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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 | |
| ABSTRACT | 1 |
| CONTENTS | 2 |
| 1. INTRODUCTION | 3 |
| 2. NUCLEAR ATTRACTIONS (BARNETT-COULSON METHOD) | 11 |
| 2.1 Two-Centre Coulomb | 12 |
| 2.2 Three-Centre Exchange | 14 |
| 3. NUCLEAR ATTRACTIONS (ELLIPSOIDAL METHOD) | 19 |
| 3.1 Two-Centre Coulomb | 21 |
| 3.2 Three-Centre Exchange | 22 |
| 4. POTENTIAL FUNCTIONS | 26 |
| 4.1 One-Centre | 31 |
| 4.2 Two-Centre | 33 |
| APPENDIX A: THE R-INTEGRALS | 37 |
| APPENDIX B: THE Y-INTEGRALS | 39 |
| APPENDIX C: THE G- AND H-INTEGRALS | 42 |
| APPENDIX D: THE NEUMANN EXPANSION | 44 |
| APPENDIX E: LEAST-SQUARES APPROXIMATION | 47 |
| ACKNOWLEDGEMENTS | 56 |
| REFERENCES | 57 |