Journal of Physical Chemistry, Vol.97, No.50, 13107-13116, 1993
Adiabaticity Factor for Electron-Transfer in the Multimode Case - An Energy Velocity Perspective
The multimode description of outer-sphere electron transfer in the Landau-Zener perspective leads to a picture of the electron-transfer event as occurring at the intersection of two N-dimensional potential energy surfaces. At this crossing scam, the behavior of the reacting system is controlled by the transmission coefficient. The usual one-dimensional Landau-Zener result with thermal equilibrium velocities can be extended to the multimode case. Dogonadze in particular has considered the Landau-Zener transmission coefficient expressions in this multimode case and derived the corresponding frequency factor in the nonadiabatic limit. The transmission coefficient for electron transfer coupled to an arbitrary number of classical molecular solvent modes is explored here in the case of general adiabaticity, and the significance of the resultant dimensionless adiabaticity parameter and its effective solvent frequency is clarified. A common feature of most electron-transfer theories is the assumption of a single outer-sphere mode. The Landau-Zener analysis, however, leads to a direct prescription for a single effective outer-sphere mode, and the nature of this reduction from the N underlying mechanical modes is ascertained. By pursuing an energy velocity perspective, the relation of the multimode Landau-Zener result to the standard single-mode result is used to illustrate general properties of dimensionless adiabaticity parameters. Modifications for the inclusion of quantum inner-sphere modes and the deep inverted region are also discussed.
Keywords:POLAR-SOLVENTS;SOLVATION DYNAMICS;DIELECTRIC FRICTION;ION-PAIRS;TRANSITION;SIMULATION;PROBABILITY;PHONONS;LIQUIDS;SYSTEM