Relation between image charge and potential alignment corrections for charged defects in periodic boundary conditions.

Charged defects are often studied within the periodic density functional theory (DFT), but this introduces strong finite-size artifacts. In this work, we develop an electrostatic image interaction correction (IIC) method based on the direct solution of the Poisson equation for charge models constructed directly from DFT calculations. These IICs are found to be detail-insensitive, depending almost entirely on bulk dielectric properties. As these IICs are not able to fully explain the observed finite-size scaling, we explore potential alignment in detail and introduce a novel decomposition to separate out different contributions. We find that the two main sources of potential alignment are defect image interactions and changes in the number of atoms present in the supercell. This first effect is accurately predicted by the periodic part of our IIC. The second contribution is unrelated to the IIC and justifies the common observation that the magnitude of finite-size dependence can strongly vary between vacancy and interstitial defects. It can be approximately predicted using atomic radius, but is strongly sensitive to the pseudopotential employed. Combined, these developments provide a new justification for known finite-size scaling rules. Our results suggest that for cubic supercells, the Lany-Zunger IIC, combined with simplified potential alignment between neutral systems, can yield accurate corrections in spite of the simplicity of the approach.

Engineering Polarons at a Metal Oxide Surface.

Polarons in metal oxides are important in processes such as catalysis, high temperature superconductivity, and dielectric breakdown in nanoscale electronics. Here, we study the behavior of electron small polarons associated with oxygen vacancies at rutile TiO_{2}(110), using a combination of low temperature scanning tunneling microscopy (STM), density functional theory, and classical molecular dynamics calculations. We find that the electrons are symmetrically distributed around isolated vacancies at 78 K, but as the temperature is reduced, their distributions become increasingly asymmetric, confirming their polaronic nature. By manipulating isolated vacancies with the STM tip, we show that particular configurations of polarons are preferred for given locations of the vacancies, which we ascribe to small residual electric fields in the surface. We also form a series of vacancy complexes and manipulate the Ti ions surrounding them, both of which change the associated electronic distributions. Thus, we demonstrate that the configurations of polarons can be engineered, paving the way for the construction of conductive pathways relevant to resistive switching devices.

First-Principles Modeling of Polaron Formation in TiO2 Polymorphs.

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 TiO2 including anatase, rutile, brookite, TiO2(H), TiO2(R), and TiO2(B). Electron polarons are predicted to form in rutile, TiO2(H), and TiO2(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 TiO2(H) and TiO2(R) the electron is distributed across two neighboring Ti sites. Hole polarons are predicted to form in anatase, brookite, TiO2(H), TiO2(R), and TiO2(B) (with trapping energies ranging from -0.16 eV to -0.52 eV). In anatase, brookite, and TiO2(B) holes localize on a single O ion, whereas in TiO2(H) and TiO2(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.

Construction of nano- and microporous frameworks from octahedral bubble clusters.

We report a general method of constructing microporous, cubic frameworks from eight different high symmetry small clusters of ZnO, which were previously predicted via the application of an evolutionary algorithm. Using interatomic potentials, the lattice energies of the structures formed are computed. We analyse the relative stabilities within particular subsets of these periodic structures, and show that frameworks constructed from edge-sharing units of clusters with the T(h) point group are predicted to be much more stable than those with T(d). Our results have general implications for the nanostructures of systems whose bulk structures are based on tetrahedral coordination.

Bubbles and microporous frameworks of silicon carbide.

We report the results of density functional theory calculations on nanostructures of SiC, including single clusters, cluster dimers, and nanoporous cluster frameworks. Our results show that at the nanoscale, there is significant charge transfer of 2.5|e| from Si to C atoms, which results in the adoption of the same structural motifs for nanoparticles of SiC that occur for ZnO, with clusters of T(h), T(d), and O symmetry. Experimental support for our models is provided by comparison of optical gaps and ionisation potentials. With the exception of the (SiC)(28) cluster, the T(h) or T(d) nanoparticles can bind into kinetically stable agglomerates on either tetragonal or hexagonal faces, with tetragonal binding energetically preferred for larger nanoclusters, which enables the construction of cubic nanoporous frameworks of varying porosities. Frameworks composed of larger clusters are softer; with bulk moduli of ca. 20 GPa while frameworks assembled from smaller clusters tend to be harder. The electronic structure of all frameworks can be analysed in terms of the adopted short-range order of the clusters, we predict that frameworks containing topological features similar to the rock-salt phase are metallic in nature.