Effective Elasticity of Anatase-Derived TiO2 Nanoclusters: Volume Normalization, Directional Response, and Structure–Property Correlations

Elastic response affects TiO2 nanostructure durability and performance and depends on particle size and morphology. We determine effective elastic coefficients, moduli, and anisotropy indices from clamped-ion density functional theory energy–strain calculations for nine anatase-derived clusters containing 10–165 Ti atoms, using a tetragonal-form model. Comparing framework convex-hull, hydroxyl-inclusive convex-hull, and bulk-equivalent volumes shows that normalization can create or reverse apparent size trends. Across all five matched parent–cut pairs, cutting and passivating the apices reduces axial stiffness relative to in-plane stiffness and increases relative in-plane coupling and shear. These directional changes are independent of the volume convention. Cutting removes asymmetric axial Ti environments, while hydroxylation satisfies local coordination without restoring the removed framework connectivity. After cutting, mean Ti–O distances shorten, their dispersion narrows, and the mean bond order around 4-coordinate Ti increases, whereas axial stiffness decreases relative to in-plane stiffness. Thus, local bond strengthening coexists with reduced relative axial stiffness. The frontier-orbital gap widens with increasing 4-coordinate Ti fraction and shorter mean Ti–O bonds, while coordination-resolved electronic descriptors also track effective stiffness and anisotropy. These descriptor associations remain exploratory because size, morphology, coordination, and passivation are coupled. Meaningful comparisons of nanocluster elasticity must therefore specify the volume convention and distinguish local bond strengthening from changes in directional stiffness.