Electron-transfer reactions involving non-linear spin-boson interactions Original Research Article

Effects of electron transfer reactions involving non-linear spin-boson interactions are examined. An analytical rate formula is derived as a convoluted integral of the Franck-Condon kernel for each mode of nuclear motion whether it is low or high frequency. For a dominant solvent mode at low frequency, the formula is equivalent to the results of the stochastic Liouville approach. Asymmetry of the Marcus rate plot between the normal and the inverted regions is illustrated. The validity of using the concept of “collapsing” multi-dimensional reaction coordinates into one effective reaction coordinate is discussed. The Duschinsky rotation is included in this generalized spin-boson model.