Marcus Theory - The Marcus Model

The Marcus Model

The consequence of an electron transfer is the rearrangement of charges, and this gravely influences the solvent environment. For the dipolar solvent molecules rearrange in the direction of the field of the charges (this is called orientation polarisation), and also the atoms and electrons in the solvent molecules are slightly displaced (atomic and electron polarization, respectively). It is this solvent polarization which determines the free energy of activation and thus the reaction rate.

Substitution, elimination and isomerization reactions differ from the outer sphere redox reaction not only in the structural changes outlined above, but also in the fact that the movements of the nuclei and the shift of charges (charge transfer, CT) on the reactions path take place in a continuous and concerted way: nuclear configurations and charge distribution are always “in equilibrium”. This is illustrated by the S_N2 substitution of the saponification of an alkyl halide where the rear side attack of the OH- ion pushes out a halide ion and where a transition state with a five-coordinated carbon atom must be visualized. The system of the reactants becomes coupled so tightly during the reaction that they form the activated complex as an integral entity. The solvent here has a minor effect.

By contrast, in outer sphere redox reactions the displacement of nuclei in the reactants are small, here the solvent has the dominant role. Donor-acceptor coupling is weak, both keep their identity during the reaction. Therefore the electron, being an elementary particle, can only “jump” as a whole (electron transfer, ET). If the electron jumps, the transfer is much faster than the movement of the large solvent molecules, with the consequence that the nuclear positions of the reaction partners and the solvent molecules are the same before and after the electron jump (Franck-Condon principle). The jump of the electron is governed by quantum mechanical rules, it is only possible if also the energy of the ET system does not change “during” the jump.

The arrangement of solvent molecules depends on the charge distribution on the reactants. If the solvent configuration must be the same before and after the jump and the energy may not change, then the solvent cannot be in the solvation state of the precursor nor in that of the successor complex as they are different, it has to be somewhere in between. For the self-exchange reaction for symmetry reasons an arrangement of the solvent molecules exactly in the middle of those of precursor and successor complex would meet the conditions. This means that the solvent arrangement with half of the electron on both donor and acceptor would be the correct environment for jumping. Also, in this state the energy of precursor and successor in their solvent environment would be the same.

However, the electron as an elementary particle cannot be divided, it resides either on the donor or the acceptor and arranges the solvent molecules accordingly in an equilibrium. The “transition state”, on the other hand, requires a solvent configuration which would result from the transfer of half an electron, which is impossible. This means that real charge distribution and required solvent polarization are not in an “equilibrium”. Yet it is possible that the solvent takes a configuration corresponding to the “transition state”, even if the electron sits on the donor or acceptor. This, however, requires energy. This energy may be provided by the thermal energy of the solvent and thermal fluctuations can produce the correct polarization state. Once this has been reached the electron can jump. The creation of the correct solvent arrangement and the electron jump are decoupled and do not happen in a synchronous process. Thus the energy of the transition state is mostly polarization energy of the solvent.