Transmission Coefficient, k, for Homogeneous Redox Reactions

Newton determined the transmission coefficient, k, for the homogeneous electron transfer reaction between Fe (H20)6 and Fe (H20)6 redox couples in solution. The transmission coefficient was expressed in terms of the Landau-Zener ° probability factor, P12, i.e., 

The wave functions iI/a and iI/b were obtained from open-shell SCF calculations based on the 11-valence-electron Hamiltonian, using the face-to-face geometry and imposing Th symmetry on the atomic configuration of each inner-sphere complex and a common point characteristic of both reactants in the activated complex. 

The off-diagonal matrix element Hab was obtained from and iI/b Since if/A and iI/b are not constructed from a common set of orthonormal MOS, Hab was evaluated using the method of corresponding orbitals. In view of the orthogonality of if/a and iI/b, the proper coupling element designated below as Hab for the use in the golden rule and Landau-Zener expression is as follows  

Transition Probability of the Electron at the Electrode-Solution Interface 

In most theory concerning the electron transfer at the electrode-solution interface, the electronic transition probability is generally kept unevaluated or determined in terms of the WKB treatment. The WKB treatment is applicable for situations where the potential at the interface does vary fairly slowly. This situation is rare. Use of time dependent perturbation theory is needed to have a proper evaluation of the transition probability, Pr, of electrons at the interface. One attempt of calculation of electronic transition probability T E) from electrode Fermi level to an available redox ion, e.g., Fe (H20)e, state is given. 

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