Assessing the performance of self-consistent hybrid functional for band gap calculation in oxide semiconductors

Low thermal expansion of layered electrides predicted by density-functional theory

Layered electrides are a unique class of materials with anionic electrons bound in interstitial regions between thin, positively charged atomic layers. While density-functional theory is the tool of choice for computational study of electrides, there has to date been no systematic comparison of density functionals or dispersion corrections for their accurate simulation. There has also been no research into the thermomechanical properties of layered electrides, with computational predictions considering only static lattices. In this work, we investigate the thermomechanical properties of five layered electrides using density-functional theory to evaluate the magnitude of thermal effects on their lattice constants and cell volumes. We also assess the accuracy of five popular dispersion corrections with both planewave and numerical atomic orbital calculations.

Efficient Hybrid Density Functional Calculations for Large Periodic Systems Using Numerical Atomic Orbitals

We present an efficient, linear-scaling implementation for building the (screened) Hartree-Fock exchange (HFX) matrix for periodic systems within the framework of numerical atomic orbital (NAO) basis functions. Our implementation is based on the localized resolution of the identity approximation by which two-electron Coulomb repulsion integrals can be obtained by only computing two-center quantities-a feature that is highly beneficial to NAOs. By exploiting the locality of basis functions and efficient prescreening of the intermediate three- and two-index tensors, one can achieve a linear scaling of the computational cost for building the HFX matrix with respect to the system size. Our implementation is massively parallel, thanks to a MPI/OpenMP hybrid parallelization strategy for distributing the computational load and memory storage. All these factors add together to enable highly efficient hybrid functional calculations for large-scale periodic systems. In this work, we describe the key algorithms and implementation details for the HFX build as implemented in the ABACUS code package. The performance and scalability of our implementation with respect to the system size and the number of CPU cores are demonstrated for selected benchmark systems up to 4096 atoms.

Crystal structure of monoclinic hafnia (HfO2) revisited with synchrotron X-ray, neutron diffraction and first-principles calculations

A study on the crystal structure of monoclinic HfO₂ has been performed using synchrotron X-ray and neutron diffraction data separately, as well as a combination of both. The precision of the structural parameters increases significantly due to application of the neutron diffraction technique. The experimental oxygen positions in HfO₂, derived precisely, are visualized only by semi-local density functional calculations in terms of the calculated electronic band gap, but are not captured as accurately by using hybrid functionals.

Accuracy of Hybrid Functionals with Non-Self-Consistent Kohn-Sham Orbitals for Predicting the Properties of Semiconductors

Accurately modeling the electronic structure of materials is a persistent challenge to high-throughput screening. A promising means of balancing accuracy against computational cost is non-self-consistent calculations with hybrid density-functional theory, where the electronic band energies are evaluated using a hybrid functional from orbitals obtained with a less demanding (semi)local functional. We have quantified the performance of this technique for predicting the physical properties of 16 tetrahedral semiconductors with bandgaps from 0.2 to 5.5 eV. Provided the base functional predicts a nonmetallic electronic structure, bandgaps within 5% of the PBE0 and HSE06 gaps can be obtained with an order of magnitude reduction in computing time. The positions of the valence and conduction band extrema and the Fermi level are well reproduced, enabling calculation of the band dispersion, density of states, and dielectric properties using Fermi's Golden Rule. While the error in the non-self-consistent total energies is ∼50 meV atom^-1, the energy-volume curves are reproduced accurately enough to obtain the equilibrium volume and bulk modulus with minimal error. We also test the dielectric-dependent scPBE0 functional and obtain bandgaps and dielectric constants to within 2.5% of the self-consistent results, which amounts to a significant improvement over self-consistent PBE0 for a similar computational cost. We identify cases where the non-self-consistent approach is expected to perform poorly and demonstrate that partial self-consistency provides a practical and efficient workaround. Finally, we perform proof-of-concept calculations on CoO and NiO to demonstrate the applicability of the technique to strongly correlated open-shell transition-metal oxides.

Quasi-degenerate states and their dynamics in oxygen deficient reducible metal oxides

The physical and chemical properties of oxides are defined by the presence of oxygen vacancies. Experimentally, non-defective structures are almost impossible to achieve due to synthetic constraints. Therefore, it is crucial to account for vacancies when evaluating the characteristics of these materials. The electronic structure of oxygen-depleted oxides deeply differs from that of the native forms, in particular, of reducible metal oxides, where excess electrons can localize in various distinct positions. In this perspective, we present recent developments from our group describing the complexity of these defective materials that highlight the need for an accurate description of (i) intrinsic vacancies in polar terminations, (ii) multiple geometries and complex electronic structures with several states attainable at typical working conditions, and (iii) the associated dynamics for both vacancy diffusion and the coexistence of more than one electronic structure. All these aspects widen our current understanding of defects in oxides and need to be adequately introduced in emerging high-throughput screening methodologies.

Assessing model-dielectric-dependent hybrid functionals on the antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO

Recently, two nonempirical hybrid functionals, dielectric-dependent range-separated hybrid functional based on the Coulomb-attenuating method (DD-RSH-CAM) and doubly screened hybrid functional (DSH), have been suggested by Chen et al (2018 Phys. Rev. Mater. 2 073803) and Cui et al (2018 J. Phys. Chem. Lett. 9 2338), respectively. These two hybrid functionals are both based on a common model dielectric function approach, but differ in the way how to non-empirically obtain the range-separation parameter. By retaining the full short-range Fock exchange and a fraction of the long-range Fock exchange that equals the inverse of the dielectric constant, both DD-RSH-CAM and DSH turn out to perform very well in predicting the band gaps for a large variety of semiconductors and insulators. Here, we assess how these two hybrid functionals perform on challenging antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO by comparing them to other conventional hybrid functionals and the GW method. We find that single-shot DD0-RSH-CAM and DSH0 improve the band gaps towards experiments as compared to conventional hybrid functionals. The magnetic moments are slightly increased, but the predicted dielectric constants are decreased. The valence band density of states (DOS) predicted by DD0-RSH-CAM and DSH0 are as satisfactory as HSE03 in comparison to experimental spectra, however, the conduction band DOS are shifted to higher energies by about 2 eV compared to HSE03. Self-consistent DD-RSH-CAM and DSH deteriorate the results with a significant overestimation of band gaps.

Influence of Spin State and Cation Distribution on Stability and Electronic Properties of Ternary Transition-Metal Oxides

This work is a systematic ab initio study of the influence of spin state and cation distribution on the stability, dielectric constant, electronic band gap, and density of states of ternary transition-metal oxides. As an example, the chemical family of spinel ferrites MFe₂O₄, with M = Mg, Sc-Zn is chosen. Dielectric constant and band gap are calculated for various spin states and cation configurations via dielectric-dependent self-consistent hybrid functionals and compared to available experimental data. When choosing the most stable spin state and cation configuration, the calculated electronic properties are in reasonable agreement with measured values. The nature of the excitation is investigated through projected density of states. A pronounced dependence of band gap energy and dielectric constant on the spin state and cation configuration is observed, which is a possible explanation for the large variation of the experimental results, in particular, if several states are energetically close.

Electronic Structure and Band Alignments of Various Phases of Titania Using the Self-Consistent Hybrid Density Functional and DFT+U Methods

To understand, and thereby rationally optimize photoactive interfaces, it is of great importance to elucidate the electronic structures and band alignments of these interfaces. For the first-principles investigation of these properties, conventional density functional theory (DFT) requires a solution to mitigate its well-known bandgap underestimation problem. Hybrid functional and Hubbard U correction are computationally efficient methods to overcome this limitation, however, the results are largely dependent on the choice of parameters. In this study, we employed recently developed self-consistent approaches, which enable non-empirical determination of the parameters, to investigate TiO₂ interfacial systems-the most prototypical photocatalytic systems. We investigated the structural, electronic, and optical properties of rutile and anatase phases of TiO₂. We found that the self-consistent hybrid functional method predicts the most reliable structural and electronic properties that are comparable to the experimental and high-level GW results. Using the validated self-consistent hybrid functional method, we further investigated the band edge positions between rutile and anatase surfaces in a vacuum and electrolyte medium, by coupling it with the Poisson-Boltzmann theory. This suggests the possibility of a transition from the straddling-type to the staggered-type band alignment between rutile and anatase phases in the electrolyte medium, manifested by the formation of a Stern-like layer at the interfaces. Our study not only confirms the efficacy of the self-consistent hybrid functional method by reliably predicting the electronic structure of photoactive interfaces, but also elucidates a potentially dramatic change in the band edge positions of TiO₂ in aqueous electrolyte medium which can extensively affect its photophysical properties.

Benzoquinone-Bridged Heterocyclic Zwitterions as Building Blocks for Molecular Semiconductors and Metals

In pursuit of closed-shell building blocks for single-component organic semiconductors and metals, we have prepared benzoquino-bis-1,2,3-thiaselenazole QS, a heterocyclic selenium-based zwitterion with a small gap (λ_max = 729 nm) between its highest occupied and lowest unoccupied molecular orbitals. In the solid state, QS exists in two crystalline phases and one nanocrystalline phase. The structures of the crystalline phases (space groups R3 c and P2₁/ c) have been determined by high-resolution powder X-ray diffraction methods at ambient and elevated pressures (0-15 GPa), and their crystal packing patterns have been compared with that of the related all-sulfur zwitterion benzoquino-bis-1,2,3-dithiazole QT (space group Cmc2₁). Structural differences between the S- and Se-based materials are interpreted in terms of local intermolecular S/Se···N'/O' secondary bonding interactions, the strength of which varies with the nature of the chalcogen (S vs Se). While the perfectly two-dimensional "brick-wall" packing pattern associated with the Cmc2₁ phase of QT is not found for QS, all three phases of QS are nonetheless small band gap semiconductors, with σ_RT ranging from 10^-5 S cm^-1 for the P2₁/ c phase to 10^-3 S cm^-1 for the R3 c phase. The bandwidths of the valence and conduction bands increase with applied pressure, leading to an increase in conductivity and a decrease in thermal activation energy E_act. For the R3 c phase, band gap closure to yield an organic molecular metal with a σ_RT of ∼10² S cm^-1 occurs at 6 GPa. Band gaps estimated from density functional theory band structure calculations on the ambient- and high-pressure crystal structures of QT and QS correlate well with those obtained experimentally.