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

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.

13 pages, 4 figures and 3 tables

References in corpus (2)

• Two electrons on a hypersphere: a quasi-exactly solvable model
• Excited states of spherium

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