Diabatic free energy profiles

The dynamical theory also provides a framework for the study of the diabatic free energy profiles as functions of the reaction coordinate required in the theory of non-adiabatic electron transfer reactions. We illustrate this new application by calculating the free energy profiles in solvents covering a wide range of polarity. 

The diabatic free energy profile for the electronic state D is defined by the equation... 

To illustrate this theory we calculate the diabatic free energy profiles F t)) and F t]) of a complex donor-acceptor solute in two solvents of different polarity. We also examine the dependence on the charge distribution of the 5 state. 

Fig. 1 The diabatic free energy profiles for NP and IP states, o ex-RISM results, dashed line 2nd order fitting profiles, solid line 4th order fitting profiles.

The diabatic free-energy profiles of the reactant and product states provide the microscopic equivalent of the Marcus parabolas.26,27 For example, in the case of the (Cl- + CH3-CI —> CICH3 + Cl-) Sn2 reaction, one obtains23 the results shown in Fig. 2. 

The diabatic free energy profiles of the reactant and product states provide the microscopic equivalent of the Marcus parabolas [29, 30]. 

The diabatic free energy profile obtained by the method is plotted in Figures 2.11. The most notable feature of the figures is that it is essentially parabolic with respect to the reaction coordinate. This is nothing but the manifestation of the central limiting theorem, and the results indicate that the response of solvent fluctuation to the electrostatic filed is linear. The behavior, however, is not trivial, because the free energy calculated via Eqs. (2.61) and (2.62) are inherently non-linear. 

The superscript d in the above equations refers to diabatic since the dia-batic basis set is used to define the electric field difference ASab- The corresponding free energy profile is obtained by projecting the nuclear polarization Vn on the direction of the solute field difference... 

Figure 1 Free energy profiles along the reaction coordinate (77) for the initial and final diabatic states, indicating the reorganization energy if), activation free energy (G ), and reaction driving force (—...

Some important free-energy relationships are presented in terms of the diabatic energy profiles G, and Gf in Figure 3. The vertical and horizontal shifts of the G/ profile relative to that for C, correspond, respectively, to the driving force of the ET process (—AG,y ) and the reorganization energy (z) of nuclear modes (shifts of equilibrium coordinate values). 

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