Semilocal properties of the Pauli kinetic potential

Abstract

The logarithmic singularity of the Lindhard linear response function plays an important role in various phenomena, such as the long-range Friedel oscillations and Kohn anomaly in phonon dispersion. Such a weak singularity cannot be captured by the known gradient expansion of the kinetic energy (KE), but it can be somewhat mimicked by the second-order gradient singularity expansion (GSE2) developed in this work. We show that the GSE2 Pauli KE potential of atoms, computed with the Kohn-Sham density, is remarkably accurate, being the best possible approximation provided by any second-order KE gradient expansion. Next, we study the utility of GSE2 for orbital-free density functional theory, and we prove that the GSE2-based KE functionals give an important and systematic improvement over other popular KE functionals.