Modified Chachiyo Formula for Correlation Energy of Uniform Electron Gas

Abstract

In 2016, Chachiyo proposed a simple expression with only three parameters for the correlation energy of the uniform electron gas in the range of . This so-called Chachiyo formula gives reasonable agreement with the results from the quantum Monte-Carlo simulations by Ceperley and Alder (CA). In this paper, I propose the TCUP formula, written as;

This is a modification of the Chachiyo formula, which can reproduce the two well-known analytic limits, i.e. the high-density and the low-density limits. In addition, this modified formula gives an excellent fitting to the Perdew-Zunger data which combines the results of CA and the analytic high-density limit. Thus, it covers the more extending range of .