Hirshfeld partitioning from non-extensive entropies

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.