Fluctuational barrier preparation

The effect we will describe in this Section is physically similar to what in the past was called fluctuational barrier preparation , where proton transfer between two heavy atoms is facilitated by an oscillation that brings these heavy atoms closer so that it lowers the potential energy barrier (see Figure 1). 

So far we have taken the tunneling matrix element A0 to be independent of vibrational coordinates. In terms of our original model with extended tunneling coordinate Q, this assumption means that the vibrations asymmetrize the instantaneous potential V(Q, < , ) but do not modulate its height or width. This model does not describe the effect of vibration on tunneling (fluctuational barrier preparation) dealt with in Section 2.5. For example, consider the OH O fragment shown in Figure 1.2. The relative 0-0 distance is clearly the same in the initial and final states, and hence the 0-0 vibration cannot be considered linearly coupled to the reaction coordinate. Such a mode (call it qx) is not... 

Flynn and Stoneham [1970] were the first to suggest that diffusion of the light impurity atom is enhanced by symmetrically coupled vibrations. To incorporate this effect, which is called fluctuational barrier preparation, the authors have proposed to take into account the dependence of the tunneling matrix element on displacements of the heavy nuclei. This approach goes beyond the familiar Condon approximation. In this version of phonon-assisted tunneling, the phonon-dressed incoherent transitions are also induced by a suitable reduction in the barrier height via emission or absorption of phonons. 

Furthermore, there are some effects related to the interaction of the reactants with the medium. We shall first consider the effects of the fluctuational preparation of the potential barrier in non-adiabatic reactions. 

Fluctuational Preparation of the Barrier and Role Played by the Excited Vibrational States in the Born-Oppenheimer Approximation... 

In this case the preparation of the barrier is performed mainly by the quantum fluctuations of the tunneling particle in the transverse direction. Note that the width of the distribution here is l/ /2 of that in the distribution function for the coordinates qp. This is due to the fact that in this case the fluctuations of the particle are of quantum character and a coherent averaging of the resonance... 

Both minima of the enthalpy, while metastable, might have a relatively long lifetime, and a system prepared in one state (common black film or Newton black film) might remain in that state during the time of the experiment, if the potential barriers are sufficiently high. However, because of the thermal fluctuations, it is possible to have, for the same experimental conditions, a transition in a range of pressures, and this explains one of the experimental results of Exerowa et al.2... 

The current status of the models of fluctuational and deformational preparation of the chemical reaction barrier is discussed in the Section 3. Section 4 is dedicated to the quantitative description of H-atom transfer reactions. Section 5 describes heavy-particle transfer models for solids, conceptually linked with developing notions about the mechanism of low-temperature solid-state chemical reactions. Section 6 is dedicated to the macrokinetic peculiarities of solid-state reactions in the region of the rate constant low-temperature plateau, in particular to the emergence of non-thermal critical effects determined by the development of energetic chains. 

Participation of low-frequency intermolecular vibrations in the fluctuation preparation of the barrier changes principally the mechanism of temperature dependence K T) compared to the one-dimensional tunneling model. According to relation (5), to the Arrhenius relationship there corresponds the predominance of thermally activated over-the-barrier transitions over the tunneling ones, which is determined in the harmonic terms model (Figure 1) by the thermal occupation of the highest vibrational sublevels of the initial... 

At present, the model of solid-state chemical reactions suggested in the literature [48-50] has won certain recognition. McKinnon and Hurd [152] and Siebrand and co-workers [153] compare the mechanism of rate constant temperature dependence by the occupation of the highest vibrational sub-levels of the tunneling particle to that of fluctuation preparation of the barrier the latter Siebrand et al. is preferred. [153] particularly emphasize the experimental proof of the linear dependence of the rate constant logarithm on the temperature predicted by this model. The importance of an account for intermolecular vibrations in the problem of heavy-particle tunneling [48-50] is also noted elsewhere [103]. 

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