Diatomics

This task tests diatomic potential-energy curves for agreement with DFT, bond geometry, and physical consistency across interatomic separations.

Reference data: PBE and r2SCAN diatomic curves. The combined diatomics score (CDS, higher is better) combines Accuracy, Geometry, Speed, and Physicality. Reference-relative scores use PBE.

Leaderboard

Interpret with caution: PBE can be unreliable for stretched diatomics, and speed compares heterogeneous hardware. Models marked * lack curves and are scored on their remaining elements. See methodology for reference quality checks and scoring exclusions.

42 of 42 eligible models · Sorted by CDS (descending) · Row numbers follow this filtered order.

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1 ORB v3 1 1.33 0.112 0.109 0.545 0.152 0.304 1.35 35.4 1.34 210 25.5 0.834 125 2.2 25.5M EFSG 2025-04-05 6 Å 6.47M (133M) MPtrj+Alex+OMat24
2 Allegro-OAM-L 1.05 1.45 0.0822 0.146 0.921 0.121 0.385 1.09 53.2 1.37 181 17.8 0.828 67.7 1.19 9.7M EFSG 2025-09-08 7 Å 6.6M (113M) MPtrj+OMat24+sAlex
3 Nequip-OAM-L 1 1.57 0.103 0.0637 0.618 0.247 0.506 0.605 70.2 1.57 202 5.59 0.818 457 8.04 9.6M EFSG 2025-09-08 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
4 Nequip-OAM-XL 1 1.31 0.105 0.0658 0.756 0.261 0.537 0.899 65.8 1.29 224 3.48 0.796 699 12.3 32.1M EFSG 2025-11-30 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
5 TACE-OAM-L 1.01 1.63 0.125 0.112 0.963 0.202 0.615 0.955 42.8 · 72/73 1.6 179 4.72 0.761 772 13.58 82.9M EFSG 2026-04-09 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
6 Allegro-MP-L 1.04 1.46 0.0692 0.243 1.23 0.112 0.469 1.87 62.4 1.48 101 3.3 0.747 84.6 1.49 18.7M EFSG 2025-09-08 6 Å 146k (1.58M) MPtrj
7 M3GNet 1.08 2.28 0.459 0.155 1.08 0.306 0.873 1.2 763 2.21 216 90.6 0.747 67.3 1.18 228k EFSG 2022-09-20 5 Å 62.8k (188k) MPF
8 AlphaNet-v1-OAM* 1.03 2.49 0.83 0.127 0.892 0.3 0.574 1.03 84.3 2 189 4.38 0.739 196 3.45 4.65M EFSG 2025-05-12 5 Å 6.6M (113M) MPtrj+OMat24+sAlex
9 MACE-MPA-0 1 1.34 0.0814 0.27 1.17 0.152 0.505 1.62 48 1.32 108 2.42 0.728 295 5.19 9.06M EFSG 2024-12-09 6 Å 3.37M (12M) MPtrj+sAlex
10 MatterSim v1 5M 1.02 2.47 0.169 0.0969 1.3 0.382 1.36 1.1 64.2 · 72/73 2.47 225 2.41 0.717 170 3 4.55M EFSG 2024-12-16 5 Å n/a MatterSim
11 Eqnorm MPtrj 1.02 1.47 0.266 0.21 1.02 0.219 0.553 1.91 61.2 1.46 138 12.4 0.711 443 7.79 1.31M EFSG 2025-05-26 6 Å 146k (1.58M) MPtrj
12 GRACE-3L-OAM-L 1.05 3.18 0.418 0.162 1.1 0.419 0.867 0.959 66.5 · 68/73 3.35 173 7.23 0.699 88.9 1.56 42.1M EFSG 2026-07-02 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
13 SevenNet-Omni-i12* 1.03 1.53 0.526 0.12 0.57 0.174 0.4 1.77 57.5 · 69/73 1.51 631 15.8 0.696 4.52k 79.56 54.9M EFSG 2026-01-12 6 Å n/a COSMOSDataset
14 GRACE-2L-OAM-L 1.05 2.18 0.616 0.141 1.93 0.201 1.53 1.29 75.2 1.9 119 5.34 0.694 102 1.79 26.4M EFSG 2025-09-09 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
15 BAM-MP-core 1.01 1.41 0.0847 0.237 1.32 0.34 1.11 1.64 82.6 1.39 107 4.42 0.685 499 8.78 17M EFSG 2026-07-16 6 Å 146k (1.58M) MPtrj
16 ORB v2 MPA 1.14 2.97 0.794 0.483 1.57 0.154 0.314 1.25 69.7 0.989 104 0.191 0.678 120 2.11 25.2M EFSD 2024-10-11 10 Å 3.25M (32.1M) MPtrj+Alex
17 MatRIS-10M-OAM 1.03 2.84 0.295 0.0793 1.23 0.21 0.652 1.55 97.8 2.82 288 35.9 0.678 783 13.78 10.4M EFSGM 2025-10-29 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
18 ORB v2 MPtrj 1.02 2.39 0.222 0.735 1.94 0.165 0.401 1.43 90.2 1 109 0.23 0.667 106 1.86 25.2M EFSD 2024-10-14 10 Å 146k (1.58M) MPtrj
19 HIENet 1.02 2.46 0.637 0.245 1.25 0.522 0.731 1.45 94.1 2.29 118 3.03 0.649 265 4.67 7.51M EFSG 2025-07-01 5 Å 146k (1.58M) MPtrj
20 eSEN-30M-OAM 1.09 2.25 0.531 0.231 1.06 0.168 0.298 2.03 40.2 · 70/73 2.32 143 38 0.648 870 15.3 30.2M EFSG 2025-03-17 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
21 EquFlashV2* 1.06 1.58 0.553 0.102 1.39 0.193 0.373 1.91 52.2 · 69/73 1.57 362 44.9 0.644 1.39k 24.5 44.9M EFSG 2026-06-11 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
22 MACE-MP-0 1.28 1.37 0.289 0.399 1.46 0.295 0.891 2.09 76 · 71/73 1.37 158 18.9 0.627 269 4.73 4.69M EFSG 2023-07-14 6 Å 146k (1.58M) MPtrj
23 Nequip-MP-L 1.03 1.83 0.248 0.196 2.01 0.296 1 3.28 110 · 72/73 1.84 373 2.19 0.573 463 8.15 9.6M EFSG 2025-09-08 6 Å 146k (1.58M) MPtrj
24 Prophet-OAME-MBD 1.23 2.54 1.47 0.235 1.1 0.0608 0.348 2 41.1 2.75 345 276 0.572 3.74k 65.8 62.3M EFSG 2026-09-13 7 Å 16.4M (324M) MPtrj+OMat24+sAlex+ELEMENTA
25 Nequix MP PFT 1.29 2.24 0.576 0.639 1.68 0.259 0.571 2.89 105 2.21 81.5 18.7 0.565 57.3 1.01 708k EFSHG 2026-01-08 6 Å 154k (1.59M) MPtrj+MDR-MP PBE ωq
26 Nequix MP 1.31 2.17 0.551 0.665 1.71 0.289 0.573 2.91 90.4 2.17 79.9 16.7 0.561 56.8 1 708k EFSG 2025-08-17 6 Å 146k (1.58M) MPtrj
27 GRACE-1L-OAM 1.09 2.38 0.899 0.155 3.43 0.197 3.26 1.68 73.2 2.15 130 3.57 0.552 79.3 1.39 3.45M EFSG 2025-02-06 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
28 DPA-3.1-3M-FT 1.77 2.47 2.1 0.262 1.12 0.183 0.398 2.37 51.6 2.84 307 270 0.533 671 11.81 3.27M EFSG 2025-06-05 6 Å n/a OpenLAM
29 SevenNet-l3i5* 1.07 1.95 1.43 0.228 1.15 0.193 7.24 2.65 149 · 72/73 2.06 564 193 0.533 2.73k 48.09 1.17M EFSG 2024-12-10 5 Å 146k (1.58M) MPtrj
30 GRACE-2L-OAM 1.07 2.48 1.72 0.138 3.42 0.265 3.28 1.53 76.1 2.19 137 3.1 0.527 90.9 1.6 12.6M EFSG 2025-02-06 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
31 eSEN-30M-MP 1.11 3.23 0.399 0.645 2.09 0.586 0.941 2.9 72.4 3.22 62 20.1 0.417 878 15.44 30.1M EFSG 2025-03-17 6 Å 146k (1.58M) MPtrj
32 EquiformerV3+DeNS-MP 1.18 4.4 0.844 0.681 1.95 0.444 0.846 3.06 84.3 4.59 78.6 28.9 0.413 684 12.04 30.3M EFSG 2026-04-07 6 Å 146k (1.58M) MPtrj
33 PET-OAM-XL 1.03 1.72 0.168 0.349 3.77 1.19 2.9 2.97 97.3 · 50/73 1.77 302 2.46 0.388 329 5.78 730M EFSG 2026-01-10 n/a 6.6M (113M) MPtrj+OMat24+sAlex
34 GRACE-2L-MPtrj 1.29 1.91 0.21 1.19 3.6 0.411 3.55 4.29 125 · 66/73 1.94 296 3.91 0.355 92 1.62 15.3M EFSG 2024-11-21 6 Å 146k (1.58M) MPtrj
35 EquFlash* 1.02 1.42 345 0.132 1.06e29 0.159 0.336 1.84e30 47.7 · 66/73 1.4 8.14e32 1.68e4 0.328 602 10.6 28.7M EFSG 2025-06-23 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
36 CHGNet 2.21 1.84 2.1 0.403 3.21 0.268 16.9 4.93 183 2.01 415 206 0.297 99.4 1.75 413k EFSGM 2023-03-03 5 Å 146k (1.58M) MPtrj
37 eqV2 M 1.93 8.57 4.16 0.724 2.15 0.379 0.994 4.98 242 2.12 345 7.94 0.283 618 10.87 86.6M EFSD 2024-10-18 12 Å 3.37M (102M) MPtrj+OMat24
38 TECE-OAM-RRA-1.0 1.33 3.81 2.72 0.307 3.92 0.695 0.773 2.31 82.4 · 68/73 3.59 300 70.1 0.270 987 17.37 222M EFSG 2026-07-05 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
39 EquiformerV3+DeNS-OAM 1.3 7.1 14.3 0.59 1.84 0.689 2.4 4.19 229 · 68/73 7.12 562 642 0.269 622 10.94 30.3M EFSG 2026-04-07 6 Å 6.6M (113M) MPtrj+OMat24+sAlex
40 MatRIS-10M-MP 1.08 3.41 0.847 0.655 3.29 0.771 1.66 3.85 253 · 72/73 3.4 60.9 19.7 0.264 788 13.87 10.4M EFSGM 2025-10-29 6 Å 146k (1.58M) MPtrj
41 eqV2 S DeNS 2.99 11.9 8.21 1.26 2.96 1.04 1.18 2.22 295 · 71/73 4.54 176 14.1 0.258 436 7.67 31.2M EFSD 2024-10-18 12 Å 146k (1.58M) MPtrj
42 DPA-4.0.1-Pro-MPtrj 2.34 4.25 1.38e3 0.538 3.48 0.33 97.2 9.06e5 5.71e3 · 69/73 4.22 1.58e9 1.76e9 0.123 702 12.35 22.8M EFSG 2026-06-11 6 Å 146k (1.58M) MPtrj
CDS weights
Other weights adjust proportionally. Total: 100%.

CDS vs twall

This defaults to a cost-vs-fidelity Pareto: each model's full diatomic-sweep wall time against its CDS, with marker size showing model parameters and color the training-set size. Use the axis/color/size selectors to compare any pair of metrics and metadata.

  • Params Params · 42 models
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Test set: Diatomic curves

92 homonuclear dimers · 92 elements · PBE and r2SCAN

Potential-energy and force curves from H₂ to U₂ probe bond geometry, dissociation, repulsion, and smoothness. PBE reference-relative errors exclude low-quality reference curves.

Public DFT curves include energies, forces, and site-projected magnetic moments. Reference-relative scores use PBE.

H 1
He 1
Li 1
Be 1
B 1
C 1
N 1
O 1
F 1
Ne 1
Na 1
Mg 1
Al 1
Si 1
P 1
S 1
Cl 1
Ar 1
K 1
Ca 1
Sc 1
Ti 1
V 1
Cr 1
Mn 1
Fe 1
Co 1
Ni 1
Cu 1
Zn 1
Ga 1
Ge 1
As 1
Se 1
Br 1
Kr 1
Rb 1
Sr 1
Y 1
Zr 1
Nb 1
Mo 1
Tc 1
Ru 1
Rh 1
Pd 1
Ag 1
Cd 1
In 1
Sn 1
Sb 1
Te 1
I 1
Xe 1
Cs 1
Ba 1
La 1
Ce 1
Pr 1
Nd 1
Pm 1
Sm 1
Eu 1
Gd 1
Tb 1
Dy 1
Ho 1
Er 1
Tm 1
Yb 1
Lu 1
Hf 1
Ta 1
W 1
Re 1
Os 1
Ir 1
Pt 1
Au 1
Hg 1
Tl 1
Pb 1
Bi 1
Po 1
At 1
Rn 1
Fr 1
Ra 1
Ac 1
Th 1
Pa 1
U 1
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
No
Lr
Rf
Db
Sg
Bh
Hs
Mt
Ds
Rg
Cn
Nh
Fl
Mc
Lv
Ts
Og
Each element is counted once per dimer.

Explore DFT reference curves using the curve viewer below. Select models there to compare predictions.

Diatomic Energy Curves

  • PBE (DFT)
  • r2SCAN (DFT)
  • Allegro-OAM-L
  • Nequip-OAM-L
  • ORB v3

H-H

He-He

Li-Li

Be-Be

B-B

C-C

N-N

O-O

F-F

Ne-Ne

Na-Na

Mg-Mg

Al-Al

Si-Si

P-P

S-S

Cl-Cl

Ar-Ar

K-K

Ca-Ca

Sc-Sc

Ti-Ti

V-V

Cr-Cr

Mn-Mn

Fe-Fe

Co-Co

Ni-Ni

Cu-Cu

Zn-Zn

Ga-Ga

Ge-Ge

As-As

Se-Se

Br-Br

Kr-Kr

Rb-Rb

Sr-Sr

Y-Y

Zr-Zr

Nb-Nb

Mo-Mo

Tc-Tc

Ru-Ru

Rh-Rh

Pd-Pd

Ag-Ag

Cd-Cd

In-In

Sn-Sn

Sb-Sb

Te-Te

I-I

Xe-Xe

Cs-Cs

Ba-Ba

La-La

Ce-Ce

Pr-Pr

Nd-Nd

Pm-Pm

Sm-Sm

Eu-Eu

Gd-Gd

Tb-Tb

Dy-Dy

Ho-Ho

Er-Er

Tm-Tm

Yb-Yb

Lu-Lu

Hf-Hf

Ta-Ta

W-W

Re-Re

Os-Os

Ir-Ir

Pt-Pt

Au-Au

Hg-Hg

Tl-Tl

Pb-Pb

Bi-Bi

Po-Po

At-At

Rn-Rn

Fr-Fr

Ra-Ra

Ac-Ac

Th-Th

Pa-Pa

U-U

Methodology

Reference provenance, scoring exclusions, and contributions

Data validation for this task is less mature than for discovery; interpret the results with caution.

The PBE/r2SCAN DFT reference curves are documented in the DFT reference provenance note, including the VASP setup, spin-ladder generation, warm-start strategy, postprocessing, and quality checks. The TMI page shows each reference curve’s per-atom magnetic moments vs separation, useful for spotting residual SCF spin-state artifacts and for benchmarking spin-aware MLIPs. Expert advice on how the DFT reference curves might be improved would be appreciated (thanks to Andrew Rosen for guidance on obtaining correct dimer PECs)!

Leaderboard metrics use the Materials Project elements between H and U. Po, At, Rn, Fr, and Ra are excluded to keep the scored set compatible with MP-derived training data. Self-consistency metrics (smoothness, flips, jumps) average over this set. Reference-relative PBE errors additionally exclude curves that fail a smoothness quality gate (energy jump ≥ 1.5 eV and ≥ 3 energy-difference sign flips inside the scored window). SCF convergence issues can make these references too jumpy to score models against. Curves excluded from metrics are still shown in the plots. Models missing curves within the scored set (marked *) are scored on their remaining elements.

With thanks to MLIP Arena by Yuan Chiang, who first benchmarked MLIPs on self-consistency metrics of homonuclear diatomic curves and inspired this task.

We welcome backfill PRs from model authors for models still missing diatomic metrics; see the diatomics runner, calculator registry, and model enum.