Oxygen vacancies on metal oxide surfaces have long been thought to play a key role in the surface chemistry. Such processes have been directly visualized in the case of the model photocatalyst surface TiO ₂ (110) in reactions with water and molecular oxygen. These vacancies have been assumed to be neutral in calculations of the surface properties. However, by comparing experimental and simulated scanning tunneling microscopy images and spectra, we show that oxygen vacancies act as trapping centers and are negatively charged. We demonstrate that charging the defect significantly affects the reactivity by following the reaction of molecular oxygen with surface hydroxyl formed by water dissociation at the vacancies. Calculations with electronically charged hydroxyl favor a condensation reaction forming water and surface oxygen adatoms, in line with experimental observations. This contrasts with simulations using neutral hydroxyl where hydrogen peroxide is found to be the most stable product.

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange–correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

Oxygen vacancies can promote Li-ion diffusion, reduce the charge transfer resistance, and improve the capacity and rate performance of Li-ion batteries. However, oxygen vacancies can also lead to accelerated degradation of the cathode material structure, and lead to phase transition etc.