用Copula方法得到强关联多电子体系的交换-相关穴

Copula Approach to Exchange-Correlation Hole in Many-Electron Systems with Strong Correlations

电子关联是多电子体系中的一个基本课题.为了描述这种关联性,人们可以引入交换-相关穴的概念、本文首先简要地回顾了交换-相关穴的定义、它与电子密度和电子对密度的关系,以及它们与概率统计学中的Copula函数之间的紧密联系.然后,提出了一个基于Copula函数的方法,从电子密度中得到交换相关穴.可以预期,所提出的方案将有助于强关联电子结构计算的未来发展.

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 work,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 will become a promising ingredient towards the future development of strongly correlated electronic structure calculations.