Adiabaticity, electron-transfer reactions

Schmickler W. 1986. A theory of adiabatic electron transfer reactions. J Electroanal Chem 204 31-43. 

When a reaction is adiabatic, the electron is transferred every time the system crosses the reaction hypersurface. In this case the preexponential factor is determined solely by the dynamics of the inner-and outer-sphere reorganization. Consequently the reaction rate is independent of the strength of the electronic interaction between the reactant and the metal. In particular, the reaction rate should be independent of the nature of the metal, which acts simply as an electron donor and acceptor. Almost by definition adiabatic electron-transfer reactions are expected to be fast. 

Figure 2.1 Parabolas representing (a) diabatic and (b) adiabatic electron transfer reactions...

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... 

Although the two-fold symmetry displayed by the reaction centre is striking, it is only a pseudo-symmetry, because differences in the amino aeid sequences of the L and M subunits result in small differences in the positions and relative orientations of equivalent cofactors on the two branehes, and in differences of the protein environment of equivalent cofactors. The root cause of the functional asymmetry that is observed when electron transfer is monitored is therefore asymmetry in the detailed structure of the cofactor protein system on the two branches. Assuming that the transmembrane electron transfer process can basically be described as a non-adiabatic electron transfer reaction according to the Marcus equation, this... 

Different solvents may exert different effects on the optimal distance of adiabatic electron-transfer reactions, due to a very strong influence on the AGJ versus d dependence. Therefore, the closest approach is not always optimal for the reaction rate and the effective distance may be strongly influenced by the structure of the solvent. 

The dynamical theory also provides a framework for the study of the diabatic free energy profiles as functions of the reaction coordinate required in the theory of non-adiabatic electron transfer reactions. We illustrate this new application by calculating the free energy profiles in solvents covering a wide range of polarity. 

In an adiabatic electron transfer reaction in aqueous solution the transfer coefficient k is 1 and e c lli ion frequency between two uncharged reactants is 10 M s (1). If other solvents are used, Z may increase in value because it depends on the time of the concerted rotations of solvent molecules. If k is smaller than 1 we speak of nonadiabatic reactions their theoretical treatment is difficult ang will not be attempted here (4). The free energy of activation (AG ) can be divided into four important parts ... 

In the diffusion transfer of heavier ions their motion is presumably classical, and the transfer is accomplished through classical overcoming the potential barrier by a system. A transition of this type is similar in some senses to the adiabatic electron transfer reaction but its calculation is more difficult. If the potential barrier separating initial and final states of a system is sufficiently narrow and high, then the process rate is low and does not violate the equilibrium distribution in coordinates and in velocities at the initial state. Such a situation can be expected in transfer of ions which are not too heavy (with the mass of the order or less than the solvent mass) in well structurized solvents at room temperature. 

Fig. 9.1. PES of the adiabatic electron transfer reaction of Eq. (9.4) in polar solvent obtained through superposition of the terms of the initial , and the final Ef states q is the reaction coordinate that includes the solvent reorganization). The process is shown schematically as a change in the polarization of the medium when passing from the equilibrium configuration (qf) of the initial state to the equilibrium configuration (qj) of the state with the transferred electron. The electron transfer occurs in the region q. When V.j. is small, there exists a probability for the reaction trajectory to cross the transition state region without leading to product formation (nonadiabatic reaction)...

If the overlaping of the donor and acceptor orbitals in the region and the corresponding split of the terms are considerable, then the electron transfer occurs in a thermal reaction by the adiabatic mechanism as a motion of the system over the lower energy surface in the transition state zone denoted in Fig. 9.1 by a dashed line. The activation energy of the adiabatic electron transfer reaction corresponds to the difference between the energy levels of the initial state and the saddle point (the top of the barrier). 

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

KoperMTM, Voth GA. 1998. A theory for adiabatic bond breaking electron transfer reactions at metal electrodes. Chem Phys Lett 282 100-106. 

Unlike the simplest outer-sphere electron transfer reactions where the electrons are the only quantum subsystem and only two types of transitions are possible (adiabatic and nonadiabatic ones), the situation for proton transfer reactions is more complicated. Three types of transitions may be considered here5 ... 

Reactions involving transfer of atoms and atomic groups represent a more complicated theoretical problem since they are often partially or entirely adiabatic and, in addition, a number of effects which are not very important in electron transfer reactions must be considered. These effects are ... 

Fig. 2 The molecular structure of I—III and the representation of the potential energy surfaces for adiabatic to nonadiabatic electron transfer reactions...

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

FIGURE 6.6 Potential energy diagram for the theory of electron transfer reactions. The activated complex is at S. For reasonably fast reactions, the reactant adheres to the lower curve and slithers into the product curve through the activated complex—that is, an adiabatic electron transfer occurs. 

As such, the thermal process in equation (60) proceeds via the same reactive intermediates (arising from an adiabatic electron transfer) as that observed in the photochemical processes in equations (57) and (58). The proposed electron-transfer activation for the thermal retropinacol reaction is further confirmed by the efficient cleavage of benzpinacol with tris-phenanthroline iron(III), which is a prototypical outer-sphere one-electron oxidant195 (equation 61). 

The extension of the same mechanistic reasoning to the corresponding thermal process (carried out in the dark) is not generally rigorous. Most commonly, the adiabatic electron-transfer step (kET) is significantly slower than the fast back electron transfer and follow-up reactions (fcf) described in Section 7, and the pseudo-steady-state concentration is too low for the ion-radical pair to be directly observed (equation 99). 

Fig. 5 Potential energy hypersurfaces as a function of the reaction coordinate for adiabatic (A, single-minimum potential B, double-minimum potential) and non-adiabatic (C) electron-transfer reactions.

Both the initial- and the final-state wavefunctions are stationary solutions of their respective Hamiltonians. A transition between these states must be effected by a perturbation, an interaction that is not accounted for in these Hamiltonians. In our case this is the electronic interaction between the reactant and the electrode. We assume that this interaction is so small that the transition probability can be calculated from first-order perturbation theory. This limits our treatment to nonadiabatic reactions, which is a severe restriction. At present there is no satisfactory, fully quantum-mechanical theory for adiabatic electrochemical electron-transfer reactions. 

Fe3+X6...Fe2+X6, which is the reactant of the outer-sphere electron transfer reaction mentioned above when X = Y. Clearly the ground state involves a symmetric linear combination of a state with the electron on the right (as written) and one with the electron on the left. Thus we could create the localized states by using the SCRF method to calculate the symmetric and antisymmetric stationary states and taking plus and minus linear combinations. This is reasonable but does not take account of the fact that the orbitals for non-transferred electrons should be optimized for the case where the transferred electron is localized (in contrast to which, the SCRF orbitals are all optimized for the delocalized adiabatic structure). The role of solvent-induced charge localization has also been studied for ionic dissociation reactions [109],... 

---