The Jahn-Teller Effect and Vibronic Interactions in Modern Chemistry

328 Pages·1984·40.372 MB·English

by  Isaak Borisovich Bersuker (auth.)

The Jahn-Teller Effect
and Vibronic Interactions
in Modern Chemistry
MODERN INORGANIC CHEMISTRY
Series Editor: John P. Fackler, Jr.
Texas A&M University
METAL INTERACTIONS WITH BORON CLUSTERS
Edited by Russell N. Grimes
HOMOGENEOUS CATALYSIS
WITH METAL PHOSPHINE COMPLEXES
Edited by Louis H. Pig no let
THE JAHN-TELLER EFFECT AND
VIBRONIC INTERACTIONS IN MODERN CHEMISTRY
I. B. Bersuker
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The Jahn-Teller Effect
and Vibronic Interactions
in Modern Chemistry
I. B. Bersuker
Institute of Chemistry
Moldavian Academy of Sciences
Kishinev, USSR
Plenum Press • New York and London
Library of Congress Cataloging in Publication Data
Bersuker, I. B. (Isaak Borisovich)
The Jahn-Teller effect and vibronic interactions in modern chemistry.
(Modern inorganic chemistry)
Bibliography: p.
Includes index.
n.
1. Jahn-Teller effect. 2. Chemical reactions. I. Title. Series.
QD461.B46 1983 541'.22 83-16070
ISBN-13: 978-1-4612-9654-6 e-ISBN-13: 978-1-4613-2653-3
DOl: 10.1007/978-1-4613-2653-3
© 1984 Plenum Press, New York
Softcover reprint of the hardcover 1s t edition 1984
A Division of Plenum Publishing Corporation
233 Spring Street, New York, N.Y. 10013
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted
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Preface
The first half of the title of this book may delude the uninitiated reader.
The term '"Jahn-Teller effect," taken literally, refers to a special effect
inherent in particular molecular systems. Actually, this term implies a new
approach to the general problem of correlations between the structure and
properties of any molecular polyatomic system, including solids. Just such a
new approach, or concept (in some sense, a new outlook or even a new way
of thinking), which leads not to one special effect but to a series of different
effects and laws, is embodied in the many ( ~ 4000) studies devoted to the
investigation and application of the Jahn-Teller effect. The term "vibronic
interactions" seems to be most appropriate to the new concept, and this
explains the origin of the second half of the title.
The primary objective of this book is to present a systematic develop
ment of the concept of vibronic interactions and its applications, and to
illustrate its possibilities and significance in modern chemistry. In the first
three chapters (covering about one-third of the book) the theoretical
background of the vibronic concept and Jahn-Teller effect is given. The
basic ideas are illustrated fully, although a comprehensive presentation of
the theory with all related mathematical deductions is beyond the scope of
this book. In the last three chapters the applications of theory to spectro
scopy, stereochemistry and crystal chemistry, reactivity, and catalysis, are
illustrated by a series of effects and laws. Greatest consideration is given to
those applications which initiate new trends in appropriate areas of
investigation.
Both the content and structure of this book are in principle different
from those of monographs in chemistry devoted to a definite class of
chemical compounds or a certain method of research. The concept of
vibronic interactions, aimed at improving the bridge between the structure
and properties of substances, is to a certain degree concerned with all kinds
of molecular systems and solids, and affects all methods of investigation
employed in chemistry. This universality of aims and methods is a
characteristic feature of the vibronic approach to the problems in modern
v
vi Preface
chemistry demonstrated in this book. Joined by a common concept, the
various phenomena arising in different systems (and observable by differ
ent methods of study) may serve as a source of new ideas: the reader may
find quite unexpected similarities between very different systems united by
the concept of vibronic interactions.
The author has tried to present the material in a way suitable for a
large number of chemists and physicists (such as scientific workers,
university professors and students, and high s-chool teachers), as well as
engineers engaged in investigating the structure and properties of matter.
For this purpose most attention is paid to the physical meaning of the
results. A limited number of mathematical expressions is analyzed briefly
(mainly in the first three chapters) in order to maintain the quantitative
level of the theory. More detailed deductions can be found easily in the
original papers cited in the References. On the other hand, applications of
the theory are given in such a form that they can be used without a detailed
study of the theory. Nevertheless, for a full understanding of this book the
reader is expected to know the basic ideas of quantum mechanics and the
theory of symmetry.
I should like to express my thanks to my co-workers and colleagues,
especially to S. A. Borshch, S. S. Budnikov, A. S. Dimoglo, M. D. Kaplan,
I. Ya. Ogurtsov, Yu. E. Perlin, V. Z. Polinger, Yu. B. Rosenfeld, B. S.
Tsukerblat, and B. G. Vekhter, with whom research on, and discussion of,
vibronic phenomena (with most of them during a long period of more than
twenty years) made possible the general presentation of the problem
treated in this book. I am grateful to A. Abragam, J. Ammeter, M. Bacci,
C. J. Ballhausen, F. Basolo, C. A. Bates, H. Bill, L. A. Boatner, J.
Brickmann, L. S. Cederbaum, R. E. Coffman, T. M. Dunn, J. Duran, R.
Englman, J. Gazo, G. L. Hofacker, B. Hoffman, O. Kahn, H. Koppel, S.
Kirschner, D. I. Khomskii, R. Lacroix, M. Lambert, S. Leach, A. D. Liehr,
K. A. Muller, M. C. M. O'Brien, R. Pearson, O. E. Polansky, A. Ranfagni,
M. Ratner, D. Reinen, J. S. Slonczewski,M. Thomas, M. Wagner, and their
co-workers for cooperation and discussions. Many thanks are due to
Professor J. P. Fackler, Jr., who read the manuscript thoroughly and made
important suggestions. Also I apologize to those readers whose contribu
tion to works on vibronic problems are not cited here. A comprehensive
list of references can be found in the specially prepared Bibliographic
Review. *
I. B. Bersuker
Kishinev
• The Jahn-Teller Effect: A Bibliographic Review, I. B. Bersuker, IFIIPlenum, New York,
1984.
Contents
. . . . . . . . . . . .
Preface. . . . . . v
Mathematical Notation . . . . . . . . . . . . xi
Introduction - The Concept of Vibronic Interactions 1
Chapter 1. Theoretical Background . . . . . . 7
1.1. The Adiabatic Approximation . . . . . . . 7
1.2. Vibronic Interactions. Linear Vibronic Constants . 10
1.3. Force Constants and Quadratic Vibronic Constants 20
1.4. Orbital Vibronic Constants as Parameters of Molecular
Dynamic Structure . . . . . . . . . . . 23
1.5. Anharmonicity and Instability of Molecular Systems . 27
1.6. The Jahn-Teller Theorem. . 32
Chapter 2. Adiabatic Potentials. 41
2.1. General Considerations. The Orbital Doublet (E Term) 41
2.2. Triplet and Quadruplet Terms 52
2.3. Pseudodegenerate States 61
2.4. The Multimode Problem 69
Chapter 3. Energy Spectra. Dynamic Distortions of Nuclear
Configurations . . . . . . 73
3.1. Some Limiting Cases. Free and Hindered Rotations of the
Distortion . . .. ..... . 73
3.2. Tunneling Splitting. Pulsating Deformations . 82
3.3. Vibronic Reduction Factors 91
3.4. Numerical Solutions . . . 96
vii
viii Contents
Chapter 4. Applications to Spectroscopy 103
4.1. Electronic Spin Resonance and Related Methods 103
The Method of ESR (103) . Vibronic Reduction in ESR Spectra (105) . Influence
of Tunneling Splitting. Transition from Dynamic to Static JTE (108) . Low
Symmetry External Perturbations (111)· The Role of Random Strain in the ESR
E-e Problem (111)· Relaxation Effects (114) . Tunneling Splitting Plus Random
Strain and Relaxation in ESR (117) . Tunneling Splitting in Mi:issbauer Spectra
(128) . Absorption of Microwaves and Ultrasonics (131)
4.2. Vibronic Infrared and Raman Spectra . 133
Vibronic IR Spectra. Selection Rules (133) . The Pure Rotational Vibronic
Spectra (138) . Vibronic Raman Spectra (144)
4.3. Electronic Spectra 148
Vibronic Fine Structure of the Spectra in Gas Phase or in Matrixes (148) .
Structure of the Zero-Phonon Line (155) . Band Shape of Electronic Absorp
tion. Semiclassical Approach (161)· Polarized Luminescence (170)· The Method
of Moments in the Analysis of Band Shapes (173)
Chapter 5. Stereochemistry and Crystal Chemistry 177
5.1. Stereochemistry Rules with JTE and PJTE . 177
Notion of Nuclear Configuration. Semiclassical Approach (177) . Relativity to
the Means of Observation (178) . Stabilization of Static Distortions by Weak
Perturbation. Vibronic Amplification (179) . Dipolar Instability and Dipole
Moments (182) . Some Qualitative Features of Vibronic Stereochemistry (186) .
Displacement of the Central Atom in Coordination Compounds (192) .
Geometry of Small Ligand Coordination to the Central Atom (198) . Examples
of Molecular Systems in Which Vibronic Effects Were Studied (203)
5.2. Cooperative Vibronic Effects in Crystals. Structural Phase
Transitions 203
Cooperative JTE (203) . Rare Earth Zircons (210) . Spinels, Perovskites, and
Other Crystals (218) . K2PbCu(N02)60 Incommensurate Phases (221) . Structural
Magnetic Transitions. Spin and Orbital Orderings (224) . Ferroelectric Phase
Transitions (231)
5.3. Vibronic Crystal Chemistry. Plasticity and Distortion Isomerism 235
Plasticity of the Coordination Sphere around Vibronic Centers (235) . Distor-
tion Isomers (243) . General Validity of the Vibronic Model in Stereochemistry,
Crystal Chemistry, and the Theory of Structural Phase Transitions (247)
Chapter 6. Activation Mechanisms in Chemical Reactions and
Catalysis . 251
6.1. Nature of Instability of the Activated State of a Chemical
Reaction and the Possibility of Its Experimental Observation. 251
Activated States of Chemical Reactions (251) . Stable Excited States of
Activated Complexes (253) • Existence of Bonding States of Arbitrary (Neutral)
Contents ix
Polyatomic Groups (255) . Possible Experimental Information about Activated
Complexes (257)
6.2. Orbital Symmetry Rules in Mechanisms of Chemical Reactions 259
The Vibronic Approach (259) . Comparison with the Classical Woodward
Hoffmann Description (265) . Example with Catalyst Participation (268)
6.3. Vibronic Activation in Elementary Acts of Chemical Reactions
and Catalysis 269
Vibronic Structure as a Basis for a New Approach to the Problem of Chemical
Transformations (269) . Change of Reactivity as a Result of Electronic Rear
rangement (274) . Parametrization (278) . Examples: Activation of Carbon
Monoxide, Nitrogen, and Nitrogen Oxide by Coordination (280) . Mechanisms
of Chemical Reactions in Systems with the JTE (286)
References. 291
Author Index 307
Subject Index 315
Mathematical Notation
Symbols used more than once, but with another meaning, have local
concern only in the corresponding chapter or section indicated in paren
theses
A,B - rotational constants
A - hyperfine constants (§4.1)
- LCAO coefficients
- anharmonicity correction coefficients (§6.3)
- barrier height
- barrier width
E - doubly degenerate representation (term)
E - energy
EJT - JT stabilization energy
e - strain components
e* - effective charge (§5.1)
'if; - electric field intensity
F - linear vibronic constant
F(D) - form function for spectroscopic transition band shapes
(§4.3)
/ - linear orbital vibronic constant
/ - angular-dependence function in ESR spectra (§4.1)
/0., - molecular field intensity (§5.2)
G - quadratic vibronic constant
G cross-section of light scattering (§4.2)
ij -
g - quadratic orbital vibronic constant (§ 1.3)
g - EPR g-factor (§4.1)
g statistical weight (§4.2)
I _
H - Hamiltonian
'Je - magnetic field intensity
'Je Hermite polynomials (§1.2)
n -
xi