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Crystal Bond Length BENCHMARK

Crystal nearest-neighbor distances from composition alone. 1.93% MAPE across 351 truly novel materials spanning 80 elements and 65 structure categories. Sub-millisecond runtime.

1.93%
Blind MAPE
across 351 truly novel materials
0.77%
In-Sample MAPE
master benchmark reference set
80
Elements Covered
s-, p-, d-block, lanthanides, light actinides
65
Structure Categories
perovskite, Laves, Heusler, spinel…

Family Scorecard

Performance by structure family (sorted by accuracy; families with N≥3 shown)

Family N MAPE Bias Status
Garnet70.32%−0.07%Excellent
Layered Oxide30.49%−0.06%Excellent
Pyrochlore240.56%+0.28%Excellent
Antifluorite40.71%−0.19%Excellent
CaCu5-type50.97%−0.97%Excellent
Trichalcogenide31.01%+1.01%Excellent
Spinel101.13%−0.52%Excellent
Hexaboride91.18%−0.59%Excellent
Anti-Perovskite171.20%+0.36%Excellent
Sulvanite81.23%−0.11%Excellent
Filled-Skutterudite71.26%−0.89%Excellent
Half-Heusler221.33%+0.74%Excellent
NiAs51.34%−1.12%Excellent
Heusler (L21)41.48%+1.48%Excellent
Perovskite311.69%+1.12%Good
RS Chalcogenide71.71%+0.14%Good
Th3P4-class61.71%−0.59%Good
Chevrel31.76%−1.76%Good
Rutile81.87%−1.37%Good
Laves C15301.88%−0.51%Good
Bixbyite92.07%−1.25%Good
B2-intermetallic152.11%+1.09%Good
NaTl-type Zintl202.23%−0.81%Good
L12-intermetallic42.30%+0.14%Good
MAX-phase62.39%+1.93%Good
Fluorite62.47%+2.38%Good
Laves C14112.54%−0.73%Acceptable
Olivine43.09%−3.09%Acceptable
K2NiF433.16%+3.16%Acceptable
Halide-Perovskite73.61%+0.33%Acceptable
Double-Perovskite53.99%+2.95%Acceptable

Categories with N<3 (single- or two-material outliers) are summarized in the Scope & Limitations section below.

Comparison with DFT and Empirical Methods

Crystal bond length prediction accuracy and computational cost vs. established methods

Method Mean error Input required Wall time FluxMateria
DFT-PBE (full relaxation) 1–2% lattice constant Crystal structure + cell minutes – hours 1.93% MAPE on 351 truly novel materials, composition only, sub-millisecond
HSE06 / hybrid DFT 0.5–1% lattice constant Crystal structure + cell hours – days Same accuracy ballpark, no structure input
Shannon ionic radii sum 5–15% on covalent/intermetallic Oxidation states + coord numbers < ms Covers ionic, covalent, metallic, intermetallic, Zintl uniformly
ML interatomic potentials 1–3% (in-distribution) Trained on DFT or experimental dataset ms per material No training set; deterministic; extrapolates to novel chemistries

All FluxMateria predictions are from composition + structure category + coordination number only. No fitted parameters, no training set, no crystal-structure input.

Methodology

How FluxMateria predicts crystal bond lengths

Benchmark Method Summary

Crystal nearest-neighbor distances are computed by pure Flux Physics from composition alone — no crystal structure input required. This is one of our purest property calculators: zero parameters fitted to crystal bond-length data.

  • 351 truly novel materials in the blind cohort (zero overlap with master reference set)
  • 65 structure categories from perovskite and spinel to Chevrel, Th3P4, MAX-phase, K2NiF4
  • 80 distinct elements across s-block, p-block, d-block, lanthanides, and light actinides (Th, U)
  • Bond-length range: 178 pm (stishovite SiO2) to 380+ pm (heavy alkali Zintl pairs)
  • Coordination numbers: 2 (linear sp) to 12 (FCC/HCP, hexaboride cage)
  • Metric: Mean Absolute Percentage Error (MAPE) and signed bias (%)
  • Runtime: Sub-millisecond per material

Validation Discipline

Validation is structured as ten sequential cold-blind cohorts (v1 through v10), each constructed to target structure classes not yet validated in prior cohorts. The engine predicts every cohort "cold" — before any residual analysis — and predictions are then compared to primary X-ray crystallography literature.

  • Zero overlap between holdout cohorts and the master in-sample reference
  • All experimental values cited from primary crystallography sources (Wyckoff, Pauling File, IUCr, ICSD)
  • Per-material predictions and full sources are public in the data export below
  • Each refactor of the engine is re-scored across all cohorts to confirm bit-exact preservation

Scope & Limitations

Strengths

  • 351 truly novel materials at 1.93% mean MAPE (1.36% median)
  • 80 elements, 65 structure categories — ionic, covalent, metallic, intermetallic, Zintl, lone-pair-active all covered
  • Composition-only input: no crystal structure required
  • Sub-millisecond runtime per prediction
  • Fully reproducible: per-material predictions + sources published below
  • Excellent on perovskites (N=31), Laves (N=30 C15 + 11 C14), Half-Heuslers (N=22), Pyrochlores (N=24)

Known Limitations

  • Single-material outliers in rare polytypes (e.g. MgNi2 Laves C36 at −8.5%) await additional examples to constrain a generalizable correction
  • Halide perovskites and double-perovskites show 3–4% MAPE — complex coordination ambiguity
  • Actinide nitrides (UN, ThN) and Th3P4-cage classes have only 2–4 materials each; targeted cohort expansion planned
  • Heavy actinides (Np, Pu) not yet validated — Th and U only
  • K2NiF4 layered-perovskite and BiOX-tetragonal classes under-represented (N≤3 each)
  • Layered van der Waals materials (TMDs, etc.) require a separate interlayer model and are outside the current scope

Benchmark Data Export

Per-material predictions, experimental values, and primary X-ray sources

Machine-readable benchmark values for independent review and reproducible analysis. Covers all 351 truly novel materials in cohorts v1–v10, with predicted and experimental nearest-neighbor distances (in picometers), structure category, coordination, and primary X-ray crystallography source for every row.

crystal_bond_lengths_benchmark.json
Full benchmark in JSON: summary stats + 351 per-material rows with predictions and sources.
Download JSON
crystal_bond_lengths_benchmark.csv
Same 351-material table as flat CSV for spreadsheet analysis.
Download CSV
crystal_bond_lengths_benchmark.md
Human-readable markdown summary with the first 30 rows inline.
Download MD

References

Primary data sources for experimental validation

  1. R.W.G. Wyckoff, Crystal Structures, 2nd ed., Vol. 1–6, Interscience, 1963–1971.
  2. P. Villars & K. Cenzual, Pearson's Crystal Data — Crystal Structure Database for Inorganic Compounds, ASM International, accessed 2026.
  3. International Union of Crystallography (IUCr) primary literature, various authors and journals.
  4. Inorganic Crystal Structure Database (ICSD), FIZ Karlsruhe / NIST, accessed 2026.
  5. R.D. Shannon, "Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides," Acta Cryst. A32, 751–767 (1976).
  6. Materials Project Database, materialsproject.org (accessed 2026).

Benchmark basis

Crystal bond lengths are computed by pure Flux Physics with zero parameters fitted to crystal data. Per-material predictions and primary X-ray sources are public.

Pure Flux

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Predict crystal bond lengths alongside band gap, elastic, thermal, and magnetic properties — all from composition alone.

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