Multiscale analysis of density functional theory

Abstract

We discuss multiscale problems that arise in the analysis of the electronic structure of materials using density functional theory. In contrast to the traditional approach which views Kohn–Sham density functional theory as a nonlinear system of eigenvalue problems, we take the viewpoint that what we are really interested in is the eigen-subspace which represents the subspace occupied by the electrons, and we discuss localized bases for such eigen-subspaces. We then discuss the continuum limit of density functional theory, sub-linear scaling algorithms based on multiscale analysis and coupled formulation between density functional theory and continuum models.