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.

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.

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 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.

Units of measure are central in all areas of science and technology. There are several ontologicalframeworks aiming to improve interoperability and precision in digital data exchange of quantitiesinvolving units. We introduce an ontology that specifically targets challenges for handling units acrossdatabases of computational and experimental data from various sources. The ontology is created usingdefinition files from the community-driven OPTIMADE standard for a common API for materialsdatabases. The resulting ontology allows addressing data integration challenges encountered in thateffort, including (i) referencing both specific and more general instances of units that have changedover time; (ii) the use of unit systems to define short domain-relevant identifiers for a collection of unitsthat make sense within a specific subdomain, rather than having to adopt globally standardized namingschemes; (iii) specifications of relationships between units that enables tools to convert between them;and (iv) units not part of the International System of Units (SI) can be represented without defining themin SI units or using SI system conventions. This paper provides a brief survey of existing ontologiesfor units of measure and then presents the design and discuss features of an ontology based on theOPTIMADE unit definitions.

Density functional theory using accepted semi-local exchange-correlation functionals is generally successful for structural properties. However, for electrical response calculations of extended molecular systems, like e.g. polyacetylene, they make large errors; for the hyperpolarizability the error can be several orders of magnitude. The errors can be traced to qualitative differences between the exchange potentials of semi-local and exact exchange methods. A recent effort has been successful in using a corrective term based on semi-local quantities to introduce the missing features directly into the exchange potential (as opposed to modeling the exchange-correlation energy). The resulting potential reproduces the derivative discontinuity, step structure, and counteracting field slope of exact exchange. It gives the polarizability of hydrogen chains with similar accuracy as exact exchange methods.

We present a large-scale density functional theory (DFT) investigation of the ABO(3) chemical space in the perovskite crystal structure, with the aim of identifying those that are relevant for forming piezoelectric materials. Screening criteria on the DFT results are used to select 49 compositions, which can be seen as the fundamental building blocks from which to create alloys with potentially good piezoelectric performance. This screening finds all the alloy end points used in three well-known high-performance piezoelectrics. The energy differences between different structural distortions, deformation, coupling between the displacement of the A and B sites, spontaneous polarization, Born effective charges, and stability is analyzed in each composition. We discuss the features that cause the high piezoelectric performance of the well-known piezoelectric lead zirconate titanate (PZT), and investigate to what extent these features occur in other compositions. We demonstrate how our results can be useful in the design of isovalent alloys with high piezoelectric 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.

We derive an exchange energy functional of generalized gradient form with a corresponding potential that changes discontinuously at integer particle numbers. The functional is semilocal, yet incorporates key features that are connected to the derivative discontinuity of Kohn-Sham density-functional theory. We validate our construction for several paradigm systems and explain how it addresses central well-known deficiencies of antecedent semilocal methods, i.e., the description of charge transfer, properly localized orbitals, and band gaps. We find, e.g., an improved shell structure for atoms, eigenvalues that more closely correspond to ionization energies, and an improved description of band structure where localized states are lowered in energy.

An exchange potential functional is constructed from semi-local quantities and is shown to reproduce hydrogen chain polarizabilities with the same accuracy as exact exchange methods. We discuss the exchange potential features that are essential for accurate polarizability calculations, i.e., derivative discontinuities and the potential step structure. The possibility of a future generalization of the methods into a complete semi-local exchange-correlation functional is discussed.

It has recently been shown that local values of the conventional exchange energy per particle cannot be described by an analytic expansion in the density variation. Yet, it is known that the total exchange-correlation (XC) energy per particle does not show any corresponding nonanalyticity. Indeed, the nonanalyticity is here shown to be an effect of the separation into conventional exchange and correlation. We construct an alternative separation in which the exchange part is made well behaved by screening its long-ranged contributions, and the correlation part is adjusted accordingly. This alternative separation is as valid as the conventional one, and introduces no new approximations to the total XC energy. We demonstrate functional development based on this approach by creating and deploying a local-density-approximation-type XC functional. Hence, this work includes both the theory and the practical calculations needed to provide a starting point for an alternative approach towards improved approximations of the total XC energy.

We design a density-functional-theory (DFT) exchange-correlation functional that enables an accurate treatment of systems with electronic surfaces. Surface-specific approximations for both exchange and correlation energies are developed. A subsystem functional approach is then used: an interpolation index combines the surface functional with a functional for interior regions. When the local density approximation is used in the interior, the result is a straightforward functional for use in self-consistent DFT. The functional is validated for two metals (Al, Pt) and one semiconductor (Si) by calculations of (i) established bulk properties (lattice constants and bulk moduli) and (ii) a property where surface effects exist (the vacancy formation energy). Good and coherent results indicate that this functional may serve well as a universal first choice for solid-state systems and that yet improved functionals can be constructed by this approach.

A viable way of extending the successful use of density-functional theory into studies of even more complex systems than are addressed today has been suggested by Kohn and Mattsson [W. Kohn and A. E. Mattsson, Phys. Rev. Lett. 81, 3487 (1998); A. E. Mattsson and W. Kohn, J. Chem. Phys. 115, 3441 (2001)], and is further developed in this work. The scheme consists of dividing a system into subsystems and applying different approximations for the unknown (but general) exchange-correlation energy functional to the different subsystems. We discuss a basic requirement on approximative functionals used in this scheme; they must all adhere to a single explicit choice of the exchange-correlation energy per particle. From a numerical study of a model system with a cosine effective potential, the Mathieu gas, and one of its limiting cases, the harmonic oscillator model, we show that the conventional definition of the exchange energy per particle cannot be described by an analytical series expansion in the limit of slowly varying densities. This indicates that the conventional definition is not suitable in the context of subsystem functionals. We suggest alternative definitions and approaches to subsystem functionals for slowly varying densities and discuss the implications of our findings on the future of functional development.

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.

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.

We develop a technique for predicting the Curie temperature of magnetic materials using density functional theory calculations suitable to include in high-throughput frameworks. We apply four different models, including physically relevant observables, and assess numerical constants by studying 32 ferro- and ferrimagnets. With the best-performing model, the Curie temperature can be predicted with a mean absolute error of approximately 126 K. As predictive factors, the models consider either the energy differences between the magnetic ground state and a magnetically disordered paramagnetic state, or the average constraining fields acting on magnetic moments in a disordered local moments calculation. Additionally, the energy differences are refined by incorporating the magnetic entropy of the paramagnetic state and the number of nearest magnetic neighbors of the magnetic atoms. The most advanced model is found to extend well into Fe1-xCox alloys, indicating the potential efficacy of utilizing our model in designing materials with tailored Curie temperatures by altering alloy compositions. This examination can illuminate the factors influencing magnetic transition temperatures in magnetic materials and provide insights into how they can be employed to make quantitative predictions of Curie temperatures. Our approach is not restricted to specific crystal structures or chemical compositions. It offers a more cost-effective alternative, in terms of human time and need for hands-on oversight, to other density functional theory methods for predicting the Curie temperature. As a result, it provides a practical strategy for conducting high-throughput screening for new technologically applicable magnetic materials. Alternatively, it can complement ML-based screening of magnetic materials by integrating physical principles into such approaches, thereby enhancing their prediction accuracy.

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.

Defects in semiconductors have in recent years been revealed to have interesting properties in the venture towards quantum technologies. In this regard, silicon carbide has shown great promise as a host for quantum defects. In particular, the ultrabright AB photoluminescence lines in 4H-SiC H-SiC are observable at room temperature and have been proposed as a single-photon quantum emitter. These lines have previously been studied and assigned to the carbon-antisite-vacancy (CAV) pair. In this paper, we report on new measurements of the AB lines' temperature dependence, and carry out an in-depth computational study on the optical properties of the CAV defect. We find that the CAV defect has the potential to exhibit several different zero-phonon luminescences with emissions in the near-infrared telecom band, in its neutral and positive charge states. However, our measurements show that the AB lines only consist of three nonthermally activated lines instead of the previously reported four lines; meanwhile, our calculations on the CAV defect are unable to find optical transitions in full agreement with the AB-line assignment. In light of our results, the identification of AB lines and the associated room-temperature emission require further study.

Defects in semiconductors have in recent years been revealed to have interesting properties in the venture towards quantum technologies. In this regard, silicon carbide has shown great promise as a host for quantum defects. In particular, the ultrabright AB photoluminescence lines in 4⁢H-Si⁢C are observable at room temperature and have been proposed as a single-photon quantum emitter. These lines have previously been studied and assigned to the carbon–antisite-vacancy (CAV) pair. In this paper, we report on new measurements of the AB lines’ temperature dependence, and carry out an in-depth computational study on the optical properties of the CAV defect. We find that the CAV defect has the potential to exhibit several different zero-phonon luminescences with emissions in the near-infrared telecom band, in its neutral and positive charge states. However, our measurements show that the AB lines only consist of three nonthermally activated lines instead of the previously reported four lines; meanwhile, our calculations on the CAV defect are unable to find optical transitions in full agreement with the AB-line assignment. In light of our results, the identification of AB lines and the associated room-temperature emission require further study.

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.

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 advent of machine learning in materials science opens the way for exciting and ambitious simulations of large systems and long time scales with the accuracy of ab initio calculations. Recently, several pretrained universal machine learned interatomic potentials (UPMLIPs) have been published, i.e., potentials distributed with a single set of weights trained to target systems across a very wide range of chemistries and atomic arrangements. These potentials raise the hope of reducing the computational cost and methodological complexity of performing simulations compared to models that require for-purpose training. However, the application of these models needs critical evaluation to assess their usability across material types and properties. In this work, we investigate the application of the following UPMLIPs: MACE, CHGNET, and M3GNET to the context of alloy theory. We calculate the mixing enthalpies and volumes of 21 binary alloy systems and compare the results with DFT calculations to assess the performance of these potentials over different properties and types of materials. We find that the small relative energies necessary to correctly predict mixing energies are generally not reproduced by these methods with sufficient accuracy to describe correct mixing behaviors. However, the performance can be significantly improved by supplementing the training data with relevant training data. The potentials can also be used to partially accelerate these calculations by replacing the ab initio structural relaxation step.

We compare the accuracy of conventional semilocal density functional theory (DFT), the DFT+U method, and the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional for structural parameters, redox reaction energies, and formation energies of transition metal compounds. Conventional DFT functionals significantly underestimate redox potentials for these compounds. Zhou et al. [Phys. Rev. B 70, 235121 (2004)] addressed this issue with DFT+U and a linear-response scheme for calculating U values. We show that the Li intercalation potentials of prominent Li-ion intercalation battery materials, such as the layered Li(x)MO(2) (M=Co and Ni), Li(x)TiS(2); olivine Li(x)MPO(4) (M=Mn, Fe, Co, and Ni); and spinel-like Li(x)Mn(2)O(4), Li(x)Ti(2)O(4), are also well reproduced by HSE06, due to the self-interaction error correction from the partial inclusion of Hartree-Fock exchange. For formation energies, HSE06 performs well for transition metal compounds, which typically are not well reproduced by conventional DFT functionals but does not significantly improve the results of nontransition metal oxides. Hence, we find that hybrid functionals provide a good alternative to DFT+U for transition metal applications when the large extra computational effort is compensated by the benefits of (i) avoiding species-specific adjustable parameters and (ii) a more universal treatment of the self-interaction error that is not exclusive to specific atomic orbital projections on selected ions.

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.

Doping of a two-dimensional (2D) material by impurity atoms occurs via two distinct mechanisms: absorption of the dopants by the 2D crystal or adsorption on its surface. To distinguish the relevant mechanism, we systematically dope 53 experimentally synthesized 2D monolayers by 65 different chemical elements in both absorption and adsorption sites. The resulting 17,598 doped monolayer structures were generated using the newly developed ASE DefectBuilder—a Python tool to set up point defects in 2D and bulk materials—and subsequently relaxed by an automated high-throughput density functional theory (DFT) workflow. We find that interstitial positions are preferred for small dopants with partially filled valence electrons in host materials with large lattice parameters. In contrast, adatoms are favored for dopants with a low number of valence electrons due to lower coordination of adsorption sites compared to interstitials. The relaxed structures, characterization parameters, defect formation energies, and magnetic moments (spins) are available in an open database to help advance our understanding of defects in 2D materials.

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).

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.

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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.

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.

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.

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.

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.

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.

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.

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.

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.

(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.

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.

The subsystem functional scheme is a promising approach recently proposed for constructing exchange-correlation density functionals. In this scheme, the physics in each part of real materials is described by mapping to a characteristic model system. The "confinement physics," an essential physical ingredient that has been left out in present functionals, is studied by employing the harmonic-oscillator (HO) gas model. By performing the potential -greater than density and the density -greater than exchange energy per particle mappings based on two model systems characterizing the physics in the interior (uniform electron-gas model) and surface regions (Airy gas model) of materials for the HO gases, we show that the confinement physics emerges when only the lowest subband of the HO gas is occupied by electrons. We examine the approximations of the exchange energy by several state-of-the-art functionals for the HO gas, and none of them produces adequate accuracy in the confinement dominated cases. A generic functional that incorporates the description of the confinement physics is needed.

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.

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.

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.

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.

Predicting the polarizabilities of extended conjugated molecules with semilocal functionals has been a long-standing problem in density functional theory. These difficulties are due to the absence of a term in the typical semilocal Kohn-Sham exchange potentials that has been named "ultranonlocal". Such a term should develop in extended systems when an external electric field is applied, and it should counteract the field. We calculate the polarizabilities of polyacetylene molecules using the recently developed extended Becke-Johnson functional. Our results show that this functional predicts the polarizabilities with much better accuracy than typical semilocal functionals. Thus, the field-counteracting term in this functional, which is semilocal in the Kohn-Sham orbitals, can realistically describe real molecules. We discuss approaches of constructing an energy functional that corresponds to this potential functional, for example, via the Levy-Perdew virial relation.

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.

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.