Journal of Physical Chemistry, Vol.99, No.9, 2469-2476, 1995
Models for Electron-Transfer with Vibrational-State Resolution
We use model calculations to study how electron-transfer rates in solution depend on populations of specific vibrational levels. The models are for nonadiabatic electron transfer with:specific quantum populations in either a 2000-cm(-1) or a 430-cm(-1) vibrational mode, characteristic of inorganic complexes in which we have previously demonstrated quantum effects. We find a major increase in the electron-transfer rate at small and large energy gaps when one or more quanta are in vibrations having large geometry changes during the electron transfer, and the effects are greater for high-frequency modes. The rates for different energy gaps, the ratio of rates for different quantum numbers, and the populations of vibrational energy after the electron transfer were shown to be useful fortesting specific molecular models of electron transfer. We also modified standard nonadiabatic models to provide rate predictions when excess energy is communicating among a subset of vibrational modes by intramolecular vibrational redistribution. This modification converts excess energy to an effective vibrational temperature, which isused in temperature-dependent Franck-Condon factors. These models show that an order of magnitude increase of rate is possible for excess energies of 2000-6000 cm(-1) but only for electron-transfer rates slower than the maximum. At the maximum rate, excess energy slows the rate. The various models demonstrate that quantum effects for electron transfer in solution can be large, and therefore, such experiments can be used to provide a new molecular level test of electron-transfer mechanisms.
Keywords:FREE-ENERGY;REORGANIZATION ENERGIES;CONDENSED PHASES;CHARGE-TRANSFER;MOLECULES;RELAXATION;CONSTANTS;DYNAMICS