Density-based mixing parameter for hybrid functionals

Abstract

A very popular ab-initio scheme to calculate electronic properties in solids is the use of hybrid functionals in density functional theory (DFT) that mixes a portion of Fock exchange with DFT functionals. In spite of their success, a major problem still remains, related to the use of one single mixing parameter for all materials. Guided by physical arguments that connect the mixing parameter to the dielectric properties of the solid, and ultimately to its band gap, we propose a method to calculate this parameter from the electronic density alone. This method is able to cut significantly the error of traditional hybrid functionals for large and small gap materials, while retaining a good description of structural properties. Moreover, its implementation is simple and leads to a negligible increase of the computational time.Density functional theory (DFT) is one of the major achievements of theoretical physics in the last decades. It is now routinely used to interpret experiments or to predict properties of novel materials. The success of DFT relies on the Kohn-Sham (KS) scheme and the existence of good approximations for the unknown exchange and correlation (xc) functional. In the standard KS formulation the xc potential is local and static. Since the original suggestion of the local-density approximation (LDA) [1], a swarm of functionals has been proposed in the literature [2]. In the ab-initio study of solids, the Perdew, Burke and Ernzerhof [5] (PBE) parametrization of the xc functional has been for many years the default choice for many applications. A good functional must yield ground states properties (like structural parameters), while it is expected that the KS gap and true quasiparticle gap differ by the derivative discontinuity [3]. Indeed, for semiconductors and insulators PBE yields good structural properties and KS band-gap energies that are at best half of their experimental value. To obtain both the ground state and quasiparticle energies correctly within one and the same formalism, one can resort to, e.g., a many-body GW calculation [6,7]. However, GW is by all measures an expensive technique, with a very unfavorable scaling with the number of atoms in the unit cell. It is therefore unpractical for the study of band structures of large systems and clearly prohibitive regarding total energy calculations even for simple realistic systems.Much of the computational effort in GW comes from the dynamically screened Coulomb interaction W . It has therefore been crucial to explore to which extent dynamical effects are mandatory, or whether non-locality is the dominating characteristic. The move from local KS potential to non-local functionals has first been pushed forward in Quantum Chemistry, where today the so-called hybrid functionals are very popular. These functionals mix a fraction α of Fock exchange with a combination of LDA and generalized gradient (GGA) functionals. The application of hybrid functionals to the solid state had a much slower start [8,9]. The situation changed recently, helped by th...

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