Self-exchange transitions

Note above that the GMH and adibatic formulations are equivalent in terms of building the CT free energy surfaces. The distinctions seen in Figure 15 may seem to contradict to this statement. The problem is resolved by noting that the requirement 0 imposed by the GMH formulation makes the diabatic energy gap nonzero for self-exchange transitions ... 

For self-exchange transitions, due to the relation 2mi2 = A/y, , one gets... 

The simplest electron transfer reactions are outer sphere. The Franck-Condon principle states that during an electronic transition, electronic motion is so rapid that the metal nuclei, the metal ligands, and solvent molecules do not have time to move. In a self-exchange example,... 

The NO/NO+ and NO/NO- self-exchange rates are quite slow (42). Therefore, the kinetics of nitric oxide electron transfer reactions are strongly affected by transition metal complexes, particularly by those that are labile and redox active which can serve to promote these reactions. Although iron is the most important metal target for nitric oxide in mammalian biology, other metal centers might also react with NO. For example, both cobalt (in the form of cobalamin) (43,44) and copper (in the form of different types of copper proteins) (45) have been identified as potential NO targets. In addition, a substantial fraction of the bacterial nitrite reductases (which catalyze reduction of NO2 to NO) are copper enzymes (46). The interactions of NO with such metal centers continue to be rich for further exploration. 

Rotzinger then evaluated and H t as a function of the distance between the two reactant metal centers. He used the Fuoss equation to calculate the ion-pairing equilibrium constant to form the precursor complex at these internuclear distances. Assembly of these data then allowed the calculation of the self-exchange rate constants as a function of the internuclear distance in the transition state, the maximum rate being taken as the actual rate. 

In the following sections the effect of pressure on different types of electron-transfer processes is discussed systematically. Some of our work in this area was reviewed as part of a special symposium devoted to the complementarity of various experimental techniques in the study of electron-transfer reactions (124). Swaddle and Tregloan recently reviewed electrode reactions of metal complexes in solution at high pressure (125). The main emphasis in this section is on some of the most recent work that we have been involved in, dealing with long-distance electron-transfer processes involving cytochrome c. However, by way of introduction, a short discussion on the effect of pressure on self-exchange (symmetrical) and nonsymmetrical electron-transfer reactions between transition metal complexes that have been reported in the literature, is presented. 

The qualitative elements of Marcus theory are readily demonstrated. For example, the process of transferring an electron between two metal ions, Fe2+ and Fe3 +, may be described schematically by Fig. 33 (Eberson, 1982 Albery and Kreevoy, 1978). The reaction may be separated into three discrete stages. In the first stage the solvation shell of both ions distorts so that the energy of the reacting species before electron transfer will be identical to that after electron transfer. For the self-exchange process this of course means that the solvation shell about Fe2+ and Fe3+ in the transition state must be the same if electron transfer is not to affect the energy of the system. In the second phase, at the transition state, the electron is transferred without... 

Because of the short timescale for the optical transition, solvent dipole orientations in the initially formed excited state are the same as in the ground state and there is no entropic change. For a self-exchange reaction, the contribution to AG is A0/4 as noted above. 

Using V = 100 cm-1 (0.012 eV) and X = 1 eV, which are reasonable parameters for a moderately rapid self-exchange reaction, t = l/ve = 6x 10 I4s (0.06ps). vet was calculated using the preexponential term in equation (30). This calculation suggests that for reactions at room temperature which are dominated by transitions near the intersection region, re < rn and the assumption that re xn is not justified. 

An important feature to emerge from the comparisons in Table 2 is that variations in the electronic coupling term play a relatively small role in dictating the magnitudes of self-exchange rate constants for outer-sphere reactions, at least for transition metal complexes. Even for reactions... 

By leaving all other terms constant one cannot expect accurate predictions of the self-exchange rates. However, the surprisingly good results (Table 10.2) indicate that the relative strain in the ground and transition states of the encounter complex is an important driving force for the electron transfer reactivity. 

For the latter reason atom or group transfer may sometimes also take place in outer-sphere processes, and it has even been suggested that atom transfer can be part of an outer-sphere mechanism, if only for the case of hydrogen atom transfer. Such a case is the Fe(II)—Fe(III) self-exchange reaction in water where hydrogen bonding between two ligands in the transition state [2] would... 

It was recently shown (Ratner and Levine, 1980) that the Marcus cross-relation (62) can be derived rigorously for the case that / = 1 by a thermodynamic treatment without postulating any microscopic model of the activation process. The only assumptions made were (1) the activation process for each species is independent of its reaction partner, and (2) the activated states of the participating species (A, [A-], B and [B ]+) are the same for the self-exchange reactions and for the cross reaction. Note that the following assumptions need not be made (3) applicability of the Franck-Condon principle, (4) validity of the transition-state theory, (5) parabolic potential energy curves, (6) solvent as a dielectric continuum and (7) electron transfer is... 

Figure 1. Potential energy as a function of reaction coordinate for a self-exchange reaction. AE, energy barrier for thermal electron transfer (weak coupling) AE2, energy of an intervalence transition which is possible for the system.

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