Iterative minimization by Kohn--Sham inversion and potential mixing

Applications of Hohenberg--Kohn--Sham density functional theory to problems in materials physics are critically dependent on algorithms for iterating the Kohn--Sham equations to self-consistency. We present an approach for obtaining the self-consistent solution, which explores a connection between iterative minimization and Kohn--Sham inversion, \textit{i.e.} finding a self-consistent potential for a given density. The central idea is to perform the Kohn--Sham inversion using a position-dependent Lagrange multiplier and to construct a new trial potential from the result. The method is variational, in contrast to commonly-used density mixing approaches, and has excellent convergence. We demonstrate the method using a real-space pseudopotential implementation with applications to small molecules.