Exchange and exchange-correlation functionals based on the gradient correction of the electron gas

We demonstrate that the functional form of the Pad\'e approximant of the second-order density gradient correction of Rasolt and Geldart [Phys. Rev. Lett. 35, 1234 (1975)] for the inhomogeneous electron gas yields excellent results when applied to atoms. The gradient correction employed by us uses the 10/7 factor as suggested by Kleinman and Lee [Phys. Rev. B 37, 4634 (1988)] with the constants of Rasolt and Geldart replaced by an empirically derived set, based upon numerical fits of the exchange and exchange-correlation energies of the atoms He through Ar. The resulting fitted nonlocal gradient corrections were then used in the minimization of the Kohn-Sham functional to solve for the exchange-only and exchange-correlation total energies. The resulting standard deviations in the calculated total energies were 0.0043 for exchange only and 0.0014 for exchange correlation.