Redox potentials measure the free energy required to transfer a mol. species (ion) between two states of different total charge. In soln. a major contribution to the redox potential is the hydration free energy difference of the ion in the two oxidn. states which can in principle be computed from classical mol. dynamics (MD) simulation. However, for redox active transition metal ions reliable force fields are in general not available and one has to use quantum chem. methods which are capable of describing large solvent fluctuations. From this point of view Car-Parrinello MD (CPMD) combining 'on the fly' electronic structure calcn. with classical mol. dynamics of the ions is the method of choice for simulation of transition metal ions. In the last years we have been developing novel schemes for the computation of redox properties from first principles. In our approach reactant and product (i.e. the two oxidn. states of an ion) are described by two potential energy surfaces which differ by the no. of electrons. The transformation between the two surfaces can be enforced using geometrical constraints, thermodn. integration techniques or grand canonical methods. In addn. to redox potential the first two methods also yield free energy curves of oxidn. which can be used to test the predictions of Marcus theory of electron transfer. In the talk our computational methods will be explained and results presented for the half reactions Ag(I) -> Ag(II) and Ru(II) -> Ru(III) in aq. soln. and Ru(II) -> Ru(III) in a de-novo designed porphyrine-protein. [on SciFinder (R)]