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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]

We present a new, nonarbitrary, internally consistent, and unambiguous framework for spin-polarized conceptual density-functional theory (SP-DFT). We explicitly characterize the convex hull of energy, as a function of the number of electrons and their spin, as the only accessible ground states in spin-polarized density functional theory. Then, we construct continuous linear and quadratic models for the energy. The nondifferentiable linear model exactly captures the simplicial geometry of the complex hull about the point of interest and gives exact representations for the conceptual DFT reactivity indicators. The continuous quadratic energy model is the paraboloid of maximum curvature, which most tightly encloses the point of interest and neighboring vertices. The quadratic model is invariant to the choice of coordinate system (i.e., { N , S } vs { N α , N β }) and reduces to a sensible formulation of spin-free conceptual DFT in the appropriate limit. Using the quadratic model, we generalize the Parr functions { P + ( r ), P - ( r )} (and their derivatives with respect to number of electrons) to this new spin-polarized framework, integrating the Parr function concept into the context of (spin-polarized) conceptual DFT, and extending it to include higher-order effects.

Accurate potential energy models of proteins must describe the many different types of noncovalent interactions that contribute to a protein's stability and structure. Pi-pi contacts are ubiquitous structural motifs in all proteins, occurring between aromatic and nonaromatic residues and play a nontrivial role in protein folding and in the formation of biomolecular condensates. Guided by a geometric criterion for isolating pi-pi contacts from classical molecular dynamics simulations of proteins, we use quantum mechanical energy decomposition analysis to determine the molecular interactions that stabilize different pi-pi contact motifs. We find that neutral pi-pi interactions in proteins are dominated by Pauli repulsion and London dispersion rather than repulsive quadrupole electrostatics, which is central to the textbook Hunter-Sanders model. This results in a notable lack of variability in the interaction profiles of neutral pi-pi contacts even with extreme changes in the dielectric medium, explaining the prevalence of pi-stacked arrangements in and between proteins. We also find interactions involving pi-containing anions and cations to be extremely malleable, interacting like neutral pi-pi contacts in polar media and like typical ion-pi interactions in nonpolar environments. Like-charged pairs such as arginine-arginine contacts are particularly sensitive to the polarity of their immediate surroundings and exhibit canonical pi-pi stacking behavior only if the interaction is mediated by environmental effects, such as aqueous solvation.

The electrostatic potential (ESP) is a powerful property for understanding and predicting electrostatic charge distributions that drive interactions between molecules. In this study, we compare various charge partitioning schemes including fitted charges, density-based quantum mechanical (QM) partitioning schemes, charge equilibration methods, and our recently introduced coarse-grained electron model, C-GeM, to describe the ESP for protein systems. When benchmarked against high quality density functional theory calculations of the ESP for tripeptides and the crambin protein, we find that the C-GeM model is of comparable accuracy to ab initio charge partitioning methods, but with orders of magnitude improvement in computational efficiency since it does not require either the electron density or the electrostatic potential as input.

Thirty years ago, Parr and Yang postulated that favorable chemical processes are associated with large changes in the electronic chemical potential or, equivalently, the electronegativity. They called this the "|Δμ| big is good" rule and noted that if the rule could be justified, then it "would constitute a validation of frontier theory from first principles." We provide a simple and insightful justification for the "|Δμ| big is good" rule, with special emphasis on electron-transfer reactions. Furthermore, we show that it implies Pearson's hard/soft acid/base principle mathematically and confirm this result with numerical examples. This supports Parr's intuition that many other reactivity precepts arise as corollaries to the more fundamental "|Δμ| big is good" rule. In all of this, it is essential to consider the intensive nature of the chemical potential.

When one defines the energy of a molecule with a noninteger number of electrons by interpolation of the energy values for integer-charged states, the interpolated electron density, Fukui function, and higher-order derivatives of the density are generally not normalized correctly. The necessary and sufficient condition for consistent energy interpolation models is that the corresponding interpolated electron density is correctly normalized to the number of electrons. A necessary, but not sufficient, condition for correct normalization is that the energy interpolant be a linear function of the reference energies. Consistent with this general rule, polynomial interpolation models and, in particular, the quadratic E vs N model popularized by Parr and Pearson, do give normalized densities and density derivatives. Interestingly, an interpolation model based on the square root of the electron number also satisfies the normalization constraints. We also derive consistent least-norm interpolation models. In contrast to these models, the popular rational and exponential forms for E vs N do not give normalized electron densities and density derivatives.

Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using the distributed nature of the electron cloud and atomic multipoles. In this work, an electrostatic force field is defined through a concise approximation of the electron density, for which the Coulomb interaction is trivially evaluated. This approximate "pro-density" is expanded in a minimal basis of atom-centered s-type Slater density functions, whose parameters are optimized by minimizing the Kullback-Leibler divergence of the pro-density from a reference electron density, e.g., obtained from an electronic structure calculation. The proposed method, Minimal Basis Iterative Stockholder (MBIS), is a variant of the Hirshfeld AIM method, but it can also be used as a density-fitting technique. An iterative algorithm to refine the pro-density is easily implemented with a linear-scaling computational cost, enabling applications to supramolecular systems. The benefits of the MBIS method are demonstrated with systematic applications to molecular databases and extended models of condensed phases. A comparison to 14 other AIM methods shows its effectiveness when modeling electrostatic interactions. MBIS is also suitable for rescaling atomic polarizabilities in the Tkatchenko-Scheffler scheme for dispersion interactions.