Lieb's most useful contribution to density functional theory?

TL;DR

This paper discusses Lieb's proof's significance in density functional theory, emphasizing the semiclassical limit where functionals become local and how this insight can enhance the accuracy of practical DFT calculations.

Contribution

It highlights the potential of Lieb-Simon's principle to identify leading corrections to local density approximations, aiming to improve DFT accuracy.

Findings

Explicit derivation of corrections in simple models yields highly accurate energies.

The principle suggests a pathway to systematically improve local density approximations.

Analytic work is needed to extend these insights to real molecular and solid-state systems.

Abstract

The importance of the Lieb-Simon proof of the relative exactness of Thomas-Fermi theory in the large-Z limit to modern density functional theory (DFT) is explored. The principle, that there is a specific semiclassical limit in which functionals become local, implies that there exist well-defined leading functional corrections to local approximations that become relatively exact for the error in local approximations in this limit. It is argued that this principle might be used to greatly improve the accuracy of the thousand or so DFT calculations that are now published each week. A key question is how to find the leading corrections to any local density approximation as this limit is approached. These corrections have been explicitly derived in ridiculously simple model systems to ridiculously high order, yielding ridiculously accurate energies. Much analytic work is needed to use this principle to improve realistic calculations of molecules and solids.