Multi-electron mechanisms

Among the factors determining low energy activation of elementary chemical steps are concerted and multi-electron mechanisms, mechanical stress on substrate and catalytic groups and optimum polarity of the active site cavity. 

Multi-electron mechanisms of redox reactions. Switching molecular devices... 

In real situations (Sections 3.1 and 3.5) sequential one-electron transfers precede the formation of electron-rich or electron deficient multi-electron catalytic complexes. Thus, such systems may be considered as devices for switching processes from the multistep one-electron mechanism to the multi-electron mechanism. 

Even though this section has been developed with the assumption that the electrode reaction is a one-step, one-electron process, many of the conclusions apply generally for chemically reversible multi-electron mechanisms. The nemstian limit is still described by (10.3.8) and Figure 10.3.2, but with a given by... 

Low Energy Activation in Each Step. In certain cases, the rules the better the thermodynamics of the step, the lower energy activation (Polanyi-Semenov, Bronsted equations, for example) are fulfilled. Among factors determining low energy activation of elementary chemical steps are concerted and multi-electron mechanisms, mechanical stress on substrate and catalytic groups, optimum polarity and electrostatic field in the active site cavity. 

When multi-electron atoms are combined to form a chemical bond they do not utilize all of their electrons. In general, one can separate the electrons of a given atom into inner-shell core electrons and the valence electrons which are available for chemical bonding. For example, the carbon atom has six electrons, two occupy the inner Is orbital, while the remaining four occupy the 2s and three 2p orbitals. These four can participate in the formation of chemical bonds. It is common practice in semi-empirical quantum mechanics to consider only the outer valence electrons and orbitals in the calculations and to replace the inner electrons + nuclear core with a screened nuclear charge. Thus, for carbon, we would only consider the 2s and 2p orbitals and the four electrons that occupy them and the +6 nuclear charge would be replaced with a +4 screened nuclear charge. 

Unfortunately, the Schrodinger equation for multi-electron atoms and, for that matter, all molecules cannot be solved exactly and does not lead to an analogous expression to Equation 4.5 for the quantised energy levels. Even for simple atoms such as sodium the number of interactions between the particles increases rapidly. Sodium contains 11 electrons and so the correct quantum mechanical description of the atom has to include 11 nucleus-electron interactions, 55 electron-electron repulsion interactions and the correct description of the kinetic energy of the nucleus and the electrons - a further 12 terms in the Hamiltonian. The analysis of many-electron atomic spectra is complicated and beyond the scope of this book, but it was one such analysis performed by Sir Norman Lockyer that led to the discovery of helium on the Sun before it was discovered on the Earth. 

Some cases are known in which Diels-Alder reactions of electron-deficient allenes and dienes compete with [2 + 2]-cycloadditions (see also Section 7.3.7) [12, 151, 335, 336]. Recently, a phosphane-catalyzed [4 + 2]-annulation starting from allenic ester 337 and N-tosylaldimines 338 was published [337]. However, the formation of the tetrahydropyridines 339 isolated in excellent yields is explained by a multi-step mechanism and only resembles a Diels-Alder reaction. 

Oxidation of Alcohols in a Direct Alcohol Fuel Cell The electrocatalytic oxidation of an alcohol (methanol, ethanol, etc.) in a direct alcohol fuel cell (DAFC) will avoid the presence of a heavy and bulky reformer, which is particularly convenient for applications to transportation and portable electronics. However, the reaction mechanism of alcohol oxidation is much more complicated, involving multi-electron transfer with many steps and reaction intermediates. As an example, the complete oxidation of methanol to carbon dioxide ... 

Electrocatalytic Reduction of Dioxygen The electrocatalytic reduction of oxygen is another multi-electron transfer reaction (four electrons are involved) with several steps and intermediate species [16]. A four-electron mechanism, leading to water, is in competition with a two-electron mechanism, giving hydrogen peroxide. The four-electron mechanism on a Pt electrode can be written as follows ... 

As an alternative to the classical mechanism shown in Scheme 29, a multi-step mechanism involving an electron donor-acceptor complex and a radical pair is shown in Scheme 30122. The distinction between the two mechanisms is difficult to make122-125. They can compete in forming the reaction products the idea that only one reaction pathway is operating, is an oversimplification. However, two relevant points cannot be disregarded ... 

It is evident that a single electron transfer photoproduct is transformed into a doubly reduced charge relay in two phase systems. The primary processes in the natural photosynthetic apparatus involve single electron transfer reactions that proceed in hydrophobic-hydrophilic cellular microenvironment. Thus, we suggest similar induced disproportionation mechanisms as possible routes for the formation of multi-electron charge relays, effective in the fixation of CO2 or N2. 

Recently we have attempted to pursue multi-electron fixation processes as models for N2 or CO2 fixation. In nature, the N2-fixation enzyme, nitrogenase, exhibits non-specificity properties, and acetylene competes for nitrogen as the fixation substrate (21). The fixation process of acetylene to methane and of nitrogen to ammonia (euqations 14 and 15) have several common features (i) both involve the cleavage of a triple bond (ii) the two reactions involve 6 electrons in the fixation mechanism. Thus, it seems that the photocleavage of acetylene to methane might offer a good model for development of -fixation cycles (22). 

Multi-electronic processes (like those consisting of two-electron transfers, EE mechanism) have been widely treated in the literature, both in their theoretical and applied aspects [4, 10, 56-68]. This high productivity measures in some way the great presence and relevance of these processes in many fields, and hence the importance of understanding them. 

In this section, the current-potential curves of multi-electron transfer electrode reactions (with special emphasis on the case of a two-electron transfer process or EE mechanism) are analyzed for CSCV and CV. As in the case of single and double pulse potential techniques (discussed in Sects. 3.3 and 4.4, respectively), the equidiffusivity of all electro-active species is assumed, which avoids the consideration of the influence of comproportionation/disproportionation kinetics on the current corresponding to reversible electron transfers. A general treatment is presented and particular situations corresponding to planar and nonplanar diffusion and microelectrodes are discussed later. 

Substituent Effects So reactive are the coordinatively unsaturated metallocenium cations that one would expect that introduction of substituents into the cyclopenta-dienyl rings would modulate catalytic activity. (11) If substituent effects could be understood, it should be possible to modify the catalyst system to produce polymers having predetermined properties. We suspect that the needed detailed understanding will be hard to achieve for two reasons. First, the polymerization involves a multi-step mechanism and substituents may affect different steps differently. Second, steric and electronic effects of substituents may act in concert or in opposition and they must therefore be disentangled. Table 1 shows the effect of structural changes... 

Research on multi-electron transfer reactions. These are different mechanisms from photovoltaics... 

Finally, it should be stressed that organic electron transfers only rarely occur as isolated steps because of the high chemical reactivity of odd-electron species. Normally, they are part of multi-step mechanisms together with other types of elementary reaction, such as bond forming and breaking. In organic electrochemistry a useful shorthand nomenclature for electrode mechanisms denotes electrochemical (= electron transfer) steps by E and chemical ones by C, and it is appropriate to use the same notation for homogeneous electron-transfer mechanisms too. Thus, an example of a very common mechanism would be the ECEC sequence illustrated below by the Ce(IV) oxidation of an alkylaromatic compound (14-17) (Baciocchi et al., 1976,... 

Peculiarities of the N2 molecule make it necessary to use special means of electron transfer to and inside the active center containing the substrate. The mechanism of the catalysis in protic surroundings, at least for dinitrogen reduction, presumably necessarily includes coupled one-electron transfer from an external electron donor and multi-electron transfer to the substrate coordinated in the polynuclear complex. The coupled electron transfer helps to activate and reduce the difficult substrate dinitrogen at ambient temperatures. 

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