Manuscripts - Postdoc - Paper I

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

Expansions and transformations

Abstract

A generalisation of the Barnett-Coulson method is developed whereby the energy and other electronic properties of a polyatomic molecule can be succinctly formulated and efficiently computed. A description and analysis of the fundamental expansion theorems is presented in a form immediately applicable to the evaluation of multicentre integrals over real Slater-type atomic orbitals for a wide variety of operators. Underlying properties of the rotational parameters, and transformations of the cubic harmonics, are derived in detail. An introductory description is given of the techniques of angular integration and radial quadrature that are required, and the necessary auxiliary functions are summarised.

Contents

Page
ABSTRACT1
CONTENTS2
1. INTRODUCTION3
2. CONVENTIONS10
3. TRANSFER OF ANGULAR FACTOR19
4. DETERMINATION OF EULER ANGLES24
5. EULERIAN ROTATION OF CUBIC HARMONICS28
6. TRANSFER OF RADIAL FACTOR34
7. COMPUTATION OF ZETA FUNCTIONS41
7.1 Derivative Method46
7.2 Quadrature Method48
7.3 Series Method50
7.4 Recursion Method53
7.5 Polynomial Method54
8. ASYMPTOTIC BOUNDS FOR ZETA FUNCTIONS55
APPENDIX A: CUBIC HARMONICS57
APPENDIX B: BESSEL FUNCTIONS63
TABLES66
ACKNOWLEDGEMENTS74
REFERENCES75