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Gaussian‐type function set without prolapse for the Dirac–Fock–Roothaan equation
Author(s) -
Tatewaki Hiroshi,
Watanabe Yoshihiro
Publication year - 2003
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.10330
Subject(s) - type (biology) , gaussian , function (biology) , set (abstract data type) , fock space , dirac (video compression format) , mathematics , mathematical physics , quantum mechanics , statistical physics , physics , computer science , geology , biology , genetics , paleontology , neutrino , programming language
A Gaussian‐type function (GTF) set without a prolapse (variation collapse) is generated for the Dirac–Fock–Roothaan (DFR) equation. The test atom was mercury. The number of primitive GTFs used is between 7and 62 (abbreviated as 7–62), 6–62, 6–62, 4–36, 4–36, 3–36, and 3–36 for s + , p − , p + , d − , d + , f − , and f + symmetries. The respective exponent parameters were determined with even‐tempered manner, which requires the minimum and maximum exponents for the respective symmetries. We prepared several sets of these. The total energy (TE) given by the numerical DF (NDF) is −19648.849250 hartree; one of the present sets with largest number of expansion terms gave −19648.849251 hartree. The error (ΔTE) relative to the NDR TE is quite small. We then applied this set to the inert gas atoms Ne (10), Ar (18), Kr (36), Xe (54), Rn (86), and No (102), and also to Es (99) as the representative of the open shell atoms. The absolute values of ΔTE were at most 2.8 × 10 −6 hartree, showing the potential of this set as a universal set. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1823–1828, 2003