Preface ........................................................ 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 Ee problem ........................................ 52
3.3 Te, Tt2, T(e + t2), and Г8(e + t2) problems ......... 62
3.4 Th,pnh,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 Eb1 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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