Generalized Gradient Approximation Correlation Energy Functionals Based on the Uniform Electron Gas with Gap Model

Abstract

We studied uniform electron gas with a gap model in the context of density functional theory. On the basis of this analysis, we constructed two local gap models that are used in generalized gradient approximation (GGA) correlation functionals that satisfy numerous exact constraints for correlation energy. The first one, named GAPc, fulfills the full second-order correlation gradient expansion at any density regime and is very accurate for jellium surfaces, comparable to state-of-the-art GGAs for atomic systems and molecular systems, and is well compatible with known semilocal exchanges. The second functional, named GAPloc, satisfies the same exact conditions, except that the second-order gradient expansion is sacrificed for a better behavior under the Thomas-Fermi scaling and a more realistic correlation energy density of the helium atom. The GAPloc functional displays a high accuracy for atomic correlation energies, still preserving a reasonable behavior for jellium surfaces. Moreover, it shows a higher compatibility with the Hartree-Fock exchange than other semilocal correlation functionals. This feature is explained in terms of the real-space analysis of the GAPloc correlation energy.

Gradient-dependent exchange-correlation kernel for materials optical properties

“…We recall that averages over the unit cell have also been used, with good results, in the development of a kinetic-energy functional for an orbital-free DFT [48], and especially in the construction of the MBJ semilocal exchange potential that is accurate for the study of band gap energies of solids [49]. Moreover, the ratio |∇n|/n is an important density indicator, being used in hybrid functionals with local range separation [50], in the MBJ semilocal exchange potential construction [49], and in local band gap models [51,52]. We fix the parameter a = 0.46, in such a way that the JGM-G kernel yields optical absorption spectra of the low-bandgap semiconductors InSb (E g = 0.23 eV) and InAs (E g = 0.43 eV) that coincide with the optical absorption spectra obtained with the JGM or JGMs kernel.…”

Comparison of dispersion-corrected exchange-correlation functionals using atomic orbitals

“…Semilocal XC functionals, which are all characterized by a localized XC hole density [5,6], can recognize various types of interactions and density regimes, such as covalent, metallic, and some short-ranged weak bonds [4,[7][8][9], can be utilized for an accurate description of surface asymptotics [10], and can describe the dimensional crossover of the XC energy [11][12][13] for various confinements [14]; but they cannot possibly describe correctly van der Waals (vdW) interactions even at short range [15]. Whenever vdW interactions play a role, one can use the so-called DFT-D semiempirical approach [16][17][18][19][20][21][22][23][24][25][26][27][28][29], which is based on the cancellation of various errors especially at a short range [15].…”

Global Hybrids from the Semiclassical Atom Theory Satisfying the Local Density Linear Response

“…GAPloc 68 or revTCA 6 ). Alternatively, the replacement of GGAs with meta-GGAs can be considered in Eq.…”

“…In this work, we will choose for DFA1 the APBE GGA functional 62 , which is one of the most accurate non-empirical GGAs with broad applicability 62,63 . For DFA2, we select the PBEloc correlation functional 66 , which has been proved to work quite well together with the Hartree-Fock exchange, even if other possibilities could also be considered 6,67,68 . Note that Eq.…”