Wannier-type orbitals derived from Mullikenʹs population analysis

A simple scheme for obtaining well-localized non-orthogonal Wannier-type orbitals (WTOs) for periodic systems is discussed. (The WTOs corresponding to the same cell are orthogonal but the WTOs of different cells are generally not.) The method uses the Magnasco–Perico localization criterion based on Mullikenʹs population analysis: Mullikenʹs net population corresponding to the elementary cell is extremized. The calculations require the systemʹs density and overlap matrices which are assumed to be known from a conventional band calculation but no explicit reference is made to the Bloch orbitals. The viability of the method is illustrated with the example of 6-31G calculations for polyacetylene and polyglycine.