Relevance of the Pauli kinetic energy density for semilocal functionals

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.…”

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

“…95). Also noteworthy is a very recent MGGA functional proposed by Patra et al 161 leading to a MAE of 0.69 eV for a set of 67 solids (comprising no AFM TM oxides), which is, however, larger than 0.44 eV obtained with mBJLDA for the same test set.…”

A general penalty method for density‐to‐potential inversion

“…The purpose of this work is to provide a general connection between the minimization method of Equation (5) and different methods proposed for performing unconstrained maximization of the functional J ρ 0 v ½ of Equation (7). We show that for each one of the latter methods, there is a corresponding method using Equation (5).…”

“…With the increasing accuracy of density functional theory (DFT) [1][2][3][4][5][6][7] calculations, it is imperative that exact results [8][9][10][11][12] also be made available wherever possible. This is important both from a fundamental point of view and for gaining insights into the working of functionals used to perform DFT calculations.…”

“…In the following, we first outline the definition of the universal functional (see Equation [9] below) of DFT and discuss how this is used to obtain the exchange-correlation potential of KSDFT through Equations (5) and (7). In particular, we describe the ZMP method for minimizing the KS kinetic energy with constraint and several methods and their universality for maximizing the functional of Equation (7). Based on the latter, we then show that the ZMP method also has a general nature, and several functionals other than those proposed by ZMP can be equally effective for obtaining the KS exchange-correlation potential.…”