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Orbital-Free Density Functional Theory (OF-DFT) promises to describe theelectronic structure of very large quantum systems, being its computationalcost linear with the system size. However, the OF-DFT accuracy strongly dependson the approximation made for the kinetic energy (KE) functional. To date, themost accurate KE functionals are non-local functionals based on thelinear-response kernel of the homogeneous electron gas, i.e. the jellium model.Here, we use the linear-response kernel of the jellium-with-gap model, toconstruct a simple non-local KE functional (named KGAP) which depends on theband gap energy. In the limit of vanishing energy-gap (i.e. in the case ofmetals), the KGAP is equivalent to the Smargiassi-Madden (SM) functional, whichis accurate for metals. For a series of semiconductors (with differentenergy-gaps), the KGAP performs much better than SM, and results are close tothe state-of-the-art functionals with complicated density-dependent kernels.

Non-local kinetic energy functional from the Jellium-with-gap model: applications to Orbital-Free Density Functional Theory