Generalization of the density-matrix method to a nonorthogonal basis

We present a generalization of the Li, Nunes, and Vanderbilt density-matrix method to the case of a nonorthogonal set of basis functions. A representation of the real-space density matrix is chosen in such a way that only the overlap matrix, and not its inverse, appears in the energy functional. The generalized energy functional is shown to be variational with respect to the elements of the density matrix, which typically remains well localized.