The variation method in quantum chemistry - 1st Edition - ISBN: 9780122405501, 9780323157476

The variation method in quantum chemistry

1st Edition

Authors: Saul Epstein
eBook ISBN: 9780323157476
Imprint: Academic Press
Published Date: 1st January 1974
Page Count: 288
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Description

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

References

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

References

Chapter III The Generalized Brillouin Theorem

10. Derivation and Applications of the Theorem

References

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

References

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

References

27. Perturbation Analysis of the Linear Variation Method

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

29. The L-1 Expansion

References

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

References

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

35. Derivation of Theorems

References

Chapter IX Corrections to Approximate Calculations

36. Mostly First-Order Corrections

References

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


Details

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

About the Author

Saul Epstein