Fermi Golden Rule Approach to Evaluating Outer-Sphere Electron-Transfer Rate Constants at Semiconductor/Liquid Interfaces

Abstract

Fermi's golden rule is used to formulate rate expressions for charge transfer of delocalized carriers in a nondegenerately doped semiconducting electrode to localized, outer-sphere redox acceptors in an electrolyte phase. If the charge-transfer rate constant is known experimentally, these rate expressions allow computation of the value of the electronic coupling matrix element between the semiconducting electrode and the redox species. This treatment also facilitates comparison between charge-transfer kinetic data at metallic and semiconducting electrodes in terms of parameters such as the electronic coupling to the electrode, the attenuation of coupling with distance into the electrolyte, and the reorganization energy of the charge-transfer event. Within this framework, rate constant values expected at representative semiconducting electrodes have been evaluated from experimental data for charge transfer from Au electrodes to ferrocene-terminated thiols, to Ru(NH₃)₅^(3+/2+)-terminated thiols, and through blocking layers to dissolved [Fe(2,2'-bipyridine)₂(CN)₂]^(+/0). Based on the experimental parameters determined for these systems, the maximum rate constant (i.e. at optimal exoergicity) for outer-sphere processes at semiconducting electrodes is computed to be in the range 10⁻¹⁷−10⁻¹⁶ cm⁴ s⁻¹. These values are in excellent agreement with prior theoretical models and experimental results for charge-transfer kinetics at semiconductor/liquid interfaces and thus serve to unify the theoretical and experimental descriptions of electrochemical processes at semiconducting and metallic electrodes.

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