Activation free energy Marcus theory

One of the most fundamental achievements of the seminal Marcus theory on electron-transfer reactions is the nowadays widely used quadratic driving force-activation free energy Marcus relationship... 

The basic assumption of Marcus theory is that the solvent free energy functions controlling ET are paraboli with equal curvatures (linear response). On the basis of this, making an assumption about the structure of the interface, and using a continuum electrostatic expression for the activation free energy,Marcus derived expressions for the bimolecular rate constant of an ET at To date, the computational work in this area has focused... 

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... 

If the interaction between the donor and acceptor in the encounter pair (D. .. A) is weak (Scheme 4.2), the rate constant kET can be estimated by the Marcus theory. This theory predicts a quadratic dependence of the activation free energy AG versus AG° (standard free energy of the reaction). 

The reorganization energy of a self-exchange reaction is denoted A(0) (from the fact that AG° = 0) and is an important quantity in the Marcus theory, where it can be shown that the activation free energy of a self-exchange reaction, AG(0), is equal to X.(0)/4. It is also possible to measure rate constants of self-exchange processes experimentally and thus get access to (0) via this relationship. 

Early theories of electron transfer attempted to give a theoretical foundation to the phenomenological rate expression (Eq. 15) and the constants A, a, and o. A brief summary of the history and references to recent reviews have recently been given by Marcus. " Marcus theory has been able to derive an expression similar to Eq. (15), in which the relationship between the activation free energy and the reaction free energy is given in terms of a new quantity called the reorganization free... 

In Marcus original formulation of ET theory, the free energy curves Gj and Gj are assumed to be quadratic in x (linear response approximation). Using this assumption, Marcus derives the relationship between the activation free energy and the reaction free energy... 

The main terms contributing to the free energy of activation in the Marcus theory are... 

The activation free energy AG is dehned by two terms. One term is the reaction free energy [AG ], which is derived from the redox potential difference of the donor and acceptor. The second term is the medium reorganization energy (k), which is the energy stored in the solvent inertial degrees of freedom when the electron is shifted suddenly from donor to acceptor (1-5). Marcus theory predicts the activation free energy ... 

According to Marcus theory [7, 8], the activation free energy (AG ) of outer-sphere electron transfers depends on the free energy (AGet) and the reorganization energy (A) as follows (Eq. 90). 

According to Marcus theory [69-71], in the absence of work terms, the Gibbs free energy of activation for an ET reaction is given by ... 

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