Energy Barrier for Outer-sphere Electron Transfer Processes

go back to Main Page, Chemistry & More, Chemical & Physical concepts

Marcus Theory of Outer-Sphere Electron Transfer

The energy barrier of a Single Electron Transfer (SET) according to Marcus Theory is determined by:

      (ΔG0 + λ)^2
ΔG˜= –––––––––––
         4λ

Here the ΔG0 parameter is the energy difference between products and reactants in their equilibrium configuration (i.e. geometry and solvent cage), which is trivial to calculate with electronic structure (ES) programs like Gaussian, etc.

The other parameter (λ) is the reorganization energy of going from reactants to products without actually transferring the electron, and can also be determined easily for intermolecular (Outer-sphere) SETs. It is divided into two parts, nuclear reorganization and solvent reorganization.

Nuclear reorganization can be calculated with Gaussian (or any ES program) by calculating the energy cost of going from the reactants to the products geometry in gas phase.

Finally, solvent reorganization is the largest contributing factor to the energy barrier. It is equal to the energy cost of rearranging the solvent cage from the reactants (R) to the products (P).

This parameter involves 3 calculations, all using the same geometry:

1- Calculate the energy of P and store the solvent cage in the checkpoint file

input1.in

2- Calculate the energy of R using the solvent cage stored in the checkpoint file and skip the SCRF cycles

input2.in

3- Calculate the energy of R and let the SCRF cycles reach the equilibrium solvent cage.

input3.in

The solvent reorganization parameter is then the Energy difference between calculations 2 and 3. If the geometries and electronic structures are the same, then the only difference is in the solvent cages (i.e. the solvent reorganization energy).

DISCLAIMER:

This approximation considers that the distance between the fragments is greater than the radius of the solvent molecules affected around each fragment, which is why the calculations of λ(solvent) are carried out for both fragments separately. You are hereby warned.