Radiationless Transitions in Polyatomic Molecules

The theory developed in this monograph as an introduction to the dynamics of electronically excited states and radiationless processes in polyatomic molecules for experimentalists, and theorists not intimately familiar with the field. For the expert it contains efficient methods to calculate transition probabilities, new applications of quasiclassical methods and fresh treatments of standard problems.

1. Introduction.- 2. Qualitative Theory of Radiationless Transitions.- 2.1 Balance Equation.- 2.2 Experimental Observations and Empirical Rules.- 2.3 Molecular Energy Level Model.- 2.4 Physical Nature of Radiationless Transitions.- 2.4.1 The Nature of the Initial State.- 2.4.2 Freed-Jortner Irreversibility Criterion.- 2.5 General Description of Luminescence Kinetics: Intermediate Case and Statistical Limit.- 2.5.1 Strong Coupling.- 2.5.2 Experimental Criterion for the Statistical Limit.- 2.5.3 Upper Limit for Radiationless Transition Rates.- 2.5.4 Weak Coupling.- 2.6 Strong-Coupling Limit.- 2.6.1 The Bixon-Jortner Model.- 2.6.2 Inclusion of Level Broadening.- 2.6.3 Mono- and Biexponential Decays.- 2.7 Weak-Coupling Limit.- 2.7.1 The Role of Vibrational Relaxation in the Final Electronic State.- 2.7.2 The Robinson-Frosch Theory.- 2.7.3 The Trifonov-Shekhtman Model.- 2.7.4 Periodic Quantum Beats and Biexponential Decay.- 2.8 Time-Dependent Perturbation Theory.- 2.9 Comparison of Various Expressions for the Transition Rate.- 2.10 Characterization of the Final States of an Isolated Molecule.- 2.11 Small, Large and Intermediate Molecules.- 3. Luminescence Intensity as a Function of Time and the Radiationless Transition Rate.- 3.1 Formulation of the Problem.- 3.2 Laplace Transformation, Green’s Functions and Resonant States.- 3.3 Computation of the Green’s Functions.- 3.4 Evolution of the Initial State and the Luminescence Intensity.- 3.5 Resonant States.- 3.5.1 Small Molecules.- 3.5.2 Intermediate Case.- 3.5.3 Statistical Limit.- 3.6 Method of Projection Operators.- 4. Matrix Elements of Intramolecular Interactions.- 4.1 Adiabatic Approximation.- 4.2 Accuracy of the Adiabatic Approximation.- 4.3 Crude Adiabatic Approximation.- 4.4 Coupling Operators.- 4.4.1 Nonadiabatic Coupling.- 4.4.2 Spin-Orbit Coupling.- 4.4.3 Rotational Matrix Elements.- 4.4.4 Coriolis Coupling.- 4.5 Condon Approximation.- 4.6 Model of Noninteracting Oscillators.- 4.7 Mechanisms and Selection Rules for Radiationless Transitions.- 4.8 Overlap Integrals for Harmonic and Morse Oscillators.- 5. Quasiclassical Methods.- 5.1 Introductory Remarks.- 5.2 Overlap Integral for a Harmonic Oscillator.- 5.2.1 Basic Derivation.- 5.2.2 Conditions for Applicability of the Quasiclassical Approximation.- 5.2.3 Comparison of Frequency and Displacement Effects.- 5.3 Overlap Integral for an Anharmonic Oscillator.- 5.3.1 Morse Oscillator with ??=0.- 5.3.2 Morse Oscillator with ???0 and Arbitrary Potentials.- 5.3.3 Selection Rule for the Morse Oscillator.- 5.4 Franck-Condon Principle for Radiationless Transitions.- 5.4.1 General Formulation.- 5.4.2 Real and Complex Term Intersections.- 5.4.3 Classical Franck-Condon Factor.- 5.4.4 Franck-Condon Principle and the Selection Rules.- 5.5 Transitions Between Parallel Terms.- 5.5.1 Model of Parallel Terms.- 5.5.2 Tunneling Nonradiative and Radiative Transitions.- 5.6 Overtone Vibrational Transitions.- 5.6.1 Derivation of the Quasiclassical Formula.- 5.6.2 Comparison with Exact Calculations.- 5.6.3 Normal Intensity Distributions.- 5.6.4 Dynamical Tunneling Depth.- 5.6.5 Intensity Anomalies in Absorption Spectra.- 5.7 Collision Model.- 5.7.1 Transition Matrix in the Linear Model.- 5.7.2 Perturbation Theory for Nonadiabatic Transitions.- 5.7.3 Method of the Classical ?-Matrix.- 5.8 Two-State Vibronic Levels.- 6. The Statistical Limit.- 6.1 Accepting Modes, Effective States and the Transition Rate.- 6.2 Generating-Function Method.- 6.3 Saddle-Point Method.- 6.3.1 First Saddle-Point Approximation (FSPA).- 6.3.2 Validity Conditions for the FSPA.- 6.3.3 Saddle-Point Method Versus Effective-States Method.- 6.4 Single Vibronic Level (SVL) Transition-Rate Dependence upon Initial Vibrational Energy.- 6.5 Transition Rate from Statistically Equilibrated Initial States.- 6.6 Summation of the Franck-Condon Factors.- 6.7 Inductive-Resonant-Transfer Mechanism.- 7. The Intermediate Case.- 7.1 Physical Effects.- 7.1.1 Absorption Spectra and Luminescence Kinetics.- 7.1.2 Pressure Dependence of the Transition Rate.- 7.1.3 Energy-Gap Dependence.- 7.1.4 Vibrational and Rotational Energy Dependence.- 7.1.5 Deuteration Effect.- 7.1.6 Comparative Description of the Intermediate Case and the Statistical Limit.- 7.2 Correlation-Function Method.- 7.3 Kinetic Model.- 8. Conclusion.- Appendix. Commutation Rules for Angular Momentum in the Laboratory and Molecular Frame.- References.