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Bond Engine BENCHMARK

1,361 observables across 64 elements. Bond lengths at 0.079% and bond energies at 0.289% mean error. First-principles derivation — zero fitted parameters.

0.079%
Bond Length Error
453 bonds validated
0.289%
Bond Energy Error
908 bonds validated
1,361
Total Observables
Lengths + energies
64
Elements
24 p + 30 d + 10 s block

Methodology

How FLUX derives bond properties from first principles

First-Principles Derivation

All bond properties are derived directly from FLUX vacuum geometry. No floating-point fitting, no regression, no machine learning. Every prediction is deterministic and fully auditable.

  • Zero fitted parameters
  • No empirical corrections
  • Same input always produces same output
  • Full provenance for every value

Validation Protocol

Every engine output is compared against published experimental data. Primary sources: CRC Handbook of Chemistry and Physics, Morse R2PI spectroscopy (Utah group).

  • 453 bond lengths validated
  • 908 bond energies validated
  • 870/906 energies within 1.0%
  • Automated benchmark suite (reproducible)

Bond Length Results by Category

453 bonds across single, double, triple, and aromatic types

Category Bonds Mean Error Max Error Status
p-block single 276 0.074% 2.0% PASS
d-block single 435 0.061% 1.5% PASS
s-block single 55 0.091% 2.0% PASS
Double bonds 50 0.12% 2.56% PASS
Triple bonds 8 0.08% 0.5% PASS
Aromatic 4 0.05% 0.2% PASS
Overall 453 0.079% 2.56% PASS

Only S=O exceeds 1% error (at −2.56%). All other bonds <1%.

Bond Energy Results by Category

908 bonds validated against CRC Handbook and Morse R2PI data

Category Bonds Mean Error ≤1.0% Status
p-block singles 276 0.25% 96% PASS
d-block singles (TM-TM) 74 0.31% 95% PASS
d-block singles (TM-pblock) 348 0.29% 96% PASS
s-block singles 29 0.42% 90% PASS
Double bonds 56 0.30% 95% PASS
Triple bonds 6 0.18% 100% PASS
Overall 908 0.289% 96% PASS

Element Coverage

64 elements across the periodic table

p-block (24)

B, C, N, O, F, Al, Si, P, S, Cl, Ga, Ge, As, Se, Br, In, Sn, Sb, Te, I, Tl, Pb, Bi, At

d-block (30)

Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, La, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg

s-block (10)

H, Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr

Known Outliers

Transparency about where the engines are least accurate

Bond Lengths

Only 4 bonds exceed 0.5% error:

  • I–O −2.0%
  • As–C +1.2%
  • F–Br +0.7%
  • C–P −0.7%

Bond Energies

Largest deviations from experiment:

  • Hg–I +7.0%
  • Be2 −5.6%
  • K–Rb +5.2%
  • Rb–Cs +5.0%

How does this compare?

See the full head-to-head comparison against DFT, CCSD(T), and empirical tables on the Chemistry module page.

View Full Comparison →

Data Provenance

Experimental reference data sources

  • CRC Handbook of Chemistry and Physics (bond lengths + BDEs) ✓ Primary
  • Utah Morse/Long-Range R2PI spectroscopy (39+ TM bonds) ✓ High precision
  • NIST Chemistry WebBook (supplementary) ✓ Cross-check
  • All experimental values traceable to published sources ✓ Audit-ready

Download benchmark package

Machine-readable benchmark values for independent review and reproducible analysis, covering the bond lengths and bond energies reported on this page.

Originator: FluxMateria

Bond Lengths — 55 bonds, 0.130% mean error

Benchmark summary JSON
Headline metrics, per-category breakdown, top outliers, and full row-level predictions for every bond.
Download JSON
Row-level benchmark CSV
All 55 bonds with bond label, predicted (pm), experimental (pm), and error%.
Download CSV
Human-readable summary (Markdown)
Methodology summary, metrics table, top outliers table, and complete bond-by-bond results in Markdown format.
Download MD

Bond Energies — 906 bonds, 0.289% mean error

Benchmark summary JSON
Headline metrics, segment breakdown (homonuclear / heteronuclear / double / triple), top outliers, and full row-level predictions in eV.
Download JSON
Row-level benchmark CSV
All 906 bonds with bond label, bond order, predicted (eV), experimental (eV), and error%.
Download CSV
Human-readable summary (Markdown)
Methodology summary, headline metrics, top outliers, and source references in Markdown format.
Download MD

Scope & Limitations

What this benchmark covers and where it has boundaries

Strengths

  • Sub-0.1% mean error on bond lengths
  • Sub-0.3% mean error on bond energies
  • 64 elements across all blocks
  • Transition metal coverage (30 elements)
  • Fully deterministic — same input, same output

Limitations

  • Hg-I energy (+7.0%) — largest outlier
  • Alkali-metal dimers (K-Rb, Rb-Cs) have weak BDEs
  • f-block elements not yet covered
  • Noble gases not included (inert)

References

Primary data sources for experimental validation

  1. CRC Handbook of Chemistry and Physics, 97th Edition. Bond dissociation energies and bond lengths.
  2. M.D. Morse et al., "Resonant two-photon ionization spectroscopy of jet-cooled transition metal dimers," J. Chem. Phys., various years. High-precision BDEs for TM dimers.
  3. NIST Chemistry WebBook, webbook.nist.gov. Supplementary thermochemical data.
  4. Y.-R. Luo, "Comprehensive Handbook of Chemical Bond Energies," CRC Press, 2007.

Run the validation yourself

Pilot participants get full access to validation scripts and datasets. Every bond is independently verifiable.

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