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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. [ABSTRACT FROM AUTHOR]

Atoms in molecules methods that rely on reference promolecular densities typically require that one define, or otherwise determine, the densities of unbound atomic anions. Whereas the isolated atomic polyanions are always physically and computationally unbound, monoanions can be either physically bound but computationally unbound (like the oxygen anion at the Hartree-Fock level of theory), or physically unbound but computationally bound (like the nitrogen anion using many DFT methods with a basis set including diffuse functions). Depending on the level of theory and basis set used, the densities of negatively charged atomic ions can decay very slowly and even be nonmonotonically decreasing. These delocalized anionic densities induce ill-behaved atomic properties for compounds containing highly reduced atoms. To treat the problem of unphysical proatom densities in iterative Hirshfeld methods, we compute the smallest (typically fractional) nuclear charge to bind all electrons, called the effective nuclear charge $$ {Z}_{\mathrm{A}}^{\mathrm{eff}} $$ of an atom A. When $$ {Z}_{\mathrm{A}}^{\mathrm{eff}}>{Z}_{\mathrm{A}} $$ at a given level of theory, the scaled density corresponding to the effective nuclear charge is used as the negatively charged proatom density. This novel approach dramatically improves the computational robustness of the iterative Hirshfeld partitioning scheme. [ABSTRACT FROM AUTHOR]

We establish the physical origins of chemical transferability from the perspective of the nearsightedness of electronic matter. To do this, we explicitly evaluate the response of electron density to a change in the system, at constant chemical potential, by computing the softness kernel, s(r, r'). The softness kernel is nearsighted, indicating that under constant-chemical-potential conditions like dilute solutions changing the composition of the molecule at r has only local effects and does not have any significant impact on the reactivity at positions r' far away from point r. This locality principle elucidates the transferability of functional groups in chemistry. [ABSTRACT FROM AUTHOR]