Guaranteed convergence of the Kohn-Sham equations

TL;DR

This paper proves that a damped iterative approach to solving the Kohn-Sham equations with the exact functional always converges to the true ground-state density in finite Coulomb systems, regardless of initial conditions.

Contribution

It provides a rigorous proof of convergence for the damped Kohn-Sham iteration with the exact functional, applicable to all finite Coulomb systems.

Findings

Numerical implementation confirms convergence of the damped KS algorithm.

More strongly correlated systems exhibit slower convergence.

The proof holds regardless of initial density or electron correlation strength.

Abstract

A sufficiently damped iteration of the Kohn-Sham equations with the exact functional is proven to always converge to the true ground-state density, regardless of the initial density or the strength of electron correlation, for finite Coulomb systems. We numerically implement the exact functional for one-dimensional continuum systems and demonstrate convergence of the damped KS algorithm. More strongly correlated systems converge more slowly.