Manuscripts - Postdoc - Paper IV

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New developments in the Barnett-Coulson method
for calculating molecular integrals

One- and two-centre potential functions; two- and three-centre nuclear attraction integrals

Abstract

General formulae are provided for the evaluation of nuclear attraction integrals over real Slater orbitals in polyatomic molecules. The Barnett-Coulson-Hobson expansion and the ellipsoidal methods are critically compared. Careful attention is given in each case to the influence of angular selection rules and to the generation of auxiliary geometric functions. Expressions are then developed for the radial potential kernels to be used in the evaluation of multi-centre electron repulsion integrals. The functional structure of these potentials is investigated and their systematic approximation using Legendre and Laguerre polynomials is described in detail. The appropriate auxiliary radial integrals are defined and formulated.

Contents

Page
ABSTRACT1
CONTENTS2
1. INTRODUCTION3
2. NUCLEAR ATTRACTIONS (BARNETT-COULSON METHOD)11
2.1 Two-Centre Coulomb12
2.2 Three-Centre Exchange14
3. NUCLEAR ATTRACTIONS (ELLIPSOIDAL METHOD)19
3.1 Two-Centre Coulomb21
3.2 Three-Centre Exchange22
4. POTENTIAL FUNCTIONS26
4.1 One-Centre31
4.2 Two-Centre33
APPENDIX A: THE R-INTEGRALS37
APPENDIX B: THE Y-INTEGRALS39
APPENDIX C: THE G- AND H-INTEGRALS42
APPENDIX D: THE NEUMANN EXPANSION44
APPENDIX E: LEAST-SQUARES APPROXIMATION47
ACKNOWLEDGEMENTS56
REFERENCES57