Hardness Profile and Activation Hardness for Rotational Isomerization Processes. 2. The Maximum Hardness Principle

Abstract

In a recent paper [/. Phys. Chem. 1995, 99, 5325] we presented a model characterizing the activation hardness in terms of the activation energy of rotational isomerization reactions. We present in this paper an extension of that model for obtaining a direct relation between hardness and potential energy profiles. The hardness is related to the potential energy through a two-term equation in which the leading term is a linear dependence on the potential energy, and the second term can be seen as a correction occurring in cases where the critical points for hardness and energy profiles do not match. It is shown that the hardness and energy profiles behave in opposite ways that can be rationalized in terms of two parameters. A qualitative proof of the maximum hardness principle (PMH), within the frame of the model potential employed, is given, and its consistency with the Hammond postulate is discussed in the light of results for different molecules presenting rotational isomerization.

A Quest for the Origin of Barrier to the Internal Rotation ofHydrogen Peroxide (H2O2) and Fluorine Peroxide (F2O2)

“…It appears from the survey of literature on the origin of barrier to internal rotation of molecules that majority of workers believe that it is a regional effect and barrier originates from some mystic reason. The physical process of generation of Cis Trans and Staggered Eclipsed conformers is in fact a rotational isomerization process and can be viewed as resulting from reorganization and redistribution of electron density among the atoms in a molecule, so that the total number of electrons is conserved even though there may be an intramolecular charge transfer process [9,10]. Thus the physical process of the dynamics of internal rotation initiates the isomerization reaction, which generates infinite number of conformations between the extreme conformations stated above.…”

Energy, chemical potential and hardness profiles for the rotational isomerization of HOOH, HSOH and HSSH

“…These results indicate that the stable conformations are not determined only by strong overlaps but also by specific through space interactions, and the associated forces should be characterized through the electrostatic Hellman-Feynman theorem [9]. This seems to be the case for hydrogen peroxide, where poo presents a maximum value not at the energy minimum but at around Po,…”

“…where Kv is a parameter associated with the reference conformations (for molecules presenting a single well with two energy barriers Kv is negative [8,9]) and AVO = ( V ( x ) -V ( 0 ) ) is the energy difference between the trans and cis isomers.…”

“…However, it has been shown that the PMH is not the product of a simple opposite relation between energy and hardness; for example, hardness and energy profiles may present critical points that are shifted one to another giving rise to peculiar types of behaviour in the { q , V ) space [9]. In the present case, an analysis of the profiles of V and q shows that globally these properties have opposite trends, although there are some discrepancies that should be due to other effects or to the fact that the PMH was shown to hold under the constraints of constant p and external potential [18].…”

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

“…32 Moreover, η profiles for internal bond rotation have also been extensively examined. 18,20,21,[33][34][35][36][37][38][39] In these papers, it has been commonly shown that a more stable structure along the reaction coordinate is associated with a higher value of η and a lower value of µ. The computed η profiles usually go through a minimum in the TS regions, although, in some cases, the position of η maximum is significantly deviated from that of the TS.…”