Evaluation of molecular integrals over Gaussian basis functions

Michel Dupuis, John Rys, Harry F. King

Research output: Contribution to journalArticlepeer-review

712 Citations (Scopus)


This paper is concerned with the efficient computation of the ubiquitous electron repulsion integral in molecular quantum mechanics. Differences and similarities in organization of existing Gaussian integral programs are discussed, and a new strategy is developed. An analysis based on the theory of orthogonal polynomials yields a general formula for basis functions of arbitrarily high angular momentum. (ηiηj∥ηkηl) = Σα=1,nIx(uα)I y(uα)Iz*(uα). By computing a large block of integrals concurrently, the same I factors may be used for many different integrals. This method is computationally simple and numerically well behaved. It has been incorporated into a new molecular SCF program HONDO. Preliminary tests indicate that it is competitive with existing methods especially for highly angularly dependent functions.

Original languageEnglish
Pages (from-to)111-116
Number of pages6
JournalJournal of Chemical Physics
Issue number1
Publication statusPublished - 1976

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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