An elementary derivation of the “|Δμ| big is good” rule and its implications in several reactivity principles

Recently, Miranda-Quintana, Heidar-Zadeh, and Ayers have elaborated a simple proof of the "Δμ big is good" rule for reactions that are dominated by charge transfer, making use of the smooth quadratic interpolation for fractional electron number and the analysis of several derivatives. In this work, we extend this approach, showing that one can derive a direct relationship of the change in the energy as a function of the change in the absolute value of the chemical potential that implies the "Δμ big is good" rule. In addition, we show that this rule plays an important role in the fulfillment of the hard and soft acids and bases (HSAB), the maximum hardness, and the minimum electrophilicity principles, as anticipated intuitively by Parr.