Comparison between static and adiabatic coupling mechanisms for nonradiative multiphonon transitions in semiclassical approximation I. Tunnelling at small relaxation

Abstract

Basic equations of the perturbational theory of nonradiative multiphonon transitions are reformulated in semiclassical approximation. They are specialized for the mechanisms of static (diabatic) and adiabatic coupling corresponding to the polar alternatives of crossing versus non-crossing oscillator potentials in a two-level-one-mode system. Tunnelling rates are calculated on the basis of contour integrals in the complex co-ordinate plane. These rates for static coupling are proportional to the square of the off-diagonal electron-oscillator interaction as commonly expected. For the alternative of adiabatic coupling we have obtained a non-monotonous (oscillating) pre-exponential transition rate factor. This unfamiliar result is based on a certain “beyondnon-Condon” procedure consisting in a consequent observation both of the familiarnon-Condon effect represented by the Lorentz function behaviour of the non-adiabaticity term and the associatedavoided- crossing (hyperbolic) behaviour of adiabatic potentials in the classical transition region. Present results confirm both the general non-equivalence of both alternative coupling mechanisms and a certain asymptotic approach between mechanism-specific tunnelling rates at small off-diagonal interactions.