Correlation energy of the uniform gas determined by ground state conditional probability density functional theory

TL;DR

This paper develops a method using conditional-probability density functional theory to accurately compute correlation energies of the uniform electron gas, providing new insights and analytic solutions relevant at high densities and temperatures.

Contribution

It introduces a detailed approach for calculating exchange-correlation energies in the uniform gas using CP-DFT, including an analytic solution to the Thomas-Fermi model and exploration of approximations.

Findings

Accurate exchange-correlation energies for the uniform gas are obtained.

High-density limit extracted using exchange hole in CP antiparallel spin calculations.

Analytic solution to the Thomas-Fermi model demonstrates performance at high temperatures.

Abstract

Conditional-probability density functional theory (CP-DFT) is a formally exact method for finding correlation energies from Kohn-Sham DFT without evaluating an explicit energy functional. We present details on how to generate accurate exchange-correlation energies for the ground-state uniform gas. We also use the exchange hole in a CP antiparallel spin calculation to extract the high-density limit. We give a highly accurate analytic solution to the Thomas-Fermi model for this problem, showing its performance relative to Kohn-Sham and may be useful at high temperatures. We explore several approximations to the CP potential. Results are compared to accurate parameterizations for both exchange-correlation energies and holes.