Fabien Tran

Band gap calculations with Becke–Johnson exchange potential

Recently, a simple analytical form for the exchange potential was proposed by Becke and Johnson. This potential, which depends on the kinetic-energy density, was shown to reproduce very well the shape of the exact exchange potential (obtained with the optimized effective potential method) for atoms. Calculations on solids show that the Becke–Johnson potential leads to a better description of band gaps of semiconductors and insulators with respect to the standard local density and Perdew–Burke–Ernzerhof approximations for the exchange–correlation potential. Comparison is also made with the values obtained with the Engel–Vosko exchange potential which was also developed using the exact exchange potential.

Implementation of screened hybrid functionals based on the Yukawa potential within the LAPW basis set

The implementation of screened hybrid functionals into the WIEN2K code, which is based on the linearized augmented plane wave (LAPW) basis set, is reported. The Hartree-Fock exchange energy and potential are screened by means of the Yukawa potential as proposed by Bylander and Kleinman [D. M. Bylander and L. Kleinman, Phys. Rev. B 41, 7868 (1990)] for the calculation of the electronic structure of solids with the screened-exchange local density approximation. Details of the formalism, which is based on the method of Massidda, Posternak, and Baldereschi [S. Massidda, M. Posternak, and A. Baldereschi, Phys. Rev. B 48, 5058 (1993)] for the unscreened Hartree-Fock exchange are given. The results for the transition-energy and structural properties of several test cases are presented. The results of calculations of the Cu electric-field gradient in Cu2O are also presented, and it is shown that the hybrid functionals are much more accurate than the standard local-density or generalized gradient approximations.

Rungs 1 to 4 of DFT Jacob’s ladder: Extensive test on the lattice constant, bulk modulus, and cohesive energy of solids

A large panel of old and recently proposed exchange-correlation functionals belonging to rungs 1 to 4 of Jacobs ladder of density functional theory are tested (with and without a dispersion correction term) for the calculation of the lattice constant, bulk modulus, and cohesive energy of solids. Particular attention will be paid to the functionals MGGA_MS2 [J. Sun et al., J. Chem. Phys. 138, 044113 (2013)], mBEEF [J. Wellendorff et al., J. Chem. Phys. 140, 144107 (2014)], and SCAN [J. Sun et al., Phys. Rev. Lett. 115, 036402 (2015)] which are meta-generalized gradient approximations (meta-GGA) and are developed with the goal to be universally good. Another goal is also to determine for which semilocal functionals and groups of solids it is beneficial (or not necessary) to use the Hartree-Fock exchange or a dispersion correction term. It is concluded that for strongly bound solids, functionals of the GGA, i.e., rung 2 of Jacobs ladder, are as accurate as the more sophisticated functionals of the higher rungs, while it is necessary to use dispersion corrected functionals in order to expect at least meaningful results for weakly bound solids. If results for finite systems are also considered, then the meta-GGA functionals are overall clearly superior to the GGA functionals.

Systematic investigation of a family of gradient-dependent functionals for solids

Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and combinations thereof. On a test set of 60 solids, we perform a system-by-system analysis for selected functionals and a full statistical analysis for all of them. The impact of restoring the gradient expansion and of tightening the Lieb-Oxford bound is discussed, and confronted with previous results obtained from other codes, functionals or test sets. No functional is uniformly good for all investigated systems, but surprisingly, and pleasingly, the simplest possible modifications to PBE turn out to have the most beneficial effect on its performance. The atomization energy of molecules was also considered and on a testing set of six molecules, we found that the PBE functional is clearly the best, the others leading to strong overbinding.

Hybrid functionals for solids with an optimized Hartree-Fock mixing parameter.

(Screened) hybrid functionals are being used more and more for solid-state calculations. Usually the fraction α of Hartree-Fock exchange is kept fixed during the calculation; however, there is no single (universal) value for α which systematically leads to satisfying accuracy. Instead, one could use a property of the system under consideration to determine α, and in this way the functional would be more flexible and potentially more accurate. Recently, it was proposed to use the static dielectric constant ε for the calculation of α (Shimazaki and Asai 2008 Chem. Phys. Lett. 466 91 and Marques et al 2011 Phys. Rev. B 83 035119). We explore this idea further and propose a scheme where the connection between ε and α is optimized based on experimental band gaps. ε, and thus α, is recalculated at each iteration of the self-consistent procedure. We present results for the bandgap and lattice constant of various semiconductors and insulators with this procedure. In addition, we show that this approach can also be combined with a non-self-consistent hybrid approximation to speed up the calculations considerably, while retaining an excellent accuracy in most cases.

Electronic structure of CrN: A comparison between different exchange correlation potentials

We report a series of electronic structure calculations for CrN using different exchange correlation potentials: PBE, LDA+

Short-range magnetic order and temperature-dependent properties of cupric oxide

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Importance of the Kinetic Energy Density for Band Gap Calculations in Solids with Density Functional Theory

, the Tran-Blaha modified Becke-Johnson, and hybrid functionals. In every case, our calculations show that the onset of magnetism in CrN should be accompanied by a gap opening. The experimentally found antiferromagnetic order always leads to an insulating behavior. Our results give further evidence that the Tran-Blaha functional is very useful for treating the electronic structure of correlated semiconductors allowing a parameter free description of the system. Hybrid functionals are also well capable of describing the electronic structure of CrN. The analysis of the system is complemented with our calculations of the thermopower that are in agreement with the experimental data.

Comparison between exact and semilocal exchange potentials: An all-electron study for solids

The temperature dependence of the optical and magnetic properties of CuO were examined by means of hybrid density functional theory calculations. Our work shows that the spin exchange interactions in CuO are neither fully one-dimensional nor fully three-dimensional. The temperature dependence of the optical band gap and the (63)Cu nuclear quadrupole resonance frequency of CuO originate from the combined effect of a strong coupling between the spin order and the electronic structure and the progressive appearance of short-range order with temperature.

Approximations to the exact exchange potential: KLI versus semilocal

Recently, exchange-correlation potentials in density functional theory were developed with the goal of providing improved band gaps in solids. Among them, the semilocal potentials are particularly interesting for large systems since they lead to calculations that are much faster than with hybrid functionals or methods like GW. We present an exhaustive comparison of semilocal exchange-correlation potentials for band gap calculations on a large test set of solids, and particular attention is paid to the potential HLE16 proposed by Verma and Truhlar. It is shown that the most accurate potential is the modified Becke–Johnson potential, which, most noticeably, is much more accurate than all other semilocal potentials for strongly correlated systems. This can be attributed to its additional dependence on the kinetic energy density. It is also shown that the modified Becke–Johnson potential is at least as accurate as the hybrid functionals and more reliable for solids with large band gaps.