Double bath model

FIGURE 1.189 Double bath model, prepared to an electroplated construction... 

The interconversion of the two tautomer forms of dimers (Fig. 2) by a concerted two proton transfer is governed by a double-well potential. In condensed phases the two possible tautomers are identical. Skinner and Trommsdorff [21 ] treated a model of crystalline benzoic acids in which the dynamics of each proton pair is uncorrelated with other pairs. Their model was based on a single doubleminimum potential coupled to a thermal bath—that is, crystal vibrations. It was believed that in a condensed phase the crystal field breaks the symmetry of the two wells (Fig. 3). If Fig. 3 indeed represents the real situation when the proton transfer from the left well to the right one should take place at the participation of vibrations of the crystal that is, phonons of some sort should activate the proton transfer. We would like to emphasize that this is the conventional viewpoint, which is widely employed by physicists. 

In Ref. 21 it was also considered the model of two interacting double wells coupled to a thermal bath. The problem was simplified by the consideration of two dimers separated by the dye molecule when the distance between the dimmers was about 1 nm. In this case the interaction Hamiltonian was... 

These requirements are usually only fulfilled by model Hamiltonians. Therefore, the number of systems which can be described by accurate path integral treatments is rather small. A relevant example has been the investigation of a double well system coupled linearly to a harmonic bath [23]. 

Recently, a QUAPI procedure was developed suitable for evaluating the full flux correlation function in the case of a one-dimensional quantum system coupled to a dissipative harmonic bath and applied to obtain accurate quantum mechanical reaction rates for a symmetric double well potential coupled to a generic environment. These calculations confirmed the ability of analytical approximations to provide a nearly quantitative picture of such processes in the activated regime, where the reaction rate displays a Kramers turnover as a function of solvent friction and quantum corrections are small or moderate, They also emphasized the significance of dynamical effects not captured in quantum transition state models, in particular under small dissipation conditions where imaginary time calculations can overestimate or even underestimate the reaction rate. These behaviors are summarized in Figure 7. 

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