Correlations half-wave potentials

Two approaches to the problem of the energetic reaction mechaonisrn may be conveniently distinguished (a) the thermo-d3mamic and kinetic, and (b) the quantum mechanical. These two approaches have been particularly applied in attempts to interpret and to correlate half-wave potential data for organic compounds. However, in order to do so, it has been necessary to construct or to postulate reaction mechanisms, upon which calculations can be based. 

It is known that tropylium may be prepared from tropylidene via hydride abstraction by PhgC or MegC carbonium ions therefore, it is very likely that here too the dehydrogenation is a hydride transfer from the 1,5-dione to an acceptor. A similar dehydrogenation of chromanones to chromones, with triphenylmethyl perchlorate was reported. A study of the electrooxidation of 1,5-diones on a rotating platinum electrode showed that 1,5-diaryl-substituted diones afford pyrylium salts in these conditions and that the half-wave potentials correlate with yields in chemical dehydrogenations. 

Using these assumptions and conventions, Imoto and co-workers have correlated a number of series of reactions of thiophenes and furans. The reactions studied are the acid-base equilibria pK values) and the acid catalyzed methylations (thiophenes only) of thiophene-and furan-carboxylic acids and the alkaline hydrolyses of their ethyl esters the side-chain bromination of the a-acetylthiophenes, and the a-mercuration of thiophenes and the polarographic half-wave potentials of the methyl esters of thiophene- and furan-carboxylic acids and of nitrothiophenes. The pK values were determined and the ester hydrolyses studied for all three substitution orientations in the thiophene series. For the 4-R-2-Y and 5-R-2-Y series, the p-values do not appear significantly different and the data could probably be combined into a single series unfortunately, however, no limits of accuracy are reported for the p-values, and some of the raw data are not readily available so recalculation is not easily possible. For the 5-R-3-Y series the p-values deviate considerably from the other values however, whereas they are higher for the pK values, they are lower for the ester hydrolyses, and it is possible that the differences are neither systematic nor significant. 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

Rather surprisingly, the differences in half-wave potentials of hydrocarbons from one solvent to another are very small. This constancy in energy values as well as slopes of correlation lines in widely varying solvents and supporting electrolytes implies that solvation energies, provided they are not small, change in the same way from system to system. 

Moreover, Brand and Snedden were also able to correlate the mass and the number of halogen substituents in the solvent with spectral changes. Even better correlation was found between the wavelength of the 307 mu band and the half-wave potential of the halide—a measure of its tendency to act as an electron acceptor. 

Owing to the presence of the amine and cyanide ligands, known to give rise to specific donor-acceptor interaction with solvents [126-130], an interesting solvatochromic behavior is observed for these species. For complex 1 the spectral changes are dominated by amine interactions with the solvents as shown by the linear correlation of the solvent donor number [131] with the IT band maxima and with the half-wave potential of the ruthenium amine moiety. 

Here, the half-wave potential for the electron transfer polarogram can be correlated with the fonnal potentials of the redox couples, [Fe(CN)6]3-/[Fe(CN)6] t in water and Fc+/Fc in NB. 

Figure 5 shows a typical cyclic voltammogram of l,4-bis(triphenylphosphonio)ben-zodiiodide in dmf it is characterized by a reversible couple followed by an irreversible reduction. The shift in half-wave potential with the substituent has been correlated with the energy of the Hiickel molecular orbital42. 

Table VI summarizes half-wave potentials of cathodic waves. These values are linearly dependent on the energies of lowest free 7r-molecular orbitals. The correlation is just about as close (Table IV) as those for analogous quantities with benzenoid and other hydrocarbons and derivatives of benzenoid hydrocarbons.

In a systematic polarographic investigation180 the half-wave potentials of a number of 1,2,4-thiadiazoles were determined and the results correlated with their structures. Measurements were made in neutral buffered solutions, the salt concentration being kept constant by the addition of lithium chloride. 

Calculated 7r- electron densities and orbital energies, obtained for chromone using a semi-empirical PPP method, were shown to correlate well with H NMR chemical shifts and polarographic half-wave potentials (78lJC(A)53l). 

As noted earlier, the polarographic half-wave potential Estandard redox potential of the couple because EVl is governed by kinetic as well as thermodynamic parameters, so that attempts to correlate EVl for irreversible couples with structural features of the complex have been very difficult to obtain. One moderately successful correlation, however, was obtained by Vlcek13 and by Crow14 for a fairly extensive series of complexes of Co111, Crm and Rhm. It was suggested that before reduction of the metal complex... 

More recently it has been found15 that a correlation exists between spectroscopic parameters of the divalent aqua ions of the metals Cr to Ni, and the polarographic y2. A linear relationship was found between A0 and crystal field splitting parameter, ot the transfer coefficient, n the number of electrons transferred in the reduction, EVl the polarographic half-wave potential and E° the standard electrode potential. The use of the crystal field splitting parameter would seem to be a more sensible parameter to use than the position of Amax for the main absorption band as the measured Amax may not be a true estimate of the relevant electronic transition. This arises because the symmetry of the complex is less than octahedral so that the main absorption band in octahedral symmetry is split into at least two components with the result that... 

The half-wave potentials for polarographic reduction of 2- and 3-substituted phenazines and phenazine-A -oxides follow a Hammett correlation only for the latter substituents,206 although independent investigations on phenazines afford a general correspondence.207-210... 

A satisfactory correlation of half-wave potentials for polarographic reduction of 2,5-diaryl-4-pyrones,221 as well as AA for the electronic absorption spectra maxima of 3-phenylazojulolidines (26) and their... 

Voltammetry studies on pyridine and pyridine derivatives have delineated some of the initial mechanistic steps of reduction.9-11 The half-wave potential was found to correlate with the n,n triplet energy.10 The mechanism of pyridine reduction in liquid ammonia was studied by Talcott among others this process was also studied on a synthetic scale.9,12 Evidence for an ECE... 

An effect of the ring-size in addition to that observed in the elimination taking place in the reduction of vicinal dibromides, has been observed for medium-sized ring compounds which carry the electro-active group either in the side-chain or directly attached to the ring. The half-wave potentials of cycloalkyl bromides can be correlated with the half-wave potentials of cyclic ketones and their derivatives (Fig. 29). The observed relation indicates that the relative effect of ring-size on the reactivity is similar in all the reaction series compared. 

If the course of the electrode process remains the same for the group R1 when it is bound on various molecular frames A, but the half-wave potentials of the compounds A — R1 depend on the kind of the molecular frame A, it is possible (7) to compare the half-wave potentials with an analogous reaction series of compounds A — R1, which carry a second electroactive group R2 on the varying frame A. If a correlation between... 

The radical path is most consistent with the existing experimental data. A correlation of half-wave potentials with Taft polar (a ) and steric (Es) constants 478)indicates that a parallel orientation of the C-X dipole with regard to the electrode suiface is most favourable for an electron transfer to the antibonding o orbital of the C-X bond. Thereby a radical anion 162) is formed 471 which rapidly dissociates to halide ion and radical. The more facile reduction of exo-2-... 

Though the validity of correlation of any homogeneous reaction kinetics with half wave potentials has been questioned 48°)j the nature of the cleavage products is most consistent with the radical mechanism. These products can be rationalized by the following scheme (Eq. (227) ) ... 

A one-electron reduction to a V111 species occurs as the first step in the electrochemical reduction of Cp2VIV complexes with a wide range of chelating ligands.448,449 A subsequent dissociation step which is markedly catalysed by oxygen occurs with some of the complexes with S donors this behaviour may be responsible for some deviations from reversible behaviour. Half-wave potentials for the first reduction step showed a reasonable correlation with the amount of charge available for donation... 

Substituent effects have been reported previously and work on this topic continues. The half wave potentials of a series of substituted benzyl chlorides and bromides gave excellent correlations with Hammett o- substituent constants48. The positive p values from these Hammett LFERs (p = 5.0 and 2.8, respectively for chlorides and bromides) suggest that the potential-determining electrochemical process involves the formation of radical anion intermediates. 

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