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arXiv · 0905.1635

Two-center two-electron integrals with exponential functions

Krzysztof Pachucki
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Abstract

We present an efficient approach to evaluate two-center two-electron integrals with exponential functions and with an arbitrary polynomial in electron-nucleus and electron-electron distances. We show that the master integral with the single negative power of all distances can be obtained from the second order differential equation in $r$, the distance between nuclei. For particular values of nonlinear parameters corresponding to the James-Coolidge basis, we find a fully analytic expression. For integrals with arbitrary powers of all distances, we construct recursion relations which starts from the master integral. The presented approach opens a window for the high precision calculations of relativistic effects in diatomic molecules.

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Krzysztof Pachucki. 2009-09-29. Two-center two-electron integrals with exponential functions. https://doi.org/10.1103/physreva.80.032520

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