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An accurate numerical multicenter integration for molecular orbital theory
Author(s) -
Ishikawa Hideaki,
Yamamoto Kazuo,
Fujima Kazumi,
Iwasawa Misako
Publication year - 1999
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/(sici)1097-461x(1999)72:5<509::aid-qua4>3.0.co;2-h
Subject(s) - numerical integration , gaussian , normalization (sociology) , gaussian quadrature , quadrature (astronomy) , anisotropy , clenshaw–curtis quadrature , tanh sinh quadrature , gauss–kronrod quadrature formula , orbital overlap , molecular orbital , multiple integral , physics , gauss–hermite quadrature , mathematical analysis , mathematics , statistical physics , integral equation , quantum mechanics , molecule , nyström method , optics , sociology , anthropology
A powerful and accurate numerical three‐dimensional integration scheme was developed especially for molecular orbital calculations. A multicenter integral is decomposed into the sum of single‐center integrals using nuclear weight functions and calculated using Gaussian quadrature rules. The decomposed single‐center integrands show strong anisotropy. With a careful selection of the Gaussian quadrature rule according to the anisotropy, it is possible to obtain an accuracy of 13 digits with a small number of integration points for the overlap integrals, normalization integrals, and molecular integrals for the hydrogen molecule. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 509–523, 1999