The w α,ij are the eigenvalues of the two-orbital RDM ρ ij and can be obtained by tracing out all other orbitals contribution from the many-particle density matrix except orbitals i and j. As the pair of spatial orbitals ti, ju can be occupied by zero to four electrons, the ρ i,j has a dimension of 16, H i,j " t|´, ´y, |´, Òy, |´, Óy, ¨¨¨, | OE, OEyu. The non-zero elements of ρ ij can again be calculated from generalized correlation functions leading to a block sparse structure. The underlying algebra can also be expressed in terms of standard particle creation and annihilation operators. For more details we guide readers to Refs. Third, the mutual information between two orbitals (iii)