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Recurrence relations for the evaluation of electron repulsion integrals over spherical Gaussian functions
Author(s) -
Fortunelli Alessandro,
Salvetti Oriano
Publication year - 1993
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.560480407
Subject(s) - hermite polynomials , cartesian coordinate system , gaussian , zero (linguistics) , momentum (technical analysis) , physics , tensor (intrinsic definition) , spherical coordinate system , angular momentum , electron , mathematics , recurrence relation , mathematical analysis , mathematical physics , classical mechanics , quantum mechanics , pure mathematics , geometry , economics , linguistics , philosophy , finance
Recurrence relations are derived for the evaluation of two‐electron repulsion integrals (ERIs) over Hermite and spherical Gaussian functions. Through such relations, a generic ERI or ERI derivative may be reduced to “basic” integrals, i.e., true and auxiliary integrals involving only zero angular momentum functions. Extensive use is made of differential operators, in particular, of the spherical tensor gradient l m (∇). Spherical Gaussians, being nonseparable in the x , y , and z coordinates, were not included in previous formulations. The advantages of using spherical Gaussians instead of Cartesian or Hermite Gaussians are briefly discussed. © 1993 John Wiley & Sons, Inc.