Redox orbital correlations

The half-wave redox potentials can be satisfactorily correlated to the energy of the highest occupied molecular orbitals in quinocyclopropenes 118—125 by calculations according to the simple HMO model7S ... 

The linear correlations of the data of the complexes [29a-29e] and [29i] displayed in Table 9 and Fig. 6 then may illustrate the alteration of the a-donor-rr-acceptor balance within the axial ligands, which is fully transmitted to the porphyrin orbitals via the metal. Linear correlations between the redox potentials and the energy of optical absorption maxima are well-known in organic molecules (95). In this case, a metal is strongly conjugated with the porphyrin system. The cis influence... 

The charge at the vanadium in the usual dithiolene complexes may be estimated49 as less than 2, and these complexes are therefore included in the section on low valence states. Various tris(dithiolene) complexes have been isolated and one-electron oxireductions studied by polarographic and voltammetric techniques. Table 3 summarizes methods of preparation and electrochemical behaviour. Schrauzer and co-workers50 correlated electrochemical data with Taft s constants the observed linear correlation reflected the ligand n orbital origin of the orbitals involved in the redox process. 

Correlation of gas-phase ionization potential data with solution redox potentials for series of organic, organometallic and coordination compounds21 23 underlines the relationship between F(E°q- ° ) and orbital energies. For example, Cr 3d binding energy data for the first ionization process of complexes [Cr(CO)5L] correlate reasonably linearly with the (E°0 E°n) parameter, J°L,23 as is illustrated by Figure 3. 

Redox potential data frequently correlate with parameters obtained by other spectroscopic measurements. The correlation of E° potentials with gas-phase ionization potentials has already been briefly discussed. Electronic transitions observed by UV-visible spectroscopy involve the promotion of an electron from one orbital to another and this can be viewed as an intramolecular redox reaction. If the promotion involves the displacement of an electron from the HOMO to the LUMO, then the redox potentials for the reduction of the compound, °REd, and for its oxidation, °ox, are of importance. For a closely related series of compounds, trends in oxidation and reduction potentials can be related to shifts in the absorption frequency, v. If the structural perturbation causes the HOMO and the LUMO to rise or fall in energy in tandem, then (E°RED — E°ox) will remain constant in such cases the HOMO—LUMO frequency (energy) will be essentially independent of the structural perturbation. Where there is a differential influence of the perturbation on the HOMO and the LUMO, then ( °red E°ox) will vary as will the energy of the electronic transition. In such cases a linear correlation of °red or E°0x may result. In the limit the energy of the HOMO, or more usually the LUMO, will be unaffected by structural perturbation where the acceptor orbital is pinned, direct linear correlation of E°Gx with v should be apparent. With E°ox and v in a common energy unit, the plot E°0x versus v should have a slope close to one.33-36... 

In view of the large difference in the reactivity of Cr+2 and Mn+2 aquo complexes it seems that the reactivity of the metal complex toward eaq is not related to the energy required to remove a second 4s electron. The similar reactivity of aquo and amino complexes makes the correlation between reactivity and redox potentials rather unlikely. As an alternative mechanism, we suggest that the availability of a vacant d orbital on the central atom and the energy gain on adding an electron are the major factors which determine the reactivity of transition metal ions. 

A point of special interest is that the electronic couplings for intramolecular ET reactions in His-58 and His-66 cytochromes are not enhanced by aromatic residues (Trp-59 and Tyr-67) in the intervening media (36). The correlation of ET rates with or does not preclude a coupling role for the ir orbitals of the aromatic groups in the pathway, but it does indicate that, in the Ru-modified cytochromes that we examined, they are no more efficient in mediating the coupling than is the (7-bonded framework. Hence, the presence of aromatic groups in the medium between redox sites does not necessarily result in faster ET than in a purely aliphatic medium (15-20, 37-41). 

Semiempirical MNDO calculations have been carried out on model pyrylium and thiopyrylium systems (88MI1). The calculated HOMO-LUMO gap in the gas phase correlates well with experimental absorption maxima obtained in solution. Ionization potentials and electron affinities predicted by Koopmans theorem with MNDO orbital energies do not track the observed trends in the experimental redox values. In contrast these are paralleled by the trends predicted by A// values calculated by MNDO and AMI for the open-shell and closed-shell species. 

Figure 49. Absolute highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies for typical semiconductors, correlated with the the redox potential scale versus SHE of some molecular species of interest (407).

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