Diatomic Interaction Potential Theory

Fundamentals

1st Edition - January 1, 1973
Author: Jerry Goodisman
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 5 6 1 3 - 4

Diatomic Interaction Potential Theory, Volume 1: Fundamentals deals with the theoretical approaches to calculations for diatomic systems in their ground states. More specifically,… Read more

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Diatomic Interaction Potential Theory, Volume 1: Fundamentals deals with the theoretical approaches to calculations for diatomic systems in their ground states. More specifically, this book considers the problem of calculating the wave function and energy for the lowest state of a system of N electrons moving in the field of two fixed point charges (the nuclei of a diatomic system) separated by a distance R. Comprised of three chapters, this volume opens with an introduction to the nature of an interatomic interaction potential or potential energy curve. The separation of nuclear from electronic motions is considered, along with the methods used to measure potential energy curves. The next chapter presents a qualitative discussion of potential energy curves, with emphasis on the effects to be expected when two atomic systems are allowed to interact at large separation. The final chapter looks at the main approaches to schemes of calculation: variation theory, perturbation theory, the virial and Hellmann-Feynman theorems, local energy principles, and quantum statistical theories. This monograph will be a useful resource for students and teachers of physical chemistry.

Preface

Notes on Notation and Coordinate Systems

Contents of Volume 2

Chapter I Introduction to Potential Curves

A. Introduction

B. Separation of Nuclear from Electronic Motions

1. Center of Mass and Relative Motion

2. Born-Oppenheimer Separation

3. Adiabatic Treatment

4. Non-crossing Rule

5. Separation of Rotation

6. Correcting for Nuclear-Electronic Interaction

C. Measurement of Potential Energy Curves

1. Spectroscopy

2. Scattering

3. Other Measurements

Supplementary Bibliography

Chapter II Qualitative Discussion of Potential Energy Curves

A. Very Large Internuclear Distances

B. Large Internuclear Distances

C. Bond Region and Smaller R

D. Forms for U(R)

1. Functional Forms

2. Theoretical Considerations

Supplementary Bibliography

Chapter III Methods of Calculation

A. Variation Methods

1. General

2. Bounds

3. Correcting Expectation Values

4. Linear Variation

5. Single-Determinant Functions

6. Density Matrix

7. Configuration Interaction

8. Pair Functions and Correlated Wave Functions

B. Perturbation Theory

1. General Formulas

2. Hartree-Fock Perturbation Theory

3. Improving a Determinantal Function

4. Perturbation Theory for Change of R

5. Double Perturbation Theory

C. Virial Theorem

1. Scaling and the Virial Theorem

2. Consequences of the Virial Theorem

D. Hellmann-Feynman Theorem

1. Hellmann-Feynman Theorem and Electrostatic Forces

2. Validity of the Theorem

3. Applications

4. Generalizations

E. Local Energy Methods

1. Basic Formulas

2. Avoiding Integral Evaluation

F. Quantum Statistical Calculations

1. Thomas-Fermi and Thomas-Fermi-Dirac Theories

2. Applications to Molecular Systems

3. Closed-Shell Systems

Supplementary Bibliography

General Bibliography

Author Index

Subject Index