Amorphous TiO₂ from a statistical view based on molecular dynamics using machine learning interatomic potentials

We use molecular dynamics with a machine-learning interatomic potential based on the higher-order equivariant message-passing atomic cluster expansion (MACE) framework to construct an ensemble of 100 amorphous TiO₂ configurations. The final structures are subject to variable-cell relaxations using density functional theory calculations, where PBEsol functional is adopted as it reproduces the experimental densities for all the three crystalline phases, namely, rutile, anatase and brookite. The mean density is calculated to be 3.94 g cm^-3. While the ensemble is dominated by 6-coordinated Ti and 3-coordinated O, the corresponding percentage is 57.4% and 66.8% only. There exist 28.9% of 5-coordinated Ti, 12.1% 7-coordinated Ti, 21.4% 2-coordinated 21.4% O and 11.8% 4-coordinated O. Using hybrid HSE06 functional with the exact-exchange fraction (α) set to 0.18, the ensemble average yields a band gap of 3.44 ± 0.12 eV for the amorphous phase, which is greater than those of the three crystalline phases obtained using the same computational framework, namely, variable-cell relaxation using PBEsol and band gap calculation using HSE06 (α=0.18). Analysis of the density of states suggests that the band-gap widening in the amorphous phase is associated with the narrowed Ti 3d band. It is potentially useful to adopt the protocol in this work to study the effect of amorphization on the electronic structures of other semiconductors.