Farnaz Heidar-Zadeh

Benchmark values of chemical potential and chemical hardness for atoms and atomic ions (including unstable anions) from the energies of isoelectronic series

We present benchmark values for the electronic chemical potential and chemical hardness from reference data for ionization potentials and electron affinities. In cases where the energies needed to compute these quantities are not available, we estimate the ionization potential of the metastable (di)anions by extrapolation along the isoelectronic series, taking care to ensure that the extrapolated data satisfy reasonable intuitive rules to the maximum possible extent. We also propose suitable values for the chemical potential and chemical hardness of zero-electron species. Because the values we report are faithful to the trends in accurate data on atomic energies, we believe that our proposed values for the chemical potential and chemical hardness are ideally suited to conceptual studies of chemical trends across the periodic table. The critical nuclear charge (Z critical) of the isoelectronic series with 2 < N < 96 has also been reported for the first time.

How pervasive is the Hirshfeld partitioning

One can partition the molecular density into its atomic contributions by minimizing the divergence of the atom-in-molecule densities from their corresponding reference pro-atomic densities, subject to the constraint that the sum of the atom-in-molecule densities is the total molecular density. We expose conditions on the divergence measure that are necessary, and sufficient, to recover the popular Hirshfeld partitioning. Specifically, among all local measures of the divergence between two probability distribution functions, the Hirshfeld partitioning is obtained only for f-divergences.

Chemical transferability of functional groups follows from the nearsightedness of electronic matter

Significance The empirically observed transferability of functional groups is shown to follow from Kohn’s nearsightedness principle for electron density. To show this, we analytically calculated and analyzed the softness kernel for molecules. The relevance of this work touches on physics (the nearsightedness principle), molecular chemistry and materials science (chemical transferability and similarity), and computer science (machine-learning approaches for pharmaceutical and materials design). 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.

Hirshfeld partitioning from non-extensive entropies

We show that the statistical divergence measures associated with non-extensive thermodynamic entropy functions—specifically the Tsallis, Réyni, Sharma–Mittal, supraextensive, and H-divergences—are associated with the Hirshfeld atoms-in-molecules partitioning. This extends the treatment of Nalewajski and Parr (J Phys Chem A 109:3957–3959, 2005), (for the extensive Shannon entropy) to non-extensive entropy measures. It also extends the work of Heidar-Zadeh and Ayers (J Chem Phys 142(4):044107, 2015), (for divergence measures that are local density functionals) to non-local functionals. These results dramatically extend the mathematical framework that one can use for similarity-based atoms-in-molecules partitioning.

Fuzzy atoms in molecules from Bregman divergences

We define the densities of atoms in molecules so that their Bregman divergence from reference proatom densities is minimized. This generalizes the information-theoretic approach to atoms in molecules and under reasonable assumptions, results in a formulation that resembles the Hirshfeld partitioning. In general, Bregman partitionings are intrinsically nonlocal, and this means that this formulation, while mathematically elegant, is computationally unwieldy.

The local response of global descriptors

We consider the problem of defining an appropriate local descriptor corresponding to an arbitrary global descriptor. Although it does not seem easy to rigorously and uniquely define local analogues of derived global descriptors (e.g., the electrophilicity) or the fundamental global descriptors associated with the canonical ensemble (e.g., the hardness), the local response of these global descriptors can be defined unambiguously. We look at the local response of the global electrophilicity and compare it to the conventional, ad hoc, definition of the local electrophilicity. The local response of global nucleofugality and electrofugality is also discussed.

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

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.

A reference-free stockholder partitioning method based on the force on electrons

We argue that when one divides a molecular property into atom‐in‐a‐molecule contributions, one should perform the division based on the property density of the quantity being partitioned. This is opposition to the normal approach, where the electron density is given a privileged role in defining the properties of atoms‐in‐a‐molecule. Because partitioning each molecular property based on its own property density is inconvenient, we design a reference‐free approach that does not (directly) refer atomic property densities. Specifically, we propose a stockholder partitioning method based on relative influence of a molecules atomic nuclei on the electrons at a given point in space. The resulting method does not depend on an “arbitrary” choice of reference atoms and it has some favorable properties, including the fact that all of the electron density at an atomic nucleus is assigned to that nucleus and the fact all the atoms in a molecule decay at a uniform asymptotic rate. Unfortunately, the resulting model is not easily applied to spatially degenerate ground states. Furthermore, the practical realizations of this strategy that we tried here gave disappointing numerical results.

Communication: Two types of flat-planes conditions in density functional theory

Using results from atomic spectroscopy, we show that there are two types of flat-planes conditions. The first type of flat-planes condition occurs when the energy as a function of the number of electrons of each spin, Nα and Nβ, has a derivative discontinuity on a line segment where the number of electrons, Nα + Nβ, is an integer. The second type of flat-planes condition occurs when the energy has a derivative discontinuity on a line segment where the spin polarization, Nα - Nβ, is an integer, but does not have a discontinuity associated with an integer number of electrons. Type 2 flat planes are rare-we observed just 15 type 2 flat-planes conditions out of the 4884 cases we tested-but their mere existence has implications for the design of exchange-correlation energy density functionals. To facilitate the development of functionals that have the correct behavior with respect to both fractional number of electrons and fractional spin polarization, we present a dataset for the chromium atom and its ions that can be used to test new functionals.

Negative Condensed-to-Atom Fukui Functions: A Signature of Oxidation-Induced Reduction of Functional Groups

We show that the orbital relaxation contribution to the Fukui function, first derived by Yang, Parr, and Pucci in 1984, is decisive for predicting redox-induced electron transfer. Specifically, we study a dinuclear cobalt complex which has been shown to exhibit redox-induced electron transfer, and show that this effect is associated, computationally, with negative values of the condensed Fukui functions. This establishes that not only can the Fukui function be negative, but negative values of the Fukui function are chemically significant.