The computational approach to the Hirshfeld ͓Theor. Chim. Acta 44, 129 ͑1977͔͒ atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting "Hirshfeld-I charges" correlate well with electrostatic potential derived atomic charges.

The fundamental principles of density functional theory are applied to achieve a better understanding of various theoretical tools for describing chemical reactivity. Emphasis is given to the Fukui function, the central site reactivity index of density functional theory, which is approached through its own variational principle. A maximum hardness principle is then developed and discussed. To make contact with an earlier proof of a maximum hardness principle, changes in chemical potential are considered.

For a linear combination of electron densities of degenerate ground states, it is shown that the value of any energy functional is the ground state energy, if the energy functional is exact for ground state densities, size consistent, and translational invariant. The corresponding functional of kinetic and interaction energy is the linear combination of the functionals of the degenerate densities. Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers. These results underscore the importance of grand canonical ensemble formulation in density functional theory.

ABSTRACT:When a molecule is in the presence of a chemical reagent, the external potential and the number of electrons in the molecule change. This leads to perturbative perspectives on chemical reactivity, wherein the response of a molecule to various "model perturbations" of the external potential and number of electrons is used to predict its reactivity. The perturbative perspective allows one to treat indices associated with conceptual density functional theory in a unified way. Here we concentrate on the implications of the perturbative perspective in describing regioselectivity and certain global properties of molecules, specifically, their electrophilicity, nucleofugality, and electrofugality.

The dependence of molecular properties on the chemical hardness is explored. As the chemical hardness of a molecule increases, its size and polarizability typically decrease and its charge and electronegativity typically increase. On the basis of these properties, the interaction energy between hard and soft acids and bases is quantified, and the physical basis of the global and local hard/soft acid/base (HSAB) principles is elucidated.

The derivation of the Hirshfeld atoms in molecules from information theory is clarified. The importance for chemistry of the concept of atoms in molecules (AIM) is stressed, and it is argued that this concept, while highly useful, constitutes a noumenon in the sense of Kant.

We propose an approach to the electronic structure problem based on noninteracting electron pairs that has similar computational cost to conventional methods based on noninteracting electrons. In stark contrast to other approaches, the wave function is an antisymmetric product of nonorthogonal geminals, but the geminals are structured so the projected Schrödinger equation can be solved very efficiently. We focus on an approach where, in each geminal, only one of the orbitals in a reference Slater determinant is occupied. The resulting method gives good results for atoms and small molecules. It also performs well for a prototypical example of strongly correlated electronic systems, the hydrogen atom chain.

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.