Approximate Equations of the Adiabatic Theory

The equivalent equations (106,III) and (124.Ill), based on the accurate adiabatic rate expression (103.Ill), involve through the corresponding actors the transition probabilities, presumed 

It is of particular interest to consider the situation in which the condition (82,111) of vibrational-rotational adiabaticity is really fulfilled throughout the reaction. Then, the reaction probabilities obey the conditions 

The conditions (133.HI) mean that the tunneling through the adiabatic potential barriers (99.HI) is neglected however, the non-adiabatic transitions from a lower to a higher electronic state are not excluded. The reflexion effects due to the reaction path curvature may be simply included in the dynamical definition (121.11) of the reaction coordinate. An adiabatic separation of that coordinate may be also used as an approximation at these conditions. Then, the transmission coefficient — 1 takes into account only sudden changes 

The semiclassical expressions (134.III) and (137.III) are equivalent since they are derived from the equivalent rate equations (106. Ill) and (124.Ill), respectively, using the same conditions (133.III). Consequently, there exists the relation 

The situation in a classical treatment of the reaction coordinate and a quantum-mechanical treatment of the non-reactive coordinates was first discussed in the framework of the adiabatic approximation by ELIASON and HIRSCHPELDER /10/. They derived in a more direct 

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