Non-empirical derivation of the parameter in the B88 exchange functional

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 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.