Conditions on the Kohn–Sham kinetic energy and associated density

Abstract

Effective, explicitly density-dependent (i.e., orbital-free) approximations to the Kohn-Sham kinetic energy functional T s remain elusive. In the course of developing such functionals in collaboration with Frank Harris, various issues have arisen that have gone unaddressed. We consider four of them here: positivity of the KS kinetic energy density, supposed requirements on its functional dependence, the use of cutoffs to insure positivity, and the role of the Coulomb virial theorem in the asymptotic analysis of T s .

Issues and challenges in orbital-free density functional calculations

“…Investigation of orbital-free density functional theory (OF-DFT) [1][2][3][4][5][6][7][8][9][10][11][12] , including development of approximate orbital-free kinetic energy (OFKE) functionals, has at least two motivations. One is simply the beguiling notion of direct realization of the content of the Hohenberg-Kohn theorem [13][14][15][16][17] .…”

Cusp relation for the Pauli potential

“…Exact relations are valuable from several points of view, e.g., helpful in constructing approximate functionals. Several fundamental characteristics have already been presented [7,[37][38][39][40][41]. In this paper, the cusp relation is explored.…”

Properties of constraint-based single-point approximate kinetic energy functionals

“…24 The remainder, T − T s , is included in the exchangecorrelation ͑XC͒ functional E xc ͓n͔. Since successful E xc approximations assume this KS KE decomposition, we focus on T s .…”