Nonadiabaticity Effects in Processes Involving Transfer of Atoms and Atomic Groups

Nonadiabaticity Effects in Processes Involving Transfer of Atoms and Atomic Groups 

The effects of deviations from the Born-Oppenheimer approximation (BOA) due to the interaction of the electron in the sub-barrier region with the local vibrations of the donor or the acceptor were considered for electron transfer processes in Ref. 68. It was shown that these effects are of importance for long-distance electron transfer since in this case the time when the electron is in the sub-barrier region may be long as compared to the period of the local vibration.68 A similar approach has been used in Ref. 65 to treat non-adiabatic effects in the sub-barrier region in atom transfer processes. However, nonadiabatic effects in the classically attainable region may also be of importance in atom transfer processes. In the harmonic approximation, when these effects are taken into account exactly, they manifest themselves in the noncoincidence of the 

According to Ref. 69, we consider potential energy surfaces of the type 

The original expression in Eq. (116) for the transition probability is transformed to the form 

The expressions for the density matrices p, and pf are written through the Feynman path integrals over x(t) and R(t).70 The path integral over x(t) can be calculated exactly for the arbitrary form of the functions /(R) and f/(R)- The path integrals over R(t) cannot, in general, be calculated exactly. However, taking into 

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