Larmor: Equivariant Graph Networks for First-Principles-Quality NMR Chemical Shift Prediction

NMR spectroscopy is the single most important structural verification tool in synthetic organic chemistry. A typical drug-discovery cycle involves dozens of synthesized analogues, each requiring ¹H and ¹³C NMR confirmation that the intended product was made. Computational prediction of chemical shifts has therefore been a long-standing target - both as a structure-elucidation aid and as a virtual screening tool to rule out candidates whose predicted spectra would be inconsistent with desired motifs.

The reigning standard, DFT-based GIAO calculations at the B3LYP or PBE0 level, achieves typical ¹H MAEs of 0.18–0.25 ppm and ¹³C MAEs of 1.5–2.5 ppm after empirical scaling correction. Crucially, a single GIAO calculation on a 30-heavy-atom drug-like molecule takes 3–30 minutes per conformer at modest basis sets, scaling to hours at triple-zeta. Screening 100,000 candidate structures is impossible.

Recent ML approaches - SchNet+NMR (2020), CASCADE (2022), NMRgnn (2024), DetaNet (2024) - have closed much of the accuracy gap. The remaining limitations are: (i) all are trained on calculated DFT shifts rather than experimental, baking in DFT's systematic errors; (ii) most rely on invariant graph features and miss geometry-dependent through-space contributions; (iii) none condition on solvent, despite chemical shifts varying by 0.05–0.30 ppm with solvent polarity.

Larmor addresses all three. We train on a curated set of 1.2M experimental shifts from nmrshiftdb2, BMRB, and Caltech/Stanford internal collections; we use full E(3)-equivariant attention over geometric features; and we condition on solvent identity, pH, and reference compound via learned embeddings.

2.1 Architecture

Larmor takes as input a 3D molecular conformer (atoms with positions in ℝ³) and predicts a per-atom isotropic shielding constant σ_iso, which is then converted to a chemical shift δ via a learned reference correction. The backbone is a stack of N E(3)-equivariant attention blocks operating jointly on scalar and equivariant features:

where r_ij = r_j − r_i is the displacement vector, attention weights α_ij are computed from invariant features only (preserving equivariance), and ϕ_m is a tensor-product update that mixes scalar and L=1 vector channels via Clebsch–Gordan coefficients. Output shielding is read from the L=0 (scalar) channel and is invariant by construction to molecular rotation.

2.2 Training data

The training corpus combines:

• nmrshiftdb2 (open): 47,235 compounds, 412,891 shifts
• BMRB ALATIS (open): 71,800 compounds, 587,302 shifts
• CSC small-molecule subset (licensed): 89,400 compounds, 158,200 shifts
• Internal Rasyn collection: 18,300 medicinal-chemistry compounds with multi-solvent shifts (44,600 shifts)

All shifts are referenced to TMS for ¹H/¹³C, NH₃ for ¹⁵N, and CFCl₃ for ¹⁹F. Conformers are generated with RDKit ETKDG-v3 and the lowest-energy 5 are averaged at inference.

2.3 Model variants

We evaluate on the standard nmrshiftdb2 held-out test split (4,712 compounds, 38,991 ¹H shifts, 19,403 ¹³C shifts) using a strict 80/10/10 scaffold-based split to prevent leakage. All ML baselines were re-trained on our identical training set for a fair comparison; DFT numbers come from B3LYP/6-31G(d,p) on the same molecules with linear-scaling correction.

Wall-clock per-molecule inference time, measured on a 30-heavy-atom drug-like molecule (averaged over 1,000 trials). Times include conformer generation. DFT timings are for a single conformer at the indicated basis set on an Intel Xeon Gold 6248R workstation; ML timings are on CPU (i9-12900K) and a single T4 GPU.

We measure the contribution of each architectural component by progressively adding features to a plain invariant-GNN baseline. Each row reports ¹H MAE on the validation set after retraining for 50 epochs with identical hyperparameters except for the indicated change.

We bucketed the 1,727 test shifts by chemical environment and measured MAE within each bucket to identify systematic failure modes.

Two failure modes dominate the long tail. Strained rings exhibit large shielding swings due to anomalous geometric effects on σ_aniso that are underrepresented in training data. Acidic/exchangeable protons (OH, NH) genuinely have no fixed chemical shift - their position depends on temperature, concentration, and trace water - and so a 0.35 ppm MAE is close to the experimental reproducibility floor.

Larmor powers three production features inside Rasyn:

Larmor closes the practical gap between DFT-quality NMR shielding prediction and the throughput requirements of modern medicinal chemistry. By training on experimental shifts with explicit solvent conditioning and using full E(3)-equivariant attention over 3D geometry, Larmor-100M achieves 0.131 ppm ¹H MAE and 1.04 ppm ¹³C MAE on nmrshiftdb2 - surpassing both DFT B3LYP/PBE0 + GIAO and all prior ML methods at ~10⁴× the speed. The remaining error budget is dominated by strained-ring through-space anisotropy and exchangeable-proton dynamics - both targets for our v2 release with explicit conformer ensemble averaging and chemical-exchange modelling.

Larmor is exposed inside Rasyn as the spectra back-calculator, the retrosynthesis pre-screening filter, and the structure-elucidation copilot. The 50M variant is available on the free API tier; the 100M variant is included in Pro.