Radiationless Transitions in Polyatomic Molecules

Radiationless transitions comprise an important class of physical phenomena occurring in the excited states of molecules. They affect the lifetimes of the ex­ cited states and govern primary photochemical and photophysical processes. Much effort has been devoted to the understanding of radiationless transi­ tions. Still, owing to recent advances, the field continues to attract attention. The demand for a book on the theory of these processes naturally arises in at­ tempting to comprehend a large body of literature, as the famous review article by K. F. Freed and the book by R. Englman do not encompass some issues of current interest. Our intent is to highlight the underlying physical principles and methods in such a way that the book both in its content and its presentation is instruc­ tive for a wide audience. The basic ideas are treated in simple mathematical terms intelligible to ex­ perimentalists and to readers unfamiliar with the field. Complicated theoret­ ical methods are always expounded from first principles, so that a knowledge of quantum mechanics and mathematics at the graduate-student level will enable the reader to easily follow the derivations. Experts will find efficient methods of calculating the transition rates, as well as new applications of quasiclassical methods and fresh treatments of standard problems. Details of measurements are not discussed, and experimental data are only invoked to illustrate the theory.

Table of Contents:
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.- 2.5 General Description of Luminescence Kinetics: Intermediate Case and Statistical Limit.- 2.6 Strong-Coupling Limit.- 2.7 Weak-Coupling Limit.- 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.- 3.6 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.- 4.5 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.- 5.3 Overlap Integral for an Anharmonic Oscillator.- 5.4 Franck-Condon Principle for Radiationless Transitions.- 5.5 Transitions Between Parallel Terms.- 5.6 Overtone Vibrational Transitions.- 5.7 Collision Model.- 5.8 Two-State Vibronic Levels.- 6. The Statistical Limit.- 6.1 Accepting Modes, Effective States and the Transition Rate.- 6.2Generating-Function Method.- 6.3 Saddle-Point 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.- 7.2 Correlation-Function Method.- 7.3 Kinetic Model.- 8. Conclusion.- Appendix. Commutation Rules for Angular Momentum in the Laboratory and Molecular Frame.- References.