Semilocal exchange-correlation potentials for solid-state calculations: Current status and future directions

Abstract

Kohn-Sham (KS) density functional theory (DFT) is a very efficient method for calculating various properties of solids as, for instance, the total energy, the electron density, or the electronic band structure. The KS-DFT method leads to rather fast calculations, however the accuracy depends crucially on the chosen approximation for the exchange and correlation (xc) functional E xc and/or potential v xc . Here, an overview of xc methods to calculate the electronic band structure is given, with the focus on the so-called semilocal methods that are the fastest in KS-DFT and allow to treat systems containing up to thousands of atoms. Among them, there is the modified Becke-Johnson potential that is widely used to calculate the fundamental band gap of semiconductors and insulators. The accuracy for other properties like the magnetic moment or the electron density, that are also determined directly by v xc , is also discussed.

Crystal structure of monoclinic hafnia (HfO2) revisited with synchrotron X-ray, neutron diffraction and first-principles calculations

“…However, at the semi-local DFT level using the PBE-GGA functional only, some moderate amount of band gap improvement ($0.1-0.3 eV) was observed for the crystal structures obtained from the present ND (or combined refinement) experiment compared with the previously reported bulk structures obtained from X-ray diffraction refinement. Despite much debate, our finding seems to be in agreement with recent theoretical observations on the electron density of nonmagnetic solids (oxides) that are better described with semi-local functionals (Patra et al, 2019;Tran et al, 2019). Thus, the more precise positions of the O atoms in HfO 2 from ND is only validated from first-principles semi-local DFT exchange-correlation functional in terms of their calculated electronic band gap, but remain almost hidden from the higher-order hybrid DFTbased calculations.…”

Ultranonlocality and accurate band gaps from a meta-generalized gradient approximation

“…Furthermore, many of these constructions, as well as the attempt to restore the functional derivative property within the GGA form [70], lead to divergences [71][72][73]. Moreover, such purely multiplicative potentials are formally inappropriate to yield the fundamental gap [74].…”

Modeling the Ternary Chalcogenide Na2MoSe4 from First-Principles

“…Note that the band topology is invariant and located at Γ (Figure 4), but a widening of the bandgap is observed. When modeling the electronic band structure of Na tential enables the modeling the electronic structures of large and chemically complex semiconducting materials as well as insulators with predictive accuracy [58,59], and is currently considered the most accurate semilocal potential for semiconductor modeling [60,61].…”