On the possibility of deriving equivalent localized basis sets from symmetry adapted ones

Abstract

It is shown that, given a symmetry adapted set of basis functions, for certain systems of high symmetry the generation of an equivalent localized set of basis functions is not always possible if the localized set is subject to the following requirements: 1) be linearly independent; 2) be partitionable into disjoint subsets each belonging to a localized site and transform according to the irreducible representations of the corresponding site symmetry; 3) symmetrically equivalent sites have equivalent subsets. The conclusion can be drawn that for highly symmetrical systems the description in terms of linearly independent localized single-particle functions may not be suitable.