Photoinduced Catalysis of Redox Reactions. Turnover Numbers, Turnover Frequency, and Limiting Processes: Kinetic Analysis and Application to Light-Driven Hydrogen Production

The energy of light is likely to be used to drive thermodynamically unfavorable redox reactions with the goal of storing energy in chemical bonds, for example, via hydrogen production. To this end, molecular systems involving at least four components (substrate, photosensitizer, sacrificial donor, and catalyst) are designed as a step toward building photoelectrochemical devices. The efficiency of such photoinduced catalysis of redox reactions is often reported as turnover numbers over time, leading to maximal turnover numbers and initial turnover frequencies. How these figures of merit are related to the properties of the system (light absorption, excited state quenching, catalytic rate constants, back electron transfers, etc.) is however lacking, thus making reliable comparison of systems difficult. Herein, we propose a general analytical kinetic framework for the analysis of photoinduced catalytic processes. In particular, we show that even for ideal systems, the turnover number does not increase linearly with time due to the increasing unproductive cycles over time via back electron transfers. We then incorporate limiting processes corresponding to the photosensitizer or catalyst degradation in the kinetic analysis, and we provide analytical expressions for the maximal turnover numbers in such situations. Finally, the kinetic model is used to successfully rationalize experimental data corresponding to light-driven hydrogen production in water using ascorbate as a sacrificial donor, a cobalt tetrazamacrocyclic complex as a catalyst, and two different photosensitizers, the classical [Ru­(bpy)₃]²⁺ and a robust triazatriangulenium organic dye TATA⁺.