Analytic evaluation of three-electron atomic integrals with Slater wave functions

Abstract

The formulas of Fromm and Hill and of Remiddi, for the three-electron correlated atomic integral using Slater-type atomic orbitals, are shown to be equivalent in their common region of applicability. The demonstration required the derivation of an identity connecting dilogarithm functions which is either new or not widely known. It is then shown how to modify the more general of these formulas ͑that of Fromm and Hill͒ to eliminate the necessity of branch tracking in the complex plane and thereby to achieve a straightforwardly computable formalism. By obtaining a formal cancellation of the individual-term singularities in the Fromm-Hill formula, problems of numerical instability are also avoided. The work is validated with a computer program and sample calculations.

Symbolic calculation of auxiliary functions for molecular integrals over slater orbitals

“…Related methods have been used in STO work [7,8]. More recently, internal potentials for STOs [9] and three-electron integrals [10] were constructed using Mathematica [11] and Maple [12], respectively.…”

Recursion relations for the generic Hylleraas three-electron integral

“…This formula was later simplified by Harris [6] to a more symmetric form, in which many spurious singularities have been eliminated. However, only few preliminary results have been reported so far with these functions, namely in Refs.…”

Explicitly correlated Gaussian calculations of the 2P o Rydberg spectrum of the lithium atom

“…[1][2][3][4][5][6][7][8][9] We have also contributed to this effort. [10][11][12] 13 basis functions because they are capable of very well describing the medium and long range electron correlations. They also have the correct behavior at short electronelectron and electron-nucleus distances.…”