  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.

Chemical Physics;Strongly Correlated Electrons