence of measurements of pKR give a special place to the OH group. However, note that the DpKR and DHIA values are not the same. This is because there is a stabilizing geminal interaction between the OH group and methyl groups attached to the a-carbon atom.44–46 These interactions are cumulative so their net contribution depends on the number of methyl groups. They also depend on the nature of the functional group if this differs from OH. As a consequence, stabilities of carbocations defined in terms of affinity for a nucleophile depend on the choice of nucleophile as emphasized by Mayr and Ofial. The magnitudes of the interactions are by no means negligible, particularly between oxygen and another electronegative atom (usually O or N). Nevertheless they are well understood and easily estimated, especially for the OH group,47 which provides the most convenient affinity (pKR) scale. As indicated above, pKR values are readily converted to an HIA scale, which provides a convenient reference for comparisons between scales as well as a better approximation to cation stabilities. However, note that even for HIAs, if cations differ significantly in substitution at their charge center, there may be uncanceled geminal interactions in the reactant hydrocarbon, for example, between methyl groups when comparing secondary and tertiary cations: this will be evident from inspection of the relevant group contributions. Of course, the ‘‘intrinsic’’ stabilities, and the evidence for localization of the influence of carbocation centers, apply only to aliphatic ions. Phenyl or vinyl substitutents lead to extended delocalization of a positive charge. More generally, however, cancellations of ‘‘group’’ contributions between reactants and

28

R. MORE O’FERRALL

products in measurements of pKR or HIAs are subsumed into analyses in terms of substituent effects. This extended discussion brings us then to the conventional conclusion that stabilities of carbocations considered in the context of comparisons of equilibrium constants, benefit from substantial cancellation of effects of noninteracting functional and substituent groups between pairs of reactants and products for structures far removed from those of simple alkyl cations.33,48

EQUILIBRIUM MEASUREMENTS OF pKR

Turning to experimental measurements, the majority of equilibrium constants measured for carbocation formation refer to ionization of alcohols or alkenes in acidic aqueous solution, and correspond to pKR or pKa. Considering the instability of most carbocations it is hardly surprising that only unusually stable ions such as the tropylium ion 149 or derivatives of the flavylium ion 250,51 are susceptible to pK measurements in the pH range. +

CH2 +

O

Me

Ph

+

Me

+

+ +

1

2

3

4.75

3.65

–1.70

4 Me

5 Me

–16.3

–11.9

6

~ –7.4

A wider range of structures can be accessed through measurements in strong acid solutions.52–55 Such solutions have the characteristic that pK values vary strongly with acid concentration. This is because H3Oþ has a uniquely high solvation energy and the depletion of water molecules at high acid concentrations leads to increasing protonation of a base (or ionization of an alcohol) if its conjugate acid (or carbocation) is less strongly solvated than H3Oþ. This is illustrated in Equation (12), in which the solvated proton is represented as H9 O 4þ . H9 O4þ þB ¼ BHþ þ 4H2 O

ð12Þ


 What is required is a value of pK extrapolated to water pKH2 O . Fortunately, the dependences of the relevant equilibrium constants on the composition of the acidic medium are well described by free energy relationships. This means that an unknown pKa (or pKR) can be obtained from measurements in concentrated acidic solutions by plotting values against known pKas for the protonation of a reference base.52,53 In practice, medium acidity parameters, Xo ¼ pKa  pKaH2 O , are conveniently defined for a family of structurally

STABILITIES AND REACTIVITIES OF CARBOCATIONS

29

related bases with a large enough range of basicities to span measurements from dilute to concentrated solutions of strong acids. Such a family is provided by primary anilines substituted with nitro and other electron-withdrawing groups. Historically, there has been an uncomfortable period of evolution of the free energy treatment of measurements of pK’s in strongly acidic media from their original formulation as acidity functions. In the context of acidity functions, a pKa was treated as fixed at its value in water, and ‘‘apparent’’ variations in equilibrium constants were assigned to changes in activity coefficient.56,57 It is now well established that plots of pKa against Xo are impressively linear and correspond to the relationship represented by Equation (13), in which m* is the slope of the plot and the pKa in water is the intercept. pKa ¼ m Xo þ pKaH2 O

ð13Þ

The value of m* reflects medium effects on the acid dissociation constant under study, as represented in Equation (14). BHþ þ H2 O ¼ B þ H3 Oþ

ð14Þ

Thus in the case that BHþ is H3Oþ, Equation (14) becomes an ‘‘identity’’ reaction, for which there is no medium effect, and m* = 0. On the other hand, if BHþ is a protonated aniline, m* = 1. These values provide fixed points on a scale of solvation energy changes associated with proton transfer between H3Oþ and the protonated base under study. Our interest in this chapter is in carbocations. In general, these are poorly solvated unless there is an OH or NH group bound to the charge center, and typically m* falls in the range 1.5–2.0. Their equilibria are accessible as pKas for protonation of carbon–carbon double bonds,58–60 or pKR values.61–64 Strictly speaking, free energy treatments of medium acidity apply to pKa rather than pKR. The relationship between these equilibria is shown for the hydration and protonation of styrene in the thermodynamic cycle of Scheme 1 and Equation (15). Thus pKR corresponds to pKa þ pKH2 O where pKH2 O is the equilibrium constant for the hydration reaction. If pKa increases with acidity +

CH CH3 + H2O pK R

pK a

pK H2O H+ + H2O +

CH=CH2

CHCH3 + H+ OH

Scheme 1

30

R. MORE O’FERRALL

in proportion to Xo, the dependence of pKR on Xo will be modified by that of pKH2 O . In practice, KH2 O is likely to increase with increasing acidity because of the premium placed on the availability of solvating water at high acid concentrations. If the variation is not too great, as suggested by data for p-methoxystyrene,65 plots of pKR against Xo should still be close to linear and extrapolate to satisfactory values of pKR in water. KH2 O ¼

KR ½ROH ¼ Ka ½alkene½H2 O

ð15Þ

In practice, extrapolations of pKR in water have usually used the older acidity function based method, for example, for trityl,61,62 benzhydryl,63 or cyclopropenyl (6) cations.66,67 These older data include studies of protonation of aromatic molecules, such as pKa = 1.70 for the azulenium ion 3,59 and Kresge’s extensive measurements of the protonation of hydroxy- and methoxy-substituted benzenes.68 Some of these data have been replotted as pKR or pKa against Xo with only minor changes in values.25,52 However, for more unstable carbocations such as 2,4,6-trimethylbenzyl, there is a long extrapolation from concentrated acid solutions to water and the discrepancy 2O ¼ 17:5,61 is greater; use of an acidity function in this case gives pKH R * compared with 16.3 (and m = 1.8) based on Xo. Indeed because of limitations to the acidity of concentrated solutions of perchloric or sulfuric acid pK’s of more weakly nucleophilic carbocations are not accessible from equilibrium measurements in these media. Care also needs to be taken with the interpretation of UV–visible spectra in concentrated acid solutions. Richard and Amyes have shown that H2 O ¼ 16:6 for the 9-methylfluorenyl cation involves an incorrect assignpK R ment of spectra and that a value based on azide clock measurements (see below) is 11.9.69 In addition to carbocations, extensive measurements of pKas of oxygen and nitrogen protonated bases have been undertaken, including pKas of protonated ketones.65,74 As described below, these lead indirectly to pKR values for a-hydroxycarbocations if the equilibrium constants for hydration of the ketones are known.

KINETIC METHODS FOR DETERMINING pKR

More recent measurements related to carbocation stabilities in strongly acidic media have involved rates of reaction rather than equilibria.52,54,72–75 Application of the Xo function to the correlation of reaction rates as well as equilibria mirrors the use of structure-based free energy relationships. Of interest is the access this gives to rate constants for (a) protonation of weakly basic alkenes and (b) acid-catalyzed ionization of alcohols to relatively unstable

STABILITIES AND REACTIVITIES OF CARBOCATIONS

31

carbocations.73–75 These are kinetic counterparts of equilibrium measurements of pKa and pKR, and allow rate constants of intrinsically slow reactions to be extrapolated to aqueous solution. They are particularly important for the determination of highly negative values of pKa or pKR through combination of the measured values with rate constants for the reverse reactions of the carbocations with water acting as a base or nucleophile. Plots of log k against Xo are consistently linear, facilitating extrapolation of rate constants as small as 1014.72 Combination with the maximum rate constant for reaction of a carbocation with aqueous solvent, which is controlled by the rotational constant for relaxation of water of 1011 s1,24,76 yields a pK of 25, significantly higher than the maximum (negative) value possible from equilibrium studies. The application of kinetic methods to determining pKa and pKR for carbocations, by combining rate constants for their formation from an alcohol or alkene with a rate constant for the reverse reaction of the carbocation with water, has provided the most important development in measurements of these equilibrium constants in recent years. The use of laser flash photolysis to generate carbocations under conditions that rates of their reactions can be monitored by rapid recording of their absorbance in the UV or visible region represents a milestone in studies of carbocations.20,77 Particularly important in this development has been a collaboration between Steenken and McClelland.19,78–84 Their work, and some of the varied photochemistry associated with it, which led to the generation not only of carbocations but of radicals, radical cations, and carbenes, has been reviewed by McClelland.3,4 Detection methods have included conductivity as well as UV–visible spectrophotometry, and the carbocations have been generated by radiolysis79,80 as well as photolysis. These studies ushered in the modern era of stability studies in carbocation chemistry which has extended over the past 20 years. Diffusion-controlled trapping of carbocations: benzylic cations A ‘‘modern era’’ of stability studies can be extended to more than 30 years by taking as its beginning the application of ‘‘clock’’ methods to the determination of rate constants for direct reactions of carbocations with water or other nucleophiles or bases. Young and Jencks used bisulfite ions to trap acetalderived alkoxycarbocations, and assigned equilibrium constants for reaction of the cations with methanol by measuring product ratios for trapping by bisulfite ion. It was assumed that reaction of the bisulfite was diffusion controlled with a rate constant 5109 M1 s1 and that the rate constants for reaction of water and methanol were the same.21 Subsequently, Jencks and Richard used trapping by azide ion to measure pKR values of a-phenethyl cations in 50:50 (v/v) trifluoroethanol (TFE)–H2O mixtures and presented strong arguments for the efficacy of azide ions as a diffusion trap.22 Their conclusions were endorsed by McClelland who measured directly rate constants for reaction of benzhydryl and trityl cations with azide ions and

32

R. MORE O’FERRALL

showed that limiting rate constants were close to 5109 M1 s1.81 Similar measurement were made for a-substituted and unsubstituted p-methoxybenzyl cations.82 It was concluded that the reaction of azide ions with carbocations is diffusion controlled provided that kH2 O , the rate constant for reaction of the carbocation with water, is >105 s1 or pKR is 30. This demonstrates the consistency of the forward and back reactions for cation formation. The behavior is little affected if the b-hydroxy group is changed to b-methoxy.88 HO

OH

OH OH

OH

OH

OH

OH

kcis /ktrans

440

4500

7

50

The interpretation offered for this surprising behavior is that the arenonium ions are stabilized by C–H hyperconjugation, the effect of which is enhanced by the contribution of an aromatic structure to the no-bond resonance form shown for the benzenonium ion 32 below.164 The difference between cis- and trans-diols then arises because reaction of the trans-diol leads initially to a carbocation in which a pseudoaxial C–OH rather than C–H bond is orientated for hyperconjugation (34 rather than 33). The difference in energies of the two conformations and its dependence on the aromaticity of the no-bond structures is confirmed by calculations, which show 9 kcal mol1 difference between the two conformations of the 2-hydroxy benzenonium ions and only 0.5 kcal mol1 for the corresponding 6-hydroxycyclohexenyl cations with one less double bond.164 + H+

H 32 OH2+ OH

H cis

OH2+ OH

+

H

+

H

H 33

H

H OH 34

trans

OH

Stabilization conferred by ‘‘aromatic’’ hyperconjugation resolves a puzzle concerning the relative stabilities of arenonium ions. As judged by rates of solvolysis reactions, normally a phenyl group is more effective than vinyl in stabilizing a carbocation center.166 This difference is moderated for cycloalkyl substrates, so that benzoannelation has little effect, for example, on the rate of hydrolysis of 3-chlorocyclohexene (Cagney H, Kudavalli JS, More O’Ferrall

62

R. MORE O’FERRALL

RA, unpublished data). By comparison, the large and unfavorable effect of benzoannelation on the stability of the benzenonium ion as reflected in its small negative pKR value (–2.3) compared with the larger negative values for the 1-naphthalenonium ion (–8.0) and 9-phenanthrenonium ion (–11.6) is surprising (cf. Table 2, p. 44). The order is explained, however, if it reflects the relative magnitudes of the hyperconjugative stabilization of the ions, which in turn depends on the aromaticity of their no-bond resonance structures. That the observed effect of benzoannelation is consistent with the aromatic character of the benzenonium ion is confirmed by comparison with corresponding effects on the stabilities of tropylium49,167 and pyrylium ions168,169 shown in Scheme 24. In both cases the stabilities of the ions are severely reduced by the additional benzene rings. Indeed, the effect may be compared with the effect of benzoannelation on the aromatic stabilization of benzene itself, which is characteristically decreased by conversion to naphthalene and phenanthrene or anthracene. The fact that, in contrast to pKR, the pKa of the benzenonium ion is increased by benzoannelation implies that benzoannelation does not have as large an effect on the ‘‘aromaticity’’ of the benzenonium ion as on benzene itself. A further indication of ‘‘aromatic’’ stability is provided by measurement of pKR for the cycloheptadienyl cation 35. This ion is a homolog of the cyclohexadienyl cation (pKR = –2.3) and might have been expected to have a similar stability. In practice, measurements in aqueous solution using the azide clock show that pKR is 11.6, which corresponds to a decrease in stability of 12.5 kcal mol1.88 It seems unlikely that this difference arises solely from strain in the cycloheptadienyl ring. Moreover, for the dibenzocycloheptadienyl cation, 36, a pKR = –8.7 can be deduced from measurements in aqueous trifluoroacetic acid (Scheme 25).170 Despite the difference in solvents it seems clear that in this case and in contrast to its effect in Scheme 24 dibenzoannelation strongly stabilizes the cation.

+

pK R

4.7

+

+

1.6

–3.7

pK R

Scheme 24

Ph(MeO)C > R(MeO) C > (MeO)2C. As Kirmse and Steenken pointed out, this does not correspond to the order of stability of the carbocation products.213 In principle, the effects of oxygen substituents are consistent with CF2 being a relatively stable carbene despite the corresponding carbocation being quite unstable. This is understandable if the dipolar structure produced by resonance interaction in the carbene (52) is compensated by an inductive ‘‘back donation’’ of electrons in the -bonds. In the cation (53), back donation accentuates rather than compensates charge separation arising from resonance

Table 5 A comparison of stabilities of singlet carbenes (pKH2 O ) and carbocations (pKR) in aqueous solution at 25C Carbocation

pKa

pKR

pKH2 O

DHhydrogen

Carbene

CHþ 3 CH3 CHþ 2 PhCHþ 2 þ Ph2CH MeOCHþ 2 ðMeOÞ2 CHþ

28 30 31 29 19 13a

–42 –29.6 –21 –12.5 –15.9 –5.7

–70 –59.3 –51.8 –41.0 –34.6 –18.6

–119.1 –107.9 –98.9 –84.3 –70.2 –40.8

CH2 CH3CH PhCH Ph2C MeOCH (MeO)2C

a

Value differs from that in Guthrie et al.132,26

STABILITIES AND REACTIVITIES OF CARBOCATIONS

71

interaction with an oxygen atom. Such a -bond interaction would also account for the fact that the resonance appears not to produce a strongly dipolar electron distribution for the carbene. + – MeO CH

MeO CH 52

+ MeO CH2

+ MeO CH2 53

HALIDE AND AZIDE ION EQUILIBRIA

So far we have considered only pKR and (occasionally) HIA as measures of carbocation stability. However, equilibrium constants for the reaction of carbocations with a variety of nucleophiles other than water have been measured. Ritchie especially has measured195 and reviewed15 values for reactions of relatively stable cations, such as trityl ions with electron-donating substituents or aryl tropylium ions, with alcohols, amines, and oxygen or sulfur anions. More recently, there has been interest in less stable cations which can be formed from solvolysis of precursors possessing good leaving groups such as chloride or azide ions. When written in the associative direction, equilibrium constants for these reactions measure the relative stabilities of the carbocations in terms of chloride or azide ion affinities. This is shown in Equation (20) in X which X is Cl or N 3 and KR is the equilibrium constant for the association reaction. RX ¼ Rþ þX  ;

KX R¼

½RX ½Rþ ½X  

ð20Þ

Chloride ions Values of KCl R for chloride ions have been determined by combining a rate constant for solvolysis ksolv (for reactions for which the ionization step is ratedetermining) with a rate constant for the reverse reaction corresponding to recombination of cation and nucleophile. The latter constant may be found (a) by generating the cation by photolysis and measuring directly rate constants for reactions with nucleophiles or (b) from common ion rate depression of the solvolysis reaction coupled with diffusion-controlled trapping by a competing nucleophile used as a clock. A further possibility arises where the carbocation intermediate of the solvolysis is so unstable as to react with water at the limiting rate of solvent relaxation with a rate constant of 1011 s1. It is then likely that the reaction with water occurs at the stage of a carbocation anion pair and that the back

72

R. MORE O’FERRALL

reaction of the ion pair to reform the reactant occurs more rapidly than the solvent relaxation, with a rate constant that may be as large as 1013 s1. Provided the back reaction is significantly faster than reaction with the solvent the measured rate constant for solvolysis should correspond to 1 1011/ K X Rs . Quite often values of K X R have been measured for cations for which pKR is not known. Thus combining Equation (20) with Equation (1) for KR (p. 21, with Hþ replacing H3Oþ) gives the ratio of equilibrium constants as Equation (21). Rewriting this ratio as pKR – pKCl R allows the difference in pK’s to be expressed in terms of free energies of formation in aqueous solution at 25 (DGf ) for the relevant alcohol and alkyl chloride as shown in Equation (22).38,43,214 KR ½Hþ ½Cl  ½ROH ¼ ½H2 O½RCl KRCl  pKR  pK RCl ¼

DGf ðHþ ; Cl  ÞþDGf ðROHÞ  DGf ðH2 OÞ  DGf ðRClÞ 1:364

ð21Þ 

ð22Þ

Experimentally, the simplest evaluation of K RCl is based on measurement of a rate constant in water for solvolysis of an alkyl halide for which reaction of the carbocation with water is at its solvent relaxation limit. An example is provided by the solvolysis of t-butyl chloride. A rate constant for solvolysis in water at 25 was measured by Fainberg and Winstein215 as 2.88102 s1. This yields pK RCl = –12.5. Substitution of the appropriate free energies of formation into Equation (22),38,214 together with an estimate of the free energy of transfer from gas to aqueous solution for t-butyl chloride,43 gives pKR – pKCl R = 4.7 and pKR = –17.2. This value is impressively close to pKR = –16.4 determined by Toteva and Richard.158 Indeed, the agreement is improved by recognizing that K RCl refers to the formation of an ion pair. Thus, taking Richard and Jencks’s value of 0.3 M1 for an ion pair association constant in water85 allows correction of pKR to 16.7. The level of agreement between values is probably fortuitous considering possible sources of discrepancy, such as a difference in solvent relaxation for an ion pair and a cation generated without a counter ion by protonation of an alkene by H3Oþ. A similar estimation for isopropyl chloride leads to a value of 17.3, which seems too low compared with 22.1 from the protonation of propene (p. 48). This is consistent with the expected intervention of an SN2 mechanism.216 The method should work better for adamantyl chlorides or norbornyl chloride for which SN2, and, presumably, preassociation processes are precluded. Speculative values of pK RCl and pKR for the relevant carbocations 54–56 are listed below based on a solvolysis rate constant in water for the

STABILITIES AND REACTIVITIES OF CARBOCATIONS

73

1-adamantyl chloride217 and ratios of values in aqueous acetone for the 1- and 2-adamantyl isomers and exo-norbornyl chloride.218 Although DGf (aq) for the alcohols and chlorides in these cases are not available, good estimates of DGf (ROH) – DGf (RCl) can be made by examining the structure dependence of Cl for OH substitutions for representative alcohols and alkyl chlorides for which free energies of formation have been measured.38,43,214

+

+ +

54

K RCl ¼ 1011=ksolv pKR – pK RCl pKR

56

55

1.31013 –4.6 –17.2

2.61016 –4.1 –20.0

2.11012 –4.1 –15.9

From the above results it can be seen that variations in pKR – pK RCl are rather small. The same is true of pK RCl for the ionization of trityl chloride and p-methoxybenzyl chloride, shown in Table 6 below, from which values of pKR – pK RCl are 4.7 and 4.75 log units, respectively.19,78,219 However, this level of uniformity is not expected of all nucleophiles and substrates. An extreme example of variation in DpKXR is provided by comparison of chloride and dimethyl sulfide as nucleophiles reacting, respectively, with the p-methoxybenzyl cation and the structurally very different electrophile, the di-trifluoromethyl quinone methide 57.220 In the case of the p-methoxybenzyl cation the addition of Me2S is more favorable than addition of chloride ion by a factor of 107-fold; for the quinone methide it is 100 times less favorable. Toteva and Richard attribute the difference to the large and unfavorable steric and polar interactions between the positively charged SMe2þ

Table 6 Comparison of pK RCl , pKR Ph3C+

, and pKR + CH2

MeO

O

C(CF3)2 57

pKR pK RCl 2þ pK RSMe

–6.6 –1.85

–13.4 –8.7 –15.7

– 4.4 6.5

74

R. MORE O’FERRALL

Me2Sþ group and the two CF3 groups in the adduct of the quinone methide. This more than balances the greater carbon affinity of the sulfur nucleophile expressed in the reaction with the p-methoxybenzyl cation. This behavior is exceptional. Nevertheless, the assumption that pKR and pK RCl measure equivalent trends in carbocation stability needs to be treated with caution. Richard and coworkers measured values of pK RCl to assess the influence of b-fluoro substituents on the stability of the a-methyl p-methoxybenzyl cation 58 (R = Me). As indicated in Scheme 29, replacement of an a-methyl by an a-trifluoromethyl group decreases the stability of the 221 carbocation by 7 powers of 10 in K Cl R. Cl However, measurements of pK R in this case lead to a lesser dependence of the equilibrium constant upon carbocation stability than pKR. Guthrie has calculated relative values of pK RCl and pKR and shown that an unfavorable geminal interaction between Cl and CF3 reduces the difference between þ Cl ArCHþ 2 and ArCHCF3 on the pK R scale by about 7 log units compared with pKR. This implies that replacing CH3 by CF3 in the p-methoxybenzyl cation decreases pKR by 14 units. Based on the value of pK RCl = –8.7 for the p-methoxybenzyl cation, pKR for the a-CF3 cation should be close to 23.5. However, note that the values of pK RCl in Scheme 29 were measured in 50–50 v:v TFE–water mixtures rather than water. In general, for anionic nucleophiles pK X R is expected to be highly sensitive to solvent. Results of Pham and McClelland222 indicate that pKR – pK RCl increases by 8 log units between water and 2% aqueous acetonitrile. The effect of a change from water to TFE–water will be much less than this, but a comparison for the p-methoxybenzyl cation shows that pK RCl decreases by 1 log unit.223 Thus neglecting any difference between pKR values in the two solvents the estimate of pKR for the a-trifluoromethyl-substituted p-methoxybenzyl cation is increased to 22.5. This value has been considered at some length because equilibrium measurements for the ions summarized as 58 are relevant to the effects of a-trifluoromethyl substituents on reactivity discussed later in the chapter (p. 80).

+ CH R

MeO 58

Cl pK R

Scheme 29

R

=

(TFE —H2O)

=

H

CH3

–9.5 –6.3

CH2F

CHF2

CF3

–9.4

–12.1

–13.4

STABILITIES AND REACTIVITIES OF CARBOCATIONS

75

Bromide and fluoride ions From the few measurements of bromide ion affinities it appears that pKBr R is similar to pK RCl . E.g. for the p-hydroxybenzyl cation, for which pKR = –9.6, pK RBr = –5.7.156 For the trityl halides on the other hand, chloride has a one log unit advantage, perhaps from a steric effect189,222,224 Probably, for the same reason, fluoride has a 107-fold greater affinity for the trityl cation19 than has the chloride ion (and is similar to that of acetate19), whereas for the p-methoxybenzyl cation the difference is only 4-fold.158 Azide ions There have been more equilibrium measurements for reactions of carbocations with azide than halide ions. Regrettably, there is little thermodynamic data on which to base estimates of relative values of pK RAz and pKR using counterparts of Equations (17) and (18) with N3 replacing Cl. Nevertheless, a number of comparisons in water or TFE–H2O mixtures have been made87,106,226,230 and Ritchie and Virtanen have reported measurements in methanol.195 The measurements recorded below are for TFE–H2O and show that whereas pK RCl is typically 4 log units more positive than pKR, pK RAz is eight units more negative. The difference should be less in water, perhaps by 2 log units, but it is clear that azide ion has about a 1010-fold greater equilibrium affinity for carbocations than does chloride (or bromide) ion. + + CHMe

MeO

pK RAz pKR

–13.3 –5.1

+ CMe2

MeO

–16.6 –8.6

–14.2 –5.9

A different picture emerges if we extend the comparison to cations with an a-methoxy substituent, as shown below.130 Now the difference between pKR and pKAz R is in the range 3–4.4 log units, which is much smaller than the eight units above. A small part of the difference may be due to a change in solvent from TFE–H2O to water, but the greater part must represent stabilization of the hemiacetal product of the KR equilibrium by the favorable interaction of geminal oxygen atoms.45,47,225 We have noted earlier that favorable interactions between OH and alkyl groups leads to differences between pKR and HIA. The oxygen–oxygen interactions are much larger.13,45

pKAz R pKR

PhCþ(OMe)Me

Me2CþOMe

PhCHþOMe

EtCHþOMe

–7.9 –4.6

–9.8 –5.4

–10.3 –7.3

–13.3 –10.3

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R. MORE O’FERRALL

Azide equilibrium measurements have also been used to demonstrate that in addition to N3 having a high affinity for carbocations, N3 as an a-substituent is nearly as strongly stabilizing as a methoxy group. The preparation and solvolysis of gem-diazide derivatives of propionaldehyde and substituted benzaldehydes has allowed Richard and Amyes to study the solvolysis and, through studies of common ion rate depression, the reverse reaction of trapping carbocation intermediates by azide ion.226 Combining solvolysis and trapping rate constants then yields equilibrium constants pK RAz = –16.4 for the a-azido propyl cation compared with pK RAz = –13.2 for the a-ethoxy cation, corresponding to only 4 kcal mol1 greater stabilization by the ethoxy than azido substituent. Comparable differences are found for the substituted a-diazobenzylic and a-methoxy benzylic carbocations. Richard points out that the strong stabilizing effect of the a-azido group has implications for the mechanism of the Schmidt reaction. Were it not for their instability, it seems clear that gem diazides would find wider applications in synthesis. This short review of equilibria for reactions with halide and azide ions illustrates the utility of measures of carbocation stability other than pKR. Provided they refer to aqueous or largely aqueous media and the carbocations do not contain b-substituents which interact strongly with the nucleophile in the cation–nucleophile adduct, such as CF3, RO, or N3, values of pK X R can usually be related to pKR with an uncertainty of less than 1 log unit. On the other hand, they clearly demonstrate the specificity of geminal interactions between the bound nucleophile and electronegative a-substituents in determining relative values of pK X R and pKR.

3

Reactivity of carbocations

An important role of equilibrium measurements is in providing a framework for studies of reactivity and, in the present context, particularly reactivities of carbocations toward nucleophiles and bases. The reactivity of carbocations is too large a topic to deal with comprehensively here, but it may be helpful to attempt an overview of selected topics. Again, important areas, including reactions of vinyl cations120–124 and of b-hydroxy-carbocations formed from acid-catalyzed ring opening of epoxides,160,161 will not be covered, partly because of a lack of equilibrium measurements. Particularly extensive data exists for the reaction of carbocations with water and it is convenient to consider this first and to progress then to a wider range of nucleophiles. Thus we make the same division as for equilibria, but whereas the equilibrium data are dominated by reactions with water, a greater proportion of the kinetic data relates to nucleophiles other than water.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

77

NUCLEOPHILIC REACTIONS WITH WATER

The starting point for most discussions of reactivity is a correlation of rate and equilibrium constants. One such correlation is shown in Fig. 1 of this chapter. It applies not to reactions of the carbocation with water as a nucleophile but to water acting as base, that is, the removal of a b-proton from the carbocation to form an alkene or aromatic product. We will consider this reaction below, but here note that for most of the carbocations in Fig. 1 values of kH2 O , the rate constants for reaction of the carbocation with water as a nucleophile are also available.25 Figure 3 shows a plot of values of log kH2 O against pKR for the carbocations of Fig. 1, namely, arenonium ions, cyclic and noncyclic secondary benzylic carbocations, and tertiary alkyl and benzylic cations.25 The plot is very similar to that reported by McClelland for other groups of carbocations including, benzhydryl, trityl, aryltropylium, and dialkoxyalkyl.3,4 One feature of Fig. 3 is that it incorporates the limiting rate constant of 1011 s1 corresponding to the rotational relaxation of water. Another is the grouping of different structural families on distinct correlation lines. Thus the tertiary alkyl cations show a steeper slope than the secondary cations. This is consistent with McClelland’s 12

log kH2O

10

8

6

4

–18

–16

–14

–12

–10

–8

–6

–4

–2

0

pKR

Fig. 3 Plot of log kH2 O against pKR. The main correlation line based on arenonium ions and secondary benzylic carbocations; the dashed line and filled circles are for tertiary cations.

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more extensive results for which the slopes range from 0.68 to 0.54. The slopes of the lines in Fig. 3 are 0.55 and 0.44. A further characteristic of Fig. 3, and of McClelland’s data, is that within structurally related reaction families the plots are quite linear, even where some of the rate constants closely approach their limiting values. This is contrary to a simplistic view that selectivity (represented by the slope of the plot) should depend on reactivity. The linearity of such plots has been analyzed in detail by Richard8 who attributes it to compensation between effects on reactivity of changes in thermodynamic driving force and changes in an intrinsic kinetic barrier to reaction. Much of this section will be devoted to explaining this proposal. Marcus analysis The idea of an intrinsic energy barrier for a reaction, or family of reactions, is embodied in Marcus’s treatment of the relationship between reaction rates and equilibria.227–229 For a family of reactions within which it remains constant an ‘‘intrinsic’’ barrier corresponds to the activation energy of a thermoneutral reaction (DG = 0). For other reactions ‘‘within the family’’ the experimental activation energy is sensitive to the thermodynamic driving force. This is represented schematically in Fig. 4, in which a change in equilibrium constant arises from a structural change (substituent effect) stabilizing the product of the reaction (by free energy DG). The effect of this change diminishes steadily along the reaction coordinate so that it has no effect on the reactant. A consequence is that the barrier to reaction is reduced and its energy maximum

Λ

x=0

x = 0.5

x = 1.0

ΔG °

Fig. 4 Marcus potential energy barrier G = 4x(1 – x)L perturbed by a substituent stabilizing the product by DG.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

79

(transition state) is moved closer to the reactants. For simple analytical representations of the barrier, it is easy to show that the position of the maximum is reflected in the slope  of a plot of activation energy DG6¼ against energy of reaction DG, which is the same as the slope of a rate–equilibrium relationship in which logs of rate constants are plotted against logs of equilibrium constants. Equations (23) and (24) summarize the relationships between DG6¼ and DG and between the slope  = dDG6¼/dDG and DG for the linear perturbation of the inverted parabola shown in Fig. 4. The parabola is represented analytically by G = 4x(1 – x)L, where L is the usual mnemonic symbol for the intrinsic barrier (DG6¼ when DG = 0) and x represents the position along the reaction coordinate between 0 for reactants and 1.0 for products. For the perturbed parabola G = 4x(1 – x)L – xDG, and DG6¼ is G when dG/dx = 0. It should be noted that, in principle, G represents free energy (which is the quantity measured experimentally) but that it is treated as if it were potential energy. It is not difficult to see that if the intrinsic barrier L remains constant Equations (23) and (24) imply that a plot of DG6¼ against DG (or log k against log K) is curved, and that the curvature, which is given by d/dDG = 1/8L, depends (inversely) on the magnitude of the intrinsic barrier. In other words log k versus log K plots for reaction families with common intrinsic barriers should be strongly curved for fast reactions and show little curvature for slow reactions. On the other hand, it can also be seen that if an increase in intrinsic barrier compensates the decrease in barrier arising from the contribution of DG2/16L as the energy of reaction (and thermodynamic driving force) becomes more favorable, then the value of  in Equation (24) and hence the slope of the correlation could remain nearly constant, or at least not decrease as much as expected. ðDG  Þ2 16L

ð23Þ

dDG6¼ DG ¼ 0:5þ dDG 8L

ð24Þ

D G6¼ ¼Lþ 0:5DGþ

ð¼xÞ ¼

Intrinsic barriers for carbocation reactions The origin of intrinsic barriers to reactions of carbocations has been discussed by Richard.8 He suggests that reaction of water with a carbocation possessing a strongly localized positive charge such as CH3 þ will not only be favorable thermodynamically but possess a very low intrinsic barrier. By contrast, a high intrinsic barrier is associated characteristically with an SN2 reaction, in which

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H2O

CH3

H2O

CH2

+ Me O H + OMe

Scheme 30

there is strong coupling between making and breaking of bonds to an incoming nucleophile and departing leaving group. Richard points to an analogy between bond breaking to the leaving group in an SN2 reaction and the internal displacement of electrons accompanying attack of a nucleophile on a delocalized carbocation (Scheme 30). He suggests that high intrinsic barriers are associated with reactions of carbocations subject to extensive delocalization of carbocationic charge. A striking instance of such delocalization has been provided by Richard in a study of the reactions with water of p-methoxybenzyl carbocations 58 bearing a-substitutents CH3, CH2F, CHF2, and CF3.230–232 Equilibrium measurements described above (p. 54) showed that the stability of the carbocations along this series of substituents decreases by 7 log units as measured by the equilibrium constant for association of the carbocation with chloride ion pK RCl (and double that on a pKR scale). Remarkably, despite this large change in stability, rate constants for attack of water for the same series of carbocations are practically unchanged (Scheme 31). Indeed, addition of a second aCF3 group actually decreases the rate constant. Richard interprets these measurements as implying an increase in delocalization of charge and increase in double bond character at the benzylic carbon atom of the carbocation as the number of electron withdrawing fluorine substituents increases. This is consistent with a changing balance of contributions of the valence bond resonance forms 59 and 60.

+ CH R

MeO 58

R

=

10–7 × kH2O =

Scheme 31

CH3

CH 2F

4.8

10.0

CHF2

10.0

CF3

5.3

ArC+(CF3)2 0.45

STABILITIES AND REACTIVITIES OF CARBOCATIONS

+ CH CX3

MeO 59

+ MeO

CH CX3

81

(X = H or F)

60

The increase in double bond character is assumed to increase the intrinsic barrier for reaction at the a-carbon atom. As this increase is greatest for the thermodynamically least stable (CF3-substituted) carbocation, changes in thermodynamic driving force and intrinsic barrier oppose each other. The constancy of the values of kH2 O thus reflects a change in intrinsic barrier overriding the second and third terms in the Marcus expression of Equation (20). This is a more radical effect than the lesser variation preserving the linearity of the plots for the reaction families in Fig. 3 (p. 77), for which only the third term is overridden. An alternative interpretation of the dependence of intrinsic barrier on charge delocalization has been provided by Bernasconi.233 Bernasconi emphasizes that in the transition state for reaction or formation of a carbocation delocalization of charge is less effective than in the carbocation itself. How this arises has been well explained by Kresge.234 Supposing that a carbocation in Scheme 31 is formed from a benzyl halide precursor and that the carbon– halogen bond is half broken in the transition state, Kresge pointed out that the charge in the transition state must be delocalized less efficiently than in the product. This is because rehybridization of the breaking sp3 C–Cl bond to generate an empty p orbital at the charge center of the carbocation will have progressed only to the extent of 50%. It follows that if (say) a charge is 80% delocalized in the fully formed cation, it will be delocalized only to the extent of 40% in the transition state. Correspondingly, there will be a greater localization of charge at the formal carbocation center in the transition state than in the product (carbocation). This phenomenon is referred to by Bernasconi as an ‘‘imbalance’’ in charge distribution between the transition state and reactants and products. In so far as delocalization is associated with stablization of charge, it is reasonable that its impairment decreases the (intrinsic) energy barrier to reaction. This modified charge distribution in the transition state leads to a mismatch between substituent effects on the rate of reaction and on the equilibrium constant. With respect to the fluorine substituents in Scheme 31, these decrease both the stability of the carbocation and the stability of the transition state. However, while there must be less carbocation character in the transition state than in the carbocation itself the positive charge is located to a greater degree on the benzylic carbon atom and therefore will be more sensitive to stabilization by substituents. If substituent effects at the a-carbon atom in the carbocation and in the transition state are then of comparable magnitude, there will be no net effect on the rate of reaction, as is observed.

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On the other hand, because of the poor delocalization of charge, substitutents in the benzene ring will have a small effect on the stability of the transition state. Their dominant effect will be stabilization or destabilization of the delocalized charge of the carbocation itself, leading to large changes in reactivity. Thus Richard reports a relatively large value of þ = –4.8 for reaction of the ring-substituted a-trifluoromethyl benzylic carbocations (e.g. 59, X=F) with water.232 It should also be noted that while an increase in the number of fluorine substituents leaves the rate of reaction of the cation with water unaffected, the reverse reaction is profoundly affected. In the latter direction the full equilibrium effect of the substituent is felt on the rate. This is because now the effects of changes in thermodynamic driving force and intrinsic barrier complement each other. The corresponding relationship between substituent effects in forward, reverse, and equilibrium reactions and transition state ‘‘imbalance’’ in carbanion reactions, of which the nitroalkane anomaly235 is a prime example, has been discussed in detail by Bernasconi.233 Linearity of log kH2 O – pKR plots If we return now to the plot of log kH2 O against pKR of Fig. 3 (p. 77), we find that the structural changes leading to charge delocalization and changes in rate and equilibrium constants are more various than in Richard’s examples (Scheme 31). However, it remains true that delocalization of charge is the main factor affecting the stability of the carbocation and that this again is expected to lead to an imbalance between the charge distribution in the reactants and transition state. The delocalization stabilizes the carbocation and, less effectively, stabilizes the transition state, so that changes in thermodynamic driving force and intrinsic barrier again complement each other. It is perhaps less obvious in this case how the two factors combine to give a linear rather than a curved free energy relationship than when the effects are opposed. However, in the reverse reaction, the changes do oppose each other. Then, in so far as the slopes of the two log k–log K plots sum to unity, and the degrees of (positive and negative) curvature of the two plots must be the same, linearity of the plot in one direction implies linearity in the other. A way in which compensation between changes in intrinsic barrier and thermodynamic driving force can be expressed in terms of Marcus’s equation has been suggested by Bunting. Bunting and Stefanidis showed that if an intrinsic barrier is taken to vary linearly with DG, that is, L = Lo(1 þ mDG), then the curvature of a plot of log k against log K is reduced.236,237 The reduction in curvature is apparent from modifying the expression for the slope of the plot deriving from Marcus’s equation, that is  = 0.5 þ DG/8L in Equation (24), which on combining with Bunting and Stefanidis’s expression for L236 is transformed to Equation (25).

STABILITIES AND REACTIVITIES OF CARBOCATIONS



DG a ¼ 0:5 þ mLo þ 8Lo



1þmDG=2 ð1þmDG  Þ2

83

! ð25Þ

While Equation (25) appears complicated, a straightforward implication is that when DG = 0, a is no longer 0.5 but 0.5 þ mLo. Moreover the term which controls the variation of a in Equation (24), (DG/8L), which increases as DG increases, is moderated in Equation (25) by a factor which reduces as DG increases. It should be noted that m may be positive or negative and that the sign depends on whether L increases or decreases with increasing DG, which in turn depends on the direction of reaction. Values of mLo typically fall in the range () 0.1–0.5. Thus the lack of effect of b-fluorine substituents on the rate of the a-methyl p-methoxybenzyl cations with water (Scheme 31) implies that a = 0 and mLo = –0.5. The sensitivity of a to DG can readily be assessed for different values of m by substituting integral multiples of Lo for DG in Equation (25). In conclusion, it can also be pointed out that in principle a large value of L is itself sufficient to account for an extended linear free energy relationship. However, as Mayr has noted this is only true if the slope of the plot is 0.5.238 Moreover, if the Marcus expression offers a quantitative guide to the degree of curvature of a free energy relationship (and it is by no means clear that it does),228 it is evident that the intrinsic barriers to reactions of carbocations with familiar nucleophiles are insufficiently large to account for the lack of curvature. Mayr has also commented on the need for compensation for Marcus curvature in an extended free energy relationship. In the context of a discussion of the reactions of carbocations with alkenes, he suggests the alternative possibility that this compensation might arise from a log K-dependent change in the relative energies of frontier orbitals on the carbocation and the nucleophile.30

Estimates of intrinsic reaction barriers Notwithstanding the possibility of variation of an intrinsic barrier within a reaction series, for comparisons between different reactions it is often convenient to assume that an unmodified Marcus expression applies. This approximation is justified partly by the high intrinsic barriers and small amounts of curvature characteristic of most reactions at carbon, including reactions of carbocations. The Marcus relationship then provides a common framework for comparisons between reactions based on the measurement of even a single combination of rate and equilibrium constants. Thus, calculation

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of an intrinsic barrier using Equation (23) (p. 79) offers greater insight into comparisons between reactions than is provided by the individual measurements. It should be noted, however, that calculation of an intrinsic barrier requires modification of a measured rate constant by kBT/h, where kB is Boltzmann’s constant and derives from Eyring’s expression for DG6¼, that is L = RT ln{ko/(kBT/h)}, where ko is the rate constant for the hypothetical thermoneutral reaction (log K = 0).239 A common practice is to refer to ko as an intrinsic rate constant and to compare values of log ko between reactions in place of L. An example of the use of values of pKR and kH2 O to calculate and compare intrinsic barriers is provided by Richard’s measurements for carbocations 61–64. The objective of Richard’s study was to compare reactions in which oxygen substituents are directly attached to a charge center with similar reactions in which the charge and substituent are separated by an aromatic ring.157 In the case of formaldehyde 64 and the quinone methide 63, the ‘‘carbocation’’ corresponds to the resonance form in which charge separation places a negative charge on the oxygen atom and positive charge on carbon. In estimating these barriers Richard addresses a problem that so far has been avoided. When discussing the correlation of log kH2 O with pKR in Fig. 3, it was implied that the rate and equilibrium constants refer to the same reaction step. That is not strictly true, because attack of water on a carbocation yields initially a protonated alcohol which subsequently loses a proton in a rapid equilibrium step. As we are reminded in Equation (26) the equilibrium constant KR refers to the combination of these two steps. To calculate an intrinsic barrier for reaction of the carbocation with water therefore the equilibrium constant KR should be corrected for the lack of stoichiometric protonation of the alcohol. Fortunately, there have been enough measurements of pKas of protonated alcohols240 (e.g. pKa = –2.05 for CH3 OH2þ ) for the required corrections to be made readily. þ Rþ þ H2 OÐROHþ 2 ÐROH þ H

ð26Þ

With the appropriate equilibrium constants in hand Richard was able to calculate the intrinsic barriers for attack of a water molecule (L, kcal mol1) shown under the carbocation structures below.157 From comparing the values it can be seen that interposing a benzene ring between the oxygen substituent and carbocation center substantially increases the barrier, consistent with the expectation that the height of an intrinsic barrier depends on the extent of delocalization of charge. Interestingly, the increase between neutral oxygen and O as a substituent is rather small, despite the fact that charge delocalization must be substantially greater in the latter case.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

+ MeO

L (kcal mol1)

+ EtO

CH2

CHEt

O

85

O CH2

CH2

61

62

63

64

11.5

6.6

13.2

8.7

Richard has also shown that intrinsic barriers for carbocation reactions depend not only on the extent of charge delocalization but to what atoms the charge is delocalized. In a case where values of pKR for calculation of L were not available, comparisons of rate constants for attack of water kH2 O with equilibrium constants for nucleophilic reaction with azide ion pKAz for 65–67 showed qualitatively that delocalization to an oxygen atom leads to a lower barrier than to an azido group which is in turn lower than to a methoxyphenyl substituent.226 + EtO Order of Λ:

CHEt

65

N

+ N N CHEt


F > AcO contrasts with the large change in equilibrium constants pK X R between the first and second pairs of nucleophiles. Comparable results for the reactions of acetate and halide ions with the quinone methide 57 have been reported by Richard and coworkers.219

O

C(CF3)2 57

A similar picture holds for other nucleophiles. As a consequence, there might seem little hope for a nucleophile-based reactivity relationship. Indeed this has been implicitly recognized in the popularity of Pearson’s concept of hard and soft acids and bases, which provides a qualitative rationalization of, for example, the similar orders of reactivities of halide ions as both nucleophiles and leaving groups in (SN2) substitution reactions, without attempting a quantitative analysis. Surprisingly, however, despite the failure of rate–equilibrium relationships, correlations between reactivities of nucleophiles, that is, comparisons of rates of reactions for one carbocation with those of another, are strikingly successful. In other words, correlations exist between rate constants and rate constants where correlations between rate and equilibrium constants fail. Mayr has amusingly described the ebb and flow of optimism and pessimism in a history of attempts to establish correlations based on varying the nature of a nucleophile.253 Initially, it was natural to seek a correlation for SN2 or other nucleophilic reactions of stable organic substrates, because there were few opportunities for measuring rate constants for reactions between nucleophiles and carbocations directly. Thus in 1953 Swain and Scott254 proposed the relationship of Equation (27) in which the parameters s and n refer to substrate (electrophile) and nucleophile, respectively. Methyl bromide was chosen initially as the reference substrate and, perhaps not altogether wisely, water was taken as the reference nucleophile. Subsequently, Pearson and Songstad measured nucleophilicity parameters nCH3 I for a wider range of nucleophiles using methyl iodide in methanol as electrophile and solvent.255

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 log

k kH2 O

 ¼ sn

ð27Þ

Swain and Scott found satisfactory correlations with Equation (27) which provided s values for a number of reactants. However, as indicated in Scheme 33, for the limited number of substrates conveniently studied,158,186 variations in s did not show a clearly discernible pattern (and no obvious correlation with reactivity). Moreover, Pearson and Songstad demonstrated that the correlations break down if extended to extremes of ‘‘soft’’ and ‘‘hard’’ electrophilic centers such as platinum, in the substitution of trans-[Pt(pyridine)2Cl2], or hydrogen in proton transfer reactions.255 Despite this, Swain and Scott’s equation has stood the test of time and it is noteworthy that a serious breakdown in the correlations occurs only when the reacting atoms of both nucleophile and electrophile are varied. In this chapter we will restrict ourselves to carbon as an electrophilic center, and particularly, although not exclusively, to carbocations. Although before the mid-1980s reactions of other than highly stabilized carbocations were not accessible to kinetic measurements, it was possible to measure ratios of products from partitioning between nucleophiles of more reactive carbocations generated in solvolysis reactions. Particularly studied was the competition between water and azide ions for carbocation intermediates produced in reactions of alkyl halides in aqueous organic solvents.28 These measurements provided values of kAz/kH2 O , determined from the ratio of azido to alcohol products. The ratios varied from 3 to 600 and showed a striking dependence on the rate constants for the solvolysis reactions, which varied over 13 powers of 10.256 In principle, these measurements represent an application of the Swain– Scott relationship to two nucleophiles only. This is apparent from Equation (28), in which nAz corresponds to n for the azide ion and the electrophilic parameter s is seen to measure the selectivity of the carbocation between azide

OTs

ArCH2 CH Me

0.27

0.34

0.43

O

O

0.77

0.87

EtOTs 0.66

OH

+

PhCH2Cl

Scheme 33

I

ArCH2 CH Me

s=

s=

Br

ArCH2 CH Me

S

0.95

Me-Br

PhSO2Cl

1.0

1.25

PhCOCl 1.43

STABILITIES AND REACTIVITIES OF CARBOCATIONS

95

and water nucleophiles. Thus the substrates for which s was measured in Scheme 33 are replaced by carbocations, including, for example, Ph2CHþ, t-Buþ and 1- and 2-adamantylþ.256  log

 kAz ¼snAz kH2 O

ð28Þ

Apparently, these results implied an inverse relationship between reactivity and selectivity, with the reactivity of the carbocation measured by the inverse of the rate constant for solvolysis. This indeed was not unexpected in the context of a general perception that highly reactive reagents, especially reactive intermediates such as carbocations, carbanions, or carbenes are unselective in their reactions.257–259 Such a relationship is consistent with a natural inference from the Hammond postulate258 and Bell–Evans–Polanyi relationship,260 and is illustrated experimentally by the dependence of the Bronsted exponent for base catalysis of the enolization of ketones upon the reactivity of the ketone,261,262 and other examples21,263 including Richard’s careful study of the hydration of a-methoxystyrenes.229 However, as has again been well summarized by Mayr,253 a striking antithesis was then established between the variation in these values of kAz/ kH2 O and measurements by Ritchie of rate constants for reactions of a wide range of nucleophiles with relatively stable carbocations such as crystal violet 72, pyronin 71, the p-dimethylaminophenyltropylium ion or the p-nitrophenyldiazonium ion. For such stable cations, direct kinetic measurements were possible using conventional spectrophotometric monitoring or, for faster reactions, a preliminary mixing of reagents by stopped flow. NMe2

+

Me2N

72 NMe2

Far from confirming a dependence of nucleophilic selectivity on the reactivity of the carbocations, Ritchie observed that selectivities were unchanged over a 106-fold change in reactivity.15 He enshrined this result in an equation (29) analogous to that of Swain and Scott, but with the nucleophilic parameter n modified to Nþ to indicate its reference (initially) to reactions of cations, and with the selectivity parameter s taken as 1.0, that is, with no dependence of the selectivity of the cation on its reactivity (as measured by the rate constant for the reference nucleophile, kH2 O for water).

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 log

k kH2 O

 ¼Nþ

ð29Þ

This lack of variation of selectivity with reactivity was confirmed in an independent study by Kane-Maguire and Sweigart who found that relative reactivities of amine and phosphine nucleophiles toward a range of organometallic cations were also independent of the nature of the electrophile.184,264 The dilemma presented by these conflicting results was resolved by TaShma and Rappoport.265 They pointed out that the apparent dependence of kAz/ kH2 O upon the reactivity of the carbocation arose because even the most stable cation reacting with azide ion did so at the limit of diffusion control. Thus while kH2 O remained dependent on the stability of the cation in the manner illustrated in Fig. 7 the rate constant for the azide ion remained unchanged. Thus the most stable cation formed in the solvolysis reactions was the trityl ion, for which direct measurements of kH2 O = 1.5105 s1 and kAz = 4.1109 now show that even for this ion the reaction with azide ion is diffusion controlled.22 The advent of laser flash photolytic studies, and the correct use of product ratios to assess reactivities of nucleophiles competing with azide ions reacting at the diffusion limit, led to direct measurements of rates of nucleophilic reactions for a much wider range of carbocation stabilities. Much of this work, which was carried out by the research groups of McClelland and Steenken and Richard and Amyes, has already been cited. We will return to these studies in the context of a further discussion of reactivity and selectivity and the failure of rate constants of reactions of nucleophile to correlate with equilibrium constants at the end of this chapter. First, however, we turn to a further investigation of carbocation reactions undertaken by Mayr and his research group in Munich. In a comprehensive series of studies Mayr has extended Ritchie’s observations and placed them in a wider context, including applications to organic synthesis. As will be seen, together with the studies of McClelland and Richard this work leads at least in outline to a coherent view of reactivity, selectivtiy and equilibrium in carbocation reactions. Nucleophile–electrophile reactions and synthesis Rappoport and TaShma’s work removed a major difficulty for Ritchie’s analysis and helped pave the way for Mayr to exploit fully the wide applicability and simplicity of Equation (29) for predicting rates of reactions of electrophiles with nucleophiles. Mayr pointed out that Equation (29) could be rewritten as Equation (30), in which log ko corresponds to the rate constant for reaction of the electrophile under study with a reference nucleophile266 (chosen as water by Ritchie) which, in so far as it is characteristic of the

STABILITIES AND REACTIVITIES OF CARBOCATIONS

97

electrophile, is sensibly denoted E. We can then rewrite Equation (30) as Equation (31), in which the measured rate constant for reaction is expressed as the sum of one parameter for the nucleophile and one for the electrophile. Log k¼log ko þNþ

ð30Þ

Log k¼EþN

ð31Þ

In Equation (31), Ritchie’s parameter Nþ is replaced by N because, as will become clear, there is a difference in the definition of these parameters, including the choice of reference nucleophile. However, the striking simplicity of the relationship in representing reactions in which the nucleophile and electrophile are equal partners is apparent. It implies that reactivity of electrophile–nucleophile combination reactions might be predicted from two parameters. The challenge of presenting this as a practical aid to organic synthesis was taken up by Mayr’s research group.267 The starting point for Mayr’s work in the mid-1980s was very different from Ritchie’s studies of mainly oxygen and nitrogen nucleophiles. Mayr’s initial aim was to measure rate constants for the synthetically important alkylation reactions of alkenes.27,268,269 As representative alkylating agents, he chose p-substituted benzhydryl cations to provide a homogeneous family of electrophiles. These ions could be generated by the addition of the appropriate benzhydryl chloride to dry methylene chloride containing BCl3. The reactions with alkenes were carried out at 70C and monitored spectrophotometrically or conductimetrically under conditions for which the rate-determining step of the reaction was attack of the electrophile on the alkene.270 The temperature dependences of the reactions were studied to extrapolate rate constants at 20C, and rate constants for a fraction of the reactions were measured directly at this temperature, with the carbocations generated from the benzhydryl chlorides by flash photolysis.27,83 Mayr initially defined a set of electrophilic parameters for the benzhydryl cations using a reference nucleophile, which was chosen as 2-methyl-1pentene.268,269 Values of E were then defined as log k/ko, where ko refers to a reference electrophile (E = 0), which was taken as the 4,40 dimethoxybenzhydryl cation. Plots of log k against E for other alkenes are thus analogous to the plots of log k against pKR in Fig. 7 except that the correlation is referenced to kinetic rather than equilibrium measurements. However, they differ from plots based on the Swain–Scott or Ritchie relationships in which log k is normally plotted against a nucleophilic parameter, that is, n or Nþ, rather than E. In practice, rate constants for only a limited range of benzhydryl cations could be measured for 2-methyl-1-pentene itself. However, it became apparent that if reaction of the cation occurred at a methylene group (=CH2) plots of

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log k versus E were almost parallel for alkenes of widely differing reactivity. This allowed E values for benzhydryl cations varying in reactivity from p,p0 -dichloro to p,p0 -bis(dimethylamino) to be assigned. When the structure of the p-nucleophile was varied more widely to include nonterminal alkenes, alkenes with O, N, or other b-substituents, alkynes, and aromatic molecules, a greater variation in the slopes of the plots was found. Fig. 8 shows plots of log k versus E for a representative group of alkene structures as well as for arenes.271 To accommodate the more reactive nucleophiles, the electrophilicity range of the benzhydryl carbocations was extended by inclusion of p-amino substituents for which the electron-donating ability of the amino group was amplified by incorporation in a tricyclic ring structure.272 Variations in slope are not large but are sufficient to merit addition of a slope parameter for each nucleophile. The logic of choosing a structurally homogeneous set of electrophiles is now evident. These can be reacted with

O N

N

OSiMe3

8

OSiMe3

O

OSiMe3 OSiMe3

OSiMe3

OPh

with s = 1

6

SiMe2Cl 4

log k

2

N = –E

0

–2

–4 –10

–8 + CH

N

2

–6

–4

+ CH

+ CH

NMe2 2

NPh2 2

–2 + CH

Ph

N

CF3 2

0 + CH

OMe 2

2

4 + CH

6 + CH

Me 2

Cl

2

with E = 0

Electrophilicity(E )

Fig. 8

Plots of log k versus E for the reaction p-nucleophiles with benzhydryl cations.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

99

nucleophiles of very different structure and differences in slope can be assigned to steric or other effects associated exclusively with the nucleophile. One way to modify Equation (31) to allow for the different slopes is to multiply the electrophilicity parameter E by a variable s as shown in Equation (32). Note again that s here differs from s in the Swain–Scott equation which refers to the slope of a plot of log k versus the nucleophilicity parameter n (or N) rather than electrophilicity parameter (E). However, the equation that Mayr adopts is not Equation (32) but Equation (33),269 in which s multiplies not only E but both E and N. This is formally equivalent to Equation (32), because s is still determined by the slope of the plot of log k against N, that is, by the dependence of log k on the nucleophile only. However, multiplication of N by s leads to some subtle changes which suit the original purpose of the study, namely, to develop synthetically useful predictions of rates of reactions of electrophiles with nucleophiles. It is an unusual but interesting and practical manipulation of an otherwise conventional free energy relationship. Log k ¼ sE þ N

ð32Þ

Log k ¼ sðN þ EÞ

ð33Þ

One virtue of Equation (33) is that it avoids long extrapolations of values of N measured for electrophiles with E values far removed from zero. This can be seen from Fig. 8 which includes plots of log k versus E for highly unreactive p-nucleophiles such as toluene and highly reactive ones such as vinyl acetals and enamines. According to Equation (33), the value of N corresponds to the intersection of the plot of log k versus E not with the vertical line (ordinate) for E = 0 but, as shown in the figure, with the horizontal line corresponding to E = –N. This intersection has the physical significance that the rate constant for combination of the relevant nucleophile and electrophile (i.e. at the E value of the intersection) is 1.0 M1 s1. Mayr points out that an advantage of this definition is that it prevents crossover of correlation lines which in some instances occur if the extrapolations are extended beyond the reactivity ranges likely to lead to reaction. Thus the relative magnitudes of N properly reflect relative reactivities of nucleophiles under realistic reaction conditions. Although not well illustrated in Fig. 8 the potential for crossover is implicit in the lack of parallelism of the correlation lines. Of course, if all lines were parallel with unit slope the relative magnitudes of N would be the same whether defined by Equation (32) or (33). In the most recent correlation analysis based on Equation (33) a ‘‘basis set’’ of 23 benzhydryl cations and 39 p-nucleophiles, for which extensive measurements are available, were selected to provide a set of reference parameters which would not require further modification as data was acquired for new

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nucleophiles, and indeed new electrophiles.272 As before the p,p0 dimethoxybenzhydryl cation was assigned the value E = 0 and the slope parameter s for 2-methyl-1-pentene was defined as 1.0. One might query the robustness of anchoring the correlation to a single s value, but the effectiveness of this is endorsed by the good overlap of plots for nucleophiles ranging from the most to the least reactive, as is evident in Fig. 8. Moreover, a comparable analysis of slopes and intercepts of plots of pKa against Xo for a ‘‘basis set’’ of weak bases undergoing protonation in strongly acidic media shows little difference from an alternative analysis in which a common slope parameter is assigned to structurally similar bases covering a range of base strengths.52,53,55 The origin of the variation in s values for the different alkenes encompassed by Equation (33) is not entirely clear but steric effects have an obvious influence. Thus, as shown in Scheme 34, alkylation of tetramethyl ethylene gives s greater than 1.0 (1.44) consistent with increased selectivity as a result of hindrance to attack of an electrophile by the methyl substituents.27 Aromatic p-systems also have high s values, especially where reaction occurs at an o-position.271 However, b-oxygen and allylic silicon, germanium, or tin substituents decrease s,269,273 while for phenylacetylene s also appears to be low.269 A tendency for less reactive nucleophiles to have larger s values may imply a mild dependence of selectivity on reactivity, but the variations in s are small and changes in reactivity large. Just as N for a nucleophile can be determined from a plot of log k against E for a series of electrophiles, in principle, the value of E for an electrophile can be determined from the intercept (at E þ N = 0) of a plot of log (k/s) versus N for a series of nucleophiles (or indeed, if need be, from the measurement for a single nucleophile). In this way E values have been determined for many electrophiles other than benzhydryl cations, including metal-coordinated cations,186 BF3-coordinated aldehydes,274 tropylium ions, and many benzylicand heteroatom-substituted carbocations. In the low reactivity range

0.98

0.94 SiMe3

0.94

OSiMe3

1.32

OPh

1.17 1.62 OSiMe3 OMe

SiMe3 1.40

Scheme 34

0.70 0.98

1.17

Ph

STABILITIES AND REACTIVITIES OF CARBOCATIONS

101

electrophiles extend to neutral molecules. These may also be included within the benzhydryl calibration framework by choosing quinone methides such as 73 in which nucleophilic attack is directed to an electrophilic carbon–carbon double bond by bulky substituents flanking the carbonyl group.275 Such quinone methides have been important in establishing N values for reactive nucleophiles such as nitroalkyl276 and other stabilized carbanions275,277 including phosphorus ylids.278 With a further extension of nucleophiles to include organometallic reagents, the range of processes embraced within the nucleophile–electrophile combinations includes Friedel–Crafts alkylations, Wittig and Mannich reactions, Nicholas propargylation, and Mukaiyama aldol cross couplings among other synthetically useful reactions.27

Me2N

O 73

It should be noted that although the core E and N values are defined for CH2Cl2 as solvent, rates of reactions between positively charged and nonhydrogen-bonded neutral reagents are normally only weakly sensitive to solvent27,270,279 so the values should provide a reasonable approximation over a range of solvents. On the other hand, for reactions of carbocations with carbanions, especially where negative charge is delocalized to oxygen, a much greater solvent sensitivity is observed and different N parameters have been determined in water and DMSO as solvents. It should be noted that the effect of solvent is expressed in the N values and that to a good approximation the E values for nonpolar solvents can be retained. The simplest demonstration of the synthetic utility of the E and N parameters follows from the approximation that all the slope parameters s in Equation (33) are 1.0 and that log k = E þ N. It is then possible to plot E parameters against N parameters to give the reactivity box shown in Fig. 9.280 A diagonal of this box corresponds to E þ N = 0 and k = 1 M1 s1. Lines parallel to this diagonal correspond to constant values of log k indicated by the appropriate (constant) value of E þ N. If the E and N values of two reagents are known or can be guessed then a reasonable assessment of the time for reaction can be made. Reactions with E þ N in the upper left of the box (i.e., with large negative values) will be relatively slow, and this area, for which k is predicted to be 1010 M–1s–1

Co2(CO)6 OMe +

No reaction at 20oC Me3C +

10 –10

0

10

20

N Fig. 9 Semiquantitative model of reactivity in electrophile–nucleophile reactions.

of a carbocation on a relatively unreactive double bond. Ionic polymerizations of vinyl derivatives are further important reactions for which Fig. 9 provides a valuable guide.281 Although for many reagents determining values of E or N may not be feasible, often an approximate value may be interpolated from comparison with the wide range of structures for which values are known. Extensions of Mayr’s work In addition to their reactions with alkenes and carbanions as nucleophiles benzhydryl cations react with hydride donors.282–284 These hydride transfer reactions show the same linear dependence of log k upon E as the reactions with alkenes and the same constant relative selectivity, that is with slopes of plots s close to 1.0, for structures ranging from cycloheptatriene to the

STABILITIES AND REACTIVITIES OF CARBOCATIONS

103

borohydride anion and dihydropyridines and solvents from methylene chloride to DMSO or aqueous acetonitrile. As with the reactions with alkenes the measurements were shown to be rather insensitive to changes in solvent. It might appear that this discussion has departed far from the original consideration of nucleophiles which was focused on anions in hydroxylic solvents. However, a feature of Mayr’s scheme is the wide range of its application. Of obvious interest is its extension to nucleophilic centers other than carbon or hydrogen and to water as a solvent. Reactions of strong nucleophiles in water are not easily observable for the more unstable benzhydryl carbocations, but are readily monitored with highly stabilized aminosubstituted cations such as those shown in Fig. 8, which were developed by Mayr as part of the benzhydryl series of compounds for this purpose. For these ions, reactions with water, hydroxide ion, other oxyanions, amines, amino acids,285 azide ion,286 and a thiolate ion have been studied.266,287 Plots of log k against E are again linear, and confirm that a consistent nucleophilic behavior is observed between p-nucleophiles and n-nucleophiles as different as olefinic hydrocarbons and the hydroxide ion. These measurements allow a comparison with the earlier analyses of reactions of n-nucleophiles in water in terms of Ritchie’s Nþ equation. A significant finding is that although plots of log k against E are linear, the slopes are significantly less than 1.0, falling consistently in the range 0.52–0.71 except for water (0.89) and –OOCCH2S (0.43). The exceptional behavior of water is consistent with difficulties Ritchie encountered in taking this as a reference nucleophile for the Nþ relationship and is in line with values for other hydroxylic solvents.288 On the other hand, the narrow range of s and N values for other nucleophiles becomes compatible with the Nþ relationship if Nþ = 0.6N. We will return to the significance of this, but note that assignment of s and N values to nucleophiles on which the Nþ relationship was based allows, in turn, assignment of E values to cations studied by Ritchie, notably trityl cations and substituted xanthylium ions and tropylium ions. It is remarkable that Mayr’s study, which originated with a very different reaction and solvent, is able to correlate satisfactorily data for nucleophilic reactions of carbocations in aqueous solution. In principle, any carbocation for which a rate constant for reaction with water below the relaxation limit has been measured, either directly by flash photolysis or indirectly by the azide clock, may be assigned an E value based on the values of N = 5.11 and s = 0.89 for water (although where possible E values are better based on reactions with more nucleophiles). On the other hand, it is to be expected that on moving beyond the structural constraints of the benzhydryl cations, the assigned E values will have less generality, if only because of the influence of steric effects. Thus the E values assigned to trityl cations overestimate by several orders of magnitude their reactivities toward alkenes. This is consistent with the known steric demands of the trityl cation289 and the likelihood that steric effects would be qualitatively different for reactions with alkenes and nitrogen or oxygen bases.

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R. MORE O’FERRALL

Likewise, although N values for alkenes and hydride donors are practically independent of the solvent, hydrogen bonding to oxygen and nitrogen nucleophiles renders their N values sensitive to the nature of the solvent. This solvent dependence has been examined in some detail for the reactions of benzhydryl cations with halide ions, for which the cations were generated by flash photolysis.251 As might be expected, a reduction in the solvent ionizing power, as judged by solvent Y values, increases reactivity. More than a 100-fold difference was found between ethanol and TFE as solvent, and intermediate values were found for water and water–acetonitrile mixtures. In a striking application of this data, combination of N and s values for solvent288 and halide ions with E values for carbocations, allows an effective analysis of the detailed course of SN1 solvolyses, especially if allowance is made for encroachment of the diffusion limit for reactions of more reactive carbocations with halide ions.251 These results are by no means unrelated to the synthetic motivation of the earlier studies of alkylation reactions in CH2Cl2 as solvent. Comparisons of N and s values of alkenes and aromatics with those of hydroxylic solvents offer a guide to the conduct of Friedel–Crafts and other electrophilic carbon-carbon bond-making reactions in hydroxylic solvents. Not surprisingly, TFE is a particularly favorable solvent for such reactions and if allowance is made for a minor solvent dependence of N values for arenes and alkenes a good estimate of the likely feasibility of such reactions can be made.290–293 Remarkably, despite earlier suggestions to the contrary294 a good correlation exists between nucleophilic parameters for reactions of carbocations and those for SN2 substitutions. This is true of the Swain–Scott parameters (or Pearson and Sonntag’s nCH3 I values), and a particularly good correlation exists between Mayr’s N values and rate constants for SN2 displacements of neutral dibenzothiophene from the S-methyldibenzothiophenium ion 73, both for a range of hydroxylic solvents studied by Kevill295 and by oxygen, amine, and even phosphorus nucleophiles measured by Mayr and coworkers.253

+ S Me

74

However, the slope of the plot of log k against N for these reactions is not 1.0 but close to 0.6. This implies that increased nucleophilicity is nearly twice as effective in promoting reaction with a carbocation as with an SN2 substrate. Although the mechanisms of these reactions are different, it is perhaps

STABILITIES AND REACTIVITIES OF CARBOCATIONS

105

surprising that a highly reactive carbocation should be less selective than relatively unreactive alkylating agents such as methyl bromide correlated by the Swain equation. This point has been discussed by Richard, Toteva, and Crugeiras, who point to a likely difference in intrinsic reactivity associated with the closed rather than open electron shell of the reaction site for reactions at a saturated carbon center.219 In recognition of the excellent correlation that exists between his own and Swain and Scott’s (or Kevill’s) parameters, Mayr suggests modifying Equation (33) to include a further electrophilic constant distinguishing reactions at sp2 and sp3 carbon atoms.29,253 He denotes this constant sE to indicate that it refers specifically to the electrophile, and introduces the subscript ‘‘N’’ for the parameter s which has so far referred to the nucleophile. Again, instead of adopting the expected conventional form of log k = sNE þ sEN he chooses Equation (34), in which values of E and N correspond to intercepts on the abscissa rather than the ordinate of plots of log k versus E or N. Of course, the original Equation (33) and indeed the Swain–Scott equation (Equation 27) are special cases of Equation (34). log k¼sE sN ðE þ NÞ

ð34Þ

In Equation (34), Mayr has not only provided a simple and comprehensive relationship embracing nucleophilic reactions at carbon, but has tested the relationship with hundreds of examples. The equation and measurements provide a practical basis for semiquantitative prediction of reaction rates embracing a large number of synthetic organic and organometallic reactions, as we have seen. Many incidental problems have also been addressed, including the choice of amine catalysts for organocatalysis,296,297 partitioning of carbocations between solvent and nucleophiles,288 competition between alkylation and hydride abstraction,283 carbocationic and carbanionic polymerizations,298 quantitative free energy profiles for SN1 nucleophilic substitutions,251 and the nature of the borderline between SN1 and SN2 mechanisms.299 An analog of Equation (33) has been applied to estimating rate constants for SN1 solvolyses in terms of parameters representing reactivities of leaving groups and incipient carbocations.300

REACTIVITY, SELECTIVITY, AND TRANSITION STATE STRUCTURE

In addition to the work on carbocation reactions already described Mayr,28 together with Richard and McClelland, has been concerned with problems raised by the lack of dependence of selectivity on reactivity apparent both from the normal constancy and specific variations in values of the slope parameters sN (and sE).28 We conclude this chapter, therefore, with a brief discussion of

106

R. MORE O’FERRALL

this problem and of additional questions raised by the lack of correlation of rate with equilibrium constants when the reacting atom of the nucleophile is varied between anionic or neutral oxygen, nitrogen, sulfur, phosphorus, or halogen atoms. We begin by considering a plot of Mayr’s E parameters against pKR in Fig. 10. For the benzhydryl cations shown as open circles the correlation is excellent. For other cations there is dispersion into structurally related groups such as trityl cations and tropylium ions. This behavior shows a close analogy with plots of log kp and log kH2 O against pKa and pKR in Figs. 1 and 3 (pp. 43 and 77) and may be considered normal for what amounts to a rate–equilibrium relationship. The slope of 0.68 for the plot is also comparable to that for plots of log kH2 O against pKR.4 There is little or no indication of curvature in Fig. 10 and in this respect the plot is again similar to those of Figs. 1 and 3. The behavior may be interpreted in terms of compensation between changes in thermodynamic driving force for the reaction and variations in intrinsic activation barrier, both depending on changes in equilibrium constant for the reaction, as discussed already (pp. 77–90). An important point made by Mayr, is that the constant slope for these relationships by no means implies a static transition state.282 This was

5

E

0

–5

–10

–10

–5

0 pKR

5

10

Fig. 10 Plot of E parameters against pKR: open circles, benzhydryl cations; filled circles, trityl cations; squares, organometallic cations; filled triangles, tropylium ions; open triangles, flavylium, xanthylium and other O-, S-, or N-conjugated cations.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

107

demonstrated in model calculations for hydride transfer between carbocation centers, which showed a systematic dependence of the degree of hydrogen transfer at the transition state upon the energy of reaction. The calculations also demonstrated that changes in intrinsic barrier occurred and were associated with a marked imbalance in charge distributions between reactants and transition state. When calculated values of the activation energy were plotted against the energy of reaction, they furnished slopes  = 0.72 for structural changes leading to changes in energy of the carbocation acting as hydride acceptor and  = 0.28 for corresponding changes in the hydride donor. These values are close to the values of 0.75 and 0.25 one might expect for a symmetrical transition state in which the hydrogen is half transferred and rehybridization of the reacting bonds had occurred to the extent of 50%, as envisaged in Kresge’s idealized model discussed above (p. 81).234 As expected the intrinsic barrier is increased by electron donating substituents (which stabilize the carbocations through delocalization of the charge) in the hydride donor and acceptor. For the carbocation, the effects of substituents on the energy of reaction and intrinsic barrier are complementary and for the donor, they are opposed. Mayr’s calculations are consistent with his experimental demonstrations that for hydride transfer the magnitudes of N and E are independent of each other. It seems likely that the same is true of reactions of carbocations with alkenes, which again yield a carbocation as immediate product of the reaction. In these reactions then, the lack of dependence of selectivity on reactivity can be interpreted in terms of the compensation between thermodynamic driving force and variable intrinsic barrier, as already discussed, which receives substantial reinforcement from Mayr’s calculations. On the other hand, it seems less likely that the relative reactivities of nnucleophiles should be independent of the reactivity of a carbocation. At least when they act as bases, there is little or no evidence that changes in structure of n-nucleophiles lead to changes in intrinsic barrier.301 One might expect therefore that carbocations of different reactivities reacting with a structurally related group of nitrogen or oxygen nucleophiles would show different slopes of plots of log k versus log K. There are some difficulties with testing this experimentally. The first is that it is not easy to match the same set of bases to electrophiles of quite different reactivity. A second is that the most readily available equilibrium constants characterizing the nucleophiles are pKas of the conjugate acids, which do not necessarily correlate reactivities toward carbocations. Thirdly, one should avoid reactions influenced by diffusion control. Finally, care has to be taken with steric and solvent effects. McClelland has studied the reaction of four primary amines with benzhydryl and trityl cations.4,302 Rate constants for reactions of most of the benzhydryl cations were close to their values for diffusion control. However, he was able to measure diffusion free rate constants for substituted trityl cations. There was a further complication, consistent with earlier measurements by Berg and

108

R. MORE O’FERRALL

Jencks303 in so far as there is a significant influence from a preequilibrium desolvation of the amine, which is larger for more basic amines. Nevertheless, based on careful measurements, McClelland was able to correct for this and demonstrate a clear dependence of slopes ( nuc) of plots of log k against the pKa of the ammonium ion upon the stability of the trityl cation as shown in Fig. 11. Interestingly, no leveling of the plot was observed for trityl cations such as crystal violet conforming to Ritchie’s equation. These measurements are consistent with earlier studies by McClelland of the trityl and xanthylium ions for which plots of log k against Nþ for a wide range of nucleophiles were recorded. The correlations showed some scatter, with a strong positive deviation of the azide ion, but it was clear that the slopes of the best straight lines through the points were considerably less than unity, being 0.33 for the trityl cation19 and 0.65 for the xanthylium ion.304 Again, the distinguishing feature of these cations compared with those studied by Ritchie was their much higher reactivity. A further dependence of the selectivity between different nucleophiles on the stability and reactivity of carbocations was found by Richard and Amyes in a study of reactions of alcohols and carboxylate anions with p-substituted a-trifluoromethyl benzyl cations (75, X = Me, OMe, SMe, N(Me)CH2CF3, and NMe2) monitored using the azide clock.305 Apart from the methylsubstituted substrate, for which the reactions approached diffusion control,

0.7

β nuc

0.6

0.5

0.4

0.3

–10

–5

0

5

pKR

Fig. 11 Plot of  nuc against pKR for reaction of primary amines with trityl cations ( values corrected by 0.2 to allow for desolvation of amines).

STABILITIES AND REACTIVITIES OF CARBOCATIONS

109

there was a strong dependence of selectivity upon the stability of the cation. The selectivities were measured from ratios of products of reactions of ethanol and TFE with the carbocations (or Bronsted exponents for reaction of carboxylate anions) and the stability was measured by the rate constant kS for reaction of the carbocation with the aqueous TFE as solvent. The variation in selectivity (kEtOH/kTFE) became saturated for the most stable p-aminosubstituted cations, for which selectivities are practically independent of the nature of the amino group. This behavior is indicated below by the substituent dependence of kEtOH/kTFE product trapping ratios, which vary by a factor of 100 between Me and Me2N. CH+

X

CF3

75

X

Me

MeO

MeS

CF3CH2(Me)N

Me2N

kEtOH/kTFE

3.1

55

71

270

330

kS (s1)

11010

5107

1.2107

2104

1. The same

SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY

125

convention, Kheavier/Klighter, is chosen for equilibrium IEs even though the IE can be >1 or 1 corresponds to an Hacid stronger than the Dacid.

2

Theory

The theory of IEs was formulated by Bigeleisen and Mayer.9 The IE on the acid–base reaction of Equation (1) is defined as the ratio of its acidity constant Ka to the acidity constant of the isotopic reaction, Equation (2). The ratio Ka/ K*a is then the equilibrium constant KEIE for the exchange reaction of Equation (3). That equilibrium constant may be expressed in terms of the partition function Q of each of the species, as given in Equation (4), which ignores symmetry numbers. HAÐHþ þ A

ð1Þ

HA ÐHþ þ A  

ð2Þ

HA þ A   ÐA þ HA

ð3Þ

KEIE ¼

QðA ÞQðHA Þ QðHAÞQðA   Þ

ð4Þ

The IE and the partition functions can be separated into three factors, MMI, EXC, and ZPE, as in Equation (5). The MMI factor comes from the ratios of molecular masses and moments of inertia, but has been simplified to Equation (6) by using the Redlich–Teller product rule, which assumes harmonic potentials. The products are over all the vibrational frequencies  i of each species. This factor is usually negligible (i.e., 1) for secondary IEs, except for very small molecules, and it is often omitted in calculations because it is sensitive to errors in calculating low frequencies. The second factor, EXC, is given by Equation (7), where ui = h i/kT and the products are over all the vibrational frequencies. This factor arises from contributions from thermally excited vibrational states. It too is usually very close to 1, because only isotopes of hydrogen show large differences in vibrational frequency, but those frequencies are so high that their excited vibrational states are not thermally populated to any significant extent. It is easy to calculate the EXC factor, but it is usually so close to 1 that it cannot be measured unambiguously, and the only experimental example that we know of is the kinetic IE for C–N rotation in HCONH2,10 where the frequency of the pyramidalization mode of the NH2 is unusually low.

126

C.L. PERRIN

KEIE ¼ MMI  EXC  ZPE

ð5Þ

MMI ¼

 i ðA Þ i ðHA Þ  i ðHAÞ i ðA Þ

ð6Þ

EXC ¼

ð1  exp ½ui ðA ÞÞ ð1  exp ½ui ðHA Þ ð1  exp ½ui ðHAÞÞ ð1  exp ½ui ðA ÞÞ

ð7Þ

The third factor, ZPE, given in Equation (8), where the sums are over all the vibrational frequencies, is the dominant contributor to the IE. It arises from the zero-point energies. Often terms cancel, so that only a single isotopesensitive vibrational mode dominates. If so, each of the sums in Equation (8) reduces to a singlepterm due to the zero-point energy of that mode. Then, because  i = (1/2p) (ki/), ZPE simplifies to the expression in Equation (9). Often the force constant k for that mode is lower in the base A and the reduced mass  is higher with the heavier isotope. Then the acid HA with the lighter isotope has the highest zero-point energy, so that the IE is >1. exp½ui ðA Þ=2 exp ½ui ðHA Þ=2  Þ=2 exp½u i ðHAÞ=2 exp ½ui ðA   X 1    ¼ exp  ½ui ðA Þ þ ui ðHA Þ  ui ðHAÞ  ui ðA Þ 2

ZPE ¼

   p 1X p 1 1 ½ kðA Þ  kðHAÞ p  p  ZPE  exp    2

ð8Þ

ð9Þ

An alternative that focuses on molecular structure rather than vibrational frequencies is the nuclear–electronic orbital approach, which calculates equilibrium IEs by treating some or all nuclei quantum mechanically on the same basis as the electrons.11 Because the Born–Oppenheimer approximation is only an approximation, light atoms, especially hydrogen, are quantum mechanical, and the electronic wave function is not independent of nuclear mass. This method provides bond lengths and atomic charges that vary with isotopic substitution. For example, in formate anion-h, -d, and -t, the (Mulliken) charges at oxygen are –0.729, –0.731, and –0.732, respectively, and the C–H, C–D, and C–T bond lengths are 1.1554, 1.1475, and 1.1441 A˚. The increasing negative charge is consistent with a greater basicity. Similarly, D and T substitution in methylamine, dimethylamine, and trimethylamine is calculated to lead to shorter C–D and C–T bonds and greater electron density at nitrogen, consistent with a greater basicity.

SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY

3

127

Methodology

pH TITRATION

Potentiometric titration and measurement of conductivity are the classic methods for determining pKa experimentally. With a differential method that involves comparison of meter readings for two substances under carefully controlled conditions, it is possible to obtain accurate differences in pKa.

NMR pH TITRATION

NMR pH titration is another method. It depends on the fact that proton transfer among acid and base forms is very fast, so that the observed chemical shift  is the average of the chemical shifts A and B of acid and base forms, but weighted by their respective concentrations, as in Equation (10). Solving Equation (10) for [B]/[A] and substituting into the Henderson–Hasselbalch equation [Equation (11)] leads to Equation (12). Finally, solving Equation (12) for  leads to Equation (13), expressing the pH dependence of the chemical shift as a familiar titration curve. By fitting the observed variation of chemical shift, or simply by finding the inflection point, where the change in chemical shift is maximum, it is possible to measure pKa. ¼

B ½B þ A ½A ½B þ ½A

ð10Þ

pH ¼ pKa þ log

½B ½A

ð11Þ

pH ¼ pKa þ log

  A B  

ð12Þ

¼

A 10  pH þ B 10  pKa 10  pH þ 10  pKa

ð13Þ

What is required is that the chemical shift change appreciably between acid and base forms. Because 13C, 15N, 19F, and 31P chemical shifts are dispersed over a large range, there is usually at least one suitable reporter nucleus near enough to the site of protonation, and even 1H chemical shifts show sufficient variation. Thus the pKa of glycine could be measured from the inflection points in the pD dependence of its 1H or 13C chemical shifts.12 Similarly, from the variation with pH of the 13C chemical shifts of acetic, propionic, and butyric acids the pKa of each acid could be measured.13 The separate pKas of four lysines in a pentadecapeptide could be measured from the pH

128

C.L. PERRIN

dependence of their "-CH2 chemical shifts, whose cross peaks with a-CH are well resolved in a 2D TOCSY spectrum.14 Moreover, because of the sensitivity of NMR chemical shifts to environment, the NMR titration can be applied to a mixture of substances, each with its own NMR spectrum, to determine differences in pKa. It is applicable even to IEs because isotope shifts (isotope effects on NMR chemical shifts)15–18 often lead to separate, resolvable, and assignable signals for isotopologues. The chemical shift of each of the substances then follows its own Equation (13), from which each pKa can be determined. It should be recognized though that chemical shifts do not always respond in the way expected from changes in electron density. For example, the 13C signal of a carboxylic acid shifts downfield on deprotonation,19 and the 15N signal of pyridine shifts upfield on protonation. A further advantage of NMR titration is that all measurements are made in a common solution, so that impurities do not interfere.

NMR TITRATION

It is desirable to avoid errors in pH measurement, which limit the accuracy of the above NMR pH titration. If an NMR titration is applied to a mixture of two acids, HA and HA0 , each of whose chemical shifts,  and 0 , follows Equation (13), it is possible to eliminate pH from the two equations and replace it with n, the number of equivalents of titrant added. Thus Ellison and Robinson obtained Equation (14), where D =  – 0 , D =  – 0 , D =  –  0 , and R = Ka/K0 a.20 Moreover, it is not necessary to prepare solutions of exact molarity, because n can be evaluated more readily as ( – )/( – ), from the variation of the chemical shift of HA during the titration. When R is near 1, this is approximately a parabolic dependence of D on n. The titration of a mixture of formic acid and 18O2–formic acid permitted the evaluation of the 18 O IE on acidity from the 13C NMR chemical shifts  and 0 of the carboxyl carbons. In practice, this involved fitting to the three parameters D, D, and R. This same equation was used with 31P chemical shifts to evaluate the 18O IE on the acidity of phosphoric acid and alkyl phosphates.21 D ¼ D þ

Rnð þDD Þ  nð Þ Rn  n þ 1

ð14Þ

Rabenstein and Mariappan applied a very similar procedure to measure the 15N IE on the acidity of glycine from the 13C NMR chemical shifts of the carboxyl carbons during titration of a mixture of glycine-14N and glycine-15N.22 The IE could be evaluated by fitting to Equation (15), where     þ 14 15 D = 14 – 15, D ¼ 14  15 , D15 ¼ 15  þ 15 , D14 ¼  14  14 , R ¼ Ka =Ka ,   þ and n ¼ ð14  14 Þ=ð14  14 Þ. This is the same as Equation (14), but with a simplification of the numerator. For glycine the carboxyl carbon is sufficiently

SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY

129

distant from the nitrogen that there is no 13C isotope shift due to 14N versus 15 N in the fully protonated or fully deprotonated material, so D = 0 and D15 = D14, which reduces Equation (15) to a two-parameter fit [Equation (16)]. D ¼ D þ

D¼

RnD 15  nD 14 Rn  n þ 1

ð15Þ

RnD 14  nD 14 Rn  n þ 1

ð16Þ

Similarly, Lippmaa and coworkers evaluated the relative acidities of linear and branched carboxylic acids from the variation with degree of protonation of the measured 13C NMR shifts.23 The method was then extended to secondary deuterium IEs, evaluated from the variation with degree of protonation of the measured 13C NMR shifts of a mixture of isotopologues.24 The data were fit by nonlinear least squares to Equation (17), where H and D are  the observed chemical shifts of undeuterated and deuterated isotopologues, H  þ and D are those chemical shifts in the deprotonated form, þ H and  D are H D those chemical shifts in the protonated form, R ¼ Ka =Ka , and n is the degree of protonation of the undeuterated material. This is the same equation as Equation (15), but adapted to deuteration, and again n is evaluated from   chemical shifts as ðH  H Þ=ðH  þ H Þ. 





H  D ¼ H  D  nðH  þ HÞ þ

Rn  ð  þ DÞ 1 þ ðR  1Þn D

ð17Þ

A further improvement in the NMR titration comes from eliminating both pH and n entirely and expressing the comparison in terms of chemical shifts only.25,26 This is applicable to any pair of acids, AHþ and BHþ, with a ratio of þ þ =KBH . It is readily shown that the chemical acidity constants K equal to KAH a a shifts are related to each other by Equation (18), where a and b are the observed chemical shifts during the titration and A, AHþ , B, and BHþ are limiting chemical shifts of unprotonated and protonated A and B. This is a nonlinear equation in the one parameter K, and it can be fit by nonlinear least squares. a ¼ A þ

ðAHþ  A Þðb  B Þ ð1  KÞðb  B Þ þ KðBHþ  B Þ

ð18Þ

A further simplification comes from linearizing this equation, to produce Equation (19). Therefore, a plot of ðb  B ÞðAHþ  a Þ versus ða  A ÞðBHþ  b Þ ought to be a straight line, with slope K and zero intercept. This too is a one-parameter equation, which can be analyzed by linear least squares. Error analysis, to obtain the standard deviation of slope and intercept, is especially easy.

130

C.L. PERRIN

ðb  B ÞðAHþ  a Þ ¼ Kða  A ÞðBHþ  b Þ

ð19Þ

The first applications of this method were to conformational analysis of mixtures of cis- and trans-4-phenylcyclohexylimidazole (1) and of the a and b anomers of glucosylimidazole (2, R = H) and its tetraacetate (2, R = COCH3), using 1H NMR. Its generality was demonstrated for other mixtures, including cis- and trans-4-tert-butylcyclohexylamine (3), cis- and trans-4-tert-butylcyclohexanecarboxylic acid (4), and the four stereoisomers of 2-decalylamine (5), using both 1H and 13C NMR.27 These examples demonstrate the power of the method for measuring relative acidities of closely related materials, without the necessity of separating them. Moreover, the method could be applied in a wide variety of solvents, including aqueous methanol, dimethyl sulfoxide (DMSO), and dichloromethane, some of which would never permit the use of a pH electrode. Still another example is the pairwise titration of PhCRR0 N(CH3)2 (R,R0 = H,CH3), showing the same relative basicity with either BF3 or CF3COOH in CDCl3.28

N Ph

N

RO RO RO

COOH t-Bu

N RO

1

4

NH2

O N t-Bu

2

3 H

H

NH2

5

It should be noted that the method depends on accurate determination of the limiting chemical shifts A, AHþ , B, and BHþ , obtained at beginning and end of the titration. Consequently, it is not very suitable for diprotic acids, unless the two pKas are very widely separated.29 This NMR titration method was subsequently applied to equilibrium IEs on acidity.30–33 Like the previous methods, it too benefits from the high sensitivity of 13C and 19F chemical shifts, and even 1H chemical shifts, to both isotopic substitution and state of protonation. Figure 1 shows the NMR titration of a mixture of tri(methyl-d)amine and tri(methyl-d2)amine in D2O, plotted according to Equation (19). The slope is 1.1618  0.0004. The intercept is –0.0061  0.0046, properly zero. The correlation coefficient is an impressive 0.999999, which is an indication of the accuracy achievable. Another remarkable result was the measurement of the relative basicity of the two exceedingly similar isotopomers of 1-benzyl-4-methylpiperidine-2,2,6-d3 (6). These are truly isotopomers (here stereoisomers), which bear the same number of isotopic substitutions and differ only in the position of the isotope, which is either axial or equatorial.

SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY

131

25

10–3 (δH+ – δH)(δD – δD°)

20

15

10

5

0

0

5

10 10–3 (δH – δH°)(δD– – δD)

15

20

Fig. 1 NMR titration [Equation (19)] of a mixture of (CH2D)3NHþ and (CHD2)3NHþ.33 Reprinted with permission from J Am Chem Soc 2008;130:11143–8. Copyright 2008 American Chemical Society. D H3C

N CH Ph 2 H D D

6

A variant that combines this NMR titration method with NMR pH titration was developed much earlier by Forsyth and Yang.34 The 19F isotope shift between N-methyl or N,N-dimethyl-4-fluoroaniline and its CD3 or (CD3)2 isotopologue shows a maximum at a pH near the pKa of the anilinium ion. Rearranging Equation (19) and ignoring intrinsic isotope shifts leads to Equation (20), where A and AHþ are chemical shifts of the aniline and the anilinium ion, respectively, assumed the same for both isotopologues. From this equation the IE on acidity could be evaluated at any pH, or preferably by averaging over all the pH values near the pKa. KaH ðh  AHþ Þðd  A Þ ¼ D Ka ðh  A Þðd  AHþ Þ

ð20Þ

The benefits of this method for measuring IEs on acidity, with its variants, are apparent. It is highly accurate, because it depends only on measurement of NMR chemical shifts, not pH or molarity or solution volume. Numerous reporter nuclei can be used, including 1H, 13C, 19F, and 31P. It is

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C.L. PERRIN

applicable to mixtures of isotopologues or isotopomers, without separating them. It is insensitive to the presence of impurities that could lead to systematic errors in comparisons of acidities between separate solutions. A wide variety of solvents can be used. It can be extended beyond IEs to measuring relative acidities of closely related substances, without the necessity of separating them.

EQUILIBRIUM PERTURBATION

A very different method, the equilibrium perturbation method, is applicable to measure equilibrium IEs when the reaction is slow enough that its rate can be measured.35,36 Let the reaction be A ! B [Equation (21)] and its isotopic variant A* ! B* [Equation (22)]. The kinetic IEs in the forward and reverse directions are kf =kf and kr =kr , respectively, and the equilibrium IE KEIE is ðkf =kf Þ=ðkr =kr Þ, or ðBinf =Ainf Þ=ðBinf =Ainf Þ in terms of equilibrium concentrations at infinite time. kf

AÐB kr

kf

B A Ð  kr

ð21Þ

ð22Þ

If a mixture is prepared with only A and B*, in an initial ratio r0 equal to A0 =B0 , the reactions of Equations (21) and (22) will occur, to establish the equilibrium. From stoichiometry, it can be shown that at equilibrium the ratio R = kr/kf = Ainf/Binf of unlabeled materials must satisfy Equation (23). This is a quadratic that could be solved to evaluate R if KEIE were known. R2 þ ð1  r0 ÞR  r0 ¼0 KEIE

ð23Þ

Because of the kinetic IE, one reaction [Equation (21) for definiteness, as is likely if the heavier isotope reacts more slowly] is faster than the other, so that the total concentration of A þ A* is temporarily depleted (or augmented) until the slower reaction restores the equilibrium. The solution to the kinetic equations is Equation (24), which will simplify because A0 ¼ 0 and Ainf þ Ainf ¼ A0 . The expression in Equation (24) reaches an maximum [or a minimum if Equation (21) corresponds to the faster reaction] given by Equation (25), where  ¼ ðkf þ kr Þ=ðkf þ kr Þ. Rearrangement of Equation (25) gives Equation (26), where A0 – Ainf is equal to A0/(1þR) and where R could be obtained from Equation (23) but is adequately approximated by r0.

SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY

A þ A ¼ Ainf þ Ainf þ ðA0  AinfÞexp ½ðkf þ kr Þt      þ A0  Ainf exp  kf þ kr t h i ðA þ A Þ max= min ¼ A0 þ ðA0  AinfÞ    = ð  1 Þ    1 = ð  1 Þ ðA þ A Þ max = min  A0 ¼    = ð  1 Þ    1 = ð  1 Þ ðA0  AinfÞ

133

ð24Þ

ð25Þ

ð26Þ

If A and A* have a characteristic spectrum, usually a UV absorbance, the time course of A þ A* can be followed, and its maximum or minimum, as in Equation (25), can be measured. The experimentally obtained quantity on the right-hand side of Equation (26) can then be solved numerically to evaluate . In practice, there are coreactants X and Y such that the reaction is A þ X Ð B þ Y. The concentrations of X and Y can be varied so as to shift the position of the equilibrium. At high [X] and low [Y] the equilibrium lies toward B, so that kf > kr and kf > kr . Under these conditions the measured   kf =kf . At low [X] and high [Y] the equilibrium lies toward A, so that kf < kr and kf < kr . Under these conditions the measured   kr =kr . Because R or Ainf/Binf, the solution to Equation (23), expresses the position of the equilibrium, the general expression is given by Equation (27). Therefore, a plot of (1þR)/ versus R is a straight line with slope kr =kr and intercept kf =kf . The ratio of slope to intercept is ðkf =kf Þ=ðkr =kr Þ, which is the desired equilibrium IE KEIE. 1þR R 1 ¼ þ  kr =kr kf =kf

ð27Þ

Usually, this method is applied to enzymatic reactions, and the equilibrium IEs are obtained along with kinetic IEs that are of greater interest. An example is the deuterium IE on the reaction of acetone-d6 with NADH, to form 2-propanol-d6 þ NADþ. A mixture of acetone-d6 and 2-propanol is prepared along with coreactants NADH and NADþ at concentrations such that the reaction is at chemical equilibrium. Isotopic equilibration is initiated by adding enzyme. In this case the spectral signature lies in the NADH, but the measured maximum or minimum of absorbance provides the right-hand side of Equation (25) or (26) and thus  for each mixture. An estimate of KEIE is needed to solve for each R in Equation (23) in order to fit the data to Equation (27), but after successive iterations the values of R and KEIE converge.

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C.L. PERRIN

Secondary deuterium isotope effects on acidities in solution

OH ACIDS

In early studies of secondary deuterium IEs on acidity, benzoic-d5 acid and phenol-d5 were found to be 2.4  0.6 and 12  2% weaker acids, respectively, than their h5 isotopologues.37 Phenol shows the larger IE because its oxyanion is better conjugated with the ring. The IE was attributed to the electrondonating ability of the deuterium, arising through anharmonicity. Streitwieser and Klein used conductivity measurements to determine the secondary deuterium IEs on acidity of some carboxylic acids.38 The data are H listed in Table 1. In all cases pKD a  pKa is > 0, meaning that the deuterated acid is the weaker. According to another study, by Bell and Miller, also in Table 1, DCOOH is a weaker acid than HCOOH, by 0.035  0.002 pK units,39 which agrees with the 0.030  0.004 of Streitwieser and Klein. Halevi, Nussim, and Ron obtained further IEs on acidity of carboxylic acids by pH titration, and they are included in Table 1.40 Their DpKa for CD3CO2H is twice that of Streitwieser and Klein, which agrees with the results of yet another study, which also fitted the temperature dependence of DpKa as –91.11/T þ 0.6449 – 0.001086T.41 These results were attributed to an inductive effect, for which the evidence adduced was the strong damping of the IE through a saturated

Table 1 Secondary deuterium IEs on acidity of carboxylic acids AcidD DCO2H DCO2H CD3CO2H CD3COOH CD3COOH CH3CD2COOH CD3CH2COOH (CD3)3CCO2H ClCD2COOH PhOCD2COOH PhSCD2COOH 2,6-C6H3D2CO2H C6D5CO2H PhCD2COOH PhCD2COOH PhCD2COOH PhCD2COOH 4-O2NC6H4CD2COOH 4-CH3OC6H4CD2COOH

H pKD a  pKa

0.030  0.004 0.035  0.002 0.014  0.001 0.026  0.002 0.015 0.034  0.002 0.007  0.001 0.018  0.001 0.0052  0.0003 0.0048  0.0003 0.0090  0.0002 0.003  0.001 0.010  0.002 0.048  0.001 0.005  0.003 0.0047  0.006 0.0031  0.0002 –0.0013  0.0009 0.0019  0.0003

Method Conductivity Conductivity Conductivity pH titration pH titration pH titration pH titration Conductivity Conductivity Conductivity Conductivity Conductivity Conductivity pH titration Differential potentiometry NMR pH titration Conductivity Conductivity Conductivity

References 38 39 38 40 41 40 40 38 43 43 43 38 38 40 42 42 44 44 44

SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY

135

carbon from CD3COOH to CD3CH2COOH. Likewise, the IE of 0.002 per D in pivalic-d9 acid is consistent with a 2.8-fold falloff factor for inductive effects. The deuterium IE on the acidity of phenylacetic acid was reinvestigated by Bary, Gilboa, and Halevi, using both the differential potentiometric method and NMR pH titration.42 The two methods give the same DpKa of 0.005. The differential potentiometric method was judged sound, but the earlier results from pH titration could not be reproduced. Substituent effects on secondary IEs on the acidity of carboxylic acids are H D included in Table 1. For 4-X-C6H4CD2COOH Ka 2  Ka 2 is 1.0072  0.0004, 0.997  0.002, and 1.0045  0.0007 for X = H, NO2, and OCH3, respectively.44 The first value is considerably smaller than that of Halevi, Nussim, and Ron, H D which was later found to be irreproducible. For XCD2COOH Ka 2  Ka 2 is larger than for the arylacetic acids, 1.012  0.0007, 1.011  0.0007, and 1.021  0.0005 for X = Cl, PhO, and PhS, respectively.43 Because the IEs vary with X, it was concluded that a simple inductive effect cannot account for them. Lippmaa and coworkers used 13C NMR titration to measure secondary deuterium IEs on acidities of carboxylic acids.24 The results are listed in Table 2. It is remarkable that the IEs show only a small attenuation with distance, so that the IE from three g-deuteriums in alanine is greater than that from two b-deuteriums in glycine. As a consequence the IEs can be detected and measured from deuteriums as far as seven bonds away from the carboxyl, as in caproic-6,6,6-d3 acid. Moreover, in benzoic acids the IE is practically independent of the site of deuteration. Table 2 Secondary deuterium IEs on acidity of carboxylic acids, by titration24 13

Acid

Reporter

Acetic-d3

COOH CH3/CD3 COOH CH2 CH3/CD3 COOH a-CH2 b-CH2 b-CH2 C1 C4 C4 C1 C1 CH2/CD2 CH

Propionic-3,3,3-d3 Butyric-4,4,4-d3 Caproic-6,6,6-d3 Benzoic-2-d Benzoic-3-d Benzoic-4-d Benzoic-2,3,5-d3 Benzoic-d5 H3NþCD2COOH H3NþCHCD3COOH

C

13

C NMR

D KH a =Ka

DpKa

1.0326  0.0008 1.0298  0.0008 1.0191  0.0006 1.0188  0.0005 1.0172  0.0009 1.0114  0.0003 1.0107  0.0003 1.0098  0.0004 1.0012  0.0003 1.0046  0.0002 1.0045  0.0002 1.0042  0.0005 1.0137  0.0002 1.0230  0.0002 1.0056  0.0002 1.0142  0.0003

0.0139 0.0128 0.0082 0.0081 0.0074 0.0049 0.0046 0.0042 0.0005 0.0020 0.0019 0.0018 0.0059 0.0099 0.0024 0.006

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Recently, Perrin and Dong measured secondary deuterium IEs on acidities of carboxylic acids (7–10, 14, 15) and phenols (11–13), using 1H, 13C, and 19F NMR titration and reporter nuclei indicated in boldface in the structures.32 H Data are presented in Table 3, where DpK ¼ pKD a  pKa . For aliphatic acids the IEs decrease as the site of deuteration becomes more distant from the OH, as expected. In contrast, IEs in both phenol and benzoic acid do not decrease as the site of deuteration moves from ortho to meta to para (as was observed by Lippmaa and coworkers).24 A notable feature in Table 3 is that the IE per deuterium is lower for hydroxyacetic acid (9) than for acetic (8). O

O

D C

CD3C OH

OH

7-d

OH D

F

11-d2

D

F

F D

12-d3

OH

9-d

10-d8

OH

D

O CHD2(CD3)2C

OH

8-d3

OH D

O HOCHD

CD3

D D

D F

COOH

COOH

13-d3

F

14-d2

D

F

F D

15-d3

IEs on acidity of alcohols have been little studied, primarily because they are not sufficiently acidic to be titratable in water, and no studies have been reported in DMSO. One exception is aqueous trifluoroethanol-d2, which is less acidic than trifluoroethanol, according to NMR pH titration, with a DpKa of 0.056.45 In an early study by UV spectroscopy, the acidity constant (pKa) in H2SO4 of protonated acetophenone-d3, PhC(=OHþ)CD3, is –6.30  0.006 (on the Ho scale), lower (more acidic) than protonated acetophenone, PhC(=OHþ)CH3, 46 H whose pKa is –6.19  0.01, corresponding to KD a =Ka ¼ 1:29, or 1.09 per D. 1 Based on H NMR chemical-shift changes in H2SO4 solution, the pKa of O-protonated acetone is –3.09, whereas for O-protonated acetone-d5 it is h d –3.14, corresponding to an equilibrium IE Ka 6 =Ka 5 of 0.87  0.04, or 0.97 47 per D. The NMR data also required inclusion of a hydrogen-bonded complex between acetone and H3Oþ, with a pKa of –1.59 for acetone and –1.68 for acetone-d5. In both these ketones the deuterated acid is more acidic, and the IE is inverse ( C–T. Various estimates of dCH–dCD all give 0.005A˚ (0.5 pm), based on a C–H frequency of 3000 cm1 and a Morse potential with dissociation energy of 100 kcal mol1, or on the spectroscopic data for HCl,148 or as the experimental Dd in C2D6.149 This is a primary IE on the bond length. It is responsible for ‘‘steric’’ kinetic IEs arising because CHn groups are effectively larger than CDn and possibly for various IEs dependent on intermolecular forces, such as those on vapor pressure, adsorption, and chromatographic separations. Secondary IEs on molecular structure arising from the anharmonicity of C–H bonds are more subtle. An example is the C–C bond in C2D6, which is calculated to be shorter by 0.0015 A˚ than that in C2H6, owing to the anharmonicity of bending modes, which also make CHn groups effectively larger than CDn.150 A prominent example is the Ubbelohde effect, where the OO distance in an ODO hydrogen bond is shorter than in an OHO hydrogen bond.151 The relevant question regarding secondary IEs on acidity is the extent to which IEs affect the electronic distribution. How can an inductive effect be reconciled with the Born–Oppenheimer approximation? Although the potential-energy function and the electronic wave function are independent of nuclear mass, an anharmonic potential leads to different vibrational wave functions for different masses. Averaging over the ground-state wave function leads to different positions for the nuclei and thus averaged electron densities that vary with isotope. This certainly leads to NMR isotope shifts (IEs on chemical shifts), because nuclear shielding is sensitive to electron density.16 A more pertinent question is the extent to which IEs affect dipole moments, which can exert an inductive effect on acidities. A benchmark is the difference between the dipole moments of HCl and DCl, which is 0.005  0.002 D, or only 0.5% of the total 1.08-D dipole moment of their very polar bond.148 The dipole moment of ND3 is 0.0135  0.001 D greater than the 1.475 D of NH3, a 1% effect, but this may be due to the anharmonicity of the bending modes.152,153 The key role of bending modes is demonstrated by the comparison of CD3F and CDF3.154 The dipole moment of the former is larger than that of CH3F by 0.0112 D, whereas the difference for CDF3 is only 0.0007 D. If the IE on dipole moment were due to electron donation from H or D to F, these two differences ought to have been similar. Another estimate of the IE on dipole moments comes from experimental measurements on (CH3)3CD and

SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY

157

(CH3)3CH (although it was acknowledged that bending modes may contribute).155 Their dipole moments differ by 0.0086 D, or 6.5%, which is high for such a nonpolar bond. This estimate was used to support an inductive contribution to deuterium IEs on acidity of carboxylic acids.38 An alternative estimate,32 based on the stretching mode alone, can be derived from the above dCH–dCD = 0.5 pm and a @/@d of 0.004e from infrared intensities of methane,156 leading to D = 0.0001 D, two orders of magnitude lower than the 0.0086 D reported.

13 Origin of secondary isotope effects on acidity Above are presented the experimental observations regarding secondary IEs on acidity and basicity, with little discussion or speculation on the causes. The final question, addressed here, is the origin of those IEs. The interpretations proposed below are often reinforced with calculations or with other types of experimental data.

EVIDENCE FROM VIBRATIONAL SPECTROSCOPY

According to Equation (8), the dominant contributor to the IE arises from zero-point energies. There is plenty evidence to support this. An early example was the use of the observed vibrational frequencies of  gas-phase HCOOH and DCOOH and of aqueous HCO 2 and DCO2 to calculate the deuterium IE on the acid dissociation constant of formic acid.157 The zero-point energy contribution was found to be the most important, especially from the isotope-sensitive C–H stretch, whose frequency decreases from 2943 cm1 in HCOOH to 2825 cm1 in HCO 2, although this is not the only contributor, and there is considerable mixing of the various vibrations. The calculated IE of 0.037 is in good agreement with the average of two contemporary experimental values, and it was concluded that there is no need to assume any electronic differences between C–H and C–D bonds. Similarly, the IEs on the acidities of CD3COOH and CT3COOH could be calculated from a force field based on observed vibra158 The IE tional frequencies of CH3COOH and adjustments for CH3CO 2. 41 for CD3COOH agrees well with the experimental value, although the agreement is very sensitive to the choice of adjustments. In support of a vibrational origin for the decreased acidity of CF3CD2OH, the Raman spectrum of aqueous CF3CHDOH shows two C–D stretches at 2217 and 2172 cm1 (assigned to two conformers), whereas the corresponding stretch in CF3CHDO is lower than either, at 2117 cm1.45 The 18O IE on acidity of carboxylic acids was estimated from known vibrational frequencies of carboxylic acids and carboxylate anions.159 The

158

C.L. PERRIN

Table 10 Vibrational frequencies159 of RCOOH(D), RC18O18OH(D), RCO-2, and RC18O2 Mode

(16O) (cm1)

(18O) (cm1)

D (cm1)

C=O C–OH O–H C€ Od Sumb Sumc

1760 1300 3000 1500a 3060 2228

1718 1271 2990 1464a 3051 2218

42 29 10 36 9 10

a

Average of symmetric and asymmetric stretches.  C=O þ  C–OH þ  O–H – 2 CO €  :  C=O þ  C–OD þ  O–D – 2 CO €  :

b c

frequencies of the labeled species were calculated by correcting for the changes in reduced mass. The values are listed in Table 10. They can be converted to the equilibrium constant for proton transfer between unlabeled and doubly 18 O-labeled acids [Equation (29)]. The net difference of 9 cm1 corresponds to a zero-point energy difference of 4.5 cm1 for the two sides of Equation (29), or to a KEIE of 1.022 at 26C, with the di-18O acid weaker. It was recognized that this calculation assumes 12C acids and doubly labeled oxygens, but these simplifications do not matter. Even for 13C-substituted acids the net D is still calculated to be 9 cm1. Also, in a mono-18O-labeled carboxylic acid the proton can be on either of its oxygens, and a calculation for the mixture of two tautomers gives a KEIE of 1.011, or simply half the effect due to double labeling. A similar calculation for RC18O18OD leads to a higher D, also included in Table 10 and corresponding to KEIE = 1.024 for Equation (30). Indeed, it is observed experimentally that the doubly 18O-labeled acids show twice the isotope shifts of the corresponding singly labeled ones, and also that KT increases in D2O.159 These calculations agree with the experimental values 16 for K18 a =Ka of carboxylic acids in Table 8. 18 18  RCCOH þ RC18 O 2 ÐRC O OH þ RCO2

ð29Þ

18 18  RCOOD þ RC18 O 2 ÐRC O OD þ RCO2

ð30Þ

The values in Table 10 allow the 18O IEs on acidity of carboxylic acids to be apportioned between primary and secondary IEs. The largest D is the 42 cm1 between C=16O and C=18O, which represents a contribution to the secondary IE. The total D of 39 cm1 from C–OH and O–H represents a contribution to the primary IE. Although these differences are nearly equal, they imply the surprising result that the secondary IE is slightly larger than the primary.

SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY

159

COMPUTATIONS

According to calculations at the STO-3G level, the C–H bonds are longer in the anions CH3NH, CH3O, and CH3S than in their protonated forms.97 To the extent that the lengthening corresponds to a weaker bond, with a lower stretching force constant, this can account for the greater acidities of gas-phase CD3NH2, CD3OH, and CD3SH, relative to their CH3 isotopologues. Calculations at the 4-31G level give KEIE = 2.4, 2.9, and 1.25 for CD3NH2, CD3OH, 160 in good agreement with the experimental values of 1.9, 2.3, and CD3NHþ 3, and 1.25, which further supports a vibrational origin for the IE. Also, according to 4-31G calculations, the basicity of CD3NH2 is 0.11 kcal mol1 greater than that of CH3NH2, which agrees with the experimental 0.10 kcal mol1 per CD3 group.100 According to further 4-31G calculations, KEIE for the acidity of þ CD3OH, CD3OHþ 2 , HOCD2OH, or CD3NH3 is 2.620, 1.149, 1.682, or 1.214, 161 respectively. The IEs are due to changes in the C–H stretching frequencies upon deprotonation. Moreover, for CD3OH the D anti to the OH contributes 1.430 to KEIE, while each gauche D contributes only 1.357. Molecularmechanics calculations provide further support for a decrease of vibrational frequency for a C–H bond antiperiplanar to a lone pair.162 However, according to MNDO calculations, KEIE for the acidity of CD3NH2, CD3OH, CD3SH, or 163 The first three are in CD3NHþ 3 is 1.71, 2.08, 1.21, or 0.97, respectively. reasonable agreement with the experimental gas-phase values, but the last is inverse and contradictory. Calculations of vibrational zero-point energies at the MP2/6-31G(d,p) level favor protonation of RNHCD3, RNHCD2CH3 and RNHCH2CD3 over their undeuterated isotopologues by 0.12, 0.09, and 0.03 kcal mol1, respectively, independently of whether R is methyl, ethyl, propyl, or butyl.101 These values are about half of the experimental enthalpies. MP2 calculations on acetaldehyde and its enolate anion show that the equilibrium IE on the C–H acidity depends on the orientation of the retained H or D with respect to the carbonyl group.47 In particular, when D is in the molecular D plane (52), KH a =Ka is 1.32, owing to reduction of the C–H out-of-plane bending D frequency as the sp3-hybridized carbon is converted to sp2, but KH a =Ka is only 1.23 for the conformer with D out of plane (53), owing to hyperconjugation, which weakens the C–H (or C–D) bond and decreases the IE. If these gas-phase IEs are recalculated for the enolate complexed with water, the IE that retains the in-plane D is lower by 30%, but the one that moves the out-of-plane D into the plane of the enolate is lower by 50%, because hyperconjugation is reduced by hydrogen bonding of the enolate lone pair. H

HH

H

HD

O

D

O

H

52

53

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The KEIE of 1.24 expressing the greater gas-phase basicity of pyridine-d5 is in good agreement with a value of 1.21 (DG = 0.52 kJ mol1) calculated at the B3LYP/cc-pVTZ level.102 The IE is associated with a weakening and lengthening of the C–N bonds upon protonation and a strengthening and shortening of the Ca–Cb, Ca–H, and Cb–H bonds. These changes in bond lengths are paralleled by changes in electron density in the bonds. There is a net difference in zero-point energies of 46 cm1, favoring Py þ (Py-d5)Hþ, although it is difficult to assign all the vibrational frequencies that are tabulated. The IE must be due to the increased strength of the C–H bonds on protonation, which increases their zero-point energies, and of the C–D to a lesser extent. Another calculation, at the B3LYP/6-311þþG(2df,2p) level, obtained a net zero-point energy difference of 0.120 kcal mol1 favoring (Py-d5)Hþ,105 which is in excellent agreement with the above 0.52 kJ mol1. This corresponds to a KEIE of 1.10 at Teff = 615 K, which is also in good agreement with the experimental KEIE of 1.09. Additional calculations at the B3LYP/6-311þþG(2df,2p) level obtained net zero-point energy differences of 0.042 kcal mol1 favoring (CH3)2COHþ over (CD3)2COHþ and 0.081 kcal mol1 favoring CH3CNHþ over CD3CNHþ.105 These do not agree with the same authors’ experimental differences in proton affinities of 0.19 and 0.34 kcal mol1 (KEIE = 0.84, 0.76). However, the calculations do reproduce qualitatively the inverse IEs here and the normal IE for pyridine-d5. The experimental IEs on the acidities of carboxylic acids and phenols in Table 3 are corroborated by B3LYP computations.32 The IEs originate in isotope-sensitive vibrations whose frequencies and zero-point energies are lowered on deprotonation. For formic acid this is the C–H vibration, in agreement with the spectroscopy. For acetic acid the three C–H distances increase. The increase is greater for the C–H that is in the molecular plane. This is consistent with the result in Table 3 that the IE per deuterium is lower for hydroxyacetic acid than for acetic, because the OH of the former lies in the molecular plane,164 relegating deuterium to a position where it affects the IE to a lesser extent. The computations reproduce the decrease of IE in aliphatic acids as the site of deuteration becomes more distant from the OH, as expected. They also reproduce the constancy of IEs in both phenol and benzoic acid as the site of deuteration moves from ortho to meta to para. However, the calculations substantially overestimate the IEs. The average ratio of calculated IE to experimental is 9. Figure 3 shows a graph of DpKa per D versus the number of bonds between D and O (or the average if there are two distances), along with the calculated DpK per D but scaled down by a factor of 6. A discrepancy is also seen between the calculated and experimental 18O IEs on the acidities of (H18O)2P18O2 and CH3OP18O218OH, although it is only approximately twofold.165 Again the IEs were attributed to changes in

161

0.032

0.032

0.028

0.028

0.024

0.024

0.020

0.020

0.016

0.016

0.012

0.012

0.008

0.008

0.004

0.004

0

2

3

4 n

5

6

ΔpKcalc/6

ΔpKexptl

SECONDARY EQUILIBRIUM ISOTOPE EFFECTS ON ACIDITY

0

Fig. 3 Deuterium IE on acidity of carboxylic acids and phenols versus number of bonds between D and O: (  ) Observed DpK per deuterium. (o) Calculated DpK per deuterium, scaled down sixfold.32 For clarity, the dashed lines connect the averages for each integer n. Reprinted with permission from J Am Chem Soc 2007;129: 4490–7. Copyright 2007 American Chemical Society.

zero-point energies. Of course, the calculations are of gas-phase IEs, whereas solvation affects the experimental IEs that are measured in aqueous solution. Indeed, calculations that included solvent molecules clustered around the phosphate ion substantially improved the agreement with experimental IEs. Nevertheless, the IEs in Table 3 in the less polar aprotic solvents DMSO-d6 and CD3CN, which better resemble the gas phase, are neither larger nor closer to the calculated values.32 The IEs on amine basicity in Table 5 depend on the dihedral angle  between the C–D bond and the nitrogen lone pair, including IEs due to synperiplanar deuterium in 21, 22, and 23. To probe such IEs, beyond the oversimplified cos2 dependence of Equation (28), calculations were performed on methylamine at the B3LYP/6-31G(d,p) level.31 It was found that the C–H bond length is maximum and the stretching frequency is minimum when the dihedral angle between the bond and the nitrogen lone pair is 180, but there is a secondary maximum of bond length and minimum of vibrational frequency at 0. This is consistent with an average IE due to synperiplanar deuterium that is approximately half as large as that of an antiperiplanar deuterium and also with an IE due to gauche deuterium that is weaker than predicted from a cos2 dependence.

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These results are consistent with 4-31G calculations of the IE on the 2 basicity of DCH2CH 2 , for which DE could be fit to 0.070 þ 0.086 cos  – 2 0.058 cos /2, where  is the dihedral angle between the lone pair and the C–D.166 This shows a maximum IE of 0.156 kcal mol1 when the lone pair is antiperiplanar to the C–D ( = 180), a minimum near 90, and a subsidiary maximum of 0.98 kcal mol1 when it is synperiplanar. Surprisingly, the maximum IE and the variation with conformation are larger for DCH2CH 2 than for DCH2CHþ 2. In summary, calculations of vibrational frequencies confirm a crucial role for zero-point energies in secondary IEs on acidity. They are especially important when the C–H bond or C–D bond is antiperiplanar or (to a lesser extent) synperiplanar to a lone pair.

CAUSE OF FREQUENCY CHANGES

With few exceptions, secondary IEs on acidity can be attributed to reductions of vibrational frequencies on deprotonation, as expressed by Equation (9). Because the zero-point energy of a C–H bond is greater than that of C–D (or more generally, the bond to a heavier element than that of a lighter one), reducing the vibrational frequency decreases the zero-point energy and stabilizes the conjugate base for the lighter isotope. This leads to an IE =Kheavier > 1. Klighter a a The remaining question is the cause of the changes in vibrational frequencies on deprotonation. This question is much easier for solvolysis, where hyperconjugation stabilizes a carbocation.166 Hyperconjugation is a stabilizing interaction between a filled C–H bonding orbital and a vacant nonbonding p orbital, as in 54. In resonance theory it corresponds to ! Hþ CH2=CR2. It is much stronger than the interaction H–CH2–CRþ 2 between a lone pair and a vacant antibonding *C–H orbital, as in 55 or 56. This is often called negative hyperconjugation, even if the species is not an anion. It corresponds to H–CH2–X: ! H CH2=Xþ. There are two possibilities for the lone pair on X, an sp3 lone pair on a nitrogen, as in 55, and a pure p lone pair on an oxygen (not an sp3 lone pair), as in 56, where the hybridized  lone pair does not contribute.167,168 Because hyperconjugation removes electron density from a bonding orbital, the C–H force constant and vibrational frequency decrease. Similarly, negative hyperconjugation adds electron density into a C–H antibonding orbital, and again the force constant and the vibrational frequency decrease. The few exceptions above, namely the inverse IEs with CD3CNHþ, PhC(=OHþ)CD3, protonated 2-pentanone-3,3-d2, and acetone-d6, are due to hyperconjugation in the cationic conjugate acids, which are stabilized by H more than by D.

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H + N

O H

H 55

54

56

Calculations on ethyl anion support the role of n–* delocalization, or negative hyperconjugation.166 In support of the lower acidity of tritiated glucose, which was responsible for its faster chromatographic elution at pH 11.7, density-functional-theory calculations obtain a tritium IE on the Ka of (CH3)2CTOH of 1.36.147 For glucose, the calculations indicate that tritiation at any carbon exerts a secondary IE on the pKa of every OH group, which further supports the conclusion that the anionic charge in the conjugate base is shared among all the oxygens. The experimental IEs on the acidities of carboxylic acids and phenols in Table 3 are corroborated by B3LYP computations.32 The IEs originate in isotope-sensitive vibrations whose frequencies and zero-point energies are lowered on deprotonation. In the simplest case, formate, the key vibration can be recognized as the C–H stretch, which is weakened by n–* delocalization of the oxygen lone pairs (57). For other acids the key isotopesensitive vibrations are less readily identifiable. Prime candidates are the C–H stretching modes, but bending modes also contribute. For acetic and pivalic acids, the average of the three or nine C–H stretching frequencies decreases from 3085 to 3007 cm1 in acetate anion or from 3105 to 3056 cm1 in pivalate anion. It is difficult to associate these changes with delocalization or negative hyperconjugation, especially in view of the overestimates in Fig. 3. For the aromatic acids delocalization cannot account for the near constancy of IEs from ortho, meta, and para deuteriums, but the observed IEs are consistent with calculated vibrational frequencies, which respond to electron densities in ways that do not lend themselves to simple pictures of delocalization. δ –O

H 57

δ –O

The IEs on amine basicity are also due to changes in vibrational frequencies, not only computationally but also experimentally. Gas-phase IEs of 0.10 kcal mol1 per CD3 group on basicities of methylamine, dimethylamine, and trimethylamine can be reproduced by ab initio force constants for C–H stretching, which increase on N-protonation.100 Infrared spectra of amines show characteristic bands (called ‘‘Bohlmann bands’’) in the 2700–2800 cm1 region, lower than the 2900 cm1 of a typical C–H stretch.169,170 Upon N-protonation these bands revert to a typical, higher frequency. Therefore the zero-point energy of the C–H increases on

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protonation, but the increase is less for C–D. Indeed, a D of 100 cm1 would produce a DpKa of 0.03, comparable to the IEs in Table 5. This good agreement supports the involvement of stretching modes, rather than the bending modes proposed for the kinetic IE in methylation of N,N-dimethylaniline-d6.171 The Bohlmann bands are associated with a C–H bond antiperiplanar to the nitrogen lone pair.172 The B3LYP/6-31G(d,p) calculations yield a minimum stretching frequency and maximum C–H bond length when the dihedral angle  between the bond and the nitrogen lone pair is 180, along with a secondary minimum of vibrational frequency at 0.31 The bond lengthening and the frequency reduction are due to delocalization of the lone pair into the C–H antibonding orbital, as in 55. The maximum delocalization is when  is 180, and the minimum is near 90, when the lone pair is orthogonal to the C–H. The variation of the experimental IEs with dihedral angle also shows that there is a stereochemical dependence of the IE, which is maximum when the C–D bond is antiperiplanar to the nitrogen lone pair and about half as large when synperiplanar. This behavior thus supports the interpretation of IEs in terms of zero-point energies that are reduced by negative hyperconjugation when the C–H or C–D is antiperiplanar to the nitrogen lone pair. This also agrees qualitatively with the absence of distinctive Bohlmann bands in those amines where the nitrogen lone pair is syn to the C–H.173,174 Also, the lower IE of 0.0434 for PhN(CH3)2, as compared to 0.058 for (CH3)2NH, is consistent with negative hyperconjugation, which is less stabilizing when the lone pair is also delocalized into the aromatic ring.

NECESSITY FOR AN INDUCTIVE EFFECT?

Calculations of vibrational frequencies are never accurate enough to verify that the secondary IE arises entirely from zero-point energies. Therefore although they do confirm a role for zero-point energies, which was never at issue, they cannot exclude the possibility of an additional inductive effect arising from changes of the average electron distribution in an anharmonic potential. The question then is whether it is necessary to invoke anharmonicity to account for a part of these secondary IEs. The calculated IEs ignore anharmonicity. Therefore, the ability of these calculations to reflect IEs discredits an inductive origin that requires anharmonicity. The calculations on carboxylic acids and phenols do overestimate the IEs, as shown in Fig. 3, but only an underestimate would be support for an inductive effect. The overestimation is likely to be due, at least in part, to the neglect of solvation, which stabilizes the anion and reduces the n–* delocalization that is responsible for the changes of vibrational frequencies. A simple inductive effect, wherein deuterium is more electron-donating than protium, cannot be responsible. If that were the case, deuterium would not only increase basicity but also accelerate solvolysis. Instead the inductive effect

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is described as one that arises as an increased electron density at a carbon bearing D, owing to anharmonicity and a shorter average C–D bond length. In solvolysis that inductive effect is overwhelmed by the greater ability for hyperconjugation with C–H. Negative hyperconjugation is weaker, so that perhaps the inductive effect can contribute to the IE on basicity. The dilemma is that negative hyperconjugation and inductive effect both increase the IE on basicity, so that it is difficult to separate their relative importance. Intriguing evidence for an inductive effect comes from computations that treat nuclei quantum mechanically.11 This takes account of anharmonicity and leads to bond lengths and atomic charges that vary with isotopic substitution. Whether those charge variations are large enough to account for the IEs on acidity, independently of changes of vibrational frequencies, is not yet clear. Evidence against an inductive contribution comes from experimental IEs on amine basicity. According to Equation (28), there is no angle-independent term. This is the term that would arise from an electrostatic interaction between a positive charge on the N and a C–H or C–D bond dipole.3 Although Equation (28) is imperfect, and there are smaller IEs from synperiplanar C–D, we conclude that an inductive effect is too small to contribute to the observed IE. Moreover, the inductive contribution of a b deuterium to the IE on amine basicity was estimated.31 The inductive effect on pK due to an sp2–sp3 C–C bond, with a dipole moment of 0.35 D, as in propene, can be assigned as 0.95, the DpK between allylamine and methylamine. Above, in connection with the structural question of the extent to which IEs affect dipole moments, dCH–dCD is 0.5 pm and @/@d is 0.004e. These combine to a DpK on deuteration of 0.001, which is much smaller than the measured IEs in Table 5. An inductive contribution does exist, but it is negligible. Another estimate seemed to support an inductive contribution to deuterium IEs on the acidity of carboxylic acids.37 This IE on acidity of some carboxylic acids was attributed to an inductive effect arising from the electrostatic interaction of the C–H or C–D dipole with the negative charge of the carboxylate, as expressed in Equation (31). The derivative @pK/@ was estimated from the effect of a C–Cl dipole on acidity, using the difference in pKas of trichloroacetic acid (0.63) and acetic acid (4.75) and the difference between the dipole moments of t-butyl chloride (2.13 D) and isobutane (–0.13 D). Next D was estimated as 0.0086 D, the difference between the dipole moments of (CH3)3CD and (CH3)3CH. Thus DpK was estimated as 0.005 per D, in excellent agreement with the observed 0.014 for acetic-d3 acid. Moreover, the IE of 0.002 per D in pivalic-d9 acid is consistent with a 2.8-fold falloff factor for inductive effects. Yet those estimates depend crucially on the difference between the dipole moments of isobutane and isobutane-d, which is unusually large, amounting to 6.5% of either’s total dipole moment.

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The alternative estimate of this D above, based on a dCH–dCD of 0.5 pm and a @/@d of 0.004e, is 0.0001 D.32 Application to Equation (31) then leads to a revised DpK per deuterium of only 0.00006, which is two orders of magnitude lower than either the earlier estimate or the observed IE. Therefore the contribution to the IE from an inductive effect dependent upon anharmonicity is again found to be negligible.

DpK ¼

DpK DpK=DnCl D D ¼ D=DnCl D

ð31Þ

Finally, an inductive effect arising from the difference between the dipole moments of C–H and C–D bonds ought to be proportional to the number of C–D bonds. Instead, with trimethylamines the increase in basicity, per deuterium, increases with the number of deuteriums.33 This nonlinearity in the basicities is strong evidence against an IE of inductive origin. It arises from zero-point energies because the IE depends on the dihedral angle between the lone pair and the C–D bond, and because there is a preference for conformations with C–H antiperiplanar to the lone pair and C–D gauche. One remaining puzzle is the decreasing DpKa per D from methylamine to dimethylamine to trimethylamine in solution. Such behavior was ascribed to an inductive effect,51,53 but inductive effects ought to be linear in the number of deuteriums. It may be that conformational restraints due to additional methyls increase the negative hyperconjugation. Computations might be informative. Nearly all the evidence adduced for an inductive origin for all the secondary IEs on acidity is equally consistent with an origin in zero-point energies, analyzed according to Equation (9). The damping of the IE falloff factor in through a CH2, as in CD3CH2COOH, or p the 2.8-fold p pivalic-d9 acid would be due to a smaller k(A) – k(HA) when there is an additional carbon. The complementary effects of CD2 on the acidity of 40 PhCH2COOH p and the p *basicity of PhCH2NH2 arise because both IEs have the same 1/  – 1/  . The principal evidence that a strongly electrondemanding environment decreases KEIE comes from comparison of anilines with phenols and of methylamine or dimethylamine with formic acid,51 but the larger IEs in the latter of each comparison are simply due to the greater electron delocalization from an oxyanion than from an amino group, so that p p k(A) – k(HA) is larger. In summary, Equation (9) can account for secondary IEs on acidity, in terms of changes of vibrational frequencies and zero-point energies. There is no need to invoke anharmonicity or inductive effects.

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Acknowledgments This article is dedicated to Jerry Kresge, one of the pioneers in isotope effects and a leader in the field of physical organic chemistry. The writing of this chapter was supported by NSF Grant CHE07-42801.

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122. Vasquez TE, Jr., Bergset JM, Fierman MB, Nelson A, Roth J, Khan SI, et al. J Am Chem Soc 2002;124:2931–8. 123. Ruszczycky MW, Anderson VE. J Mol Struct (THEOCHEM) 2009;895:107–115. 124. Filer CN. J Label Compd Radiopharm 1999;42:169–97. 125. Ishida T, Fujii, Y. In: Kohen A, Limbach HH, editors. Isotope effects in chemistry and biology. Boca Raton, FL: CRC Press; 2005, Chapter 2. pp. 41–87. 126. Valleix A, Carrat S, Caussignac C, Le´once E, Tchapla A. J Chromatogr A 2006;1116:109–26. 127. Wade D. Chem-Biol Interact 1999;117:191–217. 128. Tanaka N, Thornton ER. J Am Chem Soc 1977;99:7300–7. 129. Turowski M, Yamakawa N, Meller J, Kimata K, Ikegami T, Hosoya K, et al. J Am Chem Soc 2003;125:13836–49. 130. Kimata K, Hosoya K, Araki T, Tanaka N. Anal Chem 1997;69:2610–2. 131. Schug KA, Maier NM, Lindner W. J Mass Spectrom 2006;41:157–61. 132. Piez KA, Eagle H. J Am Chem Soc 1956;78:5284–7. 133. Tanaka N, Yamaguchi A, Araki M. J Am Chem Soc 1985;107:7781–2. 134. Tanaka N, Hosoya K, Nomura K, Yoshimura T, Ohki T, Yamaoka R, et al. Nature 1989;341:727–8. 135. Klein PD, Szczepanik PA. Anal Chem 1967;39:1276–81. 136. Lockley WJS. J Chromatogr 1989;483:413–8. 137. Hattox SE, McCloskey JA. Anal Chem 1974;46:1378–83. 138. De Ridder JJ, Van Hal HJM. J Chromatogr 1976;121:96–9. 139. Filer CN, Fazio F, Ahern DG. J Org Chem 1981;46:3344–6. 140. Yeung PKF, Hubbard JW, Baker BW, Looker MR, Midha KK. J Chromatogr 1984;303:412–6. 141. Heys JR. J Chromatogr 1987;407:37–47. 142. Masters CF, Markey SP, Mefford IN, Duncan MW. Anal Chem 1988;60:2131–4. 143. Kudelin BK, Gavrilina LV, Kaminski, Yu, L. J Chromatogr 1993;636:243–7. 144. Kaspersen FM, Funke CW, Sperling EMG, van Rooy FAM, Wagenaars GN. J Chem Soc Perkin Trans 2 1986:585–91. 145. Benchekroun Y, Dautraix S, De´sage M, Brazier JL. J Chromatogr B 1997;688:245–54. 146. Rohrer JS, Olechno JD. Anal Chem 1992;64:914–6. 147. Lewis BE, Schramm VL. J Am Chem Soc 2003;125:7872–7. 148. Bell RP, Coop IE. Trans Faraday Soc 1938;34:1209–14. 149. Bartell LS, Higginbotham HK. J Chem Phys 1965;42:851–6. 150. Bartell LS, Fitzwater S, Hehre WJ. J Chem Phys 1975;63:3042–5. 151. Limbach HH, Denisov GS, Golubev NS. In: Kohen A, Limbach HH, editors. Isotope effects in chemistry and biology. Boca Raton, FL: CRC Press; 2005, Chapter 7. pp. 193–230. 152. Scher C, Ravid B, Halevi EA. J Phys Chem 1982;86:654–8. 153. Halevi EA, Haran EN, Ravid B. Chem Phys Lett 1967;1:475–6. 154. Muenter JS, Laurie VW. J Chem Phys 1966;45:855–8. 155. Lide DR, Jr. J Chem Phys 1960;33:1519–22. 156. Oliveira AE, Guadagnini PH, Custo´dio R, Bruns RE. J Phys Chem A 1998;102:4615–22. 157. Bell RP, Crooks JE. Trans Faraday Soc 1962;58:1409–11. 158. Bron J. J Chem Soc Faraday Trans 2, 1975;71:1772–6. 159. Perrin CL, Thoburn JD. J Am Chem Soc 1989;111:8010–12. 160. DeFrees DJ, Hassner DZ, Hehre WJ, Peter EA, Wolfsberg M. J Am Chem Soc 1978;100:641–3. 161. Williams IH. J Mol Struct (THEOCHEM) 1983;14:105–17.

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Molecular dynamics simulations and mechanism of organic reactions: non-TST behaviors HIROSHI YAMATAKA Department of Chemistry, College of Science and Research Center for Future Molecules, Rikkyo University, Tokyo, Japan 1 Introduction 174 2 Nonstatistical product distribution 176 MD analyses by using model PES 176 [1,3] sigmatropic migration of bicyclo[3.2.0]hept-2-ene 177 Reaction of diaza-[2.2.1]bicycloheptane to [2.1.0]bicyclopentane Degenerate rearrangement of bicyclo[3.1.0]hex-2-ene 180 Chemistry of trimethylene 181 Vinylcyclopropane to cyclopentene rearrangement 184 Dissociation of acetone radical cation 186 The wolff rearrangement 187 3 Avoided intermediate on IRC 189 SN2 reaction 189 [3,3]Sigmatropy 189 4 Non-IRC reaction pathway 190 Photoisomerization of cis-stilbene 191 Ionic fragmentation reaction 191 Cyclopropyl radical ring-opening 192 Ionic molecular rearrangement 193 Ene reaction 196 Thermal denitrogenation 198 Unimolecular dissociation 199 SN2 reaction 200 5 Path bifurcation 200 Bifurcation on symmetrical PES 201 Dynamic bifurcation 204 Cycloaddition 206 Beckmann rearrangement/fragmentation 207 6 Reaction time course and product and energy distributions 209 SN2 reactions 209 SN2 reactions in water 210 Other reactions 211 7 Nonstatistical barrier recrossing 211 SN2 reactions 212 Vinilydene to acetylene rearrangement 213 Cycloaddition of cyclopentadiene and ketenes 214

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8 QM/MM-MD 214 9 Full quantum MD simulation in water SN2 reaction in water 215 10 Summary and outlook 218 Acknowledgments 218 References 218

1

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Introduction

History of physical organic chemistry is essentially the history of new ideas, philosophies, and concepts in organic chemistry. New instrumentations have played an essential role in the mechanistic study. Organic reaction theory and concept of structure–reactivity relationship were obtained through kinetic measurements, whose precision depended on the development of instrument. Development of NMR technique resulted in evolution of carbocation chemistry. Picosecond and femtosecond spectroscopy allowed us to elucidate kinetic behavior of unstable intermediates and even of transition states (TSs) of chemical reactions. Back in the mid-1900s, mechanistic organic chemistry, strengthened by Robinson–Ingold’s electronic theory and frontier orbital theory, enjoyed its golden age and clarified mechanisms of many organic reactions. Appreciation of organic reaction theories and reaction mechanisms allowed organic chemists to develop new synthetic reactions. It is no exaggeration to say that recent progress in many fields of chemistry such as synthetic chemistry, supramolecular chemistry, biochemistry, and nanochemistry has been realized on the basis of the knowledge and the way of thinking that arose from mechanistic study in the last century. On the other hand, mechanistic study itself has reached a stationary stage because of the maturity of experimental methodology. This brought about a recent situation that provocative and controversial issues were seldom discussed and that novel concept ceased to emerge. In these 10 years, however, development of novel and reliable simulation methods and comprehension of the importance of reaction dynamics gained from simulation studies started to produce novel results, which likely bring about a new stage or paradigm in the field of mechanistic organic reactions. The computational and experimental studies of reaction mechanisms are complementary to each other. Experiment provides a picture of the real world but hardly the whole picture even for a simple reaction. Computation gives us detailed information about reaction mechanisms, but the results ought to rely on the assumptions involved. Interplay of the two is important; reliability of the calculated results is assured by comparing with experiment, and interpretation of experimentally observed facts is strengthened by computations.

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Further, computation provides insights into reaction mechanisms that can never be reached by experiment. Huge amount of studies by means of molecular orbital (MO) calculations have been reported in the literature, which calculate the structures of reactants, products, reactive intermediates, and TSs of possible reaction pathways, as well as minimum energy paths from the TSs to both the reactant and product sides on the potential energy surface (PES). The information thus obtained, together with experimental findings, has been used to deduce reaction mechanisms. The combined use of experiment and MO calculations has become a common method for physical organic chemists. However, it should be noted that the calculated structures and energies are at 0 K and that therefore the information obtained from MO calculations may not directly be related to experimental observation at a finite temperature. Ultimate goal of mechanistic studies of chemical reactions is to see how atoms in reacting molecules behave at the molecular level and to understand why they do so. Computational study toward this goal should take the effect of temperature into account, since chemical reactions only proceed at a finite temperature. Molecular dynamics (MD) simulations can give information on the dynamic nature of a chemical event and the results are, in principle, comparable with the experiments. In a pioneer study reported in 1985, Carpenter has demonstrated a possible role of dynamics in chemical reactions.1 He showed by using a model PES that when two symmetrical products were formed from a common intermediate through isoenergetic barriers, the two products were obtained in unequal amounts depending on how the common intermediate was formed. This was a new interpretation of an old idea, a memory effect. Investigation of how chemical reaction takes place at the molecular level needs methods that describe bond-breaking/formation processes properly. It thus requires an ab initio MD method, in which the forces are derived from quantum mechanics while the nuclei are propagated via classical mechanics subject to quantum-derived forces. The methodology of the ab initio MD simulation is still in the stage of development and its application has become active only in these 10 years. Nevertheless, already during the last decade, studies by means of this new computational method have produced important findings, which require serious modification of traditional ideas regarding chemical reactivity and stimulate experimental study aiming at confirming and establishing new concepts. The ‘‘dynamics effect’’ emerged from trajectory calculations has many phases and can be argued from many points of view. Although these phases and viewpoints are not independent but strongly overlapped to each other, I will categorize them in this chapter as listed in the index and show the current status of the work in these categories.

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Nonstatistical product distribution

MD ANALYSES BY USING MODEL PES

When an organic chemist tries to elucidate the mechanism of a reaction, what is to be done first is to analyze the products of the reaction. If more than one product is formed, the product ratio is determined. The effects of substituent on the product ratio and on the rate of the reaction are the most basic information for a physical organic chemist to discuss the reaction mechanism. Suppose that there is a reaction as shown in Chart 1, in which enantiomeric reactants A and A0 yield enantiomeric products B and B0 through a common intermediate I. Regardless of whether the reaction starts from A or A0 or from a mixture of A and A0 , the product ratio B versus B0 should be unity, since they are enantiomeric. Such ordinary convention was challenged by Carpenter, inspired by critical inspection of experimental results on some unimolecular diradical-type rearrangement reactions.1 Carpenter constructed a model mathematical surface to simulate the reaction in Chart 1 and carried out dynamics simulations starting from reactant A. Initial direction of the trajectories and initial kinetic energy were varied by small increments. The product ratio was quite different from what is expected from transition state theory (TST): 89% B0 and 11% B rather than 50% B and 50% B0 . The results were interpreted that trajectories need to approach I on paths close to the diagonal line connecting A and B0 in order to climb up the barrier effectively, and that those trajectories that successfully reach the intermediate region keep going on to B0 because of conservation of momentum. It was thus suggested that for a reaction, whose reactive intermediates are connected to more than two product regions of similar energies, dynamics effect may control the product ratio that is unable to explain on the basis of a statistical TST. It was commented that ‘‘In most reactions of complex molecules the intermediate has many more degrees of freedom and so the tendency will be to spend more time near the intermediate potential minimum and, thereby, to lose the directional information in the trajectory’’, but the model simulation certainly displays a possible role of dynamics effect on chemical reaction.

′

Chart 1

′

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[1,3] SIGMATROPIC MIGRATION OF BICYCLO[3.2.0]HEPT-2-ENE

In the mechanistic study of borderline reactions, situation happens, in which stereochemical outcome is the key to decide concerted versus stepwise mechanistic possibilities. Concerted mechanism leads to a product of single stereochemistry, whereas stepwise mechanism would give a mixture of products of different stereochemistry. If the possible intermediate is symmetric with respect to the bond(s) to be formed or broken on going to the products, equal amount of two products are expected to form. One such example is the [1,3] sigmatropic migration of bicyclo[3.2.0]hept-2-ene (1) to norbornene (2) shown in Equation (1). Mechanistic argument whether the reaction proceeds through biradical intermediate has been made on the basis of product stereochemistry. It was determined experimentally that the reaction of mono-deuterated substrate 1a at 307C gave 2a and 3a in the ratio of >95% and 1 ps) biradical. The fate of these long trajectories was not followed, but it is likely that product formation would occur with equal probability of the inversion and retention stereochemistry, since the long lifetime of the intermediate would allow a redistribution of internal energy and hence intrinsic ‘‘memory’’ of the stereochemistry would be lost. It was claimed that, due to the principle of microscopic reversibility, the trajectory results would allow one to draw conclusions about the real reaction. The calculations showed an apparent preference for the inversion of configuration in the reaction, for which the PES had a very distinct local minimum corresponding to a biradical. It was suggested that an experimental observation of a preference for inversion of configuration at the migrating carbon should not be taken as definitive evidence against a biradical mechanism. The dynamics effect may make mechanistic discussion by means of product analyses less straightforward. Direct trajectory calculations for the isomerization of bicyclo[3.2.0]hept-2ene (1) and bicyclo[2.2.1]hept-2-ene (2 and 3) were further carried out more extensively at AM1 and PM3.5 Simulations were started for a quasiclassical canonical ensemble at T = 300C in the vicinity of TSs between the biradical intermediate and 2 (3). The calculated trajectories could be grouped into two types: short trajectory, which gave 1 in a single pass within 250–350 fs, and long trajectory, which stayed in the biradical region for some time before giving the stable species 1. The inversion/retention ratio in the ring closure to 1 should be statistical for long trajectory (slow closure with more lifetime as biradical), whereas it is unequal and thus nonstatistical for short trajectory (rapid closure). In other words, the inversion exit channel is much more strongly coupled to the entrance than is the retention exit channel in the biradical intermediate, despite the degeneracy that ensures identical geometries and potential energies for the two transition structures leading from biradical to compound 1. As a result, the overall preferred stereochemical outcome was inversion, which is consistent with the experimental observations.2,3 In a language of statistical kinetics, the dynamics behavior observed in this study appears to imply concurrent concerted and stepwise pathways, which in fact arises from a dynamics effect on a stepwise PES. It was claimed that bimodal lifetime distributions as was observed in this system could be common for other reactions with reactive intermediates.

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REACTION OF DIAZA-[2.2.1]BICYCLOHEPTANE TO [2.1.0]BICYCLOPENTANE

The sigmatropic isomerization of 1 and 2 þ 3 was considered to proceed through biradical intermediate [Equation (1)], whose lifetime had bimodal distribution.5 The short-lived component of such a distribution arises from direct reactive trajectories that do not randomize the internal energy of the intermediate prior to product formation. These trajectories lead to product with inversion of configuration preferentially. The longer-lived component arises from trajectories that does not form products on the first pass through the intermediate region and then become trapped in that region for some time, before exiting to products. These trajectories are expected to be energetically randomized before going on to the products. The phenomenon of such bimodal lifetime distribution proposed for reaction 1 on the basis of direct quasiclassical trajectory calculations were tested experimentally with the reaction of diaza-[2.2.1]bicycloheptane to [2.1.0]bicyclopentane [Equation (2)].6–8 Experimental study on reaction 2 showed that the exo isomer 5x is formed favorably over the endo isomer 5n by about 3:1 in the gas phase. One explanation for the preferential formation of 5x invokes a competitive concerted and stepwise mechanism; the concerted pathway directly from 4 to 5 gives 5x with the inversion of configuration at the carbon from which N2 is departing, whereas the stepwise pathway goes through the radical intermediate and leads to both 5x and 5n in equal amount. Alternatively, the product stereochemistry can be rationalized by dynamic matching between the entrance channel to the cyclopentane-1,3-diyl radical intermediate and the exit channel to bicyclo[2.1.0]pentane as was assumed for reaction 2.

(2)

Pressure effect on the product distribution in supercritical media would resolve the problem. If the reaction proceeds via the competitive concerted/ stepwise mechanism, the reaction under a higher pressure is expected to give more exo isomer because the activation volume is considered to be smaller for concerted process than the stepwise one and hence more concerted reaction is expected under a higher pressure. If, on the other hand, bimodal lifetime distribution of trajectories is the origin of the stereoselection, the product ratio is expected to approach to unity under high-pressure conditions, since energy randomization is more effective under a high pressure. The experimental results were clear-cut. The reaction under supercritical propane gave the exo/endo ratio decreasing from 5 to 2 with increasing

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pressure from 1 to 200 bar. Thus, the experimentally observed product stereoselectivity in reaction 2 was best explained by dynamics effect.

DEGENERATE REARRANGEMENT OF BICYCLO[3.1.0]HEX-2-ENE

Degenerate rearrangement of bicyclo[3.1.0]hex-2-ene (Chart 2) has a PES, in which four degenerate products are separated through four degenerate TSs with the common energy plateau on the surface.9 Here, four compounds are identical except for the position of deuterium. The rearrangement from 4-exo isomer (6x) is expected to afford 4-endo (6n), 6-exo (7x), and 6-endo (7n) isomers in equal amount if the reaction follows statistical reaction theory (TST). Thus, this reaction provides a situation previously presented by Carpenter to predict nonstatistical product distribution due to dynamics effect.1 The CASPT2(4,4)/6-31G*//CASSCF(4,4)/6-31G* calculations revealed that there are four degenerated TSs, which is 43.0 kcal mol1 higher than 6 and 7 in electronic energy. The biradical intermediate is only 0.2 kcal mol1 lower in energy than the TSs. Trajectory simulations were carried out on an AM1-SRP (specific reaction parameters) surface. The AM1-SRP has some fitted parameters that differ from the AM1 parameter set in order to reproduce the results at the above level of theory. Quasiclassical trajectory calculations were started at the TS that connects 6x and the intermediate at 498 and 528 K. Initial conditions were determined by using the TS normal-mode sampling procedure, which generates a set of initial coordinates and momenta that approximate a quantum mechanical Boltzmann distribution on the TS.

Chart 2

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The trajectories yielded 6n, 7x, and 7n as products. The product ratio determined for 4000 trajectories was not equal as expected from statistical theories but was 47:38:15 for 6n, 7x, and 7n at both temperatures of 498 and 528 K. The ratio was in excellent agreement with experimental value, 48:36:16. The relative yields were, however, time-dependent, in that 7x started to form quickly after 50 fs, the formation of 6n caught up soon in 100 fs, and 7n was formed much slowly. It appeared that many trajectories could be understood in terms of straight paths from the entrance to the various exit channels. These trajectories traversed the biradical intermediate region much faster than energy could be redistributed to other vibrational modes. Some trajectories entering the plateau from the TS moved toward the high-energy region between 7x and 6n and then led to exit channels for 7x and 6n. In contrast, trajectories that moved toward the high-energy region between 6n and 7n tended to lose initial momentum and led to one of the exit channels. It was interesting to find that the branching ratio depends on the elapsed time; trajectories were more selective when they reached product region faster. Thus, the fate of the trajectories is primarily determined by dynamics effect, or momentum, and the branching ratio depends on the shape of the surface.

CHEMISTRY OF TRIMETHYLENE

Trimethylene is an extremely reactive intermediate for isomerization of cyclopropane to propene [Equation (3)]. The lifetime of trimethylene was measured by Zewail and coworkers by molecular beam experiment as 120  20 fs,10 which was reproduced by variational Rice–Rampsperger–Kassel–Marcus (RRKM) theory,11 and by direct dynamics simulations.12 The dynamics simulations carried out on the AM1-SRP surface with the efficient microcanonical sampling or quasiclassical normal-mode sampling method revealed that the decay process exhibited double exponential decay and thus nonstatistical for low-energy simulations, which arose from incomplete intramolecular vibrational energy redistribution (IVR). The product ratio (cyclopropane/propene) was reported to decrease with increasing energy from 90/10 to 50/50 for 54.6 and 164 kcal mol1. (3) Ab initio MRCI calculations showed that the barrier from trimethylene to propene is 7.9 kcal mol1 higher than that from trimethylene to cyclopropane.11 Thus, cyclopropane stereomutation may occur through trimethylene as an intermediate (Chart 3). Trimethylene biradical may cyclize by double rotation of the two C–C bonds in conrotatory or disrotatory fashion or successive single rotation. The calculations showed that the PES at the

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Chart 3

trimethylene intermediate region is nearly flat with conrotatory double rotation being favored over single rotation and disrotation by about 1.5 and 1.0 kcal mol1, respectively. Trajectory calculations were carried out on the AM1-SRP surface, which is similar to the MRCI surface, with barriers of 0.4, 2.8, and 2.0 kcal mol1 for conrotation, disrotation, and single rotation TSs, respectively.13,14 Trajectories for fixed energy ensembles starting at the conrotatory barrier with quasiclassical normal-mode sampling revealed strong mode selectivity, in that the stereochemical outcome of the product strongly depends on the initial conditions. Thus, when all excess energy above the ZPE was given in the conrotatory reaction coordinate, product via conrotation was formed exclusively. On the other hand, when most of the excess energy was injected to the lowest orthogonal mode (disrotation), both single rotation and disrotation trajectories increased and the conrotatory trajectories became minor ones. Furthermore, the stereochemical outcome varied strongly with the ratio of kinetic to potential energy in the initial excess energy injected to the disrotational mode. The overall double/single rotation ratio from Boltzmann sampling was computed as 2.9–3.5, which is well above the value of 1.5 predicted from TST. The lifetime distribution was calculated from the ratio of the number of trajectories that had not formed product (N(t)) and the total number of trajectories (N0). Counting (N(t))/(N0) at a series of time intervals gave timedependent decay plots. The plots of (N(t))/(N0) versus time gave two separated decay plots, one for double rotation and the other for single rotation, showing the existence of short-lived and long-lived trajectories. The decay time constants were derived from straight-line part of the decay plots for the double and single rotation trajectories:  = 130 and 430 fs for double and single rotation, respectively. The calculated time constant ratio, 3.3, was essentially the same as the number calculated from the product ratio. The most double rotation trajectories underwent a set of 180 rotations and cyclized

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immediately. In contrast, the common feature of the long-lived trajectories was a mismatch of torsional phases, which appeared to prolong the trajectory. The trajectory calculations reported here were nonstatistical, indicating that both concerted (short-lived) and nonconcerted (long-lived) behavior could occur on the PES for the concerted/stepwise mechanistic borderline reaction. Trajectory calculations for cyclopropane stereomutation were further carried out on analytical PES built up by fitting parameters for three important internal coordinates, C–C–C angle and two terminal torsions, to reproduce CASPT2N/6-31G* energy.15 The MD analysis for trimethylene-1,2-d2 and trimethylene-1,3-d2 began by generation of quasiclassical canonical ensembles at 400C in the vicinities of conrotation, disrotation, and monorotation stationary points. A total of 12,000 trajectories were examined. The ratio of double to single rotations for stereomutation of cyclopropane-1,2-d2 at 400C was calculated to be 4.73  0.11. This ratio was clearly different from that deduced by TST analysis as mentioned above. It was claimed that this high value was due to dynamic matching phenomenon,4 in which trimethylene formed by distortion tends to follow direct trajectories across the surface and to exit (reclose) by distortion, despite the fact that distortion barrier is higher in energy. The lifetime distribution was found to be around 140 fs, which was in agreement with the value derived from direct dynamics on a semi-empirical surface.13,14 The reaction of trimethylene biradical was successfully treated by means of dynamics simulations by two groups with different PESs as described above.11–15 The success led one of the groups to extend the study to analyze the collisional and frictional effects in the trimethylene decomposition in an argon bath.16 A mixed QM/MM direct dynamics trajectory method was used with argon as buffer medium. Trimethylene intramolecular potential was treated by AM1-SRP fitted to CASSCF as before, and intermolecular forces were determined from Lennard-Jones 12-6 potential energy functions. Trajectories were initiated by generating initial conditions with the efficient microcanonical sampling or quasiclassical normal-mode sampling procedures at 54.6 or 146.0 kcal mol1 of vibrational energy for trimethylene. Trimethylene was then placed in the center of a box, with periodic boundary conditions, and surrounded by an argon bath with an equilibrium temperature and density. Initially, trimethylene was in a nonequilibrium state with respect to the bath, since its coordinates and momenta were held fixed while the bath was equilibrated, and the trajectories were propagated until either cyclopropane or propene was formed. Cyclopropane versus propene branching ratio was analyzed under isolate conditions in the gas phase and under the argon environment with different reduced densities (*). At a low density (* = 0.5), the branching ratio was nearly constant at 0.8–0.85, for the two initial sampling methods, with various bath temperature regions (100–1000 K) for the lower energy trajectories (54.6 kcal mol1). These numbers were similar to those (0.85–0.90) obtained

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by trajectories under isolated conditions in the gas phase. The barrier recrossing, estimated from the comparison of the cyclopropane:propene branching ratio in the first barrier crossing and in the final products, was not observed in these trajectories. Thus, the low-density trajectories showed basically similar features to those in the gas phase. The branching ratio, however, was found to strongly depend on the density. It decreased from 0.82 to 0.90 at * = 0.26 to 0.01–0.02 at * = 3.06 with the initial energy of 54.6 kcal mol1. With the higher initial energy of 146.4 kcal mol1, it changed from 0.50–0.56 at * = 0.26 to 0.01–0.03 at * = 3.06. Thus, the ring-closure channel was nearly closed under high-density conditions. The origin of the dramatic effect of the argon density on the product ratio was not very clear, but might be due to a frictional effect that retards cyclization more than H-transfer that leads to the formation of propene. With the language of physical organic chemistry, a molecule with a larger internal energy at a higher temperature may overcome a high-energy barrier. The barrier to propene is higher than that to cyclopropane, and therefore more propene formation at higher temperature is acceptable, but the observed nearly exclusive formation violates the reactivity–selectivity principle, which requires less selective product distribution at a higher temperature.

VINYLCYCLOPROPANE TO CYCLOPENTENE REARRANGEMENT

Stereochemical product distributions of [1,3] sigmatropic rearrangement of vinylcyclopropane (VCP) to cyclopentene (CP) [Equation (4)] were calculated with quasiclassical trajectory simulations on AM1-SRP PES parameterized to fit ab initio (MRCI) calculations.17–19 In Equation (4), the reaction of deuterium-labeled compound is illustrated to show the reaction stereochemistry. In the [1,3] sigmatropic rearrangement, four products can be formed from the combination of stereochemistry at the migrating methylene group (inversion (i) vs. retention (r)) and at the allyl group (suprafacial (s) vs. antarafacial (a)). Experimentally, the reaction was shown to give product distribution of si-9:sr-9:ar-9:ai-9 = 40:23:13:24.20 The ratio of Woodward–Hoffmann allows (si-9 þ ar-9) to forbidden (sr-9 þ ai-9) products was nearly 1:1. Argument had been whether the reaction proceeds via a biradical intermediate or a set of competing direct reactions.

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Chart 4

Potential energy calculations at B3LYP/6-31G* and CASSCF(4,4)/6-31G* indicated that there was no well-defined local minimum in the biradical region, and a broad flat region had a TS (TS1, Chart 4), whose IRC led to si-9. The TS was the only TS of [1,3] sigmatropy, and there were two other local TSs (TS2 and TS3) within a narrow range of energy of less than 2 kcal mol1, which were not connected to products.21–23 If the TS1 connected to si-9 gives other three products, TST cannot be used to predict product ratio. The stereochemical product distribution of the VCP rearrangement to CP was calculated based on quasiclassical trajectories (VENUS-MOPAC) run on a modified AM1 PES parameterized to reproduce ab inito energies (AM1SRP). Trajectories were initialized at TS1, TS2, and TS3 with quasiclassical TS sampling, in which initial coordinates and momenta that approximated a quantum mechanical Boltzmann distribution were generated by the TS normal-mode sampling procedure. The results showed that trajectories starting from each TS gave all four products. Furthermore, total average of the product distribution agreed with experimental observations. Thus, the TS region of the PES is shared by all four reactions, as suggested by previous PES calculations.21–23 However, trajectories initialized at the three TS structures did not give identical product distributions under any circumstances. For example, trajectories starting from TS1 gave si as a major product, and the ratio of suprafacial products (si-9 þ sr-9) amounts to 80%. Trajectories initiated at another TS2 yielded ai-9 as a major product and the products with insertion of configuration (si-9 þ ai-9) were nearly 70%. Trajectories initiated at TS3 were much less selective. These data demonstrated nonstatistical dynamics, which were inconsistent with a mechanism involving a statistical intermediate. Counting the number of products at a series of time intervals gave time-dependent product distribution. Such analysis revealed that trajectories could be classified into short-lived and long-lived ones. The short-lived trajectories were stereoselective, and the product ratio was strongly time dependent. For example, the suprafacial/ antarafacial (s/a) product ratio for the trajectories initiated at TS1 was 463 for the 100–200 fs range, while it was 2.3 for the 300–400 fs range. Likewise, inversion/retention (i/r) product ratio for the trajectories initiated at TS3 was

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88 for the 100–200 fs range, while it was 9.8 for the 300–400 fs range. For the long-lived trajectories, these ratios were similar and more or less near unity, regardless of the time range and initial conditions. Thus, short-lived trajectories were nonstatistical and mode specific, whereas long-lived trajectories showed considerable stereorandomness. The observed nonstatistical dynamics is likely due to the torsional motions that are approximately decoupled from other modes and thus do not participate in IVR before the reaction is over.

DISSOCIATION OF ACETONE RADICAL CATION

Acetone radical cation, generated in a mass spectrometer by 1,3 H migration of its enol isomer, dissociates to give acetyl cation þ methyl radical [Equation (5)]. Although the two methyl groups are symmetrical in acetone radical cation, the methyl newly formed by the hydrogen transfer is known to be lost preferentially.24 It was interesting to clarify the origin of this preference by simulations. Direct dynamics trajectory calculations were carried out on an AM1-SRP surface parameterized to fit energies and geometries of key stationary points, as determined at the B3LYP/cc-pVTZ level of theory. Trajectories were initiated at the TS for keto/enol isomerization and at the acetone radical cation minimum. The number of trajectories was 1807 for the former and 1816 for the latter set of calculations. Initial states were generated by quasiclassical normal-mode sampling, and a microcanonical ensemble of initial states was selected so that each trajectory had a total energy of 10 kcal mol1 in excess of the ZPE.

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Trajectories initiated from the vicinity of acetone radical cation showed essentially equal loss of either methyl (branching ratio 1.01  0.01). In contrast, the branching ratio observed for methyl loss in trajectories originating the TS was 1.13  0.01, which is in qualitative agreement with the experimental values of 1–1.4.24 When the trajectories were divided into time courses, with a resolution of 5 fs, a unique phenomenon appeared that the newly created methyl dissociated predominantly at very short reaction time intervals. It was found that the trajectories that would lose the newly formed methyl at very short times never entered the PES minimum of the acetone radical cation. The shortest duration trajectories simply took the exit without ever attaining the equilibrium geometry of the radical cation.

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187

An exponential fit to a plot of undissociated ions versus time yielded a halflife of the reaction as 238 fs, which was in reasonable agreement with an experimental estimate of 500 fs. It should be noted that the reaction initiated from the TS was significantly faster than that from the acetone radical cation. This phenomenon appeared to be due to nonstatistical coupling of the kinetic energy acquired during the TS to the radical cation transformation into modes of importance for the subsequent dissociation of the radical cation. It was suggested that the observed chemically significant nonstatistical dynamics for an intermediate that sits in a potential energy well some 20 kcal mol1 deep might have potential relevance to other organic reactions. The reaction was further studied by ab initio classical trajectories at the MP2/6-31G(d) level of theory using a Hessian-based predictor-corrector method25,26 implemented in the Gaussian suite of programs.27 Here, a microcanonical ensemble using quasiclassical normal-mode sampling was constructed by distributing 10 kcal mol1 of excess energy above the barrier. Trajectory started at the keto/enol tautomerization TS showed that the dissociation was again favored for the loss of the newly formed methyl group in agreement with experiments and previous simulations.24,28 The branching ratio of the methyl loss was calculated to be 1.53  0.20, which is in agreement with the experimental ratio. It was also found that the translational energy distribution of the methyl radicals was bimodal, in that the radical derived from the newly formed methyl had higher average translational energy than that from the other methyl.

THE WOLFF REARRANGEMENT

Flash vacuum thermolysis of the formal Diels–Alder adduct (10) of acetylmethyloxirene to tetramethyl-1,2,4,5-benzenetetracarboxylate to give acetylmethylketene (15, in Scheme 1) was examined in an attempt to find an example of nonstatistical dynamics effect on product distribution.29 With two carbon13-labeled starting materials (# and * show the labeled carbon in separated experiments), the reaction yielded 15 with different 13C locations. It was originally expected that 10 would give 12, which then via carbene formation would yield 15a and 15b. The ratio of the two products was anticipated to show the occurrence of nonstatistical product distributions. Compound 15c might be formed via 12 and 13, but this route was considered to be minor since 13 was much unstable than 14. The experimental finding was surprising. The product ratio of 15a, 15b, and 15c, which was determined as relative yields of diols after MeOH addition and DIBAL reduction, was 1.9–2.6:1.0:12–14.3. The predominant formation of 15c required reconsideration of the reaction pathways. Electronic-structure calculations at CCDS(T)/cc-pVTZ//CCSD/cc-pVDZ showed that carbene 13 was 8.7 kcal mol1 unstable than carbene 14 in

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Scheme 1

enthalpy, although the energy difference became much smaller (0.5 kcal mol1) in free energy. Thus, there was no reason to conclude that 12 gave 13 predominantly over 14. Thoughtful reinvestigation of the reaction energies revealed that the favorable route from 10 to 13 was through 11; 11 was 47.9 kcal mol1 more stable than 12 in enthalpy at the DFT method (MPWB1K6-31þ G(d,p)), and TSs from 10 to 11 and from 11 to 13 were more stable than the TS from 10 to 12 by 19.0 and 11 kcal mol1, respectively. The barrier from 13 to 15c was 3.4 kcal mol1 while the step from 13 to 14 required 6.4 kcal mol1, both in free energy. Thus, the formation of 15c was the primary process of the reaction of 13. The three isotopically labeled 150 s were concluded to be formed from 10 via the pathways shown in solid arrows in Scheme 1. Despite that 15a and 15b were minor products for the reaction of 10, it should be noted here that the reaction mechanism in the scheme requires that the product ratio 15a/15b to be very close to unity, if 13C kinetic isotope effect (KIE) is neglected, since they are symmetric. Thus, the observed ratio as large as 2.5 could be an indication of dynamics effect. Direct dynamics calculations were carried out with quasiclassical normalmode sampling from a canonical ensemble at 923 K (the experimental reaction temperature). Simulations initiated at the vicinity of TS for rearrangement of carbene 13 to 14 via oxirene 12, and 300 trajectories were obtained at DFT methods. The preliminary results reported in the manuscript showed that preferred formation of 15a over 15b by the ratio of 1.8–7.6 depends on the method used. The results were qualitatively consistent with the value of 2.5 deduced from the experiment. The non-unity ratio likely arises from the situation that two methyl groups in 14 are dynamically unequal on the carbene formation process.

MOLECULAR SIMULATIONS OF ORGANIC REACTIONS

3

189

Avoided intermediate on IRC

SN2 REACTION

In the previous section, examples were shown in that product distribution does not follow what is expected from statistical TST. In many cases, reactions that were formally assigned, on the basis of the analysis of PES, to proceed via a stepwise mechanism with a distinct radical intermediate actually behaved dynamically as concerted reactions. This is one way of appearance of dynamics effect. In this section further examples of the discrepancy between reaction pathways on the PESs and dynamics pathways are discussed. One of the earlier examples was reported on SN2 reactions. Basilevsky reported more than two decades ago quantum-dynamical evidence that SN2 reactions of CH3F with nucleophiles X were direct without trapping in the X   CH3F pre-reaction complex.30 Trajectory calculations were carried out in another SN2 of CH3Cl þ F.31 In this study, trajectories were initiated at the reactant state, in which the initial geometrical configurations at time zero were randomly generated in the range 180  3 for the collision angle and of RF–Cl = 6.0–6.5 A˚. The vibrational phase of CH3Cl was generated to take a temperature of 10 K. The quantum part was calculated at HF/3-21 þ G(d). The calculations showed that almost all available energy is partitioned into the relative translational mode between the products (43%) and the C–F stretching mode (57%) at zero collision energy. It was found that the lifetime of the post-reaction complexes was short enough to dissociate directly to products, while the energy was not completely distributed within the lifetime. It was concluded that the SN2 reaction proceeds nonstatistically via a direct mechanism in the case of near-collinear collision. Hase and coworkers carried out extensive trajectory calculations for the reaction of CH3F þ OH.32 The direct dynamics calculations were initiated at the central barrier at MP2/6-31þG*. Quasiclassical sampling, which includes ZPE, was used with a 300 K Boltzmann distribution for all vibrational degrees of freedom and rotations. Out of 31 trajectories, only 4 were trapped in the postreaction complex, whereas 27 gave directly the dissociated products with F approximately along the O-C   F collinear axis. Thus, only a small fraction followed the IRC pathway. It is worth noticing that the post-reaction complex has an O-H   F interaction and therefore the departing F has to be turned back to CH3OH to form the complex, which is dynamically unfavorable unless efficient IVR is realized. It was noted that the central barrier recrossing was unimportant for this reaction, consistent with the direct dissociation mechanism.

[3,3]SIGMATROPY

Experimental study on the [3,3] sigmatropic rearrangement of 1,2,6-heptatriene [Equation (6)] suggested that the reaction proceeds via a stepwise mechanism

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with a biradical intermediate (17) on the basis of the trapping experiment with O2.33 At the same time, by extrapolation of the product ratio to infinite O2 pressure, it was also deduced that roughly half of the reaction proceeds concertedly without formation of intermediate 17. Since the potential energy calculations at the CASSCF(8,8) or B3LYP level of theory did not give TS corresponding to the direct concerted rearrangement from 16 to 18, it was assumed that the diradical intermediate 17 and final product 18 are formed from TS4 by bifurcation. Bifurcation here does not mean that the path bifurcates on the way to two products, but means that trajectories may stay in the intermediate region for long enough time for statistical energy distribution or may go over the intermediate or stay in the region for only a short period of time to reach product region as if it is concerted process.34

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CASSCF(8,8) as well as AM1-SRP direct dynamics calculations revealed that when a few key normal modes were energized trajectories did not stay in the biradical region and led directly to the product, 18. AM1-SRP MD calculations using quasiclassical normal-mode sampling of the initial states from a canonical ensemble at 438 K showed that 17% of 400 trajectories run from the vicinity of TS4 bypassed biradical 17 and directly gave 18. These trajectories should be counted in as the ‘‘concerted’’ component of the reaction. The results that trajectories starting at TS4 led both to the biradical intermediate and product regions suggested that a reaction whose steepestdescent path from a TS leads only to one product may give additional products by dynamically favored non-steepest-descent paths.35

4

Non-IRC reaction pathway

Dynamics effect discussed so far deals with reaction systems, in which an unstable intermediate exists in a shallow well on the PES connecting the reactant and product states. These putative intermediates have been biradicals, radical ions, carbenes, or post-TS complexes. Trajectory calculations showed examples where reacting molecules stride over a shallow well to give product directly or cases where the lifetime of the species trapped in a well is short enough to avoid thermal equilibration and quickly escape to the product. In these cases, reactions occurred effectively in a concerted manner, although the PES dictates a stepwise mechanism.

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Another manifestation of a dynamics effect on reaction pathways is a socalled ‘‘dynamics-driven’’ reaction pathway, in which trajectories go through a nonminimum energy pathway due to a dynamics effect.

PHOTOISOMERIZATION OF CIS-STILBENE

One example of non-IRC trajectory was reported for the photoisomerization of cis-stilbene.36,37 In this study trajectory calculations were started at stilbene in its first excited state. The initial stilbene structure was obtained at CIS/631G, and 2744 argon atoms were used as a model solvent with periodic boundary conditions. In order to save computational time, ‘‘finite element interpolation’’ method was used, in which all degrees of freedom were frozen except the central ethylenic torsional angle and the two adjacent phenyl torsional angles. The solvent was equilibrated around a fully rigid cis-stilbene for 20 ps, and initial configurations were taken every 1 ps intervals from subsequent equilibration. The results of 800 trajectories revealed that, because of the excessive internal potential energy, the trajectories did not cross the barrier at the saddle point. Thus, the prerequisites for common concepts of reaction dynamics such TST or RRKM theory were not satisfied.

IONIC FRAGMENTATION REACTION

The reaction of base-mediated decomposition of peroxide had previously been studied experimentally and it was shown that the reaction of CH3OOH with F gave HF þ CH2O þ OH as major products.38 This process is an elimination reaction of H and OH from CH3OOH (ECO2). The result was surprising since the observed products were much higher in energy than HF þ CH2(OH)O, products of a sort of migration of OH from O to CH2 upon H abstraction. Scheme 2 shows the electronic energies (in kcal mol1) calculated at B3LYP/6-311þG(d,p) for the reactant complex, TS, and the two product states. Thus, HF þ CH2(OH)O are 36.5 kcal mol1 more stable than HF þ CH2O þ OH. Furthermore, IRC calculations from the TS led to HF þ CH2(OH)O rather than HF þ CH2O þ OH. Direct

Scheme 2

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trajectory calculations were carried out to examine the apparent discrepancy between the experimental observation and the expectation from PE calculations. Ab initio direct dynamics trajectory calculations were performed at the B3LYP/6-311þG(d,p) level of theory.39 The trajectories were initiated at the separated reactants, TS (HOOCH3   F), and the CH2(OH)O–H   F region on IRC, with quasiclassical sampling including ZPE. The trajectories from the reactants were started at 15 A˚ separation of the two species with small attractive potentials of –0.21 or –0.13 kcal mol1. The collision impact parameter was chosen randomly between zero and maximum. The initial CH3OOH vibrational and rotational degrees of freedom were selected from their 300 K Boltzmann distributions. Out of the 200 trajectories started at the separated reactants, 145 gave productive trajectories and 55 stayed in the reactant state. Among the 145 trajectories, 97 were trapped in the CH3OOH   F potential energy well as reactant complex and stayed up to 4 ps. Forty-five trajectories led to HF þ CH2O þ OH, which were the major products observed in the experiment, and three gave HF þ CH3OO. The path along IRC leading to a deep potential energy minimum for the CH2(OH)2   F complex followed by dissociation to HF þ CH2(OH)O was not observed by dynamics simulations, despite the fact that this path has an energy release of –63.4 kcal mol1 and is considerably more exothermic than the ECO2 path whose energy release is –27 kcal mol1. Analyses at the molecular level showed that the major products, HF þ CH2O þ OH, were formed via initial C-H   F interaction, followed by concerted OH and HF elimination to give CH2O. Trajectories started at other initial structures; TS and HOCH2O–H   F also gave HF þ CH2O þ OH, again along paths different from the IRC path. This is an example that two-bond fission is favored over one-bond fission þ intramolecular migration; the situation is similar to the Beckmann rearrangement versus fragmentation reactions that will be discussed in section ‘‘Path Bifurcation’’.

CYCLOPROPYL RADICAL RING-OPENING

The ring-opening reaction of cyclopropyl radical [Equation (7)] was shown to occur at 174C to give ally radical, but the product stereochemistry was unclear. Ab initio direct dynamics study was carried out to clarify the stereochemical course of the reaction.40 Trajectories were initiated at the ringopening TS obtained at CASSCF(3,3)/6-31G(d), with quasiclassical normal sampling at the experimental temperature of 174C. ZPE was included, and thermal vibrational energy was sampled from the normal-mode Boltzmann distribution. A rotational energy of RT/2 was added toward the allyl radical product.

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For 21 out of the total 141 trajectories examined, barrier recrossing was observed leading back to cyclopropyl radical after up to 21 fs of dynamics, which is a violation of TST. The ring-opening step from the TS to allyl radical requires rotation of the two C–C bonds. In all reactive trajectories observed, the two bond rotations were found to occur in a nonconcerted fashion in agreement with the IRC calculations. Further, 68 out of the 120 reactive trajectories followed the asynchronous disrotatory motion on the minimum energy path. However, the remaining 52 trajectories also had an asynchronous motion, but with the two terminal methylene groups rotated in the conrotatory manner. Thus, the trajectories as a whole did not follow the IRC path. The significance of small preference (57%) for disrotatory ringopening over conrotatory opening was not clear, because the number of trajectories performed in the study was limited, and it is possible that a larger ensemble of trajectories may predict no stereochemical preference for ringopening.

IONIC MOLECULAR REARRANGEMENT

Direct MD studies described above have demonstrated that reacting molecules do not necessarily follow the reaction intermediates along the IRC when kinetic energy is incorporated. A paper published in 2003 further showed that chemical reactions may in fact proceed through a reaction route totally different than the IRC path.41 The intramolecular rearrangement of protonated pinacolyl (3,3-dimethyl-2-butyl) alcohol (Me3C-CHMe-OH2þ, 19), which, upon heterolysis, gives a rearranged tertiary carbocation (20) via either a concerted or a stepwise mechanism (Scheme 3). KIE studies on the reactions of pinacolyl sulfonates in hydroxylic solvents suggested the concerted pathway, but the mechanism was still not clear.42 Ab initio calculations at the HF, MP2, and B3LYP theories with the 6-31G* and 6-311G** basis sets gave only one TS that corresponds to the saddle point of the concerted pathway, and no other TSs could be characterized as indicated in the potential energy contour map at HF/ 6-31G* (Fig. 1). The TS was 9.3 kcal mol1 above the reactant state and the reaction was exothermic by 6.3 kcal mol1 at HF, which was in semiquantitative agreement with the B3LYP/6-311G** and MP2/6-311G** results. Direct ab initio molecular dynamic simulations starting at the reactant with total Maxwell-Boltzmann equipartitioned thermal kinetic energy of 26 kcal mol1, however, demonstrated that the reaction pathway did not follow the IRC (dotted line in Fig. 1) on the PES, but that it was rather

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Scheme 3

2

reactant region

100

sec-cationic region

CH3-C-C angle/degree

6

80 TS 30

10

12

16

60

8

10

130

4 0

50 –4

4

40

2

1.5

2.0

–4

2.5

–6

3.0

product region 3.5

4.0

RC-O/Å

Fig. 1 3D map for heterolysis of 19.

controlled by the dynamics of the reaction. In most cases, trajectories were first initiated by the C–O bond cleavage to lead to a secondary carbocation intermediate (21) region, despite that there is no energy minimum at this region. The intermediate cation could have a lifetime up to 4 ps, and then yielded rearranged products, via an overall stepwise mechanism. A typical example of trajectories is illustrated in Fig. 2. The variations of three Me-C–C angles in Fig. 2c and the charges on the leaving group (H2O) and Ca in Fig. 2d showed

Potential energy (hartree)

MOLECULAR SIMULATIONS OF ORGANIC REACTIONS –310.48

195

(a)

–310.49 –310.50 –310.51 –310.52 –310.53 –310.54 6.0

(b)

RC-O (Å)

5.0 4.0 3.0 2.0 1.0 0

1000

2000

3000

2000

3000

Mulliken group change

Me-C–C angle (degree)

time (fs) 140.0

(c)

120.0 100.0 80.0 60.0 40.0 20.0 0.5

(d) Cα

0.2 0.0

H2O

–0.2

Cβ

–0.5 0

1000 time (fs)

Fig. 2 The variation of (a) potential energy, (b) C–O distance, (c) Me–Cb–Ca angles of the three Me groups, and (d) the Mulliken charge in one of the trajectories.

that none of the methyl groups started to migrate at 2700 fs, despite that the C–O bond was cleaved at a very early stage of the reaction at 100 fs. Thus, the reaction dynamics preferred the stepwise rather than the concerted pathway.

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This occurred probably because the initial motion of the reacting species was to the cationic region due to the shape of the energy surface and thus one bond cleavage was preferred over the concerted migration. These results clearly indicated that a TS of a given character may have only limited significance with respect to the actual mechanism.

ENE REACTION

Singleton and coworkers took up the ene cyclization reaction of ene-allene (Scheme 4) and carried out combined experimental-computational investigation.43 The ene reaction had been known to show mechanistic uncertainty, in particular whether it proceeds via a concerted or stepwise route, and therefore provided a challenge for dynamics study. KIE measurement for the reaction of 22 (R1 = R2 = TMS) in toluene at 50C gave kCH3/kCD3 of 1.43, which was smaller than what was normally observed in concerted ene reactions. However, the isotope effect was too large to support a stepwise ene reaction. Thus, this was in line with the idea that the mechanism is near the concerted-stepwise borderline. Computational study at B3LYP/6-31G** showed three possible pathways. The first one was the concerted process that directly gives the ene product, 25. The TS, 23, is 23.8 kcal mol1 higher in energy than 22. Biradical intermediate, 24, for a stepwise process, which is formed with an inward Me rotation optimized. However, the TS leading to 24 could not be obtained, and all attempts to locate the TS converged on 23. Alternative stepwise process with outward Me rotation gave a TS which is 8.8 kcal mol1 less stable than 23.

Scheme 4

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197

The absence of the TS leading to 24 suggested the authors to assume that the concerted and stepwise merge in the single TS, 23. KIE was calculated for the two optimized TSs. The stepwise TS with outward Me rotation gave the kCH3/kCD3 value of 1.06, which was much smaller than the observed isotope effect. The kCH3/kCD3 value for the concerted process was predicted to be 1.54. This is slightly larger than the experimental observation, and it was suggested that the observed isotope effect represents a mixture of concerted and stepwise mechanisms. Quasiclassical direct dynamics trajectory calculations at UB3LYP/6-31G** for the concerted TS of model compound (TS6) was carried out. Simulations were started either at the TS geometry or with atomic positions near the TS randomized by using linear sampling of each normal mode. The two types of simulations gave similar results. Although the minimum energy path from the concerted TS goes directly to the product, 29 out of 101 trajectories afforded diradical intermediate in the stepwise route. The result implied that the TS for the concerted process would give the ene product through the stepwise intermediate. Another interesting observation was that in another 29 trajectories the hydrogen transfer occurred ahead of the C–C bond formation, giving rise to another diradical intermediate. It should be stressed that this intermediate is not associated with a potential energy minimum; the situation is similar to the case described above for the ionic molecular rearrangement.41

It was found that this reaction is not well described by either a concerted or two-step mechanism and that the consideration of dynamic effects is necessary to understand the nature of the intriguing reaction. When a reaction involves multiple bonding changes, a question may arise whether the bonding changes occur by a stepwise or concerted pathway. An answer to such a question based on the classical reaction theory is that the reaction proceeds by a concerted pathway, by a stepwise pathway, or by a mixture of the two separate pathways. However, if one takes into account dynamic effects, the answer to the question of concerted versus stepwise may be much more complex. It is interesting to point out here that the case reported by Singleton for the ene reaction affords a case, where stepwise mechanism can dynamically operate on a concerted PES. This contrasts with the reactions described in section ‘‘Nonstatistical Product Distribution’’, in which the

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trajectories showed effectively a concerted character on the stepwise PES. Thus, a possible role of dynamics appears in different ways in mechanistic organic chemistry.

THERMAL DENITROGENATION

Concerted versus stepwise issue was studied for another radical reaction. The thermal denitrogenation of 4-spirocyclopropane-1-pyrazolines (27) gives alkylidenecyclobutanone (28) and spiropentane (29) in three possible pathways (Scheme 5), via (a) diazenyl diradical intermediate (30), (b) 1,3-diradical intermediate (31), or (c) concerted cycloreversion TS. Computational study at (U)B3LYP/6-31G* for the reaction of 27 (R = Z = H) showed that the activation barrier (DE þ ZPE correction) for the diradical (31) formation (path b) is 40.2 kcal mol1, which is 2.1 kcal mol1 lower than that for the diazenyl diradical (30) formation step (path a).44 The barrier from 31 to 29 is very small (0.6 kcal mol1), whereas the barrier from 31 to 28 is 7.0 kcal mol1. Direct formation of 28 from 27 via a [2 þ 2 þ 2] reaction did not give TS. Thus, the calculations suggested that the reaction of 27 (R = Z = H) would give 29 as a major product via path b. This is consistent with experimental report, which showed that the denitrogenation of the parent 27 nearly exclusively gave spiropentane.45

Scheme 5

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199

Calculations for 27 (R = Me, Z = CO2Me) at B3LYP/6-31G* and MP2/ 6-31G* gave qualitatively the same results as for 27 (R = Z = H). However, experimental study for 27 (R = Me, Z = CO2Me) revealed that the major product was 28 (R = Me, Z = CO2Me) rather than 29. Thus, calculations and experiment did not match for the reaction of this species. It is important to note that the experimental activation energy for the formation of 28 was determined as 26.8  0.5 kcal mol1, which is close to the value (DE6¼ þ ZPE = 26.9 kcal mol1) for the formation of 31 from 27, despite that 31 gives 29 on the PES. In order to reconcile this discrepancy, dynamics effect was examined by means of ab initio MD simulations at (U)B3LYP/6-31G*.44 Trajectories were initiated at the TS for the denitrogenation from 27 (R = Z = H) to 31 with 353 K Boltzmann distribution for the reaction coordinate translation. Out of 10 trajectories, 1 went back to the reactant, 8 gave 31, and 1 led directly to 29. Thus, the trajectory calculations reproduced experimental trend reported in the literature,45 namely spiropentane is the major product for the reaction of the parent 4-spirocyclopropane-1-pyrazoline. Analogous trajectory calculations for 27 (R = Me, Z = CO2Me) gave quite different results. Out of 31 trajectories, 25 went back to the reactant, 5 gave 28, and only 1 led to 31. In order to examine the effect of substituents, simulations were also carried out for 27 (R = H, Z = CO2Me), which showed that 11 out of 36 trajectories gave 31, and 25 led to 28. Thus, it appears that an electronwithdrawing substituent (CO2Me) plays a crucial role in the dynamics effect, which facilitates the selective production of 28 despite that the minimum energy path affords 31 and eventually 29. The effect of the electronwithdrawing substituent was considered to arise from more effective hyperconjugative interaction between the radical orbitals and the -orbitals of the cyclopropane ring in 31 (Z = CO2Me) than in 31 (Z = H), which makes the cyclopropane ring prone to ring-opening.

UNIMOLECULAR DISSOCIATION

A combined experimental and theoretical investigation of unimolecular dissociation of laser-excited formaldehyde (H2CO) to H2 and CO revealed that there exist two dissociation channels: the one proceeding through a wellestablished TS to produce rotationally excited CO and vibrationally cold H2, and the other yielding rotationally cold CO in conjunction with highly vibrationally excited H2 [Equation (8)].46 Quasiclassical trajectory calculations on a global PES constructed from least-squares fits to ab initio results suggested that this second channel represents an intramolecular hydrogen abstraction mechanism, in which one hydrogen atom is first dissociated and roams around the HCO fragment and abstracts the second H atom to give H2. Thus, this channel entirely goes off the saddle point on the PES.

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(8)

SN2 REACTION

Recent experimental advances allow one to obtain insight into the gas-phase reaction dynamics, such as the probabilities for energy redistribution within the ion-dipole complexes, their dependences on initial quantum states, the branching into different product quantum states, and the role of tunneling through the central barrier from measurements of correlated angle- and energy-differential cross sections. Such experimental study provides complementary information to dynamics calculations. For the SN2 reaction of Cl þ CH3I, MP2(fc)/EPC/aug-cc-pVDZ trajectory calculations initiated at the reactant state with 1.9-eV collision energy revealed that the reaction occurred by two mechanisms: direct and indirect ones.47 As the atomic level, the direct mechanism proceeded by the classical SN2 pathway with Cl attacking the backside of CH3I. On the other hand, the indirect mechanism occurred via a roundabout mechanism, in which Cl first stroke the side of the CH3 group, causing it to rotate around the I atom. This rotation occurred since I is a heavy atom compared to the other part of the molecule. When proper orientation was attained, then Cl attacked the backside of CH3I. The ratio of the two mechanisms depended on the collision impact factor; the ratio was 0.4, 0.8, 0.8, and 1.0 for impact factors of 0.0, 1.0, 2.0, and 3.0 A˚, respectively. The product energy partitioning for the direct mechanism was 0.04, 0.23, and 0.73 for rotation, vibration, and translation, respectively, whereas it was 0.28, 0.56, and 0.16 for indirect mechanism. The overall fraction partitioned to translation was calculated as 0.6–0.7, which was in agreement with the experimental value. Thus, the combined study of gas-phase experiment and high-level MD simulations revealed that the detailed mechanism of the SN2 reaction at the molecular level varies depending on how two reacting groups collide. Similar situation, in which trajectory largely deviates from the minimum energy path, has been reported for H þ HBr -> H2 þ Br.48

5

Path bifurcation

As is described in previous sections, dynamics effect often plays important role in determining reaction mechanisms. This is because such a reaction proceeds via a region mechanistically intermediate between two extremes, and thus the mechanism is sensitive to a subtle perturbation. In those cases, the minimum

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201

(b)

Fig. 3 Path bifurcation on (a) symmetrical PES and (b) asymmetrical PES.

energy path and the shape of PES are less relevant than ordinary thought. In this section, different types of examples of dynamics effect are presented, in which single TS gives two products through path bifurcation. There are cases where a minimum energy path from a TS leads to another TS that separates two product states.49–55 If PES is symmetrical, the minimum energy path goes to a valley-ridge inflection (VRI) point and bifurcates before reaching the product region. The situation is schematically shown in Fig. 3a. Mechanisms of reactions with such symmetrical PES are reported for ene reaction,56–59 isomerizations,60,61 Berry pseudorotation,62,63 and deazetization.64 There may be cases, where a minimum energy path from TS leads to one of the two different types of products located close to each other on the PES, and due to dynamics effect the path may bifurcate leading to two products (Fig. 3b). Examples of this kind of reactions include ET-SN2 borderline reaction,65–75 pseudorotation,76–78 isomerization,50,79–84 cycloaddition,85–87 Beckmann rearrangement,88 and sigmatropic isomerization via biradical intermediate.89 For some of the reactions dynamics simulations were carried out to study how the bifurcation occurs and the product ratio is determined.58,60,62,63,70– 75,83,84,87,90 Dynamics effect of some of these reactions are discussed below.

BIFURCATION ON SYMMETRICAL PES

Ene reaction Ene reactions of simple alkenes with singlet oxygen have been studied by both computational and experimental methods.56,57,59 The reactions may proceed via a concerted or a stepwise mechanism [Equation (9)]. For a stepwise mechanism, four types of intermediates, biradical, zwitterion, perepoxide,

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and p-complex, were proposed. Deuterium KIE study of CD3-labeled 2,3dimethyl-butenes revealed that the reaction gave only small intermolecular KIEs (kH/kD = 1.04–1.09) whereas intramolecular KIEs were of significant magnitude (1.38–1.41). The results had been interpreted to show that the reaction proceeds via rate-determining formation of symmetrical perepoxide. Intermolecular 13C KIE for Me2C=C(i-Pr)2 showed that the two olefinic carbons have small KIEs of the same magnitude, which clearly indicated that the rate-determining TS is symmetrical with respect to the two carbons. Intramolecular 13C KIE study supported the mechanism that the reaction proceeds via symmetrical TS, followed by intramolecular product-determining selection between methyl groups.

′

″

″ ′

′

″

(9) ″

″

′

′

″

″

′

′

Computational study at UHF or UB3LYP level of theory disagreed the intermediacy of perepoxide and showed that the reaction proceeds via biradical intermediate. However, calculations at CCSD(T)/6-31G*//RB3LYP/631G*, which includes substantial dynamic configuration interaction, revealed that the reaction of cis-2-butene with 1O2 proceeds through an early ratedetermining TS, and then the reaction path appears to lead toward a perepoxide-like structure (Scheme 6, R = R1 = H). The first TS (TS6) is of Cs symmetry, and the hydrogen abstraction has not yet started. The perepoxidelike structure is also of Cs symmetry and is the TS (TS7) for interconversion of the two symmetrical products. There exists VRI between TS6 and TS7. Since the minimum energy path is on a valley before VRI but it is on the ridge after

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203

Scheme 6

VRI, the actual reaction path bifurcates into two products before reaching TS7. The rate is determined by TS6, whereas the product ratio is controlled by the shape of the PES near the VRI point and TS7. Thus, a question arises: how the product selection occurs when a subtle perturbation, such as isotopic substitution, is introduced and two symmetrical products become asymmetric? Singleton et al. have carried out quasiclassical direct dynamics calculations on the B3LYP/6- 31G* PES for the ene reaction of 32.58 The trajectories were started at the point in a region between TS6 and VRI, centered on the minimum energy path with both O–C distances of 1.95 A˚. The trajectories were initialized either at 0 K, giving each mode in total only its ZPE with a random sign for its initial velocity, or at 263 K, using a Boltzmann sampling of vibrational levels. Trajectories for 32 with one of the methyl groups deuterated (CH3CH=CHCD3) gave two products, CH2=CH-CH(OOH)CD3 and CH3CH(OOD)-CH=CD2, in the ratio of 122/61 at 0 K, which corresponds to the intramolecular kH/kD of 2.1. Similarly, simulations at 263 K gave the ratio of 257/149, corresponding to kH/kD of 1.38. Thus, KIE was calculated to be smaller at a higher temperature. The magnitude of KIE at 263 K agreed with the experimental observation. The product selection obtained by these trajectory calculations is not due to any enthalpic or entropic origin. It was concluded that this selectivity is a new form of KIE, dynamical in origin, unrelated to the usual effect of ZPEs on the barriers.

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Another set of trajectory calculations for the reaction of 2-pentene (C2H5CH=CHCH3) is worth mentioning. Experimentally, the ene reaction of 2-pentene gave nearly equal amount of the two possible alkenes. However, since the two alkyl groups on the double bond are different, the PES is asymmetric and the minimum energy path does not bifurcate on the surface but leads only to the terminal alkene (C2H5CH(OOH)-CH=CH2). Trajectory calculations on such PES gave two products in 13/7 ratio, consistent with experimental observation qualitatively. This is an example of dynamic bifurcation in that the reaction path bifurcates dynamically, despite that the minimum energy path on the PES does not bifurcate. The dynamic bifurcation will be discussed in detail in section ‘‘Dynamic Bifurcation’’. The dynamics effect on path bifurcation and nonstatistical product distribution on a slightly perturbed symmetrical PES have also been reported for the C=N isomerization of benzylideneanilines.60

DYNAMIC BIFURCATION

As described above, path bifurcation is classified into two types: statistical bifurcation and dynamical bifurcation. In the statistical bifurcation, a minimum energy path down from a TS reaches another TS through a VRI point, and the actual reaction path ought to bifurcate near the VRI region. This is observed for reactions with symmetrical PESs. On the other hand, there are cases in which a minimum energy path does not bifurcate on the PES and leads to one product as in a normal reaction, but when two product regions are located close to each other on the PES and a barrier (a ridge) separating the two region is low, dynamics trajectories can give both products. This is the dynamical bifurcation. This may occur for reactions of a borderline mechanism. ET/SN2 bifurcation An early example of dynamical bifurcation is seen for SN2/ET borderline reaction shown in Scheme 7.65–68,70–75 Computational studies by Shaik, Schlegel, and coworkers on the reactions of formaldehyde anion radicals with methyl chloride demonstrated that the reaction gave two distinct TSs: SUB(O) TS that gives substitution product at O of the carbonyl function (CH2-OCH3) and ET TS that yields neutral aldehyde þ methyl radical.65–68 SUB(C) product (OCH2CH3) is formed in a stepwise manner through the ET step. Bertran et al., on the other hand, suggested that the ET TS could be viewed as an SN2 (SUB(C)) TS involving the carbon atom of CH2=O radical anion as a nucleophilic center.69 The origin of the different mechanistic assignment for the TS was analyzed by Shaik et al. on the basis of the PES calculated at the UHF/6-31G* level of theory.65–68 These

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Scheme 7 Numbers are calculated enthalpy in kcal mol1 at UHF/6-31G* (G3) relative to reactant complex.

authors showed that the reaction path descends from a broad saddle point to a flat ridge that separates the ET and SN2 products. After entering the flat ridge region the path bifurcates to the two product states. Different reaction-path methods give different mechanistic assignments as follows: the steepest-descent path in Z-matrix internal coordinates leads directly to the ET product; and the path in mass-weighted internal coordinates leads to a ridge and descends to the SN2 product. The surface calculated at the UQCISD(T)/6-31G* level resembles the UHF one, indicating that the branching of the potential surface into two mechanisms is also expected at this level. However, these discussions based on the MO calculations are only relevant for the reaction at 0 K, and the interpretation of the reaction mechanism ought to rely on reaction dynamics at finite temperature. Ab initio direct MD calculations are a means to obtain the desired dynamical characterization. Yamataka and collaborators carried out ab initio MD simulations for the reaction of CH3Cl and a H2C=O radical anion using the program packages of HONDO.70–72 Simulations were started from the ET TS. The initial atomic velocities were assigned from a random distribution with the total kinetic energy being consistent with the simulation temperatures (100, 298, and 400 K). A velocity re-scaling algorithm similar to the constant-temperature algorithm of Berendsen et al. was used. Hundred fifty-three MD simulations were performed at the UHF/6-31þG* level of theory. In the MD simulations starting from the ET TS, four types of trajectories were observed: those leading back to the reactants (36 trajectories), those leading to the SN2 product (99), those passing through the SN2 valley and crossing over to the ET valley (9),

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and those going to the ET valley directly (9). Thus, the dynamics calculations clearly confirm that the TS leads directly to both the ET and SN2 products. It was also found that the trajectories at the lower temperature (100 K) follow the IRC path, whereas at higher temperatures the kinetic energy affects the reaction route. Shaik, Schlegel, and coworkers later carried out extensive direct MD simulations on the reaction using higher levels of theory and determined the branching ratio more precisely.73–75 It was found that more ET product was obtained with more energy available, consistent with the previous observation, confirming that the kinetic energy of reacting species plays an important role in controlling the pathway of the reaction. These direct MD simulations revealed that the TS yields intrinsically the SN2 product. At finite temperature, however, a route opens up in which the system may evolve either directly or indirectly toward the ET product after passing over the barrier. It was thus demonstrated that the TS characteristics themselves do not always dictate the reaction mechanism and that the formation of two different products does not necessarily mean the presence of two independent pathways with different TSs. A possible occurrence of branching from single TS to several products introduces additional complexities in mechanistic assignment for borderline reactions. Furthermore, an observation that more ET product is formed at a higher temperature would often be taken as an indication that the reaction would follow two competitive routes with a higher activation energy for the ET route than for the SN2 route. The present analysis offers an alternative interpretation that a similar temperature effect on the product distribution can also arise from traversing single TS and undergoing temperaturemediated mechanisms to different products for a borderline reaction.

CYCLOADDITION

The cycloaddition reactions of ketenes with cyclopentadiene have been known to give formal [2 þ 2] cycloadduct (35) instead of [4 þ 2] Diels–Alder products (34) (Scheme 8). A combined computational and experimental study suggested that the reaction initially gives [4 þ 2] cycloadduct, which subsequently rearranges to 35 via [3,3] sigmatropy.91,92 The MP2/6-31G*//HF/3-21G calculations

Scheme 8 Numbers in parentheses are electronic energies in kcal mol1 relative to the separated reactants calculated at mPW1K/6-31þG**.

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for 33 showed that the [4 þ 2] cycloaddition TS is 14.6 kcal mol1 (in DG) more stable than the [2 þ 2] TS, and the TS of the [3,3] sigmatropic rearrangement from 34 to 35 is 0.6 kcal mol1 more stable than the first TS. The NMR study was consistent with the mechanism, in which 34 is formed rapidly at the early stage of the reaction and converted to the final product, 35. Recently, Singleton claimed on the basis of close examination of lowtemperature NMR results that the product composition–time dependence was most nicely fit for the mechanism, in which 35 is formed not only by the 33 ! 34 ! 35 route but also directly from 33.87 Computational study with DFT methods (mPW1K and B3LYP), however, did not support the mechanism with concurrent pathways. As is shown in Scheme 8, the mPW1K/6-31þG** PES was consistent with the consecutive mechanism. The B3LYP calculations, on the other hand, suggested slightly different picture, in which the [4 þ 2]-like TS did not give 34 but instead led to an unstable biradicaloid intermediate located in a very shallow well, and this intermediate gives 34 and 35 directly. Thus, the experimental suggestion and PES calculations disagreed to each other. In order to understand the origin of the discrepancy, quasiclassical direct trajectory calculations were carried out.87 The initial TS for each computational theory was used as the starting point, and the atomic positions were randomized using linear sampling for each normal mode. The trajectories were initiated by giving each mode a random sign for its initial velocity, along with an initial energy based on a random Boltzmann sampling of vibrational levels for 273.15 K. The imaginary frequency mode was treated as a translation and given a Boltzmann sampling of translational energy in the forward direction. The results were striking that out of 130 trajectories at mPW1K/6-31G*, 67 gave 35, 4 gave 34, and 56 recrossed the TS. Trajectories at mPW1K/631þG** and B3LYP/6-31G* gave qualitatively the same results. The trajectory calculations revealed that the two products may be formed directly from a single TS. The results were different from the expectation from either mPW1K or B3LYP PES calculations, but were consistent with experimental observations. BECKMANN REARRANGEMENT/FRAGMENTATION

The Beckmann rearrangement is a textbook reaction, in which oximes under acidic conditions give amide via an intramolecular rearrangement. Oximes may give fragmentation products when the R1 group, which is located anti to the leaving group, is stabilized as a cation by an adjacent group [Equation (10)].93

(10)

208 3.0

H. YAMATAKA 6.0

(a)

5.0

R(N-C) /Å

2.5 p-NH2 p-OMe p-Me m,m'-Me2 m-Me H p-Cl p-CHO p-CN p-NO2

2.0

1.5

1.0 0.0

(b)

1.0

2.0

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4.0 RC/amu½ Bohr

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IRC

RT TS 2.0 1.0 1.5

2.0

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4.0

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5.0

5.5

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RN-C /Å

Fig. 4 (a) IRC pathways for 36-X and (b) two-dimensional plots of MD trajectories for 36-H at HF/6-31G*.

MO calculations for the gas-phase reactions of 36-X at HF/6-31G* and MP2/6-31G* revealed that the TS structure varied smoothly from a more product-like to a more reactant-like one when the substituent varied from electron-withdrawing NO2 to electron-donating NH2, in a manner consistent with the Leffler–Hammond principle.94,95 The smooth TS variation itself was suggestive of the same reaction mechanism for all substituted substrates. The Hammett plots derived from relative activation enthalpies gave a linear correlation, which also suggested that the mechanism does not change as a function of substituent. On the other hand, IRC calculations showed that each TS led either to the fragmentation or the rearrangement product region, depending on the electronic nature of the substituent (Fig. 4a). It was clear that the IRC pathway varied with the substituent, from clear rearrangement (p-CHO, p-CN, and p-NO2) to fragmentation (X = p-NH2, p-MeO, p-Me, m,m0 -Me2, m-Me, H, and p-Cl). As a result, despite the fact that the nature of the TS in terms of energy and structure varied smoothly with substituent, the reaction product and hence the reaction mechanism on the PES exhibited a sharp change as a function of the substituent. These findings in turn mean that mechanistic variation is not necessarily accompanied by a sharp difference in reactivity and TS structure, and hence experimentally observable quantities, such as relative reactivities (Hammett equation) and KIEs, which are commonly considered to be useful means to detect a change in reaction mechanism, may not always be useful. Direct MD calculations starting at the TS of each substituted substrate were carried out in order to see how the mechanism changes with substituent.90 Three methods, HONDO, PEACH, and Gaussian (G03), were used, and total 810 trajectories were obtained at the HF/6-31G* level. Three types of productive trajectories were observed: type R leading directly to the rearrangement region, type F leading directly to the fragmentation region, and type R ! F, which initially goes to the rearrangement region and then leads to the fragmentation product.

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It was found that the three MD methods gave qualitatively the same results. Substrates with electron-donating substituents (p-MeO, p-NH2) led to fragmentation region exclusively, whereas those with an electron-withdrawing substituent (p-NO2) gave predominantly rearranged products. For the borderline substrates, however, trajectories from their respective TS gave both fragmentation and rearrangement products directly in such a manner that more F-type trajectories were obtained for a substrate with a more electron-donating substituent. Representative trajectories for 36-H are illustrated in Fig. 4b, in which the abscissa is the N–O atomic distance and the ordinate is the atomic distance between the benzylic carbon and the nitrogen. The observation that the trajectories starting from a TS led to two products indicated that the reaction path bifurcates on the way from the TS to the products, despite that IRC path on the PES is connected to either one of the two products for each borderline substrate. The path bifurcation violates of the TS-based reaction theory. The fact that more F-type trajectories were obtained for 36-X with a more electron-donating substituent was explained by the existence of the barrier separating the two product regions and the shift of the barrier with substituent. Since an electron-donating substituent makes the fragmentation product more stable, the barrier moves toward the rearrangement side, and then more trajectories go to the fragmentation side. The shift of the barrier is consistent with the Thornton rule.96 The product ratio is, thus, governed by the electronic nature of substituents in a manner consistent with traditional electronic theory. As a result, the dynamically controlled substituent effects on the product distribution are readily reconciled with traditional reaction theory, which implies that such path bifurcation phenomenon would not easily be detected by experiment, unless critical examinations of those results are made.

6

Reaction time course and product and energy distributions

SN2 REACTIONS

SN2 reactions of methyl halides with anionic nucleophiles are one of the reactions most frequently studied with computational methods, since they are typical group-transfer reactions whose reaction profiles are simple. Back in 1986, Basilevski and Ryaboy have carried out quantum dynamical calculations for SN2 reactions of X þ CH3Y (X = H, F, OH) with the collinear collision approximation, in which only a pair of vibrations of the three-center system X-CH3-Y were considered as dynamical degrees of freedom and the CH3 fragment was treated as a structureless particle [Equation (11)].30 They observed low efficiency of the gas-phase reactions. The results indicated that the decay rate constants of the reactant complex in the product direction and in the reactant direction did not represent statistical values. This constitutes a

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good early example of dynamically derived selectivity that is much different from what one would expect from statistical theory.

(11)

In 1996, Hase and coworkers reported direct dynamics simulations of the reaction, Cl þ CH3Br, using semi-empirical AM1 theory with two different sets of specific reaction parameters (SRP1 and SRP2).97 The simulations were started at the Cl   CH3Br complex with different initial nonrandom energy distributions and the total energy of 2.7 kcal mol1 plus harmonic ZPE of the complex. Excitation of different internal modes of the complex led to different results. The mode-specific dissociation trajectories were compared with previous results using analytical potential functions.98 The study showed that different PES gave quantitatively different dynamics. Hase and coworkers later carried out a full ab initio MD simulations at HF/3-21 þ G* for SN2 of CH3Cl þ Cl.99 The two reactant species were separated 10 A˚ in the initial state, and relative translational energy of 100 kcal mol1 was added. Trajectories with random initial conditions were generated and the initial Cl   CH3   Cl angle was scanned. Reaction took place by the backside attack, and the Cl–C–Cl angle at the TS increased to 180. It was suggested that extensive CH3Cl vibrational excitation should be needed to access the frontside reaction pathway. The product energy partitioning was also analyzed from the trajectories initiated at the barrier top. Quasiclassical direct dynamics trajectories at the various levels of theory were later calculated to study the central barrier dynamics for the C1 þ CH3Cl, Cl þ C2H5Cl, Cl þ CH3I, F þ CH3Cl, OH þ CH3Cl, and other SN2 reactions.31,32,47,97–108 The effect of initial reaction conditions, such as energy injection, substrate orientations, and the mode of collision, on the fate of the reaction, product, and energy distribution, was analyzed. Some of these trajectory calculations required serious modification in RRKM and TST for SN2 reactions.32,103–105

SN2 REACTIONS IN WATER

SN2 reactions are classified into two types. Type I is the reaction of neutral substrate with charged nucleophile and type II is the reaction of neutral substrate with neutral nucleophile.109,110 In contrast to the cases of type I reactions, the number of computational studies for type II SN2 is limited because the reaction generates an ion pair in the product state and hence it necessarily experiences a strong solvent effect. Therefore, it is a challenge to perform MO as well as MD studies on this type of reactions.

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The methyl chloride hydrolysis [Equation (12)] is a type II SN2 reaction. The attacking species is a water molecule, which loses a proton to a solvent water molecule with the hydroxide ion formally substituting the chloride ion in methyl chloride. Thus, during hydrolysis, bond breaking and bond formation involving both solute and solvent molecules take place. It is essential, therefore, to consider the solvent molecules explicitly in modeling the methyl chloride hydrolysis. This is in contrast to type I SN2 reactions, such as the reaction in Equation (11), in which bond breaking and bond formation occur only in the solute molecules and the solvent molecules do not participate actively in the reaction except as a medium. nH2 O þ CH3 Cl ! HOCH3 þ ðn  1ÞH2 O þ HCl

ð12Þ

Hydrolysis reactions of methyl chloride have been analyzed by with a water cluster model for CH3Cl.100,101 The CH3Cl hydrolysis does not have the TS in the gas phase, and a certain number of water molecules ought to be included in the system. The effect of the number (n) of water molecules on the activation barrier was examined with a cluster model, and it was found that a cluster model with 13 water molecules reproduced nicely the experimental activation energy. The trajectory calculations were carried out from the TS with n = 3. It was demonstrated that nucleophilic H2O attacks CH3 displacing Cl to from CH3OH2þ and proton transfer occurs afterwards to give CH3OH þ H3Oþ þ Cl. Similar trajectory calculations with a cluster model were reported for the SN2 reaction of CH3Cl with Cl.111

OTHER REACTIONS

Trajectory calculations for proton transfer and ionization in water cluster,112–116 isomerization,117 and various types of unimolecular reactions6,118–128 have been carried out, and the analyses on time course of the reaction, product ratio, and product energy distribution were reported.

7

Nonstatistical barrier recrossing

Since an early stage of the history of ab initio MD study, many cases have been observed in which the calculated trajectories do not support expectation derived from traditional reaction theories, such as RRKM and TST, and thus the applicability or suitability of these theories has been a matter of argument. In this section examples of one of those dynamics-derived phenomena are shown, namely nonstatistical barrier recrossing.

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SN2 REACTIONS

For SN2 nucleophilic substitution reactions, TST predicts that crossing the central barrier region of a PES is the rate-controlling step. Previous classical trajectory calculations on analytical PES fitted to HF/6-31G* for SN2 reaction of CH3Cl þ Cl have indicated that a significant amount of central barrier recrossing was observed in the trajectories initialized at the central barrier, which suggested that TST is an incomplete model for calculating the Cl þ CH3Cl SN2 rate constant.129 The authors found two types of recrossings in the trajectories: one was intermediate recrossings in which trajectories stayed near the central barrier and the other was complex recrossings in which trajectories was trapped in the Cl   CH3Cl complex and then returned to the central barrier region. Although RRKM theory predicted extensive dissociation of the Cl   CH3Cl complex to Cl þ CH3Cl and negligible complex recrossings, the trajectory calculations indicated that negligible Cl þ CH3Cl formation and continual complex recrossings occurred on a time scale longer than the complex’s lifetime predicted by RRKM. The disagreement between trajectory calculations and the prediction from the RRKM theory arose from decoupling between the C–Cl stretch mode of CH3Cl and other Cl   CH3Cl intermolecular modes; the former is excited for barrier crossing and the latter is important for complex association/dissociation mode. Quasiclassical direct dynamics trajectories at the MP2/6-31G* level of theory were later calculated by sampling 300 K Boltzmann energy distributions either at the central barrier on the reaction coordinate or at the reactant state.103,105 Again extensive recrossing of the central barrier was observed in the trajectories initiated at the barrier. The dynamics of the Cl   CH3Cl complex was non-RRKM and TST was indicated to be an inaccurate model for calculating the Cl þ CH3Cl SN2 rate constant. The MP2 direct dynamics trajectories further showed that trajectories from the reactant state did not form the Cl   CH3Cl complex. This confirmed the previous trajectory study based on a HF/6-31G* analytic potential energy function,129 in that weak coupling between the Cl   CH3Cl intermolecular and CH3Cl intramolecular modes prevents translation-to-vibration energy transfer. Overall, occurrence of recrossing of the barrier suggested that crossing the central barrier may not be a rate-controlling step, as assumed by statistical theories for many reactions. The MP2/6-31G* direct dynamics simulation study was later extended to cover the dynamics from the central barrier for the SN2 reaction of Cl þ C2H5Cl.104 The majority of the trajectories starting from the saddle point moved off the central barrier to form the Cl   C2H5Cl complex. The results were different from those obtained previously for the CH3Cl reaction, in which extensive recrossing was observed. The reaction of C2H5Cl was, in this sense, consistent with the prediction by the RRKM theory. However, some of the

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trajectories moved directly to products without forming the complex, which is clearly a non-RRKM result. The results for C2H5Cl were strikingly different from for CH3Cl. The origin of the remarkable difference for the two systems was not clear. A possible explanation given by the authors is that the CH3 substituent in the [Cl   CH3CH2   Cl] system enhances IVR through coupling between the CH3 rotation and low-frequency vibrations of the molecules. These interactions suppress central barrier recrossing and promote the formation of a complex after the barrier crossing. The clear different outcome for closely related systems is by itself very interesting, and further study to understand such newly discovered results is strongly desired to deepen and expand our knowledge in mechanistic organic chemistry.

VINILYDENE TO ACETYLENE REARRANGEMENT

The reaction that shows non-RRKM and non-TST reactivity is not limited to SN2, but other types of reactions have been also reported to exhibit nonstatistical behavior. CASSCF(10/10)/6-31þþG** calculations for vinylidene-acetylene rearrangement [Equation (13)] gave the activation barrier of 5.6 kcal mol1 and the reaction energy of –47.9 kcal mol1 in terms of electronic energy. Ab initio MD simulations for this unimolecular rearrangement were carried out at the CASSCF level of theory without ZPE.130 The MD simulations were first carried out for vinylidene anion, and the vinylidene-acetylene rearrangement trajectory calculations were performed for a series of coordinates taken at different times along the anion trajectory. Thus, the starting point was vibrationally excited singlet state of vinylidene, which was formally generated through electron detachment from vinylidene anion. The Born–Oppenheimer trajectories were followed for 1 ps, which was long enough compared to the estimated lifetime of vinylidene of subpicosecond range. It was found, however, that none of the vinylidenes equilibrated at 600 K (slightly below the isomerization barrier) and only 20% of the vinylidenes equilibrated at 1440 K (just above the isomerization barrier) isomerized, suggesting average lifetimes >1 ps for the vibrationally excited vinylidene. Since the anion and neutral vinylidene are structurally similar, and yet vinylidene generated by electron detachment is extremely different geometrically from the isomerization TS, it could live until it has sufficient kinetic energy in the correct vibrational modes. Thus, insufficient orbital rearrangement and IVR would be responsible to the results. Another important point observed from the simulations was that every trajectory that did isomerize violated conventional TST by recrossing back to vinylidene multiple times, even though the isomerization is highly exothermic (47.9 kcal mol1) and hence expected to be irreversible.

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CYCLOADDITION OF CYCLOPENTADIENE AND KETENES

In the course of the study of cycloaddition reaction of cyclopentadiene and ketenes [Equation (14)], Singleton and coworkers carried out ab initio dynamics simulations and observed nonstatistical recrossing of the barrier leading to the adducts.87 The authors argued that, for reactions that involve two bond-forming events in a single barrier-passing step as in reaction 14, one bond might form ahead of the other and a formally concerted reaction might dynamically fail to complete in a single barrier crossing process. It was suggested that such nonstatistical recrossing would become more common in complex reactions than simple reactions. Therefore, the consideration of trajectories would be essential to understanding the mechanism of mechanistically borderline reactions. Further analysis of dynamics effect in this reaction is presented in detail in section ‘‘Path Bifurcation’’.

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8

QM/MM-MD

I would like to summarize this chapter by briefly introducing recent advances in QM/MM methodology. QM/MM-MD is one of the promising methods to examine chemical reactions in solution. It has been used to analyze solvation structure of ions,131–133 solvation dynamics,134,135 and chemical reaction in solution.136,137 The potential mean force (PMF) calculations by using the QM/MM-MD method has been used to obtain free energy change along the reaction coordinate in solution.138–141 TS optimization and minimum energy path calculations on the PES were carried out for a methyl-transfer reaction in water, and PMF calculations along the path were used to obtain the free energy of activation of

MOLECULAR SIMULATIONS OF ORGANIC REACTIONS

215

the reaction.139 Recent development further allows one to locate TS on the free energy surface by using free energy gradient methods.142,143 Dynamics effects, which were described in previous sections, on reaction pathways, concerted-stepwise mechanistic switching, and path bifurcation have in most cases been examined for isolate systems without medium effects. Since energy distribution among vibrational and rotational modes and moment of inertia of reacting subfragment are likely to be modified by environment, it is intriguing to carry out simulations in solution. The difference or similarity in the effect of dynamics in the gas phase and in solution may be clarified in the near future by using QM/MM-MD method. Such study would provide information that is comparable with solution experiment and help us to understand reaction mechanisms in solution.

9

Full quantum MD simulation in water

SN2 REACTION IN WATER

The traditional reaction mechanism in organic chemistry considers that the hydrolyses of CH3 substrates (CH3-X, X = leaving group) proceed via a concerted pathway, in which the CH3-X bond cleavage is facilitated by the H2O– CH3 bond formation. Such a mechanism is intuitively reasonable, since solvent reorganization is believed to be faster than bonding changes in reacting substrates and hence there is enough time for a solvent molecule to react as a nucleophile. However, as is discussed in this chapter, dynamic effects may cause a behavior that differs from what is predicted by the TST and, in particular, a seemingly concerted reaction actually may take place via stepwise processes with bond-cleavage and bond-formation steps occurring successively. Reactions in solution have been analyzed computationally using the QM/ MM method. Although the QM/MM method can treat chemical events in solution at a reasonable computational expense, it has the inherent limitation that nucleophilic participation by solvent molecules cannot be treated by the classical MM scheme. Thus, a full QM method is required to describe the hydrolysis mechanism of CH3 substrates. The fragment molecular orbital (FMO)-MD scheme,144–146 which treats the whole system in a full QM fashion, makes it possible to deal with solution reaction dynamics with a reasonable number of solvent molecules explicitly with the accuracy of the given QM level. FMO-MD simulations at HF/6-31G for reaction 15 were carried out by using a water droplet model, in which CH3-N2þ was located at the center of gravity of a sphere consisting of 156 water molecules.102 The initial structure of CH3-N2þ was taken from the gas-phase optimized structure at HF/6-31G, which was equilibrated in the water droplet with the substrate structure fixed

216

H. YAMATAKA

for 0.5 ps at 300 K and then for 5.0 ps at 1000 K. Fifteen seeds from these 5-ps initial equilibrations were taken, and out of 15 runs at 700 K, 10 trajectories led to the substituted products, CH3-OH2þ þ N2. Although the number of productive trajectories was small, the results showed reasonable diversity together with some common features. The trajectories were classified into three groups: tight SN2, loose SN2, and intermediate types.

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In Fig. 5 the initial water droplet, the time course of the O–C and C–N bond lengths, and the O–C–N angle are shown for two representative trajectories: (a) tight SN2 and (b) loose SN2. Trajectory (a) provided a molecular level picture of how the tight SN2 reaction takes place. The C–N bond cleavage and the C–O bond formation occured concertedly within 100 fs around t = 5.91 ps. The transition point where the two atomic distances became equal occured with a tight structure with the distances of 2.15 A˚ at t = 5.90 ps. The O–C–N angle, which was small and less than 140 before the reaction, rapidly increased when the reaction started to occur, and became 166 at t = 5.91 ps. Thus, the results clearly indicated the synchronicity of the bond-formation–bond-cleavage processes, consistent with the qualitative picture of the enforced SN2 mechanism. Finally, one of the hydrogens (a) 12.0

150.0

8.0

120.0

6.0

2.0

90.0

RC-O

4.0 RC-N

60.0

O-C-N angle (degree)

Distance (A)

180.0

αO-C-N

10.0

αO-C-N

Distance (A)

6.0

150.0

5.0

120.0 RC-O

4.0

90.0

3.0 2.0 1.0 1.8

RC-N 1.9

60.0 2.0

2.1

2.2

2.3

2.4

2.5

2.6

O-C-N angle (degree)

30.0 0.0 1.8 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 180.0 (b) 7.0

30.0 2.7

Ttime (ps)

Fig. 5 Structure of the initial droplet, and time course of bond lengths and angles of two representative trajectories.

MOLECULAR SIMULATIONS OF ORGANIC REACTIONS

217

originally on the attacking H2O molecule started to move to a neighboring H2O when the O–C bond was formed. Trajectory (b) gave basically similar results and shared common features characteristic of concerted SN2 processes as described above. The C–N bond cleavage and the O–C bond formation occurred concertedly within the 150 fs time scale. However, trajectory (b) was different from (a) in that the transition point, where the two atomic distances became equal, was associated with a much looser structure with the distances of 2.68 A˚. It was noticeable that the C–N bond cleavage started to occur without the attacking H2O molecule coming close to the backside of CH3-N2þ. The trajectory indicated that the reaction proceeded via a two-stage concerted process, and the product CH3OH stayed in the protonated form for a longer time. Charge-transfer (CT) interaction energies between the two fragments were plotted against the C–N distance in Fig. 6. The CT interaction increased rapidly when the C–N distance increased to 1.6 A˚ for trajectory (a), whereas for trajectory (b) the CT became large only when RC–N was 2.4 A˚ or longer. Clearly the C–N bond-cleavage and O–C bond-formation events took place in a two-stage fashion in the latter case. Most of other trajectories obtained in this study exhibited intermediate characters between trajectories (a) and (b). An important message was that the chemical reaction does not always proceed through the lowest energy pathway with optimal solvation. In conclusion, the simulations for the first time illustrated how the atoms in reacting molecules behave in solution at the molecular level, which was made possible by using full QM simulations with the recently developed FMO-MD methodology.

CT Energy (kcal/mol)

0.0 –2.0 –4.0 –6.0 –8.0 –10.0 –12.0 1.2

1.4

1.6

1.8

2.0 2.2 RC-N (Å)

2.4

2.6

2.8

3.0

Fig. 6 Charge-transfer interaction energies between attacking H2O and CH3N2þ versus C–N. Open circle is for trajectory (a), and filled triangle for trajectory (b).

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10 Summary and outlook According to traditional interpretation of chemical reactivity, the reaction rate and hence the product selectivity are governed by the energy of the TS and its variation. However, ab initio direct MD simulation studies described in this chapter revealed that this is not universally true and that the organic reactivity theory must consider the effect of dynamics explicitly. In reactions of mechanistic borderline, the reaction pathway may not follow the minimum energy path, but the reaction proceeds via unstable species on the PES. In other cases, the reacting system remains on the IRC but does not become trapped in the potential energy minimum. In some cases, intermediates are formed in reactions that should be concerted, whereas in other reactions a concerted TS gives an intermediate. Thus, the question of concerted versus stepwise appears too simple and the definition of concerted and stepwise reactions becomes unclear. In some reactions, the post-TS dynamics do not follow IRCs, and path bifurcation gives two types of products through a common TS. In all these reactions, dynamics effect can govern the reaction mechanism outside of the realm of TS theory. It is hoped that computational methods outlined in this chapter would serve as a means to facilitate development of a new reaction theory in the next decade.

Acknowledgments The author gratefully acknowledges the financial support from the SFR project of Rikkyo University. The author thanks Prof. Jerry Kresge, to whom this chapter is dedicated, for his pioneering work in the field of physical organic chemistry.

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The principle of nonperfect synchronization: recent developments CLAUDE F. BERNASCONI Department of Chemistry and Biochemistry, University of California, Santa Cruz, CA 95064, USA 1 Introduction 223 Intrinsic barriers 224 Transition state imbalance and the PNS 224 Scope of this chapter 225 2 Proton transfers in solution 226 The effect of resonance on intrinsic barriers and transition state imbalances 226 Why does delocalization lag behind proton transfer? 237 Other factors that affect intrinsic barriers and transition state imbalances 238 3 Proton transfers in the gas phase: ab initio calculations 261 The CH3Y/CH2=Y Systems 261 The NCCH2Y/NCCH=Y Systems 280 Aromatic and anti-aromatic systems 282 4 Other reactions 293 Nucleophilic additions to alkenes 293 Nucleophilic vinylic substitution (SNV) Reactions 298 Nucleophilic substitution of Fischer carbene complexes 303 Reactions involving carbocations 309 Miscellaneous reactions 312 5 Summary and concluding remarks 316 Acknowledgments 319 References 319

1

Introduction

This year marks the 25th anniversary of the principle of nonperfect synchronization (PNS); it was introduced in 19851 as the principle of imperfect synchronization (PIS) but in later papers and reviews2–4 the name was changed due to the awkwardness of the acronym PIS. The foundations of the PNS rest mainly on a marriage between two fundamental concepts of physical organic chemistry, i.e., the concept of intrinsic barriers and that of transition state imbalances.

223 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44005-4

 2010 Elsevier Ltd. All rights reserved

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INTRINSIC BARRIERS

Marcus5–8 taught us that the most appropriate
and useful kinetic measure of chemical reactivity is the intrinsic barrier DG‡o rather than the actual barrier (DG‡), or the intrinsic rate constant (ko) rather than the actual rate constant (k) of a reaction. These terms refer to the barrier (rate constant) in the absence of a thermodynamic driving force (DGo = 0) and can either be determined by interpolation or extrapolation of kinetic data or by applying the Marcus equation.5–8 For example, for solution phase proton transfers from a carbon acid activated by a p-acceptor (Y) to a buffer base, Equation (1), ko may be determined from Br½nsted-type plots of log k1 or Bν + H

C

Y

k1

C

Y– + Bν+1

k–1

(1)

log k–1 versus log K1 (K1 = k1/k–1) by interpolation or extrapolation to K1 = 1,9 while DG‡o can be calculated from ko via the Eyring equation. Or, using the Marcus equation which, in its abbreviated form, is given by Equation (2), allows one to solve for DG‡o for a given set of DG‡ and DGo values.

DG ¼ ‡

DG‡o

  DGo 2 1þ 4DG‡o

ð2Þ

The benefit of determining intrinsic barriers or intrinsic rate constants as measures of chemical reactivity is that they can be used to describe the reactivity of an entire reaction family, irrespective of the thermodynamic driving force of a particular member of that family and to make comparisons between different families. For example, DG‡o or ko determined for the deprotonation of acetylacetone by a series of secondary alicylic amines may be compared with DG‡o or ko for the deprotonation of nitroacetone by the same series of secondary amines. This comparison would provide insights into how the change of one of the pacceptor groups from acetyl to nitro may affect the intrinsic proton-transfer reactivity without regard to how this change may affect the pKa value of the carbon acid. Furthermore, DG‡o or ko for the reaction of acetylacetone with secondary alicyclic amines may be compared to DG‡o or ko for the deprotonation of the same carbon acid by a series of primary amines, leading to insights as to how differences in the solvation characteristics between primary and secondary amines may affect their intrinsic kinetic reactivity. TRANSITION STATE IMBALANCE AND THE PNS

The PNS derives from the realization that the majority of elementary reactions involve more than one concurrent event such as bond formation, bond

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION Product stabilizing factor

Reactant stabilizing factor

Develops late: ko ↓; ΔGo‡ ↑

Lost early: ko ↓; ΔGo‡ ↑

Develops early: ko ↑; ΔGo‡ ↓

Lost late: ko ↑; ΔGo‡ ↓

Product destabilizing factor

Reactant destabilizing factor

Develops late: ko ↑; ΔGo‡ ↓

Lost early: ko ↑; ΔGo‡ ↓

Develops early: ko ↓; ΔGo‡ ↑

Lost late: ko ↓; ΔGo‡ ↑

225

Chart 1

cleavage, solvation/desolvation, transfer and delocalization/localization of charge, etc., and often these processes have made unequal progress at the transition state. When this is the case, the reaction is said to have an imbalanced transition state, a term introduced and popularized by Jencks,10,11 although others before him had recognized this phenomenon in various reactions, especially in E2-eliminations.12–14 The virtue of the PNS is that it establishes a connection between transition state imbalances and intrinsic barriers of reactions. Its original formulation is still valid today; it states that any product stabilizing factor whose development lags behind the main bond changes at the transition state, or any reactant stabilizing factor whose loss at the transition state is ahead of these bond changes, increases the intrinsic barrier or decreases the intrinsic rate constant. For product stabilizing factors that develop ahead of the main bond changes, or reactant stabilizing factors whose loss lags behind the bond changes, the effects are reversed, i.e., there is a decrease in DG‡o or an increase in ko. For product or reactant destabilizing factors the opposite relationships hold. Chart 1 provides a summary of these various manifestations of the PNS. Product or reactant stabilizing factors that have been studied thus far include resonance/charge delocalization, solvation, hyperconjugation, intramolecular hydrogen bonding, aromaticity, inductive, p-donor, polarizability, steric, anomeric, and electrostatic effects, as well as ring strain and soft–soft interactions. Product or reactant destabilization factors are mainly represented by anti-aromaticity, steric effects in some types of reactions, and, occasionally, electrostatic effects. What makes the PNS particularly useful is that it is completely general, mathematically provable,4 and knows no exception.

SCOPE OF THIS CHAPTER

Regarding the scope of this chapter, the main focus is on work published after my detailed 1992 review.4 Older material will only be presented when necessary

226

C.F. BERNASCONI

to put new results into perspective to emphasize important points neglected in earlier reviews or to correlate new data with old results in the form of summary tables or graphs. Proton transfers from carbon acids have continued to play a particularly prominent role in illustrating the multiple manifestations of the PNS and hence their studies constitute a major part of this chapter. This is especially true for ab initio calculations of proton transfers in the gas phase that have been performed after 1992 and have added novel insights into the workings of the PNS. Also new is an important expansion of the list of product stabilizing factors to include aromaticity and, for product destabilizing factors, anti-aromaticity. Other reactions for which a discussion of their structure-reactivity behavior in terms of the PNS has provided valuable insights include nucleophilic addition and substitution reactions on electrophilic alkenes, vinylic compounds, and Fischer carbene complexes; reactions involving carbocations; and some radical reactions. The number of reports on reactions that have been discussed in the context of the PNS or that would benefit from being treated within this framework far exceeds the space available in this chapter. Hence the purpose of this review is not to give a comprehensive account of all such reactions but rather to be selective and focus on those cases that provide genuine insights into the workings of the PNS.

2

Proton transfers in solution

THE EFFECT OF RESONANCE ON INTRINSIC BARRIERS AND TRANSITION STATE IMBALANCES

In contrast to proton transfers between normal acids and bases, which typically have very high intrinsic rate constants that are close to the diffusion-controlled limit15,16 and depend little on the nature of the acid, proton transfers from carbon acids have intrinsic rate constants that vary strongly with structure and are mostly much lower than the diffusion-controlled limit.15,17,18 Table 1 summarizes DG‡o and log ko values for a number of representative examples.4,18–28 The data show a dramatic decrease in ko (increase in DG‡o ) as the p-acceptor strength of the activating groups increases from the top to the bottom of the table. The main reason for the observed trend is that the transition state is imbalanced in the sense that the degree of charge delocalization into the p-acceptor lags behind the proton transfer. This is shown, in exaggerated form, in Equation (3) (for a more nuanced representation of the transition state see below) for a ‡

Bν + H

C

Y

k1

ν+δ B H

δ– C Y

k–1

C

Y– + BHν + 1

(3)

Entry 1

Solvent, Ta

C–H acid CH2(CN)2

H2O, 25C

50% DMSO, 20C

2 H

3

pKCH a

log kob

11.2

7.5

DG‡o kcal mol1

References

7.2

18

9.53

4.58

10.9

19

11.54

4.03

11.7

20

50% DMSO, 20C

4.70

3.90

11.9

4

50% DMSO, 20C

12.62

3.70

12.1

21

50% MeCN, 25C

12.50

3.70

12.1

22

50% DMSO, 20C

6.35

3.13

12.9

22

50% DMSO, 20C

9.12

2.75

13.4

24

H2O, 20C

7.72

2.29

14.0

20

CN

CH3

PhSO2CH2 CH3

OOC

CH3

OOC

CH2

4

5

O2N

6

(CO)5Cr

CH2CN

H2O, 20C

OMe CH3 CO CH2 CO

7 O

8

C

O

CH3CCH2CCH3

PhCCH2

+ N CH3

227

O

9

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

Table 1 Representative intrinsic rate constants (ko) and intrinsic barriers ( DG‡o ) for the deprotonation of carbon acids by secondary alicyclic amines

228

Table 1 (continued ) Entry

C–H acid

10

(CO)5Cr

11

CH3NO2

12

+ Cp*Ru

13

PhCH2NO2

Solvent, Ta

pKCH a

log kob

DG‡o kcal mol1

50% MeCN, 25C

10.40

1.86

14.6

50% DMSO, 20C

11.32

0.73

16.1

25

50% DMSO, 25C

5.90

0.10c

17.2

26

50% DMSO, 25C

7.93

–0.25

17.7

25

22

OMe C CH2Ph

CH2NO2

References

2,4-(NO)2C6H4 CH2

14

50% DMSO, 25C

10.9

–0.55

18.1

27

2,4-(NO)2C6H4

15

CH3NO2

H2O, 20C

10.28

–0.59

17.9

25

16

PhCH2NO2

H2O, 20C

6.77

–1.22

18.7

25

H2O, 25C

2.50

–2.15

20.3

28

CH3

N+ O N

17 NO2 a

50% DMSO = 50% DMSO–50% water (v/v); 50% MeCN = 50% MeCN–50% water (v/v). In units of M1 s1. c Reaction with primary aliphatic amines. b

C.F. BERNASCONI

O 2N

O–

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

229

generalized carbon acid with the p-acceptor Y. Because of the imbalance, the transition state derives only a minimal benefit from the stabilizing effect of charge delocalization into the p-acceptor, and this is the reason why the intrinsic barrier is high. It is as if at the transition state the carbon acid were less acidic than indicated by its pKa. The increase in DG‡o is perhaps even more easily understood when the reaction in the reverse direction (k–1) is considered. Here the reason for the high intrinsic barrier is that most of the resonance stabilization of the carbanion is lost at the transition state, i.e., it costs extra energy to localize the charge on the carbon in reaching the transition state. The increase in DG‡o with increasing acceptor strength thus reflects the increasing cost of localizing the charge and goes hand in hand with an increase in the imbalance. In cases where there is strong solvation of the carbanion, as for example hydrogen bonding solvation of enolate or nitronate ions in hydroxylic solvents, the intrinsic barrier is increased further because the transition state cannot benefit significantly from this solvation. This is the reason why DG‡o for the deprotonation of nitroalkanes in water is particularly high, i.e., much higher than in dipolar aprotic solvents, see, e.g., entry 11 versus 15 and entry 13 versus 16 in Table 1. These solvation effects will be discussed in more detail below. Evidence of imbalance based on Br½nsted coefficients. A. aCH > bB Since the observed trends in the intrinsic barriers can plausibly be explained by assuming that charge delocalization lags behind proton transfer (or charge localization is ahead of proton transfer in the reverse direction), this may be taken as evidence for the existence of imbalance. Nevertheless, independent evidence for the presence of transition state imbalances would be desirable. Such evidence exists in the form of structure-reactivity coefficients such as Br½nsted a and b values and has in fact been known before the connection between imbalance and intrinsic barriers was recognized. For example, assume that one of the groups attached to the carbon is an aryl group with various substituents Z [Equation (4)] and that the transition state is imbalanced in the same way as shown in Equation (3). One may, for a given B , determine a Br½nsted a value designated

‡

Bν

k1 + H

C

Z

Y

ν+δ B H

δ– Y C

C

k–1

(4) Z

Z

Y– + BHν + 1

230

C.F. BERNASCONI

as aCH (CH for carbon acid) by measuring k1 as a function of the acidity constant of the carbon acid as varied by changing Z, and, for a given Z, determine a Br½nsted b value designated as bB by measuring k1 as a function of the basicity of B . As long as B is not a carbanion with its own resonance stabilization, it has generally been assumed that bB is an approximate measure of the degree of proton transfer at the transition state.11,29,30 However, with aCH the situation is different when there is an imbalance, i.e., aCH is not a good measure of proton transfer. Rather, aCH is typically larger than bB. This is because, due to the closer proximity of the charge to the Z-substituent at the transition state compared to that in the product ion, the substituent effect on the transition state is disproportionately large relative to that on the carbanion. This means that the sensitivity of k1 to the substituent Z is disproportionately strong compared to that of is exalted, the acidity of the carbon acid and hence aCH ¼ d log k1 =d log kCH a i.e., aCH > bB. Note that for the Br½nsted coefficients determined in the reverse direction, bC ¼ d log k1 =dpKCH and aBH ¼ d log k  1 =d log KBH a a , the relationship bC < aBH holds. This is a consequence of the equalities aCH þ bC ¼ 1 and bB þ aBH = 1. Table 2 summarizes aCH and bB values for some representative proton transfers where the imbalance leads to aCH > bB;31–39 below we will discuss cases where the imbalance leads to aCH < bB. The best-known and one of the most dramatic examples of an imbalance is provided by the deprotonation of arylnitromethanes by secondary alicyclic amines in aqueous solution (entry 9 in Table 2) where aCH = 1.29 and bB = 0.56.31 In this case the imbalance is so large that aCH is greater than the boundary value of 1.0. This implies that in the reverse direction bC is negative (–0.29) which means that electronwithdrawing substituents enhance not only the rate of deprotonation (k1) but also the rate (k–1) of the protonation of the carbanion. The large magnitude of the imbalance as reflected in the large difference between aCH and bB (aCH – bB = 0.73) is the result of the exceptionally strong p-acceptor strength of the nitro group, coupled with the strong hydrogen bonding solvation of the nitronate ion in aqueous solution. This solvation reduces the need for stabilization of the nitronate ion by the Z-substituent and hence decreases the dependence of the acidity constant on Z. But since the transition state does not significantly benefit from the solvation, the dependence of the rate constant on Z changes little with the solvent and hence aCH becomes larger. We see again the direct connection between imbalance and DG‡o at work, i.e., the exceptionally large imbalance for the nitroalkanes goes hand in hand with the exceptionally high intrinsic barrier (see Table 1). A very large imbalance is also seen for the reaction of ArCH2NO2 with HO (entry 11); even though no bB value could be determined for this reaction to provide an approximate measure of proton transfer at the transition state, the mere fact that aCH > 1 demonstrates the presence of a strong imbalance. The same is true in even more dramatic fashion for the HO-promoted

Entry 1 2

C–H acid

Base

ArCH2CN ArCH2CH(CN)2 O

Solvent, T

aCH

bB

aCH – bB

References

Ar0 CH2NH2 RCOO

DMSO, 25C H2O, 25C

0.74 0.98

0.61 0.83

0.13 0.15

32 33

3

Z

RCOO

H2O, 25C

0.78

0.54

0.24

34

4 5 6 7

ArCH2NO2 ArCH2CH(COMe)COOEt ArCH2NO2 ArCH(CH3)NO2

Ar0 COO RCOO Ar0 COO R2NH

MeCN, 25C H2O, 25C DMSO, 25C H2O, 25C

0.82 0.76 0.92 0.94

0.56 0.44 0.55 0.55

0.26 0.32 0.37 0.39

35 33 36 31

R2NH

50% DMSOa, 25C

0.87

0.45

0.42

37

R2NH Ar0 COO HO

H2O, 25C MeOH, 25C H2O, 25C

1.29 1.31 1.54

0.56 0.50 –

0.73 0.81 large

31 38 31

HO

H2O, 25C

>>1

–

v. large

39

Z

8

CH2

O2N

NO2

NO2

9 10 11

ArCH2NO2 ArCH2NO2 ArCH2NO2 MeO

12

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

Table 2 Br½nsted coefficients and imbalances aCH – bB for the deprotonation of C–H acids by amines and carboxylate ions. Cases where aCH > bB

CH3

H

N+

C

CH3 S

50% DMSO–50% water (v/v).

231

a

232

C.F. BERNASCONI

deprotonation of the 2-benzylthiazolium ion shown as the last entry in Table 2. The authors39 report that with Z = (CH3)3Nþ the rate constant is about 1100values of the two compounds fold higher than with Z = H while the pKCH a differ by less than one half of a log unit, implying an aCH value  4. The reason why aCH is so large in this case must be related to the fact that the negative charge that builds up at the transition state [Equation (5)] is not only delocalized away from the substituent Z but completely disappears in the product, very insensitive to Z. rendering the pKCH a ‡ δ– HO H

OCH3 C

H

δ– OCH3 CH3 C N+

CH3

N+

HO– + Z

S

CH3

CH3

S

Z

(5)

OCH3 CH3

C N Z

S

+ H2O CH3

Coming back to the nitro compounds we note that in several cases the imbalances are not nearly as large as for the reactions of ArCH2NO2 with amines or HO in water. For example, for the reactions of ArCH2NO2 with benzoate ions in DMSO (entry 6) and MeCN (entry 4), the imbalances are much less dramatic than in water and are the result of smaller aCH values. This reduction is due to the strongly reduced solvation of the nitronate ion in dipolar aprotic solvents. There is also a reduction in the imbalance of the reaction of ArCH(CH3)NO2 (entry 7) with amines in water relative to the corresponding reaction of ArCH2NO2 (entry 9). This is again the result of a decrease in aCH and can be explained in terms of reduced charge delocalization into the nitro group of the nitronate ion due to steric hindrance of coplanarity by the methyl group. Evidence of imbalance based on Br½nsted coefficients. B. aCH < bB In all examples listed in Table 2 the lag in the charge delocalization behind proton transfer leads to aCH being greater than bB. There are, however, cases where the opposite is true, i.e., aCH < bB. Representative examples40–43 are reported in Table 3. Does this mean that the imbalance is reversed in these

Entry

C–H acid

B

Solvent, Ta

aCH

bB

aCH – bB

References

R2NH

90% DMSO, 20C

0.46

0.64

–0.18

40

R2NH

50% DMSO, 20C

0.29

0.49

–0.20

41

RND2

5% DMSO, 25C

0.46

0.70

–0.24

42

RNH2

H2O, 25C

0.27

0.55

–0.28

43

NO2

1

Z

CH2CN

2

+ PPh3

H

+ Z S(CH3)2

3

O

4 a

Z

H

PhCCH2

+ N CH2Ar

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

Table 3 Br½nsted coefficients and imbalances aCH – bB for the deprotonation of C–H acids by amines. Cases where aCH < bB

90% DMSO = 90% DMSO–10% water (v/v); 50% DMSO = 50% DMSO–50% water (v/v); 5% DMSO = 5% DMSO–95% D2O (v/v).

233

234

C.F. BERNASCONI

reactions; in other words, is charge delocalization ahead of proton transfer? Closer inspection of the situation illustrated with the example of Equation (6) demonstrates that this is ν +δ B H

CH2CN

δ– CH

NO2

‡ CHCN

CN

NO2

NO2

Bν +

Z

+ BHν + 1

(6)

Z

Z

not the case. The reason why aCH < bB is that here the lag in the charge delocalization creates a situation where it is the charge in the product ion that is closer to the substituent than the developing charge at the transition state; this is opposite to the situation in Equation (4) or all examples of Table 2. This makes aCH disproportionately small and leads to aCH < bB. The last entry in Table 3 is of particular interest because there is potential competition between two p-acceptors stabilizing the product. There is evidence indicating that resonance

O– Ph

C

O + N CH2Ar

CH

Ph

C CH

a

N

CH2Ar

b

structure b is dominant. Hence the reaction can be represented by Equation (7) which shows that at the ‡ O

Ph C

CH2

O

Ph ν +δ B

C H

δ– CH

Ph

O C CH

(7) Bν +

+ BHν + 1 N+

N+

N

CH2Ar

CH2Ar

CH2Ar

transition state the negative charge is far away from the aryl group but moves closer to it in the product, thereby neutralizing the positive charge.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

235

The above interpretation of the imbalance is supported by a comparison of 44 For the aCH values for the deprotonation of 1 and 2 by HO and CO2 3 .  reactions with HO , aCH(1) = 0.59

+ N

ArSO2CH2

+ N

PhSO2CH2

CH3

CH2Ar

2

1

and aCH(2) = 0.33, while for the reactions with CO2 3 , aCH(1) = 0.45 and aCH(2) = 0.29. The aCH(2) values are seen to be quite small for the same reason as in the reaction of Equation (7), i.e., because the product is dominated by a resonance structure that is analogous to that in Equation (7). On the other hand, aCH(1) is larger than aCH(2) because in this case the aryl group is on the other side of the molecule and hence closer to the developing negative charge at the transition state. Other examples of imbalances The determination of Br½nsted coefficients provides the most transparent tool for the evaluation of imbalances, but there are other ways to probe transition structure in search for evidence of transition state imbalances. Terrier et al.45 reported that the change to a more electron-withdrawing Zsubstituent in 3

δ– OMe X

X H

H O2N

C

NO2

Z

O2 N

C

NO2

Z Y

3

δ–

Y 4

increases the rate of deprotonation by MeO more than making X or Y more electron withdrawing, but the change in X or Y enhances the thermodynamic acidity of 3 more than the change in Z. This finding is consistent with the imbalanced transition state 4. Pollack’s group46 has studied the deprotonation of substituent 2-tetralone by HO. Based on a combination of kinetic data and 13C NMR spectra they

236

C.F. BERNASCONI

estimated the charge distributions in the transition state and anion as shown in 5 and 6, respectively. These charges imply a highly imbalanced transition state with a strong lag in the delocalization of the charge into the carbonyl group. –0.45 OH –0.33

H –0.26 –0.29 O –0.03

O

–0.68

–0.08

–0.03

0.09

5

6

Based on secondary kinetic deuterium isotope effects and some ab initio calculations, Alston et al.47 calculated that the transition state in the deprotonation of acetaldehyde by HO is imbalanced in the sense shown in Equation (3). Anslyn’s48 group examined the effect of the phenolic OD group on the deprotonation of 7 by imidazole to form the enolate ion 9. This OD group leads to a significant stabilization of the ‡

D OD

O C

B +

O

O

C

CH3

D O

δ– CH2

O– C

CH2

+ BH+

(8)

H Z 7

Z

B 8

δ+

Z 9

enolate ion 9 due to intramolecular hydrogen bonding, but its effect on the rate of deprotonation is quite small. The authors concluded that intramolecular hydrogen bonding at the transition state (8) is only minimally developed because there is only a small amount of charge on the carbonyl oxygen while most of the charge resides on the carbon. Amyes and Richard49 deduced the presence of a transition state imbalance in the deprotonation of methyl and benzylic mono carbonyl compounds by HO from the linearity of the Br½nsted plot of the rate constants versus the pKa of these carbonyl compounds. They argued that because of the large reactivity range the Br½nsted plot should have shown ‘‘Marcus curvature’’5– 8 if the intrinsic barriers for these reactions were all the same and hence the absence of such curvature indicates changes in the intrinsic barriers. They

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

237

attributed the variations in the intrinsic barriers mainly to the lag in enolate ion resonance development. However, Angelini et al.50 reached somewhat different conclusions regarding the linearity of a similar linear Br½nsted plot which were based on an examination of inductive and steric effects competing with resonance effects. According to their analysis, resonance effects play a minor role while the inductive and steric effects are dominant, a conclusion supported by additional analysis based on kinetic data for the deprotonation of 2-nitrocyclohexanone.

WHY DOES DELOCALIZATION LAG BEHIND PROTON TRANSFER?

In view of the fact that nature always chooses the lowest energy pathway, one may wonder why these reactions do not proceed via a more balanced transition state with more advanced delocalization, which would presumably lower its energy. This question has been discussed at considerable length in our 1992 review4 and hence only an abbreviated version is presented here. The reason why delocalization is not more advanced is that there are constraints imposed on the transition state that prevent extensive delocalization. This was first pointed out by Kresge51 in the context of the deprotonation of nitroalkanes, but it applies to any proton transfer from carbon. The situation is represented in Equation (9) which is a more nuanced version of Equation (3) and allows for a certain degree of charge delocalization into the p-acceptor (d Y) at the transition ‡ ν + δB

Bν + H

C

Y

B

H

–δC

–δ Y

C

Y

C

Y– + BHν + 1

(9)

state. Kresge’s argument is that d Y depends on the C–Y p-bond order as well as on the charge that has been transferred from B (d B) [Equation (10)], while the p-bond order is related to d B [Equation (11)] d Y  pb:o:  d B

ð10Þ

pb:o:  d B

ð11Þ

d Y  ðd B Þ2

ð12Þ

238

C.F. BERNASCONI

since the p-bond is created from the electron pair transferred from the base. Hence d Y is given by Equation (12); it is a small number because it represents only a fraction of a fraction. A more refined picture which takes the charge on the proton-in-flight into consideration will be presented later. However, the basic features and conclusions will remain the same. In other words, because of the constraints embodied by Equations (10–12), delocalization must always lag behind proton transfer or other bond changes in other types of reactions, i.e., there cannot be exceptions. It should be noted that the origins of the imbalance have also been discussed in the context of the valance bond configuration-mixing model proposed by Shaik and Pross.52,53 This model describes the reaction energy profile in terms of the conversion of a reactant configuration (c) into a product configuration (d) and the mixing of a third configuration (e); this latter plays a

Bν: H

C c

Y

Bν + 1 H

C d

Y–

Bν: H+ – :C

Y

e

dominant role in the transition state region. The mixing in of e confers to the transition state its carbanionic character. We prefer the Kresge model because it shows that the imbalanced character of the transition state is enforced by the constraints described by Equations (10–12) whereas the Shaik–Pross model is more a post facto explanation of the imbalance. We shall return to the question of the origin of imbalances in the section on ab initio calculations.

OTHER FACTORS THAT AFFECT INTRINSIC BARRIERS AND TRANSITION STATE IMBALANCES

There are a number of factors that affect intrinsic barriers and/or transition state imbalances. Many of these may be viewed as ‘‘derived’’ effects because they are a consequence of the imbalance caused by the presence of p-receptors, i.e., in the absence of this imbalance they would not affect the intrinsic barriers even if they affect actual barriers and equilibria. Solvation Solvation can have a large effect on intrinsic barriers or intrinsic rate constants, especially hydrogen bonding solvation of nitronate or enolate ions in hydroxylic solvents. Table 4 reports intrinsic rate constants in water and aqueous DMSO for a number of representative examples.19,20,23–25,40,54–56 Entries 1–4 which refer to nitroalkanes show large increases in log ko when

Entry

1 2 3 4 5

CH3NO2 PhCH2CH2NO2 PhSCH2NO2 PhCH2NO2 CH2(COCH3)2

log ko(RCOO)a

log ko(R2NH)a

C–H Acid H2O

50% DMSO– 50% H2O

90% DMSO– 10% H2O

H2O

–0.59 –1.16 1.02 –0.86 2.60

0.73

–0.25 2.75

3.06 2.51 4.08 1.75 3.64

2.97b

3.13

3.85

1.57

1.87

2.75

55

2.51

20

2.29

2.50

4.03

3.95

3.85

20

2.85

2.76

2.54

40

–2.10 2.89

50% DMSO– 50% H2O

90% DMSO– 10% H2O

References

–0.59 3.80

1.88 5.3

25 54 54 25 24

3.18

4.53

23

CO

6

CH2

2.64b

CO

7

PhCOCH2NO2

8

PhCOCH2

9

PhSO2CH2

+ N CH3 + N CH3

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

Table 4 Solvent effects on intrinsic rate constants for the deprotonation of C–H acids by secondary alicyclic amines and carboxylate ions at 20C

NO2 O2N

CH2CN

239

10

240

Table 4 (continued ) Entry

H2O

4.44b

11 H

log ko(RCOO)a

log ko(R2NH)a

C–H Acid

50% DMSO– 50% H2O

90% DMSO– 10% H2O

H2O

50% DMSO– 50% H2O

4.58

4.39

19

3.30

2.98

56

90% DMSO– 10% H2O

References

CN

Cr(CO)3

12 (CO)3Cr a

In units of M1 s1. 10% DMSO–90% H2O (v/v).

C.F. BERNASCONI

b

CH2

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

241

the water content of the solvent is reduced. This implies that hydrogen bonding solvation of the anion leads to particularly large increases in the intrinsic barrier. The reason for the large intrinsic barrier is that solvation of the incipient charge lags behind proton transfer, just as delocalization of the charge into the p-acceptor group lags behind proton transfer. Hence the scheme of Equation (3) may be extended to include solvation as shown in Equation (13). Again, the easiest way ‡ Bν +

H

C

Y

ν+δ B H

δ– C Y

C

Y–

H2O + BHν + 1

(13)

to understand the barrier-enhancing effect is to consider the reaction in the reverse direction. To reach the transition state, energy is required not only to localize the charge on the carbon but also to desolvate the carbanion. In other words, there is a solvational PNS effect that is superimposed on the resonance/ delocalization PNS effect. Entries 5 and 6 refer to diketones. The delocalization of the anionic charge into two carbonyl oxygens in the respective enolate ions reduces the strength of hydrogen bonding solvation relative to that of nitronate ions. This reduces the solvational PNS effect as seen in the less dramatic solvent effect on the log ko values. The same is true for nitroacetophenone (entry 7) where the negative charge is shared between the nitro and the carbonyl group. Entries 8 and 9 involve cationic acids with the main resonance structure of the conjugate base being neutral, e.g., 10b. Hence hydrogen bonding solvation plays a minimal role and there

O– PhC

O CH

N 10a

+

CH3

PhC CH

N

CH3

10b

is no significant solvent dependence of ko. Entries 10–12 also show negligible solvent effects even though the conjugate bases of the respective carbon acids are anionic. In these cases the anionic charge is so highly dispersed that, once again, hydrogen bonding solvation is insignificant. More detailed analysis of the solvent effects on intrinsic rate constants which takes into consideration potential contributions from nonsynchronous solvation/desolvation of the carbon acid itself as well as of the proton acceptors and

242

C.F. BERNASCONI

their conjugate acids have been discussed in our previous review4 and elaborated upon in some subsequent studies.20,55 They involve the determination of solvent transfer activity coefficients and an estimate of the degree of solvational imbalance at the transition state.20,56,57 Even though a somewhat more refined picture emerges from such analysis, the broad qualitative conclusions stated above which focus on the solvation of the carbanions remains the same, at least with amines as the proton acceptor. For reactions involving carboxylate ion proton acceptors, the PNS effect of early desolvation of the carboxylate58 ion can make a significant contribution to the solvent effect on ko. This is illustrated by entries 4–6 of Table 4, which show a significantly larger change in log ko(RCOO) compared to log ko(R2NH). A complementary aspect of solvation is that it affects the magnitude of the transition state imbalance. This can be seen for the reactions of ArCH2NO2 in DMSO and MeCN where the imbalances are much smaller than in water (Table 2, entries 4 and 6). Again we see the connection between imbalance and intrinsic barriers: the greater imbalance induced by solvation leads to an enhanced intrinsic barrier. Polar effect of remote substituents One of the consequences of the imbalanced nature of the transition state is that the polar effect of a remote substituent may either increase or decrease the intrinsic barrier; whether there is an increase or decrease depends on the location of the substituent with respect to the site of charge development. Let us consider a reaction of the type shown in Equation (4). In this situation an electron-withdrawing substituent Z will decrease DG‡o or increase ko. This is because there is a disproportionately strong stabilization of the transition state compared to that of the product anion due to the closer proximity of Z to the charge at the transition state than in the anion. As discussed earlier, this also leads to an exalted Br½nsted aCH value and is the reason why aCH > bB for the deprotonation of carbon acids such as 11–13 and others (Table 2).

CH2NO2

CH2CH(COMe)CO2Et O Z

Z

Z 11

12

13

A different situation exists when the substituent is attached to the Y-group as schematically shown in Equation (14). In this case Z is closer to the negative charge in the anion than at

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

243

(14)

the transition state. Hence it is the carbanion rather than the transition state that receives a disproportionately strong stabilization by an electronwithdrawing substituent. The result is an increase in DG‡o or decrease in ko which translates into a depressed aCH value and is the reason why aCH < bB for the deprotonation of carbon acids such as 14–16 and others (Table 3). Note

that for 16, upon delocalization of the initially formed negative charge, there is neutralization of the positive charge on the pyridinium nitrogen to form a neutral conjugate base, as discussed earlier [Equation (7)]. Polar effect of adjacent substituents In principle, polar substituents directly attached to the carbon, Equation (15), should have a similar effect

(15)

on DG‡o or ko as in the situation described by Equation (4) for remote substituents, i.e., an electron-withdrawing substituent should reduce DG‡o or increase ko. In practice, it is difficult to quantify such effects because in most known examples factors other than the polar effect of Z contribute to changes in ko such as steric crowding, polarizability, hyperconjugation, and charge delocalization into Z. Nevertheless, there are several cases where changes in ko could definitely be attributed to the polar effect of Z. They are summarized in Table 519,20,25,42,43,54,55,66–70 which includes log ko values as well as Taft sF and sR values71 as measures of the polar and resonance effects, respectively, of Z.

244

Table 5 Effect of adjacent polar substituents on intrinsic rate constants Entry

C–H acid

1 H

sR

0.19

0.16

0.54

0.18

4.58b

log ko(RNH2)a

log ko(RCOO)a

References

2.84b

19

3.76b

19

CO2Me

2 H

log ko(R2NH)a

sF

CN

PhCOCH2

+ N CH3

0.29

0.16

2.29c

20

4

PhSO2CH2

+ N CH3

0.59

0.12

4.03c

20

5 6 7 8 9 10 11

CH3NO2 MeO2CCH2NO2 PhCOCH2NO2 CH3CH(NO2)2 HOCH2CH2NO2 PhCH2CH2NO2 PhSCH2NO2

0 0.19 0.29 0.64 0.13 0.04 0.29

0 0.16 0.16 0.16 –0.05 –0.08 –0.05

–0.5c 1.22d 1.57c

25 66 55 67 68 54 54

1.00c

d

–0.59 –1.16d 1.02d

–2.06d –0.13d

C.F. BERNASCONI

3

H

+ SMe2

13

F3CSO2CH2

14

F3CSO2CH2

SO2CF3

In units of M1 s1. In 50% DMSO–50% water (v/v) at 20C. c In water at 20C. d In water at 25C. e In 50% DMSO–50% water (v/v) at 25C. a

b

4.1d

1.01

0.13

42

0.83

0.26

5.0e

0.83

0.26

4.2e

69

70

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

12

245

246

C.F. BERNASCONI

Comparison of entry 2 with entry 1 shows a significant increase in ko that is caused by the greater electron-withdrawing strength of the CN (sF = 0.54) relative to that of the COOMe group (sF = 0.19). The CN group is also a somewhat stronger p-acceptor (sR = 0.18) than the COOMe (sR = 0.16) group which should slightly reduce ko and hence offset some of the increase resulting from the polar effect, i.e., the increase in ko due to the larger polar effect is probably somewhat greater than the observed increase in ko. On the other hand, the large size of the COOMe group could, in principle, lead to a steric reduction of ko for the COOMe derivative relative to the CN derivative. However, it was shown that this is not the case for these reactions which involve primary aliphatic amines as the proton acceptors.41 The change from PhCO (sF = 0.20) to the much more electron-withdrawing PhSO2 group (sF = 0.59) leads to a large increase in ko as seen from entries 3 and 4, respectively. In this case there may be a small contribution to the large difference in the ko value that arises from the stronger p-acceptor effect of the PhCO group (sR = 0.16) relative to that of the PhSO2 group (sR = 0.12) which reduces ko for the PhCO derivative relative to the PhSO2 derivative. In comparing entries 6 and 7 to entry 5 we note a substantial increase in ko when replacing a hydrogen with a COOMe or PhCO group. This implies that the main resonance structures of the corresponding anions are 17a and 18a, respectively, i.e., the COOMe and

CH3O

CH3O C

NO2–

CH

O

17a

O

CH

NO2

17b

O–

O PhC

C –

CH 18a

NO2–

PhC

CH

NO2

18b

PhCO groups act mainly through their polar effects. The somewhat larger ko for the PhCO derivative is consistent with the larger sF value of the PhCO group; the difference in the log ko values of 0.35 actually underestimates the true difference because ko for the PhCO derivative was determined at 20C rather than 25C. The higher intrinsic rate constant for 1,1-dinitroethane (entry 8) compared to that for CH3NO2 is open to two interpretations but both are related to the steric hindrance of the coplanarity of the two nitro groups in the anion. According to the first interpretation one nitro group in the anion is planar

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

247

and exerts its full p-acceptor effect while the second one is largely twisted out of the plane and enhances ko by its polar effect. The second, more likely, possibility is that both nitro groups are somewhat twisted out of plane so that neither exerts its full p-acceptor effect, while both exert their polar effect. For the entries 9–14 the potential polar effects of the respective substituents are either offset or enhanced by other factors such as hyperconjugation or polarizability as discussed in the next sections. Hyperconjugation Despite the fact that the HOCH2 group is mildly electron withdrawing (sF = 0.13), the log ko(R2NH) value for HOCH2CH2NO2 (Table 5, entry 9) does not show the expected increase relative to the respective log ko value for nitromethane (entry 5). This implies the presence of a ko-reducing factor that offsets the expected increase from the polar effect. In view of the higher temperature used for the reaction of HOCH2CH2NO2 (25C) compared to that with CH3NO2 (20C), the presence of a ko-reducing factor is even more compelling. A similar reduction in ko is seen in the deprotonation of PhCH2CH2NO2: even though the PhCH2 group exerts hardly any polar effect, log ko(R2NH) is measurably lower than for CH3NO2 (Table 5, entry 10). The reason for these reductions in ko has been identified as hyperconjugation in the anion (19b, R = OH or Ph).54,68

RCH2CH 19a

+ N

O– O–

H+ RCH

O– CH 19b

N O–

This hyperconjugation contributes to the stability of the respective nitronate ions as reflected in the reduction of the pKa values for HOCH2CH2NO2 (pKa = 9.40) and PhCH2CH2NO2 (pKa = 8.55) relative to CH3NO2 (pKa = 10.29). Inasmuch as hyperconjugation is expected to follow the same pattern as resonance/delocalization, i.e., being poorly developed at the transition state, its PNS effect should lower the intrinsic rate constant, as observed. Perhaps the best-known case of such hyperconjugation at work is seen when comparing pKa values and rate constants of the deprotonation of nitromethane, nitroethane, and 2-nitropropane by HO (Table 6). The pKa values show the increased hyperconjugative stabilization of the nitronate ion by one and two methyl groups, respectively (e.g., 19b, R = H). Since the transition state hardly benefits from hyperconjugation, the rate constants remain essentially unaffected by this factor and are mainly governed by the electron donating effect of the methyl groups which leads to a reduction in kOH.

248

C.F. BERNASCONI

Table 6 Deprotonation of nitroalkanes by HO in water at 25Ca C–H acid

pKCH a

kOH, M1 s1

CH3NO2 CH3CH2NO2 (CH3)2CHNO2

10.22 8.60 7.74

27.6 5.19 0.136

a

From Reference 51.

Interestingly, the fact that the trend in the rate constants is the opposite of that in the acidity constants translates into a negative aCH value of about –0.5 which has been called ‘‘nitroalkane anomaly.’’51 A somewhat similar situation has been observed in the deprotonation of the Fischer carbene complexes 20–24 summarized in Table 7.72,73 There is an increase in acidity in the order 20 < 21 < 22 and 23 < 24 which has been Table 7 Deprotonation of Fischer carbene complexes by HO in 50% MeCN–50% water (v/v) at 25C Entry

pKCH a

Carbene complex OMe

1

(CO)5Cr

C

2

(CO)5Cr

C

3

(CO)5Cr

C

4

(CO)5Cr

CH3 OMe CH2CH3 OMe CH(CH3)2

kaOH (M1 s1)

log ka,b o

1.07

(20)c

12.78

(21)c

12.62

23.4

0.09

(22)c

12.27

10.8

–0.99

(23)d

14.77

37.0

1.36

(24)d

13.41

39.5

0.70

152

O

O

5

(CO)5Cr CH3

a

Statistically corrected for the number of acidic protons.

Estimated based on the simplified Marcus equation log ko  0.5 log KOH with KOH = KCH a /Kw, Kw = 6.46  1016 M2.

b

c

From Reference 72.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

249

attributed to an increasing stabilization of the anions in the order 20 < 21 < 2272 and 23 < 2473 by the methyl groups. This effect reflects the wellOMe (CO)5Cr

OMe

OMe C

(CO)5Cr

C

(CO)5Cr

CH2

C C(CH3)2

CHCH3

20–

21–

22–

O

O

(CO)5Cr

(CO)5Cr 23–

24– CH3

known stabilization of alkenes by methyl or alkyl groups74 and is commonly attributed to hyperconjugation as shown for the example of 21. The rate constants do not show the expected

OMe

OMe (CO)5Cr

C

(CO)5Cr CH

C CH

CH3

21–

CH2H+

21a–

increase with increasing acidity. This translates into a reduction of the intrinsic rate constants which is mainly due to the lag in charge delocalization into the (CO)5Cr group at the transition state (25). This lag not only prevents significant development of the hyperconjugative stabilization, there is also a destabilization of the transition state by the unfavorable interaction between the methyl group and the negative charge on the carbon. OMe (CO)5Cr

C

25

δ– CH

H

δ– OH

CH3

Polarizability The log ko(R2NH) value for PhSCH2NO2 of 1.02 (Table 5, entry 11) is about of 1.6 log units greater than that for CH3NO2 (–0.59) and the pKCH a

250

C.F. BERNASCONI

PhSCH2NO2 (6.67) is about 3.6 units lower than that of CH3NO2 (10.28). It was established that even though most of the increased acidity may be accounted for by the polar effect of the PhS group (sF = 0.29), at best one third or one half of the increase in log ko(R2NH) may be attributed to the polar effect.54 The rest was shown to be the result of a transition state stabilization of the negative charge on carbon by the polarizability effect of sulfur.54 The high intrinsic rate constant for the deprotonation of dimethyl-9fluorenylsulfonium ion (entry 12) has also been attributed to the polarizability of the sulfur atom.42 The same is true for the effect of the trifluoromethylsulfonyl group on the benzyltriflones in entries 13 and 14. The latter group has a very high sF value (0.83) and hence its electron-withdrawing inductive effect certainly contributes significantly to the very high ko values. However, its sR value is also very high (0.26) which implies that the resonance effect may offset a significant fraction of the ko-enhancing inductive effect. Hence, the high ko values strongly suggest a major contribution by the polarizability effect. This conclusion is strongly supported by 1H, 13C, and 19F NMR data as well as solvent effect studies on the kinetic and thermodynamic acidities of various trifluoromethylsulfonyl derivatives from Terrier’s laboratory.69,70,75,76 There is a broader significance to the conclusion regarding the importance of polarizability effects on intrinsic barriers because it also addresses the question whether d–p p bonding or negative hyperconjugation in the anion may play a significant role. The notion that d–p bonding between the carbanion lone pair and the sulfur 3d orbital (e.g., 26) may account for the stabilization of carbanions was promoted by numerous authors,77–82 although

CH3

S

CH –2

CH3

26a

S

CH2

26b

theoretical work later challenged this idea, suggesting the polarizability of sulfur as the main source of stabilization.83–86 A third potential interaction mechanism, negative hyperconjugation (e.g., 27), has also been invoked by several authors,84,86–88 and Wiberg et al.89 as well as Cuevas and Juaristi90 have concluded that this may be the main factor in the stabilization of the dimethylsulfide ion by sulfur.

CH3

S 27a

CH –2

CH3

S

CH 2

27b

If d–p bonding or negative hyperconjugation were to play an important role in the stabilization of the conjugate bases of the dimethyl-9flurorenylsulfonium ion, the benzyltriflones, or thiophenylnitromethane, one

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

251

would expect a reduction in the intrinsic rate constant. This is because these interaction mechanisms belong to the broad category of resonance effects and hence their development at the transition state is expected to lag behind proton transfer and lower the intrinsic rate constant. The large increase in log ko(R2NH) for the deprotonation of PhSCH2NO2 relative to that for CH3NO2 and the unusually high ko values in entries 12–14 indicate that the influence of these factors on ko is negligible compared to the polarizability effect. A further comment regarding the nature of the ko-enhancing effect by a polarizable substituent is in order. It is quite similar to that exerted by the polar effect of an electron-withdrawing group in that it leads to a disproportionately strong stabilization of the transition state due to the closer proximity of the substituent to the site of the incipient negative charge. However, there are some important differences between the two effects that result from the fact that polarizability effects are proportional to the square of the charge91 and drop off very steeply with the 4th power of distance,91 whereas polar effects are simply proportional to the charge and drop off only with the square of the distance.91 The steep drop off with distance may potentially render polarizability effects on intrinsic rate constants more dramatic than polar effects but only when the imbalance is large and proton transfer has made significant progress at the transition state. A more detailed discussion of these points has been presented elsewhere.3,41 Electrostatic effects Electrostatic effects may significantly affect intrinsic barriers or intrinsic rate constants, especially when there is a positive charge directly adjacent to the carbon that gets deprotonated, as exemplified by Equation (16). Keeffe and Kresge92 have shown that a large body of data on the ‡ + N

CH2 28

C

O–

O

O Ph

+ N

δ– CH

C

Ph

+ N

CH

C

Ph + H2O

(16)

H δ– OH

deprotonation of simple aldehydes and ketones by HO in water obey a linear correlation between log(kOH/p) and log ðKCH a =qÞ over a range of 11 pKa units. The points on the correlation may be understood to refer to reactions with equal or at least comparable intrinsic rate constants, while deviating points indicate higher or lower intrinsic rate constants. The point for the reaction of Equation (16)93 shows a positive deviation of almost 3 log units92 which suggests a strongly enhanced intrinsic rate constant. This increase in ko can

252

C.F. BERNASCONI

be attributed to a combination of the PNS effect by the polar effect of the pyridinio group and the electrostatic stabilization of the negative charge at the transition state which is disproportionately strong compared to that of the enolate ion due to its closer proximity to the positive charge. The deprotonation of 29 by HO93 also shows a positive deviation from the Keeffe/Kresge plot but it amounts to only about 1 log unit, as

CH2

Ph C O

N + CH3 29

expected due to the greater distance of the positive charge from the reaction site. In fact, it is not clear whether in this case the entire acceleration might be due to a polar rather than an electrostatic effect. An interesting case is the deprotonation of 30 by HO94 with a rate constant, if placed on the Keeffe/Kresge plot, would deviate positively by about 0.34 log units. The following

‡

HO– +

O

N + CH3

C CH3

N + CH3

O C δ– CH2

N

+ CH3

C

CH2 + H2O

O–

H

30

31

δ– OH

32

interpretation was given. The likely conformation of the transition state is one with the closest distance between the charges as shown in 31, while the same is true for the product 32 except that at the transition state the negative charge mainly resides on the carbon while in the product ion (32) it mainly resides on the oxygen. Hence, even though the distances between the charges are about the same in 31 and 32, to the extent that carbon is much less able to support a negative charge than oxygen, the transition state derives a disproportionately large degree of stabilization from the electrostatic effect of the positive charge compared to the product; the stabilization of the latter by the positive charge is further attenuated by the strong solvation of the anionic oxygen.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

253

The above interpretation is supported by data on the deprotonation of 33 by HO.95 In this situation, it is only the product 35 that benefits from electrostatic stabilization while the ‡ HO– +

+ H2O

δ–

N + CH3

O

N + CH3

H O

33

N + CH3

δ– OH

34

O–

35

negative charge at the transition state 34 is too far for a significant interaction with the positive nitrogen. In the terminology of the PNS this is a case where the product stabilization factor lags behind proton transfer and hence ko should be reduced. This is borne out by the fact that when the rate constant of this reaction is included on the Keeffe/Kresge correlation it shows a negative deviation of 0.85 log units. Whether the entire 0.85 log units deviation should be attributed to this PNS effect is not clear because cyclohexanone also shows a slight negative deviation from the Br½nsted line. p-Donor effects Carbon acids activated by strong p-acceptors that also contain a p-donor capable of interacting with the p-acceptor in a push–pull fashion pose an interesting problem. Fischer carbene complexes such as 20,94 23,97 36,96 37,96 38,98 and 3998 fall into this category. Thermodynamic

OCH3 (CO)5Cr

C CH3 20

OCH3 (CO)5W

C CH3

C

37

SCH3 (CO)5Cr

C CH3

23

C CH3

36

O (CO)5Cr

OCH2CH3 (CO)5Cr

38

SCH3 (CO)5W

C CH3 39

and kinetic data for these carbene complexes are reported in Table 8.96–98 There is a strong correlation between the strength of the p-donor and the pKa

254

Table 8 Acidities of Fischer carbene complexes and intrinsic rate constants for their deprotonation by secondary alicyclic amines, primary aliphatic amines and hydroxide ion in 50% MeCN–50% water (v/v) at 25C pKa

log ko(R2NH)

log ko(RNH2)

log ko(HO)

References

(36)

12.36

3.18

2.72

1.09

96

(20)

12.50

3.70

3.04

1.31

96

(37)

12.98

1.38

96

(23)

14.47

1.51

97

(39)

8.37

2.51

2.50

98

(38)

9.05

2.61

2.09

98

Entry

C

1

(CO)5W

2

(CO)5Cr

C

3

(CO)5Cr

C

4

(CO)5Cr

5

(CO)5W

6

(CO)5Cr

OCH3 CH3 OMe CH3 OCH2CH3 CH3 O

C

SCH3

C

SCH3 CH3

C.F. BERNASCONI

CH3

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

255

values, i.e., the stronger the p-donor, the lower the acidity of the carbene complex. For example, the pKa of 36 is about 4.0 units higher than that of 39 while that of 20 is about 3.5 units higher than that of 38. This reflects the fact that the MeO group is a stronger p-donor (sR = –0.43)71 than the MeS group (sR = –0.15)71 and leads to stronger resonance stabilization (40, 40) of the carbene complex which reduces its

+ XCH3

XCH3 (CO)5M

C 40

(CO)5M CH3

40±

M = Cr or W X = O or S

C CH3

acidity. The cyclic complex 23 is of particular interest with a pKa that is 2 units higher than that of 20. In this case the resonance stabilization of the carbene complex is enhanced by virtue of its cyclic structure in which the oxygen atom is locked into a position for better p-overlap with the carbene carbon.97 53Cr NMR data are in agreement with this interpretation.99 An even greater reduction in acidity is observed for the Me2N derivative, 41 (sR = –0.56)71

NMe2 (CO)5Cr

C CH3 41

which makes it impossible to determine its pKCH in an aqueous environment. a  32.5 was estimated in acetonitrile which is more than 10 However, a pKCH a 22.2 of 20 in the same solvent.100 pKa units higher than the pKCH a The p-donor effect on intrinsic rate constants is more difficult to interpret. For the alkoxy carbene complexes the log ko(HO) values are all about the same within the experimental uncertainty, suggesting that changing p-donor strength has no significant effect on the intrinsic barriers. This seems surprising because one might have expected that the push–pull resonance would follow the same PNS rules as resonance delocalization, i.e., it should lower the intrinsic rate constants due to early loss of the resonance effect at the transition state. The most plausible explanation for the results is that there is another factor that offsets the ko-lowering PNS effect. It has been suggested that this other factor comes from an attenuation of the lag in the carbanionic resonance development by the p-acceptor because the contribution of 40 to the structure of the carbene complex leads to a preorganization of the (CO)5M-moiety

256

C.F. BERNASCONI

toward its electronic configuration in the anion. This preorganization is likely to stabilize the transition state by facilitating the delocalization of the negative charge into the (CO)5M-moiety, i.e., by reducing the degree of imbalance.96–98 Additionally or alternatively, the electrostatic interaction between the partial positive charge on X and the partial negative charge at the carbon of the transition state (42) is expected to stabilize the latter and lower the intrinsic barrier. δ+ XCH3

δ– (CO)5Cr

C

42

δ– CH2

H

Bν + δ

The reduction in the imbalance by preorganizing the carbene complex structure in the manner described above also manifests itself in the Br½nsted aCH and bB values for the deprotonation of phenyl-substituted (benzylmethoxycarbene) pentacarbonyl chromium (43-Z) by amines.101

OCH3 (CO)5Cr

C

δ+ OCH3

δ– Z

(CO)5Cr

C

CH2

δ– Z

(CO)5Cr

CH2

43-Z

43-Z′

C

δ+ OCH3 δ– CH

Z

44-Z H B

δ+

The results are summarized in Table 9. They show that, within experimental error, aCH  bB rather than the expected aCH > bB. It appears, then, that the p-donor effect of the methoxy group masks the true extent of the imbalance by reducing aCH. One way to understand this reduction is to assume that the partial positive charge on the MeO group of the resonance hybrid 43-Z0 is largely maintained at the transition state 44-Z. This means that the stabilizing effect of an electron-withdrawing Z-substituent on the negatively charged carbon at the

Table 9 Reactions of 43-Z with amines in 50% MeCN–50% water (v/v) at 25Ca Reaction 43-H þ R2NH 43-H þ RNH2 a

From Reference 101.

bB

Reaction

aCH

0.48  0.07 0.54  0.04

43-Z þ piperidine 43-Z þ n-BuNH2

0.530.02 0.560.03

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

257

Table 10 Average aCH and bB values for the deprotonation of 45-Z and 46-Z by amines in 50% MeCN–50% water (v/v) at 25Ca Parameter

R2NH 45-Z 0.41 0.55 –0.15 46-Z 0.33 0.45 –0.12

aCH bB aCH – bB aCH bB aCH – bB a

RNH2 0.37 0.73 –0.36 0.33 0.47 –0.14

From Reference 102.

transition state is partially offset by its destabilizing effect on the positively charged oxygen and hence aCH is reduced.102 Supporting evidence for the above explanation comes from the study of the deprotonation of 45-Z and 46-Z by a series of amines.102 Average aCH and bB values are summarized in Table 10.

Z (CO)5Cr

Z

OCH2

S

C

(CO)5Cr

CH3

C CH3

45-Z

46-Z

Taking 45-Z as an example, the reaction can be described by Equation (17). The observation ‡ δ+ OCH2

δ– B + (CO)5W

C CH3

Z

δ– (CO)5W

C

δ+ OCH2 δ– CH2

Z

H

B δ+

45-Z′

(17) Z OCH2 (CO)5W

C

+ BH+

CH2

that aCH < bB is reminiscent of the situation described in Equation (6) and other cases summarized in Table 3. In both situations there is creation of partial negative charge on the carbon at the transition state and in both cases the Z-substituent is located far away from that carbon. In the

258

C.F. BERNASCONI

deprotonation of 2-nitro-4-Z-phenylacetonitrile [Equation (6)], the negative charge moves closer to Z and becomes a full charge in the product ion; in the deprotonation of 45-Z the negative charge also moves closer to Z but here the effect is the neutralization of positive charge on the oxygen. In terms of substituent effects, i.e., aCH versus bB, the outcome is the same in both situations. A further example of an imbalance reduction is seen in the reaction 1benzyl-1-methoxy-2-nitroethylenes (47-Z) with secondary alicyclic amines in 50% DMSO–50% water (v/v).103

OMe

H C

C

O2N

Z CH2

47-Z

47-Z is analogous to 43-Z. The reported Br½nsted coefficients are aCH = 0.84 and bB = 0.47. These values still show a large imbalance (aCH – bB = 0.37) but it is much smaller than that for the deprotonation of phenylnitromethanes (aCH = 1.29, bB = 0.56, aCH – bB = 0.73). Turning to the effect of the heteroatom, the change from MeX = MeO to MeS (36 vs. 39 and 20 vs. 38 in Table 8) leads to a decrease in log ko(R2NH) of 0.67 (M = W) and of 1.09 (M = Cr) log units, respectively, and a decrease in log ko(RNH2) of 0.22 (M = W) and of 0.95 (M = Cr) log units, respectively. Even though weaker, due to the reduced p-donor strength of the MeS group, the two compensating factors discussed for the alkoxy derivatives may still essentially offset each other. This means that the decreases in ko for the sulfur derivatives must be due to other factors. One such factor is early developing steric crowding at the transition state due to the larger size of the sulfur atom. Another is the weaker polar effect of the MeS compared to that of the MeO group which favors the methoxy derivative. Aromaticity The question how aromaticity in a reactant or product might affect intrinsic barriers has only recently received serious attention. Inasmuch as aromaticity is related to resonance one might expect that its development at the transition state should also lag behind proton transfer (or its loss from a reactant would be ahead of proton transfer) and hence lead to an increase in DG‡o , as is the case for resonance/delocalized systems. However, recent studies from our laboratory suggest the opposite behavior. The first such study involved the deprotonation of the cationic rhenium Fischer carbene complexes 48Hþ-X by primary aliphatic amines, secondary

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

259

alicyclic amines, and carboxylate ions in aqueous acetonitrile.104 The conjugate bases, 48-X, represent heterocyclic aromatic X Bν

+ + Cp(NO)(PPh3)Re

X

k1 k–1

Cp(NO)(PPh3)Re

+-O

+ BHν + 1

48-O (X = O) 48-Se (X = Se) 48-S (X = S)

(X = O) 48H 48H+-Se (X = Se) 48H+-S (X = S)

(18) derivatives of furan, selenophene, and thiophene, respectively. The increase in aromaticity along the order 48-O < 48-Se < 48-S105 is reflected in the decreasing pKa values of the respective 48Hþ-X (Table 11). The intrinsic rate constants for proton transfer follow the order ko(X = O) < ko(X = Se) < ko(X = S) for each buffer family (Table 11), i.e., they increase with increasing aromaticity of 48-X. According to the PNS, these results imply that development of the aromatic stabilization of 48-X has made more progress at the transition state than proton transfer. A second system showing similar results is that of Equation (19).108 Table 12 values and intrinsic rate constants for the reactions with summarizes pKCH a primary aliphatic and secondary O–

O k1

Bν + X

+ BHν + 1

k–1

(19)

X 49–-O (X = O) 49–-S (X = S)

49H-O (X = O) 49H-S (X = S)

alicyclic amines in aqueous solution. Again, the stronger aromatic stabilization of the sulfur heterocyclic system is reflected in the greater acidity of 49H-S Table 11 Acidities of rhenium Fischer carbene complexes and intrinsic rate constants for their deprotonation by amines and carboxylate ions in 50% MeCN–50% water (v/v) at 25Ca,b Carbene complex

pKCH a

log ko(R2NH)

log ko(RNH2)

log ko(RCOO)

48Hþ-O 48Hþ-Se 48Hþ-S

5.78 4.18 2.50

–0.46 0.92 1.05

–0.88 0.14 0.27

–0.01 0.72 1.21

a b

ko in units of M1 s1. From Reference 104.

260

C.F. BERNASCONI

Table 12 Acidities of benzofuranone and banzothiophenone and intrinsic rate constants for their deprotonation by amines in water at 25Ca,b C–H Acid

pKCH a

log ko(R2NH)

log ko(RNH2)

49H-O 49H-S

11.72 9.45

1.64 2.64

1.16 1.72

a b

ko in units of M1 s1. From Reference 108.

(pKa = 9.45) compared to that of 49H-O (pKa = 11.72) and again the intrinsic rate constants are greater for the more aromatic system. A third reaction, Equation (20), yielded somewhat ambiguous results stemming from k1

Bν +

O– + BHν + 1

O k–1

X

(20)

X 50–-O

50H-O (X = O) 50H-S (X = S)

(X = O) 50–-S (X = S)

complications due to the p-donor effects of the ring heteroatom (50H-X).109 However, a

O X 50H-X

O–

+ X ± 50H-X

detailed analysis108 revealed that here again the greater aromaticity of the sulfur derivative increases ko relative to that for the oxygen derivative. An interesting situation exists in the deprotonation of the pentacarbonyl(cyclobutenylidene)chromium complexes 51 and 52.110 These complexes are characterized by a strong Me

Ph

(CO)5Cr

NEt2 Me

H 51

(CO)5Cr

NEt2 Me

H 52

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

261

push–pull interaction represented by 53a/53b but their most interesting feature is that their R

R

(CO)5Cr Me

H

+ NEt2

(CO)5Cr

NEt2

Me

R = Me or Ph

53a

H 53b

conjugate bases are derivatives of cyclobutadiene (54) which makes them antiaromatic. This anti-aromaticity is reflected in the very high pKa values determined in acetonitrile and the R Me2N (CO)5Cr

NEt2 Me

54 (R = Me or Ph)

Me2N

P

N

NMe2 + NEt P NMe2

Me2N P2-Et

extremely low calculated gas phase acidities.110 The intrinsic rate constants for the reaction of 51 with the phosphazene base P2-Et111 in acetonitrile suggests that the anti-aromaticity of the anion has an intrinsic barrier-lowering effect, although this conclusion was tentative because ko for this reaction is affected by several other factors. The implication of this result is that the development of anti-aromaticity at the transition state may lag behind proton transfer. Possible reasons why transition state aromaticity is able to develop early while resonance development lags behind proton transfer at the transition state, and why anti-aromaticity lags behind proton transfer, will be discussed in the section on ab initio calculations. These calculations have provided important additional insights because they allow a direct probe of transition state aromaticity or anti-aromaticity.

3

Proton transfers in the gas phase: ab initio calculations

THE CH3Y/CH2=Y SYSTEMS

The computational investigation of identity proton transfers such as Equation (21) in the gas phase has been particularly useful because the barriers of such reactions are the intrinsic barriers and the

262 Y

C.F. BERNASCONI CH3 + CH2

Y–

–Y

CH2 + CH3

(21)

Y

transition state is symmetrical with respect to the proton transfer (50%) which makes it easy to recognize the presence of imbalances. These studies have provided further insights into the PNS that complement those gained from solution phase reactions. The p-acceptor groups Y examined include CH=O,112–116,118 NO2,117,118 NO,118 CH=CH2,114,115,118,119 C N,114,118 þ

þ

CH=NH,118 CH=S,118 CH=OH ,120 and NO2 H.117 The most comprehensive study which also incorporates results form earlier work is that by Bernasconi and Wenzel118; the present discussion is largely based on this paper and on references 113, 117, and 120. A major conclusion is that even though the intrinsic barriers of these gas phase reactions depend on the same factors as solution phase proton transfers such as resonance, polar, and polarizability effects, the relative importance of these factors is quite different in the gas phase, and electrostatic effects involving the proton-in-flight constitute an important additional factor. Evidence of imbalance One of the first questions we113,117,118 and others112,114,117 asked is whether the Y-group induces similar transition state imbalances as observed in solution. Calculation of geometric parameters such as bond lengths and angles as well as group charges indicate that the transition states of these reactions are indeed imbalanced in the sense that charge delocalization into the Y-group lags behind proton transfer. In order to quantify the degree of charge imbalance for a given reaction we developed a formalism based on Equation (22)113; note that in Equation (22) B stands for

–1 + χ – χ C Y

and the full representation of the

transition state is given by 55. Equation (22) represents a further ‡ –1 + δB δH

B– + H

C

Y

B

H

–δC –δY

C

–1 + χ –χ Y + BH C

Y

(22)

refinement of Equation (9) which was a more nuanced version of Equation (3); it not only allows for a certain

–δY –δC

δH

Y

H

C

55

–δC –δY

C

Y

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

263

Table 13 Relative contraction of C–Y bond in the anion and negative charge on Y-group of aniona in the CH3Y/CH2=Y and NCCH2Y/NCCH=Y systems CH3Y/CH2=Yb Y

100  DroCY =rC  Y d

CN C CH CH=CH2 CH=NH(syn) CH=NH(anti) CH=O CH=S NO2 NO þ CH=OHf,g þ NO2 Hf,h

4.10 6.69 6.86 7.11 7.14 7.64 8.94 9.18 10.8 8.26 11.3

Charge on Ye –0.356 –0.587 –0.539 –0.507 –0.548 –0.531 –0.756 –0.854 –0.866 0.086 –0.171

NCCH2Y/NCCH=Yc 100  DroCY =rC  Y d

Charge on Ye

4.63

–0.232

6.16

–0.312

8.64 8.78 10.4 11.9

–0.343 –0.544 –0.654 –0.683

a

MP2/6-311þG(d,p). From Reference 118. c From Reference 140. d % reduction of C–Y bond length upon conversion of CH3Y into CH2=Y. e NPA at MP2/MP2. f Here the conjugate base is neutral. g From Reference 117. h From Reference 114. b

amount of charge delocalization at the transition state (–d Y, Equation (9)) but also takes into account that the negative charge in the anion is not necessarily completely delocalized into the Y-group (–w) and that some positive charge may develop on the proton-in-flight at the transition state (dH). The results summarized in Table 13 indicate that even for the strongest pacceptors, NO2 and NO, the charge on Y in the anion, –w, is somewhat less than –1.0 and substantially less than –1.0 for the weaker p-acceptors. Furthermore, the results reported in Table 14 show that there is in fact a substantial positive charge on the proton-in-flight in the range of 0.3 in all cases. The refinements introduced into Equation (22) require corresponding modifications to Equations (10–12), i.e., Equation (10) becomes Equation (23), Equation (11) becomes Equation (24), and Equation (12) becomes Equation (25). The negative charge d Y  pb:o: ðd B þ dY Þu

ð23Þ

264

Table 14 NPA group charges in the CH3Y/CH2=Y systemsa,b CH3

CH2=Y

Differencec

CH3C N CH3(CH2) C N H (transferred)

0.041 –0.041

–0.644 –0.358

–0.685 –0.315

–0.446 –0.208 0.303

–0.487 –0.165

CH3C CH CH3(CH2) C CH H (transferred)

0.028 –0.028

–0.463 –0.537

–0.491 –0.509

–0.429 –0.219 0.296

–0.457 –0.191

CH3CH=CH2 CH3(CH2) CH=CH2 H (transferred)

0.003 –0.003

–0.461 –0.539

–0.464 –0.536

–0.376 –0.266 0.285

–0.379 –0.263

CH3CH=NH (syn) CH3(CH2) CH=NH H (transferred)

–0.013 0.013

–0.493 –0.507

–0.480 –0.520

–0.398 –0.246 0.293

–0.386 –0.261

CH3CH=NH (anti) CH3(CH2) CH=NH H (transferred)

0.004 –0.004

–0.452 –0.548

–0.456 –0.544

–0.366 –0.281 0.293

–0.370 –0.277

CH3CH=O CH3(CH2) CH=O H (transferred)

–0.021 0.021

–0.469 –0.531

–0.448 –0.522

–0.384 –0.266 0.301

–0.363 –0.287

Group

TS

Differenced

C.F. BERNASCONI

0.021 –0.021

–0.244 –0.756

–0.265 –0.785

–0.233 –0.413 0.291

–0.254 –0.392

CH3NO2 CH3(CH2) NO2 H (transferred)

0.244 –0.244

–0.146 –0.854

–0.390 –0.610

–0.093 (–0.060)g –0.535 (–0.582)g 0.253 (0.286)g

–0.337 (–0.304)g –0.291 (–0.388)g

CH3NO CH3(CH2) NO H (transferred)

0.155 –0.155

–0.134 –0.866

–0.289 –0.711

–0.082 –0.548 0.260

–0.237 –0.393

CH3CH=OHþe CH3(CH2) CH=OHþ H (transferred)

0.149 0.851

–0.086 0.086

–0.235 –0.765

–0.132 0.472 0.320

–0.281 –0.379

CH3NO2Hþf CH3(CH2) NO2Hþ H (transferred)

0.403 0.597

0.171 –0.171

–0.232 –0.768

0.172 0.207 0.240

–0.231 –0.390

a

MP2/6-311þG(d,p).

b

From Reference 118.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

CH3CH=S CH3(CH2) CH=S H (transferred)

Difference between anion and neutral. On the Y-group this difference corresponds to w in Equations (12–14). d Difference between TS and neutral; it corresponds to –d C and –d Y in Equations (12–14), respectively. c

From Reference 120.

f

From Reference 117.

g

CH3 NOþ 2 H/CH2=NO2H system, from Reference 117.

265

e

266

C.F. BERNASCONI

pb:o:  wðd C þ dY Þ

ð24Þ

d Y  wðd C þ d B Þn

ð25Þ

transferred from the base to the CH2Y fragment of the transition state is now d B þ dH which is equal to d C þ dY, while the p-bond order is not only related to the transferred charge but also to the degree of charge delocalization in the anion (w). Furthermore, there is no requirement that the exponents u and v be exactly 1.0 or that n be exactly 2.0; as pointed out by Kresge,51 there may not be a strict proportionality between dY and (dC þ d Y) and hence n = u þ v may be £2 or 2. Note, however, that imbalance in the sense of delayed charge delocalization requires n > 1; this is because such an imbalance implies that the ratio of the charge on Y to the charge on C is smaller at the transition state than in the anion, i.e., dC/dY < w/1– w and this is only possible for n > 1. By the same token, n = 1 would mean that delocalization is synchronous with proton transfer. Note also that Equations (23–25) are not only valid at the transition state but at any point along the reaction coordinate, including the final products where d C þ dY = 1 and hence dY = w. Table 15 summarizes the imbalance parameters n calculated from Equation (26) which is the logarithmic version of Equation (25) solved for n. The n values range from 1.28 to 1.61 in most cases

n¼

log ðdY =wÞ log ðd C þ d Y Þ

ð26Þ

except for CH3C CH where n = 2.26.121 These numbers suggest that in the gas phase the imbalances are relatively small and substantially smaller than those estimated for proton transfers in hydroxylic solvents.3,4 Calculations by Yamataka et al. of the deprotonation of several nitroalkanes by CN122 and 123 also indicate sharply reduced imbalances. For example, the HOðH2 OÞ 2 Br½nsted aCH value for the deprotonation of substituted phenylnitromethanes is ‘‘normal,’’ i.e., < 1; this contrasts with aCH = 1.54 or 1.29 for the deprotonation of substituted phenylnitromethanes in water by HO or piperidine, respectively (Table 2). Furthermore, aCH based on a comparison between CH3NO2 and CH3CH2NO2 is also normal, i.e., aCH > 0122 rather than < 0 (‘‘nitroalkane anomaly,’’ Table 6). These results are not all that surprising in view of the absence of the strong solvational contribution to the imbalance in hydroxylic solvents discussed earlier. Table 15 includes two geometric parameters that provide complementary information about transition state imbalances. They are the % progress of the

CH3Y/CH2=Ya

Y

CN C CH CH=CH2 CH=NH(syn) CH=NH(anti) CH=O CH=O(constr)f CH=S NO2 NO2 (constr)f NO CH=OHþg h NOþ 2H a

NCCH2Y/NCCH=Yb

nc

100  ðDr‡CY =DroCY Þd

100  (Da‡/Dao)e

nc

100  (Dr‡CY =DroCY )d

100  (Da‡/Dao)e

1.51 2.26 1.61 1.58 1.55 1.52 1.10 1.42 1.59 1.33 1.28 1.69 1.42

53.3 34.7 56.3 57.0 61.7 65.2 73.8 64.2 57.7 71.5 70.0 62.8 64.9

21.2 9.0 22.6 25.8 27.6 34.1 100 41.0 26.8 100 44.0 27.6 27.2

1.94

44.1

11.1

2.14

48.4

20.0

1.99

60.2

33.0

1.85 2.06

60.9 56.9

37.7 23.1

1.67

66.1

29.4

From Reference 118. From Reference 140. c From Equation (26). d % Progress of C–Y bond contraction. e % Change in pyramidal angle. f Transition state geometry constrained to be planar with a = 0. g From Reference 120. h From Reference 117.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

Table 15 Imbalance parameter n, progress in C–Y bond contraction and planarization of the a-carbon at the transition state in the CH3Y/CH2=Y and NCCH2Y/NCCH=Y systems

b

267

268

C.F. BERNASCONI

C–Y bond contractions and of the planarization of the a-carbon as measured by the % progress in the change of the pyramidal angle a. The pyramidal angle is defined as shown in 56 where the dashed lines are the projection

C

Y

H H

α

56

of the C–Y bond and the bisector of the HCH group, respectively; note that for a planar molecule or ion (sp2-carbon) a is zero. There is a strong inverse correlation between n and the progress in the planarization as well as the progress in the C–Y bond contraction. The relatively small Da‡/Dao values indicate substantial retention of the sp3 character of the a-carbon that is particularly pronounced for CH3C CH which has the largest n value, but still appreciable for CH3NO and CH3CH=S which have the smallest n values. þ Tables 13–15 include results for the CH3CH=OH/CH2=CHOH and þ

CH3 NO2 H/CH2=NO2H systems; the patterns relating to the C–Y bond contraction, planarization, and charge changes are quite similar to those observed for the respective neutral/anion systems. Regarding the imbalance parameter n, it is still given by Equation (26) because, even though the absolute charges on the various sites are different as shown in the reaction scheme of Equation (27), it is the charge changes during the reaction that determine the imbalance. ‡

B+H

C

+ YH

δB

δH

B

H

–δC 1–δY C

YH

–1 + χ 1 – χ YH + BH+ C

(27)

Additional insights into the reasons for the presence of transition state imbalances have come from the study of the CH3CH=O/CH2=CH–O113 117 and CH3NO2/CH2=NO systems for which the geometries of the transition 2 states were constrained to be planar, i.e., a = 0. The results are included in Table 15. The consequence of these constraints is a reduced n value and greater progress in the C–Y bond contraction. However, as will be discussed later, this greater charge delocalization does not result in a lower barrier but rather in a higher barrier. Similar conclusions were reached by Lee et al.116 and by the Saunders–Shaik group115,119 as discussed in more detail below.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

269

More O’Ferrall–Jencks diagrams Reactions with imbalanced transition states are conveniently described by More O’Ferrall124–Jencks125 diagrams. Such a diagram is shown in Fig. 1 for the deprotonation of a nitroalkane by the general base B which, e.g., could be an amine or HO. In reactions where both the proton donor and acceptor contain the p-acceptor group Y as in Equation (21), there is a two-fold imbalance, one for the lag in the charge delocalization into the p-acceptor of the incipient product ion and one for the advanced localization of the charge from the reactant anion. This two-fold imbalance can be represented by a sixcorner diagram; such a diagram is shown in Fig. 2 for the CH3NO2/CH2= 117 Corners 1 and 4 are the reactants and products, respectively. NO 2 system. Corners 2 and 3 are hypothetical states where the respective nitromethide ions have their charge localized on the a-carbon (57), while corners 5 and 6 are hypothetical states where the nitromethane is polarized in the manner shown in 58.

– CH2

NO2

+ HCH2

57

RCH

H+-transfer

NO–2 + BHν + 1

Delocalization

NO–2

58

Delocalization

H+ Bν + RCH

– NO2

‡

Bν + RCH2NO2

H+-transfer

–

RCHNO2 + BHν + 1

Fig. 1 More O’Ferrall–Jencks diagram for the deprotonation of a nitroalkane. The curved line shows the reaction coordinate with charge delocalization lagging behind proton transfer.

270

C.F. BERNASCONI NO– 2

CH2 CH3

NO2 4C ) t ha c rg du

ne

pro

es

hif

a eth

t (n

m itro

+ HCH2 CH2

ion

6 – NO2 C ha rge NO –

sh

ift

pro

du

g

ar – NO2 Ch 5

2

te

(ni

ate

tro

me

tha

ne

cta

nt)

CH3 CH2

s rge

NO2

2 3 nt) CH – a t c CH2 rea

NO2 NO2

n itro

t (n

hif

rea

ion

NO2

3

TS (optim)

• •

– ct) CH 2 3 CH

Proton transfer

es

TS (constr)

2

na

hi

Proton transfer

CH2 + HCH2

NO–

itro

n ft (

a

1

Ch

NO2

NO2–

Fig. 2 Modified More O’Ferrall–Jencks diagram for the CH3NO2/CH2=NO 2 system. The curved lines represent the reaction coordinates through the optimized and constrained transition state, respectively. The constrained transition state is less imbalanced as indicated by its location to the left of the optimized transition state.

Calculations suggest that corners 5 and 6 are 34.3 kcal mol1 above the level of the reactant/product corners while corners 2 and 3 are about 9.4 kcal mol1 above the reactant/product corners.117 This indicates that the energy surface defined by the diagram exhibits a strong downward tilt from left to right, suggesting that the reaction coordinate and transition state should be located in the right half of the diagram. This is consistent with the observed imbalance according to which charge shift from the nitro group toward the carbon of the reactant nitromethide anion is ahead of proton transfer and the charge shift from the carbon to the nitro group in the incipient product nitromethide anion

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

271

lags behind proton transfer. We also note that the smaller imbalance observed for the reaction through the geometrically constrained (a = 0) transition state (Table 15) requires placement of this transition state to the left of the optimized transition state, but still in the right half of the diagram; this move to the left is also in the direction of increased energy, consistent with the higher energy calculated for the constrained transition state (see below). The features and conclusions from Fig. 2 are very similar to those obtained from a similar diagram for the CH3–CH=O/CH2=CHO system,113 including the left-to-right downward tilt of the surface and the relative placement of TS(optim) and TS(constr) within the right half of the diagram. Valence bond analysis of the imbalance The Shaik–Pross valence bond (VB) configuration-mixing model mentioned earlier has been further developed and applied to Equation (21) with Y = CH=CH2115,119 and CH=O.115 Specifically, the relative importance of the various contributing VB structures to the optimized transition state structure was determined by the self-consistent field valence bond (VBSCF) method and the effect on the energy evaluated. The calculated VB structures are shown in Chart 2. The numbers in parentheses are the relative weights contributed to the transition state structure by each VB structure: the first numbers refer to X = CH2, the second to X = O. These weights were calculated by the ‘‘localized valence bond method’’ (LVB)115; the authors also calculated weights by the

X

CH

CH2

– H :CH2

CH

X

X

– CH CH2: H

φ1 (0.187, 0.151)

X

CH

CH2

H CH2

CH2

CH

X

φ3 (0.187, 0.151)

CH

X:–

–:X

CH

CH2 H

CH2

CH

X

CH

X

φ4 (0.049, 0.118)

φ2 (0.049, 0.118)

X

CH

+ – – CH2: H :CH2

CH

X

φ5 (0.402, 0.540) X

CH

+ – CH2: H CH2

CH

X:–

–:X

CH

φ7 (0.059, 0.102)

φ6 (0.059, 0.102) –:X

CH

+ CH2 H CH2

CH

φ8 (0.006, 0.029)

Chart 2

+ – CH2 H :CH2

X:–

272

C.F. BERNASCONI

‘‘delocalized valence bond method’’ (DVB).115 The main conclusion, irrespective of which method was used, is that the triple ion structure f5 is dominant which is in full agreement with the computational results summarized in Table 14. Why are carbon-to-carbon proton transfers slow? Costentin/Sav eant analysis Applying DFT and QCISD methodology, Costentin and SavO˜ant126 have analyzed Equation (21) with Y=H, CH=CH2, NO2, and CH2=CH–NO2 using a different theoretical framework in order to answer the question: why are carbon-to-carbon proton transfers slow? A major difference in their approach is that their description of the reaction coordinate only requires consideration of the distance, Q, between the two fragments CH2Y and the intramolecular reorganization (i.e., delocalization)127 that occurs during the proton transfer, but not the distance, q, that defines the location of the proton as it moves along the reaction coordinate (Scheme 1). In other words, the dynamics of the reaction is entirely governed by the heavy atom reorganization although tunneling needs to be considered as well. The major conclusions emerging from this analysis are as follows. For the carbon-to-carbon proton transfer, the rate of the reaction depends on the intramolecular reorganization127 and the characteristics of the barrier through which the proton tunnels. The relative slowness of the proton transfer in a non-activated carbon system such as CH4/CH 3 is the result of a larger distance (Q) between the carbon centers compared to that between nitrogen or oxygen in the H2O/HO or NHþ 4 /NH3 systems. In the presence of an electronwithdrawing substituent such as a nitro group, there is an increase in the C– H bond polarity which leads to a decrease in barriers but this decrease is attenuated by the imbalance in the internal reorganization (charge localization-delocalization) which occurs during the proton transfer. The conclusions reached by Costentin and SavO˜ant are in fact quite consistent with our own. The main difference is that, according to these authors, ‘‘the notion of an imbalanced transition state should be placed within the context of charge localization-delocalization heavy-atom intramolecular reorganization rather than of synchronization (or lack thereof) between charge delocalization and proton transfer.’’

Q YCH2

H q

Scheme 1

CH2Y

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

273

Gas phase acidities and reaction barriers Table 16 provides a summary of the enthalpic gas phase acidities (DHo) and enthalpic reaction barriers (DH‡) for the reactions of Equation (21).117,118,120 The table includes data for the CH4/CH 3 reference system. Broadly speaking, the acidities mainly reflect the resonance stabilization of the anion, although the field effect of the Y-group adds significantly to the stabilization of the anion and, for Y = CN, it is the dominant factor. An attempt to quantify the relative contributions of the resonance and field effects as well as the potential role played by the polarizability of the Y-group was made by correlating DDHo = DHo(CH3Y) – DHo(CH4) with the gas phase substituent constants71 sF (field effect), sR (resonance effect), and sa (polarizability effect) according to the Taft128 Equation (28). DDH o ¼ roF sF þ roR sR þ roa sa

ð28Þ

The least squares correlation is shown in Fig. 3 for those systems for which sF, sR, and sa were available; the correlation was excellent (r2 = 0.992) and yielded roF = –43.0, roR = –192.5, and roa = –4.64 (Table 17). The ro values confirm the dominance of the resonance effect for most cases as well as the significant contribution of the field effect. They also suggest that the Table 16 Gas phase acidities of CH3Y and NCCH2Y (DHo) and reaction barriers (DH‡)a Y

H CH=CH2 C CH CH=NH (anti) CH=NH (syn) CN CH=O NO2 NO CH=S CH= OHþ NOþ 2H

CH3Y/CH2=Yb DHo

DH‡

DHo

DH‡

418.1 390.2 385.9 379.8 376.1 375.4 367.2 359.0 351.9 348.7 195.0 192.6

8.1 4.7 1.8 2.9 0.3 –8.5 –0.3 (1.5)d,e –6.2 (9.8)d,f –1.1 0.3 –5.1 –1.0

375.4 354.9

–8.5 –10.6

336.3 335.5 328.3 322.5 322.1

–14.3 –8.4 –16.3 –4.7 –7.0

In kcal mol1. From Reference 118. c From Reference 140. d Geometrically constrained transition state. e From Reference 113. f From Reference 117. a

b

NCCH2Y/ NCCH=Yc

274

C.F. BERNASCONI 430 420

CH4

410

ΔHo, kcal mol–1

400 390

CH3CH = CH2

380 CH3CN

370

CH3CH = O

360

CH3NO2 CH3NO

350 340 0

10

20 30 40 50 60 –43.0σF – 192.5σR – 4.64σα

70

80

Fig. 3 Plot of DHo according to Equation (28) for the acidities of CH3Y. Table 17 Analysis of acidities and barriers by means of Taft equations CH3Y/CH2=Ya

NCCH2Y/NCCH=Yb

DDHo roF roR roa

–43.0 –192.5 –4.64

–41.1 –135 0.54

DDH‡ r‡F r‡R r‡a

–22.6 9.81 7.59

–7.01 36.6 11.9

r

a b

From Reference 118. From Reference 140.

polarizability effect is almost negligible which is perhaps surprising in view of its potential importance for certain gas phase anions.129,130 The small role played by polarizability in the present systems suggests that its effect is greatly diminished when the ionic charge mainly resides on the Y-group rather than the neighboring CH2 group, as is the case for all present anions except for CH2CN. In fact, because the sa values are defined as negative numbers,128

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

275

the slightly negative roa value suggests a small anion destabilizing effect; however, in view of the smallness of the effect, not much significance should be attached to this finding. A possible interpretation of the negative roa value is that it could result from a slight stabilization of the neutral CH3Y. A clearer indication of the absolute and relative contributions of field, resonance, and polarizability effects to the acidity of the various compounds can be obtained by calculating the individual roF sF, roR sR, and roa sa terms for each acid rather than just focusing on the roF , roR , and roa values, respectively. These terms are summarized in Table 18; for the compounds with Y-groups with unknown substituent constants (Y = C CH, CH=NH, and CH=S), these terms were calculated based on approximate substituent constants estimated as described in reference 118. The information in Table 18 is quite revealing. For example, the resonance contribution amounts to about –63 kcal mol1 for CH3CH=S, –50 kcal mol1 for CH3NO, is in the range of –26 to –36 kcal mol1 for CH3CH=CH2, CH3C CH, CH3CH=NH, CH3CH=O, and CH3NO2, and a mere –19 kcal mol1 for CH3CN. On the other hand, the field effect contribution for CH3CN (–26 kcal mol1) is larger than for any of the other compounds except for CH3NO2 (–27 kcal mol1), and for CH3C CH (–6 kcal mol1) and CH3CH=CH2 (–2.6 kcal mol1) it is very small to almost negligible. The polarizability effect, if there is any significance to it at all, is seen to lower the acidities by a mere 2.1–3.4 kcal mol1 for CH3CH=CH2, CH3CN, and CH3CH=O, and even less (1.2 kcal mol1) for CH3NO2 and CH3NO. Turning to the barriers we note that they are defined as the difference in enthalpy between the transition state and the separated reactants. This is important because in gas-phase ion-molecule reactions the transition state is typically preceded by an ion–dipole complex131–133 formed between the reactants, and the term ‘‘barrier’’ is sometimes used for the enthalpy difference between the transition state and the ion–dipole complex. However, these ion– dipole complexes have little relevance to the main topic discussed in this chapter and hence the chosen definition of DH‡ is more appropriate. For reasons explained elsewhere,118 the barriers reported in Table 16 have not been corrected for the basis set superposition error (BSSE),134 although such corrected values are available.118 The barriers for all CH3Y/CH2=Y systems are lower than for the CH4/ CH 3 system. This means that the stabilization of the transition states by the Ygroup is greater than that of the respective anions. The situation is illustrated in Fig. 4 for the case of CH3NO2; it shows that the transition state for the CH3NO2 reaction is more stable than the transition state for the methane  reaction by 73.3 kcal mol1 while CH2=NO 2 is more stable than CH3 by only 1 59.1 kcal mol . The greater stabilization of the transition state compared to that of the anion may be attributed to the fact that, because the proton in flight is positively charged, each CH2Y fragment carries more than half a negative

276 Table 18 Dissection of the contribution of field, resonance, and polarizability effects to DHo and DH‡ in the CH3Y/CH2=Y systemsa CH3Y

sF

sR

sa

DDHo [Equation (28)] roF sF

roR sR

DHo

b

DDH‡ [Equation (29)] r‡F sF,

roa sa

r‡R sR

DH‡

b

r‡a sa

CH4 CH3CH=CH2 CH3CN CH3CH=O CH3NO2 CH3NO

Y-groups with 0 0 0.06 0.16 0.60 0.10 0.31 0.19 0.65 0.18 0.41 0.26

known sF, sR, and sa values 0 0 0 0 –0.50 –2.6 –30.8 2.3 –0.46 –25.8 –19.2 2.1 –0.46 –13.3 –36.6 2.1 –0.26 –27.9 –34.6 1.2 –0.25 –17.6 –50.0 1.2

418.1 390.2 375.4 367.2 359.0 351.9

(418.6) (387.5) (375.7) (370.8) (357.2) (352.1)

0 –1.4 –13.6 –7.0 –14.7 –9.3

0 1.6 1.0 1.9 1.8 2.6

0 –3.8 –3.5 –3.5 –2.0 –1.9

8.05 (8.08) 4.65 (4.50) –8.46 (–7.98) –0.31 (–0.55) –6.15 (–6.81) –1.06 (–0.53)

CH3C CH CH3CH=NH(syn) CH3CH=NH(anti) CH3CH=S

Y-groups with 0.14 0.15 0.27 0.17 0.20 0.17 0.22 0.33

estimated sF, sR, –0.40 –6.0 –0.45 –11.6 –0.40 –8.6 –0.75 –9.5

and sa valuesc –28.9 1.8 –32.7 2.1 –32.7 1.8 –63.5 3.4

385.9 376.1 379.8 347.7

(385.5) (376.4) (379.1) (349.0)

–3.2 –6.1 –4.5 –5.0

1.5 1.7 1.7 3.2

–3.0 –3.4 –3.0 –5.7

1.75 0.30 2.90 0.32

(3.36) (0.28) (2.28) (0.58)

From Reference 118, in kcal mol1. Number in parentheses from correlation according to Equation (28) (DHo) with DDHo = –43.0sF – 192.5sR – 4.60sa or Equation (29) (DH‡) with DDH‡ = –22.6sF – 9.81sR þ 7.59sa, respectively. c sF, sR, and sa estimated as described in Reference 118. a

C.F. BERNASCONI

b

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

(H3C

277

CH3)–

H

8.0 CH4 + CH3–

–59.1

CH2NO2 + CH2

–73.3

–

NO2

–6.2 (O2NCH2

H

CH2NO2)–

 Fig. 4 Stabilization of CH2=NO 2 relative to CH3 and stabilization of the transition reaction relative to the transition state of the CH4/ state of the CH3NO2/CH2=NO 2 CH 3 reaction.

charge (Table 14). This leads to a stronger substituent effect on the transition state than on the anion that results from the interaction of the Y-group with the negative charges. It also provides additional stabilization by electrostatic/ hydrogen bonding effects between the proton in flight and the negative CH2Y fragments.135 This latter effect is consistent with Gronert’s139 findings of an inverse correlation between transition state energy and charge on the transferred proton in identity proton transfers of nonmetal hydrides. The importance of electrostatic/hydrogen bonding effects can also be seen by comparing the barrier of the reactions going through the geometrically constrained transition state with that going through the optimized transition  state for the CH3NO2/CH2=NO 2 and CH3CH=O/CH2=CH–O systems. In the former system the barrier going through TS(constr) is 16.8 kcal mol1 higher than going through TS(optim), while for the CH3CH=O/CH2=CH– O system the difference is 10.5 kcal mol1 (Table 16). Using the VB approach mentioned earlier, Harris et al.119 calculated a 8.2 kcal mol1 higher energy for the delocalized transition state relative to that of the optimized structure in the

278

C.F. BERNASCONI

CH3CH=O/CH2=CH–O system. The higher energy of TS(constr), despite the larger resonance effect, probably results mainly from the fact that the product of the positive charge on the proton-in-flight and the negative charge on the CH2Y fragments is smaller for TS(constr) than for TS(optim) (Table 14) which greatly reduces the electrostatic/hydrogen bonding stabilization. Furthermore, to the extent that more resonance delocalization into the Ygroup occurs, the field effect of Y is reduced. The barriers for the CH3CH=OHþ /CH2=CHOH and CH3 NOþ 2 H/ CH2=NO2H systems fall within the same general range as for the other systems. This seems surprising since the much higher carbon acidities of CH3CH=OHþ and CH3 NOþ 2 H might have been expected to lead to much lower barriers. The most important reason for the higher than expected barriers is likely to be the absence of the stabilizing electrostatic and hydrogen bonding effects found in the CH3Y/CH2=Y systems that arise from the interaction of the positively charged proton-in-flight with the negative CH2 groups and/or the entire CH3Y fragments at the transition state. In the CH3 YHþ /CH2=YH systems, the electrostatic stabilization is not only lost but even replaced by a destabilization since the CH2YH fragments in the transition state are positively charged and this is expected to lead to a substantial increase in the barrier. Further insights were obtained by analyzing the relative contributions of field, resonance, and polarizability effects to the barriers in a similar way as for the acidities, i.e., by correlating DDH‡ = DH‡(CH3Y) – DH‡(CH4) with the respective Taft substituent constants according to Equation (29). The correlation is shown in Fig. 5; it yielded r‡F = –22.6, r‡R = 9.81 and r‡a = 7.59 with DDH ‡ ¼ r‡F sF þ r‡R sR þ r‡a sa

ð29Þ

r2 = 0.995 (Table 17). The r‡ values indicate that the field and polarizability effects lower the barriers while the resonance effect increases the barriers. The individual r‡F sF, r‡R sR, and r‡a sa terms which allow a detailed assessment of the relative contribution of the various effects to the barriers for each system are included in Table 18. The following conclusions emerge. 1. For all systems except CH3CH=CH2 and CH3CH=S, the field effect is dominant and lowers the barrier by substantial amounts (–7.0 to –14.7 kcal mol1). The barrier-lowering effect results from the fact that the transition state stabilization corresponds to roF sF þ r‡F sF, i.e., the field effect on the transition state is (roF þ r‡F )/roF = (–43.0 – 22.6)/ (–43.0) = 1.52-fold stronger than on the anion. 2. The polarizability effect contributes –1.9 to –5.7 kcal mol1 to the lowering of the barrier. For most cases this is a minor contribution compared to that of the field effect; for CH3C CH and CH3CH=S it is comparable to the

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

279

10 CH4

8 6

CH3CH = CH2

ΔH ‡ , kcal mol–1

4 2 0 CH3NO

CH3CH = O

–2 –4 –6

CH3NO2

–8

CH3CN

–10 –5

0

5 10 –22.6σF + 9.81σR + 7.59σα

15

20

Fig. 5 Plot of DH‡ according to Equation (29) for the CH3Y/CH2=Y systems.

field effect while for CH3CH=CH2 it is the dominant factor. The lowering of the barrier by the polarizability effect comes about because the stabilization of the transition state, which is given by roa sa þ r‡a sa, more than offsets the destabilization of the anion ( roa = –4.6, r‡a = 7.59). The fact that the transition states, which have less charge on the Y-group than the anions, are stabilized but that the anions are destabilized (or hardly affected) supports our conclusion mentioned above that the polarizability effect is greatly reduced when the Y-group carries a large negative charge. Because even for the transition states there is a significant charge on the Ygroup, the polarizability effect on their stability is still rather modest. This  contrasts with the reactions of the type ZCH3 þ ZCH 2 ! ZCH2 þ ZCH3 with Z = F, Cl, Br, OH, SH where the polarizability of Z has a strong barrier-reducing effect.130 3. The resonance effect increases the barriers by 1.0 to 3.2 kcal mol1. The reason for this small increase is that the resonance stabilization of the transition state which is given by roR sR þ r‡R sR is only ( roR þ r‡R )/ roR = (–192.5 þ 9.81)/(–192.5) = 0.95 as strong as that of the anion. Note that the rather modest barrier-enhancing effect of resonance is consistent with the rather small transition state imbalances (Table 15).

280

C.F. BERNASCONI

THE NCCH2Y/NCCH=Y SYSTEMS

The reactions of Equation (30) show many similarities with those of Equation (21) but there are also important Y CH2 CNþNCCH ¼ Y Ð Y ¼ CHCNþNCCH2 Y

ð30Þ

differences resulting from the strong electron-withdrawing effect of the cyano group. The specific systems studied include Y = CN, CH=CH2, CH=O, NO2, NO, and CH=S.140 The changes in the C–Y bond lengths that result from the ionization of NCCH2Y are summarized in Table 13. They are very similar to those for the ionization of CH3Y. On the other hand, the anionic charges on the Y-groups of NCCH=Y are significantly smaller than for CH2=Y (Table 13). This is because part of the charge is delocalized into the cyano group; this latter charge varies from –0.175 to –0.267 depending on Y. The transition states for the NCCH2Y/NCCH=Y systems are more imbalanced than those of the respective CH3Y/CH2=Y systems. This is seen both in the geometric parameters and the n values summarized in Table 15. In each case the C–Y contraction and planarization of the a-carbon at the transition state is less advanced than for the respective CH3Y/CH2=Y systems while n is larger, indicating a greater lag in charge delocalization in the NCCH2Y/ NCCH=Y systems. The larger imbalance has been attributed to the strong field effect of the cyano group which, because of its proximity to the a-carbon, strongly stabilizes the negative charge on that carbon. This allows for a greater accumulation of the negative charge on the a-carbon of the transition state in the NCCH2Y/NCCH=Y systems than in the CH3Y/CH2=Y systems. As was observed for the CH3Y/CH2=Y systems, the proton that is being transferred carries a significant positive charge. For the NCCH2Y/ NCCH=Y systems this charge is about 0.30  0.03, slightly larger than the 0.275  0.025 charge for the CH3Y/CH2=Y systems (Table 14). The slightly larger positive charge in the NCCH2Y/NCCH=Y systems may be related to the larger negative charges on the NCCHY fragments and provide greater electrostatic stabilization of the transition state, a point to be elaborated upon when discussing the barriers. The acidities of NCCH2Y and barriers of the NCCH2Y/NCCH=Y systems are summarized in Table 16. As expected, the acidities of NCCH2Y are substantially higher than those of CH3Y since the respective anions are strongly stabilized by the cyano group. The acidifying effect of the cyano group decreases as the p-acceptor strength of the Y-group increases. Analysis of the acidities according to Equation (31) affords roF = –41.1, roR = –135.0, and DDH o ¼ DH o ðNCCH2 YÞ  DH o ðNCCH3 Þ ¼ roF sF þ roR sR þ roa sa

ð31Þ

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

281

roa = 0.54 (Table 17). The roF and roa values are very similar to those observed for CH3Y but roR is substantially smaller compared to that for CH3Y. This means that the presence of the cyano group mainly reduces the resonance contribution of Y to the stabilization of the anion but not the contribution by the field and polarizability effects. The reduced roR value is consistent with the reduced charge on the Y-group (Table 13). Regarding the barriers, the cyano group leads to a substantial reduction in all cases, with the largest effect being on those CH3Y/CH2=Y systems with a relatively high barrier. This barrier reduction indicates that the electronwithdrawing effect of the cyano group stabilizes the transition state to a greater extent than the anion which is consistent with the larger transition state imbalance. This effect is reminiscent of the influence of electronwithdrawing substituents on DG‡o in solution phase reactions discussed in the section on ‘‘Polar effect of adjacent substituents.’’ Of particular interest is a comparison of the relative contributions of field, resonance, and polarizability effects to the barriers for the NCCH2Y/ NCCH=Y systems relative to those for the CH3Y/CH2=Y systems. These relative contributions were obtained from the correlation according to Equation (32) which yields r‡F = –7.01, r‡R = 36.6, and r‡a = 11.9 (Table 17). These

DDH ‡ ¼ DH ‡ ðNCCH2 YÞ  DH ‡ ðNCCH3 Þ ¼ r‡F sF þ r‡R sR þ r‡a sa

ð32Þ

numbers show the same qualitative pattern as for the CH3Y/CH2=Y systems, i.e., the field and polarizability effects lower the barriers while the resonance effect increases the barriers. But there are major quantitative differences. The field effect is much smaller than for the CH3Y/CH2=Y systems. This is because the cyano group takes over much of the role played by the field effect of the Y-groups. The barrier enhancement by the resonance effect is much greater than in the CH3Y/CH2=Y systems. As stated before, a positive r‡R value does not mean that the transition state is destabilized by the resonance effect; it only means that the resonance stabilization of the transition state is weaker than that of the anion. In quantitative terms, transition state resonance stabilization is given by roR sR þ r‡R sR which yields (roR sR þ r‡R sR)/roR sR = (roR þ r‡R )/ roR = (–135 þ 36.6)/(–135) = 0.73 as the fraction of transition state stabilization relative to resonance stabilization of the anion. This compares with (roR þ r‡R )/ roR = 0.95 for the CH3Y/CH2=Y systems. The smaller resonance stabilization of the transition state in the NCCH2Y/NCCH=Y systems is a direct consequence of the larger imbalance.

282

C.F. BERNASCONI

AROMATIC AND ANTI-AROMATIC SYSTEMS

In keeping with the advantages of examining identity reactions, a number of identity proton transfers involving aromatic systems were subjected to ab initio calculations. The first study involved the highly aromatic benzene and cyclopentadienyl systems, Equations (33a) and (34a).141

H

H

H

+

+

+

+

H

(33a)

+

+

+

+

(33b)

+

–

–

+

(34a) H

H

H

+

–

–

+

H

(34b)

Calculations at the MP2/6-311þG(d,p) level showed a significantly lower ‡ DH‡ for the more aromatic C6 Hþ 7 /C6H6 system (Equation (33a), DH = –7.6 1  kcal mol ) compared to the less aromatic C5H6/C5 H5 system (Equation (34a), DH‡ = 2.2 kcal mol1). A substantial lowering of the intrinsic barrier due to aromaticity was also deduced from a comparison between the DH‡ values for the aromatic systems and those for the corresponding noncyclic reference systems, i.e., 33a versus 33b, and 34a versus 34b. The numerical results of these calculations are summarized in Table 19. These results imply a disproportionately large aromaticity development at the transition state,

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

283

Table 19 Barriers (DH‡) of reactions 34a, 34b, 35a, 35b, 36a, and 36b and aromatic stabilization energies (ASE) in the gas phasea System

Equations

C6 Hþ 7 =C6 H6 +

C5 H6 =C5 H 5 –

C4 Hþ 5 =C4 H4 +

ASE (kcal mol1)

DH‡b (kcal mol1)

DDH‡c,d (kcal mol1)

33a 33b

–36.3

–7.6 3.5

–11.1

34a 34b

–29.4

2.2 9.8

–7.6

35a 35b

38.9

3.6 –2.4

6.0

a

At MP2/6-311þG**, Reference 141. Corrected for BSSE. c DDH‡ = DH‡(cyclic) – DH‡(noncyclic). b

i.e., the sum of the aromatic stabilization energies (ASEs) of the two halves of the transition state is greater than the ASEs of the respective aromatic reactant/product. This is illustrated by the schematic energy profiles shown in Fig. 6 for reactions 33a/33b (a) and 34a/34b (b), respectively. The arrows pointing down represent the aromatic stabilization energies of the reactants (ASER), products (ASEP), and the transition state (ASETS), respectively. The greater than 50% aromaticity in both halves of the transition state is reflected in the fact that |ASETS| > |ASER| = |ASEP|. The conclusions based on energy calculations are supported by the calculation of aromaticity indices such as HOMA142,143 and NICS(1)144,145 values as well as the pyramidal angle of the transition state. The pyramidal angle, a, is defined as illustrated for the benzenium ion (59) and the transition state (60) for reaction 33a (B = benzene); this angle is 0 in the aromatic species.

B H

H α α

α H

H 59

60

The various indices are summarized in Table 20; they show that the change in these indices in going from reactants to the transition state is significantly greater than 50%.

284

C.F. BERNASCONI

(A)

+

+

+

+

ASEP

ASER HH

HH

ASETS +

+

+

+

(B) –

+

–

+

HH

HH +

–

ASER

ASETS

ASEP

–

+

(C) HH +

ASER +

+

HH

STRAIN

+

+

+

ASEP ASETS

+

+

Fig. 6 Reaction energy profile for reactions 34a/34b (A), 35a/35b (B), and 36a/36b (C). (A) and (B): Aromatic stabilization of the transition state is greater than that of benzene or cyclopentadienyl anion, respectively. (C): Anti-aromatic destabilization (positive ASE) of the transition state is less than that of cyclobutadiene; the high barrier results from the additional contribution by angular and torsional strain at the transition state.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

285

Table 20 Aromaticity indices for the reactions of Equations (34a), (35a), and (36a)a HOMA C6 Hþ 7 TS C6H6 % Progress at TSb C5H6 TS C5 H 5 % Progress at TSb C4 Hþ 5 TS C4H4 % Progress at TSb a b

NICS(1)

Equation (34a) 0.415 0.874 0.963 83.8 Equation (35a) –0.791 0.560 0.739 88.3 Equation (36a) –0.99 –0.156 –3.55 22.3

–6.05 –9.26 –10.20 77.3 –0.517 –8.33 –9.36 75.4 –13.69 –12.64 18.11 3.30

a 50.1 11.5 0.0 71.0 53.5 21.9 0.0 59.0 60.5 52.2 0.0 13.7

At MP2/6-311þG**, Reference 141. [Index(TS) – Index(Reactant)]/[Index(Product) – Index(Reactant)]  100.

A reaction of particular interest is that of Equation (35a) because it involves an anti-aromatic system. The barriers for Equation (35a) and its noncyclic reference system [Equation (35b)] are included in H

H

+

+

H +

+

H +

(35a)

+

+

+

(35b)

Table 19 while the corresponding aromaticity indices are included in Table 20. The HOMA, NICS(1), and a values all indicate a very small degree of antiaromaticity development at the transition state.146 Since the transition states for Equations (33a) and (34a) are able to benefit from the stabilization conferred by the strong development of aromaticity it seems reasonable that in Equation (35a) the transition state should be able to avoid much of the destabilization that arises from anti-aromaticity, i.e., keeping the development of anti-aromaticity lagging behind proton transfer. Hence, according to the PNS, the barrier should be lowered by this effect. However, DH‡ for Equation

286

C.F. BERNASCONI

(35a) was calculated to be higher than for Equation (35b) (Table 19) which seems inconsistent with the above conclusions unless the barrier-lowering PNS effect is masked and overshadowed by other factors. As discussed in more detail elsewhere,141 angle and torsional strains at the transition state are in fact believed to be responsible for the higher than expected barrier, i.e., in the absence of these strains the barrier would indeed be lower than for Equation (35b). This is illustrated in Fig. 6, part (C). Another study involved the identity reactions shown in Equation (36).147 Calculations at the O–

O

O–

+

O

+

(36) X

X

X

X

61H-O (X = O)

61–-O (X = O)

61–-O (X = O)

61H-O (X = O)

61H-S (X = S)

61–-S

61–-S

61H-S (X = S)

(X = S)

(X = S)

MP2/6-31þG** level yielded a DH‡ for X = S that is lower than for X = O. It was also found that DH‡ for the reactions of Equation (36) was lower than for the corresponding noncyclic reference systems of Equation (37). The results are summarized in Table 21. Furthermore, the intrinsic barrier for O–

O CH2

CH

C

CH2XCH3 + CH2

CH

C

62H-O (X = O)

62–-O (X = O)

62H-S (X = S)

62–-S (X = S)

CHXCH3

(37) O– CH2 62–-O

CH

(X = O) 62–-S (X = S)

C

O CHXCH3 + CH2

CH

C

CH2XCH3

62H-O (X = O) 62H-S (X = S)

the deprotonation of 61H-S by CN is lower than for the deprotonation of 61H-O by the same base. All these results indicate that aromaticity lowers the intrinsic barrier and increasingly so with increasing aromaticity. Further evidence showing disproportionately high transition state aromaticity comes form NICS values,144,145 Bird indices,148,149 and HOMA142,143

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

287

Table 21 Barriers of reactions 37 and 38 in the gas phasea System

DH‡ (kcal mol1)

DDH‡b (kcal mol1)

3.6 5.4 2.3 4.3

–1.8

61H-O/61-O 62H-O/62-O 61H-S/61-S 62H-S/62-S a b

–2.0

At MP2/6-31þG**, Reference 147. DDH‡ = DH‡(cyclic) – DH‡(noncyclic).

Table 22 Aromaticity indices for the identity proton transfers of Equation (36)a Species

HOMA

Bird index

NICS(–1)

61H-O TS 61-O % Progress at TSb 61H-S TS 61-S % Progress at TSb

–0.686 0.217 0.544 73.4 –0.854 0.231 0.566 76.4

22.68 36.65 40.28 80.0 31.31 53.19 64.20 66.5

–2.47 –5.46 –6.74 69.9 –2.45 –5.37 –7.33 59.8

a b

At MP2/6-31þG**, Reference 147. [Index(TS) – Index(Reactant)]/[Index(Product) – Index(Reactant)]  100.

values as indicators of aromaticity. These aromaticity indices are summarized in Table 22 for the identity reactions [Equation (36)]. As was the case for reactions 33a and 34a, the progress in the development of aromaticity at the transition state is greater than 50%. NICS, HOMA, and Bird indices were also calculated for the transition states of the reactions of 61H-O and 61H-S with a series of carbanions. The results are reported in Table 23. The trends in these parameters show a clear increase as the transition state becomes more product-like with increasing endothermicity, indicating an increase in transition state aromaticity. Even more revealing is the % progress at the transition state which indicates that this progress is >50% not only for the endothermic reactions (product-like transition states) but even for most of the exothermic reactions (reactant-like transition states) except those with strongly negative DHo values. Additional confirmation of early development of aromaticity as the reaction progresses comes from plots of NICS values and Bird indices versus the reaction coordinate for the reaction of 61H-S with CH2 NO (Figs. 7 and 8), and of 61H-O with CH2 NO2 (figures not shown). These reactions were chosen

288

Table 23 Transition state aromaticity indices for the reactions of 61H-O and 61H-S with carbanions in the gas phasea % progress at TS 1

o

DH (kcal mol )

HOMA

Bird index

NICS(–1)

HOMA

Bird index

61H-Ob  CH2CN  CH2CO2H  CH2COCH3  CH2CHO  CH2NO2 CH3 CHNO2  CH(CN)2

–19.8 –14.3 –13.0 –10.4 –1.2 –0.9 19.8

–0.097 0.083 0.105 0.132 0.115 0.126 0.245

28.99 32.58 32.81 34.04 33.34 34.04 33.89

–3.98 –4.70 –4.64 –4.99 –4.92 –4.76 –5.04

47.9 62.6 64.4 66.6 65.2 66.1 75.8

–0.097 0.083 57.6 64.6 60.6 64.6 63.7

33.3 52.1 50.7 59.0 57.3 53.5 60.2

61H-Sc CH2CN  CH2CHO  CH2NO2  CH2NO  CH2CHS  CH(CN)2  CH(NO2)2

–26.5 –17.1 –7.9 –0.3 1.3 13.1 24.7

–0.188 0.062 0.082 0.248 0.196 0.l36 0.236

42.66 48.19 48.91 54.17 53.79 51.31 53.08

–3.71 –4.69 –4.92 –5.43 –5.55 –5.03 –5.42

46.3 64.5 65.9 77.6 71.2 73.9 76.7

33.9 51.3 53.5 69.5 68.3 60.8 66.2

25.9 46.0 50.7 61.0 63.6 52.9 60.8

RCHY



At MP2/6-31þG**, Reference 147. 61H-O/61-O: HOMA – 0.686/0.544, Bird index 22.68/40.28, NICS(–1) – 2.47/–6.74. c 61H-S/61-S: HOMA – 0.854/0.566, Bird index 31.31/64.20, NICS(–1) – 2.45/–7.33. b

C.F. BERNASCONI

a

NICS(–1)

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

289

0 NICS(0)

–2

NICS(–1)

NICS value

–4

–6

–8

–10

–12 –2.0

–1.5 –1.0 –0.5

0.0

0.5

1.0

1.5

2.0

2.5

Reaction coordinate (amu½ Bohr)

Fig. 7 Plots of NICS(0) and NICS(–1) versus IRC for the reaction of 61H-S with CH2 NO.

70 65

Bird Index

60 55 40 35 30 25 20 –2.0

–1.5

–1.0

–0.5

0.0

0.5

1.0

1.5

2.0

2.5

Reaction coordinate (amu½ Bohr)

Fig. 8 Plot of the Bird index versus IRC for the reaction of 61H-S with –CH2NO.

290

C.F. BERNASCONI

because they are nearly thermoneutral (see Table 23) and have fairly symmetrical transition states as indicated by the C- --H- --B bond lengths.147 The plots show a steep rise in aromaticity as a function of the reaction coordinate as the transition state is reached and a pronounced leveling off toward the value of the anionic product once the transition state has been traversed. As indicated in Table 23, the % progress in the development of product aromaticity at the transition state of the reaction of 61H-O with CH2 NO2 is 57.3 for NICS(–1) and 60.6 for the Bird index, while for the reaction of 61H-S with CH2 NO these percentages are 61.0 and 69.5, respectively. Decoupling of aromaticity development from charge delocalization In solution phase reactions such as Equation (1) as well as in the gas phase reactions of Equation (21) charge delocalization always lags behind proton transfer at the transition state. For the solution phase reactions this feature not only manifests itself in enhanced intrinsic barriers but also in the Br½nsted coefficients. For the gas phase reactions this lag can be deduced from calculated NPA charges. An interesting question is whether in systems such as Equation (33a), (34a), or (36) the early development of aromaticity would induce charge delocalization to do the same rather than to follow the typical pattern of delayed charge delocalization found in non-aromatic systems. NPA charges for some representative systems are shown in Chart 3. They indicate that negative charge is being created at the reaction site of the transition state  which then either disappears (C6 Hþ 7 /C6H6 system) or decreases (C5H6/C5 H5 system) due to delocalization in the product. This implies that, in terms of

H

H

0.095

H

0.905

H

0.001

Chart 3

H –0.001

0.428 H –0.154

0.440

0.000

0.000 0.376 H

–0.200

H –0.275

–0.413

–0.800

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

291

charge delocalization, the transition state is imbalanced in the same way as in non-aromatic systems, i.e., development of aromaticity and charge delocalization are decoupled. Comparisons with aromatic transition states in other reactions Aromaticity in transition states is a well-known phenomenon, especially in pericyclic reactions, as recognized more than half a century ago.150–152 A prototypical example is the Diels–Alder reaction of ethylene þ 1,3-butadiene ! cyclohexene; a computational study by the Schleyer group153 has shown that the absolute value of the diamagnetic susceptibility, which is a measure of aromaticity, goes through a maximum at the transition state. Similar situations have been reported for other Diels–Alder reactions,154 for 1,3-dipolar cycloadditions,155 and enediyne cyclizations,156 where the aromaticity of reactants, products, and transition states was evaluated using NICS values. A recent report regarding transition state aromaticity in double group transfer reactions such as the concerted transfer of two hydrogen atoms from ethane to ethylene is also worth mentioning.157 For many additional examples and references, the review by Chen et al.145 should be consulted. It is important to note, though, that for these reactions the situation is quite different from that in Equations (33a), (34a), and (36). In pericyclic reactions aromaticity is mainly a special characteristic of the transition state whereas the reactants and products are not aromatic or less so than the transition state. This is quite different from the proton-transfer reactions discussed in this chapter where the aromaticity of the transition state is directly related to that of the reactants/products. An analogy with steric effects on reaction barriers may illustrate the point. In a reaction of the type of Equation (38), steric effects at the transition state will definitely increase the intrinsic A þ BÐC þ D

ð38Þ

barrier if the reactants are bulky. However, because there are no steric effects on the reactants or products, the concept of early or late development does not apply here, and the same is true for the aromaticity of the Diels–Alder transition state. In contrast, in a reaction of the type of Equation (39) there is steric crowding both in the product and the transition state. In this case, the intrinsic A þ BÐAB

ð39Þ

barrier will be enhanced if steric crowding has made disproportionately large progress relative to bond formation at the transition state, as is the case for

292

C.F. BERNASCONI

nucleophilic addition to alkenes discussed in a later section; on the other hand, DG‡o will be reduced if development of the steric effect is disproportionately small. This, then, is akin to early or late development of transition state aromaticity or anti-aromaticity in our reactions.

Aromaticity versus resonance Why does aromaticity and resonance affect intrinsic barriers differently? The lowering of the barrier by providing the transition state with excess aromatic stabilization appears to be in keeping with Nature’s principle of always choosing the lowest energy path. The fact that the transition states are able to be so highly aromatic suggests that only relatively minor progress in the creation of appropriate orbitals or the establishment of their optimal alignment and distances from each other may be required for aromatic stabilization to become effective. There are several precedents that support this notion. For example, the NICS value of KekulO˜ benzene (rCC fixed at 1.350 e´ and 1.449 e´) is only 0.8 ppm less than the NICS value for benzene itself or, with rCC = 1.33 e´ (ethylene-like) and 1.54 (ethane-like), the NICS value is only 2.6 ppm less than that for benzene.145,158 Or the NICS value for 63 (–8.1 ppm)159 is quite close to that of benzene (–9.7 ppm)145,158 even though there is strong bending of the benzene ring. Other relevant observations have been discussed elsewhere.141

CN

NC

CN

NC

63

In contrast, in reactions that lead to resonance stabilized/delocalized products such as Equation (1) or (21), the transition state is not able to maximize the potentially stabilizing effect of extensive charge delocalization. As discussed in the section ‘‘Why does delocalization lag behind proton transfer,’’ this is because delocalization can only occur if there is significant C–Y p-bond formation. Hence, the fraction of charge on Y at the transition state depends on the fraction of p-bond formation which in turn depends on the fraction of charge transferred from the base to the carbon acid. This imposes an insurmountable constraint on the transition state because the charge on Y can never be large since it is a fraction of a fraction [Equations (12) and (25)].

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

4

293

Other reactions

NUCLEOPHILIC ADDITIONS TO ALKENES

Reactions of the type of Equation (40) with nucleophiles such as HO, water, aryloxide ions, thiolate

Y Nuν +

C

C

Y–

k1 k–1

C

C

(40)

Nuν + 1

ions, and amines follow similar patterns as proton transfers of the type of Equation (1). This is not surprising since delocalization of the negative charge into the Y-group plays a similar role as in Equation (1). Most of the systematic kinetic studies of these reactions were published before 1992 and thus have been reviewed in detail in our 1992 chapter.4 Hence, only a brief summary, based on Reference 4, of the major features is given here. The main conclusions can be summarized as follows. Correlation with proton transfers There is a strong correlation between the intrinsic rate constants of reactions 40 with those of reactions 1. For example, a plot of log ko for the reactions of piperidine and morpholine with PhCH=C(CN)2, PhCH=C(COO)2C(CH3)2, PhCH=C(CN)C6H4-4-NO2, PhCH=C(CN)C6H3-2,4-(NO2)2, PhCH=CHNO2, PhCH=C(C4Cl4),160 and PhCH=C(Ph)NO2 versus the log ko for the deprotonation of CH2(CN)2, CH2(COO)2C(CH3)2, 4-NO2-C6H4CH2CN, 2,4-(NO2)2C6H3CH2CN, CH3NO2, C5H2Cl4,160 and PhCH2NO2, respectively, gives a good linear correlation. This indicates that the resonance effect of the p-acceptors is qualitatively similar in both reactions. However, there is an attenuation of this effect in Equation (40) as indicated by the slope of 0.46. This attenuation is also reflected in smaller transition state imbalances, as measured by annuc  bnnuc ; annuc was obtained from plots of log k1 versus log K1 by varying the aryl substituents and corresponds to aCH in proton transfers, while bnnuc was obtained from plots of log k1 versus log K1 by varying the nucleophile and corresponds to bB in proton transfers. A major reason for the reduced imbalances is the fact that the b-carbon in the alkene is already sp2-hybridized which facilitates p-overlap with the Y-group at the transition state. This is symbolized in 64 by showing a small degree of charge delocalization into the Y-group as indicated by the small ‘‘d–.’’

294

C.F. BERNASCONI

C

Yδ–

δ– C

Nuν + δ 64

There are other factors that contribute to the reduction in the imbalance. This can be seen by comparing intrinsic rate constants of reactions that create the same carbanions as in proton transfer reactions, e.g., comparing reactions 41 and 42. These reactions do involve sp3 ! sp2 rehydrization just as in proton transfers and hence, if hydrization were the only important factor, PhCH O

CH(CN)2

PhCH

– O + CH(CN)2

CH2NO2

PhCH

O + CH2

(41)

–

PhCH

– NO2

(42)

O–

the difference in the log ko values between Equations (41) and (42) should be comparable to that between the log ko values for the deprotonation of malononitrile and nitromethane, respectively. The difference, Dlog ko  3.9, between reactions 41 and 42 is indeed larger than for the corresponding nucleophilic addition reactions to PhCH=C(CN)2 and PhCH=CHNO2, respectively (Dlog ko  2.6), but still smaller than for the corresponding proton transfers (Dlog ko = 6.8). A smaller Dlog ko (5.1) than for proton transfers was also found by the Crampton group161,162 for reactions 43 and 44. H

CH(CN)2 NO2

O2N

NO2

O2N

– + CH(CN2)

–

NO2

NO2

H

CH2NO2 NO2

O2N

NO2

O2N

+

–

NO2

(43)

NO2

CH2

– NO2

(44)

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

295

One potential second reason for the attenuation of the imbalance is steric hindrance to perfect co-planarity of Y in the anionic adducts of Equation (40). An additional factor that may enhance the differences between the imbalances in proton transfers and those in the other carbanion forming reactions is hydrogen bonding in the transition state of proton transfer. This hydrogen bonding stabilizes the transition state by keeping more of the negative charge on the carbon. The gas phase ab initio calculations discussed earlier support this notion.

Effect of intramolecular hydrogen bonding In reactions with amine nucleophiles the reaction leads to a zwitterionic adduct that is in rapid acid–base equilibrium with its anionic form, Equation (45). In some cases, the zwitterion is strongly

Y C

C

+ RR′NH

Y–

k1 C C + RR′NH

k–1

Y–

‡

Ka

H+

C

C

(45)

RR′N

stabilized by an intramolecular hydrogen bond as in the example of the reaction of benzylideneacetylacetone (65) with secondary amines. At the transition state this hydrogen bond

CH3 Ph H

C

C

C

– C

RR′N+

O CH3

O H 65

is only weakly developed because the partial charges on the nitrogen and oxygen atoms are small and the distance between the donor and acceptor atoms is relatively large. Hence the stabilizing effect at the transition state is disproportionately small which leads to a reduction in the intrinsic rate constants of such reactions.

296

C.F. BERNASCONI

Steric effects Steric effects reduce rate and equilibrium constants of nucleophilic additions but the question how the intrinsic barrier is affected does not always have a clear answer. Comparisons of intrinsic rate constants for the addition of secondary alicyclic amines versus primary aliphatic amines suggest that ko is reduced by the F-strain. This implies that the development of the F-strain at the transition state is quite far advanced relative to bond formation. The effects of other types of steric hindrance on ko such as prevention of coplanarity of Y in the adduct or even prevention of p-overlap between Y and the C=C double bond in the alkene have not been thoroughly examined and hence are less well understood. Effect of polar substituents The polar effect of remote substituents on intrinsic rate constants is qualitatively similar to that in proton transfer, irrespective of whether the aryl group is attached to the a-carbon (e.g., 66) or the b-carbon (67); in both cases the partial negative charge in the transition state is closer to the Z

C

δ– Y C

δ– Y C

C

Nuν + δ

Z

Nuν + δ

66

67

substituent Z than in the adduct where the charge is on Y and hence an electron-withdrawing substituent will increase the intrinsic rate constant. This is also reflected in the above-mentioned fact that annuc > bnnuc . p-Donors in the para position of a-aryl groups can lead either to a reduction or an enhancement of the intrinsic rate constant. Examples where a reduction has been observed is the reaction of amines with benzylidene malononitriles, Equation (46), or with benzylidene Meldrum’s Z

Z CN C H

+ R2NH

C CN

CN

k1 k–1

H

C + R2NH

C CN

(46)

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

297

acid. This reduction may be understood in terms of the resonance stabilization of the alkene (68 ! 68). Just as is true for resonance effects in general, the loss of this reactant resonance Z

Z+ CN

CN C

C

C CN

H

H

C

– CN

68±

68

stabilization is expected to be ahead of C–N bond formation at the transition state which should decrease ko. In the reaction of piperidine with b-nitrostyrenes, Equation (47), ko for the reactions of the Z

Z H C H

C

H + R2NH

NO2

H

C + R2NH

(47)

C – NO2

p-OMe derivatives is enhanced, suggesting the above early loss of resonance is overshadowed by another effect. This effect can be understood as arising from a preorganization of the =CHNO2 group in the reactant toward its structure in the adduct (–CH=NO 2 ), thus reducing the transition state imbalance and avoiding some of the detrimental effect of the lag in the charge delocalization. This explanation is similar to that given for the p-donor effect in the deprotonation of Fischer carbenes and of 43-Z. Apparently the two types of p-donor effects operate simultaneously, with the former dominating in reaction 46 and the latter dominating in reaction 47. Polarizable nucleophiles Even though the high carbon basicity of thiolate ion nucleophiles is a major reason why their nucleophilic reactivity is much higher than that of oxyanions or amines of comparable pKa, there is an added effect that comes from a reduced intrinsic barrier. For example, intrinsic rate constants for thiolate ion addition to a-nitrostilbene or b-nitrostyrene are up to 100-fold higher than for amine addition. This has been explained in terms of the soft–soft interaction

298

C.F. BERNASCONI

responsible for the high thermodynamic stability of thiolate ion adducts developing ahead of C–S bond formation.

NUCLEOPHILIC VINYLIC SUBSTITUTION (SNV) REACTIONS

The most common mechanism of nucleophilic vinylic substitution163 is the two-step process of Equation (48) shown for the reaction of an anionic nucleophile with a vinylic substrate activated by one

Y

R Nu–

C

+

C Y′

LG

R k1

LG

C

k–1

Y

k2

C

Y

R C

C

Nu

Y′

+ LG– Y′

(48)

Nu 69

or two electron-withdrawing substituents Y and/or Y0 and a leaving group LG.163–170 The first step is essentially the same as that in nucleophilic additions to alkenes, Equation (40), except that steric and electronic effects of the leaving group affect the reactivity not only of the k2 step but also of the k1 and k–1 steps in important ways. Early mechanistic work on these reactions dealt exclusively with systems where 69 is an undetectable steady-state intermediate,163–167 making it impossible to determine intrinsic rate constants. However, more recent studies focusing on systems with strong nucleophiles such as thiolate or alkoxide ion, poor leaving groups such as alkoxide or thiolate ions, and strongly activated vinylic substrates allowed direct observation of 69 and determination of the individual rate constants k1, k–1, and k2.168,170 The reactions of 70-LG-74-LG with O

O NO2

Ph C

Ph

C

LG

O

CH3

Ph

CH3

LG

C Ph

C

LG

O O

70-H (LG = H) 70-OMe (LG = OMe) 70-Pr (LG = SPr-n) Ph C LG

Ph

NO2

LG

C

CN C

73-SMe (LG = SMe)

O

71-H (LG = H) 71-OMe (LG = OMe) 71-SMe (LG = SMe)

COOMe

C

C CN

74-H (LG = H) 74-OMe (LG = OMe)

72-H (LG = H) 72-SMe (LG = SMe)

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

299

thiolate ions171–176,178 have provided the most insights into how structural factors affect intrinsic rate constants in such systems. Table 24 summarizes  RS RS kRS 1 , K1 , and k2 values for the reactions with HOCH0 2CH2S as a repreCH2 YY values of CH2YY0 , sentative thiolate ion. Included in the table are pKa  RS log ko for the intrinsic rate constants for RS addition determined from plots PT versus log KRS values for the deprotonation of of log kRS 1 1 , and log ko 0 CH2YY by secondary alicyclic amines. CH2 YY0 Figure 9 shows an excellent correlation of log KRS for 1 with pKa 0 LG = H( ) (slope = 1.11), indicating charge stabilization by YY in the adduct is similar to that for CHYY0 . For LG = OMe () and SMe (D) the correlation is poor due to steric crowding in the adduct which is strongest for YY0 = MA,177 intermediate for YY0 = ID,177 (NO2,CO2Me) and (Ph,NO2), and smallest for YY0 = (CN)2. The leaving group steric effects follow the expected order SPr-n > SMe > OMe >> H. and log KRS are Figure 10 shows that the correlations between log kRS 1 1 RS poor, implying that ko differs substantially from substrate to substrate and not only depends on YY0 but on the leaving group as well. This is best demonstrated in Fig. 11 which shows that, for a given leaving group, there and log kPT just as had been is a linear correlation between log kRS o o observed for the correlation between log ko for the reaction of amines with alkenes [Equation (40)] and log ko for the corresponding proton transfer mentioned earlier. Also as observed for reaction 40, the slopes are less than unity (0.32 for LG = H, 0.40 for LG = OMe, and 0.56 for LG = SMe) due to the sp2 hybridization of the b-carbon which facilitates overlap with the YY0 groups at the transition state and reduces the imbalance. However, as the differences in the slopes imply, the degree by which the imbalance is reduced depends on the leaving group and is largest for LG = H and smallest for LG = SMe. This conclusion is corroborated by the Br½nsted-type coefficients annuc and bnnuc for the reactions of thiolate ions with the phenyl-substituted Meldrum’s acid derivatives of 71-H and 71-SMe: for 71-SMe, annuc – bnnuc = 0.34, for 71-H annuc – bnnuc = 0.13, implying a smaller imbalance for 71-H. We further note that the kRS o values for the reactions with LG = OMe and SMe are much lower than with LG = H, especially for LG = SMe. There are two main factors that contribute to this result. One is the p-donor effect of the OMe and SMe groups (75 $ 75) which reduces kRS o

Y

R C MeX

+ MeX

Y′ 75

Y

R

C

X = O or S

C

C Y′ 75±

300

Table 24 Rate and equilibrium constants for SNV reactions with HOCH2CH2Sin 50% DMSO–50% water at 20C 2 YY pKCH a

Substrate Ph

0

1 1 kRS s ) 1 (M

1 KRS 1 (M )

1 kRS 2 (s )

log kRS o

log kPT o

References

CN C

C

H

(74-H)

10.21

4.40  106

5.18  104

5.7

7.0

171

(70-H)

7.90

5.18  104

8.16  106

3.4

–0.25

172

(72-H)

6.35

4.47  106

1.16  109

4.8

3.13

171

(71-H)

4.70

1.44  107

5.38  1010

5.2

3.90

173

10.21

2.80  105

1.62  102

5.1

70

171

CN

Ph

Ph C

C

H

NO2 O

Ph C

C

H O O O CH3

Ph C

C

O CH3

O Ph

CN C

MeO

(74-OMe)

C CN

0.133

C.F. BERNASCONI

H

C

C

MeO

NO2

(70-OMe)

7.90

3.89  102

7.59  103

9.60  106

2.2

–0.25

174

(71-OMe)

4.70

4.40  104

2.57  104

2.16  104

3.7

3.13

175

(70-SPr)

7.90

4.70

10.4

4.50  102

0.29

2.44

175

(72-SMe)

6.35

5.62  102

2.25  102

0.245

2.5

3.90

171

(73-SMe)

5.95

2.48  102

5  104

5.80  105

£1.1

171

(71-SMe)

4.70

9.22  102

3.32  102

0.115

2.5

176

Ph O O CH3

Ph C

C MeO

O CH3

O Ph

NO2 C

C

n-PrS

Ph O

Ph C

C

MeS O Ph

Ph C

C

MeS

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

Ph

CO2Me O O CH3

Ph C

C

MeS O

O CH3

301

302

C.F. BERNASCONI 12

71-H 10

72-H

log K1RS

8

70-H 6

4

74-H

73-H 71-OME 70-OME

2

72-SMe 71-SMe

74-OME

70-SR 0 –12

–10

–8

–6

–4

–2

0

CH YY′ –pKa 2 0

2 YY Fig. 9 Plots of log KRS (RS = HOCH2CH2S) versus pKCH . a 1 LG = OMe; D, LG = SMe.

,

LG = H;

,

by the PNS effect of the early loss of the resonance stabilization of the substrate; this is similar to the effect of p-donor substituents in the phenyl group of alkenes as, e.g., in 68 $ 68. In view of the stronger p-donor effect of the OMe group,71 this factor should affect the reactions with LG = OMe more strongly than those with LG = SMe. However, since kRS o for the MeS derivatives is lower than for MeO derivatives, there must be one or more additional factors that reduce kRS o for the MeS derivatives relative to that for the MeO derivatives. One such factor appears to be steric hindrance (Fstrain) at the transition state which is quite advanced relative to the C–S bond formation and hence should result in a greater reduction of ko for the MeS derivative due to the larger size of the sulfur atom. This conclusion is in agreement with one reached for the reaction of amines with alkenes discussed earlier. Another factor may be the stronger electron-withdrawing inductive effect of the MeO group which imparts greater stabilization to the imbalanced transition state than the MeS group and hence increases the ko(OMe)/ko(SMe) ratio.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

303

8

71-H 72-H

74-H 6

log k 1RS

74-OMe 70-H

71-OMe 4

71-SMe 70-OMe

→

72-SMe

73-SMe

2

70-SPr 0

0

2

4

6

8

10

12

RS

log K1

  RS Fig. 10 Plots of log KRS 1 versus log K1 (RS = HOCH2CH2S ) generated by varying YY0 . , LG = H; , LG = OMe; D, LG = SMe.

NUCLEOPHILIC SUBSTITUTION OF FISCHER CARBENE COMPLEXES

Intrinsic rate constants The reactions of Fischer carbene complexes with an anionic nucleophile may be represented by Equation (49).179–181 Typical carbene complexes that have been the subject of kinetic studies are 76-M and XR Nu– + (CO)5Cr

C R′

77-M

182–185

XR (CO)5Cr

k –1

k2

R′

(CO)5Cr

+ RX–

C

(49)

R′

as well as others mentioned below.

C

OCH2CH2O–

SMe (CO)5M

Ph

76-Cr (M = Cr) 76-W (M = W)

C Nu

OMe (CO)5M

Nu

–

k1

(CO)5Cr

C Ph

77-Cr (M = Cr) 77-W (M = W)

C

SCH2CH2O– (CO)5Cr

C

Ph 78-Cr

Ph 79-Cr

304

C.F. BERNASCONI 6

74-H

71-H 5

72-H 74-OMe

log k ORS

4

71-OMe 70-H

3

72-SMe

2

71-SMe

70-OMe

73-SMe

1

70-SPr 0 –1

0

1

2

3 log

4

5

6

7

8

k OPT

  PT Fig. 11 Plots log kRS o (RS = HOCH2CH2S ) versus log ko . , LG = H; , LG = OMe; D, LG = SMe.

These reactions show many similarities with the SNV reactions of Equation (48) but there are differences as well. Table 25 summarizes approximate log ko values for the addition of various nucleophiles to 76-M and 77-M. The table includes results for the intramolecular reactions of 78-Cr186 and 79-Cr186 that lead to the cyclic intermediates 80-Cr and 81-Cr, respectively. For

– (CO)5Cr

O C Ph 80-Cr

– O

(CO)5Cr

S C

O

Ph 81-Cr

the purpose of comparison, log ko values for the reactions of the vinylic substrate with the highest intrinsic rate constant (74-OMe) and the ones with

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

305

Table 25 Approximate intrinsic rate constants for the reactions of Fischer carbene complexes with nucleophilesa log ko 

Nu = MeO

b



Nu = ROc

Nu = RSc

OMe (CO)5Cr

C

(76-Cr)

0.96d

0.74e

2.11f

(76-W)

1.25d

0.96e

2.56f

Ph OMe (CO)5W

C Ph OCH2CH2O–

(CO)5Cr

(78-Cr)

C

1.19g

Ph SMe (CO)5Cr

C

(77-Cr)

–0.3h

(77-W)

0.0h

Ph SMe (CO)5W

C Ph SCH2CH2O–

(CO)5Cr

(79-Cr)

C

–1.53g

Ph OMe

NC C

C

NC C

C

(70-OMe)

2.2i

(70-SPr)

0.29i

Ph

Ph

SPr-n

O 2N C

a

5.1i

OMe

O 2N

Ph

(74-OMe) Ph

C Ph

In most cases log ko was determined using the simplest version of the Marcus equation, log ko = log k1 – 0.5 log K1. b In methanol at 25C. c In 50% MeCN–50% water (v/v) at 25C. d Reference 182. e Reference 183. f Reference 184. g Reference 186. h Reference 185. i From Table 24.

306

C.F. BERNASCONI

the lowest ko values (70-OMe and 70-SMe) are included in the table. The following points are noteworthy. 1. The intrinsic rate constants for thiolate ion addition to the Fischer carbenes are close to those for thiolate addition to the respective a-nitrostilbene derivatives 70-OMe and 70-SMe but much lower than for thiolate ion addition to methoxybenzylidinemalononitrile (74-OMe); for example, log ko = 2.1 for 76-Cr versus log ko = 2.2 for 70-OMe versus log ko = 5.1 for 74-OMe, or, log ko = –0.3 for 77-Cr versus log ko = 0.29 for 70-SPr. This is consistent with the extensive charge delocalization into the (CO)5M moiety that is responsible for the relatively high stability of the addition complexes176,177,183 and the lag of this delocalization behind bond formation at the transition state, see, e.g., 82; note that to show the imbalance the partial negative charge is placed on the metal atom rather than on the entire (CO)5M group. OMe δ– (CO)5M

C

Ph

δ– Nu 82

2. The intrinsic rate constants are much lower for nucleophilic attack on the thia carbene complexes than on the oxa carbene complexes. This is true irrespective of the nucleophile. For example, log ko = –0.3 for RS attack on 77-Cr versus log ko = 2.1 for RS attack on 76-Cr, or log ko = –1.53 for cyclization of 79-Cr versus log ko = 1.19 for cyclization of 78-Cr. These findings are reminiscent of the lower intrinsic rate constants for thiolate ion addition to vinylic substrates with a MeS leaving group compared to those with a MeO leaving group and hence must have similar explanations in terms of inductive, steric and possibly p-donor effects. Specifically, the stronger inductive effect of the MeO(RO) group enhances ko(OR) relative to ko(SR) while the larger steric effect of the MeS(RS) group lowers ko(SR) relative to ko(OR); both factors lower the ko(SR)/ko(OR) ratios. As discussed for the SNV reactions, the p-donor effects may partially offset the inductive and steric effects because early loss of the resonance stabilization of the carbene complex should lower ko(OR) more than ko(SR). However, based on our discussion of the p-donor effects in the deprotonation of Fischer carbene complexes, the ko-increasing preorganization effect may counteract or even override the ko-reducing effect of the early loss of carbene complex resonance and hence contribute to the lower ko(SR)/ko(OR) ratios.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

307

3. The intrinsic rate constants for thiolate ion addition to 76-Cr and 76-W are substantially larger than those for alkoxide ion addition. This is similar to the previously mentioned higher intrinsic reactivity of thiolate ions compared to amine nucleophiles for the addition to a-nitrostilbene and b-nitrostyrene. It can be understood in terms of the soft–soft interaction of the thiolate ion with the carbene complex which is more advanced than C–S bond formation at the transition state.184 Transition state imbalances The fact that the intrinsic rate constants for nucleophilic addition to Fischer carbene complexes are relatively low, for example, much lower than for most reactions with comparable vinylic substrates or carboxylic esters,188 constitutes strong evidence for the presence of substantial transition state imbalances. However, there have only been a few studies of substituent effects that demonstrate the imbalance directly by showing annuc > bnnuc or by providing an estimate of its magnitude from the difference annuc – bnnuc . One such study is the reactions of 76-Cr-Z and 76-W-Z with HC CCH2O and CF3CH2O.183 It yielded annuc = 0.59 and bnnuc £ 0.46 for 76-Cr-Z, and annuc = 0.56 and bnnuc £ 0.42 for 76-W-Z, i.e., annuc > bnnuc as expected.

OMe (CO)5M

C

Z 76-Cr-Z (M = Cr) 76-W-Z (M = W)

Desolvation of the nucleophile There exists substantial evidence that in reactions that involve oxyanions or amines as bases or as nucleophiles, their partial desolvation, as they enter the transition state, typically has made greater progress than bond formation. In the context of the PNS, this partial loss of solvation represents the early loss of a reactant stabilizing factor and hence reduces the intrinsic rate constant. As discussed at some length in our 1992 chapter,4 for strongly basic oxyanions this desolvation effect often manifests itself in terms of negative deviations from Br½nsted plots and/or in abnormally low b or bnuc values.58,188 In fact, a number of cases have been reported where the bnuc value was close to zero or

308

C.F. BERNASCONI

even negative. Examples of negative bnuc values include the reaction of quinuclidines with aryl phosphates,193 of amines with carbocations,194,195 and of oximate ions with electrophilic phosphorous centers.192,196,197 The reactions of thiolate ions with several carbene complexes are also characterized by substantially negative bnuc values: they are –0.28 for 76-Cr,184 –0.25 for 76-W,184 –0.24 for 77-Cr,186 –0.30 for 77-W,186 –0.18 for 83-Cr,198 and –0.21 for 84-Cr198; for the reaction of 84-Cr with aryloxide ions bnuc = –0.39.199

O (CO)5Cr

C

O (CO)5Cr

Ph 83-Cr

NO2

C Ph 84-Cr

According to Jencks et al.,193 negative bnuc values result from a combination of minimal progress of bond formation at the transition state and the requirement for partial desolvation of the nucleophile before it enters the transition state. In a first approximation bnuc may be expressed by Equation (50) where bd and bnuc are defined by Equations (51) and (52), respectively. Kd represents 0

bnuc ¼ bd þ b nuc

ð50Þ

bd ¼ dlogKd =dpKaNucH

ð51Þ

0

0

b nuc ¼ dlogk1 =dpKaNucH

ð52Þ

the equilibrium constant for partial desolvation of the nucleophile while k0 1 is the rate constant for nucleophilic attack by the partially desolvated nucleophile. Since desolvation becomes more difficult with increasing basicity of the nucleophile, bd < 0 which, along with a small b0 nuc value, can lead to a negative bnuc value. A more elaborate treatment of this problem has been presented elsewhere.184 The fact that b0 nuc is so small as to lead to negative bnuc values implies a very small degree of C–S or C–O bond formation at the transition state. One factor that seems to play a role is the particularly severe steric crowding in the transition state due to the very large size of the (CO)5M group.186,200 The small degree of bond formation would seem to reduce the steric repulsion. The even more negative bnuc value for the aryloxide ion reactions is probably the result of a more negative bd value due to the stronger solvation of oxyanions compared to thiolate ions.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

309

REACTIONS INVOLVING CARBOCATIONS

Following previous studies of reactions of carbocations with nucleophiles201–204 discussed in our 1992 chapter,4 Richard’s group205,206 reports that electronwithdrawing a-substituents in 4-methoxybenzyl cations, 85, reduce the rate of nucleophilic addition of alcohols and water to

R1

+ C

R2

R1

R2 C

R1, R2 = H, CF3; CF3, CF3; H, CH2F; H, CHF2; H, COOEt; CH3, CF3

OMe 85

+ OMe 85±

these cations. This is contrary to what one would expect since the electronwithdrawing a-substituents destabilize the carbocation and should make it more reactive. The reason for the reduced reactivity is that the electronwithdrawing substituents lead to a stronger resonance effect by the methoxy group. Hence the PNS effect of the early loss of resonance stabilization at the transition state increases the intrinsic barrier sufficiently as to lower the actual rate of the reaction. A similar study by Schepp and Wirz had led to the same conclusion.207 For an interesting example where the small degree of transition state resonance stabilization corresponds to a late development of product resonance is the acid-catalyzed aromatization of benzene cis-1,2-dihydrodiols.208 The reaction is shown in Scheme 2 where the loss of water is rate limiting. The rate constants as a function of 17 Z-substituents gave a good correlation with the regular Hammett s values with r = –8.2. Interestingly, there were no deviations from the Hammett plot for the p-donor substituents MeO and EtO, i.e., there was no need to use sþ constants, implying that resonance stabilization of the transition state is of minor importance despite the strongly developed positive charge indicated by the very large r value. A situation where the late development of a product destabilizing factor lowers the intrinsic barrier is the nucleophilic addition reaction shown in Equation (53).209 Kinetic data for this reaction and the reaction of a series of thiols have led to the following conclusions. The adduct, 87, is strongly stabilized by the polar and polarizability effect of the two methyl groups on the sulfur but strongly destabilized by the electron-withdrawing CF3 groups. There is also a relatively strong stabilization of the incipient positive charge on

310

C.F. BERNASCONI

Z

Z OH

OH

OH

H+ + OH2

OH

Z

Z

OH slow –H2O

+

+

H

H

hydride shift

–H+

Z

Z OH

OH –H+

+ H H

Scheme 2 + SMe2 F3C

CF3

F3C

+ CF3

CF3

F3C

(53)

+ Me2S

O–

O–

O 86

87

the sulfur atom by the methyl groups at the transition state as indicated by bnuc > 0.5 based on the addition of thiols, but only a small destabilization of the transition state by the more distant CF3 groups. The picture that emerges is that of a transition state where bond formation to the nucleophile develops at a relatively large distance so that the interaction between the positive charge and the CF3 groups remains weak until after the transition has passed while the interaction between the positive charge and the methyl groups can be strong. This, then, leads to a lowering of the intrinsic barrier. A case where the late solvation of halogen leaving groups in a carbocation forming solvolysis reaction increases the intrinsic barrier is the one shown in Equation (54). CH2X

+

CH2

+ X–

OMe

OMe

(54)

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

311

Toteva and Richard210 showed that DG‡o for F expulsion is about 3 kcal mol1 higher than for Cl expulsion. Since solvation of the fluoride ion is much stronger than that of the chloride ion, the difference in DG‡o must arise from the PNS effect of late solvation. A PNS effect involving anomeric stabilization of a geminal dialkoxy compound has been observed when comparing kinetic and thermodynamic data of reactions 55 and 56. Reaction 55

H CF3CH2O

C

OCH2CF3

CF3CH2O

+ C

H

H+ +

+ CF3CH2OH OMe

(55)

OMe

88-(OCH3CF3)2

88-OCH2CF3

H CF3CH2S

C

OCH2CF3

CF3CH2S

+ C

H

H+ +

+ CF3CH2OH OMe

88-(OCH2CF3)(SCH2CF3)

(56)

OMe 88-SCH2CF3

was reported to be thermodynamically less favorable than reaction 56 but the rate for reaction 55 is higher than for reaction 56.211 One possible interpretation of these results offered by the authors is that stabilization of 88(OCH2CF3)2 by the geminal interaction of the two oxygens, the anomeric effect,212–216 is responsible for the less favorable thermodynamics of reaction 55 but that the loss of this interaction lags behind C–O bond cleavage at the transition state. This late loss of a reactant stabilizing factor results in a lower intrinsic barrier for reaction 55.

312

C.F. BERNASCONI

MISCELLANEOUS REACTIONS

Gas phase SNV reactions Kon ´ ˘ a et al.217 reported DFT calculations on gas phase SNV reactions such as Equations (57), (58), and other similar processes. Their calculations show the expected strong stabilization of the anionic adduct HO– + CH2

CH

– CH2

OCH3

OCH3 CH

CH2

CH

OH + CH3O–

OH

(57)

HO– + O

CH

CH

CH

– O

OCH3

OCH3 CH

CH

CH

(58)

OH O

CH

CH

CH

OH + CH3O–

in Equation (58) that results from the delocalization of the negative charge onto the carbonyl oxygen. As to the barriers, the one for the first step in Equation (58) is lower than that for the first step in Equation (57) but not by an amount that would imply a strong expression of adduct stabilization in the transition state. In other words, resonance stabilization of the transition state lags behind C–O bond formation. A similar situation exists for the second step in reaction 58, i.e., the barrier is disproportionately high because of early loss of the resonance stabilization of the intermediate. Intramolecular SN2 reactions The intramolecular SN2 reaction shown in Equation (59) is an example where the development of a product destabilizing factor lags behind bond formation which contributes to the lowering of the S

–

S CH2

CH2

CH2

CH2

+ HS–

(59)

SH

CH3S– + CH3

CH2

CH3 SH

CH2 SCH3 + HS–

(60)

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

313

intrinsic barrier. Specifically, an ab initio calculation by Gronert and Lee218 has shown that the enthalpic barrier DH‡ for Equation (59) (19 kcal mol1) is lower than for Equation (60) (24 kcal mol1), even though Equation (60) is thermodynamically much more favored (DHo = –1 kcal mol1) than Equation (59) (DHo = 19 kcal mol1). This means that the intrinsic barrier of Equation (59) is much lower than for Equation (60). The cyclization is thermodynamically unfavorable due to the large ring strain of the threemembered ring. However, at the transition state, the ring strain is small because the developing C–S bond is quite long, and hence this lowers the intrinsic barrier. Another factor that contributes to the lowering of the intrinsic barrier is what the authors call the proximity effect. This effect derives from the fact that in the cyclization reaction the nucleophilic atom is forced to be close to the a-carbon which amounts to a destabilization of the substrate by 1,3-repulsive interactions. Similar results were also reported for the reactions of Equation (61).219 X CH

– XCH CH2

CH2

CH2

(61)

CH2 + Cl–

Cl X CH O, C

CH, CN

Epoxidation of alkenes Based on a kinetic study of the epoxidation of alkenes by m-chloroperbenzoic acid, Equation (62), O

O

OH

C

C

OH

O

C

C

O

+

+ C

R

(62)

C

Cl

Cl

R

R = alkyl or aryl

Perrin’s group220 concluded that, for aromatic alkenes (R = aryl), the transition state, schematically represented as 89, may be imbalanced in that the delocalization of the positive

δ+ C

C

+ •

‡

X δ– δ+

C

Ar

Ar 89

C

90

314

C.F. BERNASCONI

charge into the aromatic ring is delayed. Specifically, they showed that the kinetic data correlated with the ionization potential of the alkenes, implying that the radical cation 90 with a significant fraction of the positive charge delocalized into the aryl group, may serve as a model for the product. There were two separate correlation lines, one for aliphatic (R = alkyl) and the other for aromatic alkenes (R = aryl), and, for a given ionization potential, the reactivity of the aromatic alkenes was lower than that of their aliphatic counterparts. These results were interpreted as being the consequence of the above-mentioned transition state imbalance, which raises the intrinsic barrier of the reaction and explains the lower reactivity of the aromatic alkenes as well as the lower sensitivity of the rate to the ionization potential. Hemiacetal decomposition McClelland et al.221 have suggested that the general acid-catalyzed decomposition of a hemiacetal anion, Equation (63), proceeds through an imbalanced transition state where sp3 to sp2

‡ O–

Ar

+ HA

C CH3

OR

Oδ–

Ar

ArCCH3 + ROH + A–

C CH3

O

OR

(63)

H Aδ–

rehybridization of the central carbon lags behind C–O bond cleavage. This imbalance is in the expected direction since sp2 hybridization allows development of the acetophenone resonance. The authors based their conclusion on a relatively large blg value (large degree of C–O bond cleavage) and a small r value determined from the aryl substituent effect (small degree of charge development in the aryl group). A similar conclusion has been reached by Kandanarachchi and Sinnott222 for the hydrolysis of orthocarbonates such as (ArO)4C, (ArO)2C(OAr0 )2, or (ArO)3COAr0 . The rate-limiting step in these reactions is the spontaneous or general acid-catalyzed cleavage of the bond between the central carbon and the oxygen of the least basic aryloxy group. Again, r and blg values suggest that resonance development in the resulting carbocation lags behind C–O bond cleavage.

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

315

Radical reactions In an attempt to understand the origin of the barrier in the fragmentation of the radical cations of 2-substituted benzothiazoline derivatives, Shukla et al.223 examined the kinetics of reaction 64 as •+ S

R

S

N

Me

+ N

Me

Me + R•

(64)

Me

a function of R (PhCH2, Ph2CH, PhCMe2, 9-MeFl, Ph2CMe) and performed DFT energy calculations. Even though the activation barriers decreased with increasing resonance stabilization of the radical R, it was shown that the lowering of the barriers was rather modest relative to the large increases in the thermodynamic driving force that resulted from the enhanced radical stability. This unusually small effect on the barrier was attributed to an increase in the intrinsic barrier with increasing resonance stabilization of the radical. The increase in the intrinsic barrier was attributed to ‘‘large reorganization energies in the product fragments.’’ The authors did not refer to the transition state as ‘‘imbalanced’’ and apparently were unfamiliar with the PNS, but their results are of course a classic example of the PNS at work. In a theoretical paper, Costentin and SavO˜ant224 examined the dimerization of neutral radicals by constructing potential energy profiles from AMI calculations, subjecting some selected dimerizations to B3LYP/6-31G* calculations and applying VB theory in analyzing the results. The dimerization of conjugated radicals, e.g., Equation (65), is subject to an 2 CH2

CH

CH2

CH2

CH

CH2

CH2 CH

CH2

(65)

activation barrier which contrasts with the barrierless dimerization of nonconjugated radicals; these barriers are higher for more highly delocalized radicals, even when the reactions are more thermodynamically favored. These results are consistent with the notion that loss of the resonance of the radicals is ahead of bond formation, or, in the reverse direction, development of the radical resonance lags behind bond cleavage. However, based on their analysis of the reaction in the reverse direction for which the resonance integral apparently increases at the same pace as bond cleavage, Costentin and SavO˜ant concluded that delocalization is synchronous with bond breaking. It would appear that further study is needed to resolve this apparent inconsistency between their conclusion and the predictions of the PNS.

316

C.F. BERNASCONI

Enzyme-catalyzed hydride transfer A biologically relevant example of a reaction with an imbalanced transition state is the hydride transfer catalyzed by dihydrofolate reductase of Escherichia coli. In a theoretical study by Pu et al.225 the hybridization changes at the donor carbon atom (C4N) and acceptor carbon atom (C6) that occur along the reaction coordinate were examined. It was shown that the changes in hybridization at both carbon centers progress in a nonlinear fashion with respect to the progress of the hydride transfer. Specifically, the change from sp3 to sp2 hybridization of C4N lags behind hydride transfer while the change from sp2 to sp3 hybridization of C6 is ahead of hydride transfer. This is strictly analogous to the findings for the proton transfer reactions of the type of Equation (21) where the change in the pyramidal angle (56) lags behind proton transfer. Additional evidence for the imbalanced nature of the transition state was deduced from an analysis of the changes in the C4–H and C6–H bond orders along the reaction coordinate.

5

Summary and concluding remarks

Most elementary reactions involve several molecular events such as bond formation/cleavage, charge transfer, charge creation/destruction, charge delocalization/localization, creation/destruction of aromaticity or antiaromaticity, increase/decrease in steric strain, etc. It is rare that all these events have made equal progress at the transition state; in other words, in most cases, the transition state is imbalanced in the sense that some process develops ahead of or lags behind others along the reaction coordinate. It has proven useful to regard the main bond changes as the ‘‘primary’’ process and to regard the development of the various product stabilizing/destabilizing factors, or the loss of the various reactant stabilizing/destabilizing factors, as ‘‘secondary’’ processes. This definition then allows us to use the extent of the bond changes as a frame of reference in gauging whether the development of a product stabilizing/destabilizing factor or the loss of a reactant stabilizing/destabilizing factor is early or late. Within this framework the various manifestations of the PNS summarized in Chart 1 are unambiguous and there can be no exceptions. What makes the PNS universal is that it is applicable to all reactions that involve bond changes. It provides a qualitative and sometimes even semiquantitative understanding of chemical reactivity using the language of physical organic chemistry. Its main virtue and usefulness is that, for the most part, a given factor follows a consistent pattern, i.e., it invariably either develops late or early, regardless of the specific reactions, and hence its effect on the intrinsic barrier is predictable. A summary of how the various factors discussed in this chapter affect intrinsic barriers/intrinsic rate constants is provided in Table 26. They include charge delocalization/resonance, solvation, aromaticity, anti-

Factor

1

Effect on molecule

Late development/ early loss

Early development/ late loss

Effect on DG‡o

ko

"

#

Ubiquitous, no exceptions, predicted by theory [Equations (12) and (25)]

" #

# "

Ubiquitous, no exceptions Limited number of known cases [Equations (18–20), (33a), (34a), and (36)] One established case [Equation (35a)], one tentative case (deprotonation of 51 and 52) Numerous cases, e.g., deprotonation of HOCH2CH2NO2, PhCH2CH2NO2, (CH3)2CHNO2, and Fischer carbenes Effect sometimes masked by preorganization (deprotonation of Fischer carbenes, nucleophilic additions) Limited number of cases (nucleophilic additions) Limited number of cases (RS as nucleophile) One tentative case [Equation (55)] Limited number of cases, e.g., 65 [Equation (45)]

Stabilizing

H

2 3

Charge delocalization (resonance) Solvation Aromaticity

Stabilizing Stabilizing

H

4

Anti-aromaticity

Destabilizing

H

#

"

5

Hyperconjugation

Stabilizing

H

"

#

6

p-Donor effect

Stabilizing

H

"

#

7

Steric effect (Fstrain) Soft–soft interactions Anomeric effect Intramolecular hydrogen bonding Ring strain

Destabilizing

H

"

#

Stabilizing

H

#

"

H

8 9 10 11

H

Comments

Stabilizing Stabilizing

H

# "

" #

Destabilizing

H

#

"

317

Limited number of cases, e.g., Equations (59) and (61)

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

Table 26 The effect of product/reactant stabilizing/destabilizing factors on DG‡o and ko

318

C.F. BERNASCONI

aromaticity, hyperconjugation, p-donor effects, F-strain, soft–soft interactions, and anomeric effects. There are other factors that can affect DG‡o and ko; they do so not because they inherently develop nonsynchronously relative to bond changes but because of delayed charge delocalization. They include the effects of remote as well as adjacent polar and polarizable substituents, of remote and adjacent charge, and of substituents that impede charge delocalization by steric crowding. They are summarized in Table 27. What the PNS cannot deal with is the effect on reactivity by factors that only operate at the transition state level but are not present in either reactant or product. Examples mentioned in this chapter include transition state aromaticity in Diels Alder reactions, steric effects on reactions of the type A þ B ! C þ D, or hydrogen bonding/electrostatic effects that stabilize the

Table 27 The effect of substituents and charges on DG‡o and ko for reactions with imbalanced transition states Factor

1 2 3

4

5 6

EW polar substituent close to charge of TS ED polar substituent close to charge of TS EW polar substituent far from charge at TS ED polar substituent far from charge at TS Adjacent polarizable substituent Adjacent positive charge

7

Remote positive charge

8

Steric hindrance of resonance by substituent

Effect on TS versus effect on product

Effect on

Comments

DG‡o

ko

Disproportionately large TS stabilization Disproportionately large TS destabilization Disproportionately small TS stabilization

#

"

"

#

"

#

Disproportionately small TS destabilization

#

"

Equation (14) (leads to aCH < bB); Equation (6)

Disproportionately large TS stabilization Disproportionately large TS stabilization Disproportionately small TS stabilization Disproportionately small TS destabilization

#

"

#

"

Proton transfer progress must be substantial e.g., Equation (16)

"

#

e.g., nucleophilic addition to 85

#

"

e.g., CH3CH(NO)2 versus CH3NO2 deprotonation

Equation (4) (leads to aCH > bB); Equation (15) Equation (4) (leads to to aCH > bB); Equation (15) Equation (14) (leads to aCH < bB); Equation (6)

THE PRINCIPLE OF NONPERFECT SYNCHRONIZATION

319

transition state of proton transfers of the type CH3Y þ CH2=Y ! CH2Y=Y þ CH3Y which are especially strong in the gas phase.

Acknowledgments I gratefully acknowledge the many outstanding contributions of all of my coworkers whose names are cited in the references and the financial support by the National Science Foundation (grant no. CHE-0446622).

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

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Dega-Szafran Z, Schroeder G, Szafran M. J Phys Org Chem 1999;12:39. Saunders WJ, Jr. J Am Chem Soc 1994;116:5400. Bernasconi CF, Wenzel PJ. J Am Chem Soc 1994;116:5405. Saunders WH, Jr, Van Verth JE. J Org Chem 1995;60:3452. Harris N, Wei W, Saunders WH, Jr, Shaik S. J Am Chem Soc 2000;122:6754. Lee I, Kim CK, Kim CK. J Phys Org Chem 1999;12:255. Bernasconi CF, Wenzel PJ, Keeffe JR, Gronert S. J Am Chem Soc 1997;119:4008. Bernasconi CF, Wenzel PJ. J Org Chem 2001;66:968. Harris N, Wei W, Saunders WH, Jr, Shaik S. J Phys Org Chem 1999;12:259. Bernasconi CF, Wenzel PJ. J Am Chem Soc 1996;118:10494. Possible reasons for the exceptionally large n values for CH3C CH have been discussed elsewhere.118 Yamataka H, Mustanir, Mishima M. J Am Chem Soc 1999;121:10225. Sato M, Kitamura Y, Yoshimura N, Yamataka H. J Org Chem 2009;74:1268. More O’Ferrall RA. J Chem Soc B 1970:274. Jencks WP. Chem Rev 1972;72:705. Costentin C, SavO˜ant J-M. J Am Chem Soc 2004;126:14787. In solution there is also solvational reorganization.126 Taft RW, Topsom RD. Prog Phys Org Chem 1987;16:1. Taft RW. Prog Phys Org Chem 1983;14:247. Van Verth JE, Saunders WH, Jr. J Org Chem 1997;62:5743. Farneth WE, Brauman JI. J Am Chem Soc 1976;98:7891. Pellerite MJ, Brauman JI. J Am Chem Soc 1980;102:5993. Moylan CR, Brauman JI. Annu Rev Phys Chem 1983;34:187. Boys SF, Bernardi F. Mol Phys 1970;19:55. Scheiner’s136–138 work is also relevant here. Cybulski SM, Scheiner S. J Am Chem Soc 1987;109:4199. Scheiner S, Wang L. J Am Chem Soc 1992;114:3650. Scheiner S. J Mol Struct (TEOCHEM) 1994;307:65. Gronert S. J Am Chem Soc 1993;115:10258. Bernasconi CF, Wenzel PJ. J Org Chem 2003;68:6870. Bernasconi CF, Wenzel PJ, Ragains. ML. J Am Chem Soc 2008;130:4934. HOMA = Harmonic Oscillator Model.139 Krygowski TM, CyrA˜nski MK. Chem Rev 2001;101:1385. NICS = Nuclear-independent chemical shift.145 Chen Z, Wannese CS, Corminboeuf C, Puchta R, Schleyer PvR. Chem Rev 2005;105:3842. The strongly negative NICS(1) value for C4 Hþ 5 has been attributed to its homoaromaticity107 which is consistent with the non-planar geometry of C4 Hþ 5 . The strongly negative NICS(1) value for the transition state suggests that the homo141 aromaticity of C4 Hþ 5 is highly preserved at the transition state. Bernasconi CF, Yamataka H, Yoshimura N, Sato M. J Org Chem 2009;74:188. Bird CW. Tetrahedron 1985;41:1409. Bird CW. Tetrahedron 1992;48:335. Evans MG. Trans Faraday Soc 1939;35:824. Dewar MJS. The molecular orbital theory of organic chemistry. New York: McGraw-Hill; 1969. pp. 316–9. Zimmerman H. Acc Chem Res 1971;4:272. Herges R, Jiao H, Schleyer PvR. Angew Chem Int Ed Engl 1994;33:1376. CossU´o FP, Morao I, Jiao H, Schleyer PvR. J Am Chem Soc 1999;121:6737. Corminboeuf C, Heine T, Weber J. Org Lett 2003;5:1127.

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147. 148. 149. 150. 151. 152. 153. 154. 155.

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156. Stahl F, Moran D, Schleyer PvR, Prall M, Schreiner PR. J Org Chem 2002;67:1453. 157. Fernandez I, Sierra MA, CossU´o FP. J Org Chem 2007;72:1488. 158. Schleyer PvR, Maerker C, Dransfeld A, Jiao A, van Eikema Hommes WJR. J Am Chem Soc 1996;118:6317. 159. Tsuij T, Okuyama M, Ohkita M, Kawai H, Suzuki T. J Am Chem Soc 2003;125:951. 160. PhCH=C(C4Cl4) = 1,2,3,4-tetrachloro-6-phenylfulvene; C5H2Cl4 = 1,2,3,4-tetrachloro-1,3-cyclopentadiene. 161. Atherton JH, Crampton MR, Duffield GL, Steven JA. J Chem Soc, Perkin Trans 2 1995:443. 162. Cox JP, Crampton MR, Wight P. J Chem Soc, Perkin Trans 2 1988:25. 163. Rappoport Z. Adv Phys Org Chem 1969;7:1. 164. Modana G. Acc Chem Res 1971;4:73. 165. Rappoport Z. Acc Chem Res 1981;14:7. 166. Rappoport Z. Recl Trav Chim Pays-Bas 1988;104:309. 167. Shainyan BA. Russ Chem Rev 1986;55:511. 168. Rappoport Z. Acc Chem Res 1992;25:474. 169. Okyama T, Lodder G. Adv Phys Org Chem 2002;37:1. 170. Bernasconi CF, Rappoport Z. Acc Chem Res 2009:42:993. 171. Bernasconi CF, Ketner RJ, Ragains ML, Chen X, Rappoport Z. J Am Chem Soc 2001;123:2155. 172. Bernasconi CF, Killion RB, Jr. J Am Chem Soc 1988;110:7506. 173. Bernasconi CF, Ketner RJ. J Org Chem 1998;68:6266. 174. Bernasconi CF, Fassberg J, Killion RB, Jr., Rappoport Z. J Am Chem Soc 1990;112:3169. 175. Bernasconi CF, Ketner RJ, Chen X, Rappoport Z. J Am Chem Soc 1998;120:7461. 176. Bernasconi CF, Ketner RJ, Chen X, Rappoport Z. Can J Chem 1999;77:584. 177. MA = Meldrum’s acid, ID = indandione. 178. Bernasconi CF, Ketner RJ, Chen X, Rappoport Z. ARKIVOC 2002 (xii) 2002:161. 179. The physical organic chemistry of Fischer carbene complexes has been reviewed;176,177 only studies relevant to the PNS will be discussed in this chapter. 180. Bernasconi CF. Chem Soc Rev 1997;26:299. 181. Bernasconi CF. Adv Phys Org Chem 2002;37:137. 182. Bernasconi CF, Flores FX, Gandler JR, Leyes AE. Organometallics 1994;13:2186. 183. Bernasconi CF, GarcU´a-RU´o L. J Am Chem Soc 2000;122:3821. 184. Bernasconi CF, Kittredge KW, Flores FX. J Am Chem Soc 1999;121:6630. 185. Bernasconi CF, Ali M, Lu F. J Am Chem Soc 2000;122:1352. 186. Bernasconi CF, Ali M. J Am Chem Soc 1999;121:11384. 187. D—tz KH, Fischer H, Hofmann R, Kreissl FR, Schubert U, Weiss K. Transition metal carbene complexes. Deerfield Beach, FL: Verlag Chemie; 1983. 188. Numerous authors189–191 have compared the reactions of Fischer carbene complexes with nucleophiles to the corresponding reactions of carboxylic esters.183,185– 187 Our view is that there is much more resemblance between the reactions of Fischer carbene complexes and SNV reaction than between the reactions of Fischer carbene complexes and reactions with esters because in the latter reactions there are no strong resonance effects. 189. Schubert U, editor. Advances in metal carbene chemistry. Dordrecht, Holland: Kluwer; 1989. 190. Werner H, Fischer EO, Heckl B, Kreiter CG. J Organomet Chem 1971;28:367.

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Kinetic studies of keto–enol and other tautomeric equilibria by flash photolysis JAKOB WIRZ Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland 1 Introduction 325 2 Methods 326 Flash photolysis 326 Derivation of the rate law for keto–enol equilibration 327 Halogen titration method 332 pH–Rate profiles 333 General acid and general base catalysis 338 3 Examples 340 4 Rate–equilibrium relationships 345 The Brønsted relation, statistical factors, and the acidity of solvent-derived species (H
and H2O) 345 Mechanism of the ‘‘uncatalyzed’’ reaction 348 The Marcus model of proton transfer 350 5 Conclusion and outlook 353 References 354

1

Introduction

Erlenmeyer was first to consider enols as hypothetical primary intermediates in a paper published in 1880 on the dehydration of glycols.1 Ketones are inert towards electrophilic reagents, in contrast to their highly reactive enol tautomers. However, the equilibrium concentrations of simple enols are generally quite low. That of 2propenol, for example, amounts to only a few parts per billion in aqueous solutions of acetone. Nevertheless, many important reactions of ketones proceed via the more reactive enols, and enolization is then generally rate-determining. Such a mechanism was put forth in 1905 by Lapworth,2 who showed that the bromination rate of acetone in aqueous acid was independent of bromine concentration and concluded that the reaction is initiated by acid-catalyzed enolization, followed by fast trapping of the enol by bromine (Scheme 1). This was the first time that a mechanistic hypothesis was put forth on the basis of an observed rate law. More recent work

E-mail: J. [email protected] 325 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44006-6


2010 Elsevier Ltd. All rights reserved

326

J. WIRZ O

slow H2O/H

OH

fast Br2

O Br

+ HBr

Scheme 1

has shown that the reaction of bromine with various acetophenone enols in aqueous solution takes place at nearly, but not quite, diffusion-controlled rates.3 In 1978, we observed that flash photolysis of butyrophenone produced acetophenone enol as a transient intermediate, which allowed us to determine the acidity constant KaE of the enol from the pH–rate profile (section ‘‘pH–Rate Profiles’’) of its decay in aqueous base.4 That work was a sideline of studies aimed at the characterization of biradical intermediates in Norrish Type II reactions and we had no intentions to pursue it any further. Enter Jerry Kresge, who had previously determined the ketonization kinetics of several enols using fast thermal methods for their generation. He immediately realized the potential of the photochemical approach to study keto–enol equilibria and quickly convinced us that this technique should be further exploited. We were more than happy to follow suit and to cooperate with this distinguished, inspiring, and enthusing chemist and his cherished wife Yvonne Chiang, who sadly passed away in 2008. Over the years, this collaboration developed into an intimate friendship of our families. This chapter is an account of what has been achieved. Several reviews in this area appeared in the years up to 1998.5–10 The enol tautomers of many ketones and aldehydes, carboxylic acids, esters and amides, ketenes, as well as the keto tautomers of phenols have since all been generated by flash photolysis to determine the pH–rate profiles for keto–enol interconversion. Equilibrium constants of enolization, KE, were determined accurately as the ratio of the rate constants of enolization, kE, and of ketonization, kK, Equation (1). KE ¼ kE =kK

ð1Þ

Strong bases in dry solvents are usually used in organic synthesis to generate reactive enol anions from ketones. Nevertheless, the kinetic studies discussed here were mostly performed on aqueous solutions. Apart from the relevance of this medium for biochemical reactions and green chemistry, it has the advantage of a well-defined pH-scale permitting quantitative studies of acid and base catalysis.

2

Methods

FLASH PHOTOLYSIS

The technique of flash photolysis, introduced in 1949 by Norrish and Porter,11 now covers time scales ranging from a few femtoseconds to seconds and has become a ubiquitous tool to study reactive intermediates. Most commonly,

KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA

327

light-induced changes in UV-Vis optical absorption are monitored, either at a single wavelength (kinetic mode) or spectrographically at a given delay with respect to the light pulse used for excitation (spectrographic mode, pump–probe spectroscopy). Instruments of a conventional design,12 which employ an electric discharge to produce a strong light flash of sub-millisecond duration, usually have sufficient time resolution and are then most suitable to study the kinetics of keto–enol tautomerization reactions. Nowadays, instruments using a Q-switched laser as an excitation source having durations of a few nanoseconds (laser flash photolysis) are much more widespread. These techniques are well known, and their properties, pitfalls, and limitations have been described.13–15

DERIVATION OF THE RATE LAW FOR KETO–ENOL EQUILIBRATION

Activation energies for unimolecular 1,3-hydrogen shifts connecting ketones and enols are prohibitive, so that thermodynamically unstable enols can survive indefinitely in the gas phase or in dry, aprotic solvents. Ketones are weak carbon acids and oxygen bases; enols are oxygen acids and carbon bases. In aqueous solution, keto–enol tautomerization proceeds by proton transfer involving solvent water. In the absence of buffers, three reaction pathways compete, as shown in Scheme 2. Four species participate in the tautomerization reaction, the ketone (K, e.g., acetone), the protonated ketone (K
), the enol (E), and its anion (E). These species are connected through two thermodynamic cycles. The Gibbs free energies for the individual elementary reactions r of any cycle must add up to naught, Equation (2). SDr Go ¼ 2:3RTSpKr ¼ 0

ð2Þ

OH K

Ka

E

k0 + kOH cOH

K K KE kH cH + k0

O

OH

′E k0′E + kOH cOH

K ′K

K

rate determining E

′K

k0 + kH c H

O

E E

Ka

E

Scheme 2

Acid-, base-, and ‘‘uncatalyzed’’ reaction paths of keto–enol tautomerism.

328

J. WIRZ

For the cycle K ! E ! E þ H
! K we get pKE þ pKEa  pKK a ¼ 0, where are the acidity KE is the equilibrium constant of enolization and KEa and KK a is defined in the direction opposite to the constants of E and K, respectively; KK a must be subtracted. Similarly, the equilibrium last process of the cycle so that pKK a constant for carbon deprotonation of the protonated ketone, K
! E þ H
, can
K
be replaced by pKE þ pKK
a , where pKa is the acidity constant of K . Thus, the equilibrium properties of Scheme 2 are fully defined by the three equilibrium constants KE, KEa , and KK
a . We turn to the kinetic parameters. When an enol E is rapidly generated in a concentration cE(t = 0) exceeding its equilibrium concentration cE(1), the decrease of cE(t) may be followed in time by, for example, some absorbance change as in flash photolysis. Deprotonation or protonation of carbon atoms is generally slow relative to the equilibration of oxygen acids with their conjugate bases. Therefore, carbon acids and bases have been called pseudo-acids and pseudo-bases. Proton transfer reactions involving carbon are the ratedetermining elementary steps of the tautomerization reactions. A shaded oblique line is drawn across these reactions in Scheme 2. Thus we posit that the protonation equilibria on oxygen that are associated with the ionization constants KEa and are established at all times during the much slower tautomerization reacKK
a tions. This assumption leads to a pH-dependent first-order rate law for keto–enol tautomerization reactions, Equation (14), which will be derived below and is found to hold in general. The pre-equilibrium assumption adopted for oxygen acids is, thereby, amply justified. We define equilibrium constants as concentration quotients, as in Equation (3) for KEa and KK
a . Provided that the experiments are done at low and constant ionic strengths, I £ 0.1 M, these can be converted to thermodynamic constants, Ka, using known or estimated activity coefficients.16 KaE ¼ cE ðtÞcH
=cE ðtÞ and KaK
¼ cK ðtÞcH
=cK
ðtÞ

ð3Þ

The total concentration of the enol and its anion is cE;tot ðtÞ  cE ðtÞ þ cE ðtÞ; inserting Equation (3) we can express the concentrations cE and cE as a function of proton concentration cH
, Equation (4). cE ð t Þ ¼

KaE

cH
KE cE;tot ðtÞ and cE ðtÞ ¼ E a cE;tot ðtÞ þ cH
Ka þ cH


ð4Þ

Protons and hydroxyl ions are not consumed by the reaction K Ð E. A temporary shift in the relative concentrations of K and E may, however, lead to a change in proton concentration cH
due to rapid equilibration with K
and E, respectively. To avoid this complication, the conditions are generally chosen such that cH
remains essentially constant during the reaction by using either a large excess of acid or base, or by the addition of buffers in near-neutral solutions (pH = 7  4). However, the addition of buffers usually

KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA

329

accelerates the rates of tautomerization. We first consider reactions taking place in wholly aqueous solutions, that is, in the absence of buffers. The handling of rate constants obtained with buffered solutions will be discussed in section ‘‘General Acid and General Base Catalysis’’. To derive the general rate law for keto–enol equilibration, we consider each of the rate-determining elementary reaction steps shown in Scheme 2 separately, beginning with enol ketonization reactions. The relevant rate constants for the and kK rate-determining ketonization reactions are kK 0 for C-protonation of H

0K E by H and solvent water, respectively, and kH
and k0K 0 for C-protonation of E by H
and water (Scheme 2). We use primed symbols k0 for the rate constants referring to ketonization of the anion E. As we shall see in a moment 0K E [Equation (7)], the terms kK 0 and kH
Ka are both independent of pH and may K be combined to a single term kuc . The associated, seemingly ‘‘uncatalyzed’’ reactions are therefore kinetically indistinguishable and additional information is required to determine, which of the corresponding mechanisms is the dominant one (see section ‘‘Mechanism of the ‘Uncatalyzed’ Reaction’’). We assume that the rate-determining reactions shown in Scheme 2 are elementary reactions, so that the corresponding rate laws are equal to the product of a rate constant and the concentrations of the reacting species. Acid-catalyzed ketonization The rate for ketone formation by carbon protonation of the enol E is given by Equation (5), where the right-hand expression is obtained by substituting cE(t) using Equation (4). K K

vK H
¼ kH
cH cE ðtÞ ¼ kH
cH

cH
cE;tot ðtÞ KaE þ cH


ð5Þ

Base-catalyzed ketonization Pre-equilibrium ionization of E generates the more reactive anion E, which may be protonated on carbon by the general acid water in the rate-determining step, Equation (6). For pH values well below pKK a , the concentration cH
is much greater than KEa , which may thus be neglected in the denominator of Equation (6). The rate of this reaction is then inversely proportional to cH
, i.e., proportional to cOH . This ‘‘apparent’’ base catalysis saturates at pH values above pKEa , when E is converted to E. The concentration cH
then becomes much smaller than KEa and may be neglected in the denominator of Equation (6). 0

0

K K  vK OH ¼ k0 cE ðtÞ ¼ k0

KaE

KaE cE;tot ðtÞ þ cH


ð6Þ

330

J. WIRZ

‘‘Uncatalyzed’’ ketonization At pH values near neutral, a pH-independent rate of ketonization is frequently observed, which may be attributed to several different mechanisms (see section ‘‘Mechanism of the ‘Uncatalyzed’ Reaction’’): carbon protonation of E by water or a concerted transfer of the enol proton to carbon through one or more solvent molecules, and carbon protonation of E by the proton, Equation (7). For pH > KEa [Equation (4)], so that the overall contribution of this path to the overall rate of reaction is pH-independent.

THE MARCUS MODEL OF PROTON TRANSFER

The experimental ketonization rate constants kK collected in Table 1 cover a range of 20 orders of magnitude. A logarithmic plot against the corresponding reaction free energies DrG reveals that these data follow a systematic, nonlinear trend, Fig. 10. The free energy of reaction associated with a given rate constant is determined by the equilibrium constant of that reaction. Thus, for the reaction , filled circles •, center), we have DrG = 2.3RT(pKE þ E þ H
! K
(kK H

)]; for the reaction E þ H
! K (k0K pKK a H
, triangles r, upper left), E DrG = 2.3RT(pKE þ pKa ); for the protonation of enolates by water, E þ E H2O ! K þ HO (k0K 0 , triangles D, lower right), DrG = 2.3RT(pKE þ pKa –
 pKw); finally, for the reaction of enols with water, E þ H2O ! K þ HO (k0 K, empty circles *, lower right), DrG = 2.3RT(pKE þ pKK a – pKw). Statistical factors (section ‘‘The Brønsted Relation, Statistical Factors, and the Acidity of Solvent-Derived Species (H
and H2O)’’) were taken into account, i.e., the rate constants were divided by the number of equivalent basic carbon atoms of the enol (e.g., q = 1 for acetone enol and q = 2 for phenol reacting to cyclohexa-2,5-dienone) and the free energy terms DrG/(2.3RT) were corrected by –log(p/q), where p is the number of equivalent acidic protons in the ketone

log k 10 ΔrG‡/(2.3RT )

0

–10

–25 –20 –15 –10

–5

0

5

10 15 20 ΔrG o/(2.3RT )

Fig. 10 Empirical relationship between the logarithm of the proton transfer rate constants (Table 1) and the corresponding free energies of reaction DrG. Triangles 1 1 1 s ). Filled circles (•): kK /(M1 s1). Empty circles (O): kK (5): k0K 0 /s . H
/(M H
0K 1 Triangles (D): k0 /s . The solid line was obtained by fitting of the Marcus Equation (19).

KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA

351

(e.g., p = 6 for acetone). These corrections are small compared to the variation of the rate constants. The dotted line shown in the upper part of Fig. 10 represents the free-energy relationship expected for ‘‘normal’’ bases, in which the nucleophilic center is an O or N heteroatom (‘‘Eigen’’-curve78); exergonic reactions are diffusion-controlled (kd  1011 M1 s1) and the rates of endergonic reactions decrease with a slope of 1 versus DrG/(2.3RT). The rate constants of the carbon bases (‘‘pseudo’’-bases) studied here are much lower than predicted by the Eigen curve, particularly in the region around DrG = 0, where the difference amounts to some 10 orders of magnitude. The systematic trend of the rate data shown in Fig. 10 is reasonably well captured by the Marcus expression for proton transfer,79 which takes the simple form of Equation (19) when work terms are omitted.80 !2   k Dr G‡ Dr G o ‡ ‡ ; where Dr G ¼ Dr G0 1 þ log ¼ ð19Þ ln ð10ÞRT kd 4Dr G‡0 The parameter DrG0‡ is called the ‘‘intrinsic’’ barrier, the barrier of a thermoneutral reaction, DrG = 0. The rate of diffusion was assumed as kd = 1  1011 M1 s1. Nonlinear least-squares fitting of Equation (19) to the set of data gave DrG0‡ = 55.6  0.7 kJ mol1. In an earlier treatment using a smaller set of data we had obtained DrG0‡ = 57  2 kJ mol1.7 In most cases, the rate constants kucK were converted to k0K H
[Equation (18)] assuming that mechanism (b) of Scheme 6 accounts for the uncatalyzed reaction. Clearly, the rate constant kK uc for phorone should not be converted to , because the uncatalyzed reaction is due to an intramolecular 1,5-H shift k0K
H rather than to pre-equilibrium ionization of the enol. Conversion of kK 0 = 2.6 11 1 1 = 1.8  10 M s , which is higher than any of the s1 would give k0K
H values observed for simple enols and more than two orders of magnitude higher than that predicted by the Marcus equation for k0K H
. Similar arguments apply to the six a-carboxy-substituted ketones that have been studied by Kresge and coworkers (entries acetoacetate to oxocyclobutane-2-carboxylate in Table 1). Kresge already noted that the rate constants kucK observed for the ‘‘uncatalyzed’’ ketonization of some of these compounds would give unrealistically high calculated values for k0K H
near or above 1011 M1 s1 using Equation (18). Indeed, these calculated values of k0K H
are about two orders of magnitude above those expected from the Marcus relation except that for 4,4,4-trifluoroacetate. The rate constants kK uc observed for the formation of these a-carboxy-substituted ketones are, however, close to K those expected for the protonation of the neutral enols by water, kK uc = k0 . The modest amount of scatter in Fig. 10 is remarkable, considering that it includes four different reaction types (carbon protonation of enols or enolates by hydronium ions or by water) and a wide range of substrates. The standard deviation between the 62 observed values of log kK and those calculated by Equation (19) is 0.95.

352

J. WIRZ


The acidity constants of protonated ketones, pKK a , are needed to deter, mine the free energy of reaction associated with the rate constants kK H

K
). Most ketones are very weak bases, pK < DrG = 2.3RT(pKE þ pKK a a
cannot be determined from the pH–rate 0, so that the acidity constant KK a profile in the range 1 < pH < 13 (see Equation (11) and Fig. 3). The acidity
of a few simple ketones were determined in highly concentrated constants KK a acid solutions.19 Also, carbon protonation of the enols of carboxylates listed in Table 1 (entries cyclopentadienyl 1-carboxylate to phenylcyanoacetate) give the neutral carboxylic acids, the carbon acidities of which are known and are listed
in the column headed pKK a . As can be seen from Fig. 10, the observed rate K constants kH
for carbon protonation of these enols (8 data points marked by the symbol • in Fig. 10) accurately follow the overall relationship that is defined 0K mostly by the data points for k0K H
and k0 . We can thus reverse the process by assuming that the Marcus relationship determined above holds for the protonato estimate the acidity tion of enols and use the experimental rate constants kK H

constants KK of ketones via the fitted Marcus relation, Equation (19). This a procedure indicates, for example, that protonated 2,4-cyclohexadienone is less
acidic than simple oxygen-protonated ketones, pKK a = 1.3. Marcus’ rate theory is useful to rationalize the connection between reactivity and the slope  of Brønsted plots. The derivative of Equation (19) with respect to DrG is the slope of the Marcus curve, which corresponds to the Brønsted exponent  for a given free energy of reaction DrG, Equation (20).74,80  ¼

@Dr G‡ @Dr Go

 p ;T

¼

1þ

Dr G o

! =2

4Dr G‡0

ð20Þ

The Brønsted parameter  varies substantially over the large range of DrG covered by the experimental data collected in Fig. 10; it ranges from 0.2 for the most reactive enolates (phenylethynol anion) to about 0.8 for the least reactive compound (1-naphthol). The -values calculated by Equation (20) are in satisfactory agreement with those determined experimentally from Brønsted plots of general acid catalysis (Table 2). The second derivative of Equation (19) with respect to DrG, Equation (21), represents the change of  with increasing DrG. Using the fitted value of DrG0‡ = 55.6 kJ mol1, one obtains @/@DrG = 0.22  103 mol kJ1. The slope of Fig. 9 amounts to (0.28  0.03)  103 mol kJ1. @ 2 Dr G ‡ @ ½ Dr

Go 2

!

 ¼ p; T

@ @Dr Go

 ¼ p; T

1 8Dr G0‡

ð21Þ

Using these relations, the rate coefficients for specific and general acid catalysis, kH
and kHA, of any keto–enol tautomeric reaction can be predicted from the appropriate free energy of reaction DrG. The required

KINETIC STUDIES OF KETO–ENOL TAUTOMERIC EQUILIBRIA

353

log(k/s–1) 5

5 OH

0

0 kucK

–5 kucK

0

2

k0'K

kH+K

4

6

8

10 12 14 pH

k0'K

kobs K kH+K

–5

kobs K

–10 –15

O

O

OH

–10 –15

0

2

4

6

8

10 12 14 pH

Fig. 11 Effect of Brønsted  on the shape of the pH–rate profile of ketonization.

thermochemical data can be estimated using group additivity rules81,82 or quantum chemical calculations. Equation (20) also rationalizes the fact that the ‘‘uncatalyzed’’, pH-independent portion of pH–rate profiles is marginal for ketones and absent for carboxylic acids with low enol content ( ! 0), but dominates the pH profile of phenol ( ! 1). The pH-independent contribution is generally due to the reaction E þ H
! K, which corresponds to the most exergonic reaction. The corresponding rate constants k0K H
are approaching the limit of diffusion control for simple ketones and are therefore much less sensitive to changes in DrG than and k0K the acid- and base-catalyzed branches of the pH profiles due to kK 0 . As H
an example, the pH–rate profiles for the ketonization of phenol and acetophenone enol are shown in Fig. 11 (thick lines), together with the contributions of 0K E the three individual terms of Equation (9) (dotted lines: kK uc ¼ kH
Ka ; dashed 0K K lines: kH
; long dashed lines: k0 ). Clearly, the uncatalyzed term that is due to the fastest rate constant k0K H
increases less than the others when going to the much more exergonic ketonization of acetophenone enol, so that it is marginalized. The extended pH-independent branch seen in the pH profile of phenylynol (Fig. 6) has an entirely different origin: due to the high acidity of the ynol, pKEa