Vibronic Interactions in Molecules and Crystals

ISBN-13: 9783642834813 / Angielski / Miękka / 2011 / 422 str.

Isaac B. Bersuker; Victor Z. Polinger

Opis

The theory of vibronic interactions is a new field of investigation in the physics and chemistry of molecules and crystals that goes beyond the separate descriptions of the motion of electrons and nuclei in the adiabatic approximation. A systematic treatment of the most important manifestations of nonadiabaticity (the Jahn-Teller, pseudo-Jahn-Teller and Renner effects) is given, including derivation of the vibronic Hamiltonian, proof of the Jahn-Teller theorem, determination of the adiabatic potentials of electronically degenerate and pseudodegenerate polyatomic systems, calculations of vibronic energy spectra and solutions of the multimode and multicenter problems. The second part of the book contains applications of the theory to optical and infrared spectroscopy, EPR and cooperative phenomena in crystals.

Spis treści

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.