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Completeness criteria for explicitly correlated Gaussian geminal bases of axial symmetry
Author(s) -
Jeziorski Bogumił,
Bukowski Robert,
Szalewicz Krzysztof
Publication year - 1997
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(1997)61:5<769::aid-qua4>3.0.co;2-u
Subject(s) - geminal , completeness (order theory) , gaussian , symmetry (geometry) , atomic orbital , function (biology) , wave function , physics , mathematics , exponent , basis (linear algebra) , basis set , statistical physics , theoretical physics , mathematical physics , quantum mechanics , mathematical analysis , chemistry , geometry , molecule , electron , linguistics , philosophy , evolutionary biology , stereochemistry , biology
The completeness criteria for the basis set of explicitly correlated Gaussian‐type geminals adapted to C ∞v symmetry are given. Specifically, we show that any pair function of Σ + symmetry can be expanded in terms of products involving two spherical Gaussian orbitals located on the internuclear axis and a Gaussian correlating factor with a positive exponent. Pair functions corresponding to other irreducible representations of C ∞v can be expressed as linear combinations of products of a σ + function and an angular factor depending on the azimuthal angles. The minimal set of the angular factors needed for completeness is given. These factors are relevant also for other explicitly correlated bases. © 1997 John Wiley & Sons, Inc.