NEBs

Li diffusion

Summary

Performance in predicting activation energies of Li diffusion along the [010] and [001] directions of LiFePO_4.

Metrics

  1. [010] (path B) energy barrier error

The initial and final structures for the diffusion of lithium along [010] are created through deletion an atom from the initial structure. These structures are relaxed, and the Nudged Elastic Band method is used to calculate the energy barrier. This is compared to the reference activation energy for this path.

  1. [001] (path C) energy barrier error

The initial and final structures for the diffusion of lithium along [001] are created through deletion an atom from the initial structure. These structures are relaxed, and the Nudged Elastic Band method is used to calculate the energy barrier. This is compared to the reference activation energy for this path.

Benchmark speed

Fast: the benchmark takes around one minute for mace-mp-0a on an A100 GPU.

Data availability

Input structure:

Reference data:

Si defects

Summary

Performance in predicting DFT singlepoint energies and forces along fixed nudged-elastic-band (NEB) images for a silicon interstitial migration pathway.

Metrics

For each of the three NEB datasets (64 atoms, 216 atoms, and 216 atoms di-to-single), MLIPs are evaluated on the same ordered NEB images as the reference.

  1. Energy MAE

Mean absolute error (MAE) of relative energies along the NEB, shifting image 0 to 0 eV for both the DFT reference and the MLIP predictions.

  1. Force MAE

Mean absolute error (MAE) of forces across all atoms and images along the NEB.

Benchmark speed

Fast: the benchmark takes around one minute for mace-mp-0a on an A100 GPU.

Data availability

Input/reference data:

  • Reference extxyz trajectories (including per-image DFT energies and forces) are distributed as a separate zip archive and downloaded on-demand from the ML-PEG data store. The calculation script uses the public ML-PEG S3 bucket to retrieve these inputs.

  • The reference DFT energies/forces come from Quantum ESPRESSO (PWscf) single-point calculations with:

    • Code/version: Quantum ESPRESSO PWSCF v.7.0

    • XC functional: input_dft='PBE'

    • Cutoffs: ecutwfc=30.0 Ry, ecutrho=240.0 Ry

    • Smearing: occupations='smearing', smearing='mv', degauss=0.01 Ry

    • SCF convergence/mixing: conv_thr=1.0d-6, electron_maxstep=250, mixing_beta=0.2, mixing_mode='local-TF'

    • Diagonalization: diagonalization='david'

    • Symmetry: nosym=.false., noinv=.false. (symmetry enabled)

    • Pseudopotential: Si.pbe-n-kjpaw_psl.1.0.0.UPF (PSLibrary)

    K-points by case:

    • 64 atoms: Γ-only (K_POINTS automatic 1 1 1 0 0 0)

    • 216 atoms: Γ-only (K_POINTS gamma)

    • 216 atoms di-to-single: Γ-only (K_POINTS gamma)

Oxygen adatom diffusion on 2D TMDs

Summary

Performance in predicting diffusion barriers for oxygen adatom migration on monolayer 2D transition metal dichalcogenide (TMD) surfaces.

Metrics

  1. Diffusion barrier error

The diffusion barrier is defined as the maximum energy along the climbing-image NEB (cNEB) minimum energy path (MEP), relative to the initial state energy. This is compared to the reference DFT-PBE calculated barrier for each material.

The benchmark includes the following 2D TMD materials (2H phase):

  • MoS₂

  • MoSe₂

  • MoTe₂

  • WS₂

  • WSe₂

  • WTe₂

For each material, the endpoints are first relaxed using LBFGS until the maximum force component is below 0.1 eV/Å or 100 steps is reached. The cNEB band is constructed with 11 images, and interpolation is attempted with pymatgen’s structure interpolation, falling back to ASEs interpolation if any exceptions are raised during optimisation, which is carried out by ASE’s NEBOptimizer.

Benchmark speed

Fast: the benchmark takes around one minute per model on an A100 GPU.

Data availability

Input structures:

Reference data:

OC20NEB

Summary

Performance in running NEB for surface reactions on multiple catalytic surfaces from OC20NEB dataset.

Metrics

  1. Reaction energy difference compared to DFT reference

  2. Activation barrier difference compared to DFT reference

  3. NEB convergence

Benchmark speed

Very slow: tests may take over 10 hours to run on GPU.

Data availability

Input structure:

Reference data: