The density functional theory based ab initio molecular dynamics method combines electronic structure calculation and statistical mechanics and should, therefore, ideally be a tool for ``first principle'' computation of redox free energies in the sense that the redox active solutes and solvent are treated at the same level of theory. In this paper, we give a brief outline how such an approach call be implemented in the framework of the Marcus theory of electron transfer. The method is illustrated and validated using results of previous work. We then continue with a theoretical analysis of the correlation between the energies of one-electron states and redox potentials exploiting the separation in vertical ionization and reorganization contributions inherent in Marcus theory. Testing this relation on the limited set of reactions investigated sofar we find that it is satisfied within the uncertainties of the computation.