Self-consistent hybrid functional for condensed systems

Abstract

A self-consistent scheme for determining the optimal fraction of exact exchange for full-range hybrid functionals is presented and applied to the calculation of band gaps and dielectric constants of solids. The exchange-correlation functional is defined in a similar manner to the PBE0 functional, but the mixing parameter is set equal to the inverse macroscopic dielectric function and it is determined self-consistently by computing the optimal dielectric screening. We found excellent agreement with experiments for the properties of a broad class of systems, with band gaps ranging between 0.7 and 21.7 eV and dielectric constants within 1.23 and 15.9. We propose that the eigenvalues and eigenfunctions obtained with the present self-consistent hybrid scheme may be excellent inputs for G$_0$W$_0$ calculations.Comment: Reprint of PRB articl

First Principles Calculations on Oxide-Based Heterogeneous Catalysts and Photocatalysts: Problems and Advances

“…The dielectric constant is computed by including the full response of the electronic density to the perturbing external electric field. In this way dielectric constants, electronic gaps, and lattice constants of a broad class of solids have been determined [61]. The results are in considerably better agreement with experiments than those obtained with the semilocal PBE and the hybrid PBE0 functionals, Table 1.…”

“…A different approach to the calculation of the band gaps with hybrid functionals has been recently followed by Galli and coworkers [61]. As we have seen before, one can use a as an adjustable parameter to reproduce the experimental band gap of solids or the band gap obtained from G 0 W 0 calculations.…”

“…). Galli and coworkers [61] have proposed a full-range, nonempirical hybrid functional where the mixing parameter a is determined self-consistently from the evaluation of the inverse static electronic dielectric constant (1/e ? ).…”

Ionization Energies, Electron Affinities, and Polarization Energies of Organic Molecular Crystals: Quantitative Estimations from a Polarizable Continuum Model (PCM)-Tuned Range-Separated Density Functional Approach

“…Skone et al presented a selfconsistent scheme for determining the optimal fraction of exact exchange (α) in the global hybrid functional PBEh via the inverse macroscopic dielectric function (1/ε). 65 Although this PBEh functional with an adjusted α parameter can reproduce reasonable solid-state gaps, gas-phase gaps and the solid-state polarization energy are not as well described. 17 Refaely-Abramson et al…”

Methods of photoelectrode characterization with high spatial and temporal resolution

“…245 The appropriate amount of exact exchange or +U to include is generally system dependent, and can be determined empirically or else directly from ab initio calculations. [246][247][248][249] In the case of hybrid functionals, the additional computational expense can also significantly limit AIMD simulation times, particularly when applied to solid-liquid interfaces. Second, DFT is inherently a ground-state method, and thus cannot in general provide an accurate description of excited-state properties.…”