Theory of torsional non-Condon electron transfer: a generalized spin-boson Hamiltonian and its nonadiabatic limit solution.

The paper develops a theory of electron transfer with torsionally induced non-Condon (NC) effects. The starting point of the theory is a generalized spin-boson Hamiltonian, where an additional torsional oscillator bilinearly coupled to other bath modes causes a sinusoidal NC modulation. We derive closed form time dependent nonadiabatic rate expressions for both sudden and relaxed initial conditions, which are applicable for general spectral densities and energetic condition. Under the assumption that the torsional motion is not correlated with the polaronic shift of the bath, simple stationary limit rate expression is obtained. Model calculations of this rate expression illustrate the effects of torsional quantization and gating on the driving force and temperature dependences of the electron transfer rate. The classical limit of the rate expression consists of three Marcus-type terms, and is shown to agree very well with the exact numerical result. 2005 American Institute of Physics.