Electron transfer rate constants, function free-energy change

Figure 6 Electron transfer rate constants as a function of free-energy change, AG, by radical anions for intermolecular ET in rigid 2-MTHF glass (top) (17), and intramolecular ET in 2-MTHF fluid at room temperature (bottom) (18), in molecules of the form ASB, where B = biphenyl, S = 3,16-androstane, and A is one of eight acceptor molecules shown. In both parts of the figure, the rate vs. AG ° curves are of equation 1 and have identical parameters except for the temperature and solvent reorganization energy.

First-order electron-transfer rate constant k > in acetonitrile as a function of the donor-acceptor distance R for a variety of the free energy change A O. 

Thus an explicit expression for the rate constants can be obtained. The above treatment, however, neglects changes in the bond distances and bond angles in the inner coordination shells of the reactants during electron transfer. Calculation of the free energy for this process requires a detailed knowledge of the potential energy for vibrational displacements, i.e., the force constants and displacements associated with vibrational modes. Inclusion of this factor adds to Aq a term, A,-, which is a function of force constants and vibrational displacements. 

Our problem now is to determine the functional form of this experimental free energy curve for the intrinsic rate constant ki for electron transfer. In addition to the Marcus eq 4, two other relationships are currently in use to relate the activation free energy to the free energy change in electron transfer reactions (15, JL6). 

Figure 3.3. Intramolecular rate constants in a 2-methyloxacyclopentane solution at 296 K, as a function of the free-energy change. The electron transfer occurs from biphenylanion to the eight different acceptor moieties (shown adjacent to the data points), in the eight bifunctional molecules of the general structure shown in the center. (From Ref. 82.)...

---