N-REPRESENTABILITY AND DENSITY-FUNCTIONAL CONSTRUCTION IN CURVILINEARCOORDINATES

In practical implementations of density-functional theory, the only te rm where an orbital description is needed is the kinetic one. Even thi s term in principle depends on the density only, but its explicit form is unknown. We provide a novel solution of the N-representability pro blem for an extended system, which implies an explicit form for the Ko hn-Sham kinetic energy in terms of the density. Our approach is based on a periodic coordinate mapping, uniquely defined by the Fourier coef ficients of the metric. The density functional is thus expressed as an explicit functional of the metric tensor: since N-representability is enforced, our constructive recipe provides a variational approximatio n. Furthermore, we show that our geometric viewpoint is quite naturall y related to the electron localization function (ELF), which provides a very informative analysis of che electron distribution. Studies of E LF, as obtained from accurate Kohn-Sham orbitals in real materials, al low an appraisal of the variational approximate density functional. We show that the value of an approximate functional-either the present g eometric-based one or some previous ones based on different constructi ve recipes-strongly depends on the nature of the chemical bonding in t he material. (C) 1998 Elsevier Science Ltd. All rights reserved.