Bonded atoms in sodium chloride - the information-theoretic approach

The information-theoretic approach to the classical problem of partitioning the molecular electron density, rho, into densities {rho (alpha)} of the bonded atoms in molecules (AIM) is briefly summarized. The minimization of the missing information (entropy deficiency) between the isolated atom densities, {rho (0)(alpha)}, which define the promolecule density, rho (0) of the molecular density difference diagrams, Delta rho = rho - rho (0), and the AIM densities {rho (alpha)} in an exhaustive partitioning of rho gives rise to the stockholder scheme of Hirshfeld. A related nonexhaustive approach is also outlined and the polarized (closed) atom densities in a molecule are obtained by simultaneously minimizing their information distance with respect to both the isolated and the Hirshfeld atomic densities. For neutral molecules these schemes are unique when the ground-state densities of isolated atoms are selected as a reference. In an attempt to validate this natural choice two sets of the stockholder atoms in NaCl, resulting from the ground-state ionic (Na+ + Cl-) and atomic(Na + Cl) promolecule references, respectively, are compared and found to be almost identical. Small differences observed in the asymptotic, low-density regions are interpreted in terms of the reverse direction of the molecular charge transfer with respect to these initial promolecule states. A concept of the molecularly promoted reference corresponding to the promolecule density involving the statistical mixture of ionic and atomic densities, with the ensemble probabilities minimizing the deviations between the ensemble and molecular densities, is introduced.