Diabatic free energy model

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. 

It is desirable to bridge the gap between the general quantal expression for /cet given by Eqs, 35-37 with its explicit summation of vibronic contributions and the simplicity of the classical, harmonic model displayed in Eqs. 33 and 34. As one device for achieving this goal, we switch perspectives from the constrained diabatic free energies, Gi t]) and Gf t]), as in Eq. 22, to an auxiliary (unconstrained) free-energy function, G(t), based on the hybrid partition function Z(r) [36, 98] (cf., Eq. 18) ... 

Figure 18.6 Top Diabatic free-energy curves for Ag" /Ag in aqueous solution (red and blue, respectively) CP2K simulations (dots) and NGS model (dotted-dashed lines). Bottom Same for Cu /Cu using the CPMD simulations of ref. 32.

Diabatic free-energies for a model polarizable aromatic molecule in aqueous solution MD simulation results from ref. 31 (squares), NGS model (solid line), and Q-model of Matyushov and Voth (dashed line). 

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]... 

There is thus an inverse relationship between the ratio of the adiabatic and diabatic dipole-moment changes and the ratio of the corresponding free-energy differences within the two-state model. 

Figure 5.6 Demonstration of the correlation between the ground-state activation free energy (AG ) and the height of the intersection between free energy functionals of the diabatic surfaces in a two-state reaction model. If the curve Ajj which describes the free energy of the state Fj, is shifted relative to A92 as shown in the figure, the activation energy (i.e. the relative energy of the transition state 2-3) will increase by approximately AAG2-.3[ ,(X)]=Ap3(X) — A3j(X)-...

---