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Algebraic solutions for point groups: Cubic groups G in the group chain G ⊃ T ⊃ D 2 ⊃ C 2
Author(s) -
Chen JinQuan,
Fan PengDong,
Paldus Josef
Publication year - 2000
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/(sici)1097-461x(2000)76:5<585::aid-qua1>3.0.co;2-n
Subject(s) - algebraic number , group (periodic table) , simple (philosophy) , point group , irreducible representation , chain (unit) , combinatorics , mathematics , symmetry group , symmetry (geometry) , pure mathematics , matrix (chemical analysis) , algebraic group , physics , mathematical physics , chemistry , quantum mechanics , geometry , mathematical analysis , philosophy , epistemology , chromatography
Concise algebraic expressions of the symmetry‐adapted functions (SAFs) for both single‐valued and double‐valued representations are derived for the group chain O ⊃ T ⊃ D 2 ⊃ C 2 and O ⊃ D 4 ⊃ D 2 ⊃ C 2 , which are functions of only the quantum numbers of the respective group chain without involving any irreducible matrix elements. It is shown that the SAFs of the cubic groups G = O , T d , T h , O h can be expressed in a simple way in terms of the SAFs of the group T . © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 585–599, 2000