Generalization of the density-matrix method to a non-orthogonal basis

TL;DR

This paper extends the density-matrix method to non-orthogonal basis sets, ensuring the energy functional remains variational and practical for localized density matrices.

Contribution

It generalizes the Li, Nunes, and Vanderbilt density-matrix approach to non-orthogonal bases, avoiding the inverse of the overlap matrix in the energy functional.

Findings

Energy functional remains variational with non-orthogonal basis

Density matrix representation avoids inverse overlap matrix

Method applicable to localized density matrices

Abstract

We present a generalization of the Li, Nunes and Vanderbilt density-matrix method to the case of a non-orthogonal 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.