Origin of static and dynamic steps in exact Kohn-Sham potentials

TL;DR

This paper investigates the properties and origins of steps in the exact Kohn-Sham exchange-correlation potential, providing insights to improve density functional approximations for both ground and time-dependent systems.

Contribution

It identifies the conditions under which steps occur in the xc potential and extends the understanding to time-dependent systems, aiding the development of better functionals.

Findings

Steps occur at points of change in local effective ionization energy.

Practical methods for determining step features based on electron density.

Extension of step concepts to time-dependent systems.

Abstract

Knowledge of exact properties of the exchange-correlation (xc) functional is important for improving the approximations made within density functional theory. Features such as steps in the exact xc potential are known to be necessary for yielding accurate densities, yet little is understood regarding their shape, magnitude and location. We use systems of a few electrons, where the exact electron density is known, to demonstrate general properties of steps. We find that steps occur at points in the electron density where there is a change in the `local effective ionization energy' of the electrons. We provide practical arguments, based on the electron density, for determining the position, shape and height of steps for ground-state systems, and extend the concepts to time-dependent systems. These arguments are intended to inform the development of approximate functionals, such as the mixed localization potential (MLP), which already demonstrate their capability to produce steps in the Kohn-Sham potential.