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Spin Eigenfunctions

Construction and Use

  • Book
  • © 1979

Overview

Authors:
  1. Ruben Pauncz

    1. Technion-Israel Institute of Technology, Haifa, Israel

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    • Ruben Pauncz
    Pages 1-8

  3. Construction of Spin Eigenfunctions from the Products of One-Electron Spin Functions

    • Ruben Pauncz
    Pages 9-32

  4. Construction of Spin Eigenfunctions from the Products of Two-Electron Spin Eigenfunctions

    • Ruben Pauncz
    Pages 33-48

  5. Construction of Spin Eigenfunctions by the Projection Operator Method

    • Ruben Pauncz
    Pages 49-75

  6. Spin-Paired Spin Eigenfunctions

    • Ruben Pauncz
    Pages 77-89

  7. Basic Notions of the Theory of the Symmetric Group

    • Ruben Pauncz
    Pages 91-115

  8. Representations of the Symmetric Group Generated by the Spin Eigenfunctions

    • Ruben Pauncz
    Pages 117-153

  9. Representations of the Symmetric Group Generated by the Projected Spin Functions and Valence Bond Functions

    • Ruben Pauncz
    Pages 153-163

  10. Combination of Spatial and Spin Functions; Calculation of the Matrix Elements of Operators

    • Ruben Pauncz
    Pages 165-179

  11. Calculation of the Matrix Elements of the Hamiltonian; Orthogonal Spin Functions

    • Ruben Pauncz
    Pages 181-207

  12. Calculation of the Matrix Elements of the Hamiltonian; Nonorthogonal Spin Functions

    • Ruben Pauncz
    Pages 209-228

  13. Spin-Free Quantum Chemistry

    • Ruben Pauncz
    Pages 229-266

  14. Matrix Elements of the Hamiltonian and the Representation of the Unitary Group

    • Ruben Pauncz
    Pages 267-300

  15. Back Matter

    Pages 301-370
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Keywords

About this book

The aim of this book is to give a comprehensive treatment of the different methods for the construction of spin eigenfunctions and to show their interrelations. The ultimate goal is the construction of an antisymmetric many-electron wave function that has both spatial and spin parts and the calculation of the matrix elements of the Hamiltonian over the total wave function. The representations of the symmetric group playa central role both in the construction of spin functions and in the calculation of the matrix elements of the Hamiltonian, so this subject will be treated in detail. We shall restrict the treatment to spin-independent Hamiltonians; in this case the spin does not have a direct role in the energy expression, but the choice of spin functions influences the form of spatial functions through the antisymmetry principle; the spatial functions determine the energy of the system. We shall also present the "spin-free quantum chemistry" approach of Matsen and co-workers, in which one starts immediately with the construction of spatial functions that have the correct permutational symmetries. By presenting both the conventional and the spin-free approach, one gains a better understanding of certain aspects of the elec­ tronic correlation problem. The latest advance in the calculation of the matrix elements of the Hamiltonian is the use of the representations of the unitary group, so this will be the last subject. It is a pleasant task to thank all those who helped in writing this book.

Authors and Affiliations

  • Technion-Israel Institute of Technology, Haifa, Israel

    Ruben Pauncz

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