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Atomic and molecular cubature grids
Author(s) -
Hall G. G.,
Rees D.
Publication year - 2006
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.21207
Subject(s) - homonuclear molecule , diatomic molecule , grid , wave function , gaussian , chemistry , physics , quantum mechanics , statistical physics , mathematics , molecule , geometry
This article presents cubature grids of the Gaussian type that are adapted for the purpose of wave function calculation on atoms and molecules. The problems of the singularity at the nucleus, the derivatives in the kinetic energy, and the presence of two‐electron integrals are shown to be resolved. Each grid has a definite degree of accuracy so that it reproduces the exact values of all the integrals in a defined class. Seventh‐degree accuracy can be obtained from a grid of 143 nodes. The grids are applied, as simple illustrations, to well‐known self‐consistent field (SCF) calculations on helium. Grids for homonuclear diatomics are also discussed and an illustrative application given to a homonuclear diatomic molecule. A comparison between a molecular grid and the union of two unmodified atomic grids shows that overlaps and distortions in weights can occur to the extent that this is not practical. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007