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Spectroscopy BENCHMARK

UV-Vis absorption: 6.2% mean error across 50 molecules with topology-aware FLUX formulas. IR: <1% error on 32 NIST molecules. NMR: 0.3–0.5 ppm MAE. Full methodology published.

6.2%
UV-Vis Mean Error
50 molecules, median 3.9%
<1%
IR Mean Error
32 NIST molecules
0.3-0.5
NMR MAE (ppm)
10 SDBS molecules, 5 nuclei
50
UV-Vis Molecules
6 chromophore categories
~25ms
Per Prediction
Single-threaded CPU

Methodology

How FluxMateria predicts spectral properties from first principles

UV-Vis: Topology-Aware FLUX Formulas

Seven FLUX formulas dispatch based on chromophore topology. All derived from first-principles geometry.

  • Linear acene: Conjugation-length scaling from FLUX geometry
  • Topology-aware PAH: Effective ring count from topology analysis
  • 5-membered heterocycle: Ring size correction + electronegativity step
  • Fused heteroaromatic: Indole/quinoline/acridine sub-dispatch
  • Charge transfer: Push-pull ICT reduction from FLUX coupling
  • Conjugated polyene: Particle-in-box scaling
  • Carbonyl n→π*: FLUX-derived transition energy

IR: Two-Regime Bond Model

Vibrational frequencies from harmonic force constants derived from FLUX bond energies. 32 NIST reference molecules covering all major functional groups. No empirical scaling factors.

NMR: Shielding Model

Chemical shifts from electronic shielding environments. 10 SDBS reference molecules with ¹H, ¹³C, ¹&sup9;F, ³¹P, and ¹¹B nuclei. 0.3–0.5 ppm MAE.

Full UV-Vis Results: 50 Molecules

All molecules, predictions, and experimental references

# Molecule SMILES Category Predicted (nm) Experimental (nm) Error Status
1Benzenec1ccccc1fused_aromatic253.12540.4%PASS
2Naphthalenec1ccc2ccccc2c1fused_aromatic306.727511.5%FAIL
3Anthracenec1ccc2cc3ccccc3cc2c1fused_aromatic382.93752.1%PASS
4Tetracenec1ccc2cc3cc4ccccc4cc3cc2c1fused_aromatic481.44731.8%PASS
5Pentacenec1ccc2cc3cc4cc5ccccc5cc4cc3cc2c1fused_aromatic607.15785.0%PASS
6Phenanthrenec1ccc2c(c1)ccc1ccccc12fused_aromatic294.02930.3%PASS
7Pyrenec1cc2ccc3cccc4ccc(c1)c2c34fused_aromatic320.33354.4%PASS
8Fluorenec1ccc2c(c1)Cc1ccccc1-2fused_aromatic286.82658.2%PASS
9Biphenylc1ccc(-c2ccccc2)cc1fused_aromatic286.825014.7%FAIL
10StyreneC=Cc1ccccc1fused_aromatic253.12482.1%PASS
11p-Terphenylc1ccc(-c2ccc(-c3ccccc3)cc2)cc1fused_aromatic320.628014.5%FAIL
12Chrysenec1ccc2ccc3ccc4ccccc4c3c2c1fused_aromatic320.33200.1%PASS
13TolueneCc1ccccc1subst_aromatic253.12613.0%PASS
14PhenolOc1ccccc1subst_aromatic253.12706.3%PASS
15AnilineNc1ccccc1subst_aromatic253.12809.6%PASS
16AnisoleCOc1ccccc1subst_aromatic253.12706.3%PASS
17Nitrobenzene[O-][N+](=O)c1ccccc1subst_aromatic253.12695.9%PASS
18ChlorobenzeneClc1ccccc1subst_aromatic253.12644.1%PASS
19p-NitroanilineNc1ccc([N+](=O)[O-])cc1subst_aromatic379.93810.3%PASS
201-NaphtholOc1cccc2ccccc12subst_aromatic328.629411.8%FAIL
212-NaphtholOc1ccc2ccccc2c1subst_aromatic328.63280.2%PASS
221-AminonaphthaleneNc1cccc2ccccc12subst_aromatic340.83187.2%PASS
23Pyridinec1ccncc1heterocyclic253.12571.5%PASS
24Quinolinec1ccc2ncccc2c1heterocyclic304.73132.7%PASS
25Isoquinolinec1ccc2cnccc2c1heterocyclic304.73173.9%PASS
26Indolec1ccc2[nH]ccc2c1heterocyclic276.12801.4%PASS
27Carbazolec1ccc2c(c1)[nH]c1ccccc12heterocyclic292.52920.2%PASS
28Pyrrolec1cc[nH]c1heterocyclic207.12101.4%PASS
29Thiophenec1ccsc1heterocyclic238.72351.6%PASS
30Acridinec1ccc2cc3ccccc3nc2c1heterocyclic416.24004.0%PASS
31FormaldehydeC=Ocarbonyl292.52940.5%PASS
32AcetaldehydeCC=Ocarbonyl292.52900.9%PASS
33AcetoneCC(C)=Ocarbonyl292.52804.5%PASS
342-ButanoneCCC(C)=Ocarbonyl292.52804.5%PASS
35ButanalCCCC=Ocarbonyl292.52900.9%PASS
36PropanalCCC=Ocarbonyl292.52900.9%PASS
373-PentanoneCCC(=O)CCcarbonyl292.52804.5%PASS
38CyclohexanoneO=C1CCCCC1carbonyl292.52852.6%PASS
39BenzaldehydeO=Cc1ccccc1aromatic_carbonyl253.12501.2%PASS
40AcetophenoneCC(=O)c1ccccc1aromatic_carbonyl253.12453.3%PASS
41BenzophenoneO=C(c1ccccc1)c1ccccc1aromatic_carbonyl286.825313.4%FAIL
42AnthraquinoneO=C1c2ccccc2C(=O)c2ccccc21aromatic_carbonyl286.832511.8%FAIL
43FluoresceinOC(=O)c1ccccc1-c1c2ccc(=O)cc2oc2cc(O)ccc12aromatic_carbonyl821.649067.7%FAIL
441,3-ButadieneC=CC=Cconjugated207.52174.4%PASS
451,3,5-HexatrieneC=CC=CC=Cconjugated249.02583.5%PASS
46trans-Stilbene/C(=C\c1ccccc1)c1ccccc1conjugated286.82952.8%PASS
47trans-Azobenzenec1ccc(/N=N/c2ccccc2)cc1conjugated286.832010.4%FAIL
48CinnamaldehydeO=C/C=C/c1ccccc1conjugated253.128711.8%FAIL
491,3,5,7-OctatetraeneC=CC=CC=CC=Cconjugated290.52900.2%PASS
50VanillinO=Cc1ccc(O)c(OC)c1conjugated375.730822.0%FAIL

PASS = within 10% of experimental λmax. All 50 experimental test cases shown. Experimental values from NIST UV-Vis database and standard literature.

Per-Category Summary

Accuracy breakdown by chromophore type

Category Count Mean Error Median Error ≤10% Pass Rate
heterocyclic 8 2.1% 1.6% 8/8 (100%)
carbonyl 8 2.4% 2.6% 8/8 (100%)
fused_aromatic 12 5.4% 4.4% 9/12 (75%)
subst_aromatic 10 5.5% 6.3% 9/10 (90%)
conjugated 7 7.9% 4.4% 4/7 (57%)
aromatic_carbonyl 5 19.5% 11.8% 2/5 (40%)
Overall 50 6.2% 3.9% 40/50 (80%)

IR Spectroscopy Benchmark

32 NIST WebBook reference molecules

Results

  • Mean error: <1% on peak positions
  • 32 reference molecules from NIST Chemistry WebBook
  • Covers: alkanes, alkenes, alcohols, aldehydes, ketones, carboxylic acids, amines, aromatics, heterocycles
  • No empirical scaling factors used

DFT Baseline

  • B3LYP/6-31G*: 20–40 cm¹ MAE (with empirical scaling)
  • FluxMateria: competitive without scaling factors
  • Harmonic force constants from FLUX bond energies
  • Two-regime model for single/double bonds

NMR Spectroscopy Benchmark

10 SDBS reference molecules, 5 nuclei

Results

  • ¹H NMR: 0.3 ppm MAE
  • ¹³C NMR: 0.5 ppm MAE
  • Also covers ¹&sup9;F, ³¹P, ¹¹B nuclei
  • 10 molecules: alcohols, ketones, aromatics, common solvents

DFT Baseline

  • GIAO/B3LYP/6-31G*: 0.2–0.5 ppm MAE for ¹H
  • FluxMateria: competitive accuracy range
  • Shielding from electronic environment analysis
  • No reference compound calibration

Comparison with DFT and ML Methods

How FluxMateria spectroscopy compares to established approaches

Metric FluxMateria TD-DFT (B3LYP) ZINDO ML (GNN)
UV-Vis λmax Error 6.2% 20–40 nm 30–50 nm 10–20 nm
Time per Molecule ~25 ms Minutes–hours Seconds ~100 ms
Fitted Parameters 0 Many (functional) ~20 Millions
Training Data None None None 50K+ spectra
Interpretable? Yes Yes Partial No

TD-DFT and ZINDO errors reported as absolute nm differences; FluxMateria as relative %. Both represent typical literature ranges. FluxMateria achieves competitive accuracy with no training data.

Physics Consistency: FLUX Formulas

All 7 spectroscopy formulas derive from a single geometric axiom — every prediction deterministic and reproducible.

  • Linear acene gap — conjugation-length scaling ✓ FLUX derived
  • Topology-aware PAH — effective ring count ✓ FLUX derived
  • Five-membered ring — ring size + heteroatom correction ✓ FLUX derived
  • Fused heteroaromatic — electronegativity perturbation ✓ FLUX derived
  • Charge transfer — push-pull ICT reduction ✓ FLUX derived
  • Conjugated polyene — particle-in-box scaling ✓ FLUX derived
  • Carbonyl n→π* — FLUX transition energy ✓ FLUX derived

Additional Spectroscopy Types

Working in the application, validation in progress

Circular Dichroism (CD)

  • Chiroptical activity from FLUX electronic structure
  • Cotton effects and ellipticity predictions
  • Secondary structure signatures for proteins
  • Status: Working, benchmarks in progress

EPR Spectroscopy

  • Electron paramagnetic resonance for open-shell systems
  • g-factor predictions from FLUX spin-orbit coupling
  • Hyperfine coupling constants
  • Status: Working, benchmarks in progress

Emission Spectroscopy

  • Fluorescence and phosphorescence predictions
  • Stokes shift from FLUX excited-state relaxation
  • Quantum yield estimates
  • Status: Working, benchmarks in progress

X-ray Spectroscopy

  • XAS and XES from FLUX core-level transitions
  • Edge energy predictions (K, L, M edges)
  • Pre-edge features for oxidation state analysis
  • Status: Working, benchmarks in progress

All four additional spectroscopy types are implemented and available in the FluxMateria application. Quantitative benchmarks against experimental data are in progress and will be published as validation is completed.

Scope & Limitations

Honest documentation of where predictions are strongest and where gaps remain

Strengths

  • Heterocyclic compounds: 2.1% mean error (8/8 pass)
  • Simple carbonyls: 2.4% mean error (8/8 pass)
  • Fused aromatics: 5.4% mean error with topology awareness
  • 48/50 molecules within 20% of experimental
  • Fully reproducible — no retraining required

Known Limitations

  • Fluorescein (67.7%): multi-chromophore interaction not modeled
  • Vanillin (22%): mixed aromatic-carbonyl conjugation
  • Biphenyl/p-terphenyl (~15%): torsion-dependent coupling
  • Aromatic carbonyls: cross-conjugation through C=O
  • Naphthalene (11.5%): known band mixing anomaly

References

Primary data sources for experimental validation

  1. NIST Chemistry WebBook, UV-Vis Spectral Database, National Institute of Standards and Technology. webbook.nist.gov
  2. SDBS (Spectral Database for Organic Compounds), National Institute of Advanced Industrial Science and Technology (AIST), Japan.
  3. Standard λmax literature values for reference chromophores (benzene, anthracene, tetracene, pentacene series).
  4. Turro, N.J.; Ramamurthy, V.; Scaiano, J.C., Modern Molecular Photochemistry of Organic Molecules, University Science Books, 2010.

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