Deriving the Hirshfeld partitioning using distance metrics

Abstract

The atoms in molecules associated with the Hirshfeld partitioning minimize the generalized Hellinger-Bhattacharya distance to the reference pro-atom densities. Moreover, the reference pro-atoms can be chosen by minimizing the distance between the pro-molecule density and the true molecular density. This provides an alternative to both the heuristic " stockholder" and the mathematical information-theoretic interpretations of the Hirshfeld partitioning. These results extend to any member of the family of f-divergences.