Generalized Hirshfeld Partitioning with Oriented and Promoted Proatoms

In this study, we show how to generalize Hirshfeld partitioning methods to possibly include non-spherical proatom densities. While this generalization is numerically challenging(requiring global optimization of a large number of parameters), it is conceptually appealing because it allows the proatoms to be pre-polarized, or even promoted, to a state that more closely resembles the atom in a molecule. This method is based on first characterizing the convex set of proatom densities associated with the degenerate ground states of isolated atoms and atomic ions. The preferred orientation of the proatoms' densities are then obtained by minimizing the information–theoretic distance between the promolecular and molecular densities. If contributions from excited states(and not just degenerate ground states) are included in the convex set, this method can describe promoted atoms. While the procedure is intractable in general, if one includes only atomic states that have differing electron-numbers and/or spins, the variational principle becomes a simple convex optimization with a single unique solution.