Activationless .process

Figure 2. Theoretical prediction for the temperature dependence of the electron transfer rate for activated and for activationless processes. Solid lines are calculated for a continuum of vibrational modes dotted lines represent the single-mode approximation (6, 8). Upper curve AE, —2000 cm 1 P, 20 and S, 20. Lower curves AE, —800 cm"1 P, 8 and S, 20.

To end this section, it may be added that a temperature-dependent electronic factor reflecting temperature-induced conformational changes has been invoked to explain the significant deviation that is sometimes observed between calculated and measured rate temperature dependences of activationless processes [122, 167, 168]. 

Keeping the reaction coordinate increment x constant, the activation barrier first decreases as the free energy becomes more favorable, from (a) towards (b) when the reaction is activationless but as the products well sinks deeper, the point of intersection moves further to the side of the reactants, and the activation barrier rises again. The plot of the rate constant k derived from Eq. 1 against the reaction free energy AG° is then predicted to be bell-shaped, with a maximum corresponding to the activationless process. The falling part of the plot beyond the maximum is known as the M.I.R. 

A third and provisionally accepted explanation is that electron transfer can take place to vibrationally excited states of the products, i.e. nuclear tunnelling of the reactants to vibrationally excited states of the products takes place (Efrima and Bixon, 1974, 1976). The potential surfaces depicted in Fig. 10 show the rationale behind this mechanism. For AG° > — X (Fig. 10a) we have the normal situation with an activation barrier for electron transfer. At AG0 = —X (Fig. 106) the maximum rate for an activationless process has been reached, whereas for AG° < —X an activation barrier appears again (Fig. 10c, representing the inverted region). With electron transfer allowed to an excited vibrational level (dotted line in Fig. 10d) we have once again an activationless reaction proceeding at the maximum rate. For large molecules there is a... 

In a wide range of temperatures both processes occur significantly faster than the media relaxation (Fig. 3.18) and, therefore, the media around the intermediates (Bph) and QA exist in the conformationally nonequilibrium state (Likhtenshtein, 1996 and references therein). In such a condition, as was mentioned above, the energy gap AGt and the reorganization energy A for primary ET are small. Hence, this activationless process is controlled by the orbital overlap factor but not by the Franck-Condon. The linear plot of log kET and the logarithm of the attenuation parameter for superexchange processes (Yet) versus the distances between the donor and acceptor centers (Fig. 3.18) support independently this conclusion. 

Subsequently, Marcus extended his theory to electrochemical electron transfer reactions/ " However, the role played by the electron energy spectrum in the electrode in these works was not elaborated. All the calculations were performed for a simplified model, where the potential energy surfaces for different electronic states were replaced by two potential energy surfaces (one for the initial state and one for the final state). Further calculations have shown that such considerations do not enable us to explain the fact that the transfer coefficient, a, for electrochemical reactions takes values in the interval from 0 to 1. In particular, it does not enable us to explain the existence of barrierless and activationless process (see Chapter 3 by Krishtalik in this volume). 

Hale in 1968 calculated the limiting electric current for an electron transfer reaction associated with the activationless process. The degenerate Fermi gas model was used to describe the electrons in the metal. 

It follows from Eq. (74) that for a barrierless process ( = 1), the ratio of ortho- to para-hydrogen should be the equilibrium value but for the activationless process ( = 0) 5o-p = 3. For small values of y = the... 

The quantum mechanical theory leads to a number of conclusions in respect to the kinetics of electrochemical reactions, in particular to the hydrogen evolution reaction. These conclusions are, to a certain degree, opposite to those of the classical approach. Thus, the consistent incorporation of the electronic energy spectrum in the electrode in the theory leads to the conclusion that barrierless and activationless transitions should be observed under certain conditions. In the theories which consider transitions to only one electronic energy level (the Fermi level), the transition probability should increase, reach a maximum, and then decrease with decrease of the reaction free energy. Experiment shows the existence of the barrierless and activationless processes. 

Initially, in the theory of barrierless and activationless processes, it was postulated that the activation energy varies monotonically with the potential after has decreased all the way to zero, its increase was considered impossible. Corroboration of this monotony principle can be found when the energy spectrum of electrons in a metal is taken into account. 

The deduction as to the preferential participation of electrons from the Fermi level (or, to be more precise, from a band several kT wide near this level, as was first shown by Gerischer ) holds true only in the case of an ordinary discharge, but is quite different with respect to barrierless and activationless processes. 

Quantitative analysis has shown that n = 1 - a, where n is the population of the level making the greatest contribution to the process. For example, for a = 0.5, n = 0.5, which corresponds to the Fermi level. When a 1, n -> 0, i.e., the principal role is played by the excited levels whose population is negligible. Similarly, in the case of activationless processes, a 0, and 1, i.e., the contribution of the deep-lying, practically filled levels is predominant. The value of a is always anywhere between 0 and 1. 

A barrierless cathodic process involves an excited electronic state. In an activationless process, electrons from deep levels take part, i.e., as a result of the reaction s elementary act, a hole is formed at a level below the Fermi level. This state is known to be a nonequilibrium one or, in other words, is characterized by an excess of energy. Thus, a barrierless process involves an excited initial state, while an activationless process, an excited final state. This holds true even in the case where not only electronic, but also other, for example, vibrational degrees of freedom may be excited. 

Consider now some specific features of the kinetics of barrierless and activationless processes. At a constant potential and for invariant double-layer structure, the discharge rate varies directly with the discharging particle concentration. This, of course, applies to any discharge process, be it an ordinary, barrierless or activationless one. If, however, we make a comparison at a constant overpotential, rather than at a constant potential, the relations... 

The rate of activationless discharge varies directly with the surface concentration of the discharging particles, i.e. with their bulk concentration and exp -zi(fiF/RT) [this can be easily seen from Eq. (92) if a = 0 is substituted therein]. A characteristic feature of an activationless process is the appearance of a limiting current not associated with the slow rate of any preceding step. 

For = 1, i.e., in the case of a barrierless discharge, the slope of the anodic curve corresponds to 0.030 V, while with j3 = 1/2 (ordinary discharge), itcorrespondsto0.040V. Near the equilibrium potential, j3 = 1, hence, a =0. In fact, in the cathodic region, a limiting current is observed, just as would be expected in an activationless process. 

In RCs from R. viridis, Rb, spaeroides, Rb. capsulatus and Rhodospi-rillutn rubrum, the rate constant kq for Reaction (1) is approximately 5-10 s at 300K [2,9,11-14] and increases by a factor of 2 between 300K and 80K, indicating an activationless process [17-22]. In general, the elec-... 

A point which should be stressed is that excited-state reactions must be very fast on the conventional chemical time-scale, since they have to compete with the photophysical deactivation processes. In practice, excited-state reactions must be almost activationless processes. Therefore, the key to understanding excited-state reactivity is the identification of low-energy channels along the excited-state surface leading, perhaps via some surface crossing, to the potential energy minima of the ground-state products. 

The current view is that the electron-transfer event itself is a fast activationless process the barrier for the reaction stems from the necessity to adjust the orientation of the solvent dipoles around ions and the lengths of some bond in the inner-coordination shells prior to the transfer step. According to this view, which was due largely to Rudolph Marcus [3], for the solvent, and to Noel Hush [4], for the metal-Ugand bond lengths, there are no proper transition states in electron-transfer reactions, because the solvent molecules are not in equilibrium distribution with the charges of the oxidised and reduced species. 

When the energy barriers provided by internal motions are extremely low, the force constant for solvent interactions becomes significant and a large percentage of the interactions along the reaction coordinate is dne to solvent motions. Molecules spend a long time in the transition-state region and dynamic motions of solvent molecules can determine the kinetics. These are the solvent-driven reactions. The role of the dynamic effect of solvents can be excluded for the vast majority of ET reactions, which we will consider. Exceptions are the virtually activationless processes , i.e., cases where AG < 5 kJ mol In the limits... 

Unlike activationless processes, the processes corresponding to a = 1 (or 3=1) require a considerable activation energy. But in contrast to the relationships for an ordinary discharge, this activation energy is equal to the heat of an elementary act of the reaction, since the activation energy of the reverse process is zero . The potential diagram of the process does not contain the usual hump (activation barrier) for this reason, such processes are called barrierless[85]. ... 

Some authors[86,87] consider that the concept of barrierless processes was introduced by Despic and Bockris[84]. As a matter of fact, however, in this paper, which appeared somewhat later than our publication[85], the authors discuss only a tendency to an activationless process and not the reverse case of a barrierless process. 

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