Activationless reactions

FIGURE 14.3 Schematic potential energy-distance curves of reactants in (1) a normal, (2) a barrierless, (3) an activationless reaction, and (4) potential energy-distance curve for the products. 

Activationless and barrierless regions cannot be realized in all reactions. Often or 1 are in regions of potentials where measurements are impossible or extremely difficult (e.g., because of parallel reactions). The crossover to the barrierless region has been demonstrated experimentally for cathodic hydrogen and anodic chlorine evolution at certain electrodes. Clear-cut experimental evidence has not yet been obtained for limiting currents appearing as a result of an activationless reaction. 

It should be noted here that the high-temperature (kT > hv) forms of the expressions in these theories (40-43) and in others (48) predict that the rate will be proportional to 1//T for an activationless reaction (the exponential term containing the activation energy divided by kT will be unity). If taken at face value, these high-temperature (classical) expressions give an increase in rate of /3 =... 

Figure 4.14 Schematic representation of the classical activation energy AG for different reaction energies AE. (a) is the normal thermodynamic region, (b) is the activationless reaction and (c) is the iinverted> region...

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... 

Relations (18) and (19) are in good agreement with the experimental dependence (17). Such consideration of the activationless reactions is given elsewhere [31,33]. An example of the tunneling electrode reaction found in ref. 34 is the electrochemical desorption of hydrogen ... 

When AG° < A., the predictions of such an equation are in agreement with the deductions of the Hammond postulate. Indeed, for exergonic reactions, tends to zero when AG° —> — A, which corresponds to an activationless reaction. Conversely, for endergonic reactions, tends to unity when AG° —>X, which features a barrierless reaction. 

Bicout and Szabo [142] found that the effective sink approximation works very well for the case of biexponential relaxation. They neglected the memory effects, however, and used the mean rate constant for the fast stage instead of ki2(x ), which resulted in some discrepancies for the activationless reaction (see Fig. 9.14), where the decay is nonexponential even when the correlation function is exponential. Similar applications of the effective sink approximation can be found in the literature [311-315]. 

Under the latter condition, feet is proportional to (// ). The value of / depends on the overlap between the electronic wavefunctions of the donor and acceptor groups, which decreases exponentially with donor-acceptor distance. It should be noticed that the amount of electronic interaction required to promote photoinduced electron transfer is very small in a common chemical sense. In fact, by substituting reasonable numbers for the parameters in (2.26), it can be easily verified that, for an activationless reaction, / values of a few wavenumbers are sufficient to give rates in the sub-nanosecond time scale, while a few hundred wavenumbers may be sufficient to reach the limiting adiabatic regime (2.25). 

Various bimolecular reactions with a very wide range of rate constants from 10 ° to lO l/(mol S) occur in solution. Activationless reactions, in particular, the recombination of atoms, ions, and many radicals, occur very promptly. In liquid the rate of such processes is determined by the frequency of bimolecular encounters and depends on diffusion. 

Fast activationless reactions, such as recombination of atoms and radicals, of course, occur more slowly in liquid than in gas because they are limited by the rate of particle self-diffusion, and diffusion in liquid occurs more slowly than in gas. Therefore, it is of interest to compare slow reactions, which are not limited by diffusion in liquid, to those with rate constants A < 1 o l/(mol s) in the gas phase. As we will see further, the solvation effects and formation of molecular complexes influence strongly on the chemical reaction in liquid. Since solvation is absent ftom the gas phase, for the correct comparison we have to consider reactions in which at least one reactant is a nonpolar particle, for example, hydrocarbon. Reactions of radicals with nonpolar C—H bonds are most suitable for this comparison. The data on such... 

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