We investigate a highly-nonlocal generalization of the Lindhard function, given by the jellium-with-gap model. We find a band-gap-dependent gradient expansion of the kinetic energy, which performs noticeably well for large atoms. Using the static linear response theory and the simplest semilocal model for the local band gap, we derive a non-empirical generalized gradient approximation (GGA) of the kinetic energy. This GGA kinetic energy functional is remarkably accurate for the description of weakly interacting molecular systems within the subsystem formulation of Density Functional Theory.
@article{arxiv.1705.06034,
title = {Jellium-with-gap model applied to semilocal kinetic functionals},
author = {L. A. Constantin and E. Fabiano and S. Śmiga and F. Della Sala},
journal= {arXiv preprint arXiv:1705.06034},
year = {2017}
}