Marcus microscopic model

It was recently shown (Ratner and Levine, 1980) that the Marcus cross-relation (62) can be derived rigorously for the case that / = 1 by a thermodynamic treatment without postulating any microscopic model of the activation process. The only assumptions made were (1) the activation process for each species is independent of its reaction partner, and (2) the activated states of the participating species (A, [A-], B and [B ]+) are the same for the self-exchange reactions and for the cross reaction. Note that the following assumptions need not be made (3) applicability of the Franck-Condon principle, (4) validity of the transition-state theory, (5) parabolic potential energy curves, (6) solvent as a dielectric continuum and (7) electron transfer is... 

To fill the above gaps, microscopic kinetic models must be employed, the Marcus-Hush model (MH) being the preferred choice. The MH model introduces the concept of reorganisation energy, A (eV), which corresponds to the energy required to distort the atomic configurations of the reactant molecule and its solvation shell to those of the product in its equilibrium configuration. Therefore, the A value has a clear connection with the properties of the system and it enables us a priori estimation of the reaction rate. 

The main feature is that the parabola in the exponential of the Marcus model electron, corresponding to transfer rate between the semiconductor surface and redox acceptor in the electrolyte, translates in curvatures. When V X, (155) reduces to the exponential dependence that was suggested above as a phenomenological approach. Furthermore, based on the microscopic model, the parameter / accepts the form (159) [16]. 

The theory for this intermolecular electron transfer reaction can be approached on a microscopic quantum mechanical level, as suggested above, based on a molecular orbital (filled and virtual) approach for both donor (solute) and acceptor (solvent) molecules. If the two sets of molecular orbitals can be in resonance and can physically overlap for a given cluster geometry, then the electron transfer is relatively efficient. In the cases discussed above, a barrier to electron transfer clearly exists, but the overall reaction in certainly exothermic. The barrier must be coupled to a nuclear motion and, thus, Franck-Condon factors for the electron transfer process must be small. This interaction should be modeled by Marcus inverted region electron transfer theory and is well described in the literature (Closs and Miller 1988 Kang et al. 1990 Kim and Hynes 1990a,b Marcus and Sutin 1985 McLendon 1988 Minaga et al. 1991 Sutin 1986). 

The parabolic form of the Marcus surfaces was obtained from a linear response theory applied to a dielectric continuum model, and we are now in a position to verify this form by using the microscopic definition (16.76) of the reaction coordinate, that is, by verifying that ln(P(A)), where P X) is defined by (16.77), is quadratic in A. Evaluating PIA) is relatively simple in systems where the initial and final charge distributions po and pi are well localized at the donor and acceptor sites so that /)o(r) = - a) + <7b <5(r - rs) and pi (r) = - fa) +... 

Unlike the original Marcus theory, which uses the continuum model for solvent, the method described above can provide a microscopic picture for the solvent fluctuation. It will be of great interest to explore the chemistry of the electron transfer reaction, including the specific dependence of the rate constant on the variety of solute and solvent. 

A detailed review of the spin-boson model can be found in [13]. In case of electron transfer in proteins, the spin-boson model can be related to a simple microscopic picture, namely, the well-known Marcus energy diagram[14, 15]. In this diagram, the free energy of both reactant and product states is described by a one-dimensional harmonic potential with identical force constants /. We assume the reactant and product free energy curves have the functional form. 

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