Convergence properties as a function of spatial dimensionality of gradient expansions for the ground-state energy of an inhomogeneous electron gas

Abstract

The extended Thomas-Fermi approximation for the ground-state energy of a many-fermion system is generalized to arbitrary spatial dimension. The authors' objective is a better understanding of convergence properties of such gradient expansions with a view to applications to systems of reduced dimensionality or esoteric geometry. The convergence is tested and found to be adequate by comparing to an exact result for the surface kinetic energy of a semi-infinite system. Both local and nonlocal contributions to the exchange energy are also given for arbitrary dimension. The extension to the thermodynamic free energy at finite temperature for arbitrary dimension is also discussed