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We define the densities of atoms in molecules so that their Bregman divergence from reference proatom densities is minimized. This generalizes the information-theoretic approach to atoms in molecules and under reasonable assumptions, results in a formulation that resembles the Hirshfeld partitioning. In general, Bregman partitionings are intrinsically nonlocal, and this means that this formulation, while mathematically elegant, is computationally unwieldy. [ABSTRACT FROM AUTHOR]

We show that the statistical divergence measures associated with non-extensive thermodynamic entropy functions-specifically the Tsallis, Réyni, Sharma-Mittal, supraextensive, and H-divergences-are associated with the Hirshfeld atoms-in-molecules partitioning. This extends the treatment of Nalewajski and Parr (J Phys Chem A 109:3957-3959, 2005), (for the extensive Shannon entropy) to non-extensive entropy measures. It also extends the work of Heidar-Zadeh and Ayers (J Chem Phys 142(4):044107, 2015), (for divergence measures that are local density functionals) to non-local functionals. These results dramatically extend the mathematical framework that one can use for similarity-based atoms-in-molecules partitioning. [ABSTRACT FROM AUTHOR]