Diatomics

Disclaimer: Take the results on this page with a grain of salt. We checked most data but not as carefully yet as the discovery task.

The PBE/r2SCAN DFT reference curves shown below 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)!

Metrics in the table below aggregate over the same element set for all models: the 87 Materials Project elements between H and U. Po, At, Rn, Fr, Ra are excluded since they’re absent from MP and hence unsupported by models trained on MP-derived data (MPtrj, OMat24, sAlex) — only a minority of models predicts them. Self-consistency metrics (smoothness, flips, jumps) average over all 87 elements. Reference-relative PBE errors skip 8 further lanthanides (Pr, Pm, Sm, Tb, Dy, Ho, Er, Tm) whose reference curves fail a smoothness quality gate (energy jump ≥ 1.5 eV and ≥ 3 energy-difference sign flips inside the scored window — f-electron SCF convergence issues make these references too jumpy to score models against). Curves excluded from metrics are still shown in the plots below. Models missing curves within the scored set (marked *) are scored on their remaining elements pending backfill runs.

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.

CDS
Accuracy 44%Geometry 22%Speed 11%Physicality 22%
Drag the knob to reweight the four CDS pillars (see ⓘ for definitions); the table updates live. Caveats: Accuracy and Geometry score agreement with PBE, which is itself unreliable for stretched diatomics, and Speed compares wall times measured on heterogeneous hardware.
Training data
Openness
Targets
Presets
#Model τ E flips E jump PBE Δr wall PBE E MAE PBE Δre PBE ΔDe PBE F MAE PBE Δω F flips F TV F jump CDS Speed Slowdown Params Targets Date Added Links rcut Training Set Org
1Allegro-OAM-L1.051.450.08220.1460.9210.1210.3851.0953.21.3718117.80.82867.71.199.7MEFSG2025-09-08 7 Å6.6M (113M) MPtrj+OMat24+sAlex
2Nequip-OAM-L11.570.1030.06370.6180.2470.5060.60570.21.572025.590.8184578.049.6MEFSG2025-09-08 6 Å6.6M (113M) MPtrj+OMat24+sAlex
3Nequip-OAM-XL11.310.1050.06580.7560.2610.5370.89965.81.292243.480.79669912.332.1MEFSG2025-11-30 6 Å6.6M (113M) MPtrj+OMat24+sAlex
4TACE-OAM-L1.011.630.1250.1120.9630.2020.6150.95542.81.61794.720.7491.3k22.8882.9MEFSG2026-04-09 6 Å6.6M (113M) MPtrj+OMat24+sAlex
5Allegro-MP-L1.041.460.06920.2431.230.1120.4691.8762.41.481013.30.74784.61.4918.7MEFSG2025-09-08 6 Å146k (1.58M) MPtrj
6AlphaNet-v1-OAM*1.032.490.830.1270.8920.30.5741.0384.321894.380.7391963.454.65MEFSG2025-05-12 5 Å6.6M (113M) MPtrj+OMat24+sAlex
7MACE-MPA-011.340.08140.271.170.1520.5051.62481.321082.420.7282955.199.06MEFSG2024-12-09 6 Å3.37M (12M) MPtrj+sAlex
8MatterSim v1 5M1.022.470.1690.09691.30.3821.361.164.22.472252.410.71717034.55MEFSG2024-12-16 5 Å17M MatterSim
9Eqnorm MPtrj1.021.470.2660.211.020.2190.5531.9161.21.4613812.40.7114437.791.31MEFSG2025-05-26 6 Å146k (1.58M) MPtrj
10GRACE-3L-OAM-L1.053.180.4180.1621.10.4190.8670.95966.53.351737.230.69988.91.5642.1MEFSG2026-07-02 6 Å6.6M (113M) MPtrj+OMat24+sAlex
11SevenNet-Omni-i12*1.031.530.5260.120.570.1740.41.7757.51.5163115.80.6964.52k79.5654.9MEFSG2026-01-12 6 Å243M COSMOSDataset
12GRACE-2L-OAM-L1.052.180.6160.1411.930.2011.531.2975.21.91195.340.6941021.7926.4MEFSG2025-09-09 6 Å6.6M (113M) MPtrj+OMat24+sAlex
13ORB v2 MPA1.142.970.7940.4831.570.1540.3141.2569.70.9891040.1910.6781202.1125.2MEFSD2024-10-11 10 Å3.25M (32.1M) MPtrj+Alex
14MatRIS-10M-OAM1.032.840.2950.07931.230.210.6521.5597.82.8228835.90.67878313.7810.4MEFSGM2025-10-29 6 Å6.6M (113M) MPtrj+OMat24+sAlex
15ORB v2 MPtrj1.022.390.2220.7351.940.1650.4011.4390.211090.230.6671061.8625.2MEFSD2024-10-14 10 Å146k (1.58M) MPtrj
16HIENet1.022.460.6370.2451.250.5220.7311.4594.12.291183.030.6492654.677.51MEFSG2025-07-01 5 Å146k (1.58M) MPtrj
17eSEN-30M-OAM1.092.250.5310.2311.060.1680.2982.0340.22.32143380.64887015.330.2MEFSG2025-03-17 6 Å6.6M (113M) MPtrj+OMat24+sAlex
18MACE-MP-01.281.370.2890.3991.460.2950.8912.09761.3715818.90.6272694.734.69MEFSG2023-07-14 6 Å146k (1.58M) MPtrj
19Nequip-MP-L1.031.830.2480.1962.010.29613.281101.843732.190.5734638.159.6MEFSG2025-09-08 6 Å146k (1.58M) MPtrj
20Nequix MP PFT1.292.240.5760.6391.680.2590.5712.891052.2181.518.70.56557.31.01708kEFSHG2026-01-08 6 Å154k (1.59M) MPtrj+MDR-MP PBE ωq
21Nequix MP1.312.170.5510.6651.710.2890.5732.9190.42.1779.916.70.56156.81708kEFSG2025-08-17 6 Å146k (1.58M) MPtrj
22GRACE-1L-OAM1.092.380.8990.1553.430.1973.261.6873.22.151303.570.55279.31.393.45MEFSG2025-02-06 6 Å6.6M (113M) MPtrj+OMat24+sAlex
23DPA-3.1-3M-FT1.772.472.10.2621.120.1830.3982.3751.62.843072700.53367111.813.27MEFSG2025-06-05 6 Å163M OpenLAM
24SevenNet-l3i5*1.071.951.430.2281.150.1937.242.651492.065641930.5332.73k48.091.17MEFSG2024-12-10 5 Å146k (1.58M) MPtrj
25GRACE-2L-OAM1.072.481.720.1383.420.2653.281.5376.12.191373.10.52790.91.612.6MEFSG2025-02-06 6 Å6.6M (113M) MPtrj+OMat24+sAlex
26eSEN-30M-MP1.113.230.3990.6452.090.5860.9412.972.43.226220.10.41787815.4430.1MEFSG2025-03-17 6 Å146k (1.58M) MPtrj
27PET-OAM-XL1.031.720.1680.3493.771.192.92.9797.31.773022.460.3883295.78730MEFSG2026-01-10 n/a6.6M (113M) MPtrj+OMat24+sAlex
28GRACE-2L-MPtrj1.291.910.211.193.60.4113.554.291251.942963.910.355921.6215.3MEFSG2024-11-21 6 Å146k (1.58M) MPtrj
29CHGNet2.211.842.10.4033.210.26816.94.931832.014152060.29799.41.75413kEFSGM2023-03-03 5 Å146k (1.58M) MPtrj
30eqV2 M1.938.574.160.7242.150.3790.9944.982422.123457.940.28361810.8786.6MEFSD2024-10-18 12 Å3.37M (102M) MPtrj+OMat24
31MatRIS-10M-MP1.083.410.8470.6553.290.7711.663.852533.460.919.70.26478813.8710.4MEFSGM2025-10-29 6 Å146k (1.58M) MPtrj
32eqV2 S DeNS2.9911.98.211.262.961.041.182.222954.5417614.10.2584367.6731.2MEFSD2024-10-18 12 Å146k (1.58M) MPtrj
33TECE-OAM-RRA-1.01.333.812.720.3073.920.6950.7722.3182.43.5930070.20.2334.51k79.28222MEFSG2026-07-05 6 Å6.6M (113M) MPtrj+OMat24+sAlex

CDS vs Speed

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 33 models
Log Scale

Diatomic Energy Curves

  • PBE (DFT)
  • r2SCAN (DFT)
  • TECE-OAM-RRA-1.0
  • GRACE-3L-OAM-L
  • TACE-OAM-L
  • SevenNet-Omni-i12
  • PET-OAM-XL

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