Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space

Abstract

The Heyd-Scuseria-Ernzerhof (HSE) density functionals are popular for their ability to improve the accuracy of standard semilocal functionals such as Perdew-Burke-Ernzerhof (PBE), particularly for semiconductor band gaps. They also have a reduced computational cost compared to hybrid functionals, which results from the restriction of Fock exchange calculations to small inter-electron separations. These functionals are defined by an overall fraction of Fock exchange and a length scale for exchange screening. We systematically examine this two-parameter space to assess the performance of hybrid screened exchange (sX) functionals and to determine a balance between improving accuracy and reducing the screening length, which can further reduce computational costs. Three parameter choices emerge as useful: "sX-PBE" is an approximation to the sX-LDA screened exchange density functionals based on the local density approximation (LDA); "HSE12" minimizes the overall error over all tests performed; and "HSE12s" is a range-minimized functional that matches the overall accuracy of the existing HSE06 parameterization but reduces the Fock exchange length scale by half. Analysis of the error trends over parameter space produces useful guidance for future improvement of density functionals.

Generalization of Dielectric-Dependent Hybrid Functionals to Finite Systems

“…(8) for the molecules studied here, i.e., α ¼ 0.72 with a range of Δα ¼ 0.19. This average mixing fraction is similar to the optimal mixing fraction reported in a previous study for the G3=99 test set [75]. In addition, Eq.…”

The screening effects of the screened exchange hybrid functional in surface systems: A case study on the CO/Pt(111) problem

“…Here, it is easier to treat the mixing percentage (HF fraction at r=0) of HF potential and the screening parameter as two independent functional parameters, as in Ref. 43. By doing so, we are able to define the "screening strength" as follows, which is directly comparable among sX, HSE06 and GGA, regardless of the mixing percentage of HF potential.…”

“…We here provide an alternative explanation based on the nature of screening: the stronger screening provided by HSE06, the weaker the Coulombic (steric) repulsion. Moussa et al 43 found that by using a single ω value in erfc(ω r) of HSE06 with 0.95 HF mixing percentage, the sX(k s ) band gaps for various semiconductors can be reproduced; but the ω value has to be large, indicating stronger screening strength than normal HSE06 is required. This further underlines the difference between sX and HSE06 in terms of the screening strength which is an important hybrid functional parameter for both bulk and surface calculations.…”

“…41,42 Moreover, varying the screening parameter was found to affect the overall accuracy of HSE06 hybrid functional. 43 Therefore, given the wide application and practical moderate computational cost of sX, studying the screening effects of sX is important in its own right and provides useful information for designing new functionals like sX+ RPA which could potentially be interesting. In this work, we thus investigate the screening effects of the screened exchange (sX) hybrid functional in CO adsorption on Pt(111) surfaces.…”

The effects of screening length in the non-local screened-exchange functional

“…On the other hand, Moussa et al [46] considered the optimisation of both parameters for some solids. The hybrid functionals have been analysed [47,48,49] and criticised [50] with respect to GW.…”