Quantum Efficiency of Charge Transfer Competing against Nonexponential Processes: The Case of Electron Transfer from CdS Nanorods to Hydrogenase

Photoexcited charge transfer from semiconductor nanocrystals to charge acceptors is a key step for photon energy conversion in semiconductor nanocrystal-based light-harvesting systems. Charge transfer competes against relaxation processes within the nanocrystals, and this competition determines the quantum efficiency of charge transfer. The quantum efficiency is a critical design element in photochemistry, but in nanocrystal-acceptor systems its extraction from experimental data is complicated by sample heterogeneity and intrinsically nonexponential excited-state decay pathways. In this manuscript, we systematically explore these complexities using TA spectroscopy over a broad range of timescales to probe electron transfer from CdS nanorods to the redox enzyme hydrogenase. To analyze the experimental data, we build a model that quantifies the quantum efficiency of charge transfer in the presence of competing, potentially nonexponential, relaxation processes. Our approach can be applied to calculate the efficiency of charge or energy transfer in any donor-acceptor system that exhibits nonexponential donor decay and any ensemble distribution in the number of acceptors, provided that donor relaxation and charge transfer can be described as independent, parallel decay pathways. We apply this analysis to our experimental system and unveil the connections between particle morphology and quantum efficiency. Our model predicts a finite quantum efficiency even when the mean recombination time diverges, as it does in CdS nanostructures with spatially separated electron-hole pairs that recombine with power-law dynamics. We contrast our approach to the widely used expressions for the quantum efficiency based on average lifetimes, which for our system overestimate the quantum efficiency. The approach developed here is straightforward to implement and should be applicable to a wide range of systems.