On-top density in the nonlinear metallic screening and its implication on the exchange-correlation energy functional

In comparison with the accurate data on the on-top electron density n(0) in the proton-embedded electron gas with the density parameter r(s) in the range 1-12 obtained by diffusion Monte Carlo (DMC) simulations, we have successfully constructed an alternative form of the exchange-correlation energy functional in the density functional theory by imposing the constraint due to the cusp theorem on the well-known Perdew-Burke-Ernzerhof (PBE) functional. Although PBE does not, our functional, referred to as the cusp-corrected PBE (ccPBE), reproduces the DMC data on n(0) in the entire range of r(s).