Tunneling Corrections Based on the Adiabatic Approximation

Multidimensional Tunneling Corrections Based on the Adiabatic Approximation 

The adiabatic separation between the reaction coordinate and all other F — 1 vibrational degrees of freedom means that quantum states in those modes are conserved through the reaction path. With this approximation, we can label the levels of the generalized transition states in terms of the one-dimensional vibrationally and rotationally adiabatic potentials 

The ground-state adiabatic potential is defined with a = 0, and only the vibrations contribute to the internal energy through zero-point energies in each mode to give 

The transmission coefficient is written in terms of the classical and quantum probabilities, Pq and Pq, respectively, for transmission through or above the adiabatic potential Va( , 

The probabilities for classical motion along the reaction coordinate within the adiabatic approximation are simply zero when the energy E is below the maximum of the vibrationally adiabatic potential for state a, and one for energies above the barrier i.e., 

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