Reorganization energy calculated

Some difficulties in comparing the experimental kinetic data with the outer-sphere reorganization energy calculated from the Marcus formula (28) result from several assumptions made in this theory. The reactant was assumed to have a spherical shape with a symmetric charge distribution. No field penetration into the metal was considered. Also, the spatial dispersion of the dielectric permittivity of the medium was not taken into account. In fact, the positions and orientations of dipoles around a given ion are correlated with each other therefore the reorientation of one dipole, under the influence of the external field, changes to some extent the reorientation of other dipoles within the distance defined by the correlation length. 

The T2 center is solvent accessible as it is involved in nitrite binding, reduction, protonation, and product release via a 1.3-nm deep hydrophobic channel (84). In contrast, the T1 center is buried inside the protein, 0.6 nm below the Connolly surface of the molecule and isolated from solvent. Nonetheless, the reorganization energy calculated for the T2 copper center is still below values quoted in the literature for low molecular weight copper complexes For Cu(phen)2 " (phen = 1,10-phenanthroline), for example, the reorganization energy has been determined to be 2.4 eV (91). 

Figure 9.6. Linear correlation between the outer-sphere reorganization energy, calculated by finite-difference solution of the Poisson-Boltzmann equation, and the inverse of the donor-acceptor distance in PCI-Am (X = CHj, R = Am) complex in acetonitrile. (Reproduced from [239] with permission. Copyright (1997) by the American Chemical Society.)...

In addition to these interactions, one must take into account that reorganization of the solvent molecules requires the expenditure of some energy Calculations show that this energy for water has values of -60 to -120kJ/mol. 

The reorganization energy of the slow polarization for the reactions at metal electrodes can be calculated with the use of Eqs. (34.11). For a spherical model of the reacting ion, it is equal approximately to... 

Let us concentrate on the thermochemical cycle of figure 5.6 that involves the disruption of the complex Cr(CO)3(C6H6). The enthalpy of this reaction, previously calculated as 497.9 10.3 kJ mol-1 from standard enthalpy of formation data, can be related (equation 5.24) to the bond enthalpy contributions EsfCr-CO ) andE s(Cr (V.He) through the reorganization energies ER(C() ) and ER(C(tHf )- Two asterisks indicate that the fragment has the same structure as... 

For a less reactive molecule like PBN, a Marcus calculation using a reorganization energy of 40kcalmor1 gives k = 104dm3mols 1 for the reaction with DBPO in acetonitrile at 25°C, just to select a solvent which does not cause complications from the consideration of electrostatic terms. Clearly this is of a similar order of magnitude as the rate constants determined in benzene. 

Figure 5. Mean band energy (E) vs. total reorganization energy [Eq. (18)]. The dashed curve is the equation, E = Et. The solid curves are calculated from an analytical expression (9). The solid dots are calculated from a diagonalization of the two-mode model secular determinant with c = —6.0, Ac, = 1.1, and vc, =...

In the high temperature limit where all the nuclear motions coupled to the process can be described classically, the nuclear factor is expressed in terms of only two parameters the driving force of the reaction AG°, and the whole reorganization energy X (expressions (13) and (14)). Detailed calculations carried out in the case of cytochrome c have demonstrated that AG° is a complex quantity, which depends not only on the electronic properties of the redox centers but also on those of the protein and of the surrounding solvent [100]. Usually, AG can be evaluated from measurements of redox potentials and of eventual interaction energies between the different parts of the systems (Appendix). 

Another important result that was obtained recently concerns the evaluation of the contribution to the reorganization energy arising from the polarization of the medium, protein and solvent from a microscopic model including the residual charges and induced dipoles of the protein as well as bound water molecules, a value of about 0.2 eV was calculated for different eleetron transfer processes [97], This weak value results from the apolar character of the medium, and is compatible with the kinetic data which indicate that reorganization energies are small in the reaction center (Sect. 3.2.2)... 

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