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Configuration interaction matrix elements. I. Algebraic approach to the relationship between unitary group generators and permutations
Author(s) -
Wormer P. E. S.,
Paldus J.
Publication year - 1979
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.560160610
Subject(s) - antisymmetric relation , unitary group , unitary state , unitary matrix , simple (philosophy) , group (periodic table) , matrix (chemical analysis) , mathematics , group theory , algebraic number , spin (aerodynamics) , physics , combinatorics , pure mathematics , quantum mechanics , mathematical physics , chemistry , mathematical analysis , philosophy , epistemology , chromatography , thermodynamics , political science , law
Abstract Matrix elements of unitary group generators between spin‐adapted antisymmetric states are shown to be proportional to spin matrix elements of so‐called “line‐up” permutations. The proportionality factor is given explicitly as a simple function of the orbital occupation numbers. If one bases the theory on ordered orbital products, the line‐up permutations are given a priori . The final formulas have a very simple structure; this is a direct consequence of the fact that the spin functions have been taken to be geminally antisymmetric.