Real-Space Constrained Density Functional Theory Investigation of Site-Specific, Interfacial Charge Recombination Dynamics Across the Au Nanoparticle/TiO ₂ Heterojunction

Au nanoparticle (NP)/TiO₂ heterojunction is a representative system to study interfacial charge transfer in photocatalysis and photovoltaics, where suppressing recombination from TiO₂ to Au can enhance hot carrier extraction. We apply real-space constrained density functional theory (CDFT) with Marcus theory to quantify charge recombination time scales across Au/TiO₂. This approach enables direct control and visualization of charge-separated states, aligning with site-specific probes like time-resolved X-ray photoelectron spectroscopy (trXPS). We find that the charge-separated state features a bipolaron, with recombination dominated by TiO₂ LUMO to Au HOMO transitions, primarily at interfacial Au sites. Marcus rate predictions are benchmarked with surface hopping methods, quantifying differences in time scales and computational efficiency. Lastly, we examine how the Au cluster size affects the free energy change (Δ<i>G</i>) and reorganization energy (λ), explaining trends in closed-shell systems and highlighting challenges for open-shell extrapolations. Overall, CDFT + Marcus theory provides efficient, mechanistically transparent interfacial charge transfer modeling, and we clearly defined its applicability and limitation.