  Very accurate wave functions are calculated for small transition metal oxide
molecules. These wave functions are decomposed using reduced density matrices
to study the underlying correlation of electrons. The correlation is primarily
of left-right type between the transition metals and the oxygen atoms, which is
mediated by excitations from the nominal single Slater ground state into
antibonding and d-type orbitals. In a localized representation, this
correlation manifests itself in a 2-electron hopping term that is off-diagonal.
This term is of similar magnitude to the commonly considered Hubbard-type
on-site interaction.
