1st Edition

The Symmetric Group in Quantum Chemistry

ISBN 9781315898124
Published December 8, 2017 by CRC Press
342 Pages

USD $250.00

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Book Description

This is the first book to provide comprehensive treatment of the use of the symmetric group in quantum chemical structures of atoms, molecules, and solids. It begins with the conventional Slater determinant approach and proceeds to the basics of the symmetric group and the construction of spin eigenfunctions. The heart of the book is in the chapter dealing with spin-free quantum chemistry showing the great interpretation value of this method. The last three chapters include the unitary group approach, the symmetric group approach, and the spin-coupled valence bond method. An extensive bibliography concludes the book.

Table of Contents

1. The Quantum Mechanical Background: Introduction 2. Spin-free Hamiltonian 3. The Antisymmetry Principle 4. Atomic and Molecular Orbitals 5. Slater Determinant 6. The Self-consistent-field Method 7. Configuration Interaction Method 8. Slater-Condon Rules 9. L wdin Rules 10. The Symmetric Group: Introduction 11. Permutations 12. The Symmetric Group 13. Cyclic Permutation 14. Classes of the Symmetric Group 15. Subgroups of the Symmetric Group 16. Double Cosets 17. Representation of SN: Reps of the Symmetric Group 18. Young Tableaux 19. Young's Orthogonal Representation 20. The Branching Law of the Symmetric Group 21. The Conjugate Representation 22. The Coset Representation 23. Decomposition of the Coset Representation 24. Characters of the Symmetric Group 25. Calculation of the Characters 26. The Subgroup S2 S2... S2 27. The Symmetric Group Algebra: Algebraic Notions. Class Operators 28. Matric Basis of the Group Algebra 29. Matric Basis for the Centrum of the Algebra 30. The Young Operator Basis 31. Spin Eigenfunctions: Introduction 32. Construction of Spin Eigenfunctions 33. The Genealogical Construction 34. The Branching Diagram 35. Reps of the SN Generated by the Spin Fns 36. Yamanouchi-Kotani Method for the Reps 37. Branching the Diagram Fns and Young Tableaux 38. Serber Spin Functions 39. Projected Spin Eigenfunctions 40. Spin-paired Spin Eigenfunctions 41. Spatial Functions: Antisymmetric Wavefunction 42. Decomposition of the Wavefunction 43. Reps of SN by the Spatial Functions 44. Branching Diagram Functions 45. Serber Wavefunction 46. Projected Wavefunction 47. Valence Bond Wavefunction 48. Spin Free Quantum Chemistry: Introduction 49. Orbital Product Functions 50. Invariance Group of the Primitive Ket 51. Spin-Free Exclusion Principle 52. Structure Projections 53. Spin-free Counterpart of AFVSk 54. Spin-free Counterpart of the Projected Fn 55. Gallup's Tableau Operators 56. Calculation of the Pauling Numbers 57. Li's Algorithm 58. Unitary Group Approach: Introduction 59. Basic Notions 60. Tensor Space 61. Model Hamiltonian 62. Reps of the Unitary Group 63. The Branching Law of the Unitary Group 64. Representation Matrices

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