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The numerical ill‐conditioning associated with approximating an electron density with a convex sum of Gaussian or Slater‐type functions is overcome by using the (extended) Kullback–Leibler divergence to measure the deviation between the target and approximate density. The optimized densities are non‐negative and normalized, and they are accurate enough to be used in applications related to molecular similarity, the topology of the electron density, and numerical molecular integration. This robust, efficient, and general approach can be used to fit any non‐negative normalized functions (e.g., the kinetic energy density and molecular electron density) to a convex sum of non‐negative basis functions. We present a fixed‐point iteration method for optimizing the Kullback–Leibler divergence and compare it to conventional gradient‐based optimization methods. These algorithms are released through the free and open‐source BFit package, which also includes a L2‐norm squared optimization routine applicable to any square‐integrable scalar function. [ABSTRACT FROM AUTHOR]

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 molecule's 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. © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

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]

We present explicit formulas for arbitrary-order derivatives of the energy, grand potential, electron density, and higher-order response functions with respect to the number of electrons, and the chemical potential for any smooth and differentiable model of the energy versus the number of electrons. The resulting expressions for global reactivity descriptors (hyperhardnesses and hypersoftnesses), local reactivity descriptors (hyperFukui functions and local hypersoftnesses), and nonlocal response functions are easy to evaluate computationally. Specifically, the explicit formulas for global/local/nonlocal hypersoftnesses of arbitrary order are derived using Bell polynomials. Explicit expressions for global and local hypersoftness indicators up to fifth order are presented. [ABSTRACT FROM AUTHOR]