Obtaining Kohn-Sham potential without taking the functional derivative

Abstract

Over the past decade and a half, many new accurate density functionals, based on the generalized gradient approximation, have been proposed, and they give energies close to chemical accuracy. However, accuracy of the energy functional does not guarantee that its functional derivative, which gives the corresponding potential, is also accurate all over space. For example, although the Becke88 exchange-energy functional gives very good exchange energies, its functional derivative goes as −1/r² m comparison to the correct −1/r for r→∞ where r is the distance of the electron from a finite system. On the other hand, accuracy of the potential is of prime importance if one is interested in properties other than the total energy; properties such as optical response depend crucially on the potential in the outer regions of a system. In this paper we present a different approach, based on the ideas of Harbola and Sahni, to obtain the potential directly from the energy density of a given approximation, without taking recourse to the functional derivative route. This leads to a potential that is as accurate as the functional itself. We demonstrate the accuracy of our approach by presenting some results obtained from the Becke88 functional.