We present a computationally efficient and predictive methodology for modeling the formation and properties of electron and hole polarons in solids. Through a nonempirical and self-consistent optimization of the fraction of Hartree-Fock exchange (α) in a hybrid functional, we ensure the generalized Koopmans' condition is satisfied and self-interaction error is minimized. The approach is applied to model polaron formation in known stable and metastable phases of TiO including anatase, rutile, brookite, TiO(H), TiO(R), and TiO(B). Electron polarons are predicted to form in rutile, TiO(H), and TiO(R) (with trapping energies ranging from -0.02 eV to -0.35 eV). In rutile the electron localizes on a single Ti ion, whereas in TiO(H) and TiO(R) the electron is distributed across two neighboring Ti sites. Hole polarons are predicted to form in anatase, brookite, TiO(H), TiO(R), and TiO(B) (with trapping energies ranging from -0.16 eV to -0.52 eV). In anatase, brookite, and TiO(B) holes localize on a single O ion, whereas in TiO(H) and TiO(R) holes can also be distributed across two O sites. We find that the optimized α has a degree of transferability across the phases, with α = 0.115 describing all phases well. We also note the approach yields accurate band gaps, with anatase, rutile, and brookite within six percent of experimental values. We conclude our study with a comparison of the alignment of polaron charge transition levels across the different phases. Since the approach we describe is only two to three times more expensive than a standard density functional theory calculation, it is ideally suited to model charge trapping at complex defects (such as surfaces and interfaces) in a range of materials relevant for technological applications but previously inaccessible to predictive modeling.

We evaluate the accuracy of electron densities and quasiparticle energy gaps given by hybrid functionals by directly comparing these to the exact quantities obtained from solving the many-electron Schrödinger equation. We determine the admixture of Hartree-Fock exchange to approximate exchange-correlation in our hybrid functional via one of several physically justified constraints, including the generalized Koopmans' theorem. We find that hybrid functionals yield strikingly accurate electron densities and gaps in both exchange-dominated and correlated systems. We also discuss the role of the screened Fock operator in the success of hybrid functionals.

The formation of nanoscale phases at grain boundaries in polycrystalline materials has attracted much attention, since it offers a route toward targeted and controlled design of interface properties. However, understanding structure−property relationships at these complex interfacial defects is hampered by the great challenge of accurately determining their atomic structure. Here, we combine advanced electron microscopy together with ab initio random structure searching to determine the atomic structure of an experimentally fabricated Σ13 (221) [11̅ 0] grain boundary in rutile TiO 2 . Through careful analysis of the atomic structure and complementary electron energyloss spectroscopy analysis we identify the existence of a unique nanoscale phase at the grain boundary with striking similarities to the bulk anatase crystal structure. Our results show a path to embed nanoscale anatase into rutile TiO 2 and showcase how the atomic structure of even complex internal interfaces can be accurately determined using a combined theoretical and experimental approach.