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The atoms in molecules associated with the Hirshfeld partitioning minimize the generalized Hellinger-Bhattacharya distance to the reference pro-atom densities. Moreover, the reference proatoms 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. [ABSTRACT FROM AUTHOR]

Condensed-to-atom Fukui functions which reflect the atomic reactivity like the tendency susceptible to either nucleophilic or electrophilic attack demonstrate the bonding trend of an atom in a molecule. Accordingly, Fukui functions based concepts, that is, bonding reactivity descriptors which reveal the bonding properties of molecules in the reaction were put forward and then applied to pericyclic and cluster reactions to confirm their effectiveness and reliability. In terms of the results from the bonding descriptors, a covalent bond can readily be predicted between two atoms with large Fukui functions (i.e., one governs nucleophilic attack while the other one governs electrophilic attack, or both of them govern radical attacks) for pericyclic reactions. For SinOm clusters' reactions, the clusters with a low O atom ratio readily form a bond between two Si atoms with big values of their Fukui functions in which they respectively govern nucleophilic and electrophilic attacks or both govern radical attacks. Also, our results from bonding descriptors show that Si—Si bonds can be formed via the radical mechanism between two Si atoms, and formations of Si—O and O—O bonds are possible when the O content is high. These results conform with experimental findings and can help experimentalists design appropriate clusters to synthesize Si nanowires with high yields. The approach established in this work could be generalized and applied to study reactivity properties for other systems. [ABSTRACT FROM AUTHOR]

We develop a variational procedure for the iterative Hirshfeld (HI) partitioning scheme. The main practical advantage of having a variational framework is that it provides a formal and straightforward approach for imposing constraints (e.g., fixed charges on certain atoms or molecular fragments) when computing HI atoms and their properties. Unlike many other variants of the Hirshfeld partitioning scheme, HI charges do not arise naturally from the information-theoretic framework, but only as a reverse-engineered construction of the objective function. However, the procedure we use is quite general and could be applied to other problems as well. We also prove that there is always at least one solution to the HI equations, but we could not prove that its self-consistent equations would always converge for any given initial pro-atom charges. Our numerical assessment of the constrained iterative Hirshfeld method shows that it satisfies many desirable traits of atoms in molecules and has the potential to surpass existing approaches for adding constraints when computing atomic properties. [ABSTRACT FROM AUTHOR]