Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals

TLDR

Hybrid density functionals decompose exchange into short‑ and long‑range parts, with their admixture governed by short‑range mixing, long‑range mixing, and a range‑separation parameter. The study investigates how varying these parameters influences the accuracy of hybrid functionals for thermochemical and kinetic predictions. The authors evaluate three non‑empirical density‑functional approximations—LDA, GGA, and meta‑GGA—and compare treating long‑range exchange with Hartree‑Fock to recover correct asymptotics versus using screened hybrids that omit long‑range Hartree‑Fock exchange. They find that the mixing parameters can be flexibly chosen, short‑ and long‑range Hartree‑Fock exchange affect errors similarly, and screened hybrids preserve most benefits while substantially lowering computational cost for extended systems.

Abstract

We consider a general class of hybrid density functionals with decomposition of the exchange component into short-range and long-range parts. The admixture of Hartree-Fock (HF) exchange is controlled by three parameters: short-range mixing, long-range mixing, and range separation. We study how the variation of these parameters affects the accuracy of hybrid functionals for thermochemistry and kinetics. For the density functional component of the hybrids, we test three nonempirical approximations: local spin-density approximation, generalized gradient approximation (GGA), and meta-GGA. We find a great degree of flexibility in choosing the mixing parameters in range-separated hybrids. For the studied properties, short-range and long-range HF exchange seem to have a similar effect on the errors. One may choose to treat the long-range portion of the exchange by HF to recover the correct asymptotic behavior of the exchange potential and improve the description of density tail regions. If this asymptote is not important, as in solids, one may use screened hybrids, where long-range HF exchange is excluded. Screened hybrids retain most of the benefits of global hybrids but significantly reduce the computational cost in extended systems.