Reorganization free energy

Studies of ferredoxin [152] and a photosynthetic reaction center [151] have analyzed further the protein s dielectric response to electron transfer, and the protein s role in reducing the reorganization free energy so as to accelerate electron transfer [152], Different force fields were compared, including a polarizable and a non-polarizable force field [151]. One very recent study considered the effect of point mutations on the redox potential of the protein azurin [56]. Structural relaxation along the simulated reaction pathway was analyzed in detail. Similar to the Cyt c study above, several slow relaxation channels were found, which limited the ability to obtain very precise free energy estimates. Only semiquantitative values were... 

As with the Marcus-Hush model of outer-sphere electron transfers, the activation free energy, AG, is a quadratic function of the free energy of the reaction, AG°, as depicted by equation (7), where the intrinsic barrier free energy (equation 8) is the sum of two contributions. One involves the solvent reorganization free energy, 2q, as in the Marcus-Hush model of outer-sphere electron transfer. The other, which represents the contribution of bond breaking, is one-fourth of the bond dissociation energy (BDE). This approach is... 

The reorganization free energy /.R represents the electronic-vibrational coupling, ( and y are fractions of the overpotential r] and of the bias voltage bias at the site of the redox center, e is the elementary charge, kB the Boltzmann constant, and coeff a characteristic nuclear vibration frequency, k and p represent, respectively, the microscopic transmission coefficient and the density of electronic levels in the metal leads, which are assumed to be identical for both the reduction and the oxidation of the intermediate redox group. Tmax and r max are the current and the overvoltage at the maximum. 

The main utility of recent molecular dynamics calculations has been first to determine if the assumption of quadratic free energy curves holds and second, to calculate the reorganization free energy in order to test Eqs. (24) and (25). In principle, a molecular dynamic simulation of the free... 

The main shortcoming of the molecular dynamics approach discussed in the previous section is that it ignores the fact that an electron transfer at the solution/metal interface occurs between an ion in a well-defined electronic state and a continuum of electronic states in the metal. For example, depending on the ion s orbital energy, the reorganization free energy and the overpotential, the electron could be transferred from, or to, any level around the Fermi level of the metal. Therefore, a sum over all these possibilities must be performed. Analytical theories of electron transfer at the solution/metal interface recognized this issue very early on, and the reader is referred to many excellent expositions on this sub-... 

From the values of and Ao, 2 Table 2 and by using the Hush equations the reorganization free energy, k, and the free energy change, AG°, corresponding to the electron transfer processes were obtained. The values of these parameters are also included in Table 2. 

Figure 7. A schematic representation of the solvent free energy functions involved in charge transfer reactions in the condensed phase. Indicated are the reaction free energy and the reorganization free energy defined in equations (22) and (27). The activation free energy and the photo absorption energy hco discussed below are also indicated.

I. Benjamin and Y. I. Kharkats, Reorganization free energy for electron transfer reactions at liquid/liquid interfaces, Electrochimica Acta, in press (1998). 

In addition to the driving force or overpotential, the activation free energy contains the nuclear reorganization free energy, r, addressed further in Section 2.2.2. 

We address briefly the two central quantities, the nuclear reorganization free energy and the electronic turmeling factor. 

The molecular redox level, say the oxidized, electronically empty level at electrochemical equilibrium, is located well above the substrate Fermi energy, that is, by the reorganization free energy r. Figure 2.3 shows explicitly the configuration for positive bias voltage, so that the tip Fermi level is located below the substrate Fermi level. 

An expression for the reorganization free energy can be derived within the classical framework. This free-energy expression which should be compared with the potential-energy expression [Eq. (f) 12.2.3.2. l]j, is ... 

The dependence of the reorganization free energy on the free-energy change for the electron transfer can be obtained by differentiating Eq. (a) ... 

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