Dynamics of Molecular Collisions: Part A(2 Modern Theoretical Chemistry)

Activity in any theoretical area is usually stimulated by new experimental techniques and the resulting opportunity of measuring phenomena that were previously inaccessible. Such has been the case in the area under consideration here beginning about fifteen years ago when the possibility of studying chemical reactions in crossed molecular beams captured the imagination of physical chemists, for one could imagine investigating chemical kinetics at the same level of molecular detail that had previously been possible only in spectroscopic investigations of molecular stucture. This created an interest among chemists in scattering theory, the molecular level description of a bimolecular collision process. Many other new and also powerful experimental techniques have evolved to supplement the molecular beam method, and the resulting wealth of new information about chemical dynamics has generated the present intense activity in molecular collision theory. During the early years when chemists were first becoming acquainted with scattering theory, it was mainly a matter of reading the physics literature because scattering experiments have long been the staple of that field. It was natural to apply the approximations and models that had been developed for nuclear and elementary particle physics, and although some of them were useful in describing molecular collision phenomena, many were not. The most relevant treatise then available to students was Mott and Massey's classic The Theory of Atomic Collisions, * but, as the title implies, it dealt only sparingly with the special features that arise when at least one of the collision partners is a molecule.

Table of Contents:
1. The N Coupled-Channel Problem.- 1. Introduction.- 2. Coupled-Channel Equations.- 2.1. Preliminaries-Single-Channel Scattering.- 2.2. Many-Channel Scattering.- 3. Coupled-Equation Approaches.- 3.1. Effective Potential Method.- 3.2. Coupled-States Method.- 4. Uncoupled-Equation Approaches.- 4.1. Sudden Approximation.- 4.2. Distorted Wave Approximation.- References.- 2. Effective Hamiltonians in Molecular Collisions.- 1. Introduction.- 2. Conventional Treatment of Two Vibrating-Rotating Molecules.- 3. Effective Potential Method.- 4. Centrifugal Decoupling Hamiltonians.- 5. Partitioning Theory.- 6. Related Techniques with Effective Hamiltonians.- 6.1. Quantum Mechanical Impact Parameter Methods.- 6.2. Sudden Approximation.- 7. Applications and Conclusions.- 7.1. Applications to Atom-Molecule Scattering.- 7.2. Applications to Molecule-Molecule Scattering.- 7.3. Applications to Model Systems.- 7.4. Conclusion.- References.- 3. Optical Models in Molecular Collision Theory.- 1. Introduction.- 2. Physical Models of Optical Potentials.- 2.1. Flux Loss in Molecular Collisions.- 2.2. Partial Wave Analysis.- 2.3. Elastic, Absorptive, and Total Cross Sections.- 2.4. Computational Methods.- 2.5. Perturbation Expansions.- 2.6. Resonance Scattering and Time Delay.- 2.7. Stationary Phase Approximation to Scattering Amplitudes.- 2.8. Asymptotic Approximation to Phase Shifts.- 2.9. Simple Opacity Models: Orbiting, Absorptive Sphere, and Curve Crossing.- 2.10. Two Applications: Scattering of Alkali Atoms and of Metastable Noble Gas Atoms.- 3. Formal Theory of Optical Potentials.- 3.1. Definition of Effective Hamiltonians.- 3.2. Energy Dependence of Optical Potentials.- 3.3. Elastic, Absorptive, and Total Cross Sections.- 3.4. Two-Potential Scattering.- 3.5. Rearrangement Scattering.- 3.6. Perturbation Theory of Effective Hamiltonians.- 3.7. Example for Atom-Diatomic Collisions.- References.- 4. Vibrational Energy Transfer.- 1. Introduction.- 2. Basic Theory.- 2.1. Simple Collision Model.- 2.2. Classical Dynamical Approach.- 2.3. Semiclassical Method.- 2.4. Quantum Mechanical Calculation.- 2.5. Thermal Average Transition Probability.- 3. WKB Method.- 3.1. WKB Calculation of Transition Probabilities.- 3.2. Effects of Molecular Attraction.- 3.3. Role of High-Order Angular Momenta.- 4. Operator Solution of the Schrodinger Equation.- 5. Effects of Molecular Orientations on Vibrational Energy Transfer.- 6. Vibration-Rotation Energy Transfer.- 7. Vibration-Vibration Energy Transfer.- 8. Effects of the Multiplicity of Impacts on Vibration-Translation Energy Transfer.- 9. Concluding Remarks.- References.- 5. The Scattering of Atoms and Molecules from Solid Surfaces.- 1. Introduction.- 2. Elastic Scattering.- 2.1. Close Coupling Approach.- 2.2. Approximate Quantum Techniques.- 2.3. Classical and Semiclassical Studies.- 3. Gas-Solid Energy Transfer.- 3.1. CubeModels.- 3.2. Semiclassical Techniques.- 3.3. Quantum Theories.- 4. Reactive Scattering, Embedding.- References.- 6. Nonradiative Processes in Molecular Systems.- 1. Introduction.- 1.1. Outline and Definitions.- 1.2. Radiative and Nonradiative Transitions.- 1.3. Reversibility and Irreversibility.- 1.4. TheMolecule.- 2. Radiationless Phenomena.- 2.1. Electronic Relaxation.- 2.2. Vibrational Relaxation.- 2.3. Dissociation and Photochemical Reaction.- 2.4. Line Broadening.- 2.5. Anomalously Long Lifetimes.- 2.6. QuantumBeats.- 2.7. Resonance Scattering.- 3. Theoretical Methods and Models.- 3.1. Time-Dependent Perturbation Theory.- 3.2. The Configuration Interaction Method.- 3.3. Scattering Theory.- 3.4. ModelSystems.- 4. Physical Interpretation.- 4.1. Nature of the Spectroscopic States.- 4.2. Vibronic Coupling.- 4.3. Spin-Orbit Coupling.- 4.4. Vibrational Overlap.- 4.5. Concluding Remarks.- References.- Author Index.