Relations between Potential Energy, Electronic Chemical Potential, and Hardness Profiles

Abstract

In recent papers we defined a theoretical frame aimed at characterizing the hardness and potential energy profiles along a reduced reaction coordinate (ω) 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 (μ) and the molecular hardness (η). Important results have been obtained: (a) the potential energy profile can be expressed in terms of the μ and η profiles through an equation which is analogous to that used by Parr and Pearson to demonstrate the HSAB principle; (b) the chemical potential along ω 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 ⇌ 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.

Chemical reactivity indexes in density functional theory

“…0 adiabatic value , as first suggested in early works. 102 A relationship between energy and global hardness differences was established by Gazqueź et al, 103 whereas Toro-Labbe et al 104 established á more general relation between potential energy, Ž . chemical potential i.e., electronegativity , and hardness profile.…”

Characterization of Chemical Reactions Through Classical Concepts and DFT Descriptors

“…The correctness of the trends shown by the different properties indicate that inversion may be the right mechanism for isomerization of diimine, the other mechanisms that has been suggested is a rotation around the double bond but it presents a higher energy barrier 39,55 …”

“…(ll)-(13) we use a prescription we gave in previous works 36~38 . It is important to point out that since V, fi and rj depend on the same function f(u>) it is possible to establish analytic relations between them although the extend of the application of this relations is still matter of research 39 .…”

Internal Bond Rotation in Substituted Methyl Radicals, H2B−CH2, H3C−CH2, H2N−CH2, and HO−CH2: Hardness Profiles

“…82 Bader 83 pointed out that a TS structure is usually accompanied by a low-lying excited state, which results in small HOMO-LUMO gap. A large number of observations [19][20][21][22][23][24][25][26][33][34][35][36][37][38][39] suggesting that Datta's corollary phenomenally holds in various chemical reactions appear to be more directly related with the presence of the low-lying excited state for the TS rather than the PMH.…”

“…η profile, has been discussed in the light of the PMH. There have been reported a large number of papers regarding η profiles of various types of chemical reactions, such as isomerization reactions, [19][20][21][22][23] intermolecular- 24,25 and intramolecular-protontransfer reactions, 15,26 cycloaddition reactions, [27][28][29][30] intramolecular rearrangement reactions, 31 and van der Waals complexes. 32 Moreover, η profiles for internal bond rotation have also been extensively examined.…”