Hardness potential derivatives and their relation to Fukui indices.

A simple as well as easy to compute formalism of hardness potential (originally defined by Parr and Gazquez, J. Phys. Chem., 1993, 97, 3939) is presented. Use of hardness potential formally resolves the N-dependence problem of local hardness. However, the hardness potential cannot describe the intra as well as intermolecular reactivity sequence satisfactorily of some chemical systems. The corresponding electrophilic [Δ(+)h(k)] and nucleophilic [Δ(-)h(k)] variants of the hardness potential are also developed, which measure the reactivity toward a nucleophilic (i.e., Nu(-)) and an electrophilic (i.e., El(+)) reagent, respectively. Interestingly, these two variants of the hardness potential lead to the right and left derivatives of Fukui potential. The proposed reactivity descriptors correctly predict the expected reactivity trends in the chosen systems. It has also been illustrated that the values of the variants of hardness potential (or Fukui potential) at the atomic nucleus have the ability to explain the intramolecular reactivity of biologically active indole derivatives. The future scope of applications as well as limitations of the proposed descriptors is also highlighted.