Tunneling of heavy particles

C. Can Coherent Tunneling of Heavy Particles Be More Probable than That of Light Particles The Role of Proton—Phonon Coupling... 

Thus far the only known example of tunneling exchange of heavy particles is automerization of cyclobutadiene [Dewar et al. 1984 Carsky et al. 1988],... 

Muller first noted field desorption for layers of barium on tungsten (1). He concluded correctly that tunneling could hardly be responsible for the ionization of heavy particles and assumed that the potential curve for the ad-atom substrate complex was deformed to the point where activated desorption over the barrier could take place. This view was supported by the fact that he found that the field necessary for the desorption of thorium was quite temperature dependent, changing from the (remarkably low) value of 6.7 X 10 v./cm. at room temperature to 3.5 X 10 v./cm. at 1500°K (1). Similar results were found by him for barium... 

It should be noted that relation (2.51) is valid within the sudden approximation. However, the relaxation of heavy particle impurities typically involves motion that is slow compared with vibrations of the host lattice (i.e., the tunneling takes place in the adiabatic limit). The net effect of the adiabatic approximation is to renormalize the effective moment of inertia of the particle. This approach was used, for example, to describe vacancy diffusion in light metals. The evolution of the rate constant from Arrhenius behavior to the low-temperature plateau was described within the framework of one-dimensional tunneling of a... 

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]. 

Although the effects related to the proton tunneling and to the non-equilibrium nature of the coordinate of heavy particles are essentially quantum-mechanical, they noticeably differ in their mechanism. For this reason we prefer to retain the term "barrierless for processes in which the intermediate product stabilizes only due to a low proton tunneling probability from its ground state (in principle we could also include here the processes with a low electron transition probability), applying the term "quasibarrierless" to the second type of processes. 

When the mass of the tunneling particle is extremely small, it tunnels in the one-dimensional static barrier. With increasing mass, the contribution from the intermolecular vibrations also increases, and this leads to a weaker mass dependence of k, than that predicted by the onedimensional theory. That is why the strong isotope H/D effect is observed along with a weak k m) dependence for heavy transferred particles, as illustrated in fig. 18. It is this circumstance that makes the transfer of heavy reactants (with masses m < 20-30) possible. 

In some of the metal-insulator transitions discussed here the use of classical percolation theory has been used to describe the results. This will be valid if the carrier cannot tunnel through the potential barriers produced by the random internal field. This may be so for very heavy particles, such as dielectric or spin polarons. A review of percolation theory is given by Kirkpatrick (1973). One expects a conductivity behaving like... 

In a typical case, the barrier widths in heavy-particle tunneling reactions correspond to transfer distances that are much smaller than that for hydrogen transfer and are not usually realized at van der Waals interreactant spacings in solids. Therefore, chemical conversions associated with heavy-particle tunneling are rare, often occurring in exoergic reactions where d is much smaller than the geometric transfer distance. A few examples of these reactions are cited in Section 9.2. 

Unfortunately, the quantum-mechanical tunneling approach does not lead to any better understanding of why a should be temperature dependent in many reactions, if only for the reason that in most of the cases where such behavior is observed, the reactions involve heavy particles for which quantum effects are negligible. O2 reduction, however, could be quantally controlled if... 

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