The second-order response of the electron density with respect to changes in electron number, known as the dual descriptor, has been established as a key reactivity indicator for reactions like pericyclic reactions, where reagents accept and donate electrons concurrently. Here we establish that the dual descriptor is also the key reactivity indicator for ambiphilic reagents: reagents that can act either as electrophiles or as nucleophiles, depending on the reaction partner. Specifically, we study dual atoms (which are proposed to act, simultaneously, as an electron acceptor and an electron donor), dual molecules (which react with both electrophiles and nucleophiles, generally at different sites), and dual ion-molecule complexes (which react with both cations and anions). On the basis of our analysis, the dual atom (an Al(I) that has been purported to be dual in the literature) is actually pseudodual in the sense that it does not truly accept electrons from a nucleophiles; rather, it serves as a conduit through which an electrophile can donate electrons to the attached aromatic ring. For understanding dual ion-molecule complexes, it helps to understand that the dual descriptor makes a key contribution to the long-range portion of the quadratic hyperpolarization. In all cases, a complete description of the reactivity of the ambiphilic reagent requires considering both an orbital-based descriptor of electron transfer (the dual descriptor or the local hypersoftness) and the electrostatic potential. The local hypersoftness strongly resembles the dual descriptor.

Density-functional-theory-based chemical reactivity indicators are formulated for degenerate and near-degenerate ground states. For degenerate states, the functional derivatives of the energy with respect to the external potential do not exist, and must be replaced by the weaker concept of functional variation. The resultant reactivity indicators depend on the specific perturbation. Because it is sometimes impractical to compute reactivity indicators for a specific perturbation, we consider two special cases: point-charge perturbations and Dirac delta function perturbations. The Dirac delta function perturbations provide upper bounds on the chemical reactivity. Reactivity indicators using the common used "average of degenerate states approximation" for degenerate states provide a lower bound on the chemical reactivity. Unfortunately, this lower bound is often extremely weak. Approximate formulas for the reactivity indicators within the frontier-molecular-orbital approximation and special cases (two or three degenerate spatial orbitals) are presented in the supplementary material. One remarkable feature that arises in the frontier molecular orbital approximation, and presumably also in the exact theory, is that removing electrons sometimes causes the electron density to increase at the location of a negative (attractive) Dirac delta function perturbation. That is, the energetic response to a reduction in the external potential can increase even when the number of electrons decreases.

In the course of a reaction it is the shape of the Fukui potential that guides a distant reagent toward the site where an electrophile/nucleophile is willing to accept/donate charge. In this paper we explore the mathematical characteristics of the Fukui potential and demonstrate its relationship to the hardness and the ability of an atom in a molecule to change its charge. The Fukui potential not only determines the active site for electron transfer, but it also approximates the distribution of hardness of a molecule: it is the Coulomb contribution to the frontier local hardness. The Fukui potential at the position of the nuclei is equal to the variation of the chemical potential with the nuclear charge and therefore measures the sensitivity of the system to changes in atom type. In the specific case of atoms and slightly charged ions, the Fukui potential at the nucleus measures the hardness. The strong correlation between the hardness and the Fukui potential at the nucleus suggests that the Fukui potential at the nucleus is an alternative definition for the chemical hardness.

Despite recent advances in computing negative electron affinities using density-functional theory, it is an open issue as to whether it is appropriate to use negative electron affinities, instead of zero electron affinity, to compute the chemical hardness of atoms and molecules with metastable anions. We seek to answer this question using the accepted empirical rules linking the chemical hardness to the atomic size and the polarizability; we also propose a new correlation with the C6 London dispersion coefficient. For chemical reactivity in the gas phase, it seems to make no difference whether negative, or zero, electron affinities are used for systems with metastable anions. For reactions in solution the evidence that is presently available is insufficient to establish a preference. In addressing this issue, we noted that electron affinity data from which atomic chemical hardness values are computed are out of date; an update to Pearson's classic 1988 table [Inorg. Chem., 1988, 27, 734-740] is thus provided.

A system in a spatially degenerate ground state responds in a qualitatively different way to positive and negative point charges. This means that the molecular electrostatic potential is ill-defined for degenerate ground states due to the ill-defined nature of the electron density. It also means that it is impossible, in practice, to define fixed atomic charges for molecular mechanics simulations of molecules with (quasi-)degenerate ground states. Atomic-polarizability-based models and electronegativity-equalization-type models for molecular polarization also fail to capture this effect. We demonstrate the ambiguity in the electrostatic potential using several molecules of different degree of degeneracy, quasi-degeneracy, and symmetry.

The chemical space contains all possible compounds that can be imagined. Its size easily equals the number of fundamental particles in the observable universe. Rational design of compounds aims to find those sectors of the chemical space where compounds optimize a set of desired properties. Then, rational design demands tools to efficiently navigate the chemical space. Ab initio alchemical derivatives offer the possibility to navigate, without empiricism, the energy landscape through alchemical transformations. An alchemical transformation is any process, physical or fictitious, that connects to points in the chemical space. In this work, those transformations are constructed as a perturbative expansion of the energy with respect to perturbations in the stoichiometry. The response functions of that expansion are what is called alchemical derivatives. In this work we assess how effective alchemical derivatives are in predicting energy changes associated to changes in the composition. We do this by including in the expansion, for the first time, electrostatic, polarization and electron-transfer effects. The system we chose is one that challenges alchemical derivatives because none of these effects dominates its behavior. The transmutations studied here correspond to substitutional doping of Al with up to four atoms of Si, AlSi. Two types of transformations are considered, those in which the number of electrons remains constant and those in which the number of electrons also changes. It is found that contrary to what has been reported before, polarization cannot be neglected. If polarization is not included, alchemical derivatives fail to predict the change of energy and the relative energy between isomers. For isoelectronic substitution of four or more atoms, the perturbative approach collapses because the strength of the perturbation becomes too strong to guarantee convergence of the series. It is shown, however, that if only one atom is mutated at a time, alchemical derivatives rank pretty well the isomers of AlSi according to their energy. In the case of non-isoelectronic transformations, it is observed that the series rapidly diverges with increasing number of electrons. In this situation, it becomes more important to keep the degree of transmutation of the parent system small.

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.

In this article, we study theoretically the properties of hematene, a new antiferromagnetic 2D material exfoliated from hematite. Hematene is not a van-der Waals material, but it can still be obtained by liquid exfoliation of hematite crystals. Its properties might be quite different from those of the bulk and to establish such differences is one of the aims of this study. A detailed study of hematene by density functional theory has been carried out to look at the electronic properties of this iron oxide material. Results show that freestanding hematene is antiferromagnetic with a magnetic moment of 4 per atom and an insulator/semiconductor with a bandgap of almost 1.0 eV. The stability of hematene is confirmed by calculating its phonon spectrum. Hematene supported on gold and stanene was also investigated: while no significant changes are found for the contact with the former, the interaction with the latter turn Hematene into a 2D ferrimagnet.