Phase-fixed double-group 3-Γ symbols. II. General features of double groups and their 3-Γ symbols |
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| Authors: | Ture Damhus Sven E. Harnung Claus E. Schäffer |
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| Affiliation: | (1) Chemistry Department I, H. C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark;(2) Present address: Department of Pharmaceutical Chemistry AD, Royal Danish School of Pharmacy, Universitetsparken 2, DK-2100 Copenhagen Ø, Denmark |
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| Abstract: | Following a general exposition of the theory of 3- symbols [1], we now focus on the particular features encountered when dealing with double groups of (proper as well as improper) point groups.The paper starts with a brief outline of the definition of double groups adopted in the present work. After this, some properties of double group 3- symbols are discussed which are independent of the way the 3- symbols have been constructed. The main part of the paper then deals with the actual generation of 3- symbols for the non-commutative double groups.In the approach described, the 3- symbols become determined in part by adaption of the standard matrix irreps to subgroup hierarchies and then completely, phases included, by the specification of standard basis functions (or, equivalently, standard subduction coefficients). |
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| Keywords: | double groups for proper and improper point groups subduction coefficients basis functions for standard irreducible matrix representations phase-fixation of three-gamma symbols and coupling coefficients triple coefficients |
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