  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.
