Gradient expansion for Ts

Abstract

The convergence of the gradient expansion (GE) for the kinetic energy functional ${\mathit{T}}_{\mathit{s}}$[n] is tested on the basis of the spherical jellium model for metal clusters. By insertion of Kohn-Sham densities into the GE it is found that fourth-order contributions to the GE are more important for jellium spheres than for atoms, indicating that these corrections might also be relevant for the description of solids. By solution of the Euler-Lagrange equations resulting from the GE truncated at second or fourth order, it is demonstrated that the variational accuracy of the GE is considerably lower than that obtained by insertion of high-quality densities. Furthermore, it is shown that a GE to second order with an adjusted prefactor of the gradient term does not give variational results for jellium spheres superior to a fourth-order GE as in the case of atoms.