  A range-separation of the Coulomb hole into two components, one of them being
predominant at long interelectronic separations (hcI ) and the other at short
distances (hcII ), is exhaustively analyzed throughout various examples that
put forward the most relevant features of this approach and how they can be
used to develop efficient ways to capture electron correlation. We show that
hcI , which only depends on the first-order reduced density matrix, can be used
to identify molecules with a predominant nondynamic correlation regime and
differentiate between two types of nondynamic correlation, types A and B.
Through the asymptotic properties of the hole components, we explain how hcI
can retrieve the long-range part of electron correlation. We perform an
exhaustive analysis of the hydrogen molecule in a minimal basis set, dissecting
the hole contributions into spin components. We also analyze the simplest
molecule presenting a dispersion interaction and how hcII helps identify it.
The study of several atoms in different spin states reveals that the Coulomb
hole components distinguish correlation regimes that are not apparent from the
entire hole. The results of this work hold the promise to aid in developing new
electronic structure methods that efficiently capture electron correlation.
