Nonempirical Density Functionals Investigated for Jellium: Spin-Polarized Surfaces, Spherical Clusters, and Bulk Linear Response

TL;DR

This paper evaluates various nonempirical density functionals, including TPSS and PBE, for modeling jellium systems, focusing on surface energies, work functions, magnetism, and linear response, and compares results with Quantum Monte Carlo data.

Contribution

It provides a comprehensive comparison of nonempirical density functionals for jellium, highlighting their accuracy in surface properties, magnetism, and linear response, with new insights into their equivalence and limits.

Findings

TPSS matches PBE in surface correlation energy at normal densities

TPSS offers a consistent estimate for the low-density limit

All tested functionals accurately reproduce the linear response up to twice the Fermi wavevector

Abstract

Earlier tests show that the Tao-Perdew-Staroverov-Scuseria (TPSS) nonempirical meta-generalized gradient approximation (meta-GGA) for the exchange-correlation energy yields more accurate surface energies than the local spin density (LSD) approximation for spin-unpolarized jellium. In this study, work functions and surface energies of a jellium metal in the presence of ``internal'' and external magnetic fields are calculated with LSD, Perdew-Burke-Ernzerhof (PBE) GGA, and TPSS meta-GGA and its predecessor, the nearly nonempirical Perdew-Kurth-Zupan-Blaha (PKZB) meta-GGA, using self-consistent LSD orbitals and densities. The results show that: (i) For normal bulk densities, the surface correlation energy is the same in TPSS as in PBE, as it should be since TPSS strives to represent a self-correlation correction to PBE; (ii) Normal surface density profiles can be scaled uniformly to the low-density or strong-interaction limit, and TPSS provides an estimate for that limit that is consistent with (but probably more accurate than) other estimates; (iii) For both normal and low densities, TPSS provides the same description of surface magnetism as PBE, suggesting that these approximations may be generally equivalent for magnetism. The energies of jellium spheres with up to 106 electrons are calculated using density functionals and compared to those obtained with Diffusion Quantum Monte Carlo data, including our estimate for the fixed-node correction. Finally we calculate the linear response of bulk jellium using these density functionals, and find that not only LSD but also PBE GGA and TPSS meta-GGA yield a linear-response in good agreement with that of the Quantum Monte Carlo method, for wavevectors of the perturbing external potential up to twice the Fermi wavevector.