Toward routine Kohn-Sham inversion using the "Lieb-response" approach

27 January 2023, Version 2
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

Kohn-Sham inversion, in which the effective Kohn-Sham mean-field potential is found for a given density, provides insights into the nature of exact density functional theory (DFT) that can be exploited for the development of density functional approximations. Unfortunately, and despite significant and sustained progress in both theory and software libraries, KS inversion remains rather difficult in practice, and especially in finite basis sets. The present work presents a Kohn-Sham inversion method, dubbed the “Lieb-response” approach, that naturally works with existing Fock-matrix DFT infrastructure in finite basis sets, is numerically efficient, and directly provides meaningful matrix and energy quantities for pure-state and ensemble systems. Some additional work yields potentials. It thus enables the routine inversion of even difficult KS systems, as illustrated on a variety of problems within this work; and provides outputs that can be used for embedding schemes or machine learning of density functional approximations. The effect of finite basis sets on Kohn-Sham inversion is also analysed and investigated.

Keywords

Kohn-Sham
DFT
Density functional theory
Inversion

Supplementary weblinks

Comments

Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.