Pose a serious challenge to the experimentalist

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pose a serious challenge to the experimentalist; unless this is gone, the factors that determine the kinetic activation barrier for the electron-transfer step cannot be identified with certainty. The surfaces depicted in Figure 6.21 presume that the electrons remain lo- calized on the donor and acceptor; as long as this situation prevails, no electron transfer is possible. Thus some degree of electronic interaction, or coupling, is required if the redox system is to pass from the precursor to the successor com- plex. This coupling removes the degeneracy of the reactant and product states at the intersection of their respective zero-order surfaces (points S in Figure 6.21) and leads to a splitting in the region of the intersection of the reactant and product surfaces (Figure 6.22). If the degree of electronic interaction is suffi- ciently small, first-order perturbation theory can be used to obtain the energies of the new first-order surfaces, which do not cross. The splitting at the intersec- tion is equal to 2H AB , where H AB is the electronic-coupling matrix element. The magnitude of H AB determines the behavior of the reactants once the intersection region is reached. Two cases can be distinguished. First, H AB is very small; for these so-called "nonadiabatic" reactions, there is a high proba- bility that the reactants will "jump" to the upper first-order potential energy surface, leading to very little product formation. If the electronic interaction is sufficiently large, as it is for "adiabatic" reactions, the reactants will remain on the lower first-order potential energy surface upon passage through the transi- tion-state region. >- E R E R E R E R i'? Q) c Q) ca .~ Q) 0 0.. nuclear coordinate (A) (B) (C) Figure 6.22 Potential energy diagrams: (A) R AB = 0, K = ° (no transfer); (B) R AB small, K « 1 (nonadi- abatic transfer); (C) R AB large, K = 1 (adiabatic transfer). The arrows indicate the relative prob- ability of crossing to the product surface (E R to E p ).
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III. ELECTRON-TRANSFER THEORY 339 The tenn adiabatic (Greek: a-dia-bainein, not able to go through) is used in both thermodynamics and quantum mechanics, and the uses are analogous. In the former, it indicates that there is no heat flow in or out of the system. In the latter, it indicates that a change occurs such that the system makes no transition to other states. Hence, for an adiabatic reaction, the system remains on the same (i.e., lower) first-order electronic surface for the entire reaction. The probability of electron transfer occurring when the reactants reach the transition state is unity. The degree of adiabaticity of the reaction is given by a transmission coefficient, K, whose value ranges from zero to one. For systems whose H AB is sufficiently large (>kBT, where k B is the Boltzmann constant), K = l. This situation occurs when the reacting centers are close together, the orbital sym- metries are favorable, and no substantial changes in geometry are involved. The transmission coefficient is generally very small (K < 1) for electron-transfer re- actions of metalloproteins, owing to the long distances involved.
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