Non-empirical 'derivation' of B88 exchange functional

TL;DR

This paper provides a non-empirical derivation of the B88 exchange functional by analyzing local approximations and their behavior in the large number limit, offering insights into the functional's parameter without empirical fitting.

Contribution

It introduces a theoretical approach to derive the B88 exchange functional's parameter without relying on empirical data, based on local approximation analysis.

Findings

Local approximations become relatively exact in the large number limit

The usual gradient expansion does not become exact in this limit

Generalized gradient approximations can capture leading corrections

Abstract

The B88 exchange energy density functional (created by Becke in 1988) is a crucial part of the most popular density functional in use today, B3LYP. B88 contains one empirical parameter which was fitted to Hartree-Fock exchange energies for the noble gas atoms. We show how local approximations to exchange become relatively exact under a very specific approach to the limit of large numbers, but that the usual gradient expansion does not. The leading corrections can be captured by generalized gradient approximations, producing a non-empirical derivation of the parameter in B88.