MC3D: Inorganic 3D Structure Database
- MC3D is a curated database of 3D inorganic crystal structures derived from nearly one million experimental entries, yielding 72,589 unique stoichiometric records.
- The database employs automated DFT workflows with AiiDA provenance tracking, ensuring full reproducibility and compliance with more-than-FAIR standards.
- MC3D supports high-throughput benchmarking, diffraction simulation, and machine-learning screening, making it a versatile resource for computational materials science.
The Materials Cloud Three-Dimensional Structure Database (MC3D) is an online database of computed three-dimensional (3D) inorganic crystal structures made available on the Materials Cloud portal. It was constructed by importing close to a million experimentally reported structures from the COD, ICSD and MPDS databases, parsing and filtering them to yield a collection of 72,589 unique and stoichiometric structures, and then optimizing the geometries with density-functional theory (DFT) using automated workflows and curated input protocols. The latest version, MC3D PBEsol-v2, comprises 32,013 unique structures, and the database includes the full provenance graph of all calculations driven by the automated workflows, establishing full reproducibility and “more-than-FAIR” procedures (Huber et al., 26 Aug 2025). Within the broader Materials Cloud infrastructure, MC3D inherits an archival and dissemination model in which data are persistently archived, citable, and linked to AiiDA provenance graphs that allow one to retrace and reproduce computed results (Talirz et al., 2020).
1. Institutional setting and database scope
MC3D is a domain database within Materials Cloud, a platform designed to enable open and seamless sharing of resources for computational science, driven by applications in materials modelling. Materials Cloud hosts archival and dissemination services for raw and curated data together with their provenance graph, modelling services and virtual machines, tools for data analytics and pre-/post-processing, and educational materials. Data on the platform are citable and archived persistently, and the infrastructure leverages the AiiDA framework to record the provenance of entire simulation pipelines in the form of graphs (Talirz et al., 2020).
The scope of MC3D is narrower than the scope of the platform as a whole. The database focuses on 3D bulk, stoichiometric inorganic crystal structures and, in the source curation stage, labels each final unique structure as “MC3D-source” (“mc3ds”). The project focuses on experimentally known materials, but a minority of entries are flagged as theoretical in the source databases. This also clarifies a recurrent point of confusion: in MC3D, “three-dimensional” refers to bulk inorganic crystal structures, not to lower-dimensional slabs, interfaces, defects, or processed structures, and not to generic 3D data objects (Huber et al., 26 Aug 2025).
A second point of scope is methodological. MC3D is not only a collection of final relaxed geometries. The database is embedded in a workflow-centric environment in which peers can browse the interconnected record of simulations, download individual files or the full database, and start their research from the results of the original authors. This suggests that MC3D is intended as both a reference structure set and a reproducible computational substrate (Talirz et al., 2020).
2. Source databases and curation pipeline
The initial structure corpus was assembled from three source databases: COD (Crystallographic Open Database, rev. 213553), ICSD (Inorganic Crystal Structure Database, version 2017.2), and MPDS (Materials Platform for Data Science, version 1.0.2). The total number of imported structures was ~901,210. All entries were imported in CIF format, parsed with pymatgen, cleaned with cod-tools, normalized, and converted to primitive cells with SeeK-path/spglib (Huber et al., 26 Aug 2025).
The curation process applied several successive filters. Invalid or unparseable CIFs were discarded; non-stoichiometric structures containing partial occupations were removed; duplicates within and across the databases were identified with pymatgen’s StructureMatcher; and molecular crystals were excluded because the project focuses on inorganic materials. The summary provided for the database notes that metal hydrides might have been excluded as a side effect (Huber et al., 26 Aug 2025).
| Stage | Count or criterion | Outcome |
|---|---|---|
| Imported source structures | ~901,210 | COD, ICSD, MPDS |
| Invalid or unparseable CIFs discarded | ~178,045 | Removed at parsing/cleaning stage |
| Non-stoichiometric structures discarded | ~244,962 | Partial occupations filtered out |
| Duplicates discarded | ~197,105 | Within and across source databases |
| Molecular crystals excluded | ~208,509 | Inorganic focus |
After filtering, the final curated MC3D-source set contains 72,589 unique structures. Of these, up to 69,284 are flagged by the source databases as experimentally known and 3,305 as theoretical. The abstract of the MC3D paper summarizes this stage as a reduction from close to a million imported structures to 72,589 unique and stoichiometric structures, of which 95% are, to date, classified as experimentally known (Huber et al., 26 Aug 2025).
The curation logic matters scientifically. By combining multiple source databases, normalizing cell representations, and deduplicating by reduced chemical formula and space group before structure matching, MC3D attempts to turn heterogeneous crystallographic records into a single, internally curated source set. A plausible implication is that MC3D is designed to be conservative with respect to structural identity before any DFT relaxation is attempted.
3. DFT workflows, protocols, and release versions
The DFT optimization stage excludes lanthanides and actinides for technical and physical accuracy reasons, and includes all structures up to 64 atoms per cell, with some larger ones also processed but not analyzed in v2. The workflows are implemented in AiiDA, the DFT code is Quantum ESPRESSO (pw.x), and the calculations are SIRIUS-accelerated for GPU/CPU compatibility. Pseudopotentials are taken from the SSSP library, with protocol versions v1.2/v1.3 and functional-specific efficiencies for PBE and PBEsol (Huber et al., 26 Aug 2025).
The input protocols are explicitly curated. Energy cutoffs are chosen per structure as the maximum among the constituent elements, as recommended by SSSP. The k-point mesh density is at least 0.15 Å using a Monkhorst–Pack mesh with gamma included. All runs are spin-polarized, initialized as high-spin for elements with open d/f shells. Occupations use Marzari–Vanderbilt cold smearing, with 0.01 Ry or 0.02 Ry depending on the protocol version. The convergence criteria are: electron convergence Ry/atom, forces Ry/Bohr, stress kbar, and stepwise energy Ry/atom (Huber et al., 26 Aug 2025).
Three protocol/function versions are distinguished in the database description. PBE-v1 uses SSSP v1.2 PBE, an older workflow, and 0.01 Ry cold smearing. PBEsol-v1 uses SSSP v1.2 PBEsol with the same older workflow logic. PBEsol-v2, the latest workflow, uses SSSP v1.3 PBEsol, 0.02 Ry cold smearing, and improved restarts, error handling, and k-mesh updating (Huber et al., 26 Aug 2025).
The workflow itself is staged. The paper lists: 1. Initial loose optimization; 2. Production-level optimization; 3. Check for basis/k-point mesh sufficiency; 4. Automated error handling/retries (up to 5 restarts); 5. Final stress check; and 6. Magnetization re-initialized at production step (Huber et al., 26 Aug 2025). This workflow decomposition is important because MC3D does not present relaxed structures as isolated end products; the optimization history is part of the scientific object being disseminated.
4. Provenance model, dissemination, and “more-than-FAIR”
A defining feature of MC3D is its integration with the provenance machinery of Materials Cloud and AiiDA. Materials Cloud uses AiiDA to record the provenance of entire simulation pipelines—calculations performed, codes used, and data generated—in the form of graphs that allow one to retrace and reproduce computed results (Talirz et al., 2020). In the MC3D description, all steps from CIF import, parsing, normalization, filtering, DFT calculation, error handling, and postprocessing are tracked via AiiDA provenance (Huber et al., 26 Aug 2025).
Mathematically, the workflow can be represented as a directed acyclic graph , where are nodes for inputs, outputs, calculations, and codes, and are directed edges linking inputs to calculations and calculations to outputs. In the AiiDA-based view emphasized by Materials Cloud, nodes can also encode metadata such as timestamps, user, and computational environment, while links encode dependencies between data and calculations (Talirz et al., 2020).
The dissemination layer has several components. On the Materials Cloud Archive, MC3D provides AiiDA archive files with full provenance for open data. The web application interface includes a landing page with version selection and an interactive periodic table for elemental filtering, a dynamic results table, and a structure detail page with structure data, computed materials properties, powder XRD patterns generated with pymatgen and user-customizable broadening, and direct links to calculation provenance. Download options include optimized structures in CIF and other formats, as well as exportable filtered results. Programmatic access is provided through a REST API, including an OPTIMADE-compliant endpoint, and provenance navigation is exposed through the Explore frontend (Huber et al., 26 Aug 2025).
The platform-level archival guarantees contextualize this dissemination model. Materials Cloud’s moderated archive provides long-term storage (at least 10 years), persistent DOIs for every record, and backups to tape and object storage; metadata conform to Dublin Core and Schema.org, and datasets are openly accessible and indexed in global data registries (Talirz et al., 2020). MC3D describes its own reproducibility standard as “more-than-FAIR”: not only are raw data available, but the entire computational process and workflow are also available, enabling reruns and modifications. One caveat is explicitly stated: for the commercial ICSD and MPDS sources, original CIFs and part of the provenance tree are trimmed for license compliance (Huber et al., 26 Aug 2025).
5. Release statistics, coverage, and distinctiveness
For MC3D PBEsol-v2, the current main release, 38,739 optimized input geometries were attempted and 33,142 crystals were successfully optimized, corresponding to an 85.5% success rate after error recovery. After post-relaxation deduplication, this yields 32,013 unique optimized structures. The release therefore covers about 44% of the initial 72,589-structure MC3D-source set, and 95% of the optimized set are experimentally known according to source metadata (Huber et al., 26 Aug 2025).
This difference between successful optimizations and unique optimized structures is itself informative. The database description notes that all geometry optimizations start from unique MC3D-source structures, but further duplicates can arise due to structures relaxing to the same local minima. That statement is significant for database users because it indicates that structural uniqueness is defined at more than one stage: first at the crystallographic-source level, and later at the relaxed-geometry level (Huber et al., 26 Aug 2025).
Relative to other computational materials databases, the MC3D paper reports that 3,328 structures are not present in the Materials Project or OQMD by structure matching. The detailed breakdown given for the union of Materials Project and OQMD is 1,245 structures with different composition, 1,065 with the same composition but new space group, and 1,018 with the same composition and space group but new structure (Huber et al., 26 Aug 2025). The database description also characterizes MC3D by several linked features: inclusion of several source databases, broader coverage than Materials Project/OQMD, consistent optimization with Quantum ESPRESSO and SSSP pseudopotentials, focus on experimentally known materials, an open-source workflow ecosystem based on AiiDA + Quantum ESPRESSO, and full provenance with workflow-centric reproducibility (Huber et al., 26 Aug 2025).
A common misconception is that a database of this type is merely a larger version of a structure repository. MC3D departs from that model in two ways stated explicitly in the source material: it is a computed database rather than only a crystallographic one, and it treats the provenance graph as part of the disseminated object. This suggests that database comparison should not be limited to composition/structure coverage alone.
6. Use in high-throughput benchmarking and machine-learning screening
MC3D has already been used as a benchmark and screening substrate in later work. In “Rust-accelerated powder X-ray diffraction simulation for high-throughput and machine-learning-driven materials science” (Lebeda et al., 12 Feb 2026), MC3D is described as a publicly available database of experimentally known stoichiometric inorganic crystal structures and is used as one of two principal benchmarking datasets for XRD-Rust, a Rust-accelerated implementation of the pymatgen powder XRD calculator. The benchmark includes all 33,142 structures in MC3D (as of 29/12/2025), with powder XRD patterns simulated in the range from 2° to 60° using Mo K radiation. On this dataset, XRD-Rust achieves an average speedup of 4.7 ± 1.6 times and a maximum speedup of 25×, with the largest single-structure improvement reducing simulation time from 34.9 s to 1.4 s for MC3D structure ID mc3d-261, involving 17,924 reflections (Lebeda et al., 12 Feb 2026).
The same paper reports that in approximately 1.9% of cases (654 structures) XRD-Rust was slightly slower or comparable to pymatgen, and attributes these cases to structures with only a very small number of reflections and already very low total runtimes. The MC3D dataset is described there as a rigorous test-bed because it contains structures ranging from small, high-symmetry crystals to very complex, large-unit-cell inorganics (Lebeda et al., 12 Feb 2026). This supports an interpretation of MC3D as a workload representative of realistic high-throughput diffraction pipelines.
MC3D has also been used for property-driven machine learning. In “Spectral Operator Representations” (Zadoks et al., 2024), the database serves as the basis for the discovery of transparent conducting materials (TCMs) using spectral operator representation (SOREP) descriptors. The study reports ~35,240 materials in MC3D, of which 30,054 single-shot DFT SOREP feature calculations were completed within computational limits; 22,200 systems with available band structure data were used for TCM screening and classification, including 2,527 TCM candidates and 19,673 non-TCMs. A random forest classifier trained on 1% of the materials in MC3D is reported to correctly label 76% of entries in the database that meet common screening criteria for promising TCMs (Zadoks et al., 2024).
The MC3D-based TCM workflow is notable because it uses electronic-structure-based descriptors rather than local atomic-environment descriptors. The paper argues that such spectral features are better aligned with properties such as band gaps and mobilities, which are not readily atomically partitioned (Zadoks et al., 2024). In that sense, MC3D functions not only as a structure repository but also as a statistically meaningful corpus for testing representation learning strategies tied to global electronic properties.
Taken together, these downstream studies show two concrete modes of reuse already realized in the literature: high-throughput simulation benchmarking and machine-learning screening on large, provenance-rich materials corpora. That pattern is consistent with the way MC3D is constructed and disseminated on Materials Cloud: as a curated, reproducible, and computationally actionable database rather than a static collection of final structures.