Constrained iterative Hirshfeld charges: A variational approach

Abstract

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 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. The procedure we use is quite general, however, 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 desirable traits of atoms in molecules and surpasses existing approaches.

Atomic charges in molecules defined by molecular real space partition into atomic subspaces

“…Recently, several reviews have contributed to the studies and discussions on ACs. [2][3][4][5][6][7][8] Cho et al 2 presented the trees of the AC forest in detail, in which its notion, meaning, and classification were shown as central concepts. Particularly, principal component analysis of approximately two dozen charge distributions for a sample containing 42500 main group molecules was presented.…”