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One‐ and two‐particle fractional parentage for arbitrary point groups, configurations, and coupling schemes
Author(s) -
Fieck Gerhard,
Wirsich Joachim
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.560180309
Subject(s) - point group , symmetry (geometry) , quantization (signal processing) , point (geometry) , theoretical physics , physics , coupling (piping) , second quantization , group (periodic table) , matrix (chemical analysis) , representation (politics) , group theory , mathematics , quantum mechanics , pure mathematics , creation and annihilation operators , quantum , combinatorics , geometry , algorithm , mechanical engineering , materials science , politics , political science , law , engineering , composite material
The fractional parentage coefficients ( CFPS ) for arbitrary symmetry (including non‐simply reducible point groups), different coupling schemes, and several open shells are discussed with emphasis on the common features. The differences between the coupling schemes arise merely from a different interpretation of the relevant symmetry group. The formulation uses the particle‐number representation (so‐called second quantization), in which the CFPS appear as the reduced matrix elements of the creation or annihilation operators. This shows, that there is no principal difference in the fractional parentage scheme of one or several open shells. For the latter case the theory of adjective CFPS is worked out and applied to an example of octahedral symmetry.