Generating a molecule's real 3D shape from its connectivity alone

01 — the problemOnly one shape out of thousands matters

The emitter molecules inside an OLED display are floppy. A single molecule can fold into thousands of distinct three-dimensional shapes, and only the lowest-energy one meaningfully exists in a working device. Colour, efficiency and lifetime all follow from that geometry.

Finding it conventionally means quantum chemistry, run per molecule and per candidate shape. It is accurate and it is slow — and on the iridium and palladium complexes that make the best phosphorescent emitters, the cheap quantum methods frequently fail to converge at all.

The target we set: produce the lowest-energy shape to within 2 kcal/mol of the reference minimum — the threshold where a result is good enough to make design decisions on — and generate it, rather than perturbing a rule-based guess.

02 — scopeWhat the models cover

Molecules trained on

2.4 M117 M conformers

Elements

11incl. Ir, Pd, Pt

Validated size

≤ 80atoms per molecule

Demonstrated to

100atoms — the frontier

Training data is a corpus of relaxed conformers with quantum-chemical energies and forces. Evaluation is on molecules held out at the molecule level — every conformer of a test molecule is excluded from training, so no molecule is ever seen in both.

03 — approach oneGenerate, refine, then choose

The first model is a generator: an equivariant flow model that starts from random noise and draws a plausible 3D structure. The second is a scorer that has learned molecular energy and forces — it settles each rough draft downhill into a genuinely stable geometry, then ranks the candidates and selects one.

On a held-out panel of 408 molecules, the single conformer this pipeline ships lands within 2 kcal/mol of the reference 87.6% of the time, at a median gap of 0.04 kcal/mol.

The quantum method is used only to score the final answer. It never moves an atom and never chooses the shipped conformer — selection is entirely the learned model's, and it agrees with the physics ranking almost exactly.

04 — approach twoOne model that generates and judges

The second approach trains a single energy-based model over conformers. Because what it learns is an energy landscape rather than a mapping, the same model that generates a structure can also score it — one model, one forward pass, generate and judge.

That matters most exactly where conventional tooling struggles. On held-out iridium and palladium complexes, it selects the true lowest-energy conformer 98% of the time — including on molecules where the cheap quantum method fails to converge and simply returns nothing.

Getting there required correcting a subtle and instructive bug. The per-element noise schedule inherited from prior work scaled with atomic mass, which gives the heavy metal centre the most positional noise. In the data the metal is the most rigid atom in the molecule. Over-noised, the metal began each generation flung outside its own ligand cage and could never dock back into it. Replacing that with a learned, geometry-free per-atom flexibility term — supervised on how much each atom actually moves across an ensemble — eliminated the failure entirely.

05 — the result we did not design forIt learned the isomer preference

For iridium emitters, one of the properties chemists care most about is the isomer: the same atoms and the same bonds, arranged two different ways around the metal centre. The two forms behave differently in a device, and which one you get is a real design question.

The model was never given an isomer label. It saw geometries and energies, nothing else. And its training corpus is skewed towards the less stable arrangement — roughly three to two — an artefact of how those structures were originally produced. It saw both forms for almost every molecule.

It generates the more stable arrangement close to seven times more often than the other. Measured one molecule at a time, it prefers it on 93 of 102 molecules.

We then established which form genuinely is lower in energy — around thirty thousand molecules measured with a machine-learned oracle, and a higher-level reference calculation on a sample to arbitrate. All 61 arbitrated cases agreed, at a gap of roughly 6 kcal/mol.

The model did not reproduce the statistics of its training data. It learned the physics that produced them — and it prefers the arrangement that is genuinely more stable, against the bias of its own corpus, having never been told the concept exists.

06 — infrastructureOur own quantum engine, differentiable

Both approaches sit on a quantum-chemistry engine we wrote from scratch for GPU. It makes no calls to third-party quantum software at runtime, which removes an entire class of licensing and dependency risk. More importantly, it is differentiable — so it can sit inside a training loop and supply physics directly to a model being trained, rather than only being used to check answers afterwards.

Neither model uses pretrained third-party weights. Both are trained from scratch on the conformer corpus described above.

07 — limitationsWhat we have not solved

• The learned ranking still trails the physics oracle. Ranking conformers with the model alone is measurably worse than ranking them with the quantum method. Closing that is the most valuable remaining lever, and we track it as the headline model-quality metric.
• We cannot yet request a specific isomer on demand. The preference described above is a property of what the model generates, not a control surface. Making it steerable is active work.
• Above roughly 80 atoms, generation quality falls off. Molecules at the 100-atom frontier are demonstrable but not yet reliable, and drawing more samples does not fix it.
• Isomer supervision exists for iridium only. Nothing transfers to platinum or palladium by supervision; a label-free route is the intended path and is not yet validated.
• Results are single-seed regime reproductions, not bit-exact reruns — the generator is stochastic by design, so comparisons between model variants are distributional.