Effect of the Gradient of the Spin-Polarization in Density Functional Approximations
Rohan Maniar, John P. Perdew
TL;DR
This paper addresses the limitation that the gradient of the relative spin polarization, $ abla \zeta$, is omitted in the correlation part of the SCAN functional, potentially hindering transition-metal chemistry. The authors introduce a controlled scheme to reintroduce these terms by combining high-density and low-density gradient expansions (HDL/LDL) with an $r_s$-dependent interpolation and damping via the iso-orbital indicator $\alpha$, yielding the gradient-zeta-corrected SCAN (gzc-SCAN) with fitted parameters $\beta_1=0.240$ and $\beta_2=0.033$. The results show that gzc-SCAN preserves much of SCAN’s accuracy for $sp$-systems while delivering improvements for transition-metal atoms, ionization energies, and dimers (notably correcting Cr$_2$ underbinding at large separations and reducing the FM–AFM gap in Mn$_2$). This approach offers a practical route to extend existing semi-local DFAs to better capture spin-polarization effects in challenging systems, with potential applicability to other GGAs/meta-GGAs and future refinements such as restoring the Lieb–Oxford bound.
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 $\nabla ζ$-dependent terms in the gradient expansion of the correlation have been dropped, where $ζ$ 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 $\nabla ζ$-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.