7 Springer Series on Fluorescence Methods and Applications Series Editor: O.S. Wolfbeis
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Advanced Fluorescence Reporters in Chemistry and Biology I Fundamentals and Molecular Design Volume Editor: A.P. Demchenko Vol. 8, 2010 Lanthanide Luminescence Photophysical, Analytical and Biological Aspects Volume Editors: P. Ha¨nninen and H. Ha¨rma¨ Vol. 7, 2011 Standardization and Quality Assurance in Fluorescence Measurements II Bioanalytical and Biomedical Applications Volume Editor: Resch-Genger, U. Vol. 6, 2008
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Lanthanide Luminescence Photophysical, Analytical and Biological Aspects Volume Editors: Pekka Ha¨nninen Harri Ha¨rma¨
With contributions by
T. Ala-Kleme J.-C.G. Bu¨nzli H. Bazin S.V. Eliseeva S. Faulkner P. Ha¨nninen H. Ha¨rma¨ I. Hemmila¨ I. Hyppa¨nen J. Kankare S. Kulmala A. Kuusisto V. Laitala G. Mathis T. Nann M. Scha¨ferling T. Soukka C. Spangler U.-H. Stenman J. Suomi D. Sykes H.J. Tanke P.A. Tanner H.-Q. Wang M.H.V. Werts
Volume Editors Prof. Dr. Pekka Ha¨nninen Dr. Harri Ha¨rma¨ University of Turku Department of Cell Biology and Anatomy Tykisto¨katu 6A 20520 Turku, Finland
[email protected] [email protected] ISSN 1617-1306 e-ISSN 1865-1313 ISBN 978-3-642-21022-8 e-ISBN 978-3-642-21023-5 DOI 10.1007/978-3-642-21023-5 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011930252 # Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg, Germany Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Series Editor Prof. Dr. Otto S. Wolfbeis Institute of Analytical Chemistry Chemo- and Biosensors University of Regensburg 93040 Regensburg Germany
[email protected] Aims and Scope Fluorescence spectroscopy, fluorescence imaging and fluorescent probes are indispensible tools in numerous fields of modern medicine and science, including molecular biology, biophysics, biochemistry, clinical diagnosis and analytical and environmental chemistry. Applications stretch from spectroscopy and sensor technology to microscopy and imaging, to single molecule detection, to the development of novel fluorescent probes, and to proteomics and genomics. The Springer Series on Fluorescence aims at publishing state-of-the-art articles that can serve as invaluable tools for both practitioners and researchers being active in this highly interdisciplinary field. The carefully edited collection of papers in each volume will give continuous inspiration for new research and will point to exciting new trends.
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Preface
Lanthanides have fascinated scientists for more than two centuries now – first starting at the end of eighteenth century because they presented previously unknown metals from “missing” block of the periodic table and further because of their properties. This book is about luminescence of these elements, maybe the most intriguing feature of lanthanides; luminescence that has so many uses – industrial and research. These unique luminescence properties have led to broad industrial exploitation of these f-block elements of the periodic table: bioanalytics, lasers, illumination, and displays – the role of luminescent lanthanides is extensive and rapidly growing. Lanthanides plus yttrium and scandium are also known as “rare earths” – a historical misinterpretation that stems from the way that these metals were first discovered. For those who have been working with sensitive lanthanide-based assays and especially for those who have been building instrumentation for time-resolved measurements, the luminescent lanthanides are far from rare – especially glass components of almost any glass will show unwanted background at lanthanide emission wavelengths. The word lanthanide has its origins in Greek and its meaning “lying hidden” is maybe the best explanation for why these naturally abundant elements were considered rare: separation of them from other minerals was not trivial for early day metallurgists since the lanthanides were “hiding” from other minerals. Once efficient separation techniques were established 50 years ago, the use of the lanthanides found their way into industrial exploitation and our everyday life. - For once so scarce they lie no longer hidden but illuminate our lives and serve us well Luminescence of lanthanides in crystalline form is maybe the best-known application for the common people. The lighting and display industry has utilized the unique long lifetime luminescence as phosphors and laser industry has exploited lanthanide crystals since population inversion is easy to achieve with long lifetime laser materials. Beyond the luminescence use, lanthanides are used in magnets, glass production, as colorants, contrast agents, in computer memories – the
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application field is broad, but as said, this book is about luminescence of these compounds with special emphasis on bioanalytics. Whereas the applications of solid luminescent lanthanides can well be paired with the progress of the electronics industry, the use of the lanthanides in biomedical field started from the need to change the way the researchers and industry were operating, and it certainly took its own pace. Already in 1942, Weissman had discovered the sensitizing of lanthanide luminescence by organic ligands, but the first bioapplications were not proposed until in the 1970s when Vallarino and Leif suggested the use of lanthanide labels in cytometry – it took an industrialist to generate the “breakthrough” in the field of bioanalytics! Radioimmunoassays (RIAs) were dominating the bioassaying during the 1960s and 70s. Although sensitive, the problems related to the use of radioactive tracers were eminent, and already in the late 1960s, ideas of assays based on the use of enzymatic reactions or the use of fluorescent tracers were presented. However, the new methods could not compete with RIA in all of its flavors, the field was open for new ideas. The use of rare-earths in immunoassays as labels was first discussed by two physicists when Erkki Soini, the director of research at company Wallac visited researcher Reino Laiho at the Wihuri Physical Laboratory, University of Turku. Research of time-resolved luminescence had already started at Wallac earlier but Wallac did not have a suitable label. The trials with conventional fluorochromes had led to serious problems on developing instrumentation that could be routinely used. The spectroscopic properties of lanthanides were well known from solid state physics, and after the discussion, the research at Wallac got a new course. Wallac, a small Turku-based company had grown in 1960s and 1970s building beta- and gamma counters for various purposes – in the 70s the fastest growing field was RIA but the company research was set a new course by these new ideas. The use of lanthanides in bioassays evolved rapidly from Wallac’s DELFIA principle to first directly luminescent chelates and to TR-FRET, first proposed by Morrison and then pioneered by Mathis – developments that took the use of lanthanides from clinical routines to research and discovery. With applications in microscopy pioneered by Tanke, Seveus, and others, the lanthanides are now among the most important tools in bioanalysis – listing of all applications would certainly be appropriate to honor everybody involved, but is well beyond this preface. The purpose of this book is not to give a complete overview on lanthanide luminescence but rather highlight the special aspects of their luminescence with emphasis toward biological research without forgetting their basic luminescent properties – both in liquid and in solid materials. If readers intend to step into the use of lanthanides or refine their ways of using them, we hope that this book can serve as a comprehensive handbook and help them toward their goals. Although the history of utilizing lanthanide luminescence by now is long, they are still today’s news since new ways of putting lanthanide luminescence into use appear constantly. We ourselves have been intrigued by the special properties of the lanthanides that can so well be utilized in bioanalytics – having worked with several different luminescent molecules and materials we still turn back to lanthanide labels whenever there is a problem with sensitivity. We also hope that this book can be
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seen as a tribute to all the people who have contributed to the field in our hometown. Turku has played a central role with discovery of “rare earths” and putting them into use. From professor Johann Gadolin who at the Academy of Turku discovered yttrium more than 200 years ago to Erkki Soini, Ilkka Hemmila¨, and many others who at their turn have put lanthanide luminescence to practical work. Turku, March 2011
Pekka Ha¨nninen, Harri Ha¨rma¨
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Contents
Basics of Lanthanide Photophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Jean-Claude G. Bu¨nzli and Svetlana V. Eliseeva Stable Luminescent Chelates and Macrocyclic Compounds . . . . . . . . . . . . . . . 47 G. Mathis and H. Bazin Lanthanide Nanoparticules as Photoluminescent Reporters . . . . . . . . . . . . . . 89 Tero Soukka and Harri Ha¨rma¨ Upconverting Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Hai-Qiao Wang and Thomas Nann Near-Infrared Luminescent Labels and Probes Based on Lanthanide Ions and Their Potential for Applications in Bioanalytical Detection and Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Martinus H.V. Werts Lanthanide Assemblies and Polymetallic Complexes . . . . . . . . . . . . . . . . . . . . . 161 Stephen Faulkner and Daniel Sykes Lanthanide Luminescence in Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Peter A. Tanner Luminescent Chemical and Physical Sensors Based on Lanthanide Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Corinna Spangler and Michael Scha¨ferling Time-Domain Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Ari Kuusisto and Pekka Ha¨nninen Frequency-Domain Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Jouko Kankare and Iko Hyppa¨nen Imaging of Lanthanide Luminescence by Time-Resolved Microscopy . . . . 313 H.J. Tanke
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Clinical Application of Time-Resolved Fluorometric Assays . . . . . . . . . . . . . 329 Ulf-Ha˚kan Stenman Electrochemiluminescence of Lanthanides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 S. Kulmala, T. Ala-Kleme, and J. Suomi Sensitized Bioassays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Ilkka Hemmila¨ and Ville Laitala Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
Basics of Lanthanide Photophysics Jean-Claude G. Bu¨nzli and Svetlana V. Eliseeva
Abstract The fascination for lanthanide optical spectroscopy dates back to the 1880s when renowned scientists such as Sir William Crookes, LeCoq de Boisbaudran, Euge`ne Demarc¸ay or, later, Georges Urbain were using luminescence as an analytical tool to test the purity of their crystallizations and to identify potential new elements. The richness and complexity of lanthanide optical spectra are reflected in an article published in 1937 by J.H. van Vleck: The Puzzle of Rare Earth Spectra in Solids. After this analytical and exploratory period, lanthanide unique optical properties were taken advantage of in optical glasses, filters, and lasers. In the mid-1970s, E. Soini and I. Hemmila¨ proposed lanthanide luminescent probes for time-resolved immunoassays (Soini and Hemmila¨ in Clin Chem 25:353–361, 1979) and this has been the starting point of the present numerous bio-applications based on optical properties of lanthanides. In this chapter, we first briefly outline the principles underlying the simplest models used for describing the electronic structure and spectroscopic properties of trivalent lanthanide ions LnIII (4fn) with special emphasis on luminescence. Since the book is intended for a broad readership within the sciences, we start from scratch defining all quantities used, but we stay at a descriptive level, leaving out detailed mathematical developments. For the latter, the reader is referred to references Liu and Jacquier, Spectroscopic properties of rare earths in optical materials. Tsinghua University Press & Springer, Beijing & Heidelberg, 2005 and Go¨rller-Walrand and Binnemans, Rationalization of crystal field parameters. In: Gschneidner, Eyring (eds) Handbook on the physics and chemistry of rare earths, vol 23. Elsevier BV, Amsterdam, Ch 155, 1996. The second part of the chapter is devoted to practical aspects of lanthanide luminescent probes, both from the point of view of their design and of their potential utility.
J.-C.G. Bu¨nzli (*) and S.V. Eliseeva Laboratory of Lanthanide Supramolecular Chemistry, E´cole Polytechnique Fe´de´rale de Lausanne, BCH 1402, 1015 Lausanne, Switzerland e-mail:
[email protected] P. Ha¨nninen and H. Ha¨rma¨ (eds.), Lanthanide Luminescence: Photophysical, Analytical and Biological Aspects, Springer Ser Fluoresc (2011) 7: 1–46, DOI 10.1007/4243_2010_3, # Springer-Verlag Berlin Heidelberg 2010, published online: 13 July 2010
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Keywords Crystal-field analysis Energy transfer f–f Transition Intrinsic quantum yield Lanthanide bioprobe Lanthanide luminescence Lanthanide spectroscopy Lifetime Luminescence sensitization Population analysis Quantum yield Radiative lifetime Selection rule Site symmetry Stern–Volmer quenching
Contents 1
Electronic Structure of Trivalent Lanthanide Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Atomic Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Electronic Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 The Ions in a Ligand Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Absorption Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1 Induced ED f–f Transitions: Judd–Ofelt Theory [5, 6] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 4f–5d and CT Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Emission Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4 Sensitization of Lanthanide Luminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.1 Design of Efficient Lanthanide Luminescent Bioprobes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 Practical Measurements of Absolute Quantum Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5 Information Extracted from Lanthanide Luminescent Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.1 Metal Ion Sites: Number, Composition, and Population Analysis . . . . . . . . . . . . . . . . . . . 29 5.2 Site Symmetry Through Crystal-Field Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.3 Strength of Metal–Ligand Bonds: Vibronic Satellite Analysis . . . . . . . . . . . . . . . . . . . . . . 31 5.4 Solvation State of the Metal Ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.5 Energy Transfers: Donor–Acceptor Distances and Control of the Photophysical Properties of the Acceptor by the Donor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.6 FRET Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.7 Ligand Exchange Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.8 Analytical Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 6 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.1 Site Symmetry Determination from EuIII Luminescence Spectra . . . . . . . . . . . . . . . . . . . . 39 6.2 Examples of Judd–Ofelt Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.3 Examples of Reduced Matrix Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6.4 Emission Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Abbreviations AO CF CT DMF DNA dpa dtpa EB ED
Acridine orange Crystal field Charge transfer Dimethylformamide Deoxyribonucleic acid Dipicolinate (2,6-pyridine dicarboxylate) Diethylenetrinitrilopentaacetate Ethidium bromide Electric dipole
Basics of Lanthanide Photophysics
EQ FRET hfa ILCT ISC JO LLB LMCT MD MLCT NIR PCR SO tta YAG
3
Electric quadrupole Fo¨rster resonant energy transfer Hexafluoroacetylacetonate Intraligand charge transfer Intersystem crossing Judd–Ofelt Lanthanide luminescent bioprobe Ligand-to-metal charge transfer Magnetic dipole Metal-to-ligand charge transfer Near-infrared Polymerase chain reaction Spin–orbit Thenoyltrifluoroacetylacetonate Yttrium aluminum garnet
1 Electronic Structure of Trivalent Lanthanide Ions 1.1
Atomic Orbitals
In quantum mechanics, three variables depict the movement of the electrons around the positively-charged nucleus, these electrons being considered as waves with wavelength l ¼ h/mv where h is Planck’s constant (6.626 1034 J s1), m and v the mass (9.109 1031 kg) and velocity of the electron, respectively: – The time-dependent Hamiltonian operator H describing the sum of kinetic and potential energies in the system; it is a function of the coordinates of the electrons and nucleus. – The wavefunction, Cn, also depending on the coordinates and time, related to the movement of the particles, and not directly observable; its square (Cn)2 though gives the probability that the particle it describes will be found at the position given by the coordinates; the set of all probabilities for a given electronic Cn, is called an orbital. – The quantified energy En associated with a specific wavefunction, and independent of the coordinates. These quantities are related by the dramatically simple Schro¨dinger equation, which replaces the fundamental equations of classical mechanics for atomic systems: HCn ¼ En Cn :
(1)
Energies En are eigenvalues of Cn, themselves called eigenfunctions. In view of the complexity brought by the multidimensional aspect of this equation
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(3 coordinates for each electron and nucleus, in addition to time) several simplifications are made. Firstly, the energy is assumed to be constant with time, which removes one coordinate. Secondly, nuclei being much heavier than electrons, they are considered as being fixed (Born–Oppenheimer approximation). Thirdly, since the equation can only be solved precisely for the hydrogen atom, the resulting hydrogenoid or one-electron wavefunction is used for the other elements, with a scaling taking into account the apparent nucleus charge, i.e., including screening effects from the other electrons. Finally, to ease solving the equation for non-H atoms, the various interactions occurring in the electron-nucleus system are treated separately, in order of decreasing importance (perturbation method). For hydrogen, the Hamiltonian simply reflects Coulomb’s attraction between the nucleus and the electron, separated by a distance ri, and the kinetic energy of the latter:1 1 1 H0 ¼ D i ri 2
@2 @2 @2 : D¼ þ þ @x2 @y2 @z2
(2)
Each wavefunction (or orbital: the two terms are very often, but wrongly, taken as synonyms) resulting from solving (1) is defined by four quantum numbers reflecting the quantified energy of the two motions of the electrons: the orbital motion, defined by the angular momentum ~ ‘, and the spin, characterized by the angular momentum ~ s. If polar coordinates (r, #, ’) are used, wavefunctions are expressed as the product of a normalizing factor N, of a radial function ð2‘ þ 1Þ; J ¼ Jmax :
Note that if the sub-shell is half filled, then L = 0 and J = S. Additionally, J may take half-integer values if S is half-integer. The set of levels is referred to as a multiplet and this multiplet is a regular one if n < (2ℓ + 1), the energy of the levels increasing with increasing values of J, while it is inverted if n > (2ℓ + 1). This is illustrated with EuIII (4f6) for which the ground level is 7F0 while it is 7F6 for TbIII (4f8). Finally, the energy difference between two consecutive spin–orbit levels with quantum numbers J and J0 = J + 1 is directly proportional to J0 : DE ¼ l J 0 :
(8)
The electronic properties of the trivalent 4f free ions are summarized in Table 1.
1.3
The Ions in a Ligand Field
The above developments are valid for free ions. When a LnIII ion is inserted into a chemical environment, the spherical symmetry of its electronic structure is destroyed and the remaining (2J þ 1) degeneracy of its spectroscopic levels is partly lifted, depending on the exact symmetry of the metal–ion site. In view of the
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Table 1 Electronic properties of LnIII free ions Multiplicity No. of terms No. of levels Ground level z/cm1,a l/cm1,a fn 0 14 1 1 f f 1 1 1 S0 S0 – – – – 2 f1 f13 14 1 2 F5/2 2F7/2 625 2,870 625 2,870 3 7 13 H4 3H6 740 2,628 370 1,314 f2 f12 91 4 f3 f11 364 17 41 I9/2 4I15/2 884 2,380 295 793 5 5 47 107 I4 I8 1,000 2,141 250 535 f4 f10 1,001 6 f5 f9 2,002 73 198 H5/2 6H15/2 1,157 1,932 231 386 7 6 8 7 f f 3,003 119 295 F0 F6 1,326 1,709 221 285 8 3,432 119 327 S7/2 1,450 0 f7 a For aqua ions, except for CeIII (Ce:LaCl3) and YbIII (Yb3Ga5O12), from [2]. The first column refers to f1–7 and the second to f8–14
inner character of the 4f wavefunctions their mixing with the surrounding orbitals remains small and so is the resulting level splitting (a few hundreds of cm1), so that this perturbation can be treated last. Nevertheless, the resulting Hamiltonian gets very complex, so that a simplifying concept has been put forward by H. Bethe in 1929: the ligands are replaced by (negative) point charges generating a crystal (or ligand) electrostatic field which, in turn, interacts with the moving 4f electrons, generating a ligand-field (or crystal-field, or Stark) splitting of the spectroscopic levels. With the parameterization introduced by B. G. Wybourne in 1965, the final Hamiltonian becomes: H¼
X n n X X Z0 1 1 ~ S~ þ Di þ þlL Bkq CðkÞ q ðiÞ; r 2 r i i¼1 k;q;i i6¼j ij
(9)
where the summation involving i is on all the 4f electrons, Bqk are ligand-field parameters, commonly treated as phenomenological parameters, and C(k)q are components of tensor operators C(k) which transform like the spherical harmonics used for the analytical form of the 4f wavefunctions. The running number k must be even and smaller than 2ℓ; for 4f electrons it can, therefore, take values of 0, 2, 4, and 6. The values for q are restricted by the point group of symmetry into which the LnIII ion is embedded, but in any case, jqj k. The Bqk parameters may be complex numbers but they have to be real for any symmetry group with a 180 rotation about the y axis or with the xy plane being a mirror plane. The relationship between the 32 crystallographic symmetry groups and the Bqk parameters is given in Table 2. In order to compare the ligand field strengths in different compounds, F. Auzel has proposed the following expression for an “average” total ligand-field effect: "
2 #1=2 1 X ðBkq Þ : Nv ¼ 4p k;q ð2k þ 1Þ
(10)
Basics of Lanthanide Photophysics
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Table 2 Non-zero crystal-field parameters for fn electronic configurations and examples of corresponding crystal hosts [1] Symmetry Site symmetry Crystal field parameters Example 2 4 6 2 4 6 4 6 6 Monoclinic C1, CS, C2, C2h, LaF3 B0 ; B0 ; B0 ;
