Hybrid functionals for solids with an optimized Hartree–Fock mixing parameter

Abstract

(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 and phase stability of oxide semiconductors: Performance of dielectric-dependent hybrid functional DFT, benchmarked againstGWband structure calculations and experiments

“…The authors of Refs. [20,25] and [27] also computed optimized lattice parameters for a set of solids, showing that an accuracy comparable to that of standard hybrid functionals is achieved. What has not been assessed so far is if the method is also capable to provide good results in terms of the energetics and thermochemistry of semiconducting materials.…”

“…The corresponding hybrid xc functional is referred to as "dielectric-dependent" in the following. Since the paper of Alkauskas et al, several works have appeared in the literature adopting this paradigmatic scheme and evaluating ∞ by means of different computational approaches [20][21][22][23][24][25][26][27]. Marques et al [21] computed ∞ within the GGA Perdew-Burke-Ernzerhof [16] approximation; alternatively, they suggested a relationship between α and a densitydependent estimator of the band gap, which they used for defining a material-dependent hybrid functional.…”

Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation

“…The advantage of the second class of approaches via hybrid functionals is that they incorporate a system-dependent fraction of exact exchange, which is determined based on rigorous DFT arguments instead of globally fixing it or by fitting it to experiment [8]. That the fraction of exact exchange should be system dependent was argued via its relationship to the dielectric constant and has also been exploited for the construction of hybrid functionals [81][82][83][84].…”

Generalization of Dielectric-Dependent Hybrid Functionals to Finite Systems

“…Another interesting example is that of Koopman's-complaint functionals [42]. Motivated by the COHSEX approximation used within MBPT [43], an alternative class of hybrid functionals for solids, referred to as dielectric-dependent hybrids, were introduced by equating the optimal mixing fraction of exact exchange with the inverse of the bulk dielectric constant [44][45][46][47][48][49][50][51]. The generalization of dielectric hybrid functionals to finite systems is not straightforward, as there is no unique definition of an average dielectric constant for molecules or nanoparticles.…”