Free diabatic

One can see that the dressed potential energy matrix elements of Eq. (7.24) have the same form than the field-free diabatic potential energy matrix elements of Eq. (7.4). Thus, analytical expressions for the positions and energies of the minima of the dressed upper adiabatic PES and MECI can be obtained by replacing Ej by... 

FIGURE 35.2 Scheme of diabatic (solid line) and adiabatic (dashed line) free-energy curves for a simple electrochemical redox reaction Ox —> Red. 

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

Thus, to calculate the transition probability for the non-adiabatic reaction it is sufficient to know the diabatic free energy... 

Fig. 12.2. Free energy data for electron transfer between the protein cytochrome c and the small acceptor microperoxidase-8 (MP8), from recent simulations [47]. Top Gibbs free energy derivative versus the coupling parameter A. The data correspond to solvated cytochrome c the MP8 contribution is not shown (adapted from [47]) Bottom the Marcus diabatic free energy curves. The simulation data correspond to cyt c and MP8, infinitely separated in aqueous solution. The curves intersect at 77 = 0, as they should. The reaction free energy is decomposed into a static and relaxation component, using the two steps shown by arrows a static, vertical step, then relaxation into the product state. All free energies in kcalmol-1. Adapted with permission from reference [88]...

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...

The adiabatic free energy curve can be calculated by umbrella sampling using the adiabatic Hamiltonian Hgj as discussed earlier. If the coupling r is constant (independent of nuclear positions), then it is possible to show that the adiabatic free energy curve can be obtained from the diabatic free energy curve according to... 

Figure 1 Left Enol-keto tautomerism in salicylaldimine (SA) and normal mode displacements for skeleton modes 1 4 and 1/30. Middle H/D diabatic potential energy curves Ua(Qu) for mode i/u (lowest states ground state, bolding and stretching fundamental, first bolding overtone arrows indicate laser excitation). Right two-dimensional (Qj4,Q3o) cuts through the adiabatic PES (obtained upon diagonalizing the field-free part of Eq. (1)) which has dominantly H/D stretching character but includes state and mode couplings (contours from 0 to 7400 cm-1).

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.

The free energies of the initial (i) and final (f) states, the so-called diabatic states in the ET process (discussed in more detail in Section 3.54, Reaction Field Hamiltonian, Electronic Structure models), are given by [28]... 

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