Physical Origin of the One-Quarter Exact Exchange in Density Functional Theory

TL;DR

This paper explains why hybrid density functional theory often uses a 25% exact exchange by linking it to fundamental quantum mechanical principles and electron correlation effects.

Contribution

It reveals the physical origin of the 1/4 exact exchange fraction in hybrid DFT, connecting it to the quantum treatment of electron pairs and correlation interactions.

Findings

1/4 exact exchange aligns with the quantum mechanical exchange energy of an electron pair.

The 1/4 fraction mimics correlation effects between doubly-excited configurations.

The results clarify the empirical success of hybrid DFT approximations.

Abstract

Exchange interactions are a manifestation of the quantum mechanical nature of the electrons and play a key role in predicting the properties of materials from first principles. In density functional theory (DFT), a widely used approximation to the exchange energy combines fractions of density-based and Hartree-Fock (exact) exchange. This so-called hybrid DFT scheme is accurate in many materials, for reasons that are not fully understood. Here we show that a 1/4 fraction of exact exchange plus a 3/4 fraction of density-based exchange is compatible with a correct quantum mechanical treatment of the exchange energy of an electron pair in the unpolarized electron gas. We also show that the 1/4 exact-exchange fraction mimics a correlation interaction between doubly-excited electronic configurations. The relation between our results and trends observed in hybrid DFT calculations is discussed, along with other implications.