Cluster models of photocatalytic anatase TiO2 nanoparticles and their computational characterization

• Frozen and relaxed clusters of anatase with size up to 2.5 nm were developed.
• Their stability and enthalpy of formation were evaluated.
• PM6 semiempirical method describes clusters much better than newer PM7 method.
• Frozen clusters have band gap from 2.9 to 3.5 eV.
• Relaxed clusters have all characteristic features of real anatase nanoparticles.

Modeling of anatase nanoparticles (ANP) with the size below 10 nm represents great interest for development of insights into the mechanisms of processes taking place over nanopowders. Large fraction of surface atoms in the corners, vertices, edges, distortion of the lattice and consequent electronic structure changes make catalytic activity of ANP different. The goal of this study is creation of cluster models of ANP of size below 2.5 nm and checking the applicability of modern semiempirical methods PM6 and PM7 for their description.The clusters were prepared by translation of the anatase elementary cell along [1 0 0], [0 1 0] and [0 0 1] directions. The clusters contained from 1 × 1 × 1 to 4 × 4 × 2 cells, (0 0 1), (0 1 0) as well as (0 0 1) facets, and were made charge neutral by adding oxygen atoms and hydroxyl groups which were then optimized. The frozen-core and fully relaxed clusters were (TiO2)13, (TiO2)34(H2O)2, (TiO2)59(H2O)2, (TiO2)114, and (TiO2)187(H2O)2 and they have TiO bonds at vertices of length 1.64–1.69 Å in agreement with experiments. PM6 method was confirmed to describe anatase lattice much better than PM7 method but the geometries obtained differ somewhat from those obtained by DFT calculation. Fully relaxed clusters have a core with mean deviation from ideal lattice < 0.32 Å/atom and semiamorphous surface layer with mean deviation 0.44–1.06 Å/atom in agreement with literature core–shell models for very small ANP. Enthalpy of formation (ΔfH) per TiO2 unit of the frozen-core and relaxed clusters agrees with the bulk anatase ΔfH to within 7% by subtracting surface tension contribution of 1.5 and 1 J/m2 for non-relaxed and relaxed surfaces, respectively. The calculated with PM6 or PM7 optical band gap of the frozen-core clusters (2.9–3.5 eV) is close to experimental values while optical band gap of relaxed clusters (4.6–5.7 eV) is overestimated. Electronic band gap is always overestimated by ∼4 eV but a clear quantum size effect is observed for relaxed clusters only. The clusters developed can be utilized in diverse catalytic studies.

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