A local density functional for the short-range part of the electron-electron interaction

TL;DR

This paper develops a new local density functional for the short-range electron-electron interaction by fitting diffusion Monte Carlo data of a uniform electron gas with a modified interaction, improving the treatment of short-range correlations in density functional theory.

Contribution

It introduces an accurate analytic representation of the short-range correlation energy based on Monte Carlo data, incorporating exact limits for improved density functional calculations.

Findings

The correlation energy fits Monte Carlo data well.

The functional includes exact limits for the short-range interaction.

Provides a reliable short-range local-density functional.

Abstract

Motivated by recent suggestions --to split the electron-electron interaction into a short-range part, to be treated within the density functional theory, and a long-range part, to be handled by other techniques-- we compute, with a diffusion Monte Carlo method, the ground-state energy of a uniform electron gas with a modified, short-range-only electron-electron interaction $\erfc(\mu r)/r$, for different values of the cutoff parameter $\mu$ and of the electron density. After deriving some exact limits, we propose an analytic representation of the correlation energy which accurately fits our Monte Carlo data and also includes, by construction, these exact limits, thus providing a reliable ``short-range local-density functional''.