Entropic and difference bond multiplicities from the two-electron probabilities in orbital resolution

The bond-order indices derived from the displacements ΔΓ=Γ−Γ0 of the pair-diagonal part of the two-electron density matrix Γ in the orthogonalized atomic orbital (OAO) representation, relative to the atomic promolecule reference Γ0, are reexamined. The corresponding sum rules are discussed and the new index J=tr ΔΓ is introduced. The entropy deficiency interpretation of the bond entropy is given and the information measures of bond multiplicity are approximately related to ΔΓ. Illustrative results for model systems, including 2- and 3-OAO models and π-electron systems in the Hückel approximation, demonstrate that these two-electron indices compare favorably with chemical intuition.