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Auxiliary functions for molecular integrals with Slater‐type orbitals. I. Translation methods
Author(s) -
Fernández J. J.,
López R.,
Ema I.,
Ramírez G.,
Fernández Rico J.
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.21002
Subject(s) - slater integrals , translation (biology) , order of integration (calculus) , function (biology) , atomic orbital , range (aeronautics) , field (mathematics) , volume integral , mathematics , physics , pure mathematics , quantum mechanics , mathematical analysis , chemistry , integral equation , electron , materials science , biochemistry , evolutionary biology , biology , messenger rna , composite material , gene
Many types of molecular integrals involving Slater functions can be expressed, with the ζ‐function method in terms of sets of one‐dimensional auxiliary integrals whose integrands contain two‐range functions. After reviewing the properties of these functions (including recurrence relations, derivatives, integral representations, and series expansions), we carry out a detailed study of the auxiliary integrals aimed to facilitate both the formal and computational applications of the ζ‐function method. The usefulness of this study in formal applications is illustrated with an example. The high performance in numerical applications is proved by the development of a very efficient program for the calculation of two‐center integrals with Slater functions corresponding to electrostatic potential, electric field, and electric field gradient. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006