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Matrix elements for Ĵ 2 and Ĵ z operators over explicitly correlated Cartesian Gaussian functions
Author(s) -
Kozlowski Pawel M.,
Adamowicz Ludwik
Publication year - 1995
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.560550502
Subject(s) - cartesian coordinate system , gaussian , formalism (music) , adiabatic process , exponential function , physics , cartesian product , quantum mechanics , mathematical physics , mathematics , mathematical analysis , geometry , combinatorics , visual arts , art , musical
General formalism for evaluation of multiparticle integrals involving J̌ 2 and J̌ z operators over explicitly correlated Cartesian Gaussian functions is presented. The integrals are expressed in terms of the general overlap integrals. An explicitly correlated Cartesian Gaussian function is a product of spherical orbital Gaussian functions, powers of the Cartesian coordinates of the particle, and exponential Gaussian factors, which depend on interparticular distances. This development is relevant to both adiabatic and nonadiabatic calculations of energy and properties of multiparticle systems. © 1995 John Wiley & Sons, Inc.