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Atom - Molecule Collision Theory A Guide for the Experimentalist

The broad field of molecular collisions is one of considerable current interest, one in which there is a great deal of research activity, both experi­ mental and theoretical. This is probably because elastic, inelastic, and reactive intermolecular collisions are of central importance in many of the...

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Bibliographic Details
Other Authors: Bernstein, Richard Barry (Editor)
Format: eBook
Language:English
Published: New York, NY Springer US 1979, 1979
Edition:1st ed. 1979
Series:International Studies in Economic Modelling
Subjects:
Physical Chemistry
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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 theClassical 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
  • 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
  • 3.4.3
  • 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
  • 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
  • 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-FollowingTechnique
  • 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
  • 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
  • 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
  • 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 SectionsII: 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

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