Adiabatic electron-transfer reactions

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. 

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

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. 

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.

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. 

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],... 

In electron transfer reactions one studies the conversion of an electron state localized on A to one localized on B. One can also consider the relaxation of a charge localized state to the adiabatic delocalized state [366],... 

An important conclusion that can be drawn from the above discussion is that most outer-sphere electron transfer reactions of metal complexes are, at best, marginally adiabatic and that the reaction will rapidly become nonadiabatic with increasing separation of the reactants. In view of these considerations, eq 11 can be integrated to give (50)... 

Figure 13. Adiabatic free energy curves for the electron transfer reaction Fe + e" for...

The rates of electron-transfer reactions can be well predicted provided that the electron transfer is a type of adiabatic outer-sphere reaction and the free-energy change of electron transfer and the reorganization energy (X) associated with the electron transfer are known [1-7]. This means that electron-transfer reactions can be designed quantitatively based on the redox potentials and the reorganization energies of molecules involved in the electron-transfer reactions. 

We turn to the chemical behavior of cycloalkane holes. Several classes of reactions were observed for these holes (1) fast irreversible electron-transfer reactions with solutes that have low adiabatic IPs (ionization potentials) and vertical IPs (such as polycyclic aromatic molecules) (2) slow reversible electron-transfer reactions with solutes that have low adiabatic and high vertical IPs (3) fast proton-transfer reactions (4) slow proton-transfer reactions that occur through the formation of metastable complexes and (5) very slow reactions with high-IP, low-PA (proton affinity) solutes. 

The development of a consistent theory for a dissociative electron transfer is a recent challenge in the field of theoretical electrocatalysis. Progress in this field of electrochemistry has involved the use of an harmonic Morse curves [25] instead of harmonic approximations. Applying the principles of the theory of the activated complex to adiabatic dissociative electron transfer reactions, the work of Saveant resulted in the following expressions [24] for the Gibbs energy of activation... 

Fig. 9.16. Adiabatic free energy curves for the electron-transfer reaction for Fe +e-Fe2+ for an overpotential q and electronic coupling coefficient, r. (Reprinted from I. Benjamin and D. A. Rose, J. Chem. Phys. 100 3545, 1994 with permission of the American Institute of Physics.)...

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 use of the terms adiabatic and non-adiabatic in this way leads to a source of confusion. Normally, in describing surface-crossing processes, a process which remains on the same potential curve is called adiabatic and in that sense every net electron transfer reaction is an adiabatic process. Processes which involve a transition between different states as between the two different potential curves in Figure lb are usually called non-adiabatic. Such processes have some special features and will be returned to in a later section dealing with the inverted region and excited state decay. 

Normally, it is not possible to explore this domain experimentally using bimolecular electron transfer reactions. In the absence of an activational requirement, electron transfer becomes sufficiently facile that the reactions are partly or wholly diffusion-limited and kabs ta kD. The exception is for reactions which have a large non-adiabatic contribution so that ket = vcKA and if ve is sufficiently small, kobs = vcAa.73... 

The cuprous-cupric electron transfer reaction is believed to be the rate-limiting step in the process of stress corrosion cracking in some engineering environments [60], Experimental studies of the temperature dependence of this rate at a copper electrode were carried out at Argonne. Two remarkable conclusions arise from the study reviewed here [69] (1) Unlike our previous study of the ferrous-ferric reaction [44], we find the cuprous-cupric electron transfer reaction to be adiabatic, and (2) the free energy barrier to the cuprous cupric reaction is dominated in our interpretation by the energy required to approach the electrode and not, as in the ferrous-ferric case, by solvent rearrangement. 

The theory of electron transfer in chemical and biological systems has been discussed by Marcus and many other workers 74 84). Recently, Larson 8l) has discussed the theory of electron transfer in protein and polymer-metal complex structures on the basis of a model first proposed by Marcus. In biological systems, electrons are mediated between redox centers over large distances (1.5 to 3.0 nm). Under non-adiabatic conditions, as the two energy surfaces have little interaction (Fig. 5), the electron transfer reaction does not occur. If there is weak interaction between the two surfaces, a, and a2, the system tends to split into two continuous energy surfaces, A3 and A2, with a small gap A which corresponds to the electronic coupling matrix element. Under such conditions, electron transfer from reductant to oxidant may occur, with the probability (x) given by Eq. (10),... 

---