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12.92616812719913,  10.723388636516303,  6.7958908013407004  ],  [
1.510109732800872,  3.785911553483698,  6.7958908013407004  ],  [  0,
10.478360217883642,  4.664412075489127  ],  [  0,  4.030939972116357,
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13.046967868713258,  11.254827303760516,  9.59430786  ]  ],  "nsites": 216,
"species": [  {  "name": "Si",  "chemical_symbols": [  "Si"  ],
"concentration": [  1  ],  "mass": null,  "original_name": null,  "attached":
null,  "nattached": null },  {  "name": "O",  "chemical_symbols": [  "O"  ],
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null,  "nattached": null }  ],  "species_at_sites": [  "Si",  "Si",  "Si",
"Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",
"Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",
"Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",
"Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",
"Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",
"Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",
"Si",  "Si",  "Si",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
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"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O",  "O",  "O"  ],  "assemblies": null,  "structure_features":
[],  "_mp_stability": {  "gga_gga+u_r2scan": {  "thermo_id":
"mp-1205213_GGA_GGA+U_R2SCAN",  "energy_above_hull": 0.07174161092592435,
"formation_energy_per_atom": -2.974076409629632,  "last_updated_thermo":
"2023-04-27T01:11:08Z"  },  "gga_gga+u": {  "thermo_id":
"mp-1205213_GGA_GGA+U",  "energy_above_hull": 0.07174161092592435,
"formation_energy_per_atom": -3.1962904782407415,  "last_updated_thermo":
"2023-04-27T01:12:03Z"  }  },  "_mp_chemical_system": "O-Si"  }  },  {  "id":
"mp-554397",  "type": "structures",  "attributes": {  "immutable_id":
"645d2c0ebcd30f748b4779ee",  "last_modified": "2021-02-04T10:32:28Z",
"elements": [  "O",  "Si"  ],  "nelements": 2,  "elements_ratios": [
0.3333333333333333,  0.6666666666666666  ],  "chemical_formula_descriptive":
"O16Si8",  "chemical_formula_reduced": "O2Si",  "chemical_formula_hill":
"O16Si8",  "chemical_formula_anonymous": "A2B",  "dimension_types": [  1,  1,
1  ],  "nperiodic_dimensions": 3,  "lattice_vectors": [  [  4.719159,  0,  0
],  [  0,  7.122919,  0  ],  [  0,  0,  9.774747  ]  ],
"cartesian_site_positions": [  [  1.07011649484,  3.019597682913,
5.886704534292  ],  [  1.07011649484,  0.541861817087,  0.9993310342919999  ],
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4.1033213170869995,  8.775415965708  ],  [  3.6490425051600006,
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5.886704534292  ],  [  3.6490425051600006,  3.019597682913,
0.9993310342919999  ],  [  3.6490425051600006,  4.1033213170869995,
3.8880424657079997  ],  [  0,  3.5614595,  0  ],  [  3.1309354768680002,
3.5614595,  2.44368675  ],  [  2.3595795,  0,  0  ],  [  0,  5.34218925,
3.318125841873  ],  [  2.3595795,  0,  4.8873735  ],  [  0,  1.78072975,
6.4566211581270005  ],  [  0,  1.78072975,  1.5692476581269998  ],  [
3.1309354768680002,  0,  7.33106025  ],  [  0,  5.34218925,  8.205499341872999
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1.588223523132,  0,  2.44368675  ],  [  2.3595795,  3.5614595,  0  ],  [
1.588223523132,  3.5614595,  7.33106025  ],  [  0,  0,  0  ],  [  0,
3.5614595,  4.8873735  ]  ],  "nsites": 24,  "species": [  {  "name": "Si",
"chemical_symbols": [  "Si"  ],  "concentration": [  1  ],  "mass": null,
"original_name": null,  "attached": null,  "nattached": null },  {  "name":
"O",  "chemical_symbols": [  "O"  ],  "concentration": [  1  ],  "mass": null,
"original_name": null,  "attached": null,  "nattached": null }  ],
"species_at_sites": [  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",
"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O"  ],  "assemblies": null,  "structure_features": [],
"_mp_stability": {  "gga_gga+u_r2scan": {  "thermo_id":
"mp-554397_GGA_GGA+U_R2SCAN",  "energy_above_hull": 0.6576060429166652,
"formation_energy_per_atom": -2.3882119776388913,  "last_updated_thermo":
"2023-04-27T01:11:08Z"  },  "gga_gga+u": {  "thermo_id":
"mp-554397_GGA_GGA+U",  "energy_above_hull": 0.6576060429166661,
"formation_energy_per_atom": -2.6104260462499997,  "last_updated_thermo":
"2023-04-27T01:12:03Z"  }  },  "_mp_chemical_system": "O-Si"  }  },  {  "id":
"mp-1365799",  "type": "structures",  "attributes": {  "immutable_id":
"645d2c0ebcd30f748b477a1a",  "last_modified": "2020-05-02T07:15:08Z",
"elements": [  "O",  "Si"  ],  "nelements": 2,  "elements_ratios": [
0.3333333333333333,  0.6666666666666666  ],  "chemical_formula_descriptive":
"O32Si16",  "chemical_formula_reduced": "O2Si",  "chemical_formula_hill":
"O32Si16",  "chemical_formula_anonymous": "A2B",  "dimension_types": [  1,  1,
1  ],  "nperiodic_dimensions": 3,  "lattice_vectors": [  [  -8.837414,
8.860732,  8.911577  ],  [  8.837414,  -8.860732,  8.911577  ],  [  8.837414,
8.860732,  -8.911577  ]  ],  "cartesian_site_positions": [  [
-2.8587063883378505e-16,  9.505119873968,  0.9842480333420002  ],  [
10.24923507357,  -2.1863944817319996,  3.0447561325509995  ],  [
7.425592926430001,  -2.1863944817320005,  5.866820867449  ],  [
7.42559292643,  -2.1863944817320005,  3.0447561325509995  ],  [
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10.24923507357,  -2.1863944817319996,  5.8668208674489986  ],  [
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1.4118210735699996,  11.047126481732,  5.866820867449  ],  [
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5.388675048398001,  -3.7691338745,  4.455797411577  ],  [  8.837405162586002,
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11.047126481732,  3.0447561325510004  ],  [  -2.7005016204640007,
5.668405196504,  12.019026076746  ],  [  6.13692121695,  3.1923179427640003,
-3.1074401651690002  ],  [  7.489036721536,  -1.1770064744879998,
1.7581650263299995  ],  [  5.096324555863999,  12.340873100320001,
4.455788499999998  ],  [  7.489036721536,  -1.1770064744879998,  7.15341197367
],  [  6.13692121695,  -3.192335664228,  5.804136834831  ],  [
11.537915620464,  3.192326803496,  -3.1074490767459992  ],  [
-2.700501620464,  12.053058803496,  3.1074490767459997  ],  [
5.527663435529462e-16,  5.818984476112,  11.902694350588  ],  [
2.700492783049999,  5.668414057236,  12.019017165168998  ],  [
8.837422837414001,  -3.04175638462,  5.920450737835001  ],  [
3.7410894441360005,  -3.4801411003200005,  4.4557885  ],  [  3.741089444136,
3.480141100320001,  13.367365499999998  ],  [  8.837405162586,
0.9831247975959996,  8.256103776919002  ],  [  10.185791278464,
-1.1770064744880004,  7.15341197367  ],  [  10.185791278464,
-1.1770064744880004,  1.7581650263300006  ],  [  8.837414,
0.9831159368640003,  0.6554821346579994  ],  [  -1.3483772784640011,
10.037738474488,  1.7581650263299997  ],  [  7.373549395384001,
-1.3311300468960006,  4.455788500000001  ],  [  5.096324555864,
5.3805908996800005,  -4.4557885  ],  [  2.700492783049999,
12.053067664228001,  3.1074401651689993  ],  [  8.837414,  3.041747523888,
-2.9911173505879995  ],  [  -1.3483772784640002,  10.037738474488,
7.153411973669998  ],  [  1.3483772784640002,  10.037738474488,
7.153411973669999  ],  [  1.3483772784639994,  10.037738474488,  1.75816502633
],  [  0.000008837413999440885,  7.8776072024040005,  0.6554732230810002  ],
[  1.4638646046159995,  10.191862046896,  4.455788500000001  ],  [
-0.000008837414000306419,  11.902488384620002,  2.9911262621649994  ],  [
11.537915620464,  -3.192326803496,  5.804127923254  ],  [  10.301278604616,
-1.3311300468959992,  4.4557885  ],  [  -1.4638646046160002,  10.191862046896,
4.4557885  ],  [  6.218970218228037e-16,  7.877616063136,  8.256094865342  ]
],  "nsites": 48,  "species": [  {  "name": "Si",  "chemical_symbols": [  "Si"
],  "concentration": [  1  ],  "mass": null,  "original_name": null,
"attached": null,  "nattached": null },  {  "name": "O",  "chemical_symbols":
[  "O"  ],  "concentration": [  1  ],  "mass": null,  "original_name": null,
"attached": null,  "nattached": null }  ],  "species_at_sites": [  "Si",
"Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",  "Si",
"Si",  "Si",  "Si",  "Si",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",
"O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O",  "O"  ],
"assemblies": null,  "structure_features": [],  "_mp_stability": {
"gga_gga+u_r2scan": {  "thermo_id": "mp-1365799_GGA_GGA+U_R2SCAN",
"energy_above_hull": 0.1988256095833325,  "formation_energy_per_atom":
-2.846992410972225,  "last_updated_thermo": "2023-04-27T01:11:10Z"  },
"gga_gga+u": {  "thermo_id": "mp-1365799_GGA_GGA+U",  "energy_above_hull":
0.1988256095833325,  "formation_energy_per_atom": -3.069206479583333,
"last_updated_thermo": "2023-04-27T01:12:06Z"  }  },  "_mp_chemical_system":
"O-Si"  }  }  ],  "meta": {  "query": {  "representation":
"/structures?filter=chemical_formula_reduced=%22O2Si%22"  },  "api_version":
"1.1.0",  "more_data_available": true,  "schema":
"https://schemas.optimade.org/openapi/v1.1.0/optimade.json",  "time_stamp":
"2023-06-26T09:24:12Z",  "data_returned": 321,  "provider": {  "name":
"Materials Project - OPTIMADE",  "description": "The Materials Project
OPTIMADE endpoint",  "prefix": "mp",  "homepage":
"https://materialsproject.org"  },  "data_available": 154387,
"implementation": {  "name": "OPTIMADE Python Tools",  "version": "0.24.1",
"source_url": "https://github.com/Materials-Consortia/optimade-python-tools",
"maintainer": {  "email"<EMAIL_ADDRESS>},  "issue_tracker":
"https://github.com/Materials-Consortia/optimade-python-tools/issues"  }  },
"included": [],  "links": {  "next":
"http://optimade.materialsproject.org/v1/structures?filter=chemical_formula_reduced%3D%22O2Si%22&page_offset=20"
}  }

An excerpt of the JSON response showing the material attributes for one of the
returned entries.

###  2.1 OPTIMADE core design principles

Figure 1: Schematic for how databases with different backends may provide
their own web-based user interfaces and database-specific APIs alongside the
OPTIMADE API. A single client can then interact with the databases via the
OPTIMADE API without having to be aware of these differences.

A materials database provider that implements the OPTIMADE API will have a
database backend and one or more interfaces available to clients. These
interfaces include the OPTIMADE API, but can also provide access by other
means, e.g., a database-specific API or web-based graphical user interface.
Figure 1 serves as a schematic illustration of this point.

The providers that presently support the OPTIMADE API represent a wide range
of underlying backends. The primary backend component is, usually, a database
engine, but the backend covers all parts of the system that manages the stored
data. Relevant backends for OPTIMADE implementations range from simple flat
files in a filesystem, to sophisticated setups with load-balanced distributed
cloud hosting of relational database engines (e.g., Structured Query Language,
SQL-based) or non-relational key-value, document or graph database engines
(so-called NoSQL).

There exists a multitude of APIs for data access and storage (both for
materials databases and more generally) that have been designed for a specific
database backend. These APIs are typically designed around specific features
the backend provides in terms of, e.g., browse, search, and retrieval, and,
crucially, _how_ these features are implemented by the backend. The API then
typically becomes a thin wrapper for these features, which exposes the
functionality of the backend implementation. There is thus a crucial need for
a generic database interface, which should be based on the central principles:

  * •

A core feature set that any reasonable materials database backend can
implement via cheap, single-pass, on-the-fly translations in the API layer.
Furthermore, the translations should be possible _without_ modifying the
underlying backend – i.e., participating databases should not be required to
reformat or amend the stored data, software features, etc. to provide these
core OPTIMADE features.

  * •

Extended features beyond the core features that are shared among multiple (but
not all) backends should be standardised as _optional_ features. It may appear
that this design works against interoperability, as it may lead to query $Q$
working for databases $A$ and $B$, but not for database $C$. However, if the
database backend for $C$ _cannot_ support the type of query that $Q$
represents (for example, a database containing molecular dynamics calculations
of proteins cannot sensibly be searched on the chemical formula in the
simulation cell), it means that there exists no way to make that query
interoperable across $A$, $B$, and $C$ (without altering the backend of $C$).
Hence, the highest level of interoperability is achieved by standardising $Q$
as an optional feature.

  * •

For standardised optional features, multiple overlapping representations of
the same features and/or data should be avoided. The reason is that, for two
different ways of providing feature $Q$ as $Q_{1}$ and $Q_{2}$, we may end up
with database $A$ supporting only $Q_{1}$ and database $B$ supporting only
$Q_{2}$. Hence, the client either has to tailor the query differently
depending on the destination or provide multiple versions of the query in the
request, which is an undesirable burden to put on clients and works against an
interoperable design. What is strictly standardised is how a database that
does not implement a certain feature should respond should that feature be
requested.

  * •

Those features and data that only occur in a particular database should be
provided in isolated database-specific namespaces that other databases can
recognise and handle appropriately. The OPTIMADE specification describes how
references to such fields should be announced by the particular database and
also how clients making multi-provider queries should handle in the response
in various situations for optimal interoperability. The latest version of
OPTIMADE even outlines a mechanism for creating sub-specifications that allow
multiple database providers to collaborate on custom communal definitions, as
shall be discussed later.

###  2.2 Recent OPTIMADE improvements

Since the initial v1.0 release 12 of the OPTIMADE API in July 2020, many
features have been added, driven by user feedback and use cases. The major
enhancements to the specification introduced in versions 1.1 14 and 1.2 are
discussed below, with the full changelog and specification text available
online on GitHub at Materials-Consortia/OPTIMADE 8.

####  2.2.1 Property definitions

In previous versions of OPTIMADE, the information served through introspection
for a provided property was limited to a single specification of an OPTIMADE
type, which is far from sufficient for a client to use the data. For standard
fields, clients were referred to the human readable descriptions in the
OPTIMADE specification, and for database-specific fields to side channel
information, e.g., at the website of the database.

OPTIMADE v1.2 includes a full schema format, based on – and compatible with –
JSON Schema 97, capable of fully describing in a machine-readable way what a
property is (including definition of sophisticated data structures with
multiple layers of lists and dictionary subfields). All properties are given
clear versioned stable identifiers (URIs) that can be used to identify that
multiple databases refer to the exact same property.

Furthermore, a browsable interface to these definitions for the OPTIMADE
standard properties is available at https://schemas.optimade.org/. There is
related work outside of the specification on providing an enlarged set of
shared definitions that can be incrementally adopted by the subsections of the
community. This will allow databases to point to and share the same property
definition without requiring the slow consensus-building step for the relevant
fields to be promoted to the main specification. This is especially useful in
cases where this shared information is the defining feature of a given
database; for example, the first target namespace is that of stability
predictions arising from density-functional theory calculations, the key
property required to truly enable materials discovery applications with
OPTIMADE (see 4.1.2 later for more information).

####  2.2.2 Streaming of partial data

So far, OPTIMADE has been based on the JSON format, which has the advantage
that it is relatively human readable and well supported by most programming
languages. Most tools, however, can only process an entire JSON file and thus
do not support streaming processing, which makes it difficult to handle large
JSON files. In addition, JSON does not support binary data: a response with
large amounts of numerical data needs to be encoded (e.g., in base64 or
similar encodings), significantly increasing the size of the data to be
transferred over the network. Adding support for a format like BSON, which
does support binary data, or JSON variants which do support streamed
processing (such as JSON Lines) could therefore improve the data transfer
rates for OPTIMADE requests, and allow for immediate visualisation of partial
results.

In previous versions of OPTIMADE, the size of property data was limited so
that a single database entry could fit in a one HTTP response. In the most
recent version of OPTIMADE, the implementation can decide to defer large
properties to be communicated over a separate simplified streamable protocol,
which in practice can be implemented by serving large static files over HTTP.
This addition was driven by the future application of serving trajectory data
with OPTIMADE (see 5 for more information) where individual “properties”, such
as atomic positions in each frame of a trajectory, can individually be
prohibitively large.

####  2.2.3 Other technical and scientific enhancements

There have been several other extensions of the format since version 1.0:

Symmetry information for structures

The latest OPTIMADE release includes a set of standardised and comprehensive
descriptions of structural symmetry. This has been achieved with 5 fields that
can be variously used for filtering by symmetry and for reconstructing atomic
site positions, building on existing standards laid out by the IUCr and
others:

  * •

space_group_symmetry_operations_xyz,

  * •

space_group_symbol_hall,

  * •

space_group_symbol_hermann_mauguin,

  * •

space_group_symbol_hermann_mauguin_extended,

  * •

space_group_it_number.

/files endpoint

The OPTIMADE specification has been extended to enable the description of
files and their precise relationships to other OPTIMADE entries. To implement
this, a new /files entry endpoint has been defined. This addition allows, for
example, linking /structures entries with their representations in widely used
structural data formats such as CIF, POSCAR, and SDF, or linking directly to
the raw input or output files associated with a calculation involving a
structure.

Per property and per entry metadata

We plan to create a mechanism to provide metadata per property for each
individual entry. This metadata could, for example, be confidence intervals,
or information about how a property was calculated.

Request delay

In order not to overload a particular OPTIMADE server, the metadata property
request_delay appears in the latest release to allow an implementation to
suggest a specific back-off time delay between subsequent requests. It is up
to the given server implementation to decide what to do with clients violating
the requested delay: refuse to serve, intentionally delay the response, or
ignore.

Licensing

The possibility of unsupervised database harvesting raises a need for machine-
readable definition of data licenses. Whilst OPTIMADE is an open format, it
can be used to serve proprietary or otherwise restricted data, the usage terms
of which must be described. The latest OPTIMADE release addresses this issue
by introducing the metadata fields license, available_licenses, and
available_licenses_for_entries. The property license is intended for databases
to link to human-readable licensing terms, while available_licenses and
available_licenses_for_entries allow specifying machine-readable license
identifiers following the Software Package Data Exchange (SPDX) standard,
making interpreting requirements easier for automated clients and web
crawlers. This standardised way to announce that either the whole database, or
the individual entries, are explicitly available under certain licenses
enables machine-actionable licensing decisions, e.g. for commercial re-use and
republishing of data.

Substring comparisons on list elements

The OPTIMADE filter grammar defines substring comparison operators to match
either the start, end or any part of a property value. However, until version
1.2, such comparisons could not be carried out on list elements. The latest
version of OPTIMADE now explicitly supports such substring queries on elements
of list properties.

Boolean values

Although there are no Boolean fields in the main OPTIMADE specification, the
latest version of the OPTIMADE specification includes support in the filter
grammar for defining and filtering on such custom fields defined by data
providers.

###  2.3 Associated software tools

####  2.3.1 optimade-python-tools

optimade-python-tools is an open-source software (MIT license) package that
provides tooling for serving, validating and consuming OPTIMADE APIs in Python
43, available on GitHub at Materials-Consortia/optimade-python-tools. Now in
version 1.0, it provides a highly extensible reference server implementation
of an OPTIMADE API, with support for different database backends. This server
is provided as a Docker container for easy deployment and can be configured to
use an existing database, or generate one from scratch in the OPTIMADE format.
The package contains isolated modules for various OPTIMADE-related
functionalities, for example, a grammar and parser for the OPTIMADE filter
language, mappers for querying different database backends, and a fuzzy
validator that can dynamically generate requests to an OPTIMADE server to
assess its compliance with the standard (which is also used to generate the
OPTIMADE provider dashboard: optimade.org/providers-dashboard) 9. In addition
to server-focused functionalities, the package also includes reusable code
that can OPTIMADE consumers and clients, including adapters for converting
OPTIMADE entries into common formats used in the community, such as ASE Atoms
75, pymatgen Structures 90 and AiiDA nodes 65.

The package also contains an advanced asynchronous HTTP client that can be
used within Python code or at the command line to concurrently filter multiple
OPTIMADE databases with multiple queries, paginating and validating the
results, as well as searching across databases for supported properties. Users
can provide callbacks to store the results in local secondary databases for
re-use in other projects.

optimade-python-tools is fully documented online at optimade.org/optimade-
python-tools with guides for setting up and validating an API, deploying a
server and using the client. In this way, optimade-python-tools significantly
lowers the barrier to retrieving data from OPTIMADE APIs, and to the
development of new server implementations. Future developments will focus on
extending the use cases of optimade-python-tools to operating on static data,
so that it can be embedded within archival infrastructure, such as Materials
Cloud 123, to serve user data without any additional input.

####  2.3.2 optimade-gateway

optimade-gateway is an open-source software (MIT license) package implementing
a RESTful API in Python for querying OPTIMADE databases, available on GitHub
at Materials-Consortia/optimade-gateway. This provides a powerful yet
straightforward tool to allow users of the Python programming language (that
is widespread in machine learning and other branches of data science) to
access material database results. optimade-gateway supports both synchronous
and asynchronous searches via HTTP GET and POST requests, respectively. It can
return search results in the standard OPTIMADE data format, as well as a
custom OPTIMADE-inspired data format. The main purpose and goal of the
deployed service is to be a client backend. A gateway to version 0.4 is
running at mmp-optimade-gateway.materialscloud.io as well as at optimade-
gateway.fly.dev. Both services utilise a MongoDB database for time-limited
caching of the query results, increasing response speeds for common queries.

####  2.3.3 Optimade.Science

Optimade.Science is a minimalist in-browser OPTIMADE aggregator, written in
the TypeScript language on top of the Svelte frontend framework 7. It fetches
the official OPTIMADE providers list, looks for the structure endpoints, and
allows simultaneous querying against all of them, collecting the results
together on a single webpage. Technically, this is just the single file
index.html and is thus highly-portable, can be opened from anywhere, on any
environment (e.g., on a smartphone or locally from a USB stick). To increase
ease-of-use, a simple pattern-matching library was developed (mpds-
io/optimade-mpds-nlp), transforming the free-text user input into a standard
OPTIMADE query (e.g., a keyword ternary is transformed into nelements=3). A
separate Svelte user interface kit (basf/svelte-spectre) was developed
offering a range of the modular GUI components, willingly accepted by the
frontend community and already re-used in many other web-projects, including
commercial ones. A standalone OPTIMADE client written in TypeScript was
employed, being fully isomorphic (that is, the same code can be used inside
the web browser and on the web server).

##  3 Contributing databases

The burgeoning community of materials databases are the core that underpins
the OPTIMADE consortium. Therefore, below we discuss the major materials
databases that make data available through the OPTIMADE API. We first briefly
introduce each database and its offering, and we then discuss its particular
OPTIMADE implementation. Finally, we provide an updated table from our
previous work 13 that compares the amount of compliant data available in
different databases.

###  3.1 AFLOW

_Database_ : One of the largest open-access databases for inorganic materials,
with 4 million compounds and 800 million associated properties 41, 91, which
also includes the 2000+ entries of the AFLOW Encyclopedia of Crystallographic
Prototypes 84, 60, 61. The data has been employed for the discovery of new
permanent magnets 105, superalloys 89, 102, high-entropy high-hardness
plasmonic carbides 11, super-hard disordered carbides 106, borides and carbo-
nitrides 37, and phase-change memory compositions 74, and has also been used
to study bulk metallic glasses 96, 44, superconductors 67, 121, and
thermoelectrics 127. The data can be retrieved conveniently through the AFLUX
search API 103 with a minimal, flexible, and human-readable query language.

_OPTIMADE implementation_ : The AFLOW OPTIMADE API builds on AFLUX to offer a
common query syntax across multiple materials databases, mapping AFLOW
property labels to that of OPTIMADE while still offering access to AFLOW-
specific properties with the _aflow_ prefix. A full list of keywords available
to use with OPTIMADE to query AFLOW are available at the info endpoint
/info/structures.

_Base URL_ : https://aflow.org/API/optimade

###  3.2 Alexandria

_Database_ : Comprises both hypothetical and existing compounds, which have
been relaxed using density functional theory (DFT). Currently, the database
contains 5,062,521 entries, spanning nearly the entire periodic table with 89
elements. The database was primarily generated by scanning binary, ternary,
and quaternary prototypes to identify stable compounds. This process employed
crystal graph attention networks 112, 114, 115 to predict the stability of all
potential compositions for each prototype. Compounds that were found to be
close to stability were subsequently confirmed using DFT. Additionally, the
database includes compounds obtained from traditional high-throughput searches
conducted previously 111, 110, 129.

Most entries were calculated using the PBE functional with parameters mostly
consistent with those of the Materials Project 70, and includes 3D (4 489 295
entries), 2D (137 833) and 1D (13 295 entries) compounds. Additionally, a
total of 422 098 materials were computed using the PBEsol and SCAN functionals
to yield more precise geometries, formation energies, and bandgaps 113. The
PBE version of the Alexandria database, which comprises 115 535 potentially
stable materials, represents the most extensive publicly available DFT convex
hull of thermodynamic stability in our knowledge. Furthermore, 771 696
materials lie within a distance of less than 50 meV/atom from the convex hull.
The database encompasses various properties, including structure (lattice and
atomic positions), energy distance to the convex hull, formation energy and
direct as well as indirect bandgaps. Continuous expansion of the database is
underway through further ongoing high-throughput searches.

_OPTIMADE implementation_ : Uses the optimade-python-tools 43 reference
implementation and provides a list of extra properties with the _alexandria_
prefix. Prior to this development, the Alexandria database was made available
solely as a static archive that users had to download in its entirety to
explore, but now the OPTIMADE format supports filtering on both composition
and the predicted stability of database entries.

_Base URL_ : https://alexandria.icams.rub.de

###  3.3 BioExcel COVID-19

_Database_ : A platform designed to provide online access to atomistic
molecular dynamics trajectories for biological macromolecules related to the
COVID-19 disease 22. The project is part of the open access initiatives
promoted by the world-wide scientific community to share information about
COVID-19 research and integrate technology developed in previous biology
related projects 63, 139, 16, 64.

_OPTIMADE implementation_ : A web-server interface https://bioexcel-
cv19.bsc.es presents the MD trajectories, with a set of quality control
analyses and system information. Using an extension of version 1.1.0 of the
OPTIMADE specification, a basic OPTIMADE server based on the optimade-python-
tools has been set up, which provides the trajectory data at the /trajectories
endpoint. This server also provides protein specific properties and metadata
under database specific fields with the _bioxl_ prefix. Querying has been
partially implemented, but is not yet available for all fields. No atomistic
structures are shared, so the /structures endpoint is not available.

_Base URL_ : https://bioexcel-cv19.bsc.es/optimade/

###  3.4 Computational Materials Repository (CMR)

_Database_ : CMR is a repository of databases containing calculated atomic
structures and basic properties of a broad set of materials. The CMR databases
can be browsed online using a simple querying system or downloaded in various
formats (https://cmr.fysik.dtu.dk). Currently, the CMR holds more than 30
different databases.

The flagship database in CMR is the Computational Two-Dimensional Materials
Database (C2DB) 88, 55, 49 that contains structural, thermodynamic, elastic,
electronic, magnetic, and optical properties of more than 15,000 two-
dimensional (2D) monolayer materials computed using the GPAW 40, 86 package.
The core set of materials in C2DB have been obtained by extracting monolayers
from experimentally known layered van der Waals crystals. Subsequently, new
monolayers have been generated by systematic atom-substitution applied to the
core materials, or using deep generative AI models 80. Recently, the C2DB has
been complemented by the BiDB database containing homobilayers formed by
stacking 1,000 of the most stable monolayers from the C2DB in all possible
commensurate configurations 93.

_OPTIMADE implementation_ : CMR implements the OPTIMADE API through the OASE
package, utilising the optimade-python-tools library. At present only a subset
of C2DB is available via an OPTIMADE API, but in the future other CMR
databases will also be available via OPTIMADE.

_Base URL_ : https://cmr-optimade.fysik.dtu.dk

###  3.5 Crystallography Open Database (COD)

_Database_ : The largest open access collection of _experimental_ crystal
structures 54. It is widely used by the scientific community to explore
different material categories such as superconductors 30, metal-organic
frameworks 21, high entropy alloys 116, organic molecules 26 as well as for
conformer sampling 85 or custom force field generation 50. Having a set of
experimental structures readily available under the same format as is required
for computational materials research is highly beneficial since these
structures serve as initial points for material property calculations 123 or
for the search of new materials 99. They also serve as experimental points
that theoretical computations can be checked against 130.

_OPTIMADE implementation_ : The COD database currently implements version
v1.1.0 of the OPTIMADE standard. The new OPTIMADE version will allow this
implementation to be enriched with new features that are required for the
faithful representation of experimental data, thus making computations from
these data and comparisons of theory and experiments more accurate. Being an
experimental structure database, the COD requires a slightly different data
presentation than computational material databases. Structures from the COD
are evaluated using a set of experimental data quality criteria, established
by the IUCr and the chemical crystallography community 68. An OPTIMADE
response within the core features does not contain all of the necessary fields
to convey these additional data elements; however, the OPTIMADE standard
allows introducing database-specific fields in a regular way. As a result, all
established crystallographic quality criteria are included into a COD response
as COD-specific fields with the _cod_ prefix. This allows OPTIMADE to include
experimental position and composition disorder information following the
Crystallographic Information Framework 56.

_Base URL_ : https://www.crystallography.net/cod/optimade

###  3.6 Joint Automated Repository for Various Integrated Simulations
(JARVIS)

_Database_ : A repository designed to automate materials design using
classical force-field, density functional theory (DFT), machine learning
calculations and experiments. The JARVIS-DFT originated about 5 years ago and
contains millions of properties materials with carefully converged atomic
structures as well as tight convergence parameters and various exchange-
correlation functionals. The JARVIS-DFT contains metallic, semiconducting,
insulator, superconductor, high-strength, topological, solar, thermoelectric,
piezoelectric, dielectric, two-dimensional, magnetic, porous, defect and
various other classes of materials 133, 31.

_OPTIMADE implementation_ : Based on the Django Rest Framework and the JARVIS-
Tools packages to follow OPTIMADE protocols of filtering and curating data.
JARVIS-DFT specific fields are included in the results with the_jarvis_
prefix.

_Base URL_ : https://jarvis.nist.gov/optimade/jarvisdft

###  3.7 Materials Cloud

_Database_ : A platform created to enable sharing and dissemination of
resources in computational materials science 123. A major service offered is
the archiving and publishing of research data for the community via the open
Materials Cloud Archive service (https://archive.materialscloud.org).
Moreover, several databases that are generated within the AiiDA 65, 98, 125
framework are published in the Materials Cloud Explore section, which enables
users to interactively browse the data and its provenance. Curated
visualisations of these databases are also provided in the Materials Cloud
Discover section. These databases are accessible via the OPTIMADE RESTful API.
The databases are divided into flagship and contributed databases. The current
flagship databases are MC3D and MC2D 87, 24 hosting over 34,000 3D crystals
and 3,000 2D crystals, respectively, providing properties of experimentally-
known inorganic compounds obtained via DFT simulations. The contributed
databases include 2D topological insulators, pyrene-based metal organic
frameworks, high-throughput Wannierisation, SrTiO3-CeO2 interfaces, tail-
corrections in the molecular simulations of porous materials, hidden
spontaneous polarisation in the chalcohalide photovoltaic Sn2SbS2I3, and the
CURATED covalent organic frameworks database. The data has been used to
investigate transport properties such as mobility 119, 120, to search for
$\mathbb{Z}_{2}$ topological order 82, to screen and discover quantum Spin-
Hall insulators 81, 52 and Weyl semimetals 53, to obtain tight-binding-like
Wannier Hamiltonians in a fully automated fashion 101, and to develop machine-
learning methods for fast identification of low-dimensional materials 126.

Current developments are focusing on a second “Materials Cloud Archive”
provider, allowing submissions to Materials Cloud Archive to specify whether
and how data contributed by users should be served via an OPTIMADE API, to
enable advanced federated search over archived data. The first proof-of-
concept of this integration is a recently published dataset of novel electride
materials 131, 132. The full list of OPTIMADE databases served by the
Materials Cloud can be explored at the /main/v1/links endpoint, with a similar
list for the Materials Cloud Archive available at /archive/v1/links. A landing
page for both OPTIMADE providers is available at
https://www.materialscloud.org/optimade.

_OPTIMADE implementation_ : The data on the backend of Materials Cloud is
managed via AiiDA. Along with a custom REST API, AiiDA can serve data in the
OPTIMADE format thanks to the AiiDA-OPTIMADE
(https://github.com/aiidateam/aiida-optimade) plugin, that is thus also used
to serve the main Materials Cloud data. The OPTIMADE implementation of the
Materials Cloud Archive provider is instead based directly on the optimade-
python-tools 43 package. In addition to the server implementations, Materials
Cloud also offers users several web applications that include clients of the
OPTIMADE API, as we describe in more detail in Section 4.2.1.

_Index base URL_ : https://www.materialscloud.org/optimade/main

_Index base URL_ : https://www.materialscloud.org/optimade/archive

###  3.8 Materials Platform for Data Science

_Database_ : Materials Platform for Data Science (MPDS) serves the Pauling
File dataset 6. Started in 1993, Pauling File is the oldest privately funded
initiative for the curation and standardisation of the published inorganic
chemistry data111The double awarded Nobel laureate Linus Pauling personally
endorsed this project and gave an explicit written permission to use his name.
In 2019, the Pauling File’s founder Pierre Villars was acknowledged with the
NIMS Award (Tsukuba, Japan) for the fundamental research for data-driven
materials development.. Data is drawn from nearly 400 thousand publications
and backs up such commercial products as Springer Materials, ICDD PDF 4+,
ASM’s Alloy Phase Diagram Database and Pearson’s Crystal Data, MedeA, and
AtomWork Advanced.

_OPTIMADE implementation_ : MPDS presents curated experimental data of three
types: crystalline structures (/structures endpoint), physical properties
(/extensions/properties endpoint), and phase diagrams
(/extensions/phase_diagrams endpoint). These three data types are inter-linked
into about 200 thousand distinct phases (/extensions/phases endpoint). Any
distinct phase is uniquely determined by the chemical formula, space group,
and Pearson symbol. Furthermore, each distinct phase has the permanent integer
identifier phase_id, e.g., see brookite. The MPDS OPTIMADE implementation is
specifically designed for the low response time and high retrieval speed,
therefore some expensive operators (ANY, OR) are currently not supported (cf.
Table 1).

_Base URL_ : https://api.mpds.io

###  3.9 Materials Project

_Database_ : This multi-institution, multi-national effort 70 aims at
computing the properties of all inorganic materials and providing the data and
associated analysis algorithms for every materials researcher free of charge.
Currently, over 172k molecules and over 154k inorganic compounds are included
in the database. The project was established in 2011 with an emphasis on
battery research, but includes property calculations for many areas of clean
energy systems such as photovoltaics, thermoelectric materials, and catalysts.

_OPTIMADE implementation_ : The Materials Project (MP) 70 makes use of the
reference server implementation provided by the optimade-python-tools 43.
Since May 2022, Materials Project has been serving formation energy data via
its OPTIMADE API. In June 2023, MP started exposing additional thermodynamic
stability in the form of energy distance to the convex hull via OPTIMADE for
all 154k materials in its core database. The convex hull distance to the
Materials Project is one of the most important properties of theoretical
structures for experimentalists and simulators alike, as it indicates whether
a postulated material is potentially synthesisable.

The MP OPTIMADE integration is complemented by a convenient open-source
pymatgen 90 interface in the form of the OptimadeRester class, designed to
streamline access to these resources for existing users of pymatgen and the
Materials Project. Additionally, efforts are underway to further expose the
full set of MP summary data via the OPTIMADE endpoint under the _mp_
namespace, mirroring the complete set of data recorded in the emmet
SummaryDoc.

_Base URL_ : https://optimade.materialsproject.org

###  3.10 Material-Property-Descriptor Database

_Database_ : Material-Property-Descriptor Database (MPDD) is an extensive
database (4M+) of _ab initio_ relaxations of 3D crystal structures, combined
with an infrastructure of tools allowing efficient descriptor calculation
(featurization), as well as the deployment of ML models. The most critical
feature of the MPDD is the retention of intermediate modelling data, including
structure-informed descriptors, which typically cost orders of magnitude more
computational time than any of the other steps performed during ML model
deployment 72. Thus, many ML models can be run at a small fraction of the
original cost if the same descriptor (or, more commonly, a subset chosen
through feature selection) is used. This benefit applies regardless of whether
a model is just another iteration, e.g., fine-tuned to a specific class of
materials like perovskites, or an entirely new model for a different property.
Furthermore, MPDD’s access to stored atomic structures and associated metadata
has been shown to be useful, for instance, in the fully data-driven prediction
of atomic structures (validated with DFT and experiments), allowing quick
identification of unknown structures in Nd-Bi 66 and Al-Fe 117 systems.

_OPTIMADE implementation_ : MPDD has a stable OPTIMADE API that serves the
entire core MPDD dataset, fully implementing v1.1.0 of the OPTIMADE standard
through a server based on optimade-python-tools 43. Making the MPDD available
via OPTIMADE was initially challenging, as MPDD stores and exchanges data in a
way that prioritises high throughput and low storage requirements, including
binary data, making it difficult or slow to make MPDD queryable as an OPTIMADE
API on-the-fly. However, issues have been resolved by establishing a self-
updating mirror of the dataset where structures are made OPTIMADE-compliant
during transfer and with most associated MPDD-specific data available under
the _mpdd_ namespace, including dictionaries of metadata, properties, and
descriptors.

_Base URL_ : http://mpddoptimade.phaseslab.org

###  3.11 Materials Properties Open Database

_Database_ : The Material Properties Open Database (MPOD) 95, 45 is a web-
based, open access repository of experimentally determined quantitative
information about the physical properties of crystalline materials. MPOD is
oriented at design engineers, scientists, science teachers and students.
Properties are generally treated as tensor magnitudes. In MPOD the compact
matrix notation is applied. To bring an intuitive view of tensor properties,
so-called longitudinal properties surfaces are displayed. 3D printing of
properties surfaces is implemented via creation of STL files. A dictionary of
properties definitions is included. Eventually, comments are added. Syntax and
notation in MPOD files are oriented towards matching IUCr standards and so
tries to comply with CIF format.

_OPTIMADE implementation_ : The integration of OPTIMADE with MPOD encompassed
two distinct phases. Initially, the process entailed migrating all data from
the MySQL database to MongoDB. This was followed by the mapping of MPOD
objects to OPTIMADE, utilizing optimade-python-tools 43. In this context, the
prefix _mpod_ was employed to delineate specific database fields.

_Base URL_ : http://mpod_optimade.cimav.edu.mx

###  3.12 Materials Resource Registry

_Database_ : A federated, decentralised registry of resources in the domain of
materials science. It exposes these resources to users and machines via XML
and OAI-PMH APIs 100.

_OPTIMADE implementation_ : OPTIMADE has been added to the Materials Resource
Registry as an API format that other services and datasets can link to, to
indicate their own compliance. Materials Resource Registry’s rich semantic
description of databases, with regards to their scientific content,
techniques, and material focus 83, as curated by the provider, enables users
to make expressive queries over OPTIMADE providers, to narrow down which
databases may be of interest to them. This makes it much easier to discover
data and direct clients to the resources that are scientifically the most
relevant to them.

###  3.13 Matterverse

_Database_ : A database of yet-to-be-synthesised materials predicted using
state-of-the-art ML models, currently comprised of 31,664,858 hypothetical
materials. The current structures were generated by combinatorial isovalent
ionic substitutions on 5,283 binary, ternary, and quaternary structural
prototypes from the 2019 version of the ICSD database. A critical enabler for
this database is the Materials 3-body Graph Network (M3GNet) universal
interatomic potential encompassing 89 elements of the periodic table 27. Along
with the information of lattice parameters, atom coordinates and
$E_{\text{hull}}$, matterverse.ai also provides the predicted formation
energies, bandgaps (of multiple fidelities, including PBE, HSE and
experimental), and bulk and shear moduli. As an ongoing effort, matterverse.ai
is growing in two directions, (i) increasing the number of hypothetical
materials via various structure generation strategies, and (ii) increasing the
number of ML-predicted properties.

_OPTIMADE implementation_ : Support of the OPTIMADE API is under active
development, with so far successful mapping of data to the OPTIMADE format
using the optimade-python-tools 43.

###  3.14 NOMAD

_Database_ : An open-source software and free service for managing and
publishing FAIR 108 materials science data. NOMAD 38, 39 was made publicly
available in 2014; it provides over 12 million data entries from over 500
researchers 109. Originally, NOMAD focused on ab initio codes based on
density-functional theory (DFT), automatically extracting data and metadata
from input and output files. Meanwhile, NOMAD was significantly expanded in
scope by the consortium FAIRmat (fairmat-nfdi.eu). It now supports file types
from over 60 simulation codes, it encompasses advanced many-body calculations,
including GW, the Bethe-Salpeter equation (BSE), and dynamical mean-field
theory (DMFT), and classical molecular dynamics simulations. It can cope with
different types of experimental data. For instance, it provides support for
electronic lab notebooks and the NeXus format. NOMAD can track data provenance
in complex simulation and experiment workflows.

NOMAD enables individual researchers to make their data available to a wide
range of possible clients and applications. All data is formally described
through rich metadata schema 46 and can be analyzed with build in
containerised tools and notebooks 107. Data in NOMAD is provided through the
OPTIMADE API, NOMAD specific APIs, and a rich graphical user interface with
faceted search, (meta)data explorer, and visualisations for material
properties. API access is particularly important for re-use of the data, e.g.
with artificial-intelligence (AI) methods. A collection of AI tools is
available in the NOMAD AI Toolkit 107. Besides supporting the community with
the central data infrastructure, NOMAD offers the same software 109 for local
installation through NOMAD Oasis, which allows research groups to manage and
provide their own research data individually and customise the software
accordingly.

_OPTIMADE implementation_ : NOMAD supports a full OPTIMADE API implementation
based on the 43 using the Elasticsearch database engine, and a web-based
search interface that allows users to formulate queries based on the
standardised OPTIMADE query strings. Furthermore, NOMAD users can search for
related resources from all other OPTIMADE database providers in the OPTIMADE
provider list.

_Base URL_ : https://nomad-lab.eu/prod/rae/optimade

###  3.15 Open Database of Xtals (odbx)

_Database_ : A small database serving selected phase diagrams studied with _ab
initio_ crystal structure prediction techniques 57, 42. Recently, _odbx_ has
been used to ingest new materials discovery datasets into the OPTIMADE
ecosystem as part of the optimade-misc.odbx.science sub-database, as will be
discussed in 4.1.2.

_OPTIMADE implementation_ :  _odbx_ was created using the matador 42 and
optimade-python-tools 43 packages. As well as serving the standard OPTIMADE
properties, _odbx_ also serves stability data (hull distances, formation
energies) and the DFT parameters used to relax the structures under the _odbx_
namespace. _odbx_ serves multiple distinct datasets; the links endpoint of the
index base URL below can be used to retrieve them.

_Index base URL_ : https://optimade-index.odbx.science

###  3.16 Open Materials Database (_omdb_)

_Database_ :  _(omdb)_ provides materials properties and is maintained by the
developers of the High-Throughput Toolkit _(httk)_ 17. It contains 205264
structures for access via programmatic interaction using this toolkit. The
structures are also accessible via a web interface. Recently, it is being
integrated in the broader database effort Anyterial
(https://www.anyterial.se/), which also includes the ADAQ database of point
defects 34.

_OPTIMADE implementation_ :  _omdb_ uses the built-in implementation of the
OPTIMADE API provided in _httk_. This implementation is written in Python
using no dependencies beyond the Python standard library. Work is currently
ongoing to extend the implementation to fully support version v1.1.0.

_Base URL_ : https://optimade.openmaterialsdb.se

###  3.17 Open Quantum Materials Database

_Database_ : The Open Quantum Materials Database (OQMD) holds over 1 million
materials, consisting of both experimental and hypothetical compounds 104,
118. The overarching interest of OQMD is to understand the competing stability
between known and unknown compounds by generating large-scale convex hulls – a
stable yet-to-be-synthesised material should fall along or close to this
convex hull. In addition, OQMD grows and develops organically with interests
in Wolverton group, including calculations targeting thermoelectrics 58,
battery materials 18, and high-strength alloys 71.

_OPTIMADE implementation_ : OQMD currently utilises v1.0.0 of the OPTIMADE
standard and will adopt newer versions of OPTIMADE to replace OQMD’s current
qmpy API. OQMD offers database specific properties through the _oqmd_ prefix,
including formation energies, bandgap, and stabilities of compounds.

_Base URL_ : https://oqmd.org/optimade

###  3.18 Comparison of data available

PROVIDER | N1 | N2 | N3 | Ntot
---|---|---|---|---
AFLOW |  704,302 (700,192) |  63,017 (62,293) |  413,797 (382,554) | 3,530,330
Alexandria⋆ | 939,084 | 48,510 | 437,768 | 5,055,842
COD |  452,574 (416,314) |  4,046 (3,896) |  34,739 (32,420) | 506,394
CMR | 147 | 147 | 0 | 1,536
JARVIS-DFT | 9,017 | 1,426 | - | 77,096
Materials Cloud⋆ | 961,564 | 4,218 | 136,176 | 4,515,120
MPDD | 811,136 | 80,195 | 490,900 | 3,975,666
MPOD | 91 | 8 | 16 | 401
MPDS | - | - | - | 507,178
NOMAD |  4,451,056 (3,359,594) |  587,923 (532,123) |  2,092,989 (1,611,302) | 12,116,021
_odbx_ ⋆ |  14,490 (55) |  2,921 (54) |  7,684 (0) | 138,278
_omdb_ |  58,718 (58,718) |  690 (690) |  7,428 (7,428) | 68,566
OQMD |  204,143 (153,113) |  12,467 (11,011) |  81,673 (70,252) | 1,022,603
TCOD |  2,634 (2,631) |  296 (296) |  662 (660) | 2,922
2DMatpedia | 1,172 | 739 | 255 | 6,351
Table 1: The table from Ref. 13 recreated in 2024, with new providers.
Providers that serve multiple databases are indicated with $\star$. The
corresponding values from the 2021 paper 13 are provided in brackets, where
appropriate.

A key benefit of a universal API format such as OPTIMADE is the ability to
simultaneously request and unify results from different databases. The full
list of implementations tested and confirmed to support the OPTIMADE API is
shown in Table 1. These databases are all openly accessible and provide users
with a broad range of materials classes, applications and modalities.

The table shows the return from three requests that explore materials that
contain at least one element from Group 14 (N1), and then constrains the
search to cover only binary materials (N2), and only ternary materials without
toxic lead (N3):

N1

/v1/structures?filter=elements HAS ANY "C","Si","Ge","Sn","Pb"

N2

/v1/structures?filter=elements HAS ANY "C","Si","Ge","Sn","Pb" AND nelements=2

N3

/v1/structures?filter=elements HAS ANY "C","Si","Ge","Sn" AND NOT elements HAS
"Pb" AND elements LENGTH 3

These calls directly duplicate the three detailed in the 2021 OPTIMADE paper
13. The ability to repeat the query attests to the repeatability of the
OPTIMADE API.

Comparison of this table to that in Ref. 13 bears witness to the growth and
impact of OPTIMADE. We see several additional providers (Alexandria, BioExcel,
CMR, JARVIS, MPOD, MPDD and 2DMatpedia) that now support OPTIMADE, and several
new databases hosted by pre-existing providers. Furthermore, among the
databases that did support OPTIMADE in 2021, there has been an impressive
growth in the volume of returned data, reflecting their continued efforts to
assimilate further data.

##  4 Application of OPTIMADE to real-life problems

A key goal for the OPTIMADE API is for it to act as an enabling technology for
materials discovery, design and other new research avenues. Feedback from
users is crucial to motivate the future development of the API. Therefore, in
the following sections, we spotlight several use cases of the application of
the OPTIMADE API to real-life systems, firstly in Section 4.1 by supplying
data for machine learning, and secondly in Section 4.2 by providing data for
screening and other studies.

Furthermore, there has been additional use of OPTIMADE in the literature:
firstly how OPTIMADE has been a central tool to access materials data for
materials discovery, secondly as a template for materials data curation and
access, and thirdly through online web-based interfaces:

Discovery

The hard-coating alloys database (HADB) 77 exploited the OPTIMADE API to
rapidly and easily provide the browser-based graphical web interface as well
as a RESTful API. A second application of the OPTIMADE API was to query and
retrieve an unprecedented volume of data to train an attention-based crystal
graph convolutional neural network to accurately predict the formation energy,
total energy, bandgap, and Fermi energy of a broad range of crystals 128.
Finally, OPTIMADE has found application in materials discovery, where it was
used in Ref. 59 to assess the novelty of a predicted structures in a high-
throughput study on quaternary mixed metal chalcohalide perovskites using the
optimade-python-tools client 43. As these structures were ingested into an
OPTIMADE-compliant database, in this case NOMAD 109, any future OPTIMADE
queries for novelty in this chemical space will yield the results of this
study.

Template

Development of the OPTIMADE API has motivated and guided data access in other
ongoing projects. For example, firstly OPTIMADE API collaborates with, and is
being used in, the development of the FAIRmat metadata, dictionaries, and
materials ontology 108. The inclusion in other community efforts reflects the
maturity and uptake of the OPTIMADE API. A second example is the BIG-MAP
Project, where the consortium plans to use the OPTIMADE API to guide the
access of the data gathered in the Battery Interface Genome 25.

Interfaces and integrations

The MarketPlace Project 1 has integrated the OPTIMADE Gateway (Section 2.3.2)
into the platform, which will make it possible to perform OPTIMADE queries
through its global search functionality. OntoTrans 3 has developed the Open
Translation Environment to perform ontology-driven data pipelines to retrieve,
parse, map, and transform data. As part of the project, an OPTIMADE plugin has
been developed for the system, making it possible to request and digest
OPTIMADE resources. The next steps include semantic mappings for the OPTIMADE
data models for true semantic data interoperability.

###  4.1 Machine learning

Machine learning is a promising tool that is already having a significant
impact in the materials sciences. Machine learning starts from already
computed data about a system and trains a model to capture trends. The machine
learning model can then make predictions and design materials quicker and more
cost effectively than performing additional experiments.

Machine learning relies on having a pool of historical data available. This is
where the OPTIMADE API offers a significant boost, by opening access to a wide
range of materials databases that hold complementary data. We highlight the
help offered by the OPTIMADE API to machine learning with two case studies.

####  4.1.1 High-entropy alloys

High-entropy alloys are comprised of roughly equal parts of five or more
elements. This endows the alloy with a high entropy of mixing, which in turn
delivers excellent high-temperature properties, such as strength-to-weight
ratio, corrosion resistance, and fracture resistance. These favourable
properties have driven an acceleration in research into high-entropy alloys
over the last decade, but this means that there is still relatively little
historical data available for methods such as machine learning.

We use the OPTIMADE API to retrieve high-entropy alloy materials using the
filter query

elements HAS ANY "W","Al","Cd","Zn" AND NOT
elements HAS ANY "B","Cl","F","H","N","O","S" AND
nelements$>$=5

from three different providers (P1, P2, P3).

The complete dataset obtained using OPTIMADE is split into training and
testing sets (4:1 ratio) while ensuring that ratio of entries from each
provider is the same in both training and testing sets. The training set is
used to train the “combined” model M-C. Data points from the providers P1, P2,
and P3 that appear in the training set are used to train the models M-P1,
M-P2, M-P3, respectively. The predictive power of the models is assessed by
calculating the $R^{2}$ on the same test set.

We choose Random Forest Regressor (with default parameters, from the scikit-
learn 1.2 package in Python 94) to construct the machine learning models for
our example. Standard structural entries of the OPTIMADE specification,
species_at_sites and lattice_vectors, are used to construct vectors codifying
the composition of each material and also to calculate the density of each
material. The ‘composition vectors’, described above, are used as input to
machine learning models that are trained to predict the densities (output).
Models that are trained on data from only one provider (M-P1, M-P2, and M-P3)
perform poorly when tested on data from all the providers ($R^{2}=0.316$,
$0.104$, $-2.79$ for M-P1, M-P2, and M-P3 respectively). Meanwhile, the
“combined” model that is trained on data from all providers (M-C) performs
very well ($R^{2}=0.995$). A comparison of the $R^{2}$ values is shown in the
top-left of Fig. 2.

We can get a better insight into the benefits of leveraging data from multiple
providers by looking at comparison of actual density values and those
predicted by the machine learning models for small random sampling of
materials (scatter plot in Fig. 2). For models trained only on data from a
single provider (M-P1, M-P2, and M-P3), the prediction is quite accurate when
tested on data from the same provider (indicted by ‘cross’ markers). However,
most of the predictive power is lost when tested on data from another provider
(‘dot’ markers). This explains their poor $R^{2}$ values. Meanwhile, the model
which is trained on data from all providers (M-C) retains its predictive power
when tested on data from all the providers. The number of materials returned
by each provider is shown in the bar-graph on the bottom right of Fig. 2. A
Venn diagram of unique elements that appear in the materials from each
provider are shown in the centre right in Fig. 2. Therefore, the OPTIMADE API
offers the significant benefit to merge the information from the datasets
together.

Figure 2: Scatter plot showing the comparison between actual density values
and those predicted by the models trained on data obtained using OPTIMADE
(M-P1, M-P2, M-P3 for three providers, and M-C trained on all data). For a
particular provider, the $\times$ symbols are those points validated against
blind data from the same provider, the • symbols those validated against blind
data from a different provider. The top inset shows the $R^{2}$ values for
each of the models. The bottom inset shows the number of entries returned by
each provider. The inset on the centre-right shows the Venn diagram of unique
elements in the entries returned by each of the three providers.

####  4.1.2 Materials discovery and accelerated design

Recent advances in AI-driven materials discovery have created an abundance of
hypothetical crystal structures that are expected to be stable 129, 27, 138,
51, 76. New datasets targeted towards materials discovery have been ingested
and made available as OPTIMADE APIs within the _odbx_ provider 42, 57.
Typically, these datasets would only be explored by other materials discovery
specialists, at least until a more established DFT database ran them through
their pipelines. With OPTIMADE, this dissemination process can be automated
and greatly accelerated. Anyone can register as a provider and have their
novel crystal structures appear in searches by other data-driven applications,
such as the XRD phase identification to be discussed below. As OPTIMADE is not
limited to purely theoretical crystal structures, any future experimental
confirmation of a structure could also be served through OPTIMADE and used to
further improve generative models for materials discovery.

Another possible application is to repeat previous high-throughput materials
design campaigns on the wider set of structures now available through
OPTIMADE. As each structure is time-stamped, active or ongoing workflows can
be implemented to constantly monitor and screen new crystal structures against
the search criteria of the campaign, to avoid having to redo such searches
from scratch. Structure-based property prediction models, e.g., MODNet (for
small structure-property datasets) 35, 36, 78 or graph-based models (where
larger structure-property datasets are available) 28, 134, 29, can be
leveraged to sift through huge swathes of available crystal structures, with
the results being used to prioritise future calculations, attempts at
synthesis, characterisation experiments or model retraining, by selecting for
structures with combinations of particular target properties.

###  4.2 Data provision

The OPTIMADE API has also been used to provide data for a rich variety of
other scientific analysis approaches, below we highlight three projects that
take advantage of the comprehensive range of data offered by OPTIMADE.

####  4.2.1 OPTIMADE client: a web-based GUI to find and import structures

Figure 3: The search interface of the standalone OPTIMADE client. The user can
select any OPTIMADE-compliant database and make a query based on filters
specified through GUI elements.

The primary input to a first-principles materials calculation is the structure
of the system. Experimental or computational crystal databases are commonly
used as sources for the input structures of first-principles simulation
software. To find the target structure in these databases, a query with filter
conditions needs to be prepared, and then the structure needs to be
downloaded, inspected, possibly converted into a different format, and finally
used in simulations.

To facilitate this goal, Materials Cloud 123 provides the OPTIMADE client, a
web application to perform the structure search task via a unified and user-
friendly GUI, empowering users to not only generate and execute complex
OPTIMADE queries, but also to provide immediate graphical access and
visualisation of the resulting structures. The OPTIMADE client can be embedded
in other applications or used as a standalone tool, which is hosted on
Materials Cloud at optimadeclient.materialscloud.io. The filtering section of
the GUI is shown in Fig. 3. A dropdown (at the top) is provided to select any
of the known and automatically discovered OPTIMADE database providers. A
periodic table widget allows users to select which elements need to be
included (green) or excluded (red) in the compounds; additional filtering
tools are also provided, such as for the number of elements and of sites, and
for the dimensionality. An OPTIMADE query string is then produced (which can
be optionally manually modified). After the search button is clicked, the
OPTIMADE query is sent to the selected database provider. The results are
curated and shown in the results widget. Here, the structures are visualised
and can be downloaded.

Materials Cloud also provides various tools that leverage the power of the
OPTIMADE client. One example is the Quantum ESPRESSO input generator,
available as a tool at
https://www.materialscloud.org/work/tools/qeinputgenerator. A structure can be
sent directly to this tool using a button in the OPTIMADE client (shown at the
bottom of Fig. 3). The Quantum ESPRESSO input generator enables any user to
obtain a working input file for the Quantum ESPRESSO DFT code 47, 48,
including an automated selection of all numerical parameters, by just
specifying a crystal structure (either by uploading it, or by selecting it
from OPTIMADE). A second example is the Quantum ESPRESSO app
(https://aiidalab-qe.readthedocs.io) developed within the AiiDAlab platform
135. It allows users to run complex computational workflows from the web
browser, using straightforward graphical user interfaces for structure
selection (including via OPTIMADE), parameter selection and inspection of the
results.

####  4.2.2 Automatic phase identification from X-ray diffraction

The Xerus (X-ray Estimation and Refinement Using Similarity) 19, 124, 69, 92
software package implements procedures to refine and screen measured X-ray
diffraction patterns of inorganic crystals against databases of crystal
structures reported in the literature and beyond. By querying for all possible
structures in a given chemical space, Xerus excels at multiphase fits and
performs competitively against more specialised and compute-intensive models
constructed with machine learning.

Xerus uses a straightforward OPTIMADE interface to connect to the multiple
databases hosted by members of the OPTIMADE consortia. The dynamic OPTIMADE
providers list allows new databases to be automatically included in Xerus
search results. Additional filtering parameters can be used to refine the
searches towards materials stable (or predicted to be stable) at the
experimental conditions (e.g., low temperature or high pressure).

####  4.2.3 Workflows for automated and simultaneous queries of different
databases

Figure 4: (a) Workflow architecture for automated simulations using BIOVIA
Pipeline Pilot. The workflow queries the structure and energies from the main
and archive databases, analyses the available data, and performs CASTEP
calculations for the missing data. (b) Screenshot of the app that reports the
corresponding electrochemical properties, such as Intercalation Voltage and
Crystal structures.

BIOVIA Pipeline Pilot 33 is a scientific workflow system that allows users to
automate calculations and visualise and report research results by graphically
composing a protocol from hundreds of different configurable components. As a
technology demonstrator, we investigate the intercalation voltage of a series
of cathode materials with the workflow in Figure 4(a). It uses OPTIMADE to
adopt the available structures and energetics from different providers and
performs complementary calculations using the CASTEP DFT code 32.

Results are shown in Fig. 4(b), where we plot the intercalation voltage of Li-
Ni-O materials from the extracted VASP 73 data in Materials Project and NOMAD
and compare predictions to those from CASTEP. The comparability of results
illustrates the functionality of the workflow. Since databases contain
different structures, the OPTIMADE API facilitates the process of materials
investigations by aggregating the query of all of them.

MatCloud (http://matcloud.com.cn) is a cloud-based integrated high-throughput
computational materials infrastructure, which is directly connected to
computing clusters and material property databases 137, 136. Users worldwide
can visually design structures, create and run simulation jobs through
workflows, and retrieve crystal structures from multiple databases using
OPTIMADE; all the user needs is a web browser. MatCloud provides a Graphical
User Interface (GUI)-based environment for users to intuitively create, enact
and monitor a workflow. The MatCloud workflow system includes a front-end
workflow designer and a back-end workflow engine, and supports the creation of
workflows by a drag-and-drop approach.

Fig. 5a shows a workflow that retrieves a Si8 crystal structure from the MPDS
database through OPTIMADE, and replaces two Si atoms with Ge to produce
structures in the Si-Ge chemical space (Fig. 5b). The band structure and
density of states (DOS) are then simulated respectively over the chemical
space in a high-throughput manner. Figs. 5c and 5d show the visualisation
results for the band structure and total DOS of the structures.

Figure 5: (a) MatCloud workflow of crystal structure retrieval through
OPTIMADE, and job setup. (b) Visualisation of one of the Si-Ge structures. (c)
Computed band structure for the Si-Ge structure. (d) Total DOS of the Si-Ge
structure.

##  5 Future of OPTIMADE

The rapid expansion of materials databases, the use cases presented, and the
adoption of machine learning motivate the continued work on the OPTIMADE API.
We describe below firstly the ongoing tutorials that introduce new users to
OPTIMADE, secondly the workshops that enable the development and promulgation
of the OPTIMADE API, and finally the features currently under development
coming out of those recent workshops.

###  5.1 Workshops & tutorials

The OPTIMADE consortium originated from the workshop “Open Databases
Integration for Materials Design”, held at the Lorentz Center in Leiden,
Netherlands in October 2016. There were follow-up workshops held at CECAM in
Lausanne, Switzerland annually from 2018 to 2023, with events since 2020 also
supporting remote attendees. The workshops in 2022 and 2023 were accompanied
by on-site tutorials during the first two days. There was also a partner
workshop, “Ontologies for machine learning driven materials design” held at
Linköping University, Sweden in 2021. Going forward, the OPTIMADE API will
undergo continued development through further annual workshops and publicly
advertised monthly video calls. There are continual efforts to reach out to
new databases to help accelerate their adoption of the format.

Several tutorial exercises have been developed and delivered at a variety of
conferences and topical workshops, outside of the OPTIMADE annual meetings.
Eight different exercises developed by the community are now hosted on the
GitHub repository Materials-Consortia/optimade-tutorial-exercises, ranging
from the basics of the OPTIMADE filter syntax and URL structure, to machine-
learning pipelines operating on database-specific properties, all the way up
to hosting an OPTIMADE API for a new database.

###  5.2 Upcoming features for future OPTIMADE releases

The ongoing real-life use cases of the OPTIMADE API have identified a series
of opportunities to extend the API and make it more applicable to a wide range
of materials systems. The features currently under development include:

/trajectories endpoint

So far, OPTIMADE can only be used to describe static structures. We are,
however, working to expand the OPTIMADE specification, so that OPTIMADE can be
used for sharing trajectory data as well. Such data can originate from
structural optimisations, or from Monte Carlo and molecular dynamics
simulations. These trajectories could be used as a starting point for new
simulations, to train machine learning potentials or to extract dynamical
properties.

/collections endpoint

Several groups have asked the OPTIMADE developers whether it would be possible
to have a method to create groups entries. For example, all the structures
that were used to generate a certain machine-learning potential, or all the
structures that pertain to a certain research project. We therefore plan to
introduce a /collections endpoint, which would contain metadata for the
collection as a whole, as well as references to all the individual entries
that belong to this collection.

Ontologies and semantics

Building on the expanded property definitions outlined above, semantic
mappings to existing and in-development materials and crystallography domain
ontologies can be developed. These mappings can be expressed using the
expanded property definitions and utilised in external semantic data
interoperability frameworks. OPTIMADE consortium members are tightly involved
in development of a crystallography domain ontology within the EMMO ecosystem
2.

SMILES property

So far, OPTIMADE has mostly been designed around describing inorganic crystal
structures. There are, however, plenty of materials that are (at least
partially) comprised of organic constituents. To make it easier to find and
select these, we plan to implement a SMILES field and a SMARTS filter for the
organic parts of a structure.

Biomolecular fields

One major use case of the upcoming /trajectories endpoint is to handle
biomolecular structures, which can only be described statistically as a
trajectory with multiple configurations. The OPTIMADE specification will
therefore be extended to standardise the various dynamical fields and order
parameters that are used to describe biomolecular structures. This covers
fields that are typically stored in PDB files such as insertion codes, Chain
IDs and sequence information of proteins, DNA and RNA.

Proliferation of domain-specific namespaces

As mentioned in 2.2, we have already added a mechanism for multiple providers
to collaborate on subsets of shared property definitions. It is hoped that
many such namespaces will arise to improve coverage of OPTIMADE data across
various domains of atomistic science, potentially including the
cheminformatics and biomolecular-focused fields above. Other immediate targets
include stability information from density-functional theory calculations and
magnetic properties.

##  6 Conclusion

The OPTIMADE API provides users with easy access to many of the world leading
materials databases. Since the initial release, the OPTIMADE API has not only
been adopted by scientists as a tool to drive innovation, but furthermore
served as a template for data curation. In this paper, we have provided use
cases for how the breadth of data made available through OPTIMADE enables
discovery in both academia and industry. The development of the OPTIMADE API
has continued apace. Major new support for enhanced property definitions and
partial data formats have recently been added and will underpin future work on
trajectories and biomolecular data. The concept that sub-consortia of
databases are responsible for the definition of new sets of shared properties
will accelerate the extension of the OPTIMADE API to other disciplines and
fields.

Through monthly meetings, and with the continuing support of CECAM, the
developers are continuing to extend the range of properties accessible via
OPTIMADE APIs. Plans to both expand the format to cover challenges arising
from dealing with molecular dynamics data, and continued outreach to support
the adoption of the API by additional databases, will further expand the range
of scientific use cases that OPTIMADE enables. Increasingly, use cases will
take advantage of the unique advantages OPTIMADE has to offer; namely the
robust and straightforward aggregation and data unification from the multitude
of growing and federated data sources.

## Acknowledgments

The authors acknowledge support from CECAM in Lausanne (Switzerland) and the
Lorentz Center in Leiden (Netherlands) for hosting OPTIMADE workshops. G.J.C.
would like to acknowledge financial support from the Royal Society. M.L.E.
thanks the BEWARE scheme of the Wallonia-Brussels Federation for funding under
the European Commission’s Marie Curie-Skłodowska Action (COFUND 847587). CT
thanks NSF (DMR-2219788). M.S. and C.D. acknowledge support from the German
Research Foundation (DFG) through the NFDI consortium FAIRmat (project
460197019). K.E., J.Y., N.M. and G.P. acknowledge funding by the NCCR MARVEL
(a National Centre of Competence in Research, funded by the Swiss National
Science Foundation, grant No. 205602). G.P. acknowledge funding by the Open
Research Data Program of the ETH Board (project “PREMISE”: Open and
Reproducible Materials Science Research). R.A. and O.B.A. acknowledges
Vetenskapsrådet Grant No. 2020-05402 and the Swedish e-Science Research
Centre. A.M., A.V. and S.G. acknowledge funding under the Programme
"University Excellence Initiatives" of the Ministry of Education, Science and
Sports of the Republic of Lithuania (Measure No. 12-001-01-01-01 "Improving
the Research and Study Environment"). A.J.M. acknowledges support from EPSRC
via CCP-NC (EP/T026642/1), CCP9 (EP/T026375/1), UKCP (EP/P022561/1) and
Baskeville (EP/T022221/1). The work by J.S, D. W. and K.A.P were supported by
the U.S. Department of Energy, Office of Science, Office of Basic Energy
Sciences, Materials Sciences and Engineering Division under contract no. DE-
AC02-05-CH11231; the Materials Project program (KC23MP). D.B, A.H. and M.O.
acknowledge funding by the European Union’s Horizon 2020 programme under grant
agreements No. 675728 (BioExcel), No. 823830 (BioExcel-2), No. 720270 (Human
Brain Project SGA1), No. 785907 (Human Brain Project SGA2), No. 945539 (Human
Brain Project SGA3) and by the Horizon Europe Programme under No. 101093290
(BioExcel-3) and No. 101094651 (Molecular Dynamics Data Bank). K.C.
acknowledges funding support from the CHIPS Metrology Program, part of CHIPS
for America, National Institute of Standards and Technology, U.S. Department
of Commerce. X.Y. acknowledges the funding support from National Natural
Science Foundation of China (NSFC) under the grant No. 62376258.

## Author information

These authors were active developers and reviewers of the specification: Johan
Bergsma, Matthew L. Evans, and Andrius Merkys.

These authors were active developers of implementations for database providers
and/or made contributions to specification: Johan Bergsma, Matthew L. Evans,
Andrius Merkys, Oskar B. Andersson, Casper W. Andersen, Daniel Beltrán, Evgeny
Blokhin, Tara Boland, Rubén Castañeda Balderas, Kamal Choudary, Alberto Díaz
Díaz, Rodrigo Domínguez García, Hagen Eckert, Kristjan Eimre, María Elena
Fuentes Montero, Adam M. Krajewski, Jens Jørgen Mortensen, José Manuel Nápoles
Duarte, Jacob Pietryga, Ji Qi, Felipe de Jesús Trejo Carrillo, Antanas
Vaitkus, Jusong Yu, Adam Zettel.

These authors primarily contributed to the paper (along with all other
authors): Pedro Baptista de Castro, Johan Carlsson, Tiago F. T. Cerqueira,
Simon Divilov, Hamidreza Hajiyani, Felix Hanke, Kevin Jose, Corey Oses, Janosh
Riebesell, Jonathan Schmidt, Donald Winston, Christen Xie, Xiaoyu Yang.

These authors managed individual databases that have implemented the OPTIMADE
API: Sara Bonella, Silvana Botti, Stefano Curtarolo, Claudia Draxl, Luis
Edmundo Fuentes Cobas, Adam Hospital, Zi-Kui Liu, Miguel Marques, Nicola
Marzari, Andrew Morris, Shyue Ping Ong, Modesto Orozco, Kristin A. Persson,
Kristian Thygesen, Chris Wolverton.

These authors are organisers of the OPTIMADE API and are also senior
developers who contributed to code and/or to the specification: Rickard
Armiento, Gareth J. Conduit, Saulius Gražulis, Giovanni Pizzi, Gian-Marco
Rignanese, Markus Scheidgen, Cormac Toher.

## Competing interests

G.J.C. is a shareholder and Director of Intellegens Ltd.
G.-M.R. is a shareholder and Chief Innovation Officer of Matgenix SRL.
E.B. is a shareholder and Director of Materials Platform for Data Science OÜ.

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