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WIREs Comput Mol Sci
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Multi‐electron integrals

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Abstract This review presents techniques for the computation of multi‐electron integrals over Cartesian and solid‐harmonic Gaussian‐type orbitals as used in standard electronic‐structure investigations. The review goes through the basics for one‐ and two‐electron integrals, discuss details of various two‐electron integral evaluation schemes, approximative methods, techniques to compute multi‐electron integrals for explicitly correlated methods, and property integrals. © 2011 John Wiley & Sons, Ltd. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

Illustration of the Gaussian product rule.

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The McMurchie–Davidson algorithm for four‐center two‐electron integrals. The computational costs of the steps are given to the right, p and c being the numbers of primitive and contracted functions of a given AO shell and l, the angular‐momentum quantum number (assuming that these are the same for all orbitals).

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The Boys function Fn(x) for n ≥ 0. Functions of different n may be distinguished by noting that Fn(0) = 1/(2n + 1).

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Electronic Structure Theory > Ab Initio Electronic Structure Methods

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