Homonuclear diatomics

Evaluating MLIP dissociation energy curves for elemental homonuclear pairs — the most fundamental test of interatomic interactions.

Physical motivation

The potential energy curve of a homonuclear diatomic molecule A₂ encodes the most basic interaction between two atoms of the same element. A physically correct model must:

• Predict a bound state with a well-defined equilibrium bond length and dissociation energy
• Approach a flat asymptote as the two atoms are pulled apart (the dissociation limit)
• Produce continuous and smooth forces at all distances
• Respect the correct atomic limit: at large separation, the energy should equal twice the isolated-atom energy

MLIPs trained on bulk and surface datasets often fail this test because their training data contains no examples of truly isolated diatomic fragments. Failures appear as spurious minima, non-monotonic behavior far from equilibrium, or incorrect dissociation limits.

PBE reference energies and forces are included in the leaderboard for visual comparison only. Due to known plane-wave DFT convergence issues with diatomic molecules and differences in training datasets, PBE values are excluded from rank aggregation.

What is measured

For each element, the benchmark scans the interatomic distance from very short to well beyond the equilibrium bond length and records:

• Energy E(r) in eV, shifted so that E at the largest separation equals zero
• Force F(r) in eV/Å on one atom, computed as the negative gradient of the energy

The scan covers all 118 elements for which a homonuclear diatomic can be constructed. Each model is evaluated on the elements it can support (element coverage varies by model family and training set).

Metrics

The following quantities are extracted from each E(r) curve:

Metric	Description
Equilibrium bond length r₀	Distance at the energy minimum
Dissociation energy Eₐ	Depth of the potential well relative to the asymptote
Curve smoothness	Presence of spurious oscillations or discontinuities
Asymptotic behavior	Whether E(r) approaches zero correctly at large r

The leaderboard ranks models on the shape and smoothness of their E(r) curves. PBE comparison is provided for reference but is not used in scoring.

Model support

The following models have results for this benchmark. Support is determined by the gpu-tasks: homonuclear-diatomics entry in the model registry.

Model	Family	Training data	Predictions
MACE-MP(M)	mace-mp	MPTrj	EFS
MACE-MPA	mace-mp	MPTrj, Alexandria	EFS
MACE-OFF(M)	mace-off	SPICE	EFS
CHGNet	chgnet	MPTrj	EFSM
M3GNet	matgl	MPF	EFS
MatterSim	mattersim	MPTrj, Alexandria	EFS
ORBv2	orb	MPTrj, Alexandria	EFS
ORB	orb	MPTrj, Alexandria	EFS
SevenNet	sevennet	MPTrj	EFS
eqV2(OMat)	fairchem	OMat, MPTrj, Alexandria	EFS
eSEN	fairchem	OMat, MPTrj, Alexandria	EFS
EquiformerV2(OC22)	equiformer	OC22	EF
EquiformerV2(OC20)	equiformer	OC20	EF
eSCN(OC20)	escn	OC20	EF
ANI2x	ani	SPICE	EFS
ALIGNN	alignn	MP22	EFS

Models trained on catalysis datasets (OC20, OC22) have limited element coverage compared to universal potentials trained on MPTrj or Alexandria. Their curves may be missing for many elements.

How to run

Using the Prefect flow

The benchmark is wrapped in a Prefect flow in mlip_arena.flows.diatomics:

from prefect.task_runners import ThreadPoolTaskRunner
from mlip_arena.flows.diatomics import homonuclear_diatomics

homonuclear_diatomics.with_options(
    task_runner=ThreadPoolTaskRunner(max_workers=3)
)(
    model="MACE-MPA"  # or any model name from MLIPEnum
)

Replace "MACE-MPA" with any model name from mlip_arena.models.MLIPEnum, or pass a custom ASE Calculator instance.

See benchmarks/diatomics/run.ipynb for a complete example.

Viewing raw data

Results for each model are stored as JSON files in benchmarks/diatomics/<family>/<model>.json. Each file contains arrays of distances R, energies E, and forces F for every element pair.

Interpreting results

A well-behaved dissociation curve has these properties:

1. Single minimum at the equilibrium bond length with no secondary wells
2. Monotonic approach to the asymptote — energy increases smoothly as the bond stretches and levels off at zero
3. No force discontinuities — the force curve should be the smooth derivative of the energy curve
4. Correct atomic limit — at very large separations the energy should be close to the isolated-atom reference

Common failure modes seen in practice:

• Oscillatory tails beyond the cutoff radius of message-passing layers
• Spurious energy wells at multiples of the nearest-neighbor distance (artifacts of the radial basis)
• Incorrect asymptotes for molecules containing elements underrepresented in training data
• Unphysical repulsion at very short distances for models lacking core-electron information

Use the force curve view on the leaderboard to quickly spot discontinuities that are not obvious from the energy curve alone.