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The molecular density-partition problem is reexamined and the information-theoretic (IT) justification of the stockholder division rule is summarized. The ensemble representations of the promolecular and molecular mixed states of constituent atoms are identified and the electron probabilities in the isoelectronic stockholder atoms-in-molecules (AIM) are used to define the molecular-orbital ensembles for the bonded Hirshfeld atoms. In the pure quantum state of the whole molecular system its interacting (entangled) fragments are described by the subsystem density operators, with the subsystem physical properties being generated by the partial traces involving the fragment density matrices.

Interacting Subsystems and Their Molecular Ensembles