Electron repulsion integral approximations and error bounds: Molecular applications

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Abstract
In a previous study of Coulombic potential energy integrals, an approximation theory was discussed which led to rigorous error bounds on the difference between exact integrals and proposed approximations. The simple structure of the bound provides a favorable context for introducing approximations of two‐particle electron repulsion integrals which occur in molecular structure theory. Studies of the ethylene and pyridine molecules are reported in an investigation of the utility of the approximations. Comparisons of exact and approximate integrals and theoretical error bounds and analysis of entire integral distributions are presented. Ground state SCF total energies, orbital energies, and molecular orbitals show excellent agreement with the results of computations using exact integrals.