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Symmetry adapted formulation of the generalized Brillouin theorem
Author(s) -
Godefroid M.,
Lievin J.,
Metz J.Y.
Publication year - 1991
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.560400207
Subject(s) - brillouin zone , homogeneous space , wave function , formalism (music) , excited state , point group , molecular symmetry , symmetry group , physics , symmetry (geometry) , quantum mechanics , mathematical physics , mathematics , geometry , molecule , art , musical , visual arts
The singly excited functions satisfying Brillouin theorem are expressed as linear combinations of configuration‐state functions for any spin and spatial symmetries (atomic or molecular) and for any reference wave function. The generality of the formulation is ensured by the use of the irreducible tensor method that can be adapted to any symmetry point group of interest. The expansion coefficients are simply written as products of fractional parentage coefficients, spin‐ and orbit‐recoupling coefficients, and phase factors. The formalism is illustrated for some atomic ( K h ) and molecular ( C ∞ v , C 3 v , and T d ) configurations. Group theoretical techniques are also used to correlate the Brillouin conditions within a chain of groups.