Abstract
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.
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Notes
This is more than is required, mathematically. The following analysis will hold for any twice-integrable function.
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Acknowledgements
The authors thank NSERC and Compute Canada for funding. FHZ acknowledge support from Vanier-CGS fellowship and Ghent University Scholarship for a Joint Doctorate.
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Heidar-Zadeh, F., Ayers, P.W. Fuzzy atoms in molecules from Bregman divergences. Theor Chem Acc 136, 92 (2017). https://doi.org/10.1007/s00214-017-2114-y
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DOI: https://doi.org/10.1007/s00214-017-2114-y