Determining 3D structure from molecular formula and isotopologue rotational spectra in natural abundance with reflection-equivariant diffusion
Bibliographic record
Abstract
Structure determination is necessary to identify unknown organic molecules, such as those in natural products, forensic samples, the interstellar medium, and laboratory syntheses. Rotational spectroscopy enables structure determination by providing accurate 3D information about small organic molecules via their moments of inertia. Using these moments, Kraitchman analysis determines isotopic substitution coordinates, which are the unsigned |x|, |y|, |z| coordinates of all atoms with natural isotopic abundance, including carbon, nitrogen, and oxygen. While unsigned substitution coordinates can verify guesses of structures, the missing +/- signs make it challenging to determine the actual structure from the substitution coordinates alone. To tackle this inverse problem, we develop Kreed (Kraitchman REflection-Equivariant Diffusion), a generative diffusion model that infers a molecule's complete 3D structure from only its molecular formula, moments of inertia, and unsigned substitution coordinates of heavy atoms. Kreed's top-1 predictions identify the correct 3D structure with near-perfect accuracy on large simulated datasets when provided with substitution coordinates of all heavy atoms with natural isotopic abundance. Accuracy decreases as fewer substitution coordinates are provided, but is retained for smaller molecules. On a test set of experimentally measured substitution coordinates gathered from the literature, Kreed predicts the correct all-atom 3D structure in 25 of 33 cases, demonstrating experimental potential for de novo 3D structure determination with rotational spectroscopy.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".