High-density correlation energy expansion of the one-dimensional uniform electron gas

TL;DR

This paper derives the high-density correlation energy for a one-dimensional uniform electron gas using perturbation theory and combines it with low-density results to create a local-density approximation functional that closely matches benchmark calculations.

Contribution

It provides a new high-density correlation energy expansion and a corresponding local-density approximation functional for the 1D electron gas.

Findings

Derived the high-density correlation energy expansion using perturbation theory.

Proposed a local-density approximation functional with minimal deviation from benchmark data.

Achieved a maximum deviation of 0.1 millihartree compared to DMC calculations.

Abstract

We show that the expression of the high-density (i.e small-$r_s$) correlation energy per electron for the one-dimensional uniform electron gas can be obtained by conventional perturbation theory and is of the form $\Ec(r_s) = -\pi^2/360 + 0.00845 r_s + ...$, where $r_s$ is the average radius of an electron. Combining these new results with the low-density correlation energy expansion, we propose a local-density approximation correlation functional, which deviates by a maximum of 0.1 millihartree compared to the benchmark DMC calculations.