Reorganization Energy
In a mixed solvent, the solvent component with the larger permanent dipole moment or the larger polarizability is enriched around the charged solutes to lower the free energy of the system. We expect that the local solvent composition around the charged redox centers, instead of the bulk solvent composition, would have a dominant effect over the ET dynamics in mixed solvents. Here, we examine the connection between the solvent composition around the donor-acceptor complex and the solvent reorganization energy in Mixtures A, B, and C. The three mixtures have different relative permanent dipole moments and polarizabilities between the two components, and each represents a class of binary solvent mixtures. Using both the DSCFT and the MD simulations, we calculate the equilibrium solvent composition profiles around the redox centers, with results displayed in Figs. 6.1 and 6.2. In addition, the solvent reorganization energy as a function of the bulk solvent composition for the Fe2+/Fe3+ exchange reaction are computed using both methods, with results plotted in Fig. 6.3. Below, we discuss the connection between the local solvent composition and the reorganization energy in each of the three mixtures.
Mixture A can be described as permanent-dipole dominated, as water has a larger permanent dipole moment than MODEL-A while the two have equal polarizability.
The larger permanent dipole moment on water interacts more favorably with the the strong electric field around the multiply-charged solutes, causing water to be enriched around the charged species. In Figs. 6.1(a) and 6.2(a), both the DSCFT and the MD simulation predict that, in Mixture A at ϕ(w∞) = 0.35, the region around the redox
centers is predominantly water. The enrichment of water around the redox centers results in water dominating the solvent reorganization energy in Mixture A. As we observe in Fig. 6.3, both the DSCFT and the MD simulations predict that the solvent reorganization energy at intermediate compositions of Mixture A is approximately equal to that in the pure water.
Mixture B is a induced-dipole dominated mixture, as the two components have equal permanent dipole moments but MODEL-B has a much larger polarizability. As observed in Figs. 6.1(b) and 6.2(b), MODEL-B is enriched around the redox centers in this case, because its higher polarizability allows larger induced dipole moments to be developed in very strong electric field around the ions. We also find that the region where MODEL-B is enriched is more extensive around the Fe3+ than
the Fe2+, as the larger ionic charge on Fe3+ polarizes MODEL-B to a greater extent. Due to the enrichment of MODEL-B around the donor-acceptor complex, the solvent reorganization energy in Mixture B is predominantly determined by MODEL-B, as Fig. 6.3 shows that the solvent reorganization energy at intermediate compositions of Mixture B is comparable to that in the pure MODEL-B.
Mixture C represents a more interesting case, as MODEL-C has a larger polariz- ability but a smaller permanent dipole moment than water, resulting in permanent- and induced-dipole competition around the charged solute. In this case, both water and MODEL-C may be enriched around the redox centers. In Fig. 6.1(c), the DSCFT predicts that the region within approximately 2 ˚A from the ions is favored by the more polarizable MODEL-C, while water is favored in the region between 2 ˚A to 5 ˚A from the ions. Additionally, the MODEL-C-enriched region is larger around the Fe3+ than
around the Fe2+, suggesting that MODEL-C is more favorable around Fe3+. On the other hand, with explicit molecular structures taken into account, the MD simulation predicts that there is a region enriched with MODEL-C in the immediate vicinity of
0 0.2 0.4 0.6 0.8 1 50 60 70 80 90 100 110
Mole % water in the bulk solvent
λ [kcal/mol] Mixture A (DSCFT) Mixture B (DSCFT) Mixture C (DSCFT) Mixture A (MD) Mixture B (MD) Mixture C (MD)
Figure 6.3: The solvent reorganization energy vs. the bulk solvent composition as calculated by the DSCFT and the MD simulations.
Fe3+, but not around the Fe2+. Both the DSCFT and the MD simulations suggest
that, at equilibrium, the solvent compositions in the immediate vicinity of the donor and the acceptor are unequal. The spatial inhomogeneity in the solvent composition would lead to an additional contribution to the solvent reorganization energy beyond that contributed by the orientational polarization. As observed in Fig. 6.3, both the DSCFT and the MD simulations predict that the solvent reorganization energy in mixtures of water and MODEL-C are significantly greater than that in either of the pure solvents due to the additional compositional contribution.
6.4
Effects of Polarizability on Solvent Reorgani-
zation Energy
In comparing the solvent reorganization energies for Fe2+/Fe3+ exchange in pure wa-
ter and MODEL-B, we find that both the DSCFT and the MD simulations suggest that the reorganization energy is larger in the more polarizable MODEL-B (Fig. 6.3). This is in contrast to the prediction of the commonly-used Marcus theory for re-
organization energy, which predicts that the solvent reorganization decreases with increasing solvent polarizability.1 There are two competing effects at work when the polarizability increases: on one hand, a more polarizable solvent is able to respond to electronic transitions more easily, and thus reduces the free energy for reorgani- zation; on the other hand, a more polarizable solvent may also interacts with the charged solutes more favorably at the equilibrium state, which lowers the equilibrium free energy and results in a larger energy barrier for the ET process. In this case, the later outpowers the former because of the favorable nonlinear solvent-induced dipole interaction around the redox centers; this nonlinear solvent-solute interaction can be captured with MD simulations or the molecularly-based DSCFT, but not by a linear-dielectric description of solvent as in the Marcus theory.