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arXiv · 1704.08051

Three- and four-electron integrals involving Gaussian geminals: fundamental integrals, upper bounds and recurrence relations

Giuseppe M. J. Barca·Pierre-François Loos
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Abstract

We report the three main ingredients to calculate three- and four-electron integrals over Gaussian basis functions involving Gaussian geminal operators: fundamental integrals, upper bounds, and recurrence relations. In particular, we consider the three- and four-electron integrals that may arise in explicitly-correlated F12 methods. A straightforward method to obtain the fundamental integrals is given. We derive vertical, transfer and horizontal recurrence relations to build up angular momentum over the centers. Strong, simple and scaling-consistent upper bounds are also reported. This latest ingredient allows to compute only the $\order{N^2}$ significant three- and four-electron integrals, avoiding the computation of the very large number of negligible integrals.

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Giuseppe M. J. Barca, Pierre-François Loos. 2017-04-26. Three- and four-electron integrals involving Gaussian geminals: fundamental integrals, upper bounds and recurrence relations. https://doi.org/10.1063/1.4991733

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