# Real-Space Constrained Density Functional Theory Investigation of Site-Specific, Interfacial Charge Recombination Dynamics Across the Au Nanoparticle/TiO2 Heterojunction

## TL;DR

This paper uses advanced theory to study how charges recombine at the interface of gold nanoparticles and titanium dioxide, important for improving solar energy technologies.

## Contribution

The study introduces a novel combination of real-space constrained DFT and Marcus theory to model interfacial charge recombination dynamics.

## Key findings

- Charge recombination is dominated by transitions from TiO2 LUMO to Au HOMO at interfacial Au sites.
- Marcus theory predictions align with surface hopping methods but differ in time scales and efficiency.
- Au cluster size influences free energy and reorganization energy, affecting charge transfer trends.

## Abstract

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 (ΔG) 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.