Phase stability predictions are central to computational materials discovery efforts and have been made possible by large databases of computed properties from high-throughput density functional theory (DFT) calculations. Such databases now contain millions of calculations at the generalized gradient approximation (GGA) level of theory, representing an enormous investment of computational resources. Although it is now feasible to carry out large numbers of calculations using more accurate methods, such as meta-GGA functionals, recomputing the entirety of a database with a higher-fidelity method is impractical and would not effectively leverage the value embodied in existing calculations. Instead, we propose in this work a general procedure by which higher-fidelity, low-coverage calculations (e.g., meta-GGA calculations for selected chemical systems) can be combined with lower-fidelity, high-coverage calculations (e.g., an existing database of GGA calculations) in a robust and scalable manner to yield improved phase stability predictions. We demonstrate our scheme using legacy GGA(+\textit{U}) calculations and new r$^2$SCAN meta-GGA calculations from the Materials Project and illustrate its application to solid and aqueous phase stability. We discuss practical considerations for constructing mixed phase diagrams and present guidelines for prioritizing high-fidelity calculations for maximum benefit.

The Materials Project was launched formally in 2011 to drive materials discovery forwards through high-throughput computation and open data. More than a decade later, the Materials Project has become an indispensable tool used by more than 600,000 materials researchers around the world. This Perspective describes how the Materials Project, as a data platform and a software ecosystem, has helped to shape research in data-driven materials science. We cover how sustainable software and computational methods have accelerated materials design while becoming more open source and collaborative in nature. Next, we present cases where the Materials Project was used to understand and discover functional materials. We then describe our efforts to meet the needs of an expanding user base, through technical infrastructure updates ranging from data architecture and cloud resources to interactive web applications. Finally, we discuss opportunities to better aid the research community, with the vision that more accessible and easy-to-understand materials data will result in democratized materials knowledge and an increasingly collaborative community.

In this work, we extend the source-free (SF) exchange correlation (XC) functional developed by Sangeeta Sharma and co-workers to plane-wave density functional theory (DFT) based on the projector augmented wave (PAW) method. This constraint is implemented by the current authors within the VASP source code, using a fast Poisson solver that capitalizes on the parallel three-dimensional fast Fourier transforms (FFTs) implemented in VASP. Using this modified XC functional, we explore the improved convergence behavior that results from applying this constraint to the GGA-PBE+U+J functional. In the process, we compare the non-collinear magnetic ground state computed by each functional and their SF counterpart for a select number of magnetic materials in order to provide a metric for comparing with experimentally determined magnetic orderings. We observe significantly improved agreement with experimentally measured magnetic ground state structures after applying the source-free constraint. Furthermore, we explore the importance of considering probability current densities in spin polarized systems, even under no applied field. We analyze the XC torque as well, in order to provide theoretical and computational analyses of the net XC magnetic torque induced by the source-free constraint. Along these lines, we highlight the importance of properly considering the real-space integral of the source-free local magnetic XC field. Our analysis on probability currents, net torque, and constant terms draws additional links to the rich body of previous research on spin-current density functional theory (SCDFT), and paves the way for future extensions and corrections to the SF corrected XC functional.

The elasticity tensor that describes the elastic response of a material to external forces is among the most fundamental properties of materials. The availability of full elasticity tensors for inorganic crystalline compounds, however, is limited due to experimental and computational challenges. Here, we report the materials tensor (MatTen) model for rapid and accurate estimation of the full fourth-rank elasticity tensors of crystals. Based on equivariant graph neural networks, MatTen satisfies the two essential requirements for elasticity tensors: independence of the frame of reference and preservation of material symmetry. Consequently, it provides a unified treatment of elasticity tensors for all seven crystal systems across diverse chemical spaces, without the need to deal with each separately.. MatTen was trained on a dataset of first-principles elasticity tensors garnered by the Materials Project over the past several years (we are releasing the data herein) and has broad applications in predicting the isotropic elastic properties of polycrystalline materials, examining the anisotropic behavior of single crystals, and discovering new materials with exceptional mechanical properties. Using MatTen, we have discovered a hundred new crystals with extremely large maximum directional Young's modulus and eleven polymorphs of elemental cubic metals with unconventional spatial orientation of Young's modulus.

Spectator ions have known and emerging roles in aqueous metal-cation chemistry, respectively directing solubility, speciation, and reactivity. Here, we isolate and structurally characterize the last two metastable members of the alkali uranyl triperoxide series, the Rb+ and Cs+ salts (Cs-U-1 and Rb-U-1). We document their rapid solution polymerization via small-angle X-ray scattering, which is compared to the more stable Li+, Na+ and K+ analogues. To understand the role of the alkalis, we also quantify alkali-hydroxide promoted peroxide deprotonation and decomposition, which generally exhibits increasing reactivity with increasing alkali size. Cs-U-1, the most unstable of the uranyl triperoxide monomers, undergoes ambient direct air capture of CO2 in the solid-state, converting to Cs-4[(UO2)-O-VI(CO3)(3)], evidenced by single-crystal X-ray diffraction, transmission electron microscopy, and Raman spectroscopy. We have attempted to benchmark the evolution of Cs-U-1 to uranyl tricarbonate, which involves a transient, unstable hygroscopic solid that contains predominantly pentavalent uranium, quantified by X-ray photoelectron spectroscopy. Powder X-ray diffraction suggests this intermediate state contains a hydrous derivative of (CsUO3)-O-V, where the parent phase has been computationally predicted, but not yet synthesized.

DFT+U provides a convenient, cost-effective correction for the self-interaction error (SIE) that arises when describing correlated electronic states using conventional approximate density functional theory (DFT). The success of a DFT+U(+J) calculation hinges on the accurate determination of its Hubbard U and Hund's J parameters, and the linear response (LR) methodology has proven to be computationally effective and accurate for calculating these parameters. This study provides a high-throughput computational analysis of the U and J values for transition metal d-electron states in a representative set of over 2000 magnetic transition metal oxides (TMOs), providing a frame of reference for researchers who use DFT+U to study transition metal oxides. In order to perform this high-throughput study, an atomate workflow is developed for calculating U and J values automatically on massively parallel supercomputing architectures. To demonstrate an application of this workflow, the spin-canting magnetic structure and unit cell parameters of the multiferroic olivine LiNiPO4 are calculated using the computed Hubbard U and Hund J values for Ni-d and O-p states, and are compared with experiment. Both the Ni-d U and J corrections have a strong effect on the Ni-moment canting angle. Additionally, including a O-p U value results in a significantly improved agreement between the computed lattice parameters and experiment.

Co_1-xMn_xCr_2O_4 crystallizes as a normal spinel in the cubic Fd 3m space group, and the end members have been reported to display a region of collinear ferrimagnetism as well as a low-temperature spin-spiral state with variable coherence lengths from 3 nm to 10 nm in polycrystalline samples. Here, we present the synthesis of the entire solid solution, and data showing that the ferrimagnetic ordering temperature as well as the spin-spiral lock-in temperature are tunable with the Co/Mn ratio. The peak magnetocaloric entropy change was determined to be Δ S_M = -5.63 J kg^-1 K^-1 in an applied magnetic field change of Δ H = 0 T to 5 T for the Mn end-member at the ferrimagnetic ordering temperature. Using density functional theory (DFT), we explore the shortcomings of the magnetic deformation proxy to identify trends in Δ S_M across composition in this spinel system, and explore future extensions of theory to address these discrepancies.

Co$_{1-x}$Mn$_x$Cr$_2$O$_4$ crystallizes as a normal spinel in the cubic $Fd \overline{3}m$ space group, and the end members have been reported to display a region of collinear ferrimagnetism as well as a low-temperature spin-spiral state with variable coherence lengths from 3 nm to 10 nm in polycrystalline samples. Here, we present the synthesis of the entire solid solution, and data showing that the ferrimagnetic ordering temperature as well as the spin-spiral lock-in temperature are tunable with the Co/Mn ratio. The peak magnetocaloric entropy change was determined to be $\Delta S_M$ = -5.63 J kg$^{-1}$ K$^{-1}$ in an applied magnetic field change of $\Delta H$ = 0 T to 5 T for the Mn end-member at the ferrimagnetic ordering temperature. Using density functional theory (DFT), we explore the shortcomings of the magnetic deformation proxy to identify trends in $\Delta S_M$ across composition in this spinel system, and explore future extensions of theory to address these discrepancies.

The elasticity tensor that describes the elastic response of a material to external forces is among the most fundamental properties of materials. The availability of full elasticity tensors for inorganic crystalline compounds, however, is limited due to experimental and computational challenges. Here, we report the materials tensor (MatTen) model for rapid and accurate estimation of the full fourth-rank elasticity tensors of crystals. Based on equivariant graph neural networks, MatTen satisfies the two essential requirements for elasticity tensors: independence of the frame of reference and preservation of material symmetry. Consequently, it provides a unified treatment of elasticity tensors for all seven crystal systems across diverse chemical spaces, without the need to deal with each separately.. MatTen was trained on a dataset of first-principles elasticity tensors garnered by the Materials Project over the past several years (we are releasing the data herein) and has broad applications in predicting the isotropic elastic properties of polycrystalline materials, examining the anisotropic behavior of single crystals, and discovering new materials with exceptional mechanical properties. Using MatTen, we have discovered a hundred new crystals with extremely large maximum directional Young's modulus and eleven polymorphs of elemental cubic metals with unconventional spatial orientation of Young's modulus.

# Elasticity tensors of 10276 crystals from density functional theory (DFT) computations This dataset consists of three data files in the json format. Each file is explained below. ## crystal_elasticity_tensor.json DFT computed elastic tensors of 10276 crystals used for developing the MatTen model. structure: crystal structure of the materialformula_pretty: chemical formulacrystal_system: crystal systemelastic_tensor: full fourth-rank elastic tensorelastic_tensor_voigt: 6x6 Voigt matrix of the elastic tensorsplit: split of the data into train, validation, and test subsets for model development ## max_directional_E.json New crystals with large maximum directional Young's modulus. material_id: Materials Project identifierformula_pretty: chemical formula structure_original: crystal structure from the Materials Project databaseelastic_tensor_matten_original: MatTen predicted elastic tensor using `structure_original`max_directional_E_matten_original: MatTen predicted maximum directional Young's modulus using `structure_original` structure: further DFT optimized structure with a tigher criterionelastic_tensor: DFT elastic tensor corresponding to `structure`max_directional_E: DFT maximum directional Young's modulus using `structure`elastic_tensor_matten: MatTen predicted elastic tensor using `structure`max_directional_E_matten: MatTen predicted maximum directional Young's modulus using `structure` ## elemental_cubic_metal_max_E_along_100_direction.json New crystals with its maximum directional Young's modulus along the [100] direction. material_id: Materials Project identifierformula_pretty: chemical formula structure_original: crystal structure from the Materials Project databaseelastic_tensor_matten: MatTen predicted elastic tensor using `structure_original`Delta_S_matten: value of $S_{1111} - S_{1122} - 2*S_{2323}$ using `elastic_tensor_matten` structure: further DFT optimized structure with a tigher criterionelastic_tensor: DFT elastic tensor corresponding to `structure`Delta_S: value of $S_{1111} - S_{1122} - 2*S_{2323}$ using `elastic_tensor`

Many semiconductors present weak or forbidden transitions at their fundamental band gaps, inducing a widened region of transparency. This occurs in high-performing n-type transparent conductors (TCs) such as Sn-doped In2O3 (ITO), however thus far the presence of forbidden transitions has been neglected in searches for new p-type TCs. To address this, we first compute high-throughput absorption spectra across 18,000 semiconductors, showing that over half exhibit forbidden or weak optical transitions at their band edges. Next, we demonstrate that compounds with highly localized band edge states are more likely to present forbidden transitions. Lastly, we search this set for p-type and n-type TCs with forbidden or weak transitions. Defect calculations yield unexplored TC candidates such as ambipolar BeSiP2, Zr2SN2 and KSe, p-type BAs, Au2S, and AuCl, and n-type Ba2InGaO5, GaSbO4, and KSbO3, among others. We share our data set via the MPContribs platform, and we recommend that future screenings for optical properties use metrics representative of absorption features rather than band gap alone.

Advanced chemical research is increasingly reliant on large computed datasets of molecules and reactions to discover new functional molecules, understand chemical trends, train machine learning models, and more. To be of greatest use to the scientific community, such datasets should follow FAIR principles (i.e. be findable, accessible, interoperable, and reusable). In this work, we present a FAIR expansion of the Materials Project database ("MPcules") that adds more than 170,000 molecules studied using density functional theory (DFT) to the existing data, which comprises crystalline solids. MPcules is a diverse collection of DFT calculated molecular properties, with an emphasis on reactive, open-shell, and charged species - relevant for studying reaction pathways - and a wide array of structural, electronic, vibrational, and thermodynamic properties. This database can be queried through an OpenAPI-compliant application programming interface and a featureful web application. We continue to expand the data available on MPcules and encourage contributions from the community.

Crystal Toolkit is an open source tool for viewing, analyzing and transforming crystal structures, molecules and other common forms of materials science data in an interactive way. It is intended to help beginners rapidly develop web-based apps to explore their own data or to help developers make their research algorithms accessible to a broader audience of scientists who might not have any training in computer programming and who would benefit from graphical interfaces. Crystal Toolkit comes with a library of ready-made components that can be assembled to make complex web apps: simulation of powder and single crystalline diffraction patterns, convex hull phase diagrams, Pourbaix diagrams, electronic band structures, analysis of local chemical environments and symmetry, and more. Crystal Toolkit is now powering the Materials Project website frontend, providing user-friendly access to its database of computed materials properties. In the future, it is hoped that new visualizations might be prototyped using Crystal Toolkit to help explore new forms of data being generated by the materials science community, and that this in turn can help new materials scientists develop intuition for how their data behaves and the insights that might be found within. Crystal Toolkit will remain a work-in-progress and is open to contributions from the community.

Co$_{1-x}$Mn$_x$Cr$_2$O$_4$ crystallizes as a normal spinel in the cubic $Fd \overline{3}m$ space group, and the end members have been reported to display a region of collinear ferrimagnetism as well as a low-temperature spin-spiral state with variable coherence lengths from 3 nm to 10 nm in polycrystalline samples. Here, we present the synthesis of the entire solid solution, and data showing that the ferrimagnetic ordering temperature as well as the spin-spiral lock-in temperature are tunable with the Co/Mn ratio. The peak magnetocaloric entropy change was determined to be $\Delta S_M$ = -5.63 J kg$^{-1}$ K$^{-1}$ in an applied magnetic field change of $\Delta H$ = 0 T to 5 T for the Mn end-member at the ferrimagnetic ordering temperature. Using density functional theory (DFT), we explore the shortcomings of the magnetic deformation proxy to identify trends in $\Delta S_M$ across composition in this spinel system, and explore future extensions of theory to address these discrepancies.

We propose and implement a novel hybrid meta-heuristic optimization algorithm for the identification of non-collinear global ground-states in magnetic systems. The inputs to this optimization scheme are directly from non-collinear density functional theory (DFT), and the workflow is implemented in the atomate code framework, making it suitable to run on high-performance computing architectures. The hybrid algorithm provides a seamless theoretical extension of particle swarm optimization (PSO) algorithms to continuous $\mathcal S^2$ spins, giving it the name SpinPSO. The hybrid nature of the algorithm stems from setting the dynamics of individual spins to be governed by physically motivated atomistic spin dynamics. Using this algorithm, we are able to achieve convergence to experimentally resolved magnetic ground-states for a set of diverse test case materials that exhibit exotic spin textures.

Conventionally, high-throughput computational materials searches start from an input set of bulk compounds extracted from material databases, but, in contrast, many real functional materials are heavily engineered mixtures of compounds rather than single bulk compounds. We present a framework and open-source code to automatically construct and analyze possible alloys and solid solutions from a set of existing experimental or calculated ordered compounds, without requiring additional metadata except crystal structure. As a demonstration, we apply this framework to all compounds in the Materials Project to create a new, publicly available database of >600,000 unique "alloy pair" entries that can be used to search for materials with tunable properties. We exemplify this approach by searching for transparent conductors and reveal candidates that might have been excluded in a traditional screening. This work lays a foundation from which materials databases can go beyond stoichiometric compounds and approach a more realistic description of compositionally tunable materials.

To accelerate the development of ion conducting materials, we present a general graph-theoretic analysis framework for ion migration in any crystalline structure. The nodes of the graph represent metastable sites of the migrating ion and the edges represent discrete migration events between adjacent sites. Starting from a collection of possible metastable migration sites, the framework assigns a weight to the edges by calculating the individual migration energy barriers between those sites. Connected pathways in the periodic simulation cell corresponding to macroscopic ion migration are identified by searching for the lowest-cost cycle in the periodic migration graph. To exemplify the utility of the framework, we present the automatic analyses of Li migration in different polymorphs of VO(PO 4 ), with the resulting identification of two distinct crystal structures with simple migration pathways demonstrating overall <300 meV migration barriers.

Nanobelts, nanoribbons and other quasi-one-dimensional nanostructures formed from layered, so-called, van der Waals semiconductors have garnered much attention due to their high-performance, tunable optoelectronic properties. For layered alloys made from the gallium monochalcogenides GaS, GaSe, and GaTe, near-continuous tuning of the energy bandgap across the full composition range has been achieved in GaSe1-xSx and GaSe1-xTex alloys. Gold-catalyzed vapor-liquid-solid (VLS) growth of these alloys yields predominantly nanobelts, nanoribbons and other nanostructures for which the fast crystal growth front consists of layer edges in contact with the catalyst. We demonstrate that in the S-rich, GaS1-xTex system, unlike GaSe1-xSx and GaSe1-xTex, the Au-catalyzed VLS process yields van der Waals nanowires for which the fast growth direction is normal to the layers. The high mismatch between S and Te leads to extraordinary bowing of the GaS1-xTex alloy's energy bandgap, decreasing by at least 0.6 eV for x as small as 0.03. Calculations using density functional theory confirm the significant decrease in bandgap in S-rich GaS1-xTex. The nanowires can exceed fifty micrometers in length, consisting of tens of thousands of van der Waals-bonded layers with triangular or hexagonal cross-sections of uniform dimensions along the length of the nanowire. We propose that the low solubility of Te in GaS results in an enhancement in Te coverage around the Au catalyst-nanowire interface, confining the catalyst to the chalcogen-terminated basal plane (rather than the edges) and thereby enabling layer-by-layer, c-axis growth.

The local structure of a transition metal (TM) ion is a function of cation elements and valence states. More than that, in this work, by employing a trove of first-principles data of TM oxides, the local structures of TM cations are statistically analyzed to extract detailed information about cation site preference, bond length, site structural distortion, and cation magnetization. It is found that cation radius alone poorly describes the local structure of a transition metal oxide, while the statistics of coordination number as well as the TMO bond length distribution, especially that of the 3d TMs, can provide comprehensive knowledge for understanding the behavior of TM elements. Based on these statistics, the interplay of site distortion due to the Jahn-Teller effect, cation site similarity, and a new set of ionic radii are all obtained to chart the "persona" of transition metal ions in solids.

The recent rise of computational, data-driven research has significant potential to accelerate materials discovery. Automated workflows and materials databases are being rapidly developed, contributing to high-throughput data of bulk materials that are growing in quantity and complexity, allowing for correlation between structural-chemical features and functional properties. In contrast, computational data-driven approaches are still relatively rare for nanomaterials discovery due to the rapid scaling of computational cost for finite systems. However, the distinct behaviors at the nanoscale as compared to the parent bulk materials and the vast tunability space with respect to dimensionality and morphology motivate the development of data sets for nanometric materials. In this review, we discuss the recent progress in data-driven research in two aspects: functional materials design and guided synthesis, including commonly used metrics and approaches for designing materials properties and predicting synthesis routes. More importantly, we discuss the distinct behaviors of materials as a result of nanosizing and the implications for data-driven research. Finally, we share our perspectives on future directions for extending the current data-driven research into the nano realm.