Is it always correct to use the Marcus cross relation for calculations of electron self-exchange rates?

The rate constant of the electron self-exchange reaction, which proceeds via the outer sphere mechanism, k11, of a redox couple, reflects the basic tendency of the reaction to participate in redox processes. Often k11 is derived from the rate constant of a redox reaction, k12, by applying the Marcus cross relation: k12 = (k11k22K12f12)1/2W12. This derivation is based on the assumption that the products of the cross reaction are formed in their ground states. However, the k11 values obtained by this method for several redox systems, e.g. for [Co(NH3)6]3+/2+, Cu2+/+(aq) and Eu3+/2+(aq), depend strongly on the redox reaction studied for its derivation. It is proposed that these discrepancies are due to the formation, in some of these reactions, of products in vibrationally excited states and/or as isomers of the final products. Thus, the lowest value of k11 obtained experimentally is either correct or an upper limit for the correct value if correct k22 are used.

Graphical abstractThe rate constant of the electron self-exchange reaction, which proceeds via the outer sphere mechanism, k11, of a redox couple, reflects the basic tendency of the reaction to participate in redox processes. Often k11 is derived from the rate constant of a redox reaction, k12, by applying the Marcus cross relation. However, the k11 values obtained by this method for several redox systems, eg,: depend strongly on the redox reaction studied for its derivation.It is proposed that these discrepancies are due to the formation, in some of these reactions, of products in vibrationally excited states and/or as isomers of the final products. Thus, the lowest value of k11 obtained experimentally is either correct or an upper limit for the correct value if correct k22 are used.Figure optionsDownload full-size imageDownload as PowerPoint slide