README.md

---
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  - name: chemical_formula_anonymous
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  - name: forces
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configs:
- config_name: compatible_pbe
  data_files:
  - split: train
    path: compatible_pbe/train-*
- config_name: compatible_pbesol
  data_files:
  - split: train
    path: compatible_pbesol/train-*
- config_name: compatible_r2scan
  data_files:
  - split: train
    path: compatible_r2scan/train-*
- config_name: compatible_scan
  data_files:
  - split: train
    path: compatible_scan/train-*
- config_name: non_compatible
  data_files:
  - split: train
    path: non_compatible/train-*
---


Note: For PBE we are in the process of providing a precomputed energy_corrected scheme based on [Materials Project 2020 Compatibility Scheme](https://www.nature.com/articles/s41598-021-94550-5)

## Dataset Description

- **Homepage:** https://www.lematerial.org/
- **Repository:** https://github.com/lematerial/lematerial
- **Point of Contact:** [email protected]


**Motivation**: check out the blog post [https://huggingface.co/blog/lematerial](https://huggingface.co/blog/lematerial) to hear more about the motivation behind the creation of our datasets.

## Download and use within Python
```python
from datasets import load_dataset

dataset = load_dataset('LeMaterial/LeMat-Traj', 'compatible_pbe')
```

## Data fields

| **Feature name** | **Data type** | **Description** | **[Optimade](https://www.optimade.org/optimade) required field** |
| --- | --- | --- | --- |
| **elements** | Sequence[String] | A list of elements in the structure. For example a structure with composition Li2O7 will have `[”Li”,”O”]` in its elements.  Notes: Currently not necessarily sorted but future iteration will be sorted by alphabetic order. | ✅ |
| **nsites** | Integer | The total number of sites in the structure. For example a structure with an un-reduced composition of Li4O2 will have a total of `6` sites. | ✅ |
| **chemical_formula_anonymous** | String | Anonymous formula for a chemical structure, sorted by largest contributing species, and reduced by greatest common divisor. For example a structure with a O2Li4 un-reduced composition will have a anonymous formula of `A2B`. “1”’s at the end of an element composition are dropped (ie not A2B1) | ✅ |
| **chemical_formula_reduced** | String | Reduced by the greatest common divisor chemical composition. For example a structure with a un-reduced composition of O2Li4 will have a reduced composition of `Li2O`. Elements with a reduced composition of 1 have the “1” dropped. Elements are sorted by alphabetic ordering. Notes: Not using the same method of Pymatgen’s composition reduction method which takes into account certain elements existing in diatomic states. | ✅ |
| **chemical_formula_descriptive** | String | A more descriptive chemical formula for the structure, for example a fictive structure of a 6-fold hydrated Na ion might have a descriptive chemical formula of Na(H2O)6, or a Titanium chloride organic dimer might have a descriptive formula of [(C5H5)2TiCl]2. Note: this field is absolutely not standardized across the database. Where possible if available we scrapped as is from the respective databases. Where not possible this may be the same as the chemical formula reduced. | ✅ Note: not standardized in naming approach. |
| **nelements** | Integer | Total number of different elements in a structure. For example Li4O2 has only `2` separate elements. | ✅ |
| **dimension_types** | Sequence[Integer], shape = 3x1 | Periodic boundary conditions for a given structure. Because all of our materials are bulk materials for this database it is `[1, 1, 1]`, meaning it is periodic in x, y, and z dimensions. | ✅ |
| **nperiodic_dimensions** | Integer | The number of repeating periodic boundary conditions, because all our structures in this database are bulk structures, they are repeating in x, y, and z dimensions and thus they have `3` periodic dimensions. | ✅ |
| **lattice_vectors** | Sequence[Sequence[Floats]], shape = 3x3 | The matrix of the structures. For example a cubic system with a lattice a=4.5 will have a `[[4.5,0,0],[0,4.5,0],[0,0,4.5]]` lattice vector entry. | ✅ |
| **immutable_id** | String | The material ID associated with the structure from the respective database. Note: OQMD IDs are simply integers, thus we converted them to be “oqmd-YYY” | ✅ |
| **cartesian_site_positions** | Sequence[Sequence[Floats]], shape = Nx3 | In cartesian units (not fractional units) the coordinates of the species. These match the ordering of all site based properties such as `species_at_sites`, `magneitc_moments` and `forces`. For example a material with a single element placed at a fractional coordinate of [0.5, 0.5, 0.5] with a cubic lattice with a=2, will have a cartesian_site_positions of `[1, 1, 1]`. | ✅ |
| **species** | JSON | An [Optimade](https://www.optimade.org/optimade) field that includes information about the species themselves, such as their mass, their name, their labels, etc. Note: we have not currently filled out the mass portion of the species. Additionally, none of our inputted structures should be solid solution thus the on-site concentration for all our species should be [1]. This is an Optimade field. | ✅ |
| **species_at_sites** | Sequence[String] | An array of the chemical elements belonging to each site, for example a structure with an un-reduced composition of Li2O2 may have an entry of `[”Li”, “Li”, “O”, “O”]` for this field, where each species should match the other site based properties such as `cartesian_site_positions`. | ✅ |
| **last_modified** | Date/time | The date that the entry was last modified from the respective database it was pulled from. Note: we could not find this information in OQMD so we used the date of the latest database release as the input for this field. | ✅ |
| **elements_ratios** | Dictionary | The fractional composition for a given structure in dictionary format. For example a structure with an unreduced composition of Li2O4 would have an entry of `{’Li’:0.3333, ‘O’:0.6667}` | ✅ |
| **stress_tensor** | Sequence[Sequence[Float]], shape = 3x3 | The full 3x3 vector for stress tensor in units of kB. Note: for OQMD stress tensor were given in Voigt notation, and were converted to the full tensor. |  |
| **energy** | Float | The uncorrected energy from VASP in eV. |  |
| **energy_corrected** | Float | For the PBE subset: Materials Project 2020 compatibility scheme across the entire dataset |  |
| **magnetic_moments** | Sequence[Floats] | The magnetic moment per site given in µB. |  |
| **forces** | Sequence[Sequence[Floats]], shape = 3xN | The force per site, in the proper order of the sites based on other site specific fields for each site in the x, y and z directions, given in eV/A. |  |
| **functional** | String, either ‘pbe’, ‘pbesol’ or ‘scan’ | What functional was used to calculate the data point in the row. |  |
| **space_group_it_number** | Integer | The international space group of the bulk structure as computed by Moyopy | ✅ |
| **id** | String | The id of the frame containing a trajectory number, functional and relaxation step |  |
| **cross_compatibility** | Boolean | Whether or not this data can be mixed with other rows from a DFT calculation parameter perspective. More information on our approach below. |  |
| **relaxation_step** | Integer | The current step along the trajectory. For double relaxation calculations for example, where the previous calculation took 3 total steps, the first image of the next relaxation should be relaxation_step=3. |  |
| **relaxation_number** | Integer | The step along the trajectory for example for Alexandria with triple relaxations, this might be relaxation_step=0, 1 or 2. |  |

## Available subsets

To better support the diverse communities that may utilize this dataset, we are providing the following subsets of our database:

- **Compatible, PBE (default)**: This subset includes rows filtered to ensure cross-compatibility from a DFT perspective. For details on the filtering methodology, see the section below. Only PBE records are included. We designate this as the default subset to prevent accidental training of models on non-compatible data.
- **Compatible, PBESol**
- **Compatible, SCAN**
- **Compatible, r2SCAN**
- **All**: This includes all records formatted as described above. **Disclaimer**: Researchers must carefully evaluate the suitability of individual rows for their specific applications.

### `compatible_pbe`

| **Database** | **Number of trajectories** | **Number of structures*** |
| --- | --- | --- |
| Materials Project | 195,721 | 3,649,785 |
| Alexandria | 3,414,074 | 110,804,226 |
| OQMD | 135,966 | 264,782 |

### `compatible_pbesol`

| **Database** | **Number of trajectories** | **Number of structures*** |
| --- | --- | --- |
| Materials Project | 39,981 | 309,873 |
| Alexandria | 252,791 | 6,099,623 |

### `compatible_scan`

| **Database** | **Number of trajectories** | **Number of structures*** |
| --- | --- | --- |
| Materials Project | 7,756 | 180,528 |

### `compatible_r2scan`

| **Database** | **Number of trajectories** | **Number of structures*** |
| --- | --- | --- |
| Materials Project | 37,888 | 516,576 |

### `non_compatible`

| **Database** | **Number of structures*** |
| --- | --- |
| Materials Project | 546,716 |
| Alexandria | 95,869 |
| OQMD | 128,816 |

## Method for compatibility compliance

To ensure compatibility of rows from a DFT perspective, we implemented the following compatibility scheme:

- **Pseudopotentials**: Calculations were verified to use consistent pseudopotentials. Notably, most pseudopotentials were aligned between MP and Alexandria, except for vanadium (where Alexandria used V_sv and MP used V_pv) and cesium (where Alexandria used a later version of the generic pseudopotential). For OQMD, this resulted in incompatibilities across records involving the following elements: `Ca, Ti, V, Cr, Mn, Ru, Rh, Ce, Eu, Yb`. We note that at the time of this release Materials Project deprecated all Yb containing materials due to the use of a pseudopotential that led to different than expected results. Thus no Yb containing materials from MP are in our database.
- **Hubbard U Parameters**: To ensure uniformity in Hubbard U parameters, we excluded records containing oxygen (O) and any of the following elements: `V, Cr, Mn, Fe, Ni, Cu, Th, U, Np, Pu, Mo, W`. Similarly, records containing fluorine (F) and any of the following elements: Co, Cr, Fe, Mn, Mo, Ni, V, W were also excluded. This exclusion applied specifically to OQMD, which used different Hubbard U parameters compared to MP and Alexandria. However, records from OQMD containing `O` and `Co` were retained, as their Hubbard U parameter differed by only 0.02 eV.
- **Spin Polarization**: OQMD only considered spin-polarized calculations for structures with d or f electrons. While non-spin-polarized calculations are not inherently incompatible (as they represent higher-energy magnetic phases compared to the ground state), we decided to exclude non-spin-polarized calculations for this release. This led to the removal of structures containing only the following elements: `H, Li, Be, Na, Mg, K, Ca, Rb, Sr, Cs, Ba, Fr, Ra, B, C, N, O, F, Ne, He, Al, Si, P, S, Cl, Ar, Ga, Ge, As, Se, Br, Kr, In, Sn, Sb, Te, I, Xe, Tl, Pb, Bi, Po, At, Rn` from OQMD.
- **Convergence Criteria**: OQMD typically used a larger plane-wave cutoff but a less dense k-point grid. Despite these differences, we did not exclude records based on these parameters, assuming that OQMD, Alexandria, and MP operated within acceptable convergence zones for energy calculations. A similar approach was applied to other VASP parameters, though we welcome feedback on this assumption.
- **Convergence**: Across all databases, we identified numerous records with potentially non-convergent calculations or high-energy configurations, often evidenced by significant atomistic forces. We chose not to exclude these records, as users can filter them easily using the “forces” tag if needed.

The “all” split does not contain any filtering based on this approach, so all records can be downloaded.

## Criteria for trajectory subsampling
We mostly borrowed from research from the Materials Project including research on r2SCAN data curation from [Xu Huang, Bowen Deng, Peichen Zhong, Aaron D. Kaplan, Kristin A. Persson, Gerbrand Ceder](https://www.arxiv.org/abs/2504.05565) and from the ChgNet data curation from [Bowen Deng, Peichen Zhong, KyuJung Jun, Janosh Riebesell, Kevin Han, Christopher J. Bartel & Gerbrand Ceder ](https://www.nature.com/articles/s42256-023-00716-3#Sec11). However we made a key change. The selection criteria includes:
- Within the trajectories frames were discarded if they deviated more than 1eV/atom from the final frame, to ensure that no frames are included which may not be fully converged.
- Where possible to identify, if the electronic SCF test did not converge, we did not include the frame.
- We have not kept structures with missing energy, and forces. For people wanting to do something similar to OCP's initial structure to relaxed structure (IS2RE) task, this can be added as a separate split.
- We kept multiple trajectories for the same material from the Materials Project for the structure optimization tasks that are not deprecated.
- We did not downsample based on trajectory length or similar structure to try to enhance diversity, rather opting for full trajectory dataset that others can use.
- Because we added data from other databases, we provide compatibility compliance subset as described above.

## Stay tuned for future updates
In the longer run we plan to release additional datasets including surface, adsorbates, and molecules.

And more! Stay tuned.

## **Support**

If you run into any issues regarding feel free to post your questions or comments on any of the following platforms:

- [**HF Discussions**](https://huggingface.co/datasets/LeMaterial/LeMat-Bulk/discussions)
- [**Github Issues**](https://github.com/LeMaterial/lematerial/issues)
- [**Slack**](https://lematerial.slack.com)


## Citation Information

We are currently in the process of creating a pre-print to describe our methods for compatibility. For now however the following can be cited:

```
@misc {lematerial_2025_traj,
	author = { {Martin Siron}, {Inel Djafar}, {Ali Ramlaoui},  {Lucile Ritchie}, {Etienne Du-Fayet}, {Amandine Rossello}, {Leandro von Werra}, {Thomas Wolf}, {Alexandre Duval} },
	title = { LeMat-Traj Dataset },
	year = 2024,
	url = { https://huggingface.co/datasets/LeMaterial/LeMat-Traj },
	doi = {  },
	publisher = { Hugging Face }
}
```

[CC-BY-4.0](https://creativecommons.org/licenses/by/4.0/) (license used for Materials Project, Alexandria, OQMD) requires proper acknowledgement. 

Thus, if you use materials data which include (”mp-”) in the immutable_id, please cite the [Materials Project](https://pubs.aip.org/aip/apm/article/1/1/011002/119685/Commentary-The-Materials-Project-A-materials). 

If you use materials data which include (”agm-”) in the immutable_id, please cite [Alexandria, PBE](https://www.science.org/doi/10.1126/sciadv.abi7948) or [Alexandria PBESol, SCAN](https://www.nature.com/articles/s41597-022-01177-w). 

If you use materials data which include (”oqmd-”) in the immutable_id, please cite [OQMD](https://link.springer.com/article/10.1007/s11837-013-0755-4). 

If you make use of Optimade in your research, please cite [Optimade](https://doi.org/10.1038/s41597-021-00974-z)

Finally, if you make use of the Phase Diagram for visualization purposes, or the crystal viewer in the Materials Explorer, please acknowledge [Crystal Toolkit](https://github.com/materialsproject/crystaltoolkit).

## License

This database is licensed by [Creative Commons Attribution 4.0 License](https://creativecommons.org/licenses/by/4.0/). 

Disclaimer: it is made up of Alexandria, Materials Project and OQMD materials, which are all licensed by [Creative Commons Attribution 4.0 License](https://creativecommons.org/licenses/by/4.0/).