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A numerical integration scheme for the evaluation of correlation energy functionals
Author(s) -
Fortunelli Alessandro,
Salvetti Oriano
Publication year - 1993
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.560470205
Subject(s) - scheme (mathematics) , diatomic molecule , partition (number theory) , numerical integration , basis (linear algebra) , correlation , energy (signal processing) , statistical physics , mathematics , physics , mathematical analysis , geometry , quantum mechanics , molecule , combinatorics
A numerical integration scheme is presented for three‐dimensional integrals occurring in electronic structure calculations, concentrating attention on the evaluation of the correlation energy through a density‐functional expression. The scheme is based on the choice of density‐based weight functions that naturally partition the space into “atomic” volumes (in which the integration is performed in terms of spherical coordinates) and “diatomic” volumes (in which the integration is performed in terms of confocal elliptical coordinates). Such a choice is justified on the basis of the analytical behavior of the integrand. The attainable accuracy and the required computational effort within the proposed scheme are discussed in detail in a test application on the C 60 molecule in the symmetrical configuration. Finally, a comparison with previously proposed schemes is presented. © 1993 John Wiley & Sons, Inc.