Failure of the Bornndash;Oppenheimer and Franckndash;Condon approximations for long distance electron transfer rate calculations

摘要

Quantum mechanical and semiclassical formulations of nonadiabatic electron transfer theory are usually implemented within a Bornndash;Oppenheimer regime. Calculations on real weakly interacting systems are so difficult that this approximation is rarely questioned. The Bornndash;Oppenheimer approximation becomes qualitatively wrong for electron transfers atverylarge distances. A model vibronic problem is exactly solved and compared with the Bornndash;Oppenheimer result. Rate expressions are derived from the wave functions using the lsquo;lsquo;golden rulersquo;rsquo; approximation. Electron propagation is intimately correlated to nuclear motion so that the vibrational energy left on the donor critically affects the electronic decay length. Several deviations from the usual predictions appear for transfers over very large distances.