Types of single particle symmetry breaking in transition metal oxides   due to electron correlation
  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. 
Lucas K. Wagner
cond-mat.str-el