Perturbed reactivity descriptors in the two parabolas model of fractional electron number

A new procedure based on the two parabolas model of the energy and the electronic density for fractional electron number is used with the assumption that the changes to the isolated values of these two quantities due to the presence of another interacting species can be incorporated through a multiplicative constant in the second order term. The expressions thus obtained for the chemical potential, hardness, Fukui function and dual descriptor reactivity indexes of conceptual density functional theory have the same form of those obtained through a first order perturbation approach within the grand canonical ensemble. The perturbation parameters are then evaluated by imposing the chemical potential and hardness equalization principles for the interaction between species A and B to form AB, and it is applied to show for a group of substituted ethenes that the condensed to atom perturbed local chemical potential and local hardness evaluated at the carbon atom that follows the Markovnikov’s rule lead to better correlation with the activation energy of their reaction with HCl than the unperturbed descriptors. A similar situation is found for the correlation of the condensed to atom local chemical potential evaluated at N in the aniline molecules with the experimental pKa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{p}K}_{\mathrm{a}}$$\end{document} values. The results obtained indicate that through the perturbed descriptors, that introduce information of the electronic structure on each species of the other one with which it interacts allow one to obtain an improved description of their chemical reactivity.