Local Symmetries and Forbidden Coset Representations

Abstract

In the preceding chapter, we have discussed SCR notations, which are based on the correspondence between coset representations (CRs) and orbits (sets of equivalent atoms). Without taking account of this correspondence, enumeration of such orbits has been done by Brester^[1], Jahn-Teller^[2], Boyle^[3] and Fowler- Quinn^[4] for most point groups. By these conventional methods, each orbit (O _A ) is usually characterized by the site symmetry group (H _A) that stabilizes (or fixes) one site (A) of the orbit. This characterization is accomplished by using tables presented by Fowler and Quinn.^[4] The site symmetry group (H _A ) for a non-center atom is shown to be one of C₁, C _s , C _n , or C _nv (n ≥ 2);^[3] several subsymmetries of G are incapable of being site symmetry groups.

Reprinted in part from S. Fujita, Theor. Chim. Acta, 78, 45–63 (1990). ©(1990) Springer-Verlag.