The variation method in quantum chemistry

The variation method in quantum chemistry

1st Edition - January 1, 1974

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  • Author: Saul Epstein
  • eBook ISBN: 9780323157476

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The Variation Method in Quantum Chemistry is generally a description of the basic theorems and points of view of the method. Applications of these theorems are also presented through several variational procedures and concrete examples. The book contains nine concise chapters wherein the first two ones tackle the general concept of the variation method and its applications. Some chapters deal with other theorems such as the Generealized Brillouin and Hellmann-Feynman Theorems. Also covered in the discussion is the relation of the Perturbation Theory and the Variation Method. This book will be of great help to students and researchers studying quantum chemistry.

Table of Contents

  • Preface

    Chapter I General Theory of the Variation Method

    1. Some Background

    2. The Variation Principle

    3. The Variation Method: Introduction

    4. The Variation Method: Details

    5. The Variation Method and Moments of the Schrödinger Equation


    Chapter II Applications of the Variation Method

    6. The Linear Variation Method

    7. Linear Spaces and Excited States

    8. The Unrestricted Hartree-Fock Approximation

    9. The Unrestricted Self-Consistent Field Approximation


    Chapter III The Generalized Brillouin Theorem

    10. Derivation and Applications of the Theorem


    Chapter IV Special Theorems Satisfied by Optimal Trial Functions

    11. Introduction

    12. Reality

    13. Unitary Invariance

    14. Symmetry

    15. Generalized Hellmann-Feynman Theorems

    Chapter V Perturbation Theory and the Variation Method: General Theory

    16. Hypervirial Theorems: General

    17. Momentum Theorems

    18. Force Theorems

    19. Torque Theorems

    20. Virial Theorems

    21. Orthogonality and Related Theorems


    Chapter VI Perturbation Theory and the Variation Method: Applications

    22. The Variation Principle and Perturbation Theory

    23. Perturbation Analysis of the Variation Method: Introduction

    24. Perturbation Analysis of the Variation Method: General Formalism

    25. Variation Methods within the Variation Method

    26. The ?2n+1 Theorem and Interchange Theorems


    27. Perturbation Analysis of the Linear Variation Method

    28. Perturbation Analysis of USCF and UHF: One-Particle Perturbations

    29. The L-1 Expansion


    Chapter VII The Hylleraas Variation Method

    30. Perturbation Analysis of the Variation Principle and the Hylleraas Variation Method

    31. The Second-Order Hylleraas Variation Method: Details

    32. The Linear Hylleraas Variation Method

    33. Improvable Upper Bounds to Second-Order Energies for Excited States

    34. The Second-Order Hylleraas Variation Method with Two Perturbations


    Chapter VIII Special Theorems Satisfied by Optimal First-Order Trial Functions

    35. Derivation of Theorems


    Chapter IX Corrections to Approximate Calculations

    36. Mostly First-Order Corrections


    Appendix A The Max-Min Theorem

    Appendix B Lagrange Multipliers

    Appendix C Theorems Satisfied by Optimal Time-Dependent Variational Wave Functions

    Appendix D Various Hypervirial Theorems in the Presence of Magnetic Fields

    Appendix E Proof That (33-18) Is an Improvable Bound

    Author Index

    Subject Index

Product details

  • No. of pages: 288
  • Language: English
  • Copyright: © Academic Press 1974
  • Published: January 1, 1974
  • Imprint: Academic Press
  • eBook ISBN: 9780323157476

About the Author

Saul Epstein

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