Manuscripts - Postdoc - Paper III

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

One- and two-centre matrix elements for overlap and related operators

Abstract

Certain formulae are introduced that enable the action of several important one-electron operators upon a Slater orbital to be expressed as linear combinations of other such orbitals with simple numerical coefficients, the matrix elements of such operators thereby reducing to linear combinations of the corresponding overlap integrals. The appropriate coefficients are tabulated for all Slater orbitals with principal quantum number n<5. Optimum master formulae are presented for the computation of overlap integrals by analytic integration or by quadrature, including the first demonstration of the global Barnett-Coulson-Hobson expansion described heretofore. Attention is adverted to parallel work on the two-centre coulomb and hybrid repulsion integrals.

Contents

Page
ABSTRACT1
CONTENTS2
1. INTRODUCTION3
2. OPERATIONS UPON SLATER-TYPE ORBITALS5
2.1 Elecric Dipole11
2.2 Linear Momentum13
2.3 Angular Momentum15
2.4 Mass Polarisation17
2.5 Kinetic Energy & Nuclear Attraction18
3. MATRIX ELEMENT TRANSFORMATIONS19
4. THE OVERLAP INTEGRAL25
4.1 One-Centre26
4.2 Two-Centre (Barnett-Coulson)28
4.3 Two-Centre (Ellipsoidal)30
TABLES33
APPENDIX A: THE Z-INTEGRALS50
ACKNOWLEDGEMENTS54
REFERENCES55