Fully self-consistent optimized effective potentials from a convex minimization problem

TL;DR

This paper formulates the optimized effective potential method as a convex minimization problem, enabling fully self-consistent calculations without assumptions on v-representability, and extends its applicability to other density-functional theories.

Contribution

It introduces a convex minimization framework for the optimized effective potential method, allowing for self-consistent calculations and extensions to other density-functional theories.

Findings

Framework does not require v-representability assumptions

Enables joint optimization of non-local and local potentials

Suitable for extensions to current-density functional theory

Abstract

The optimized effective potential method is formulated as a convex minimization problem. This formulation does not require assumptions about $v$-representability nor functional differentiability. The formulation provides a natural framework for fully self-consistent calculations where both a Kohn--Sham system with a non-local potential and an additional system with a local potential are jointly optimized. The formulation is also well suited for extensions to other flavors of density-functional theory, e.g. current-density functional theory, where there are additional potentials besides the ordinary electrostatic potential.