ORBITAL-FREE DENSITY FUNCTIONAL THEORY OF ATOMS, MOLECULES, AND SOLIDS

Abstract

Density functional (DF) theory has proved to be a powerful way to determine the ground state energy of atoms, molecules, and extended systems. An important part of the theory requires one to determine the kinetic energy of the ground state of a system of N noninteracting electrons in a general external field. Kohn and Sham showed how this can be numerically calculated very accurately using a set of N orbitals. However this prevents the simple linear scaling in N that would arise if the kinetic energy could be directly expressed as a functional of the electron density, as is done with other components of the total energy like the exchange-correlation energy. Orbital free methods attempt to calculate the noninteracting kinetic energy directly by approximating the universal but unknown kinetic energy density functional. However simple local approximations are inaccurate and it has proved very difficult to devise generally accurate nonlocal approximations. We focus instead on the kinetic potential, the functional derivative of the kinetic energy DF, which appears in the Euler equation for the electron density. We argue the kinetic potential is more amenable to simple physically motivated approximations in many relevant cases. We propose a family of nonlocal orbital free kinetic potentials that reduce to the known exact forms for both slowly varying and rapidly varying perturbations and also reproduce exact results for the linear response of the density of the homogeneous system to small perturbations. A simple and systematic approach for generating accurate and weak ab initio local pseudopotentials describing a smooth slowly varying valence component of the electron density is proposed for use in orbital free DF calculations of molecules and solids. The use of these local pseudopotentials further minimizes the possible errors arising from use of the approximate kinetic potentials. A linear scaling method for treating large extended systems is proposed for fast computations. Our theory yields results for the total energies and ionization energies of atoms, and for the shell structure in the atomic radial density profiles that are in very good agreement with calculations using the full Kohn-Sham theory. We describe the first use of nonlocal orbital free methods to determine the ground-state bond lengths and binding energies of diatomic molecules. These results and the ground-state lattice parameters, and total energy of bulk aluminum and bulk silicon are in generally good agreement with detailed calculations using the full Kohn-Sham theory.