Molecular function electron transfer, Marcus theory

This section contains a brief review of the molecular version of Marcus theory, as developed by Warshel [81]. The free energy surface for an electron transfer reaction is shown schematically in Eigure 1, where R represents the reactants and A, P represents the products D and A , and the reaction coordinate X is the degree of polarization of the solvent. The subscript o for R and P denotes the equilibrium values of R and P, while P is the Eranck-Condon state on the P-surface. The activation free energy, AG, can be calculated from Marcus theory by Eq. (4). This relation is based on the assumption that the free energy is a parabolic function of the polarization coordinate. Eor self-exchange transfer reactions, we need only X to calculate AG, because AG° = 0. Moreover, we can write... 

The approach used to obtain the EVB free-energy functionals (the Ag of Equation (7)) has been originally developed in Ref. 25 in order to provide the microscopic equivalent of the Marcus theory for electron transfer (ET) reactions.38 This approach allows one to explore the validity of the Marcus formula and the underlying linear response approximation (LRA) on a microscopic molecular level.39 While this point is now widely accepted by the ET community,40 the validity of the EVB as perhaps the most general tool in microscopic LFER studies is less appreciated. This issue will be addressed below. 

The main result regarding the electron transfer rates evaluated is that for a spectral function consistent with molecular dynamics simulations the spin-boson model at physiological temperatures predicts transfer rates in close agreement with those predicted by the Marcus theory. However, at low temperatures deviations from the Marcus theory arise. The resulting low temperature rates are in qualitative agreement with observations. The spin-boson model explains, in particular, in a very simple and natural way the slow rise of transfer rates with decreasing temperature, as well as the asymmetric dependence of the redox energy. 

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