Vibronic Interactions in Molecules and Crystals

1. Introduction.- 2. Vibronic Interactions and the Jahn-Teller Theorem.- 2.1 Adiabatic Approximation.- 2.1.1 Proper Adiabatic Approximatio.- 2.1.2 Born-Oppenheimer Approximatio.- 2.2 The Vibronic Hamiltonian.- 2.2.1 Reference Nuclear Configuration.- 2.2.2 Matrix Vibronic Hamiltonian.- 2.2.3 Primary Force Constants. Linear and Quadratic Vibronic Coupling.- 2.3 The Jahn-Teller Theorem.- 3. Adiabatic Potentials.- 3.1 The Orbital Doublet (E Term).- 3.1.1 E?e Case: The Mexican Hat and the Tricor.- 3.1.2 E? (b1+b2) Case. The Method of öpik and Pryc.- 3.2 Symmetry of Jahn-Teller Systems.- 3.2.1 Lee Symmetry of the Jahn-Teller Hamiltonian.- 3.2.2 Symmetry Properties of Adiabatic Potential Energy Surfaces.- 3.3 Triplet and Quadruplet Terms.- 3.3.1 T? d problem (d Mode Approximation).- 3.3.2 T ? (e+t2) Problem.- 3.3.3 Cubic Quadruplet Terms: F8? (e+t2) Problem.- 3.4 Pseudodegenerate Electronic Terms (Pseudo-Jahn-Teller Effect).- 3.4.1 The Two-Level Case.- 3.4.2 Dipole Instability in Systems with an Inversion Center.- 3.4.3 Vibronic Origin of Molecular Dynamic Instability.- 3.5 Adiabatic Potentials for Multimode Systems.- 3.5.1 Ideal and Multimode Vibronic Systems.- 3.5.2 The Two-Mode E?(b1 +b1) Problem.- 3.5.3 General Case.- 3.6 The Jahn-Teller Effect in Polynuclear Clusters.- 3.6.1 Vibronic Interactions in a Bioctahedron.- 3.6.2 Electron Localization and Delcalization in Mixed-ValenceCluster Compounds.- 4. Solution of Vibronic Equations. Tunneling Splitting.- 4.1 Weak Vibronic Coupling. Perturbation Theory.- 4.1.1 Operator Version of Perturbation Theory.- 4.1.2 Weak Coupling Case in the E?e Problem.- 4.1.3 Perturbation Treatment of Other Jahn-Teller Problems (E?b1, E?b2, T?e, T?t2, ?8?e, ?8?t2).- 4.1.4 Weak Pseudo-Jahn-Teller Effect.- 4.2 Strong Vibronic Coupling. Free Rotation of Distortions.- 4.2.1 The Adiabatic Separation of Nuclear Motion. Elastically and Centrifugally Stabilized States.- 4.2.2 Quasi-Classical Approach to Jahn-Teller Problems.- 4.3 Hindered Rotations and Pulse Motions of Distortions. Tunneling Splitting.- 4.3.1Warping Terms in the E?e Problem as Small Perturbations.- 4.3.2 Hindered Rotations of Jahn-Teller Distortions.- 4.3.3 Tunneling of Jahn-Teller Distortions Through Potential Barriers. Tunneling Splitting.- 4.3.4 Symmetry Properties and Group-Theoretical Classification of Tunneling States.- 4.4 Numerical Solutions of Vibronic Equations.- 4.5 Multiparticle Methods in the Theory of the Jahn-Teller Effect.- 4.5.1 General Relationships.- 4.5.2 The Case of Weak Coupling. Perturbation Theory in the Green’s Function Method.- 4.5.3 The Method of Unitary Transformations.- 4.6 The Multimode Jahn-Teller Effect. Phonon Dispersion in Crystals.- 4.6.1 Qualitative Discussion.- 4.6.2 The Case of Weak Coupling. Perturbation Theory.- 4.6.3 Strong Coupling Case.- 4.6.4 Intermediate Coupling. Low-Energy Approximation.- 4.6.5 Other Models and Approximations.- 4.7 Factors of Vibronic Reduction.- 4.7.1 General Discussion.- 4.7.2 Concrete Analytical and Numerical Calculations of the Vibronic Reduction Factors.- 4.7.3 Vibronic Reduction in Second-Order Perturbation Theory.- 4.7.4 Vibronic Amplification of Nuclear Displacement Operators.- 5. Spectroscopic Manifestations of Vibronic Effects.- 5.1 The Shape of Optical Bands of Electron Transitions Between Degenerate Electronic Terms.- 5.1.1 General Theory of Multiplet-Multiplet Optical Transitions.- 5.1.2 The Jahn-Teller Effect in the Excitation Spectrum of the A ? E Transition.- 5.1.3 Manifestations of Vibronic Interactions in the Optical Spectra of the A ? T Transition.- 5.1.4 Other Vibronic Effects in Electron Excitation Spectroscopy.- 5.1.5 The Jahn-Teller Effect in Radiative and Nonradiative Decay.- 5.1.6 Multimode Vibronic Effects in Electronic Spectra.- 5.1.7 The Method of Moments and Polarization Dichroism of Jahn-Teller Systems.- 5.2 Splitting of the Zero-Phonon Lines of the Optical Absorption and Luminescence.- 5.2.1 Vibronic Splitting and Broadening of the Zero-Phonon Line.- 5.2.2 Effect of External Field and Strain. Tunneling Splitting of the Zero-Phonon Line.- 5.3 Vibronic Effects in Infrared Absorption and Raman Spectra.- 5.3.1 Vibronic Effects in Vibrational Infrared Spectra.- 5.3.2 Rotational Vibronic Infrared Spectra of Free Oriented Molecules.- 5.3.3 Vibronic Nonresonant Raman Spectra.- 5.3.4 Vibronic Effects in Resonant Raman Scattering.- 5.3.5 Birefringence in Jahn-Teller Spherical Top Molecules.- 5.4 The Dynamic Jahn-Teller Effect in Magnetic Resonance Spectra.- 5.4.1 Effect of Vibronic Reduction of the Angular Momentum of Electrons in EPR Spectra. Two-State Model.- 5.4.2 Effect of Random Strain.- 5.4.3 Motional Narrowing of the EPR Broadened Band.- 5.5 Electron Paramagnetic Resonance. The Static Jahn-Teller Effect.- 5.5.1 Nature of the Isotropic EPR Spectrum of Cubic Paramagnetic Systems. Three-State Model.- 5.5.2 Effect of Random Strain. Angular Dependence of Spectra.- 5.5.3 Magnetic Resonance Spectra for Jahn-Teller Orbital TripletCenters.- 6. Cooperative Phenomena. Structural Phase Transitions.- 6.1 Ordering of Distortions in Crystals. Cooperative Jahn-Teller Effect.- 6.1.1 The Hamiltonian of the Jahn-Teller Crystal. Correlation of Local Distortions with Electronic States of Jahn-Teller Ions.- 6.1.2 Mean Field Approximation.- 6.1.3 A Simple Example: The E?b1 Jahn-Teller Crystal.- 6.1.4 Cooperative Jahn-Teller Effect in Cases of Weak, Strong and Intermediate Vibronic Coupling.- 6.1.5 Jahn-Teller Crystals with Insignificant Nonadiabaticity. Shift Transformation.- 6.1.6 Dynamics of Elementary Excitations.- 6.1.7 Interaction with the Macroscopic Deformations. Ferroelastic Phase Transitions.- 6.2 Pseudo-Jahn-Teller Mechanism of Spontaneous Polarization of Crystals. The Vibronic Theory of Ferroelectricity.- 6.2.1 The Simplest Case: Two-Band Model.- 6.2.2 Adiabatic Approach to Spontaneous Polarization.- 6.2.3 Perovskites.- 6.3 The Vibronic Theory of Structural Transformations in CondensedMedia.- 6.3.1 Vibronic Origin of Instability of the High Symmetry Configuration of Dielectric Crystals.- 6.3.2 The Peierls-Fröhlich Theorem. The Band Jahn-Teller Effect.- 6.3.3 General Model of Structural Transformations in CondensedMatter.- Appendix A. Expansion of the Full Vibrational Representation in Terms of Irreducible Ones.- Appendix B. Expansion of the Symmetric and Antisymmetric Products of Degenerate Representations.- Appendix C Proof of the Jahn-Teller Theorem.- References.