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New developments in the Barnett-Coulson method
for calculating molecular integrals
Further expansions and transformations;
Ancillary techniques and basic integrals
Abstract
The Laplace expansion of real Slater atomic orbitals is developed in terms of the Barnett-Coulson zeta functions, the Gaunt coefficients, and regular solid harmonics of the displacement vector. A related expansion is also derived for the vibrational derivatives of such orbitals. Powerful techniques are applied to the acceleration of convergence and the retrieval of auxiliary functions from structured lists. A detailed description is given of certain important basic integrals.
Contents
| Page | |
| ABSTRACT | 1 |
| CONTENTS | 2 |
| 1. INTRODUCTION | 3 |
| 2. THE HOBSON-BARNETT-COULSON EXPANSION | 6 |
| 3. THE EXPANSION FOR ORBITAL GRADIENTS | 10 |
| 4. DISPLACEMENT DERIVATIVES OF ZETA FUNCTIONS | 14 |
| 5. THE SHANKS-WYNN TRANSFORMATION | 19 |
| 6. LIST-GENERATION AND INDEXED RETRIEVAL | 35 |
| APPENDIX A: BASIC ALGEBRAIC INTEGRALS | 63 |
| APPENDIX B: BASIC AZIMUTHAL INTEGRALS | 75 |
| APPENDIX C: BASIC POLAR INTEGRALS | 80 |
| ACKNOWLEDGEMENTS | 88 |
| REFERENCES | 89 |