Quantum Effects in Electron Transfer Reactions and Solvation Dynamics

Citation

Song, Xueyu (1996) Quantum Effects in Electron Transfer Reactions and Solvation Dynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ejw2-cy95. https://resolver.caltech.edu/CaltechTHESIS:02172022-225929135

Abstract

This thesis focuses on the quantum effects of electron transfer reactions in solutions and solvation dynamics of pure solvent. A prototypical model system, the Fe⁺² + Fe⁺³ ⇌ Fe⁺³ + Fe⁺² reaction in water, is treated using the spin-boson Hamiltonian model. The spectral density is related to the experimentally accessible data on the dielectric dispersion of the solvent, using a dielectric continuum approximation. On this basis the quantum correction for the ferrous-ferric electron transfer rate is found to be a factor of 9.6, which is significantly smaller than the corresponding values calculated from molecular models which neglect the electronic and vibrational polarization of the solvent. Using an imaginary free energy method, a general formula for the rate valid in all orders of perturbation in electronic coupling is derived for a renormalized classical bath. It is found that the quantum degrees of freedom can be effectively eliminated from the model by renormalizing the electronic coupling matrix element to the first order approximation for the quantum modes. Furthermore, a similar result is obtained for the quantum bath with a better approximation scheme. In application it has been shown that the rate has a nonmonotonic behavior as a function of the coupling matrix element in the inverted region. In the solvent dynamics controlled regime a one-particle Green function method is used to calculate the electron transfer reaction rate with a spin-boson Hamiltonian. A quantum version of Zusman’s result on solvent dynamical effect in electron transfer reactions is obtained for the symmetric case. It is shown that the quantum effect for most of the realistic systems is not significant at room temperature and it would become important for some fast dielectric relaxation solvents like water. In solvation dynamics studies a Gaussian field model is used to obtain the charge density correlation function of the solution in terms of charge density correlation function of the solvent. It then becomes possible to calculate the time-dependent solvation free energy without using the "uniform dielectric approximation." It is found that the nonuniformity in the vicinity of the solute indeed retards the solvation relaxation.

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