### Abstract

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) = Σ_{α=1,n}I_{x}(u_{α})I _{y}(u_{α})I_{z}*(u_{α}). 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 language | English |
---|---|

Pages (from-to) | 111-116 |

Number of pages | 6 |

Journal | Journal of Chemical Physics |

Volume | 65 |

Issue number | 1 |

Publication status | Published - 1976 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*65*(1), 111-116.

**Evaluation of molecular integrals over Gaussian basis functions.** / Dupuis, Michel; Rys, John; King, Harry F.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 65, no. 1, pp. 111-116.

}

TY - JOUR

T1 - Evaluation of molecular integrals over Gaussian basis functions

AU - Dupuis, Michel

AU - Rys, John

AU - King, Harry F.

PY - 1976

Y1 - 1976

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36749119370&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749119370&partnerID=8YFLogxK

M3 - Article

VL - 65

SP - 111

EP - 116

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 1

ER -