Accurate Kohn-Sham auxiliary system from the ground state density of solids

TL;DR

This paper develops highly accurate exchange-correlation potentials for solids using ground state densities from Quantum Monte Carlo, improving understanding of the Kohn-Sham system and its band gap predictions.

Contribution

It introduces a method to determine accurate xc potentials for solids from QMC densities, revealing their ensemble nature and implications for KS band gaps.

Findings

Accurate xc potentials for Si and NaCl obtained from QMC densities.

Kohn-Sham band gaps are larger than LDA predictions but smaller than photoemission gaps.

Different xc potentials can produce similar densities and observables, questioning the significance of potential details.

Abstract

The Kohn-Sham (KS) system is an auxiliary system whose effective potential is unknown in most cases. It is in principle determined by the ground state density, and it has been found numerically for some low-dimensional systems by inverting the KS equations starting from a given accurate density. For solids, only approximate results are available. In this work, we determine accurate exchange correlation (xc) potentials for Si and NaCl using the ground state densities obtained from Auxiliary Field Quantum Monte Carlo calculations. We show that these xc potentials can be rationalized as an ensemble of environment-adapted functions of the local density. The KS band structure can be obtained with high accuracy. The true KS band gap turns out to be larger than the prediction of the local density approximation, but significantly smaller than the measurable photoemission gap, which confirms previous estimates. Finally, our findings show that the conjecture that very different xc potentials can lead to very similar densities and other KS observables is true also in solids, which questions the meaning of details of the potentials and, at the same time, confirms the stability of the KS system.