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Transferable integrals in a deformation density approach to crystal orbital calculations. IV. Evaluation of angular integrals by a vector‐pairing method
Author(s) -
Avery John,
ørmen PerJohan
Publication year - 1980
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.560180405
Subject(s) - angular momentum , cartesian coordinate system , invariant (physics) , fourier transform , total angular momentum quantum number , projection (relational algebra) , physics , numerical integration , coordinate system , orthogonal coordinates , classical mechanics , pairing , mathematical analysis , mathematics , mathematical physics , quantum mechanics , geometry , algorithm , superconductivity
A general method for performing angular integrations is presented. The method depends on the fact that the integral must be invariant under rotations of the coordinate system, and it also makes use of combinatorial analysis. In most cases the method presented is computationally much faster than alternative methods of angular integration using Condon–Shortley coefficients. Applications to charge density analysis and Fourier transforms are discussed, and a general formula for the action of angular momentum projection operators on functions of the Cartesian coordinates is derived. A general angular integration formula for an m ‐dimensional space is also given.