An investigation of the sensitivity of the Fermi surface to the treatment of exchange and correlation

TL;DR

This study examines how different exchange-correlation approximations in density functional theory affect the predicted Fermi surface of transition metals, highlighting SCAN's relative accuracy and persistent discrepancies in magnetic properties.

Contribution

It systematically compares LDA, GGA, SCAN, and GW methods in predicting Fermi surface features, revealing the sensitivity of p-character bands to exchange-correlation treatment.

Findings

LDA and GGA overestimate N hole ellipsoid sizes

GW predicts slightly too small Fermi surface features

SCAN provides the most accurate Fermi surface predictions

Abstract

The Group V and VI transition metals share a common Fermi surface feature of hole ellipsoids at the N point in the Brillouin zone. In clear contrast to the other Fermi surface sheets, which are purely of d character, these arise from a band that has a significant proportion of p character. By performing local density approximation (LDA), generalized gradient approximation (GGA), strongly constrained and appropriately normed (SCAN) meta-GGA, and GW approximation calculations, we find that the p character part of this band (and therefore the Fermi surface) is particularly sensitive to the exchange-correlation approximation. LDA and GGA calculations inadequately describe this feature, predicting N hole ellipsoid sizes that are consistently too large in comparison to various experimental measurements, whereas quasiparticle self-consistent GW calculations predict a size that is slightly too small (and non-self-consistent GW calculations that use an LDA starting point predict a size that is much too small). Overall, for the metals tested here, SCAN provides the most accurate Fermi surface predictions, mostly correcting the discrepancies between measurements and calculations that were observed when LDA calculations were used. However, none of the tested exchange-correlation approximations succeeds in simultaneously bringing all of the measurable properties of these metals into good experimental agreement, particularly where magnetism is concerned. The SCAN calculations predict antiferromagnetic moments for Cr that are 3 times larger than the experimental value (1.90 $\mu_B$ compared to 0.62 $\mu_B$).