# Marcus Theory of Electron Transfer

The Marcus theory states that the probability that an electron will transfer from a donor to an acceptor during a transition state decreases with increasing distance between the donor and acceptor. Factors that control the rate constant of electron transfer (k_{et}) involved in a unimolecular electron transfer, in which the probability of transfer from a donor to an acceptor is identified by the term kT/h, include: the distance between donor-acceptor complex; the Gibbs energy of activation; and the reorganization of energy.

- The distance between the donor-acceptor complex (r) determines the probability of an electron transferring and is the general concept of Marcus theory of electron transfer.
- The Gibbs energy of activation (ΔG) is determined by the standard reaction Gibbs energy (ΔG°) and the reorganization energy (λ).
- The reorganization energy (λ) is an energy change resulting from the molecular rearrangement that occurs as the charge is distributed throughout the donor- acceptor complex in the medium.

The expression of the rate constant for electron transfer is given below:

\[k = e^{-\alpha r} \cdot e^{- \alpha \Delta G/RT}\]

where

- r = distance between donor and acceptor
- T = constant (temperature)
- α is a constant dependent on the medium through which the electron must travel between the donor and acceptor.

\[\Delta G = \frac{(\Delta G° + \lambda)^2}{ 4\lambda}\]

### References

- Atkins, Peter and de Paula, Julio. New York (NY): W.H. Freeman and Company. p.323-325

### Contributors

- Salvador Corral