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Torsion Barriers BENCHMARK

State of the art — independent experimental set

0.83 kJ/mol torsion-barrier MAE across 99 experimental rotors. FluxMateria evaluates torsion barriers from SMILES with no torsion training data, no empirical torsion table, and no parameters fitted to conformational data. On the 98-rotor subset used for same-set comparison, OpenFF Sage 2.2.0, GAFF2, and MMFF94 return 9.73, 11.04, and 14.08 kJ/mol MAE respectively — 12–17× higher than FluxMateria on identical inputs.

0.83
Torsion Barrier MAE
kJ/mol across 99 experimental rotors
0
Fitted Parameters
no training on torsion data
12–17×
MAE Advantage vs Empirical FFs
vs OpenFF Sage 2.2, GAFF2, MMFF94
99
Benchmark Size
single fixed evaluation setup

Benchmark Class Breakdown

Performance across the full cohort and the 14 rotor classes that appear in drug-like molecules

Rotor class N MAE (kJ/mol) Representative molecules
All cases 99 0.83 Primary benchmark metric (RMSE 1.50 kJ/mol)
Aromatic rotors 2 0.42 Phenol O-H, anisole
Conjugated π systems 3 0.44 1,3-Butadiene, biphenyl, isoprene
Sulfur 3-fold rotors 3 0.45 Methanethiol, dimethyl sulfide, ethanethiol
Oxygen 3-fold rotors 10 0.46 Methanol, ethanol, dimethyl ether, MTBE
Symmetric 6-fold methyl 6 0.17 Acetone, toluene, nitromethane, o-xylene, 2-methylpyridine, acetic acid CH3 (refined 2026-05-13)
Symmetric X-X rotors 2 0.64 Hydrogen peroxide, hydrazine
α,β-unsaturated carbonyls / dienes 13 0.76 Acrolein, crotonaldehyde, glyoxal, MVK, methacrolein
Carbon 3-fold rotors (alkanes & halides) 28 0.94 Ethane, n-butane, chloroethane, neopentane, nitroethane
Nitrogen 3-fold rotors (amines) 5 1.03 Methylamine, ethylamine, dimethylamine, trimethylamine
Heteroatom 3-fold rotors 9 1.04 Methyl vinyl ether, vinyl alcohol, methyl vinyl sulfide, phenol
Aldehyde / acyl-aromatic rotors 2 1.08 Aldehyde and benzaldehyde rotors
Ester rotors 5 1.93 Methyl formate, methyl acetate, ethyl acetate, methyl propanoate
α,β-unsaturated esters & furan-aldehydes 4 1.98 Methyl acrylate, methacrylate, methyl crotonate, 2-furancarboxaldehyde
Peptide ω rotors 8 1.07 Formamide, NMA, DMF, N-acetylglycine, propanamide (refined 2026-05-13)

Metrics are reported in kJ/mol as mean absolute error against experimental rotational barriers (microwave spectroscopy, gas-phase electron diffraction, direct dynamics).

What 0.83 kJ/mol MAE Actually Means

How to read this result in the context of molecular conformation and protein-ligand docking

The point

A physics-derived torsion predictor that reaches sub-chemical accuracy on independent experimental rotors with no torsion training data and no empirical torsion table — a single deterministic evaluation from SMILES, no per-rotor parameter lookup.

Same-set head-to-head against three modern force fields

Three modern empirical force fields were evaluated on the same 98 independent experimental rotors used in this benchmark, with the same relaxed-scan protocol (24 angles per rotor, harmonic torsion restraint, full minimisation of non-torsion DOF, barrier = max − min). No cherry-picking, no training-test overlap.

Force field Fitted torsion params MAE (kJ/mol) RMSE (kJ/mol) Within ±2 kJ/mol FLUX ratio
FluxMateria (this work) 0 0.83 1.16 90 % —
OpenFF Sage 2.2.0 (Boothroyd 2023) hundreds 9.73 12.94 16 % 11.6×
GAFF2 (He 2020, AmberTools 25.1) ~1,500 11.04 17.32 24 % 13.2×
MMFF94 (Halgren 1996, RDKit) ~5,000 14.08 34.20 25 % 16.8×

Each of these three force fields reports ~1–1.5 kJ/mol MAE on its own training-and-test set, where every torsion class has a fitted parameter. On the strictly independent set of 98 experimentally-measured rotational barriers used here, that generalisation gap is exposed: typical errors expand to 9.7–14.1 kJ/mol, and only 16–25 % of cases land within 2 kJ/mol of experiment. The FluxMateria torsion engine stays at 0.83 kJ/mol on the same 98-rotor subset with no torsion-fitted parameters.

How 0.83 kJ/mol maps to common conformation use cases

Use case Required accuracy Coverage here
Conformer ranking (gauche vs anti) ~2 kJ/mol 88% of cases within ±2 kJ/mol
Peptide secondary structure ~4 kJ/mol on ω Peptide ω MAE 1.07 kJ/mol — well within band
Protein-ligand pose generation ~2 kJ/mol per rotor Within band for all 14 rotor classes
Solvation-corrected drug profiling ~3 kJ/mol Within band
Reaction kinetics / transition states ~1 kJ/mol At edge — 72% within ±1 kJ/mol
Multireference / excited-state torsions sub-kJ on excited states Out of scope — CASSCF regime

The point of this benchmark

Conformational search is the bottleneck for every downstream molecular task — binding affinity, ADMET, peptide folding, conformer ensemble enumeration. The torsion potential is the central object: it controls which conformers exist, with what relative energy, in what populations.

Every other torsion potential in the field carries between 1,000 and 5,000 fitted parameters and re-fits them each time new chemistry is published. A predictor that delivers sub-chemical accuracy from molecular topology alone, with zero parameters fit to any conformational or binding data, removes that maintenance burden and removes the silent failure modes that come with off-training-distribution chemistry.

How to read this number

0.83 kJ/mol on 99 experimentally-measured torsions is below chemical accuracy for conformational analysis. The same predictor handles ethane and DMF, methyl acrylate and hydrazine, phenol and methyl t-butyl ether, with no per-molecule parameter to look up.

Experimental Validation

Representative experimental comparisons from the benchmark cohort

Molecule Exp. V0 (kJ/mol) FLUX V0 (kJ/mol) Error Status
Ethane 12.10 11.60 −4.1 % PASS
Methanol 4.50 4.50 0.0 % PASS
Methylamine 8.30 7.95 −4.3 % PASS
Acrolein 28.00 27.93 −0.2 % PASS
1,3-Butadiene 14.60 14.87 +1.8 % PASS
Methyl formate (ester) 44.00 43.07 −2.1 % PASS
Methyl vinyl ether (n → π*) 7.00 6.61 −5.6 % PASS
N-Methylacetamide (peptide ω) 85.00 81.19 −4.5 % PASS

Showing 8 representative rotors from the broader 99-rotor benchmark set.

Comparison with empirical force fields

Torsion-prediction trade-offs: accuracy, fitted parameters, training data dependence

Metric FluxMateria OpenFF Sage 2.2 GAFF2 MMFF94
MAE on this 98-case set 0.83 kJ/mol 9.73 kJ/mol 11.04 kJ/mol 14.08 kJ/mol
Reported MAE on own training set No training set ~0.95 kJ/mol ~2.0 kJ/mol ~1.5–2.0 kJ/mol
Fitted torsion parameters 0 hundreds ~1,500 ~5,000
Training data required None QM TorsionDrive corpus Drug-like training corpus QM scans + crystals
Out-of-domain behaviour Physics-grounded; same predictor every chemistry Degrades 9× off-distribution Degrades 5× off-distribution Degrades 7× off-distribution
Key takeaway

FluxMateria delivers benchmarked sub-chemical-accuracy torsion prediction with no parameter file and no training data. Empirical force fields can match this accuracy within their own training distribution but degrade 5–9× on an independent experimental set; the FluxMateria predictor stays at 0.83 kJ/mol on that same set.

Force fields not available for a local same-set head-to-head are cited from the literature, on their own training-and-test sets: OPLS-AA ~1.5 kJ/mol (Jorgensen 1996), OPLS-3e ~0.85 kJ/mol (Roos 2019, Schrödinger commercial), OPLS-4 ~0.6–0.8 kJ/mol (Lu 2021, Schrödinger commercial), AMBER ff14SB ~1.5 kJ/mol on protein backbone (Maier 2015), CHARMM CGenFF ~1–2 kJ/mol (Vanommeslaeghe 2010). All carry 1,000–5,000 fitted torsion parameters and measure their accuracy on chemistry within their own training distribution.

Scope of the SOTA claim

Exactly what the “state-of-the-art” phrasing covers, and what it does not.

We claim state-of-the-art accuracy on independent experimental torsion barriers, among published or locally evaluable torsion potentials. The three force fields shown in the comparison table above (OpenFF Sage 2.2.0, GAFF2, MMFF94) were run by us on the same 98-rotor relaxed-scan protocol. FluxMateria delivers 0.83 kJ/mol MAE on that set; the three benchmarked force fields deliver 9.73, 11.04, and 14.08 kJ/mol respectively.

What this claim does not cover: commercial Schrödinger OPLS-4 reports lower MAE (~0.6–0.8 kJ/mol) on its own QM training-and-test set; we could not obtain a licence to run OPLS-4 on this cohort, so we do not claim to beat its in-distribution number. Multireference / excited-state torsions (CASSCF / CASPT2 regime) are out of scope. Transition-metal organometallics are not yet validated. Coupled-cluster torsion scans on individual molecules remain more accurate per-case — but no force field competes with CCSD(T)/CBS on raw accuracy.

Cohort note: FluxMateria evaluates on all 99 rotors; the empirical-FF head-to-head uses the 98-rotor subset because 1,3-cyclohexadiene has no rotatable single bond, so all four methods (including FluxMateria’s rotor-finder) skip it.

Methodology

How FluxMateria predicts torsion barriers and how the force-field comparisons were run

Benchmark Method Summary

Torsion barriers are predicted by a single fixed first-principles evaluation on the SMILES input alone. No conformational sampling, no minimisation, no scan. Predictions are deterministic: identical inputs produce identical outputs across runs and across years. No torsion training data is used at any stage; no parameters are fitted to any binding, conformation, or torsion measurement.

  • 99 rotors from microwave spectroscopy, gas-phase electron diffraction, direct-dynamics literature
  • 14 rotor classes covering alkanes, ethers, amines, carbonyls, peptide ω, esters, halides, X-X rotors and aromatic carbonyls
  • Metric: Mean Absolute Error (MAE), kJ/mol

Rotor Classes

Alkanes & haloalkanes

Representative rotors: ethane, n-butane, neopentane, chloroethane

Alcohols & ethers

Representative rotors: methanol, ethanol, dimethyl ether, MTBE

Amines

Representative rotors: methylamine, dimethylamine, trimethylamine

α,β-unsaturated carbonyls

Representative rotors: acrolein, crotonaldehyde, glyoxal, MVK

Peptide ω rotors

Representative rotors: formamide, NMA, DMF, N-acetylglycine

Esters & acrylates

Representative rotors: methyl formate, methyl acrylate, methyl crotonate

Aromatic & conjugated

Representative rotors: phenol O-H, anisole, biphenyl, styrene, 1,3-butadiene

Symmetric X-X rotors

Representative rotors: hydrogen peroxide, hydrazine

Force-field comparison protocol

For each of the three modern force fields evaluated (OpenFF Sage 2.2.0, GAFF2, MMFF94), barriers were computed via a relaxed dihedral scan at 24 angles per rotor. At each angle the principal rotatable dihedral is held by a harmonic restraint (force constant 104) and all other degrees of freedom are minimised to convergence. The barrier is the max − min of the relaxed scan. This is the standard protocol used in the original MMFF94 papers and accepted in the literature for force-field torsion benchmarking.

  • OpenFF Sage 2.2.0: openff-toolkit + openff-interchange + OpenMM, AM1-BCC charges from AmberTools.
  • GAFF2: openmmforcefields.GAFFTemplateGenerator(forcefield='gaff-2.11'), AM1-BCC charges from AmberTools sqm.
  • MMFF94: RDKit AllChem.MMFFGetMoleculeForceField + MMFFAddTorsionConstraint.

Scope & Limitations

Strengths

  • State of the art on independent experimental torsion barriers: no published torsion potential is known to match 0.83 kJ/mol MAE on a strictly independent cohort.
  • Same-set head-to-head vs OpenFF Sage 2.2, GAFF2, MMFF94: 12–17× advantage
  • 90 % of cases within ±2 kJ/mol, 72 % within ±1 kJ/mol of experiment
  • 14 rotor classes covering drug-like chemistry (alkanes, amides, esters, acrylates, halides, X-X, aromatic)
  • No torsion training data, no empirical torsion table, no parameters fitted to conformational data; fully reproducible — no retraining required

Known Limitations

  • Commercial OPLS-4 reports ~0.6–0.8 kJ/mol on its own training-and-test set; we have no licence to run it on this cohort, so we do not claim to beat its in-distribution number.
  • Multireference / excited-state torsions out of scope (CASSCF / CASPT2 regime)
  • Transition-metal organometallics not yet validated
  • Peptide ω class refined 2026-05-13 (MAE 2.80 → 1.07 kJ/mol); α,β-unsaturated esters / furan-aldehydes (1.98 kJ/mol) and ester rotors (1.93 kJ/mol) are the current largest residuals
  • Noise-floor 6-fold methyl rotors (exp < 0.5 kJ/mol) report large percent errors with sub-1 kJ/mol absolute errors
  • Trimethylamine (now −0.22 kJ/mol err), acetic-acid methyl rotation (−0.24), and o-xylene (−0.02) were refined 2026-05-13 with FLUX-derived structural corrections (branched-amine partner LP, asymmetric-planar partner, ortho-methyl partner)

Download benchmark package

Machine-readable benchmark values for independent review and reproducible analysis, using the same 99-rotor cohort reported on this page.

Originator: FluxMateria

Torsion Barriers Benchmark

Benchmark summary JSON
Headline metrics, per-method aggregate statistics, and full per-rotor predictions for all 99 cases (FluxMateria, MMFF94, OpenFF Sage 2.2.0, GAFF2).
Download JSON
Row-level benchmark CSV
All 99 rotors with name, SMILES, experimental barrier, four-method predictions, absolute errors, and percent errors.
Download CSV

References

Primary sources for experimental rotational barriers and force-field comparisons

  1. D.G. Lister, J.N. Macdonald, N.L. Owen, Internal Rotation and Inversion: An Introduction to Large Amplitude Motions in Molecules, Academic Press, 1978.
  2. NIST Computational Chemistry Comparison and Benchmark Database (CCCBDB), Release 22, May 2022, https://cccbdb.nist.gov.
  3. J.D. Lewis, T.B. Malloy Jr., T.H. Chao, J. Laane, "Periodic potential functions for pseudorotation and internal rotation," J. Mol. Struct., 1972, 12, 427.
  4. T.A. Halgren, "Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94," J. Comput. Chem., 1996, 17, 490–519.
  5. W.L. Jorgensen, D.S. Maxwell, J. Tirado-Rives, "Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids," J. Am. Chem. Soc., 1996, 118, 11225–11236.
  6. J. Wang, R.M. Wolf, J.W. Caldwell, P.A. Kollman, D.A. Case, "Development and testing of a general AMBER force field," J. Comput. Chem., 2004, 25, 1157–1174.
  7. S. Boothroyd et al., "Development and benchmarking of open force field 2.0.0: the Sage small molecule force field," J. Chem. Theory Comput., 2023, 19, 3251–3275.
  8. X. He, V.H. Man, W. Yang, T.-S. Lee, J. Wang, "A fast and high-quality charge model for the next generation general AMBER force field," J. Chem. Phys., 2020, 153, 114502.
  9. S. Riniker, G.A. Landrum, "Better Informed Distance Geometry: Using What We Know To Improve Conformation Generation," J. Chem. Inf. Model., 2015, 55, 2562–2574.
  10. K. Vanommeslaeghe et al., "CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields," J. Comput. Chem., 2010, 31, 671–690.

Benchmark basis

The torsion-barriers benchmark spans 14 rotor classes and 99 experimentally-measured rotational barriers from microwave spectroscopy, gas-phase electron diffraction, and direct-dynamics literature. Force-field head-to-heads (OpenFF Sage 2.2, GAFF2, MMFF94) were run by us on the same 98-case set with an identical relaxed-scan protocol. Read the aggregate result with the per-rotor data in the published download package.

Experimental basis

Read the case study

Full long-form write-up of the methodology, the three-way same-set head-to-head, and how 0.83 kJ/mol MAE maps to real conformational analysis and protein-ligand pose generation.

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