Particle transfer, intermolecular vibrations

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. 

The evaluation made in the preceding section shows the possibility of a natural explanation of the regulation of low-temperature solid-state reactions in a model accounting for barrier parameter oscillations resulting from intermolecular vibrations. A consistent analysis of such a model is required. A mathematical body used for this purpose is, conceptually, close to the common theory of nonradiative transitions, but unlike the latter it enables us to exceed the limits of the one-dimensional Franck-Condon approximation which is inapplicable in treatment of heavy-particle transfer. 

There are no K(T) computations for specific reactions with heavy-particle transfer at present. In ref. 174 it is only noted that experimental values of K(0) ( 10 s ) for the reaction R -1- CI2 -> RCl -l- Cl correspond to the reasonable values of barrier height (0.2 eV) and intermolecular vibration frequencies (2 x 10 s ) at Rq = 3 A. The higher X(0) values, compared to H-transfer reactions, are explained by the decreased barrier height due to higher exothermicity of the reaction. Another example of the heavy-particle quantum transition is discussed in Section 5. 

Hence, the double-proton transfer was assumed to proceed via a concerted mechanism, with the one-dimensional kinetic-energy matrix appropriate to one particle of twice the proton mass. A similar model is widely used to analyze the vibrations of cyclic hydrogen-bonded dimers (for example, see Ref. [59]). The O -O coordinate in this case symbolizes the intermolecular stretching of a doubly H-bonded system. The problem of the double-proton transfer for the benzoic acid dimer is thereby reduced to a problem conceptually similar to that for a single O -H -O entity except for the denoted light atom mass and consequences of the asymmetric 2D PES. 

Intermolecular forces involving sulfur hexafluoride molecules have been discussed in several papers (91, 121, 122, 194, 350, 296). Other studies include (a) molecular volume (254), (b) stopping of alpha particles (16,117), (c) transfer of energy by collision (205), (d) mutual diffusion of H2 and SF6 (291), (e) mutual solubilities of gases, including SF , in water (197), (f) salting out of dissolved gases (219), (g) compressibility (193) (h) Faraday effect (161), (i) adsorption on dry lyophilized proteins (14), (j) effect of pressure on electronic transitions (231), (k) thermal relaxation of vibrational states (232), (1) ultraviolet spectrum (295), (m) solubility in a liquid fluorocarbon (280). 

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