Quantum chemical investigation of cluster models for TiO ₂ nanoparticles with water-derived ligand passivation: Studies of excess electron states and implications for charge transport in the Gratzel cell

We present hybrid DFT calculations for large TiO ₂ cluster models in the gas phase and in solution. Two clusters are investigated, one derived from the anatase bulk structure and the second from rutile. The surfaces are passivated with hydroxyl and water ligands, and continuum solvation is used to model bulk solvent in a subset of calculations. The geometrically optimized bonding patterns, structures, and electronic properties are similar in the two clusters. The distinction between anatase and rutile is minor at this small size. The HOMO and LUMO of the clusters are delocalized, and qualitatively resemble those observed in bulk for both the anatase and rutile derived species. When an additional electron is added, the wave function is again delocalized and there is little change in geometry, and hence minimal polaronic self-trapping. Removal of a surface ligand, creating a defect in that location, does lead to localization of the wave function, but it is unclear whether this actually occurs in real nanocrystalline TiO ₂ systems. Our results suggest that modeling of electron transport in TiO ₂ nanocrystal photovoltaic cells may require the presence of electrolyte ions to stabilize localized trapping states.