The Symmetric Group in Quantum Chemistry

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:
The Quantum Mechanical Background Introduction Spin-free Hamiltonian The Antisymmetry Principle Atomic and Molecular Orbitals Slater Determinant The Self-consistent-field Method Configuration Interaction Method Slater-Condon Rules Löwdin Rules The Symmetric Group Introduction Permutations The Symmetric Group Cyclic Permutation Classes of the Symmetric Group Subgroups of the Symmetric Group Double Cosets Representation of SN Reps of the Symmetric Group Young Tableaux Young's Orthogonal Representation The Branching Law of the Symmetric Group The Conjugate Representation The Coset Representation Decomposition of the Coset Representation Characters of the Symmetric Group Calculation of the Characters The Subgroup S2ƒS2...ƒS2 Appendix 1 The Symmetric Group Algebra Algebraic Notions Class Operators Matric Basis of the Group Algebra Matric Basis for the Centrum of the Algebra The Young Operator Basis Spin Eigenfunctions Introduction Construction of Spin Eigenfunctions The Genealogical Construction The Branching Diagram Reps of the SN Generated by the Spin Fns Yamanouchi-Kotani Method For the Reps Branching the Diagram Fns and Young Tableaux Serber Spin Functions Projected Spin Eigenfunctions Spin-paired Spin Eigenfunctions Correspondence Between Spin-paired Functions and Young Tableaux Spatial Functions Antisymmetric Wavefunction Decomposition of the Wavefunction Reps of SN by the Spatial Functions Branching Diagram Functions Serber Wavefunction Normalization Integral The Lineup Permutation The Wavefunctions Form an Orthonormal Set The Form of the Hamiltonian Reduction of the Sum Over the Permutations Reduction of the Sum Over Electron Pairs Matrix Elements of the Hamiltonian for Special Cases Projected Wavefunction Valence Bond Wavefunction Spin Free Quantum Chemistry Introduction Orbital Product Functions Invariance Group of the Primitive Ket Spin-Free Exclusion Principle Structure Projections The Pair Diagram The Pair Operators Spin-free Pair Functions Pair Projections in the Function Space Spin-Free Exclusion Principle for Structure Projections Spin-free Counterpart of AFVSk Spin-free Counterpart of the Projected Fn Gallup's Tableau Operators Calculation of the Pauling Numbers Li's Algorithm Unitary Group Approach Introduction Basic Notions Tensor Space Model Hamiltonian Reps of the Unitary Group The Branching Law of the Unitary Group Representation Matrices of the Generators Weyl Tableaux Electronic Gel'fand State Paldus Arrays Graphical Unitary Group Approach Direct Configuration Interaction Method Symmetric Group Approach in CI Introduction Representation Matrices Sarma and Rettrup Algorithm Duch and Karwowski Algorithm Symmetric Group Graphical Approach Spin-coupled Functions Introduction Historical Development Spin-coupled Wave Functions SCVB Functions Core-Valence s-c Wave Function Bibliography Index

About the Author :
Pauncz; Ruben Technion,