Lieb’s most useful contribution to density functional theory?

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.