Theoretical Study Of Electron Transfer Rate In Solution

For intramolecular electron transfer(ET) reactions in solution,the fluctuations of the intramolecular vibrational modes are much faster than that of solvent mode.Thus,the reaction-diffusion equation is commonly used to describe the motion of solvent,with a sink function to treat the vibrational high-frequency mode.Based on this theory-so -called the Sumi-Marcus theory,we proposed an imaginary-time split operator approach to solve the reaction-diffusion equation.The approach is applied to evaluate the intermolecular ET rate between oxazine 1 and N,N-dimethlaniline.By measuring the two average survival times of the donor state probability and the rate constant in long time limit,the full kinetics of the ET is revealed with a variety of sink functions.In order to deal with the ET reaction in wide electronic coupling regions,we introduced the R-matrix method to treat the sink function. Together with the imaginary-time split operator approach,we investigated the quantum effect of intramolecular high-frequency vibrational modes in the Marcus inverted region.The numerical results illustrate that the adiabatic suppression obtained from the R-matrix approach is much smaller than that from the Laudau-Zener theory whereas it cannot be predicted by the perturbation theory.The jointed effects of the electronic coupling and solvent relaxation time on the rates are also explored.The proposed ET approaches are extended to investigate realistic systems together with ab initio calculations.The bis(hydrazine) radical cations are taken as examples.The predicted rates are in good agreement with the the experiments.Meanwhile,we also revealed the isomeric effects on ET.When the harmonic approximation is breakdown,the Morse potential is taken as the free energy surface to study the anharmonic effects of solvent mode and vibrational mode.The results show:(1) the anharmonicity of the intramolecular modes always enhances the rate while the solvent anharminicity decreases the rate,compared with the harmonic modes.(2) the relation between the ET rate and the solvent relation time does not satisfy the power law for the nuclear tunneling effect.