Effect of Size and Structure on the Ground-State and Excited-State Electronic Structure of TiO<sub>2</sub> Nanoparticles

We investigated the influence of size and structure on the electronic structure of TiO<sub>2</sub> nanoparticles 0.5–3.2 nm in diameter, in both vacuum and water, using density functional theory (DFT) calculations. Specifically, we tracked the optical and electronic energy gap of a set of (TiO<sub>2</sub>)<sub>n</sub> nanoparticles ranging from small non-bulklike clusters with <i>n</i> = 4, 8, and 16, to larger nanoparticles derived from the anatase bulk crystal with <i>n</i> = 35 and 84. As the difference between these two energy gaps (the exciton binding energy) becomes negligible in the bulk, this magnitude provides an indicator of the bulklike character of the electronic structure of the nanoparticles under study. Extrapolating our results to larger sizes, we obtain a rough estimate of the nanoparticle size at which the electronic structure will begin to be effectively bulklike. Our results generally confirmed that the electronic structure of the nanoparticle ground state and excited state has a more pronounced structure dependency than size dependency within a size range of 0.5–1.5 nm. We also showed that the thermodynamic preference for the photocatalytic species is the first S<sub>1</sub> exciton. This S<sub>1</sub> exciton is stable under vacuum but may evolve to free charge carriers upon structural relaxation in an aqueous environment for particles 0.5–1.5 nm in size studied in the present article. An analysis of ionization potentials and electron affinities, relative to the standard reduction potential for the water splitting half-reactions, revealed the importance of considering the structural relaxation in the excited states and the presence of water for assessing the thermodynamic conditions for photocatalytic water splitting.