Modeling the electronic kinetic energy density and Pauli potential by orbital free density functional theory.

Abstract

In Kohn-Sham (KS) density functional theory, the kinetic energy (KE) functional is described by fictitious Kohn-Sham (KS) orbitals. This causes a computational bottleneck for large systems that require many KS orbitals. Much recent research is going into OrbitalFree Density Functional Theory (OFDFT), which models the kinetic energy as a functional of density and other ingredients that are derived from density directly, avoiding the need for orbitals. There are reasonable OFDFT models for kinetic energy at the meta-GGA level, such the Perdew-Constantin model, that properly treat the non-negativity constraint for the Pauli contribution to the kinetic energy density (KED), which describes the correction to the von-Weizs¨acker KED, which describes the KE of a single electron pair. However, an issue arises of Pauli potentials that are not physically reasonable and difficult to find convergent solutions for. We construct and test a computational tool to calculate Pauli potentials efficiently and diagnose the reasons for physically unreasonable behavior of meta-GGA and other semi-local level models. This will help construct models with potentials which vary smoothly. We test them against calculations of the exact Kohn-Sham KE and potential for atoms, with atomic densities constructed from the FHI98PP code.