  The account of electron correlation and its efficient separation into dynamic
and nondynamic parts plays a key role in the development of computational
methods. In this paper we suggest a physically-sound matrix formulation to
split electron correlation into dynamic and nondynamic parts using the
two-particle cumulant matrix and a measure of the deviation from idempotency of
the first-order density matrix. These matrices are applied to a two-electron
model, giving rise to a simplified electron correlation index that ($i$)
depends only on natural orbitals and their occupancies, ($ii$) can be
straightforwardly decomposed into orbital contributions and ($iii$) splits into
dynamic and nondynamic correlation parts that ($iv$) admit a local version.
These expressions are shown to account for dynamic and nondynamic correlation
in a variety of systems containing different electron correlation regimes, thus
providing the first separation of dynamic and nondynamic correlation using
solely natural orbital occupancies.
