In pursuit of negative Fukui functions: molecules with very small band gaps.

A justification for the likely presence of negative Fukui functions in molecules with small band gaps is given, and a computational study performed to check whether molecules with small band gaps have negative Fukui functions to a chemically significant extent is reported. While regions with negative Fukui functions were observed, significantly negative values for the atom-condensed Fukui functions were not observed.

In pursuit of negative Fukui functions: examples where the highest occupied molecular orbital fails to dominate the chemical reactivity.

In our quest to explore molecules with chemically significant regions where the Fukui function is negative, we explored reactions where the frontier orbital that indicates the sites for electrophilic attack is not the highest occupied molecular orbital. The highest occupied molecular orbital (HOMO) controls the location of the regions where the Fukui function is negative, supporting the postulate that negative values of the Fukui function are associated with orbital relaxation effects and nodal surfaces of the frontier orbitals. Significant negative values for the condensed Fukui function, however, were not observed.

The unconstrained local hardness: an intriguing quantity, beset by problems.

Developing a mathematical approach to the local hard/soft acid/base principle requires an unambiguous definition for the local hardness. One such quantity, which has aroused significant interest in recent years, is the unconstrained local hardness. Key identities are derived for the unconstrained local hardness, δµ/δρ(r). Several identities are presented which allow one to determine the unconstrained local hardness either explicitly using the hardness kernel and the inverse-linear response function, or implicitly by solving a system of linear equations. One result of this analysis is that the problem of determining the unconstrained local hardness is infinitely ill-conditioned because arbitrarily small changes in electron density can cause enormous changes in the chemical potential. This is manifest in the exponential divergence of the unconstrained local hardness as one moves away from the system. This suggests that one should be very careful when using the unconstrained local hardness for chemical interpretation.

Chemical reactivity descriptors for ambiphilic reagents: dual descriptor, local hypersoftness, and electrostatic potential.

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.