Ab initio study of electronic coupling in the aqueous Fe2+–Fe3+ electron exchange process

Abstract

Electronic Hamiltonian matrix elements between initial and final zeroth order states associated with electron exchange in the hexa-aquo Fe2+/Fe3+ redox system have been calculated in terms of self-consistent field (SCF) ab initio wave functions. The face-to-face and apex-to-apex approach geometries of the quasioctahedral reactants have been modeled, respectively, by the [Fe(H2O)3–Fe(H2O)3]5+ cluster (S6 symmetry) and the [Fe(H2O)–Fe(H2O)]5+ cluster (D2h symmetry). For the latter cluster, the Condon approximation has been tested and found to be accurate to within ∼1 cm−1 for the important range of inner-shell FeO distances. The calculations employ ab initio effective core potentials for inner-shell electrons and explicitly include all metal and ligand valence electrons. Due to weak 3d–3d overlap, the energy-preferred SCF solutions are charge localized (i.e., symmetry broken: S6→C3 and D2h→C2v). The present results for the interpenetrating face-to-face approach geometry are quite similar to earlier results based on a crystal-field model, implying an electronic transmission factor 〈κ〉 of ∼1/5 at the most probable reactive encounter separation (5.3 Å). The alternative apex-to-apex approach geometry is found to be less kinetically favorable. Attempts to fit calculated values of the electronic matrix elements to functions of the form Pn(r)rm exp(−αr) for the range r∼5–8 Å, where r is the Fe⋅⋅⋅Fe separation in Å and Pn(r) is a polynominal, yield values of α ranging from 0.8 to 2.4 Å−1, depending on the values of n and m, the orientation of reactants, and the model employed for the ligands. The calculated matrix elements are found to be rather insensitive with respect to variation of certain features of the SCF wave functions.