Complex adiabatic energies, comparison

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

We note that additional approximations are not necessary to represent the equations of the adiabatic rate theory in a thermodynamic form (94.Ill) of Eyring s expression, as seen in a comparison with the exact equations (107.Ill) and (130.Ill), as well as with the approximate ones (135.Ill) and (138.Ill), which correspond to the high temperature limits of the former. There is, of course, an essential difference between the free energies of activation in Eyring s equation and the two kinds of formulations of the adiabatic theory this difference results from the varying definitions of the activated complex in each of these cases. 

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