Consequences for exchange energy density functional of exponentially decaying nature of atomic electron densities

A simple model is studied for the atomic exchange energy density functional, which is based on the exponential decaying feature of the density and the Fermi-Amaldi model for exchange correlation. The model is exact for hydrogen-like atoms. It is shown to provide a reasonable approximation for many-electron atoms. The local exchange energy density and potential are expressed as universal functions of r, rho(r), and \del rho(r)\, and go beyond the generalized gradient approximation (GGA) framework in which E-x[rho] = integral e(x)(rho, del rho) dr. The conclusion reached previously by Gill and Pople (Phys. Rev. A 1993, 47, 2383), that the general atomic exchange functional cannot be of the GGA form, is supplemented by the more optimistic conclusion that it could well have the form E-x[rho] = integral e(x)(r, rho, del rho) dr. (C) 1999 John Wiley & Sons, Inc.