Hardness charge transfer process

Two formal proofs of the HSAB principle with a restriction of common chemical potential for the partners have been provided very recently [15]. The first proof makes use of the maximum hardness principle. The energy change (to first order) associated with the charge transfer process described above is given by... 

In the situations in which the units used for the energy and potentials are the electron-volts, the measurement unit for the orbital strength is Volt per electron, i.e., the same size as the electric capacity. This analogy allows a better intuition of the physical—chemical significance of the chemical hardness in the charge transfer processes and the bonds formation. 

We suggest that electron transfer and electrophilic substitutions are, in general, competing processes in arene oxidations. Whether the product is formed from the radical cation (electron transfer) or from the aryl-metal species (electrophilic substitution) is dependent on the nature of both the metal oxidant and the aromatic substrate. With hard metal ions, such as Co(III), Mn(III), and Ce(IV),289 reaction via electron transfer is preferred because of the low stability of the arylmetal bond. With soft metal ions, such as Pb(IV) and Tl(III), and Pd(II) (see later), reaction via an arylmetal intermediate is predominant (more stable arylmetal bond). For the latter group of oxidants, electron transfer becomes important only with electron-rich arenes that form radical cations more readily. In accordance with this postulate, the oxidation of several electron-rich arenes by lead(IV)281 289 and thallium(III)287 in TFA involve radical cation formation via electron transfer. Indeed, electrophilic aromatic substitutions, in general, may involve initial charge transfer, and the role of radical cations as discrete intermediates may depend on how fast any subsequent steps involving bond formation takes place. 

With the physical process of charge transfer during chemical reaction leading to bond formation, the hardness kernel of atoms change and in the process, it would increase somewhere and decrease elsewhere ultimately the hardness values of the caomic fragments will equalize to some intermediate values common to all. 

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