Correction to kinetic energy density functional using exactly solvable model

Herein we present an accurate correction to the Thomas-Fermi (TF) approximation for the non-interacting kinetic energy. The correction is derived from an entirely solvable model and not through the application of the truncated gradient expansion. The used approach exploits the comparable nature of the difference between the TF approximation and the non-interacting kinetic energy and its analogue within a model of non-interacting electrons that resembles the actually studied problem. For the atom, the used model is a system of N non-interacting electrons moving independently in the Coulomb field of the nuclear charge. It is shown numerically that this correction enhances the accuracy of the TF approximation for atoms by an order of magnitude.