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Two‐electron repulsion integrals over Gaussian s functions
Author(s) -
Gill Peter M. W.,
Johnson Benny G.,
Pople John A.
Publication year - 1991
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560400604
Subject(s) - multipole expansion , interpolation (computer graphics) , gaussian , scheme (mathematics) , mathematics , gaussian integral , function (biology) , electron , ab initio , multiple integral , point (geometry) , quantum mechanics , physics , mathematical physics , mathematical analysis , classical mechanics , geometry , motion (physics) , evolutionary biology , biology
We present an efficient scheme to evaluate the [ 0 ] ( m ) integrals that arise in many ab initio quantum chemical two‐electron integral algorithms. The total number of floating‐point operations ( FLOPS ) required by the scheme has been carefully minimized, both for cases where multipole expansions of the integrals are admissable and for cases where this is not so. The algorithm is based on the use of a modified Chebyshev interpolation formula to compute the function exp(− T ) and the integral F m ( T ) = ∫ 0 1 u 2 m exp(− Tu 2 ) du very cheaply.