The Open Databases Integration for Materials Design (OPTIMADE) application programming interface (API) empowers users with holistic access to a growing federation of databases, enhancing the accessibility and discoverability of materials and chemical data. Since the first release of the OPTIMADE specification (v1.0), the API has undergone significant development, leading to the v1.2 release, and has underpinned multiple scientific studies. In this work, we highlight the latest features of the API format, accompanying software tools, and provide an update on the implementation of OPTIMADE in contributing materials databases. We end by providing several use cases that demonstrate the utility of the OPTIMADE API in materials research that continue to drive its ongoing development. The Open Databases Integration for Materials Design (OPTIMADE) application programming interface (API) empowers users with holistic access to a federation of databases, enhancing the accessibility and discoverability of materials and chemical data.

Color centers in diamond are at the forefront of the second quantum revolution. A handful of defects are in use, and finding ones with all the desired properties for quantum applications is arduous. By using high-throughput calculations, we screen 21,607 defects in diamond and collect the results in the ADAQ database. Upon exploring this database, we find not only the known defects but also several unexplored defects. Specifically, defects containing sodium stand out as particularly relevant because of their high spins and predicted improved optical properties compared to the NV center. Hence, we studied these in detail, employing high-accuracy theoretical calculations. The single sodium substitutional (NaC) has various charge states with spin ranging from 0.5 to 1.5, ZPL in the near-infrared, and a high Debye-Waller factor, making it ideal for biological quantum applications. The sodium vacancy (NaV) has a ZPL in the visible region and a potential rare spin-2 ground state. Our results show sodium implantation yields many interesting spin defects that are valuable additions to the arsenal of point defects in diamond studied for quantum applications.

In a GraphQL Web API, a so-called GraphQL schema defines the types of data objects that can be queried, and so-called resolver functions are responsible for fetching the relevant data from underlying data sources. Thus, we can expect to use GraphQL not only for data access but also for data integration, if the GraphQL schema reflects the semantics of data from multiple data sources, and the resolver functions can obtain data from these data sources and structure the data according to the schema. However, there does not exist a semantics-aware approach to employ GraphQL for data integration. Furthermore, there are no formal methods for defining a GraphQL API based on an ontology.In this work, we introduce a framework for using GraphQL in which a global domain ontology informs the generation of a GraphQL server that answers requests by querying heterogeneous data sources.The core of this framework consists of an algorithm to generate a GraphQL schema based on an ontology and a generic resolver function based on semantic mappings. We provide a prototype, OBG-gen, of this framework, and we evaluate our approach over a real-world data integration scenario in the materials design domain and two synthetic benchmark scenarios (Linköping GraphQL Benchmark and GTFS-Madrid-Bench). The experimental results of our evaluation indicate that: (i) our approach is feasible to generate GraphQL servers for data access and integration over heterogeneous data sources, thus avoiding a manual construction of GraphQL servers, and (ii) our data access and integration approach is general and applicable to different domains where data is shared or queried via different ways.

In the materials design domain, much of the data from materials calculations is stored in different heterogeneous databases with different data and access models. Therefore, accessing and integrating data from different sources is challenging. As ontology-based access and integration alleviates these issues, in this paper we address data access and interoperability for computational materials databases by developing the Materials Design Ontology. This ontology is inspired by and guided by the OPTIMADE effort that aims to make materials databases interoperable and includes many of the data providers in computational materials science. In this paper, first, we describe the development and the content of the Materials Design Ontology. Then, we use a topic model-based approach to propose additional candidate concepts for the ontology. Finally, we show the use of the Materials Design Ontology by a proof-of-concept implementation of a data access and integration system for materials databases based on the ontology.

The diamond nitrogen vacancy (NV) center remains an ever-increasing topic of interest. At present, it is considered an ideal example of a solid-state qubit applicable in quantum communication, computing, and sensing alike. With its success, the search for defects that share or improve upon its advantageous features is an ongoing endeavor. By performing large-scale high-throughput screening of 52 600 defects in 4H silicon carbide (SiC), we identify a collection of NV-like color centers of particular interest. From this list, the single most promising candidate consists of a silicon vacancy and chlorine substituted on the carbon site, and is given the name of chlorine vacancy (ClV) center. Through high-accuracy first-principle calculations, we confirm that the ClV center is similar to the NV center in diamond in its local structure and shares many qualitative and quantitative features in the electronic structure and spin properties. In contrast to the NV center, however, the ClV center in SiC exhibits emission in the telecom range near the C band.

Data-driven approaches are becoming increasingly valuable for modern science, and they are making their way into industrial research and development (R&D). Supervised machine learning of statistical models can utilize databases of materials parameters to speed up the exploration of candidate materials for experimental synthesis and characterization. In this paper we introduce the HADB database, which contains properties of industrially relevant chemically disordered hard-coating alloys, focusing on their thermodynamic, elastic and mechanical properties. We present the technical implementations of the database infrastructure including support for browse, query, retrieval, and API access through the OPTIMADE API to make this data findable, accessible, interoperable, and reusable (FAIR). Finally, we demonstrate the usefulness of the database by training a graph -based machine learning (ML) model to predict elastic properties of hard-coating alloys. The ML model is shown to predict bulk and shear moduli for out out-of-sample alloys with less than 6 GPa mean average error.

A GraphQL server contains two building blocks: (1) a GraphQL schema defining the types of data objects that can be requested; (2) resolver functions fetching the relevant data from underlying data sources. GraphQL can be used for data integration if the GraphQL schema provides an integrated view of data from multiple data sources, and the resolver functions are implemented accordingly.However, there does not exist a semantics-aware approach to use GraphQL for data integration.We proposed a framework using GraphQL for data integration in which a global domain ontology informs the generation of a GraphQL server. Furthermore, we implemented a prototype of this framework, OBG-gen. In this paper, we demonstrate OBG-gen in a real-world data integration scenario in the materials design domain and in  a synthetic benchmark scenario.

Due to importance of data FAIRness (Findable, Accessible, Interoperable, Reusable), ontologies as a means to make data FAIR have attracted more and more attention in different communities and are being used in semantically-enabled applications. However, to obtain good results while using ontologies in these applications, high quality ontologies are needed of which completeness is one of the important aspects. An ontology lacking information can lead to missing results. In this paper we present a tool, Phrase2Onto, that supports users in extending ontologies to make the ontologies more complete. It is particularly suited for ontology extension using a phrase-based topic model approach, but the tool can support any extension approach where a user needs to make decisions regarding the appropriateness of using phrases to define new concepts. We describe the functionality of the tool and a user study using Pizza Ontology. The user study showed  a good usability of the system and high task completion. Further, we report on a real application where we extend the Materials Design Ontology.

The negatively charged silicon vacancy (V-Si(-)) in silicon carbide is a well-studied point defect for quantum applications. At the same time, a closer inspection of ensemble photoluminescence and electron paramagnetic resonance measurements reveals an abundance of related but so far unidentified signals. In this study, we search for defects in 4H-SiC that explain the above magneto-optical signals in a defect database generated by automatic defect analysis and qualification (ADAQ) workflows. This search reveals only one class of atomic structures that exhibit silicon-vacancy-like properties in the data: a carbon anti-site (C-Si) within sub-nanometer distances from the silicon vacancy only slightly alters the latter without affecting the charge or spin state. Such a perturbation is energetically bound. We consider the formation of V-Si(-) + C-Si; up to 2 nm distance and report their zero phonon lines and zero field splitting values. In addition, we perform high-resolution photoluminescence experiments in the silicon vacancy region and find an abundance of lines. Comparing our computational and experimental results, several configurations show great agreement. Our work demonstrates the effectiveness of a database with high-throughput results in the search for defects in quantum applications.

To speed up the progress in the field of materials design, a number of challenges related to big data need to be addressed. This entry discusses these challenges and shows the semantic technologies that alleviate the problems related to Variety, Variability, Veracity and FAIRness.

There has been a recent surge of interest in using machine learning to approximate density functional theory in materials science. However, many of the most performant models are evaluated on large databases of computed properties of, primarily, materials with precise atomic coordinates available, and which have been experimentally synthesized, i.e., which are thermodynamically stable or metastable. These aspects provide challenges when applying such models on theoretical candidate materials, for example for materials discovery, where the coordinates are not known. To extend the scope of this methodology, we investigate the performance of the crystal graph convolutional neural network on a data set of theoretical structures in three related ternary phase diagrams (Ti,Zr,Hf)-Zn-N, which thus include many highly unstable structures. We then investigate the impact on the performance of using atomic positions that are only partially relaxed into local energy minima We also explore options for improving the performance in these scenarios by transfer learning, either from models trained on a large database of mostly stable systems, or a different but related phase diagram. Models pretrained on stable materials do not significantly improve performance, but models trained on similar data transfer very well. We demonstrate how our findings can be utilized to generate phase diagrams with a major reduction in computational effort.

We propose a machine learning approach to predict the shapes of the longitudinal spin fluctuation (LSF) energy landscapes for each local magnetic moment. This approach allows the inclusion of the effects of LSFs in, e.g., the simulation of a magnetic material with ab initio molecular dynamics in an effective way. This type of simulation requires knowledge of the reciprocal interaction between atoms and moments, which, in principle, would entail calculating the energy landscape of each atom at every instant in time. The machine learning approach is based on the kernel ridge regression method and developed using bcc Fe at the Curie temperature and ambient pressure as a test case. We apply the trained machine learning models in a combined atomistic spin dynamics and ab initio molecular dynamics (ASD-AIMD) simulation, where they are used to determine the sizes of the magnetic moments of every atom at each time step. In addition to running an ASD-AIMD simulation with the LSF machine learning approach for bcc Fe at the Curie temperature, we also simulate Fe at temperature and pressure comparable to the conditions at the Earth's inner solid core. The latter simulation serves as a critical test of the generality of the method and demonstrates the importance of the magnetic effects in Fe in the Earth's core despite its extreme temperature and pressure.

Accelerated design of hard-coating materials requires state-of-the-art computational tools, which include data-driven techniques, building databases, and training machine learning models. We develop a heavily automated high-throughput workflow to build a database of industrially relevant hard-coating materials, such as binary and ternary nitrides. We use the high-throughput toolkit to automate the density functional theory calculation workflow. We present results, including elastic constants that are a key parameter determining mechanical properties of hard-coatings, for X_1-xY_xN ternary nitrides, where X,Y ∈ {Al, Ti, Zr, Hf} and fraction . We also explore ways for machine learning to support and complement the designed databases. We find that the crystal graph convolutional neural network trained on ordered lattices has sufficient accuracy for the disordered nitrides, suggesting that existing databases provide important data for predicting mechanical properties of qualitatively different types of materials, in our case disordered hard-coating alloys.

A fundamental challenge in materials science pertains to elucidating the relationship between stoichiometry, stability, structure, and property. Recent advances have shown that machine learning can be used to learn such relationships, allowing the stability and functional properties of materials to be accurately predicted. However, most of these approaches use atomic coordinates as input and are thus bottlenecked by crystal structure identification when investigating previously unidentified materials. Our approach solves this bottleneck by coarse-graining the infinite search space of atomic coordinates into a combinatorially enumerable search space. The key idea is to use Wyckoff representations, coordinate-free sets of symmetry-related positions in a crystal, as the input to a machine learning model. Our model demonstrates exceptionally high precision in finding unknown theoretically stable materials, identifying 1569 materials that lie below the known convex hull of previously calculated materials from just 5675 ab initio calculations. Our approach opens up fundamental advances in computational materials discovery.

Ontologies have been proposed as a means towards making data FAIR (Findable, Accessible, Interoperable, Reusable). This has attracted much interest in several communities and ontologies are being developed. However, to obtain good results when using ontologies in semantically-enabled applications, the ontologies need to be of high quality. One of the quality aspects is that the ontologies should be as complete as possible. In this paper we propose a first version of a tool that supports users in extending ontologies using a phrase-based approach.  To demonstrate the usefulness of our proposed tool, we exemplify the use by extending the Materials Design Ontology.

Ontologies have been proposed as a means towards making data FAIR (Findable, Accessible, Interoperable, Reusable) and has recently attracted much interest in the materials science community. Ontologies for this domain are being developed and one such effort is the Materials Design Ontology. However, to obtain good results when using ontologies in semantically-enabled applications, the ontologies need to be of high quality. One of the quality aspects is that the ontologies should be as complete as possible. In this paper we show preliminary results regarding extending the Materials Design Ontology using a phrase-based topic model.

Automatic Defect Analysis and Qualification (ADAQ) is a collection of automatic workflows developed for high-throughput simulations of magneto-optical properties of point defects in semiconductors. These workflows handle the vast number of defects by automating the processes to relax the unit cell of the host material, construct supercells, create point defect clusters, and execute calculations in both the electronic ground and excited states. The main outputs are the magneto-optical properties which include zero-phonon lines, zero-field splitting, and hyperfine coupling parameters. In addition, the formation energies are calculated. We demonstrate the capability of ADAQ by performing a complete characterization of the silicon vacancy in silicon carbide in the polytype 4H (4H-SiC).

Chromium-nitride based materials have shown unexpected promise as thermo-electric materials for, e.g., wasteheat harvesting. Here, CrN and (Cr,V)N thin films were deposited by reactive magnetron sputtering. Thermoelectric measurements of pure CrN thin films show a low electrical resistivity between 1.2 and 1.5 x 10(-3) Omega cm and very high values of the Seebeck coefficient and thermoelectric power factor, in the range between 370-430 mu V/K and 9-11 x 10(-3) W/mK(2), respectively. Alloying of CrN films with small amounts (less than 15 %) of vanadium results in cubic (Cr,V)N thin films. Vanadium decreases the electrical resistivity and yields powerfactor values in the same range as pure CrN. Density functional theory calculations of sub-stoichiometric CrN1-delta and (Cr,V)N1-delta show that nitrogen vacancies and vanadium substitution both cause n-type conductivity and features in the band structure typically correlated with a high Seebeck coefficient. The results suggest that slight variations in nitrogen and vanadium content affect the power factor and offers a means of tailoring the power factor and thermoelectric figure of merit.

Important phenomena such as magnetostriction, magnetocaloric, and magnetoelectric effects arise from, or could be enhanced by, the coupling of magnetic and structural degrees of freedom. The coupling of spin and lattice also influence transport and structural properties in magnetic materials, in particular around phase transitions. In this paper we propose a method for screening materials for a strong magnetostructural coupling by assessing the effect of the local magnetic configuration on the atomic forces using density functional theory. We have employed the disordered local moment approach in a supercell formulation to probe different magnetic local configurations and their forces and performed a high-throughput search on binary and ternary compounds available in the Crystallography Open Database. We identify a list of materials with a strong spin-lattice coupling out of which several are already known to display magnetolattice coupling phenomena such as Fe3O4 and CrN. Others, such as Mn2CrO4 and CaFe7O11, have been less studied and have yet to reveal their potentials in experiments and applications.

The Open Databases Integration for Materials Design (OPTIMADE) consortium has designed a universal application programming interface (API) to make materials databases accessible and interoperable. We outline the first stable release of the specification, v1.0, which is already supported by many leading databases and several software packages. We illustrate the advantages of the OPTIMADE API through worked examples on each of the public materials databases that support the full API specification.

(Ti-0.5, Mg-0.5)N thin films were synthesized by reactive dc magnetron sputtering from elemental targets onto c-cut sapphire substrates. Characterization by theta-2 theta X-ray diffraction and pole figure measurements shows a rock-salt cubic structure with (111)-oriented growth and a twin-domain structure. The films exhibit an electrical resistivity of 150 m omega center dot cm, as measured by four-point-probe, and a Seebeck coefficient of -25 mu V/K. It is shown that high temperature (similar to 800 degrees C) annealing in a nitrogen atmosphere leads to the formation of a cubic LiTiO2-type superstructure as seen by high-resolution scanning transmission electron microscopy. The corresponding phase formation is possibly influenced by oxygen contamination present in the as-deposited films resulting in a cubic superstructure. Density functional theory calculations utilizing the generalized gradient approximation (GGA) functionals show that the LiTiO2-type TiMgN2 structure has a 0.07 eV direct bandgap.

Rock-salt scandium nitride has gained interest due to its thermoelectric properties including a relatively high Seebeck coefficient. This motivates research for other semiconductor materials that exhibit similar electronic structure features as ScN. Using density functional theory calculations, we have studied disordered solid solutions of (Zr-0.5, Mg-0.5)N and (Hf-0.5, Mg-0.5)N using the special quasi-random structure model. The results show that within a mean-field approximation for the configurational entropy, the order-disorder phase transformation between the monoclinic LiUN(2)prototype structure and the rock-salt cubic random alloy of these mentioned solid solutions occur at 740 K and 1005 K for (Zr-0.5, Mg-0.5)N and (Hf-0.5, Mg-0.5)N, respectively. The density-of-states for the two ternary compounds is also calculated and predicts semiconducting behavior with band gaps of 0.75 eV for (Zr-0.5, Mg-0.5)N and 0.92 eV for (Hf-0.5, Mg-0.5)N. The thermoelectric properties of both compounds are also predicted. We find that in the range of a moderate change in the Fermi level, a high Seebeck coefficient value at room temperature can be achieved.

In the materials design domain, much of the data from materials calculations are stored in different heterogeneous databases. Materials databases usually have different data models. Therefore, the users have to face the challenges to find the data from adequate sources and integrate data from multiple sources. Ontologies and ontology-based techniques can address such problems as the formal representation of domain knowledge can make data more available and interoperable among different systems. In this paper, we introduce the Materials Design Ontology (MDO), which defines concepts and relations to cover knowledge in the field of materials design. MDO is designed using domain knowledge in materials science (especially in solid-state physics), and is guided by the data from several databases in the materials design field. We show the application of the MDO to materials data retrieved from well-known materials databases.

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In the materials science domain the data-driven science paradigm has become the focus since the beginning of the 2000s. A large number of research groups and communities are building and developing data-driven workflows. However, much of the data and knowledge is stored in different heterogeneous data sources maintained by different groups. This leads to a reduced availability of the data and poor interoperability between systems in this domain. Ontology-based techniques are an important way to reduce these problems and a number of efforts have started. In this paper we investigate efforts in the materials science, and in particular in the nanotechnology domain, and show how such ontologies developed by domain experts, can be improved. We use a phrase-based topic model approach and formal topical concept analysis on unstructured text in this domain to suggest additional concepts and axioms for the ontology that should be validated by a domain expert. We describe the techniques and show the usefulness of the approach through an experiment where we extend two nanotechnology ontologies using approximately 600 titles and abstracts.

In the data-driven workflows in the materials science domain, much of the data and knowledge is stored in different heterogeneous data sources maintained by different groups. This leads to a reduced availability of the data and poor interoperability between systems in this domain. Ontology-based techniques are an important way to reduce these problems and a number of efforts have started. In this paper, we use a phrase-based topic model approach and formal topical concept analysis on unstructured text in this domain to suggest additional concepts and axioms for the ontology that should be validated by a domain expert.

Point defects in semiconductors are relevant for use in quantum technologies as room temperature qubits and single photon emitters. Among suggested defects for these applications are the negatively charged silicon vacancy and the neutral divacancy in SiC. The possible nonequivalent configurations of these defects have been identified in 4H-SiC, but for 6H-SiC, the work is still in progress. In this paper, we identify the different configurations of the silicon vacancy and the divacancy defects to each of the V1-V3 and the QL1-QL6 color centers in 6H-SiC, respectively. We accomplish this by comparing the results from ab initio calculations with experimental measurements for the zero-phonon line, hyperfine tensor, and zero-field splitting. Published under license by AIP Publishing.

To speed up the progress in the field of materials design, a number of challenges related to big data need to be addressed. This entry discusses these challenges and shows the semantic technologies that alleviate the problems related to variety, variability, and veracity.

Study and design of magneto-optically active single point defects in semiconductors are rapidly growing fields due to their potential in quantum bit (qubit) and single photon emitter applications. Detailed understanding of the properties of candidate defects is essential for these applications, and requires the identification of the defects microscopic configuration and electronic structure. In multicomponent semiconductors point defects often exhibit several non-equivalent configurations of similar but different characteristics. The most relevant example of such point defect is the divacancy in silicon carbide, where some of the non-equivalent configurations implement room temperature qubits. Here, we identify four different configurations of the divacancy in 4H-SiC via the comparison of experimental measurements and results of first-principle calculations. In order to accomplish this challenging task, we carry out an exhaustive numerical accuracy investigation of zero-phonon line and hyperfine coupling parameter calculations. Based on these results, we discuss the possibility of systematic quantum bit search.

Certain excitations, especially ones of long-range charge transfer character, are poorly described by time-dependent density functional theory (TDDFT) when typical (semi-)local functionals are used. A proper description of these excitations would require an exchange-correlation response differing substantially from the usual (semi-) local one. It has recently been shown that functionals of the generalized gradient approximation (GGA) type can yield unusual potentials, mimicking features of the exact exchange derivative discontinuity and showing divergences on orbital nodal surfaces. We here investigate whether these unusual potential properties translate into beneficial response properties. Using the Sternheimer formalism we closely investigate the response obtained with the 2013 exchange approximation by Armiento and Kummel (AK13) and the 1988 exchange approximation by Becke (B88), both of which show divergences on orbital nodal planes. Numerical calculations for Na-2 as well as analytical and numerical calculations for the hydrogen atom show that the response of AK13 behaves qualitatively different from usual semi-local functionals. However, the AK13 functional leads to fundamental instabilities in the asymptotic region that prevent its practical application in TDDFT. Our findings may help the development of future improved functionals. They also corroborate that the frequency-dependent Sternheimer formalism is excellently suited for running and analyzing TDDFT calculations.

Scandium nitride has recently gained interest as a prospective compound for thermoelectric applications due to its high Seebeck coefficient. However, ScN also has a relatively high thermal conductivity, which limits its thermoelectric efficiency and figure of merit (zT). These properties motivate a search for other semiconductor materials that share the electronic structure features of ScN, but which have a lower thermal conductivity. Thus, the focus of our study is to predict the existence and stability of such materials among inherently layered equivalent ternaries that incorporate heavier atoms for enhanced phonon scattering and to calculate their thermoelectric properties. Using density functional theory calculations, the phase stability of TiMgN2, ZrMgN2 and HfMgN2 compounds has been calculated. From the computationally predicted phase diagrams for these materials, we conclude that all three compounds are stable in these stoichiometries. The stable compounds may have one of two competing crystal structures: a monoclinic structure (LiUN2 prototype) or a trigonal superstructure (NaCrS2 prototype; RmH). The band structure for the two competing structures for each ternary is also calculated and predicts semiconducting behavior for all three compounds in the NaCrS2 crystal structure with an indirect band gap and semiconducting behavior for ZrMgN2 and HfMgN2 in the monoclinic crystal structure with a direct band gap. Seebeck coefficient and power factors are also predicted, showing that all three compounds in both the NaCrS2 and the LiUN2 structures have large Seebeck coefficients. The predicted stability of these compounds suggests that they can be synthesized by, e.g., physical vapor deposition.

We propose a multi-body solver that extends the Material Point Method (MPM) to simulate cracks in computer animation. We define cracks as the intersection between pieces of bodies created by a pre-fracture process and held together by massless particle constraints (glue particles). These pieces are simulated using a MPM multi-body solver extended by us to efficiently handle N-body collisions. Benefits of the present work include (1) low computational overhead compared to a normal MPM algorithm; (2) good scaling in three dimensions due to our use of sparse grids for background computations; (3) allowing for an easy and controllable setup phase to simulate a desired material failure mode, which is especially useful for computer animation. 

The Becke-Johnson model potential [A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 ( 2006)] and the potential of the AK13 functional [R. Armiento and S. Kummel, Phys. Rev. Lett. 111, 036402 ( 2013)] have been shown to mimic features of the exact Kohn-Sham exchange potential, such as step structures that are associated with shell closings and particle-number changes. A key element in the construction of these functionals is that the potential has a limiting value far outside a finite system that is a system-dependent constant rather than zero. We discuss a set of anomalous features in these functionals that are closely connected to the nonvanishing asymptotic potential. The findings constitute a formidable challenge for the future development of semilocal functionals based on the concept of a nonvanishing asymptotic constant.

Nodal surfaces of orbitals, in particular of the highest occupied one, play a special role in Kohn-Sham density-functional theory. The exact Kohn-Sham exchange potential, for example, shows a protruding ridge along such nodal surfaces, leading to the counterintuitive feature of a potential that goes to different asymptotic limits in different directions. We show here that nodal surfaces can heavily affect the potential of semilocal density-functional approximations. For the functional derivatives of the Armiento-Kummel (AK13) [Phys. Rev. Lett. 111, 036402 (2013)] and Becke88 [Phys. Rev. A 38, 3098 (1988)] energy functionals, i.e., the corresponding semilocal exchange potentials, as well as the Becke-Johnson [J. Chem. Phys. 124, 221101 (2006)] and van Leeuwen-Baerends (LB94) [Phys. Rev. A 49, 2421 (1994)] model potentials, we explicitly demonstrate exponential divergences in the vicinity of nodal surfaces. We further point out that many other semilocal potentials have similar features. Such divergences pose a challenge for the convergence of numerical solutions of the Kohn-Sham equations. We prove that for exchange functionals of the generalized gradient approximation (GGA) form, enforcing correct asymptotic behavior of the potential or energy density necessarily leads to irregular behavior on or near orbital nodal surfaces. We formulate constraints on the GGA exchange enhancement factor for avoiding such divergences.

The electronic properties of monolayer graphene grown epitaxially on SiC(0001) are known to be highly sensitive to the presence of NO2 molecules. The presence of small areas of bilayer graphene, on the other hand, considerably reduces the overall sensitivity of the surface. We investigate how NO2 molecules interact with monolayer and bilayer graphene, both free-standing and on a SiC(0001) substrate. We show that it is necessary to explicitly include the effect of the substrate in order to reproduce the experimental results. When monolayer graphene is present on SiC, there is a large charge transfer from the interface between the buffer layer and the SiC substrate to the molecule. As a result, the surface work function increases by 0.9 eV after molecular adsorption. A graphene bilayer is more effective at screening this interfacial charge, and so the charge transfer and change in work function after NO2 adsorption is much smaller.

The recent nonempirical semilocal exchange functional of Armiento and Kummel [Phys. Rev. Lett. 111, 036402 (2013)], AK13, incorporates a number of features reproduced by higher-order theory. The AK13 potential behaves analogously with the discontinuous jump associated with the derivative discontinuity at integer particle numbers. Recent works have established that AK13 gives a qualitatively improved orbital description compared to other semilocal methods, and reproduces a band structure closer to higher-order theory. However, its energies and energetics are inaccurate. The present work further investigates the deficiency in energetics. In addition to AK13 results, we find that applying the local-density approximation (LDA) non-self-consistently on the converged AK13 density gives very reasonable energetics with equilibrium lattice constants and bulk moduli well described across 13 systems. We also confirm that the attractive orbital features of AK13 are retained even after full structural relaxation. Hence, the deficient energetics cannot be a result of the AK13 orbitals having adversely affected the quality of the electron density compared to that of usual semilocal functionals; an improved orbital description and good energetics are not in opposition. This is also confirmed by direct calculation of the principal component of the electric field gradient. In addition, we prove that the non-self-consistent scheme is equivalent to using a single external-potential-dependent functional in an otherwise consistent, nonvariational Kohn-Sham density-functional theory (KS DFT) scheme. Furthermore, our results also demonstrate that, while an internally consistent KS functional is presently missing, non-self-consistent LDA on AK13 orbitals works as a practical nonempirical computational scheme to predict geometries, bulk moduli, while retaining the band structure features of AK13 at the computational cost of semi-local DFT.

Elpasolite is the predominant quaternary crystal structure (AlNaK2F6 prototype) reported in the Inorganic Crystal Structure Database. We develop a machine learning model to calculate density functional theory quality formation energies of all ∼2×10⁶ pristine ABC₂D₆ elpasolite crystals that can be made up from main-group elements (up to bismuth). Our model’s accuracy can be improved systematically, reaching a mean absolute error of 0.1  eV/atom for a training set consisting of 10×10³ crystals. Important bonding trends are revealed: fluoride is best suited to fit the coordination of the D site, which lowers the formation energy whereas the opposite is found for carbon. The bonding contribution of the elements A and B is very small on average. Low formation energies result from A and B being late elements from group II, C being a late (group I) element, and D being fluoride. Out of 2×10⁶ crystals, 90 unique structures are predicted to be on the convex hull—among which is NFAl₂C_a6, with a peculiar stoichiometry and a negative atomic oxidation state for Al.

The phase diagrams of the Ti-Zn-N, Zr-Zn-N, and Hf-Zn-N systems are determined using large-scale high-throughput density functional calculations. Thermodynamically stable ordered phases of TiZnN2, ZrZnN2, and HfZnN2 have been found to be promising candidates in piezoelectric devices/applications for energy harvesting. The identified stable phase of TiZnN2 is an ordered wurtzite superstructure, and the stable phases of ZrZnN2 and HfZnN2 have a layered structure with alternating tetrahedral ZnN and octahedral (Zr, Hf)N layers. All of the TMZnN2 (TM = Ti, Zn, Hf) structures exhibit electronic bandgaps and large piezoelectric constants, d(33)(TiZnN2) = 14.21; d(24)(ZrZnN2) = -26.15, and d(24)(HfZnN2) = -21.99 pC/N. The strong piezoelectric responses and their thermodynamical stability make materials with these phases promising candidates for piezoelectric applications. Published by AIP Publishing.

We investigate the structural and electronic properties of Li-intercalated monolayer graphene on SiC(0001) using combined angle-resolved photoemission spectroscopy and first-principles density functional theory. Li intercalates at room temperature both at the interface between the buffer layer and SiC and between the two carbon layers. The graphene is strongly n-doped due to charge transfer from the Li atoms and two pi bands are visible at the (K) over bar point. After heating the sample to 300 degrees C, these pi bands become sharp and have a distinctly different dispersion to that of Bernal-stacked bilayer graphene. We suggest that the Li atoms intercalate between the two carbon layers with an ordered structure, similar to that of bulk LiC6. An AA stacking of these two layers becomes energetically favourable. The pi bands around the (K) over bar point closely resemble the calculated band structure of a C6LiC6 system, where the intercalated Li atoms impose a superpotential on the graphene electronic structure that opens gaps at the Dirac points of the two pi cones.

Transition metal diborides are ceramic materials with potential applications as hard protective thin films and electrical contact materials. We investigate the possibility to obtain age hardening through isostructural clustering, including spinodal decomposition, or ordering-induced precipitation in ternary diboride alloys. By means of first-principles mixing thermodynamics calculations, 45 ternary (M1-xMxB2)-M-1-B-2 alloys comprising (MB2)-B-i (M-i = Mg, Al, Sc, Y, Ti, Zr, Hf, V, Nb, Ta) with AlB2 type structure are studied. In particular Al1-xTixB2 is found to be of interest for coherent isostructural decomposition with a strong driving force for phase separation, while having almost concentration independent a and c lattice parameters. The results are explained by revealing the nature of the electronic structure in these alloys, and in particular, the origin of the pseudogap at E-F in TiB2, ZrB2, and HfB2.

The electronic properties of epitaxial graphene grown on SiC(0001) are known to be impaired relative to those of freestanding graphene. This is due to the formation of a carbon buffer layer between the graphene layers and the substrate, which causes the graphene layers to become strongly n-doped. Charge neutrality can be achieved by completely passivating the dangling bonds of the clean SiC surface using atomic intercalation. So far, only one element, hydrogen, has been identified as a promising candidate. We show, using first-principles density functional calculations, how it can also be accomplished via the growth of a thin layer of silicon nitride on the SiC surface. The subsequently grown graphene layers display the electronic properties associated with charge neutral graphene. We show that the surface energy of this structure is considerably lower than that of others with intercalated atomic nitrogen and determine how its stability depends on the N-2 chemical potential.

We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a dataset of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37eV/atom for the respective representations.

A recently published generalized gradient approximation functional within density functional theory (DFT) has shown, in a few paradigm tests, an improved KS orbital description over standard (semi) local approximations. The characteristic feature of this functional is an enhancement factor that diverges like s ln(s) for large reduced density gradients s which leads to unusual properties. We explore the improved orbital description of this functional more thoroughly by computing the electronic band structure, band gaps, and the optical dielectric constants in semiconductors, Mott insulators, and ionic crystals. Compared to standard semilocal functionals, we observe improvement in both the band gaps and the optical dielectric constants. In particular, the results are similar to those obtained with orbital functionals or by perturbation theory methods in that it opens band gaps in systems described as metallic by standard (semi) local density functionals, e. g., Ge, alpha-Sn, and CdO.

Band structure engineering for specific electronic or optical properties is essential for the further development of many important technologies including thermoelectrics, optoelectronics, and microelectronics. In this work, we report orbital interaction as a powerful tool to finetune the band structure and the transport properties of charge carriers in bulk crystalline semiconductors. The proposed mechanism of orbital interaction on band structure is demonstrated for IV-VI thermoelectric semiconductors. For IV-VI materials, we find that the convergence of multiple carrier pockets not only displays a strong correlation with the s-p and spin-orbit coupling but also coincides with the enhancement of power factor. Our results suggest a useful path to engineer the band structure and an enticing solid-solution design principle to enhance thermoelectric performance.

We screen a large chemical space of perovskite alloys for systems with optimal properties to accommodate a morphotropic phase boundary (MPB) in their composition-temperature phase diagram, a crucial feature for high piezoelectric performance. We start from alloy end points previously identified in a high-throughput computational search. An interpolation scheme is used to estimate the relative energies between different perovskite distortions for alloy compositions with a minimum of computational effort. Suggested alloys are further screened for thermodynamic stability. The screening identifies alloy systems already known to host an MPB and suggests a few others that may be promising candidates for future experiments. Our method of investigation may be extended to other perovskite systems, e.g., (oxy-)nitrides, and provides a useful methodology for any application of high-throughput screening of isovalent alloy systems.

Only a single linearly dispersing π-band cone, characteristic of monolayer graphene, has so far been observed in Angle Resolved Photoemission (ARPES) experiments on multilayer graphene grown on C-face SiC. A rotational disorder that effectively decouples adjacent layers has been suggested to explain this. However, the coexistence of μm-sized grains of single and multilayer graphene with different azimuthal orientations and no rotational disorder within the grains was recently revealed for C-face graphene, but conventional ARPES still resolved only a single π-band. Here we report detailed nano-ARPES band mappings of individual graphene grains that unambiguously show that multilayer C-face graphene exhibits multiple π-bands. The band dispersions obtained close to the K-point moreover clearly indicate, when compared to theoretical band dispersion calculated in the framework of the density functional method, Bernal (AB) stacking within the grains. Thus, contrary to earlier claims, our findings imply a similar interaction between graphene layers on C-face and Si-face SiC.

We derive a closed-form expression for the quantum corrections to the kinetic energy density in the Thomas-Fermi limit of a linear potential model system in three dimensions (the Airy gas). The universality of the expression is tested numerically in a number of three-dimensional model systems: (i) jellium surfaces, (ii) confinement in a hydrogenlike potential (the Bohr atom), (iii) particles confined by a harmonic potential in one and (iv) all three dimensions, and (v) a system with a cosine potential (the Mathieu gas). Our results confirm that the usual gradient expansion of extended Thomas-Fermi theory does not describe the quantum oscillations for systems that incorporate surface regions where the electron density drops off to zero. We find that the correction derived from the Airy gas is universally applicable to relevant spatial regions of systems of types (i), (ii), and (iv), but somewhat surprisingly not (iii). We discuss possible implications of our findings to the development of functionals for the kinetic energy density.

Hybrid functionals serve as a powerful practical tool in different fields of computational physics and quantum chemistry. On the other hand, their applicability for the case of correlated d and f orbitals is still questionable and needs more considerations. In this article we formulate the on-site occupation dependent exchange correlation energy and effective potential of hybrid functionals for localized states and connect them to the on-site correction term of the DFT+ U method. The resultant formula indicates that the screening of the onsite electron repulsion is governed by the ratio of the exact exchange in hybrid functionals. Our derivation provides a theoretical justification for adding a DFT+ U-like on-site potential in hybrid-DFT calculations to resolve issues caused by overscreening of localized states. The resulting scheme, hybrid DFT+ V-w, is tested for chromium impurity in wurtzite AlN and vanadium impurity in 4H-SiC, which are paradigm examples of systems with different degrees of localization between host and impurity orbitals.

We have previously proposed that further improved functionals for density functional theory can be constructed based on the Armiento-Mattsson subsystem functional scheme if, in addition to the uniform electron gas and surface models used in the Armiento-Mattsson 2005 functional, a model for the strongly confined electron gas is also added. However, of central importance for this scheme is an index that identifies regions in space where the correction provided by the confined electron gas should be applied. The electron localization function (ELF) is a well-known indicator of strongly localized electrons. We use a model of a confined electron gas based on the harmonic oscillator to show that regions with high ELF directly coincide with regions where common exchange energy functionals have large errors. This suggests that the harmonic oscillator model together with an index based on the ELF provides the crucial ingredients for future improved semi-local functionals. For a practical illustration of how the proposed scheme is intended to work for a physical system we discuss monoclinic cupric oxide, CuO. A thorough discussion of this system leads us to promote the cell geometry of CuO as a useful benchmark for future semi-local functionals. Very high ELF values are found in a shell around the O ions, and take its maximum value along the Cu–O directions. An estimate of the exchange functional error from the effect of electron confinement in these regions suggests a magnitude and sign that could account for the error in cell geometry.

Constructing approximations for the exchange-correlation (xc) potential in density functional theory instead of the energy appears attractive because it may provide for a way of easily incorporating desirable features such as a particle number discontinuity into xc functionals. However, xc potentials that are constructed directly are problematic: An xc potential that is not a priori derived as a functional derivative of some xc energy functional is most likely not a functional derivative of any density functional at all. This severely limits the usefulness of directly constructed xc potentials, e.g., for calculating electronic excitations. For the explicit example of the Becke-Johnson (BJ) potential we discuss defining corresponding energy expressions by density path integrals. We show that taking the functional derivative of these energies does not lead back to potentials that are close to the BJ one, and the new potentials do not share the attractive features of the original BJ expression. With further examples we demonstrate that this is a general finding and not specific to the BJ potential form.