On-Top Density in the Nonlinear Metallic Screening and its Implication on the Exchange-Correlation Energy Functional

TL;DR

This paper develops a cusp-corrected PBE functional that accurately reproduces on-top electron density data from DMC simulations in a proton-embedded electron gas, improving exchange-correlation energy modeling.

Contribution

It introduces the ccPBE functional, incorporating cusp theorem constraints to enhance the PBE functional's accuracy for on-top electron densities.

Findings

ccPBE matches DMC data across all r_s values

Improved modeling of exchange-correlation energy

Demonstrates the importance of cusp constraints in functional design

Abstract

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.