Hybrid Functional Calculations Research Articles

Tucker Tensor Approach for Accelerating Fock Exchange Computations in a Real-Space Finite-Element Discretization of Generalized Kohn-Sham Density Functional Theory.

The evaluation of Fock exchange is often the computationally most expensive part of hybrid functional density functional theory calculations in a systematically improvable, complete basis. In this work, we employ a Tucker tensor based approach that substantially accelerates the evaluation of the action of Fock exchange by transforming three-dimensional convolutional integrals into a tensor product of one-dimensional convolution integrals. Our numerical implementation uses a parallelization strategy that balances the memory and communication bottlenecks, alongside overlapping compute and communication operations to enhance computational efficiency and parallel scalability. The accuracy and computational efficiency are demonstrated on various systems, including Pt clusters of various sizes and a TiO2 cluster with 3684 electrons.

High-throughput hybrid-functional DFT calculations of bandgaps and formation energies and multifidelity learning with uncertainty quantification

High-throughput hybrid-functional DFT calculations of bandgaps and formation energies and multifidelity learning with uncertainty quantification

Nonempirical semilocal density functionals for correcting the self-interaction of polaronic states

Through the use of the piecewise-linearity condition of the total energy, we correct the self-interaction for the study of polarons by constructing nonempirical functionals at the semilocal level of theory. We consider two functionals, the γDFT and μDFT functionals, both of which are based on the addition of a weak local potential to the semilocal Hamiltonian to enforce the piecewise-linearity condition. We show that the resulting polaron properties are in good agreement with reference hybrid functional calculations. This supports the use of semilocal functionals for calculating polaron properties.

Surface termination modulation for superior S-Scheme Bi2WO6/BiOI heterojunction photocatalyst: a hybrid density functional study

The prevailing theoretical frameworks indicate that depending on the growth conditions, the Bi2WO6(001) surface can manifest in three distinct terminations—DL-O–Bi (DL: double layers), O–Bi, and O–W. In this study, we conduct a comprehensive examination of the interplay between these terminations on Bi2WO6(001) and the 1I-terminated BiOI(001) facet, especially focusing on their impact on the photocatalytic activity of Bi2WO6/BiOI heterostructure, applying hybrid functional calculations. The models formulated for this research are designated as Bi2WO6(O–Bi)/BiOI(1I), Bi2WO6(DL-O–Bi)/BiOI(1I), and Bi2WO6(O–W)/BiOI(1I). Our findings reveal that Bi2WO6(O–Bi)/BiOI(1I) shows a type II band alignment, which facilitates the spatial separation of photo-generated electrons and holes. Notably, the Bi2WO6(DL-O–Bi)/BiOI(1I) configuration has the lowest binding energy and results in an S-scheme (or Step-scheme) heterostructure. In contrast to the type II heterostructure, this particular configuration demonstrates enhanced photocatalytic efficiency due to improved photo-generated carrier separation, augmented oxidation capability, and better visible-light absorption. Conversely, Bi2WO6(O–W)/BiOI(1I) presents a type I projected band structure, which is less conducive for the separation of photo-generated electron–hole pairs. In summation, this investigation points out that one could significantly refine the photocatalytic efficacy of not only Bi2WO6/BiOI but also other heterostructure photocatalysts by modulating the coupling of different terminations via precise crystal synthesis or growth conditions.

An investigation on electronic and magnetic properties of Cr substituted MoS2 monolayer and multilayers—hybrid functional calculations

An investigation on electronic and magnetic properties of Cr substituted MoS2 monolayer and multilayers—hybrid functional calculations

Complex-Valued K-Means Clustering of Interpolative Separable Density Fitting Algorithm for Large-Scale Hybrid Functional Enabled Ab Initio Molecular Dynamics Simulations within Plane Waves.

K-means clustering, as a classic unsupervised machine learning algorithm, is the key step to select the interpolation sampling points in interpolative separable density fitting (ISDF) decomposition for hybrid functional electronic structure calculations. Real-valued K-means clustering for accelerating the ISDF decomposition has been demonstrated for large-scale hybrid functional enabled ab initio molecular dynamics (hybrid AIMD) simulations within plane-wave basis sets where the Kohn-Sham orbitals are real-valued. However, it is unclear whether such K-means clustering works for complex-valued Kohn-Sham orbitals. Here, we propose an improved weight function defined as the sum of the square modulus of complex-valued Kohn-Sham orbitals in K-means clustering for hybrid AIMD simulations. Numerical results demonstrate that the K-means algorithm with a new weight function yields smoother and more delocalized interpolation sampling points, resulting in smoother energy potential, smaller energy drift, and longer time steps for hybrid AIMD simulations compared to the previous weight function used in the real-valued K-means algorithm. In particular, we find that this improved algorithm can obtain more accurate oxygen-oxygen radial distribution functions in liquid water molecules and a more accurate power spectrum in crystal silicon dioxide compared to the previous K-means algorithm. Finally, we describe a massively parallel implementation of this ISDF decomposition to accelerate large-scale complex-valued hybrid AIMD simulations containing thousands of atoms (2,744 atoms), which can scale up to 5,504 CPU cores on modern supercomputers.

Broad luminescence from Zn acceptors in Zn doped β-Ga2O3

Zn-related defects in β-Ga2O3 were studied using photoluminescence (PL) spectroscopy combined with hybrid functional calculations and secondary ion mass spectrometry. We have in-diffused Zn by heat treatments of β-Ga2O3 in Zn vapor to promote the formation of the ZnGaZni complex as the dominating Zn configuration. Subsequently, we did heat treatment in oxygen ambient to study the dissociation of the donor complex ZnGaZni into the ZnGa acceptor. The PL spectra revealed a broad band centered at 2.5 eV. The signature has a minor contribution to the overall emission of as-grown and Zn-annealed samples but increases dramatically upon the subsequent heat treatments. The theoretical predictions from hybrid functional calculation show emission energies of 2.1 and 2.3 eV for ZnGa10/− and ZnGa20/−, respectively, and given that the previously observed deviation between the experimental and calculated values for the self-trapped holes in β-Ga2O3 is about 0.2 eV, we conclude that the 2.5 eV emission we observe herein is due to the Zn acceptor.

Absolute deformation potentials and absolute energy levels of III-N, ZnO, and II-IV-N2 semiconductors for optoelectronic applications

Absolute deformation potentials and absolute energy levels for III-N, ZnO, and II-IV-N2 semiconductors are systematically determined from hybrid-functional calculations. Separate bulk and slab calculations are combined and the vacuum level is taken as the common reference. The trends in the absolute deformation potentials are rationalized by the kinetic energy effect and the bonding (or antibonding) character of the band edge states. The calculated absolute energy levels can be used to obtain the natural band alignment between these semiconductors and are in accordance with the available results. The determined parameters are of practical importance to the optoelectronic devices designs.

Enhanced visible-light photocatalytic activity of BiOBr/BiOCl heterojunctions: A hybrid density functional investigation on the key roles of crystal facet and I-doping

In this work, (001) and (010) facets of BiOBr and BiOCl are selected to construct BiOBr(001)/BiOCl(001), BiOBr(010)/BiOCl(010), BiOBr(001)/BiOCl(010) and BiOBr(010)/BiOCl(001) heterostructure models for investigating the effect of crystal facet engineering on the photocatalytic activity of BiOBr/BiOCl through hybrid functional calculations. We found that the crystal facet is critical to the photocatalytic performance of BiOBr/BiOCl. The BiOBr(001)/BiOCl(001) and BiOBr(010)/BiOCl(010) with the same facet combinations in BiOBr/BiOCl present the unexpected type I band alignments and the poor photocatalytic activities. In contrast, the BiOBr(001)/BiOCl(010) and BiOBr(010)/BiOCl(001) with different facet combinations present the type II and direct Z-scheme characters, respectively, so that they can effectively separate the photo-excited electron-hole pairs in space. Especially, the direct Z-scheme BiOBr(010)/BiOCl(001) heterostructure can exhibit the stronger redox ability and better visible light absorption, further presenting excellent photocatalytic performance, in contrast to the type II BiOBr(001)/BiOCl(010). The investigations also show that Iodine (I) element doping can make type I BiOBr(001)/BiOCl(001) change to a direct Z-scheme band alignment and dramatically enhance its photocatalytic activity. This helps to interpret the related experimental results. Notably, I doping can significantly improve the visible light absorption of BiOBr(010)/BiOCl(001) heterostructure, enhance the solar-to-hydrogen (STH) efficiency, and still maintain its superior direct Z-scheme character. Therefore, these theoretical studies can provide valuable guidance in developing novel BiOBr/BiOCl heterostructures with high photocatalytic activities.

RPA, an Accurate and Fast Method for the Computation of Static Nonlinear Optical Properties.

The accurate computation of static nonlinear optical properties (SNLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic connection fluctuation theorem is known to be a reliable and cost-effective method to render electronic correlation effects when combined with density-fitting techniques and integration over imaginary frequencies. We explore the ability of the RPA energy expression to predict SNLOPs by evaluating RPA electronic energies in the presence of finite electric fields to obtain (using the finite difference method) static polarizabilities and hyperpolarizabilities. We show that the RPA based on hybrid functional self-consistent field calculations yields accurate SNLOPs as the best-tuned double-hybrid functionals developed today, with the additional advantage that the RPA avoids any system-specific adjustment.

Dangling Bonds as Possible Contributors to Charge Noise in Silicon and Silicon-Germanium Quantum Dot Qubits.

Spin qubits based on Si and Si1-xGex quantum dot architectures exhibit among the best coherence times of competing quantum computing technologies, yet they still suffer from charge noise that limit their qubit gate fidelities. Identifying the origins of these charge fluctuations is therefore a critical step toward improving Si quantum-dot-based qubits. Here, we use hybrid functional calculations to investigate possible atomistic sources of charge noise, focusing on charge trapping at Si and Ge dangling bonds (DBs). We evaluate the role of global and local environment in the defect levels associated with DBs in Si, Ge, and Si1-xGex alloys, and consider their trapping and excitation energies within the framework of configuration coordinate diagrams. We additionally consider the influence of strain and oxidation in charge-trapping energetics by analyzing Si and GeSi DBs in SiO2 and strained Si layers in typical Si1-xGex quantum dot heterostructures. Our results identify that Ge dangling bonds are more problematic charge-trapping centers both in typical Si1-xGex alloys and associated oxidation layers, and they may be exacerbated by compositional inhomogeneities. These results suggest the importance of alloy homogeneity and possible passivation schemes for DBs in Si-based quantum dot qubits and are of general relevance to mitigating possible trap levels in other Si, Ge, and Si1-xGex-based metal-oxide-semiconductor stacks and related devices.

New Family of Interstitial Oxygen Ion Conductor Discovered By High-Throughput Computational Screening

Discovery and design of highly efficient oxygen-active materials which react with, absorb, and transport oxygen is essential for fuel cells and related applications. Currently, the predominant families of oxygen-active materials used in commercial devices are perovskites and fluorites, which diffuse oxygen via a vacancy mechanism and only have adequate oxygen diffusivity and surface exchange at high temperatures (e.g., ~800 ˚C), impeding their use at lower temperatures desirable for more cost-effective and long-lasting device operation. The development of alternative electrolyte/electrode materials with high oxygen ionic conductivity at low temperatures (e.g., room temperature to 400 °C) is of great interest. Interstitial oxygen ion conductors typically have significantly lower migration barriers than even state-of-the-art vacancy-mediated oxygen conductors, which can provide orders of magnitude kinetic enhancement at low temperatures. In addition, the interstitial oxygen defects typically become more thermodynamically favorable as the temperature is lowered, potentially providing an additional boost to the oxygen conductivity at low temperatures from a higher mediating defect concentration. The synergistic combination of low migration barriers and thermodynamically favorable interstitial oxygen content at low temperatures provides the tantalizing possibility that interstitial oxygen conductors may lead to transformative performance improvements in oxygen-active materials.In this work, we developed an approach to discover new interstitial-mediated oxygen conductors by performing high-throughput computational screening of the 34k oxide materials from the Materials Project database and discovered a new structural family of interstitial oxygen diffusers, perrierite-type oxide La4Mn5Si4O22+ 𝜹 (LMS). We used a hierarchy of screening criteria including the geometric free space, thermodynamic stability, synthesizability, redox-active elements, and presence of short diffusion pathways. This approach, based largely on simple, physically intuitive properties, quickly winnowed the field of 34k oxides down to just 345 oxides, an approximate 99% reduction in the search space considered, with essentially no significant computational cost. From this reduced set of promising materials, ab initio simulations were performed to calculate the interstitial oxygen formation energy and migration energy. Our screening has yielded several material families to date, among which the A4B5C4O22+ 𝜹, with La4Mn5Si4O22+ 𝜹 (LMS) as a representative material, was selected for investigation with higher-fidelity DFT hybrid functional calculations and experimental validations. The calculated formation energy of interstitial oxygen is -0.11 eV at a concentration of 2.3% under air condition, indicating that LMS is predicted to be oxygen hyperstoichiometric with an expected composition of La4Mn5Si4O22+0.5 in air. Two separate interstitial and interstitialcy (“kick-out”) diffusion mechanisms are revealed by ab initio molecular dynamics (AIMD) simulation. For the interstitial diffusion pathway, the moves through the channel in between the zigzag-arranged sorosilicate Si2O7 groups, with a barrier of 0.69 eV. For the interstitialcy diffusion pathway, the moves along the corner-sharing Si2O7-MnO2-Si2O7 framework by kicking out the lattice oxygen, with a barrier of 0.74 eV. These results align well with the experimental findings of stable interstitial oxygen content and high oxygen mobility in LMS (Please see a separate poster from Md Sariful Sheikhfor experimental results). This work provides a systematic approach to screening a large number of prospective materials and opens a new avenue of finding promising interstitial oxide ion conducting materials for potential applications in a range of fast oxygen ion conduction-based technologies.

Raising TC of ferromagnetic semiconductors through doping control: The case of GaMnAs

The difficulty of increasing the Curie temperature TC of magnetic semiconductors such as (Ga,Mn)As above the room temperature is related to the p-type doping bottleneck in this system, which has hindered the further development of dilute magnetic semiconductors. To overcome the p-type doping bottleneck, we investigate the doping properties of Mn in GaAs with hybrid functional calculations and propose strategies that can improve the p-type dopability in (Ga,Mn)As. We find that tensile strain and high temperature quenching are effective approaches to enhance p-type doping in epitaxial (Ga,Mn)As. The tensile strain applied, e.g., by the substrate with a larger lattice constant can decrease the formation energy of the substitutional dopant MnGa−, which is an acceptor with large size, and increase that of interstitial Mni2+, which is a small size compensating donor, thus improving the p-type dopability. The high temperature quenching also can achieve higher hole density by limiting the formation of compensating interstitial Mn. We suggest that the combination of these two schemes would effectively enhance the p-type dopability and further raise the Curie temperature TC of (Ga,Mn)As.

Efficient implementation of analytical gradients for periodic hybrid functional calculations within fitted numerical atomic orbitals from NAO2GTO.

The NAO2GTO scheme provides an efficient way to evaluate the electron repulsion integrals (ERIs) over numerical atomic orbitals (NAOs) with auxiliary Gaussian-type orbitals (GTOs). However, the NAO2GTO fitting will significantly impact the accuracy and convergence of hybrid functional calculations. To address this issue, here we propose to use the fitted orbitals as a new numerical basis to properly handle the mismatch between NAOs and fitted GTOs. We present an efficient and linear-scaling implementation of analytical gradients of Hartree-Fock exchange (HFX) energy for periodic HSE06 calculations with fitted NAOs in the HONPAS package. In our implementation, the ERIs and their derivatives for HFX matrix and forces are evaluated analytically with the auxiliary GTOs, while other terms are calculated using numerically discretized GTOs. Several integral screening techniques are employed to reduce the number of required ERI derivatives. We benchmark the accuracy and efficiency of our implementation and demonstrate that our results of lattice constants, bulk moduli, and band gaps of several typical semiconductors are in good agreement with the experimental values. We also show that the calculation of HFX forces based on a master-worker dynamic parallel scheme has a very high efficiency and scales linearly with respect to system size. Finally, we study the geometry optimization and polaron formation due to an excess electron in rutile TiO2 by means of HSE06 calculations to further validate the applicability of our implementation.

Strain-Induced SiP–PtS2 Heterostructure with Fast Carrier Transport for Boosted Photocatalytic Hydrogen Conversion

Earth-abundant silicon-, phosphorus-, and sulfur-related compounds are crucial for optoelectronic application. Specifically, experimentally proven monolayer SiP has attracted a great deal of attention in above listed field owing to its unique properties but is plagued with challenges such as photocorrosion and poor charge separation. Moreover, theoretical understanding on the relationship of the interface and photocatalytic activity in SiP-based chemicals is not well understood. In this work, hybrid functional first-principles calculations were used to explore the photocatalytic hydrogen evolution activity of SiP–PtS2 heterostructure. Further examination of phonon, ab initio molecular dynamics (AIMD), and elastic property simulations confirms its dynamical stability. Its computed band gap of 1.59 eV is suitable for maximizing solar energy conversion efficiency, with noticeable strong absorption coefficients of 105 cm–1 order across visible–ultraviolet domains, asymmetric decent carrier mobility (∼103 cm2 V–1 s–1), and low exciton binding energy (0.56 eV). Differences in charge density and Bader and Mulliken population analyses reveal that charge flows from the SiP to the PtS2 layers, performing the dual functions of segregating photoinduced charge carriers and increasing their lifetimes. The relative band alignment of the monolayers promotes a spatial separation of the charges. An important feature of this heterostructure is that the band edges cross the water redox potential at pH of 0 upon −2% of compressive biaxial straining, with ΔG for hydrogen evolution reaction (HER) barrier lower than −0.2 eV. The quadratic relationship between biaxial strain and atomic energy indicates that both the system and strains are elastic. Redox thermodynamic analysis predicts facile hydrogen production on the heterostructure. In particular, the calculated maximum solar power conversion efficiency (PCE) and solar-to-hydrogen (STH) efficiency can reach 22.9 and 23.8%, respectively.

Computational and experimental study on undoped and Er-doped lithium tantalate nanofluorescent probes

We present a combined density functional theory (DFT) and experimental work on lithium tantalate LiTaO3 (LT) and its Er-doped counterparts. We calculate the electronic and optical properties for both LT and LT:Er+3, with Er occupying either Li or Ta sites, at 4.167 mol%. The generalized gradient approximation (GGA) calculations show that the Er-4 f bands appear closer to the conduction band bottom and to the valance band top, for the first and second doped configurations, respectively. This agrees with changes in the imaginary part of the frequency dependent dielectric function between the doped configurations. There are striking differences between the GGA and the hybrid functional HSE06 calculations for the band structures of the doped configurations. HSE06 accurately predicts the location in energy for all Er-4 f orbitals: These are now spread in energy and appear above and below the Fermi energy. We synthesized LT:Er+3 nanoparticles, validated through X-ray diffraction and Scanning Electron Microscopy. Differential scanning calorimetry and thermogravimetric analysis confirmed increases in the activation energy and lowering of the reaction temperature due to Er+3 doping. The LT:Er+3photoluminescence showed strong f–f emission in the visible and near-infrared regions, in an excellent agreement with the HSE06 electronic information.

Computational study of defect complexes in β-LiGaO2 and their relation to the donor–acceptor-pair recombination

Hybrid functional calculations are presented for defects in LiGaO2 with the fraction of non-local exchange adjusted to reproduce the recently reported exciton gap of 6.0 eV. We study how the defect transition levels of the main native defects change with respect to the band edges compared to earlier calculations which assumed a smaller bandgap near 5.1 eV. In addition, we consider defect complexes formed by combining the main native donor GaLi with the main acceptors, VLi and LiGa antisites as a function of their relative position. These results are used to tentatively identify the photoluminescence bands previously assigned to donor–acceptor-pair recombination.

Prediction and Synthesis of a Selenide Perovskite for Optoelectronics

The advent of halide perovskites in recent years has opened an avenue for redeveloping perovskite materials as semiconductors. In the quest for semiconducting perovskites, chalcogenides, which exhibit higher stability than their halide siblings and often direct band gaps for optoelectronics, have attracted more and more attention. So far, functional chalcogenide perovskites have been exclusively sulfides. Here, employing first-principles calculations and the criterion of phase stability in addition to the commonly used thermodynamic and dynamical criteria, we precisely predict the existence of LaScSe3 as a thermodynamically stable selenide perovskite, which is validated by our experimental synthesis. Combining hybrid functional and many-body quasi-particle (G0W0 and Bethe–Salpeter equation) calculations, we predict that LaScSe3 is a direct-gap semiconductor having the band gap in the green-to-blue region and capable of p- and n-type bipolar doping, potentially for optoelectronic applications.

Low-rank approximations for accelerating plane-wave hybrid functional calculations in unrestricted and noncollinear spin density functional theory.

The adaptively compressed exchange (ACE) operator combined with interpolative separable density fitting (ISDF) decomposition has been utilized to accelerate plane-wave hybrid functional calculations for restricted Kohn-Sham density functional theory (DFT), but the neglect of spin degree of freedom has limited its application in the exploration of systems where the spin property of the electron is critical. Herein, we derive the ACE-ISDF formulation for hybrid functional calculations in both unrestricted and noncollinear spin DFT with plane waves and periodic boundary conditions. We proposed an improved ISDF algorithm for the sum of Kohn-Sham orbital pairs to further reduce the computational cost for the spin-noncollinear case. Numerical results demonstrate that these improved ACE-ISDF low-rank approximations can not only significantly reduce the computational time by two orders of magnitude compared with conventional plane-wave hybrid functional calculations but also lead to a good convergence behavior when a moderate rank parameter is set, even for complex periodic magnetic systems. By using these ACE-ISDF approximations, we investigate the electronic and magnetic properties of two-dimensional periodic ferromagnetic semiconductors consisting of triangular zigzag graphene quantum dots and transition metal atoms. Our computational results showcase that hybrid functional calculations in spin DFT can provide not only accurate electronic structures but also accurate magnetic order temperature of ferromagnetic semiconductors compared to local or semilocal functional calculations.

Diffusion of Sn donors in β-Ga2O3

Diffusion of the n-type dopant Sn in β-Ga2O3 is studied using secondary-ion mass spectrometry combined with hybrid functional calculations. The diffusion of Sn from a Sn-doped bulk substrate with surface orientation (001) into an epitaxial layer is observed after heat treatments in the temperature range of 1050–1250 °C. Calculated formation energies of Sn-related and intrinsic defects show that the migration of Sn is mediated by Ga vacancies (VGa) through the formation and dissociation of intermittent mobile VGaSnGa complexes. The evolution of the Sn concentration vs depth profiles after heat treatments can be well described by a reaction–diffusion model. Using model parameters guided by the hybrid functional calculations, we extract a VGaSnGa complex migration barrier of 3.0 ± 0.4 eV with a diffusion coefficient of 2 × 10−1 cm2/s. The extracted migration barrier is consistent with our theoretical predictions using the nudged elastic band method, which shows migration barriers of 3.42, 3.15, and 3.37 eV for the [100], [010], and [001] directions, respectively.