Half-wave potentials energies

The ESR spectrum of the pyridazine radical anion, generated by the action of sodium or potassium, has been reported, and oxidation of 6-hydroxypyridazin-3(2//)-one with cerium(IV) sulfate in sulfuric acid results in an intense ESR spectrum (79TL2821). The self-diffusion coefficient and activation energy, the half-wave potential (-2.16 eV) magnetic susceptibility and room temperature fluorescence in-solution (Amax = 23 800cm life time 2.6 X 10 s) are reported. 

Dioxins aromaticity, 3, 945 deprotonation, 3, 972 electronic energy levels, 3, 946 electrophilic reactions, 3, 965 half-wave potential, 3, 968... 

NMR and, 3, 951 aromaticity, 3, 945 delocalization energy, 3, 959 deprotonation, 3, 972 disulfones reactions, 3, 970 double bond character, 3, 945 electronic energy levels, 3, 946 electrophilic reactions, 3, 965 electrophilic substitution, 3, 960 half-wave potential, 3, 968 NMR, 3, 952 H NMR, 3, 951 nucleophilic reactions, 3, 969 oxidation, 3, 967 oxides... 

For the reduction of metal complexes, the half-wave potential is shifted to more negative potentials (vs. the true metal ion), reflecting the additional energy required for the decomposition of the complex. Consider the reversible reduction of a hypothetical metal complex, MLp ... 

Gibbs transfer energy of an ion i from phase a to p AG g Gibbs energy for ion-solvent interaction in phase a A log P partition coefficient difference between two solvent systems A 0 Galvani potential difference between a and p phases Ag(pi/2 half-wave potential... 

Complexes [Ni(H)(diphosphine)2]+ can be prepared by two ways, either by reaction of [Ni11 (diphosphine)2]2+ with H2 in the presence of base, or by reaction of [Ni°(diphosphine)2] with NH4+. A linear free energy relationship exists between the half-wave potentials of the Ni /Ni" couples of different [Ni(diphosphine)2] complexes and the hydride donor ability of the corresponding [Ni(H)(diphosphine)2]+.2320 Several methods have been used to determine those hydride... 

There is on the other hand a great deal of evidence showing that the electrochemical reduction of 1,2-dihalides to olefins can occur via a concerted pathway, i.e., via a transition state (39) in which both carbon-halogen bonds are partially broken and the carbon-carbon double bond is partially formed. An important, indeed critical, point of evidence supporting the conclusion that reduction is concerted lies in the remarkable ease with which vicinal dihalides are reduced. For example, the half-wave potentials of ethyl bromide and 1,2-dibromoethane are -2.08 V and -1.52 V (vs. s.c.e.), respectively 15 >46) those of ethyl iodide and /J-chloroethyl iodide are -1.6 V and -0.9 V, respectively 47). These very large differences must reflect the lower energy of delocalized transition state 39 relative to the transition state for reduction of an alkyl monohalide. 

The direct access to the electrical-energetic properties of an ion-in-solution which polarography and related electro-analytical techniques seem to offer, has invited many attempts to interpret the results in terms of fundamental energetic quantities, such as ionization potentials and solvation enthalpies. An early and seminal analysis by Case etal., [16] was followed up by an extension of the theory to various aromatic cations by Kothe et al. [17]. They attempted the absolute calculation of the solvation enthalpies of cations, molecules, and anions of the triphenylmethyl series, and our Equations (4) and (6) are derived by implicit arguments closely related to theirs, but we have preferred not to follow their attempts at absolute calculations. Such calculations are inevitably beset by a lack of data (in this instance especially the ionization energies of the radicals) and by the need for approximations of various kinds. For example, Kothe et al., attempted to calculate the electrical contribution to the solvation enthalpy by Born s equation, applicable to an isolated spherical ion, uninhibited by the fact that they then combined it with half-wave potentials obtained for planar ions at high ionic strength. 

E = Faraday constant). The equilibrium potential E is dependent on the temperature and on the concentrations (activities) of the oxidized and reduced species of the reactants according to the Nemst equation (see Chapter 1). In practice, electroorganic conversions mostly are not simple reversible reactions. Often, they will include, for example, energy-rich intermediates, complicated reaction mechanisms, and irreversible steps. In this case, it is difficult to define E and it has only poor practical relevance. Then, a suitable value of the redox potential is used as a base for the design of an electroorganic synthesis. It can be estimated from measurements of the peak potential in cyclovoltammetry or of the half-wave potential in polarography (see Chapter 1). Usually, a common RE such as the calomel electrode is applied (see Sect. 2.5.1.6.1). Numerous literature data are available, for example, in [5b, 8, 9]. 

Thermodynamic reduction potentials of numerous aromatics were first measured by Hoijtink and van Schooten in 96% aqueous dioxane, using polarography [15, 16]. These fundamental works were decisive tests of the HMO theory, showing that the polarographic half-wave potentials vary linearly with the HMO energies of the lowest unoccupied molecular orbitals (LUMO) of the hydrocarbons [1]. Hoijtink etal. had already noticed that most aromatics can be further reduced to their respective dianions [17]. They proposed a... 

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. 

Conjugation with an electron-withdrawing group substantially lowers the energy of the lowest unoccupied molecular n-orbital, which results in less negative reduction potentials for the alkene system. The class of compounds is referred to as activated alkenes, Polarographic half-wave potentials for some activated alkenes in aprotic solvents are listed in Table 3.3... 

Almost all reactions of alkylidenecycloproparenes lead to opening of the cyclopropane ring. A notable exception to this is the reversible electrochemical reduction of237 and 240 which leads to the stablfe radical anions 396 and 397, with half-wave potentials of -2.32 and -1.93 V, respectively, and their oxidation to the quasi-stable radical cations 398 and 399 ( i/2(ox) = +0.68 and +0.81). The cations may be further oxidized to the corresponding very short-lived dications. In contrast, the photoelectron spectra of 237 and 240 reveal practically identical first-oxidation potentials of both compounds, which indicates that the difference in half-wave potentials for oxidation (in condensed phase) of 237 and 240 does not exist in the gas phase. This has been attributed to structure-specific solvation energies in the radical cations 398 and 399. °... 

This chapter gives a selected compilation of the standard and other characteristic (formal, half-wave) potentials, as well as a compilation of the constant of solubility and/or complex equilibria. Mostly, data obtained by electrochemical measurements are given. In the cases when reliable equilibrium potential values cannot be determined, the calculated values (calcd) for the most important reactions are presented. The data have been taken extensively from previous compilations [5-13] where the original reports can be found, as well as from handbooks [13-16], but only new research papers are cited. The constant of solubility and complex equilibria were taken from Refs 6-11,13,17-21. The oxidation states (OSs), ionization energies (IBs) (first, second, etc.), and electron affinities (EAs) of the elements and the... 

Comparison of Half-Wave Potential Increments and Singlet Emission Energies... 

The strength of metal ion solvation affects not only the half-wave potentials but also the rates of electrode reactions of metal ions. For the reduction of a given metal ion, the reaction rate tends to decrease with increasing strength of solvation. The linear relation in Fig. 8.5 was obtained for the reduction of a sodium ion AG°v(Na+) is the solvation energy of Na+ and ks is the standard rate constant at the formal potential [23 a].2 For alkali metal ions in the same solvent, the rate... 

Relation between the LUMO and the half-wave potential of the first reduction wave When an organic compound, Q, is reduced, it accepts an electron from the electrode to its lowest unoccupied molecular orbital (LUMO). Here, the energy of the LUMO of Q corresponds to its electron affinity (EA). If the energies of LUMO ( lu) for a series of analogous compounds are obtained by the molecular orbital method, there should be a relationship ... 

Fig. 8.14 Half-wave potentials of the first wave of various conjugated hydrocarbons in 96% dioxane-water and the calculated values of the energy of LUMO obtained by (a) Huckel s and (b) Wheland s approximation. Plotted from the data in Hoijink, G.J. Rec. Trait Chim. 1955, 74, 1525.

It is certain that, in the first reduction step in aprotic solvents, an electron is accepted by the LUMO of the organic compound. However, it was fortunate that this conclusion was deduced from studies that either ignored the influence of solvation energies or used the results in different solvents. Recently, Shalev and Evans [55] estimated the values of AG V(Q/Q ) for 22 substituted nitrobenzenes and nine quinones from the half-wave potentials measured by cyclic voltammetry. For quinones and some substituted nitrobenzenes, the values of AG V(Q/Q ) in a given solvent were almost independent of the EA values. Similar results had been observed for other aromatic hydrocarbons in AN (Section 8.3.2) [56]. If AG V(Q/ Q ) does not vary with EA, there should be a linear relation of unit slope between El/2 and EA. Shalev and Evans [55], moreover, obtained a near-linear relation between AG V(Q/Q ) and EA for some other substituted nitrobenzenes. Here again, the Ey2-EA relation should be linear, although the slope deviates from unity.8)... 

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. 

Like benzenoid hydrocarbons, pyridine-like heterocycles give well-developed two-electron waves on reduction at the dropping mercury electrode. The latter are polarographically much more reducible than the former. This can be explained easily in terms of the HMO theory It is assumed (cf. ref. 3) that the value of the half-wave potential is determined essentially by the energy of the lowest free 7r-molecular orbital (LFMO) of the compound to be reduced, and for models of hetero analogues this quantity is always lower than that for the parent hydrocarbons. Introduction of an additional heteroatom into the molecule leads to a further enhancement of the ease of polarographic reducibility.95 On the other hand, anodic oxidation of the heterocyclic compounds is so much more difficult in comparison with benzenoid hydrocarbons that they are not oxidizable under the usual polarographic conditions. An explanation in terms of the HMO theory is obvious. 

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.

A mathematical analysis of all four isomeric thiadiazoles by the simple molecular orbital method has provided molecular diagrams of the free base and conjugate acid of each thiadiazole, with electron densities, bond orders, and free valencies. On this basis, predictions have been made concerning the reactivities of the six non-equivalent carbon atoms, the basicities of the nitrogen atoms, and the delocalization energies in these molecules. The 5-position in free 1,2,4-thiadiazole should possess maximum reactivity in nucleophilic substitution reactions. The treatment also accounts for the order of the polarographic half-wave potentials and the position of the absorption maxima in the ultraviolet region of the spectra of 1,2,4- and 1,3,4-thiadiazoles.4... 

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). 

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