PRECISION IN THE NUMERICAL-INTEGRATION OF THE THOMAS-FERMI-DIRAC KINETIC-ENERGY AND EXCHANGE-ENERGY FUNCTIONALS USING A MODELED ELECTRON-DENSITY

In the Hohenberg and Kohn formulation of density-functional theory of an electronic system, such as the nondegenerate ground state of an atom, the basic variable is the electron density. This quantity. however, is not known. For this reason, in an actual calculation of the ground-state energy, one may resort to a modeled electron density. This poses the question: what is the accuracy beyond which one cannot penetrate in the numerical evaluation of certain integrals when using the modeled electron density and an integration technique? The present work attempts to provide an answer to this question by considering the Ne atom as an example, by using the Thomas-Fermi-Dirac energy-density functional, a modeled electron density, and Simpson's (three-point) rule for the numerical integration.