Properties of Single Oxygen Vacancies on a Realistic (TiO₂)₈₄ Nanoparticle: A Challenge for Density Functionals

Based on all electron relativistic density functional theory calculations, the properties of single oxygen vacancies in TiO₂ nanoparticles (NPs) have been obtained using a suitable representative model consisting of an octahedral (TiO₂)₈₄ nanoparticle of ∼3 nm size terminated with (101) facets. This nanoparticle can be safely considered at the onset of the so-called scalable regime where properties scale linearly with size toward bulklike limit, and hence results can be more directly compared to experiment. A set of reduced Ti₈₄O₁₆₇ nanoparticles are selected to investigate the geometric, energetic, and electronic properties by using PBE semilocal functional with three different amounts of Fock exchange: 0% (PBE), 12.5% (PBEx), and 25% (PBE0). In particular, using the PBEx hybrid functional, previously validated for bulk anatase and rutile, it is predicted that the highly (three)-coordinated oxygen atom, located in the subsurface, and the least coordinated one at top sites are energetically the most suitable candidate for generating the oxygen vacancy. The subsurface case is in line with conclusions from experiments carried out on (101) single crystal anatase surfaces. The electronic structure of the reduced particles suggests that these would have better photocatalytic activity than their stoichiometric counterparts. Nevertheless, several properties of reduced TiO₂ NPs are strongly affected by the choice of the exchange-correlation functional, implying that, in absence of validation by comparison to experiment, predictions must be taken with caution