Tunneling generalized coordinate

In order to model glass properties and to discuss experimental observations, we need a model of tunneling systems. A schema of a TLS, and its potential along the generalized coordinate is presented in Fig. 1. Independently of the nature of this coordinate, which determines the mass m of the tuimeling particle, the TLS is characterized by the barrier width d (taken as the distance between minima in each well), the barrier height V, and the asymmetry A or energy difference between the wells. 

A general method for the calculation of the transition probability in the harmonic approximation developed in Ref. 44 enabled us to take into account, in a rigorous way, both the dependence of the tunneling of the quantum particles on the coordinates of other degrees of freedom of the system and the effects of the inertia and nonadiabaticity of the tunneling particle, taking into account the mixing of the normal coordinates of the system in the initial and... 

In 1983, Huskey and Schowen tested the coupled-motion hypothesis and showed it to be inadequate in its purest form to account for the results. If, however, tunneling along the reaction coordinate were included along with coupled motion, then not only was the exaltation of the secondary isotope effects explained but also several other unusual feamres of the data as well. Fig. 4 shows the model used and the results. The calculated equilibrium isotope effect for the NCMH model (the models employed are defined in Fig. 4) was 1.069 (this value fails to agree with the measured value of 1.13 because of the general simplicity of the model and particularly defects in the force field). If the coupled-motion hypothesis were correct, then sufficient coupling, as measured by the secondary/primary reaction-coordinate amplimde ratio should generate secondary isotope effects that... 

From the general formulae describing the kinetics of electron tunneling reactions it follows that with the constant value of the parameter ae the kinetic curves represent the function of the dimensionless parameter. t. Therefore, kinetic curves obtained at different temperatures with the coordinates concentration vs. log observation time must be just shifted with respect to the time axis. Consequently, the lack of temperature dependence... 

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