RELATIONS BETWEEN POTENTIAL-ENERGY, ELECTRONIC CHEMICAL-POTENTIAL, AND HARDNESS PROFILES

In recent papers we defined a theoretical frame aimed at characterizin g the hardness and potential energy profiles along a reduced reaction coordinate (omega) varying from 0 to 1. In this paper we generalize th at model to propose a global procedure that allows one to consider sim ultaneously the evolution of the potential energy (V) in connection wi th that of the electronic chemical potential (mu) and the molecular ha rdness (eta) important results have been obtained: (a) the potential e nergy profile can be expressed in terms of the mu and eta profiles thr ough an equation which is analogous to that used by Parr and Pearson t o demonstrate the HSAB principle; (b) the chemical potential along ome ga is in turn written in terms of the hardness profile, an equation wh ich is analogous to that proposed by the same authors to quantify the electron tranfer induced by a chemical potential gradient; and (c) use ful 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 rotatio n or an inversion mechanism. The most relevant result concerning the c hemical system is that for both mechanisms the principle of maximum ha rdness holds even though the electronic chemical potential strongly va ries along the reaction coordinates. Our analysis suggests that if a s ystem is constrained to chose among different reaction paths connectin g two stable states, it will prefer the one presenting a minimum chemi cal potential.