The variation method in quantum chemistry
- 1st Edition - November 11, 2012
- Latest edition
- Author: Saul Epstein
- Language: English
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… Read more
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.
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
- Edition: 1
- Latest edition
- Published: November 11, 2012
- Language: English
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