Kinetic energy functionals from the Kohn–Sham potential

A method which uses Kohn–Sham solutions to assess and improve the accuracy of kinetic energy functionals in density functional theory (DFT) calculations is introduced. To within a constant μ, the “kinetic potential ” corresponding to the functional derivative of the non-interacting kinetic energy may be obtained directly from the orbitals and eigenvalues of a Kohn–Sham DFT calculation. This Kohn–Sham kinetic potential has been examined for several small molecules. We demonstrate, with simple functional forms, a semi-empirical parametrization to minimize the difference between the functional derivative (of a trial functional) and the Kohn–Sham kinetic potential. The form of our functionals includes ρ5/3 times an enhancement factor comprised of simple, dimensionless variables of the density, the gradient of the density, and the laplacian of the density. The difference between the uniform electron gas and the Kohn–Sham kinetic potential is vastly reduced in our functionals by the fitting of this enhancement factor. However, tests of the resulting functionals with variationally optimized densities yield discouraging results. Nonetheless, the Kohn–Sham kinetic potential remains a ready tool for the parametrization of future kinetic energy functionals, as well as a helpful test of the accuracy of their functional derivatives.