Premium
Fast and stable algorithm for the analytical computation of two‐center Coulomb and overlap integrals over Slater‐type orbitals
Author(s) -
Hierse W.,
Oppeneer P. M.
Publication year - 1994
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.560520602
Subject(s) - atomic orbital , coulomb , computation , center (category theory) , slater integrals , angular momentum , physics , scaling , quantum mechanics , slater type orbital , type (biology) , kernel (algebra) , mathematical physics , mathematics , linear combination of atomic orbitals , algorithm , chemistry , pure mathematics , geometry , ecology , biology , crystallography , electron
Proceeding from analytical expressions for two‐center kernel functions that we derived recently, we present new analytical formulas for the two‐center Coulomb and overlap integrals over Slater‐type orbitals. These formulas are of an exceptionally simple analytical structure and high numerical efficiency. An especially important point is that for the most frequently needed ranges of discrete quantum numbers, the formulas are completely stable in the cases of nearly equal scaling parameters or vanishing interatomic distances, except for one particular case of the Coulomb integral. No special asymptotic formulas are needed any more to compute the two‐center integrals over Slater‐type orbitals in these case. Furthermore, a largely recursive formulation makes the integral evaluation very economical and fast. In particular, we assess the numerical performance of a new kind of angular momentum recurrences that we have proposed in a previous article [W. Hierse and P.M. Oppeneer, J. Chem. Phys. 99 , 1278 (1993)]. © 1994 John Wiley & Sons, Inc.