Copula approach to exchange-correlation hole in many-electron systems with strong correlations

TL;DR

This paper introduces a novel copula-based method to estimate the exchange-correlation hole in many-electron systems, linking probability theory with electronic structure to improve strongly correlated calculations.

Contribution

It proposes a new copula approach to characterize exchange-correlation holes, bridging probability theory and electronic density analysis for better strongly correlated systems.

Findings

Establishes a theoretical connection between copula functions and exchange-correlation holes.

Provides a framework for estimating exchange-correlation effects from electron density.

Suggests potential for improved electronic structure calculations in strongly correlated systems.

Abstract

Electronic correlation is a fundamental topic in many-electron systems. To characterize this correlation, one may introduce the concept of exchange-correlation hole. In this paper, we first briefly revisit its definition and relation to electron and geminal densities, followed by their intimate relations to copula functions in probability theory and statistics. We then propose a copula-based approach to estimate the exchange-correlation hole from the electron density. It is anticipated that the proposed scheme would become a promising ingredient towards the future development of strongly correlated electronic structure calculations.