Generalized-Wannier-function solutions to model surface potentials

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Abstract
The generalized-Wannier-function (GWF) formalism is used to calculate the electronic structure associated with the lowest bands of several one-dimensional model surfaces. The results are compared with exact solutions obtained independently. The GWF calculations, which are variational in nature, are found to give very satisfactory accuracy with simple trial functions which employ, at most, four variational parameters. The GWF's damp very rapidly to the bulk Wannier function. Only those in the two lattice sites closest to the surface are significantly different. This implies, for filled bands, a similar rapid damping of the charge density. These facts, which might be anticipated for tightly bound electrons, hold even in the case of weak pontentials in which the electrons are nearly free.