Nonlocal vs Local Pseudopotentials Affect Kinetic Energy Kernels in Orbital-Free DFT

TL;DR

This paper investigates how local and nonlocal pseudopotentials influence the kinetic energy kernel in orbital-free DFT, revealing that nonlocal pseudopotentials cause significant deviations at short wavelengths, impacting KE functional accuracy.

Contribution

It introduces a methodology to compute the KE kernel from Kohn-Sham DFT and analyzes the effects of pseudopotential types on the KE kernel in bulk materials.

Findings

Local pseudopotentials yield accurate KE kernels in interstitial regions.

Nonlocal pseudopotentials cause deviations at short wavelengths.

Most KE functionals assume no effect from nonlocal pseudopotentials.

Abstract

The kinetic energy (KE) kernel, which is defined as the second order functional derivative of the KE functional with respect to density, is the key ingredient to the construction of KE models for orbital free density functional theory (OFDFT) applications. For solids, the KE kernel is usually approximated using the uniform electron gas (UEG) model or the UEG-with-gap model. These kernels do not have information about the effects from the core electrons since there are no orbitals for the projection on nonlocal pseudopotentials. To illuminate this aspect, we provide a methodology for computing the KE kernel from Kohn-Sham DFT and apply it to the valence electrons in bulk aluminum (Al) with a face-centered cubic lattice and in bulk silicon (Si) in a semiconducting crystal diamond state. We find that bulk-derived local pseudopotentials provide accurate results for the KE kernel in the interstitial region. The effect of using nonlocal pseudopotentials manifests at short wavelengths, defined by the diameter of an ion surrounded by its core electrons. Specifically, we find that the utilization of nonlocal pseudopotentials leads to significant deviations in the KE kernel from the von Weizsacker result in this region, which is, as a rule, explicitly enforced in most widely used KE functional approximations for OFDFT simulations.