SYMMETRIC GROUP IN QUANTUM CHEMISTRY

Content: 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