Probability of electron transfer

Any alteration in AG will thus affect the rate of the reaction. If AG is increased, the reaction rate will decrease. At equilibrium, the cathodic and anodic activation energies are equal (AG 0 = AG 0) and the probability of electron transfer is the... 

The physical picture of the transition is different here from that for nonadiabatic reaction. Equation (34.34) shows that the probability of electron transfer becomes equal to 1 when the acceptor energy level passes a small energy interval Ae 1/(2jiYlzP) near the Fermi level. However, unUke the nonadiabatic case,... 

This is called a chemical, radical or stepwise mechanism. Or was it (ii) by the action of the bridging group to increase the probability of electron transfer by tunneling, termed resonance transfer 56,9i... 

As mentioned in Section 3.4, clusters of metal atoms of varying sizes can be prepared. The presence of alkali atom clusters in the vapour phase is well documented. Such clusters have a much lower ionization energy than that of an isolated atom and also have a high electron affinity. The probability of electron transfer is therefore considerably greater in a metal cluster. It is indeed known in the case of caesium that as the density of caesium increases (from isolated atoms in a low-density gas to a liquid), larger clusters form and charge-transfer becomes increasingly favoured as the density... 

Returning to equation (38), in the limit that ve vn, Ke = 1 and vet = vn. Electron transfer reactions that fall into this domain where the probability of electron transfer is unity in the intersection region have been called adiabatic by Marcus. Reactions for which Kei < 1, have been called non-adiabatic . In the limit that ve 2vn and e = vjvn, the pre-exponential term for electron transfer is given by vet = ve. This was the limit assumed in the quantum mechanical treatment using time dependent perturbation theory. 

The probability of the atom ionization per unit of time is in proportion with the probability of electron transfer through the barrier created by the potential (5). Most probable is tunneling along the direction of the field so, to a first approximation, one-dimensional rather than three-dimensional considerations can be used (see Fig. 3)... 

The cross-section of electron transfer to a multiply charged ion can be calculated by solving a set of coupled equations which take into account the probability of electron transfer on to different levels. Such calculations are extremely tedious (for a review, see ref. 21). At the same time, the presence of transitions into a large number of states makes it possible to describe the charge transfer in terms of the formalism, based on the idea of electron tunneling from one potential well to another. Using such an approach, Chibisov [22] has obtained an analytical expression for the charge transfer cross-section. 

The basic kinetic characteristic of ordinary chemical reactions is their rate constant, k. However, to describe the kinetics of electron tunneling reactions in solid matrices, a parameter such as the rate constant is inconvenient since its magnitude changes with time. In the previous chapter it was shown that the kinetics of an electron tunneling reaction can usually be well described by approximating the dependence of the probability of electron transfer on the distance between the reagents, R, by the simple expression... 

At equilibrium, AGf = AG, as shown in Figure 2.15, where the probability of electron transfer is the same in each direction, -ib = if = i0, where i0 is the exchange current density. Under nonequilibrium conditions favoring the cathodic reaction (O —> R), AGf < AG by an amount of free energy given by -nF(E - E° ), where E° is the formal potential of the couple O/R. 

This direct oxidation generates itself a proton and is probably only a minor pathway under superacidic condition where, in the absence of the proton trap, protolysis of the C—H and C—C bond occurs very rapidly. The mechanism is most probably of electron transfer nature as suggested in Eq. (5.22) and (5.23)... 

The situation is different when donor and acceptor molecules are located at different interfaces, that are separated by a fatty acid monolayer of well defined thickness. There are no longer close pairs of donor and acceptor with a high probability of electron transfer as in the "contact" case. Consequently, no change in relative fluorescence intensity with increasing donor density is expected, contrary to the former case. Indeed, in systems with a spacer monolayer of... 

Finally, xel is the electronic transmission coefficient that accounts for the probability of electron transfer upon reaching the configuration of the transition state. Note that it has been assumed that the electronic interaction between the redox species and the energy levels in the electrode is independent of the energy of such level x, so the electronic and nuclear factors can be treated separately. 

Theory (1) The effective energy barrier between the two harmonic oscillators, AE (oo IT), which determines the probability of electron transfer along the conjugated chain decreases with increasing temperature thus, conductivity is semiconductor-like. (2) The spin susceptibility is due only to the unpaired Ji-electrons from TTF (all the 7i-electrons on TCNQ are in the paired state). Thus, the susceptibility is weak. (3) The spin-paired n-electrons on TCNQ resonate between the two harmonic oscillator states at frequency, . Such oscillation can perturb the g-factor of (TTF)+. As the increases with the temperature rise, the perturbation becomes greater, and the g-factor deviates more from that of the pure (TTF)+. 

One may see that in Eq. (2.18) O0/3> depends linearly on the concentration of the quencher, which is inconsistent with the experiment (see Fig. 2.15). Therefore, in further description of experimental data we use Eq. (2.19), which corresponds to the case when the recombination sites are not identical to the adsorption sites. In this case, A and Kads are the varied fitting parameters. Physical meaning of parameter A corresponds to the ratio between the probability of electron transfer to the quencher molecules and the total probability to disappear upon recombination. 

In the case of adiabatic electron transfer reactions, it is found that the potential energy profiles of the reactant and product sub-systems merge smoothly in the vicinity of the activated complex, due to the resonance stabilization of electrons in the activated complex. Resonance stabilization occurs because the electrons have sufficient time to explore all the available superposed states. The net result is the attainment of a steady, high, probability of electron transfer. By contrast, in the case of -> nonadiabatic (diabatic) electron transfer reactions, resonance stabilization of the activated complex does not occur to any great extent. The result is a transient, low, probability of electron transfer. Compared with the adiabatic case, the visualization of nonadiabatic electron transfer in terms of potential energy profiles is more complex, and may be achieved in several different ways. However, in the most widely used conceptualization, potential energy profiles of the reactant and product states... 

The long-wave bands of 182a and 183a (which are probably due, as in the azulenium ion,129 for example, to electron transfer from the phenyl group to the 1,2-dithiolium or tropylium ion) are very similar in position and maximum extinction they suffer bathochromic shifts of similar magnitudes when identical donor substituents such as OCHs or N(CHS)2 are introduced into the p-positions of the phenyl groups, with a consequent increase in the probability of electron transfer. 

The initial electron acceptor can be made to accumulate in the reduced state (I ) if reaction centers which have bound (or added) cytochromes are illuminated continuously after the reduction of [56,67-69]. Each time the radical-pair state P I is formed, has a brief opportunity to oxidize the cytochrome instead of recovering an electron from I. The probability of electron transfer from the cytochrome is low, because the back reactions between P and I are much faster than the cytochrome oxidation. After many turnovers, however, essentially all of the reaction centers may be left with I reduced, particularly if the return of electrons... 

The first conclusion which may be drawn from this elementary introduction is that a chemical bond between two atoms is only possible when the atoms or molecules concerned have approached as close as approximately io cm., since only at such distances is the probability of electronic transfer sufficiently great to produce bonding. The interaction energies fall off rapidly as the distance between the nuclei increases and from the point of view of chemical reaction, a distance between nuclei of lO cm may be regarded as infinite. 

One of the goals of current efforts in the field is to discriminate between possible ground-state isomers of inter- and of intramolecular adducts. The basic idea behind this effort is that the geometry of the molecular pair involved in the electron transfer may affect the probability of electron transfer. The work of several groups (Piuzzi, Levy, Itoh) showed that this is indeed the case several different spectroscopic series of lines were found for a given system, which were assigned to different structural isomers. As discussed in Section 4.2, the barrier to electron transfer appears to be different for different isomers. The task is to correlate the observed spectra with calculated structures. 

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