Evaluation of Electronic Coupling in Transition-Metal Systems Using DFT: Application to the Hexa-Aquo Ferric-Ferrous Redox Couple

We present a density-functional theory (DFT) approach, with fractionally occupied orbitals, for studying the prototypical ferric-ferrous electron-transfer (ET) process in liquid water. We use a recently developed ab initio method to calculate the transfer integral (also named electronic-coupling or ET matrix element) between the solvated ions. The computed transfer integral is combined with previous ab initio values of the reorganization energy, within the framework of Marcus' theory, to estimate the rate of the electron self-exchange reaction. The self-interaction correction incorporated (through an appropriate treatment of the electronic correlation effects) into a Hubbard U extension to the DFT scheme leads to a theoretical value of the ET rate relatively close to an experimental estimate from kinetic measurements. The use of fractional occupation numbers (FON) turned out to be crucial for achieving convergence in most self-consistent calculations because of the open-shell d-multiplet electronic structure of each iron ion and the near degeneracy of the redox groups involved. We provide a theoretical justification for the FON approach, which allows a description of the chemical potential and orbital relaxation, and possible extension to other transition-metal redox systems. Accordingly, the methodology developed in this paper, which rests on a suitable combination of Hubbard U correction and a FON approach to DFT, seems to offer a fruitful approach for the quantitative description of ET reactions in biochemical systems.