Effect of the Gradient of the Spin-Polarization in Density Functional Approximations

TL;DR

This paper introduces a scheme to incorporate the gradient of spin polarization into density functional approximations, improving accuracy for transition-metal systems while maintaining performance for other systems.

Contribution

A novel method to reintroduce $ abla ext{zeta}$ terms into existing functionals, demonstrated by creating a corrected SCAN functional that enhances predictions for transition metals.

Findings

Improved accuracy for transition-metal atoms and molecules.

Corrected binding energy curve for Cr$_2$ dimer.

Maintains accurate description of $sp$-systems.

Abstract

The construction of non-empirical density functional approximations is typically guided by the satisfaction of exact constraints. An important constraint is the recovery of the gradient expansion for slowly varying electron densities. In prior constructions of semilocal density functional approximations, the $\nabla \zeta$-dependent terms in the gradient expansion of the correlation have been dropped, where $\zeta$ is the relative spin polarization. We propose a scheme by which such terms can be reintroduced into already constructed functionals without significantly affecting other constraints and norms. We implement this scheme on the Strongly Constrained and Appropriately Normed (SCAN) functional to construct a $\nabla \zeta$-corrected version of SCAN. The resulting functional is shown to provide improvements in transition-metal atoms and molecules without significantly affecting SCAN's accurate description of $sp$-systems. For the binding energy curve of the chromium dimer Cr$_2$, the SCAN underbinding is fully corected at large bond lengths and reduced at short bond lengths.