Supported solid catalysts are useful as functional materials and are used in many industrial processes. Nanoparticles of active elements are dispersed on the surface of carrier in supported solid catalysts, yielding a high surface-area to volume ratio. Titanium dioxide is of paramount technological importance and it is widely used for photo-catalytic processes and photo-electrochemistry. It is also one of the most well-studied oxide materials. In this work, we use density functional theory (DFT) calculations to investigate and de-convolute the geometric and electronic finite-size effects of rutile titania clusters. We determine the size of titania clusters at which the surface energy converges to the infinite slab limit. Surface energies are calculated for rutile titania clusters ranging from 24 to 384 atoms. We observe that surface energies of the clusters are very close to the infinite slab limit at 384 atoms. Finite-size effects are observed below this critical size which are due to geometric and electronic structure effects. The geometric defects are due to the presence of edge, corner and sub-surface atoms that have unique geometric configurations and are classified using machine-learning fingerprints. This approach enables identification of the length scale where electronic finite size effects are significant, suggesting that particles with a minimum dimension &gt; 1 nm can be accurately modeled using the slab approximation. We also utilize hybrid functionals to analyze the optical properties of the particles, revealing that defect states play a key role in determining the bandgap of nanoparticles, and that optical properties converge much more slowly than surface properties.

Investigation of finite-size effects of rutile titanium dioxide clusters

ACS Fall 2021

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