A method to get an analytical expression for the non-interacting kinetic energy density functional

On the basis of the equation obtained by differentiating the virial theorem with respect to the density and the homogeneity property of the non-interacting kinetic energy functional T[rho], a generalized Weizsacker kinetic energy functional is shown to be the only possible form for T[rho], provided T[rho] = integral t(rho((r) over right arrow), del rho((r) over right arrow)) d (r) over right arrow, which has the consequence that the exact functional T[rho] cannot have a form of this kind. The presented method, with the proposed mathematical formalism to treat multiple spatial derivatives of rho in functional differentiations simply, can be used to get more general analytical expressions for T[rho] making less restrictive assumptions about its form (allowing dependence on higher-order derivatives of rho as well) and involving further relations. (C) 2000 Elsevier Science B.V. All rights reserved.