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

One-, two-, three- and four-centre electron repulsion integrals; Associated transformations over two and four indices

Abstract

Detailed formulae are developed for all the electron-repulsion integrals over a Slater basis in polyatomic molecules of arbitrary geometry, using the Barnett- Coulson expansion for multi-centre integrals; alternative approaches to the one- and two-centre integrals are reviewed. Corresponding formulae are derived for the vibrational derivatives of all such integrals. The data-driven transformation of both one- and two-electron molecular integrals is surveyed, and extended to various novel applications such as the generation of linearly- dependent integrals in symmetric molecules. Asymptotic formulae are derived for the long-range one- and two-electron integrals between polyatomic molecules with arbitrary relative orientation. The analytic approximation of electronic property curves, surfaces and hyper-surfaces is investigated.

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