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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

UV-Vis Molecules

6 chromophore categories

~25ms

Per Prediction

Single-threaded CPU

Full UV-Vis Results: 50 Molecules

All molecules, predictions, and experimental references

#	Molecule	SMILES	Category	Predicted (nm)	Experimental (nm)	Error	Status
1	Benzene	c1ccccc1	fused_aromatic	253.1	254	0.4%	PASS
2	Naphthalene	c1ccc2ccccc2c1	fused_aromatic	306.7	275	11.5%	FAIL
3	Anthracene	c1ccc2cc3ccccc3cc2c1	fused_aromatic	382.9	375	2.1%	PASS
4	Tetracene	c1ccc2cc3cc4ccccc4cc3cc2c1	fused_aromatic	481.4	473	1.8%	PASS
5	Pentacene	c1ccc2cc3cc4cc5ccccc5cc4cc3cc2c1	fused_aromatic	607.1	578	5.0%	PASS
6	Phenanthrene	c1ccc2c(c1)ccc1ccccc12	fused_aromatic	294.0	293	0.3%	PASS
7	Pyrene	c1cc2ccc3cccc4ccc(c1)c2c34	fused_aromatic	320.3	335	4.4%	PASS
8	Fluorene	c1ccc2c(c1)Cc1ccccc1-2	fused_aromatic	286.8	265	8.2%	PASS
9	Biphenyl	c1ccc(-c2ccccc2)cc1	fused_aromatic	286.8	250	14.7%	FAIL
10	Styrene	C=Cc1ccccc1	fused_aromatic	253.1	248	2.1%	PASS
11	p-Terphenyl	c1ccc(-c2ccc(-c3ccccc3)cc2)cc1	fused_aromatic	320.6	280	14.5%	FAIL
12	Chrysene	c1ccc2ccc3ccc4ccccc4c3c2c1	fused_aromatic	320.3	320	0.1%	PASS
13	Toluene	Cc1ccccc1	subst_aromatic	253.1	261	3.0%	PASS
14	Phenol	Oc1ccccc1	subst_aromatic	253.1	270	6.3%	PASS
15	Aniline	Nc1ccccc1	subst_aromatic	253.1	280	9.6%	PASS
16	Anisole	COc1ccccc1	subst_aromatic	253.1	270	6.3%	PASS
17	Nitrobenzene	[O-][N+](=O)c1ccccc1	subst_aromatic	253.1	269	5.9%	PASS
18	Chlorobenzene	Clc1ccccc1	subst_aromatic	253.1	264	4.1%	PASS
19	p-Nitroaniline	Nc1ccc([N+](=O)[O-])cc1	subst_aromatic	379.9	381	0.3%	PASS
20	1-Naphthol	Oc1cccc2ccccc12	subst_aromatic	328.6	294	11.8%	FAIL
21	2-Naphthol	Oc1ccc2ccccc2c1	subst_aromatic	328.6	328	0.2%	PASS
22	1-Aminonaphthalene	Nc1cccc2ccccc12	subst_aromatic	340.8	318	7.2%	PASS
23	Pyridine	c1ccncc1	heterocyclic	253.1	257	1.5%	PASS
24	Quinoline	c1ccc2ncccc2c1	heterocyclic	304.7	313	2.7%	PASS
25	Isoquinoline	c1ccc2cnccc2c1	heterocyclic	304.7	317	3.9%	PASS
26	Indole	c1ccc2[nH]ccc2c1	heterocyclic	276.1	280	1.4%	PASS
27	Carbazole	c1ccc2c(c1)[nH]c1ccccc12	heterocyclic	292.5	292	0.2%	PASS
28	Pyrrole	c1cc[nH]c1	heterocyclic	207.1	210	1.4%	PASS
29	Thiophene	c1ccsc1	heterocyclic	238.7	235	1.6%	PASS
30	Acridine	c1ccc2cc3ccccc3nc2c1	heterocyclic	416.2	400	4.0%	PASS
31	Formaldehyde	C=O	carbonyl	292.5	294	0.5%	PASS
32	Acetaldehyde	CC=O	carbonyl	292.5	290	0.9%	PASS
33	Acetone	CC(C)=O	carbonyl	292.5	280	4.5%	PASS
34	2-Butanone	CCC(C)=O	carbonyl	292.5	280	4.5%	PASS
35	Butanal	CCCC=O	carbonyl	292.5	290	0.9%	PASS
36	Propanal	CCC=O	carbonyl	292.5	290	0.9%	PASS
37	3-Pentanone	CCC(=O)CC	carbonyl	292.5	280	4.5%	PASS
38	Cyclohexanone	O=C1CCCCC1	carbonyl	292.5	285	2.6%	PASS
39	Benzaldehyde	O=Cc1ccccc1	aromatic_carbonyl	253.1	250	1.2%	PASS
40	Acetophenone	CC(=O)c1ccccc1	aromatic_carbonyl	253.1	245	3.3%	PASS
41	Benzophenone	O=C(c1ccccc1)c1ccccc1	aromatic_carbonyl	286.8	253	13.4%	FAIL
42	Anthraquinone	O=C1c2ccccc2C(=O)c2ccccc21	aromatic_carbonyl	286.8	325	11.8%	FAIL
43	Fluorescein	OC(=O)c1ccccc1-c1c2ccc(=O)cc2oc2cc(O)ccc12	aromatic_carbonyl	821.6	490	67.7%	FAIL
44	1,3-Butadiene	C=CC=C	conjugated	207.5	217	4.4%	PASS
45	1,3,5-Hexatriene	C=CC=CC=C	conjugated	249.0	258	3.5%	PASS
46	trans-Stilbene	/C(=C\c1ccccc1)c1ccccc1	conjugated	286.8	295	2.8%	PASS
47	trans-Azobenzene	c1ccc(/N=N/c2ccccc2)cc1	conjugated	286.8	320	10.4%	FAIL
48	Cinnamaldehyde	O=C/C=C/c1ccccc1	conjugated	253.1	287	11.8%	FAIL
49	1,3,5,7-Octatetraene	C=CC=CC=CC=C	conjugated	290.5	290	0.2%	PASS
50	Vanillin	O=Cc1ccc(O)c(OC)c1	conjugated	375.7	308	22.0%	FAIL

PASS = within 10% of experimental λ_max. 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 λ_max 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. Method notes identify where formula predictions, calibrated spectral results, or known-compound baselines are involved.

Physics Consistency: FLUX Formulas

Formula routes are deterministic and reproducible; calibrated and known-reference routes are labeled separately above.

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.

Methodology

How FluxMateria predicts spectral properties by modality

UV-Vis: Topology-Aware FLUX Formulas

FluxMateria uses topology-aware FLUX formulas that adapt to the major chromophore families represented in the benchmark. Known-molecule dictionary routes are tracked separately from formula predictions.

Linear acene: Conjugation-length scaling from Flux physics
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.

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

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

Benchmark basis

Spectroscopy reports multiple modalities on one page. The table below labels the main result families so formula predictions and calibrated spectral results are not conflated.

Mixed basis

Result family	Basis	How to read it
UV-Vis formula route	Flux Physics	Computed from Flux Physics UV-Vis formulas.
IR and NMR routes	Flux-Calibrated Physics	Flux spectral physics with fixed modality calibration.
Known-molecule spectral baselines	Mixed basis	Known-compound baselines are separated from formula-route predictions in the benchmark notes.

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