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Molecular one‐electron integrals over slater‐type atomic orbitals and irregular solid spherical harmonics
Author(s) -
Steinborn E. Otto,
Ruedenberg Klaus
Publication year - 1972
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.560060304
Subject(s) - spherical harmonics , slater type orbital , legendre polynomials , atomic orbital , legendre function , physics , operator (biology) , charge density , quantum mechanics , diatomic molecule , slater integrals , electron , center (category theory) , harmonics , orbital overlap , type (biology) , linear combination of atomic orbitals , atomic physics , chemistry , molecule , biochemistry , repressor , transcription factor , gene , crystallography , ecology , voltage , biology
The one‐electron integral over Slater‐type atomic orbitals centered at A and B and irregular solid spherical harmonics as operator centered at C is evaluated analytically by using elliptical coordinates and translation of the solid spherical harmonics from center C to either focus A or B. A special case is the three‐center nuclear attraction integral which is also evaluated by means of the Neumann expansion and expressed without associate Legendre functions of the second kind. The strict observation of the charge distribution concept leads to compact expressions for the integral. It has the further advantage that the charge density distributions which have been developed for the two‐center cases and used in calculations for diatomic molecules can be utilized.