The Jahn–Teller Effect

Cambridge University Press
0521822122 - The Jahn–Teller Effect - by Isaac B. Bersuker
Frontmatter/Prelims

THE JAHN–TELLER EFFECT

The Jahn–Teller effect is one of the most fascinating phenomena in modern physics and chemistry, providing a general approach to understanding the properties of molecules and crystals and their origins. The effect inspired one of the most important recent scientific discoveries, the concept of high-temperature superconductivity. This comprehensive volume presents the background of the theory and its main applications in physics and chemistry, along with more recent achievements. Full descriptions are presented alongside thorough references to original material. The book contains over 200 figures to aid visual explanation and avoids bulky mathematical deductions and overly technical language. It is intended for graduate students and academic researchers working in solid-state physics, theoretical, physical, and quantum chemistry, crystallography, spectroscopy, and materials science.

ISAAC B. BERSUKER is a Senior Research Scientist and Adjunct Professor of Theoretical Chemistry at the University of Texas at Austin. His main scientific interest is in the theory of vibronic interactions and Jahn–Teller Effect with applications to solid-state physics, chemistry, and biology. He is the author and co-author of 12 books, 25 major reviews, and more than 300 original publications.

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THE JAHN–TELLER EFFECT

ISAAC B. BERSUKER

The University of Texas at Austin

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In memory of my wife Liliya Bersuker

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CAMBRIDGE UNIVERSITY PRESS
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© I. B. Bersuker 2006

This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.

First published 2006

Printed in the United Kingdom at the University Press, Cambridge

A catalog record for this publication is available from the British Library

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ISBN-13 978-0-521-82212-1 hardback

ISBN-10 0-521-82212-2 hardback

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Contents

Preface				page xi
Abbreviations				xv
1	Introduction			1
	1.1	The history and evolution of understanding of the Jahn–Teller effect (JTE)		1
	1.2	The role and place of the JT vibronic coupling effects in modern molecular structure and condensed matter theory		6
	1.3	The main goals of this book and means of their realization		9
	References			10
2	Vibronic interactions			12
	2.1	The adiabatic approximation		12
	2.2	Vibronic interactions. Vibronic coupling constants		17
	2.3	Orbital vibronic constants		27
	2.4	Force constants, anharmonicity, and instability		31
	2.5	The Jahn–Teller theorem		35
	References			43
3	Formulation of Jahn–Teller problems. Adiabatic potentials			45
	3.1	Basic formulations. The simplest E ⊗ b1 and E ⊗ (b1 + b2) problems		45
	3.2	The E ⊗ e problem		52
	3.3	T ⊗ e, T ⊗ t2, T ⊗ (e + t2), and Γ8 ⊗ (e + t2) problems		62
	3.4	T ⊗ h, pn ⊗ h, G ⊗ (g + h), and H ⊗ (g + h) problems for icosahedral systems		73
	3.5	Adiabatic potentials in the multimode problem		91
	3.6	Multicenter systems		95
	References			106
4	Pseudo Jahn–Teller, product Jahn–Teller, and Renner–Teller effects			110
	4.1	Two-level and multilevel pseudo JT (PJT) problems. Uniqueness of the PJT origin of configuration instability and its bonding nature		110
	4.2	Pseudo JT (A + E) ⊗ e, (A + T) ⊗ t, (T1 + T2) ⊗ e, and combined JT and PJT problems		122
	4.3	Product JTE problems		135
	4.4	The Renner–Teller effect		151
	4.5	Reformulation of the JT theorem		155
	References			160
5	Solutions of vibronic equations. Energy spectra and JT dynamics			162
	5.1	Weak vibronic coupling, perturbation theory		162
	5.2	Strong vibronic coupling		169
	5.3	Tunneling in JT systems		179
	5.4	Numerical methods and general solutions		198
	5.5	Solutions of multimode problems		212
	5.6	Vibronic reduction factors		227
	5.7	The topological phase problem		248
	References			254
6	The JTE in spectroscopy: general theory			263
	6.1	Electronic spectra		263
		6.1.1	Optical band shapes	263
		6.1.2	Vibronic fine structure, zero-phonon lines, and tunneling splitting	278
		6.1.3	The JTE in excited-state decay	289
	6.2	Vibronic infrared and Raman spectra		291
		6.2.1	Vibronic infrared absorption	291
		6.2.2	Raman spectra and birefringence	305
	6.3	Magnetic resonance and related spectra		318
		6.3.1	The JTE in electron paramagnetic resonance spectra	318
		6.3.2	Random strain and relaxation in EPR	325
		6.3.3	Nuclear γ-resonance, microwave absorption, and ultrasonic attenuation	340
	References			345
7	Geometry, spectra, and reactivity of molecular systems			353
	7.1	General: JT vibronic coupling effects in geometry and reactivity		353
		7.1.1	Dynamic molecular shapes of JT systems. Pseudorotation	354
		7.1.2	Types of JT and PJT distortions. The lone-pair effect	361
		7.1.3	JT-induced reactivity and chemical activation	367
		7.1.4	Mutual influence of ligands	373
	7.2	Linear configurations of simple molecules		377
		7.2.1	Linear triatomic and tetraatomic systems	377
		7.2.2	“Quasilinear” molecules	388
	7.3	Trigonal molecular systems		393
		7.3.1	Triangular triatomics X3	393
		7.3.2	Trigonal tetraatomic AB3 systems	402
		7.3.3	Other systems with a threefold symmetry axis	406
	7.4	Distorted tetrahedral and square-planar systems		410
		7.4.1	Tetraatomic X4 and pentaatomic MX4 systems	410
		7.4.2	Cyclobutadiene, cyclobutane, and tetrahedrane radical cations	416
	7.5	The benzene and cyclopentane families and some larger systems		422
		7.5.1	The benzene-family molecular and radical cation and anion systems	422
		7.5.2	The cyclopentadienyl radical and cyclopentane: puckering	427
		7.5.3	Larger organic systems	431
	7.6	Clusters, coordination and mixed-valence compounds		437
		7.6.1	JT clusters and coordination systems	438
		7.6.2	Vibronic coupling in mixed-valence systems	452
	References			461
8	Solid-state problems: local properties and cooperative phenomena			479
	8.1	The JTE in local properties of solids		479
		8.1.1	Impurity centers in crystals	479
		8.1.2	The local JTE in formation of special crystal structures	495
	8.2	Cooperative phenomena		504
		8.2.1	Ordering of JT distortions and structural phase transitions	504
		8.2.2	The simplest cooperative JT E ⊗ b1 problem: rare-earth zircons	511
		8.2.3	Ordering of JT tri-minima distortions	519
		8.2.4	Helicoidal structures, incommensurate phases, and structural–magnetic ordering	525
		8.2.5	The band JTE, Peierls distortions, and first-order phase transitions. A general view on symmetry breaking	539
	8.3	The cooperative PJTE. Ferroelectric phase transitions		551
	8.4	The JTE in high-temperature superconductivity and colossal magnetoresistance		566
	References			581
Appendix				598
Subject index				605
Formula index				609

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