Vibronic Interactions in Molecules and Crystals

1. Introduction.- 2. Vibronic Interactions and the Jahn-Teller Theorem.- 2.1 Adiabatic Approximation.- 2.2 The Vibronic Hamiltonian.- 2.3 The Jahn-Teller Theorem.- 3. Adiabatic Potentials.- 3.1 The Orbital Doublet (E Term).- 3.2 Symmetry of Jahn-Teller Systems.- 3.3 Triplet and Quadruplet Terms.- 3.4 Pseudodegenerate Electronic Terms (Pseudo-Jahn-Teller Effect).- 3.5 Adiabatic Potentials for Multimode Systems.- 3.6 The Jahn-Teller Effect in Polynuclear Clusters.- 4. Solution of Vibronic Equations. Tunneling Splitting.- 4.1 Weak Vibronic Coupling. Perturbation Theory.- 4.2 Strong Vibronic Coupling. Free Rotation of Distortions.- 4.3 Hindered Rotations and Pulse Motions of Distortions. Tunneling Splitting.- 4.4 Numerical Solutions of Vibronic Equations.- 4.5 Multiparticle Methods in the Theory of the Jahn-Teller Effect.- 4.6 The Multimode Jahn-Teller Effect. Phonon Dispersion in Crystals.- 4.7 Factors of Vibronic Reduction.- 5. Spectroscopic Manifestations of Vibronic Effects.- 5.1 The Shape of Optical Bands of Electron Transitions Between Degenerate Electronic Terms.- 5.2 Splitting of the Zero-Phonon Lines of the Optical Absorption and Luminescence.- 5.3 Vibronic Effects in Infrared Absorption and Raman Spectra.- 5.4 The Dynamic Jahn-Teller Effect in Magnetic Resonance Spectra.- 5.5 Electron Paramagnetic Resonance. The Static Jahn-Teller Effect.- 6. Cooperative Phenomena. Structural Phase Transitions.- 6.1 Ordering of Distortions in Crystals. Cooperative Jahn-Teller Effect.- 6.2 Pseudo-Jahn-Teller Mechanism of Spontaneous Polarization of Crystals. The Vibronic Theory of Ferroelectricity.- 6.3 The Vibronic Theory of Structural Transformations in CondensedMedia.- 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.