Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation

Abstract

We present a comprehensive study of single-point kinetic energy density functionals (KEDFs) to be used in orbital-free density functional theory (DFT) calculations. We first propose a new form of KEDFs based on a pointwise Kohn-Sham (KS) kinetic energy density (KED) and electron localization function (ELF) analysis. We find that the ELF and modified enhancement factor have a very strong and transferable correlation with the reduced density in various bulk metals. The non-self-consistent kinetic energy errors predicted by these new KEDF models are decreased greatly compared to previously-reported generalized gradient approximation (GGA) KEDFs.Second, we perform self-consistent calculations with various single-point KEDFs and investigate their numerical convergence behavior. We find striking numerical instabilities for previous GGA KEDFs; most of the GGA KEDFs fail to converge and show unphysical densities during the optimization. In contrast, our new KEDFs demonstrate stable convergence, and their self-consistent results of various bulk 2 properties agree reasonably well with KSDFT. A further detailed KED analysis reveals an interesting bifurcation phenomenon in defective metals and alloys, which may shed light on directions for future KEDF development.

A simple approximation for the Pauli potential yielding self-consistent electron densities exhibiting proper atomic shell structure

“…On the other hand, the proposed procedure provides a method how to obtain fast and reliable convergence, a frequently encountered problem for this kind of differential equations. [4,34] Usually, the desired stability of the process is introduced by mixing the solutions of two consecutive steps. [39,40] This method will fail here, as iteratively solving…”

The Importance of Being Inconsistent

“…Furthermore almost all semilocal approximations fail to converge in self-consistent calculations. [XC15] The focus should be on improving the functional derivative rather than the energy itself, and the measure of improvement should be the reduction of the density-driven error.…”

Reply to “Comment on ‘Single-point kinetic energy density functionals: A pointwise kinetic energy density analysis and numerical convergence investigation’ ”

“…6 in Ref. 2). It will be interesting to do a similar analysis in all-electron Kohn-Sham (KS) density functional theory (DFT), where we suspect the multi-valuedness also exists because any artifacts due to pseudopotentials will be confined to near-nucleus regions.…”

“…In S. B. Trickey, V. V. Karasiev, and D. Chakraborty's interesting comment 1 on our previous paper, 2 two major issues are discussed: the multi-valuedness of the G factor versus the reduced gradient (s) 2 and the numerical stability of the VT84F 3 kinetic energy density functional (KEDF). On one hand, we still believe in the existence and significance of G-s multi-valuedness, despite possible pseudopotential artifacts and the global kinetic energy upper bound.…”