Bulk Crystals

Lattice constants

Summary

Performance in evaluating lattice constants for 23 solids, including pure elements, binary compounds, and semiconductors.

Metrics

  1. MAE (Experimental)

Mean lattice constant error compared to experimental data

For each formula, a bulk crystal is built using the experimental lattice constants and lattice type for the initial structure. This structure is optimised for each model using the LBFGS optimiser, with the FrechetCellFilter applied to allow optimisation of the cell, until the largest absolute Cartesian component of any interatomic force is less than 0.03 eV/Å. The lattice constants of this optimised structure are then compared to experimental values.

  1. MAE (PBE)

Mean lattice constant error compared to PBE data

Same as (1), but optimised lattice constants are compared to reference PBE data.

Computational cost

Low: tests are likely to less than a minute to run on CPU.

Data availability

Input structures:

  • Built from experimental lattice constants from various sources

Reference data:

  • Experimental data same as input data

  • DFT data

    • Batatia, I., Benner, P., Chiang, Y., Elena, A.M., Kovács, D.P., Riebesell, J., Advincula, X.R., Asta, M., Avaylon, M., Baldwin, W.J. and Berger, F., 2025. A foundation model for atomistic materials chemistry. The Journal of Chemical Physics, 163(18).

    • PBE-D3(BJ)

Elasticity

Summary

Bulk and shear moduli calculated for 12122 bulk crystals from the materials project.

Metrics

  1. Bulk modulus MAE

Mean absolute error (MAE) between predicted and reference bulk modulus (B) values.

MatCalc’s ElasticityCalc is used to deform the structures with normal (diagonal) strain magnitudes of ±0.01 and ±0.005 for ϵ11, ϵ22, ϵ33, and off-diagonal strain magnitudes of ±0.06 and ±0.03 for ϵ23, ϵ13, ϵ12. The Voigt-Reuss-Hill (VRH) average is used to obtain the bulk and shear moduli from the stress tensor. Both the initial and deformed structures are relaxed with MatCalc’s default ElasticityCalc settings. For more information, see MatCalc’s ElasticityCalc documentation.

Analysis excludes materials with:

  • B ≤ 0, B > 500 and G ≥ 0, G > 500 structures.

  • H2, N2, O2, F2, Cl2, He, Xe, Ne, Kr, Ar

  • Materials with density < 0.5 (less dense than Li, the lowest density solid element)

  1. Shear modulus MAE

Mean absolute error (MAE) between predicted and reference shear modulus (G) values

Calculated alongside (1), with the same exclusion criteria used in analysis.

Computational cost

High: tests are likely to take hours-days to run on GPU.

Data availability

Input structures:

  • 1. De Jong, M. et al. Charting the complete elastic properties of inorganic crystalline compounds. Sci Data 2, 150009 (2015).

  • Dataset release: mp-pbe-elasticity-2025.3.json.gz from the Materials Project database.

Reference data:

  • Same as input data

  • PBE