Information-Theoretic Approaches to Atoms-in-Molecules: Hirshfeld Family of Partitioning Schemes

Abstract

Many population analysis methods are based on the precept that molecules should be built from fragments (typically atoms) that maximally resemble the isolated fragment. The resulting molecular building blocks are intuitive (because they maximally resemble well-understood systems) and transferable (because if two molecular fragments both resemble an isolated fragment, they necessarily resemble each other). Information theory is one way to measure the deviation between molecular fragments and their isolated counterparts, and it is a way that lends itself to interpretation. For example, one can analyze the relative importance of electron transfer and polarization of the fragments. We present key features, advantages, and disadvantages of the information-theoretic approach. We also codify existing information-theoretic partitioning methods in a way that clarifies the enormous freedom one has within the information-theoretic ansatz.

The Atomic Partial Charges Arboretum: Trying to See the Forest for the Trees

“…Stockholder‐type charges have been rationalized based on information theory and were the subject of a recent review . (We considered Salvador's topological fuzzy Voronoi charges for a representative sample consisting of the W4‐17 benchmark, and found said charges to be very similar in practice to Bader QTAIM charges, R 2 =0.97.…”

“… fitting to an observable quantity such as the molecular electrostatic potential on the van der Waals surface, such as done in CHELP (charges from electrostatic potentials), CHELPG (ditto using a grid), Merz‐Kollman, and HLY (Hu−Lu‐Yang) charges; partitioning in terms of atomic orbitals, such as done in Mulliken charges and their variants, Natural Population Analysis (NPA), and Intrinsic Bond Orbitals, (IBO, also known as Quasi‐Atomic Natural Bond Orbitals); atoms‐in‐molecules partitioning of the electron density, either into disjoint QTAIM or Voronoi cells, or into overlapping “stockholder domains” (such as the original Hirshfeld population analysis and its manifold offspring, e. g.,). …”

“…atoms‐in‐molecules partitioning of the electron density, either into disjoint QTAIM or Voronoi cells, or into overlapping “stockholder domains” (such as the original Hirshfeld population analysis and its manifold offspring, e. g.,).…”

“…A number of review articles have been devoted to partial charges, such as Wiberg and Rablen, Bachrach, Cramer and Truhlar, and most recently Ayers and coworkers (which focuses principally on Hirshfeld‐type approaches from an information theoretical point of view).…”

Information equilibria, subsystem entanglement, and dynamics of the overall entropic descriptors of molecular electronic structure

“…The IT approach has proven its utility in a variety of molecular scenarios, e.g., [39–42]. In this analysis we examined mutual relations between densities of the classical and nonclassical components of the resultant information/entropy measures, combining the probability contributions of Fisher or Shannon and their associated phase/current supplements.…”