Tunneling in Three Center Collinear Reactions

Tunneling in VTST is handled just like tunneling in TST by multiplying the rate constant by k. The initial tunneling problem in the kinetics was the gas phase reaction H -(- H2 = H2 + H, as well as its isotopic variants with H replaced by D and/or T. For the collinear reaction, the quantum mechanical problem involves the two coordinates x and y introduced in the preceding section. The quantum kinetic energy operator (for a particle with mass fi) is just 

The potential energy is illustrated in Fig. 6.3a. While one can in principal calculate the exact quantum mechanical Born-Oppenheimer surface, the figure presents a semi-empirical surface constructed to yield the exact spectral properties of reactants and products and the correct activation energy (taken as the difference in energy between the energy (potential) in the reactant valley (x = oo) and the maximum of the MEP (minimum energy pathway).) 

6 Kinetic Isotope Effects Continued Variational Transition State Theory and Tunneling 

Because of the success of the Marcus-Coltrin tunneling path for H + H2, the same procedure was applied to other collinear three center reactions including 

Here it was found that the tunneling factor k is very close to unity. However this result is uncertain because the magnitude of k is sensitive to the choice of the potential energy surface which is not as well established for reaction 6.20 as it is for 6.6. For that matter, learning whether a given reaction rate is significantly influenced by tunneling either on the basis of theory or experiment is not a trivial problem as will be pointed out in further discussion. 

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