Parameter-free exchange functional

Conventional generalized-gradient approximations for exchange energy are derived to obey the fundamental conditions of the exact exchange functional. We present a simple analytic exchange functional that does not contain a semiempirical parameter or an adjusted fundamental constant. We show that this functional satisfies several significant and strict fundamental conditions, and gives accurate exchange energies for the atoms, hydrogen through argon, within a margin of error of a few percent. It can be updated for any kind of kinetic-energy density. Surprisingly, the present formalism exactly gives the gradient expansion coefficient for slowly varying density.