Algebraic solutions for point groups: The octahedral group for the group chain O superset of T superset of C-3

摘要

Using the right-induced technique and the eigenfunction method, concise algebraic expressions of the projection operators for both single-valued and double-valued representations are found for the group chain O superset of T superset of C-3 in terms of the projection operators of T superset of C-3. Extremely simple relations are discovered between the symmetry adapted functions (SAFs) of the groups T and O; namely the SAFs of the subgroup T which have proper symmetry are the SAFs of the group O. The projection operators and SAFs are functions of only the quantum numbers of the group chain [the analogy of (j, m) for the group chain SO3 superset of SO2], without involving any irreducible matrix elements. (C) 2001 John Wiley & Sons, Inc. Int J Quantum Chem 83: 259-270, 2001. [References: 25]