Surface diabatic free energy

Introducing the diabatic free energy surfaces of the initial and final states,... 

The inequalities in Eq. [75] also define the condition for the generating function (Eq. [23]) to be analytic in the integration contour in Eq. [25]. This condition is equivalent to the linear connection between the diabatic free energy surfaces, Eq. [24]. The Q model solution thus explicitly indicates that the linear relation between the diabatic free energy surfaces is equivalent to the condition of thermodynamic stability of the collective nuclear mode driving ET. 

The two-dimensional electron transfer diabatic free energy surfaces in Figure 7 have been analyzed with the Golden Rule rate expression given in Eq. 46. This analysis suggests that FT and EPT are possible for both systems, but FT is the dominant path due to significant overlap between the proton vibrational wave... 

Figure 8. Slices of the two-dimensional ET diabatic free energy surfaces along the reaction path indicated in Figure 7 for (a) DNOA and (b) DONA. The ET diabatic states are labeled according to the dominant VB states.

The diabatic free energy curves for the adsorption of and I near Pt(lOO) were calculated. is the energetically favorable species in solution, while the more stable species on the surface is I . The crossing between the two diabatic curves occurs at short distances, when the ion has already penetrated the adsorbed water layer. 

Figure 9.10. Diabatic free energy curves illustrating (a) photoinduced ET reaction and (b) back ET reaction in a ID solvation coordinate system. A resonant optical pulse brings a stationary nuclear wave packet from the ground potential surface to the donor surface, where it relaxes toward equilibrium with concomitant ET to the acceptor state.

Fig. 1. The Marcus parabolic free energy surfaces corresponding to the reactant electronic state of the system (DA) and to the product electronic state of the system (D A ) cross (become resonant) at the transition state. The curves which cross are computed with zero electronic tunneling interaction and are known as the diabatic curves, and include the Born-Oppenheimer potential energy of the molecular system plus the environmental polarization free energy as a function of the reaction coordinate. Due to the finite electronic coupling between the reactant and charge separated states, a fraction k l of the molecular systems passing through the transition state region will cross over onto the product surface this electronically controlled fraction k l thus enters directly as a factor into the electron transfer rate constant...

Free energy surfaces were constructed analogously to the diabatic case at fixed z using... 

In Fig. 22, the lower of the each of the two diabatic surfaces in shown. The free energy as a function of AF. at fixed z is close to parabolic for each surface (due to the approximately gaussian sampling of AE), and the curvature and... 

Figure 22. Free energy surfaces in the diabatic limit.

Figure 3.45 Schematic free energy curves in the solvent coordinate z for the discussion of the equilibrium solvation location of the Cl seam in Figure 3.42 Solid curves are the adiabatic curves for very small but finite electronic coupling, while the dashed curves are diabatic curves for zero coupling, (a) The symmetric case, where the filled circle represents the location of the minimum free energy in the upper adiabatic state in the presence of finite electronic coupling, while the open circle represents a free energy minimum when the electronic coupling vanishes exactly (6 = 90°). (b) An asymmetric case where the two surfaces intersect for z > 1 and the equilibrium location of the Cl seam fails.

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