Laplacian-level meta-generalized gradient approximation for solid and liquid metals

TL;DR

This paper introduces a new Laplacian-level meta-GGA functional, OFR2, that improves the accuracy of ground-state property predictions for metals, balancing between molecular and solid-state applications.

Contribution

We develop a Laplacian-level meta-GGA functional, OFR2, that restores the fourth-order gradient expansion and enhances the accuracy of metallic property predictions.

Findings

OFR2 matches SCAN in predicting lattice constants.

OFR2 improves equilibrium properties of various metals.

OFR2 outperforms r2SCAN-L for solid-state properties, but r2SCAN-L better predicts molecular atomization energies.

Abstract

We derive and motivate a Laplacian-level, orbital-free meta-generalized-gradient approximation (LL-MGGA) for the exchange-correlation energy, targeting accurate ground-state properties of $sp$ and $sd$ metallic condensed matter, in which the density functional for the exchange-correlation energy is only weakly nonlocal due to perfect long-range screening. Our model for the orbital-free kinetic energy density restores the fourth-order gradient expansion for exchange to the r$^2$SCAN meta-GGA [Furness et al., J. Phys. Chem. Lett. 11, 8208 (2020)], yielding a LL-MGGA we call OFR2. OFR2 matches the accuracy of SCAN for prediction of common lattice constants and improves the equilibrium properties of alkali metals, transition metals, and intermetallics that were degraded relative to the PBE GGA values by both SCAN and r$^2$SCAN. We compare OFR2 to the r$^2$SCAN-L LL-MGGA [D. Mejia-Rodriguez and S.B. Trickey, Phys. Rev. B 102, 121109 (2020)] and show that OFR2 tends to outperform r$^2$SCAN-L for the equilibrium properties of solids, but r$^2$SCAN-L much better describes the atomization energies of molecules than OFR2 does. For best accuracy in molecules and non-metallic condensed matter, we continue to recommend SCAN and r$^2$SCAN. Numerical performance is discussed in detail, and our work provides an outlook to machine learning.