Manuscripts - Postdoc - Paper II

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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
ABSTRACT1
CONTENTS2
1. INTRODUCTION3
2. THE HOBSON-BARNETT-COULSON EXPANSION6
3. THE EXPANSION FOR ORBITAL GRADIENTS10
4. DISPLACEMENT DERIVATIVES OF ZETA FUNCTIONS14
5. THE SHANKS-WYNN TRANSFORMATION19
6. LIST-GENERATION AND INDEXED RETRIEVAL35
APPENDIX A: BASIC ALGEBRAIC INTEGRALS63
APPENDIX B: BASIC AZIMUTHAL INTEGRALS75
APPENDIX C: BASIC POLAR INTEGRALS80
ACKNOWLEDGEMENTS88
REFERENCES89