Relations between potential energy, electronic chemical potential, and hardness profiles

In recent papers we defined a theoretical frame aimed at characterizing the hardness and potential energy profiles along a reduced reaction coordinate (omega) varying from 0 to 1. In this paper we generalize that model to propose a global procedure that allows one to consider simultaneously the evolution of the potential energy (V) in connection with that of the electronic chemical potential (mu) and the molecular hardness (eta) important results have been obtained: (a) the potential energy profile can be expressed in terms of the mu and eta profiles through an equation which is analogous to that used by Parr and Pearson to demonstrate the HSAB principle; (b) the chemical potential along omega is in turn written in terms of the hardness profile, an equation which is analogous to that proposed by the same authors to quantify the electron tranfer induced by a chemical potential gradient; and (c) useful expressions for the activation properties have been derived. As an illustration we study the trans reversible arrow cis isomerization of diimide, a reaction that may occur through either an internal rotation or an inversion mechanism. The most relevant result concerning the chemical system is that for both mechanisms the principle of maximum hardness holds even though the electronic chemical potential strongly varies along the reaction coordinates. Our analysis suggests that if a system is constrained to chose among different reaction paths connecting two stable states, it will prefer the one presenting a minimum chemical potential.