Non-local approximations to the kinetic energy functional

The construction of approximate kinetic energy functionals of the electron number and spin densities, for use in density functional formalism, is investigated. Based on a partial resummation of its gradient expansion, a representation of the kinetic energy is developed in terms of a non-local and non-linear kernel. Tests of this representation are made on the resulting ground-state energies of a variety of atoms using parametrised densities in variational calculations. When compared with the corresponding results of using low-order gradient expansions and Hartree-Fock calculations, the principal conclusion is that the prescriptions used here are too simple to reasonably account for the highly non-linear structure of such functionals. The approach is shown, however, to exhibit some useful features, such as an exact treatment of the kinetic energy at the atomic nucleus. More detailed results of testing the low-order gradient expansions of the kinetic and exchange energies in atoms are also presented, and their convergence properties discussed.