Advances in multi-photon processes and spectroscopy. Volume 15

ADVANCES IN MULTI-PHOTON PROCESSES AND SPECTROSCOPY

ADVANCES IN MULTI-PHOTON PROCESSES AND SPECTROSCOPY

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ADVANCES IN MULTI-PHOTON PROCESSES AND SPECTROSCOPY S'*'-* Volume 0 5 )

Edited by

SHLin Institute of Atomic and Molecular Sciences, TAIWAN & Arizona State University, USA

A A Villaeys Institut de Physique et Chimie des Materiaux de Strasbourg, FRANCE

Y Fujimura Graduate School of Science Tohoku University, JAPAN

V f e World Scientific wb

New Jersey • London • Singapore • Hong Kong

Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

ADVANCES IN MULTI-PHOTON PROCESSES AND SPECTROSCOPY — Vol. 15 Copyright © 2003 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 981-238-263-1

This book is printed on acid-free paper. Printed in Singapore by Mainland Press

V

Preface In view of the rapid growth in both experimental and theoretical studies of multiphoton process and multiphoton spectroscopy of atoms, ions and molecules in chemistry, physics, biology, materials science, etc., it is desirable to publish an Advanced Series that contains review papers readable not only by active researchers in these areas, but also by those who are not experts in the field but who intend to enter the field. present series attempts to serve this purpose.

The

Each review article is

written in a self-contained manner by the experts in the area so that the readers can grasp the knowledge in the area without too much preparation. The topics covered in this volume are "Polarizabilities and Hyperpolarizabilities of Dendritic Systems", "Molecules in Intense Laser Fields: Nonlinear Multiphoton Spectroscopy and Near-Femtosecond To Sub-Femtosecond (Attosecond) Dynamics", and "Ultrafast Dynamics and non-Markovian Processes in Four-Photon Spectroscopy".

The editors

wish to thank the authors for their important contributions.

It is hoped

that the collection of topics in this volume will be useful not only to active researchers but also to other scientists in biology, chemistry, materials science and physics. S. H. Lin A. A. Villaeys Y. Fujimura

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Contents

Preface

Part One:

v

Polarizabilities and Hyperpolarizabilities of Dendritic Systems

1

Masayoshi Nakano and Kizashi Yamaguchi

Part Two:

Molecules in Intense Laser Fields: Nonlinear Multiphoton Spectroscopy and Near-Femtosecond To Sub-Femtosecond (Attosecond) Dynamics

147

Andre D. Bandrauk and Hirohiko Kono

Part Three: Ultrafast Dynamics and non-Markovian Processes in Four-Photon Spectroscopy B. D. Fainberg

215

PART ONE Polarizabilities and Hyperpolarizabilities of Dendritic Systems

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3

Polarizabilities and Hyperpolarizabilities of Dendritic Systems Masayoshi Nakano and Kizashi Yamaguchi Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Contents

Abstract

6

1. Introduction

8

2. Polarizabilities and Hyperpolarizabilities of Dendritic Aggregate Systems 2.1. Aggregate Models 2.2. Density Matrix Formalism for Molecular Aggregate under Time-Dependent Electric Field 2.3. Nonperturbative (Hyper)polarizabilities and Their Partition into the Contribution of Exciton Generation 2.4. Off-Resonant Polarizabilities of Dendritic Aggregates 2.4.1. One-Exciton States and Their Spatial Contribution to a 2.4.2. Effects of Intermolecular Interaction and Relaxation on the Spatial Contribution of One-Exciton Generation to a 2.4.3. Comparison of Polarizabilities of Dendritic Aggregates with Those of One-Dimensional (Linear) and Two-Dimensional (Square-Lattice) Aggregates 2.5. Off-Resonant Second Hyperpolarizabilities of Dendritic Aggregates 2.5.1. Two Types of Dendritic Aggregates with and without a Fractal Structure 2.5.2. Spatial Contributions of One- and Two-Exciton Generations to y of D10 2.5.3. Effects of Intermolecular Interaction and Relaxation on the Spatial Contributions on One- and Two-Exciton Generation to y of D10 2.5.4. Spatial Contributions on One- and Two-Exciton Generations to yof D25 2.5.5. Effects of Intermolecular Interaction and Relaxation on the Spatial Contributions of One- and Two-Exciton Generations to yof D25 2.6. Near-Resonant Second Hyperpolarizabilities of Dendritic Aggregates 2.7. Summary 3. Polarizabilities and Hyperpolarizabilities of Dendrimers 3.1. Cayley-Tree-Type Dendrimers with ^-Conjugation 3.2. Finite-Field Approach to Static (Hyper)polarizabilities 3.3. Hyperpolarizability Density Analysis 3.4. Size Dependencies of a and yof Oligomer Models for Dendron Parts 3.4.1. Model Oligomers 3.4.2. Comparison of the a and y Values and Their Density Distributions of Stilbene Calculated by the PPP CHF Method with Those by the B3LYP Method 3.4.3. Size Dependencies of a and y for Model Oligomers 3.4.4. a and yDensity Distributions for Model Oligomers

11 11 14 17 20 21 24

26 28 28 30 31 33 34 35 37 41 41 43 47 53 53

55 57 59

3.5. Second Hyperpolarizabilities of Cayley-Tree-Type Phenylacetylene Dendrimers 3.5.1. Calculation of yof D25 3.5.2. Comparison of the y Value and /Density Distribution of Diphenylacetylene Calculated by the INDO/S CHF Method with Those by the B3L YP Method 3.5.3. y and y Densities of D25 3.6. Summary 4. Extensions of Models and Analysis 4.1. Master Equation Approach Involving Explicit Exciton-Phonon Coupling 4.1.1. Model Hamiltonian Involving Exciton-Phonon Coupling 4.1.2. Master Equation Approach 4.2. Analytical Expression of Hyperpolarizability Density 4.2.1. Analytical Formula of Hyperpolarizability Density 4.2.2. Imy Density of trans-Stilbene 4.3. Summary

62 63

63 64 67 69 69 70 74 79 81 89 91

5. Concluding Remarks

92

Acknowledgments References

95 96

6

Abstract Recently, a new class of polymeric systems, i.e., dendrimers, has attracted much attention because of their high controllability of architecture and several interesting properties, e.g., high light-harvesting and drug delivery properties. "Dendrimers" are characterized by a large number of terminal groups originating in a focal point (core) with at least one branch (linear-leg region) at each repeat unit. Such attractive architecture is expected to have a close relation to various chemical and physicsl functionalities of systems. In this review, we focus on the theoretical studies on optical response properties such as polarizabilities and hyperpolarizabilities for these systems from the view point of the relation among the unique architecture (dendritic structure) and the optical response properties. As an example, we consider Cayleytree-type dendrimers, which are known to have fractal antenna architectures and to exhibit high light-harvesting properties. Since exciton migration is pre imed to be essential for the high light-harvesting properties for these dendrimers, we firstly consider exciton models, i.e., molecular aggregate models with fractal antenna structures composed of two-state monomers.

We apply the numerical Liouville

approach to the exciton migration dynamics and investigate the influence of the multistep exciton states and relaxation processes among exciton states on the polarizabilities (a) and second hyperpolarizabilities (f).

It is found that the dominant spatial

contributions of excitons to a nd y are localized in linear-leg regions and reflect the dendritic structures. The difference among the spatial dimensions of structures is also found to remarkably affect the size dependency of intermolecular-interaction effects on a.

Second, the longitudinal a and y values of dendron parts (oligomers) involved in

7 Cayley-tree-type dendrimers composed of phenylene vinylene units and the /values of a phenylacetylene dendrimer are examined using the molecular orbital (MO) method. With the aid of (hyper)poarizability density analyses, such dendrimers with fractal antenna structures are found to provide spatially localized contributions of electrons to (hyper)polarizabilities similarly to the dendritic aggregate case and are predicted to have the possibility of controlling the magnitude and sign of their (hyper)polarizabilities by changing the size of generations and the connection forms between linear-leg regions. These features are expected to be advantage to the molecular design of novel (controllable) nonlinear optical materials.

8

1.

Introduction

A new class of polymeric systems, i.e., dendrimers, has been synthesized and has attracted much attention because of their unique chemical, transport and optical properties [1-10]. In general, dendritic molecules are characterized by a large number of terminal groups originating in a focal point (core) with at least one branch at each repeat unit. The efficient excitation energy cascades to the core is predicted to be caused by the fact that the molecular architecture provides an energy gradient as the energy decreases as a function of position from the periphery to the core and has the relaxation in the exciton states [11-19]. In particular, exciton funnels are expected to exist along the antenna structures in Cayley-tree-type dendrimers, which possess a fractal

structure composed of linear-leg regions (para-connected units, e.g.,

phenylacetylenes) and meto-connected branching points, e.g., benzene rings. There have been lots of theoretical and experimental investigations on such dendritic aggregate models and dendrimers. Judging from these results, the efficient energy transfer from the periphery to the core due to the energy gradient and the relaxation among exciton states are expected to strongly depend on the architecture, the size and the unit molecular species. On the other hand, there have been a small number of studies on the optical response properties, e.g., nonlinear optical (NLO) properties, for such systems [21-27] though the first-order optical processes, i.e., absorption and emission of light, have been investigated actively. For the past two decades, organic molecular systems with large NLO response properties have attracted great attention both in scientific and technological fields due to their large susceptibilities, fast responsibility and possibility of modification [28-32].

9 The organic NLO effects originate in the microscopic nonlinear polarization mainly enhanced by ^-electron conjugation at the molecular level.

Such microscopic

nonlinear polarization is characterized by the hyperpolarizabilities.

A variety of

organic ^-conjugated molecular systems, e.g., donor-acceptor substituted polymeric systems, polyaromatic systems and molecular crystal systems, have been intensely investigated due to their low-excitation energies and large transition properties. Considering the feature that the molecular (hyper)polarizabilities remarkably depend on the slight variations in quantities (transition energies and transition moments) of excited states, the optical response properties of such dendritic systems are predicted to sensitively reflect the effects of the unique structure, i.e., dendritic structures with fractal antenna shapes.

In this review, we firstly consider dendritic molecular

aggregates modeled after phenylacetylene dendrimers: simple aggregate models are composed of two-state monomers which interact with each other by the dipole-dipole coupling [19,20,24,25,33,34]. The structure of exciton states and its dependency on the configuration of monomers are elucidated.

The polarizabilities (a) and second

hyperpolarizabilities {j) are calculated using the definition of nonperturbative (hyper)polarizabilities in the numerical Liouville approach (NLA) [35-39]. The spatial contributions of one- and two-excition generations and the relaxation (among exciton states) effects to a and y are elucidated in dendritic aggregate systems. The size dependencies of intermolecular-interaction effects on a of dendritic aggregate systems are also compared to those of aggregate systems with other spatial configurations, i.e., linear-chain (one-dimensional) and square-lattice (two-dimensional) systems.

Second,

we consider supramolecular systems composed of ^-conjugated units (phenylacetylenes or phenylene vinylenes) linked with each other by para- or meta-connection.

In order

10

to elucidate the effects of fractal structures with meta- and para-connected benzene rings on the a and y, we consider several oligomers modeled after dendron parts. Further, the several components of y of a real Cayley-tree-type phenylacetylene dendrimer (D25) composed of 24 units of phenylacetylenes are investigated using the coupled-Hartree-Fock (CHF) calculations [40] at the INDO/S approximation level [41]. In the analysis of these (hyper)polarizabilities, the spatial distributions of (hyper)polarizability densities [42-45], which are defined (in the static case) as the derivatives of charge densities with respect to applied electric fields, are employed in order to elucidate the structure-property relation of (hyper)polarizabilities for these dendritic systems. The present review is organized as follows.

In Sec. 2, the calculation methods

of exciton dynamics and nonperturbative a and y are described in the numerical Liouville approach [35-39]. The spatial contributions of exciton generations to a and y are analyzed and the size and spatial-dimension dependencies of a and y are investigated in the off-and near-resonant regions. In Sec. 3, the size dependencies of a and yof phenylene vinylene oligomers and the /values of a phenylacetylene dendrimer (D25) are investigated using (hyper)polarizability density analysis.

Section 4

describes an extension of the procedure treating exciton dynamics, i.e., an explicit treatment of relaxation originating in the exciton-phonon coupling, and presents an analytical expression of dynamic (hyper)polarizability densities, which are useful for investigating the imaginary y describing two-photon absorption (TPA) spectra of dendritic systems. In conclusion (Sec. 5), the results obtained here are discussed from the viewpoint of the relation between the (non)linear optical response properties and the unique spatial structures of systems, i.e., dendritic structures with fractal-antenna

11

shapes.

2. Polarizabilities and Hyperpolarizabilities of Dendritic Aggregate Systems 2.1. Aggregate Models

The spatial architectures of fractal-antenna dendrimers, e.g., phenylacetylene dendrimers,

shown in Fig.l are composed of branchings at the meta positions of the

benzene nodes [11-19]. The fractal nature in the number of units involved in the linear-leg regions is caused by the meta-position substitutions.

Other types of

branchings, i.e., para- and ortfco-positions, will generate a linear chain and will terminate the tree structure due to the steric hindrance.

It is found from recent

calculations that ^-conjugation is well decoupled at the zneta-positions [16,26,27], and that the meta-position branchings allow some distortions from a planar structure, the feature of which enables us to synthesize larger dendritic systems by overcoming steric hindrance. As simple models of the fractal antenna dendrimers, we consider molecular aggregates (D4, D10, D25, D58 and D127 shown in Fig.2) in which a monomer is assumed to be a dipole unit (a two-state monomer, which is illustrated by an arrow) arranged as modeled after the dendritic structure shown in Fig. 1 [19,24]. The klh monomer possesses a transition energy, £*,(= E\ — E\~), and a transition moment, /if2. This approximation is considered to be acceptable if the intermolecular distance (R kl ) is larger than the size of a monomer.

These aggregate models possess slight

intermolecular interactions between adjacent legs at the branching points since their intermolecular distance (i?V3) is larger than that (/?) in the same leg regions. It is

12

noted that such decreases in the intermolecular interactions at the branching points are similar to the situation in real dendrimers, in which the meta-branching points destroy the TT-electronic conjugation between adjacent linear legs. For two dipoles k and /, the angle between a dipole k(l) and a line drawn from the dipole site k to / is 9k(8l ). The Hamiltonian for the aggregate model (composed of N monomers) is written by [19]

= ttEt