Atom - Molecule Collision Theory : A Guide for the Experimentalist

Chap. 1. Introduction to Atom—Molecule Collisions : The Interdependency of Theory and Experiment -- 1. General Introduction -- 2. The Experimentalist’s “Need to Know” -- 3. Overview of Experiments in Atom—Molecule Collisions -- 3.1. Elastic Scattering -- 3.2. Inelastic Scattering -- 3.3. Electronic Excitation and Curve Crossing -- 3.4. Reactive Scattering -- 4. Experimental Examples -- 4.1. Elastic Scattering -- 4.2. Rotationally Inelastic Scattering -- 4.3. Vibrationally Inelastic Scattering -- 4.4. Electronic Excitation and Charge Transfer -- 4.5. Reactive Atom—Molecule Scattering -- 4.6. Collision-Induced Dissociation -- 5. Information Content of Atom—Molecule Molecule Collision Cross Sections -- 6. Future Theoretical Demands of the Experimentalist -- References -- Chap. 2. Interaction Potentials I : Atom—Molecule Molecule Potentials -- 1. Current State of Ab Initio Electronic Structure Theory -- 2. Philosophy : Judicious Synthesis of Theory and Experiment -- 3. Brief Survey of Methods -- 3.1. Basis Sets -- 3.2. The Problem of Electron Correlation -- 3.2.1. The Concept -- 3.2.2. Configuration Interaction (CI) -- 4. Examples -- 4.1. Nonreactive -- 4.1.1. Li+—H2 -- 4.1.2. He—H2CO -- 4.2. Reactive -- 4.2.1. H + H2 -- 4.2.2. Fluorine—Hydrogen Systems -- 4.2.3. N+ + H2 -- 4.2.4. H + Li2, F + Li2 -- 4.2.5. H + C1H, H + BrH -- 5. Concluding Remarks -- References -- Chap. 3. Interaction Potentials II: Semiempirical Atom—Molecule Potentials for Collision Theory -- 1. Introduction -- 1.1. Potential Surfaces for Collision Theory -- 1.2. Requisites for the Potential Energy Surface and Its Representation -- 1.2.1. Physical Requirements -- 1.2.2. Computational Requirements -- 1.3. Selection of Methods -- 2. The Method of Diatomics-in-Molecules (DIM) -- 2.1. Introduction -- 2.2. General Formulation -- 2.2.1. Defining the Scope of the Problem -- 2.2.2. The DIM Basis Set -- 2.2.3. The DIM Hamiltonian Matrix -- 2.2.4. The DIM Eigenvalues -- 2.3. A Specific Example: FH2 -- 2.3.1. Define the Coordinate System -- 2.3.2. Define the Atomic Basis Functions and Fragment Matrices -- 2.3.3. Define the Diatomic Basis and Fragment Matrices -- 2.3.4. Compute the Rotated Fragment Matrices -- 2.3.5. Construct the Triatomic Basis -- 2.3.6. Construct the Atomic Matrices B -- 2.3.7. Construct the Diatomic Matrices B -- 2.3.8. Find the DIM Eigenvalues -- 2.4. Simple Systems: An Alternative Formulation -- 2.5. Coupling -- 2.5.1. Spin—Orbit Coupling -- 2.5.2. Nonadiabatic Coupling -- 3. Methods Related to DIM -- 3.1. The LEPS Method -- 3.2. Method of Blais and Truhlar -- 3.3. Valence-Bond Methods -- 3.3.1. Porter—Karplus Surface for H3 -- 3.3.2. Valence-Bond Methods with Transferable Parameters -- 3.4. Simple Approach to Nonadiabatic Coupling -- References -- Chap. 4. Elastic Scattering Cross Sections I: Spherical Potentials -- 1. Introduction -- 2. Intermolecular Potential -- 2.1. The Concept of an Intermolecular Potential -- 2.2. General Behavior of the Intermolecular Potential -- 2.3. Potential Models Used in the Evaluation of Scattering Cross Sections -- 2.3.1. Basic Potential Models -- 2.3.2. Modifications of the Basic Potentials and Piecewise Analytic Potentials -- 2.3.3. The Simons—Parr—Finlan (SPF) Modified Dunham Expansion -- 3. Definitions of the Quantities That Can Be Measured in Elastic-Scattering Experiments. Influence of Experimental Conditions -- 4. Classical Scattering Theory -- 4.1. Basic Formulas -- 4.2. Differential Cross Section -- 4.2.1. Small-Angle Scattering -- 4.2.2. Glory Scattering -- 4.2.3. Rainbow Scattering -- 4.2.4. Large-Angle Scattering -- 4.2.5. Orbiting Collisions -- 4.2.6. Summary of the Classical Results for the Differential Scattering Cross Section and Limits of Validity -- 4.3. Total Elastic Cross Sections -- 4.4. Identical Particles -- 4.5. First-Order Momentum Approximation and Results for the Basic Potentials -- 5. Quantal Treatment -- 5.1. Introduction -- 5.2. Stationary Scattering Theory and Partial-Wave Analysis -- 5.3. Examples of Numerical Results -- 5.3.1. Differential Cross Sections -- 5.3.2. Total Scattering Cross Section -- 5.4. Resonance Scattering -- 5.5. Identical Particles -- 6. Semiclassical Approximation -- 6.1. General Assumptions and Introductory Remarks -- 6.2. Special Features of the Differential Cross Section -- 6.2.1. Interference Effects -- 6.2.2. Rainbow Scattering -- 6.2.3. Orbiting Collisions -- 6.2.4. Large-Angle Scattering -- 6.2.5. Glory Scattering -- 6.2.6. Small-Angle Scattering (Forward Diffraction Peak) -- 6.3. Special Features of the Total Elastic Scattering Cross Section -- 6.4. Identical Particles -- 6.5. High-Energy Approximation -- 6.5.1. Brief Outline of the Method -- 6.5.2. Results for the Basic-Potential Models -- 7. Methods for the Evaluation of Potentials from Experimental Scattering Data -- 7.1. General Survey -- 7.2. Semiclassical Inversion Procedures -- 7.2.1. Determination of the Repulsive Part of the Potential from the s-Phase as a Function of the Energy -- 7.2.2. Determination of the Potential from the Phase Shift Function or the Deflection Function at a Fixed Energy -- 7.2.3. Determination of the Phase Shift Function ?(?) or the Classical Deflection Function ?(?) from an Analysis of Differential Cross Section Data -- 7.2.4. The Inverse Problem in the High-Energy Approximation -- 7.3. The Trial and Error Method and Regression Procedures -- 7.4. The Use of Pseudopotentials -- References -- Chap. 5. Elastic Scattering Cross Sections II: Noncentral Potentials -- 1. Introduction -- 2. Angular-Dependent Potentials -- 2.1. The General Form -- 2.2. The Long-Range Terms -- 2.3. Eccentricity Effects -- 2.4. Action Integrals -- 3. General Expressions and Close-Coupling Calculations -- 4. The Distorted-Wave Approximation -- 5. Sudden Approximation -- 6. The Calculation of Cross Sections in Sudden Approximation -- 6.1. The Differential Cross Section in Sudden Approximation -- 6.2. The Integral Cross Section in Sudden Approximation: The Nonglory Contribution -- 6.3. The Total Integral Cross Section in Sudden Approximation: The Glory Contribution -- 7. Conclusions -- Glossary of Abbreviations -- References -- Chap. 6. Inelastic Scattering Cross Sections I: Theory -- 1. Introduction -- 2. Observables and Averaging -- 3. Quantum Theory of Inelastic Scattering -- 3.1. Formal Quantum Theory -- 3.2. Angular Momentum Conservation, Parity, and Close-Coupled Equations -- 3.3. Asymptotic Forms and the S Matrix -- 3.4. Symmetry and Microscopic Reversibility -- 3.5. Integral Equations and Square Integrable Techniques -- 4. Approximate Approaches -- 4.1. Dimension-Reducing Approximations (DRA’s) -- 4.2. Perturbation Theory -- 4.3. Chemical Dynamics -- References -- Chap. 7. Inelastic Scattering Cross Sections II: Approximation Methods -- 1. Introduction -- 2. Rotational Excitation -- 3. Vibrational Excitation -- 4. Electronic Excitation -- References -- Chap. 8. Rotational Excitation I: The Quantal Treatment -- 1. Introduction -- 2. The Coupled Equations for Rotational Scattering -- 3. Solution of the Close-Coupling Equations -- 4. Methods of Solution of the Coupled Scattering Equations -- 4.1. The Approximate-Solution Approach in the Solution-Following Technique: The Method of Sams and Kouri -- 4.2. The Approximate-Potential Approach in the Solution-Following Technique -- 4.3. The Approximate-Potential Approach in the Invariant-Imbedding: Technique: The R-Matrix Method -- 4.4. The Approximate-Solution Approach in the Invariant-Imbedding Technique: The Log-Derivative Method -- References -- Chap. 9. Rotational Excitation II: Approximation Methods -- 1. Introduction -- 2. The CS Approximation -- 2.1. The Basic CS Equations -- 2.2. The CS Scattering Amplitude and Boundary Conditions -- 2.3. CS Differential and Integral Cross Sections -- 2.4. CS Approximation for General Relaxation Cross Sections -- 3. The IOS Approximation -- 3.1. Basic IOS Equations and Boundary Conditions -- 3.2. IOS Cross Sections and Factorizations -- 3.3. IOS Factored Rates and Transport Properties -- 4. The lz-Conserving Energy Sudden Approximation -- 4.1. Basic lz-Conserving Equations and Boundary Conditions -- 4.2. Factorization of lz-Conserving Amplitudes and Cross Sections -- 5. The Decoupled l-Dominant Approximation -- 6. Exponential Distorted-Wave Approximation -- 7. Semiclassical Approximation -- 8. Method Selection -- 8.1. Energy Sudden Approximation -- 8.2. Centrifugal Sudden Approximation -- 8.3. Infinite-Order Sudden Approximation -- 8.4. lz-Conserving and DLD Approximations -- 8.5. Exponential Distorted-Wave Approximation -- 8.6. Semiclassical Approximations -- 8.7. Full Close Coupling -- References -- Chap. 10. Rotational Excitation III: Classical Trajectory Methods -- 1. Introduction -- 2. Ingredients of a Trajectory Calculation -- 2.1. Equations of Motion -- 2.2. Selection of Initial Conditions -- 2.3. Integration of Equations of Motion -- 2.4. Analysis of Final Conditions -- 3. Construction of a Trajectory Program -- 4. Efficiency-Improving Techniques -- 4.1. Alternative Sampling Schemes -- 4.2. Moment Methods -- 5. Concluding Remarks -- References -- Chap. 11. Vibrational Excitation I: The Quantal Treatment -- 1. Introduction -- 2. Angular Momentum Decoupling Approximations -- 3. Asymptotic Expansion Technique for Handling Long-Range Potentials -- 4. Effects of the Dissociative Continuum -- References -- Chap. 12. Vibrational Excitation II: Classical and Semiclassical Methods -- 1. Introduction -- 2. Quasiclassical Methods -- 3. Semiclassical Methods -- 3.1. Quantal Internal Modes Coupled through the Interaction Potential to Classical Translational Motion -- 3.2. Classical S-Matrix Theory -- 3.3. Classical—Quantal Correspondence Methods -- 3.3.1. The decent and indecent Methods -- 3.3.2. The Strong-Coupling Correspondence Principle -- 3.4. Models for Special Cases -- 3.4.1. itfits Models -- 3.4.2. Angular Dependence of Impulsive Energy Transfer -- 3.