Can language models discover faster molecular geometry optimizers?

Why force calls, not steps, set the price

Geometry optimization is one of the most frequently performed operations in computational chemistry, and the paper measures its cost by the number of interatomic force evaluations. On a cheap potential such as an empirical force field, that cost can be comparable to the cost of the optimization algorithm itself. At the density-functional theory (DFT) level, gradient calculations dominate the wall time of a relaxation, so the number of steps an optimizer needs effectively determines the price of the job.

That framing matters for reading every number below. A reduction in force calls is not a cosmetic speedup of the algorithm's own arithmetic; under DFT it lowers the cost of the calculation roughly in proportion. The paper's target is therefore narrow and machine-checkable: rewrite the optimizer so that it reaches the same energy reduction in fewer force evaluations, without stopping early and without overfitting to the molecules used during the search.

Two admission gates block premature stopping and overfitting

The autoresearch loop lets an agent rewrite the optimizer code itself, scored on force-call counts. Left alone, such a loop has an obvious failure mode: an optimizer that declares convergence early will look cheap. The paper restrains the search with two admission gates. One rejects premature stopping, and the other rejects improvements that do not generalize to unseen molecules.

Those gates are the reason the reported savings can be read as real rather than as a scoring artifact. A candidate that only wins by quitting early, or that only wins on the molecules it was tuned against, does not get admitted. The search started from Sella, described in the paper as the fastest open-source optimizer available, and produced a family of two optimizers: AutoSella-F, from a run driven by Claude Fable 5.1 (max), and AutoSella-A, from a run driven by GPT-6 Astra (high).

How the two agents searched differently

Both runs were measured over 66 active research hours, a budget that includes development and analysis inside an isolated container as well as remote evaluation. Within that window, Fable committed 108 evaluated candidates and accepted 37 improvements, while Astra committed 672 candidates and accepted 29. Fable had fewer evaluation errors (3, or 2.8%, versus 35, or 5.2%) and fewer candidates rejected for insufficient mean energy recovery (8, or 7.4%, versus 115, or 17.1%).

The commit spacing shows two different research rhythms: the mean gap between consecutive candidate commits was 36.32 ± 32.08 minutes for Fable and 5.88 ± 3.66 minutes for Astra. The paper notes that Fable's logs document extended local analysis inside its container, including a 160-minute interval between cycles 87 and 88 spent inspecting molecular structures saved from earlier calculations and reading the optimizer code, which led to a targeted change in how optimization is initialized. The smaller candidate count therefore does not imply less research.

The final algorithms reached mean per-molecule force-call ratios of 65.13% and 74.51% on training and 64.99% and 76.66% on validation, relative to the original Sella. The paper reports that Fable's larger gains came from combining corrections to the physical model with more effective reuse of previous force evaluations, while Astra's later accepted gains were small and many subsequent variants either increased force-call cost or passed training but failed the validation cost or energy tests.

Savings hold on unseen molecules and new chemical domains

The first generalization axis is molecules. The optimizers were tested on four held-out datasets: 500 PubChem molecules selected to be dissimilar from the training and validation sets, 673 dipeptides, 475 amino acid–ligand pairs, and 100 Solvated PubChem systems. The amino acid–ligand pairs test optimization on systems with non-covalent interactions beyond the small dimers used in training, and Solvated PubChem tests complex multi-fragment systems with a drug-like solute surrounded by water.

On GFN2-xTB, the potential the search itself ran on, AutoSella-F was cheapest in every block, at 39.86–73.25% of the baseline's force calls per molecule, and its mean energy recovery was above the baseline on all four datasets. The paper reports that the median final-energy difference ranges from −8×10⁻⁶ to −5×10⁻⁶ kcal mol⁻¹ on Test, Dipeptides, and amino acid–ligand pairs, and is −1.30 kcal mol⁻¹ on Solvated PubChem, so AutoSella-F reaches lower final energies than the reference on most molecules.

AutoSella-A used 78.14–92.57% of the baseline's force calls per molecule on the first three datasets but regressed on Solvated PubChem, requiring 118.77% while recovering less energy. The two variants are therefore not interchangeable: the same search paradigm produced one optimizer that generalizes across all four held-out sets and one that does not extend to complex multi-fragment systems.

Transfer to potentials the search never saw

The second generalization axis is the potential. Every candidate was scored on GFN2-xTB alone, so the open question is whether the mechanisms behind the improvement are general or fitted to that potential. The paper repeats the measurement on the classical force field GFN-FF and on DFT at the r2SCAN-3c level through ORCA, neither of which the search encountered.

The savings carry over. AutoSella-F saves more force calls than AutoSella-A in every available comparison. At the r2SCAN-3c level, AutoSella-F required 75.98% of Sella's force calls per molecule on Test, 72.27% on Dipeptides, 65.50% on amino acid–ligand pairs, and 38.69% on Solvated PubChem, with mean energy recovery above the baseline on all four datasets. The largest saving occurs on Solvated PubChem, where it requires only 40.24% of Sella's force calls while achieving 1.27% greater mean energy recovery.

AutoSella-A again fails to extend to the multi-fragment case under DFT, using 109.06% of Sella's force calls per molecule and recovering less energy on Solvated PubChem. The paper emphasizes that under DFT the force call dominates the calculation, so the reduction in force calls lowers the cost of the job proportionally, and that this was obtained without the autoresearch ever evaluating a DFT gradient.

Which mechanisms produce the savings

Ablations highlight three key contributors to AutoSella-F's savings: improved curvature models and coordinates, explicit handling of disconnected fragments, and Hessian updates that reuse previous gradient information while accounting for changes in geometry. The paper reports that the physical-model and coordinate family has the largest measured single-removal cost increase in both series, with one block adding 15.57 and 18.68 percentage points and another adding 8.82 points on validation.

The blocks are not independent. The paper supplements single-block removals with joint removals and finds that for all four tested pairs on validation, joint removal increases cost less than the sum of the individual removal penalties, so the single-block effects cannot be treated as independent, additive contributions. Of all evaluations, only five complete evaluations fall below the energy threshold, and only three contain optimizer errors.

The paper also reports a separate run with Grok 4.6 at xhigh reasoning effort through the Cursor agent harness, using the same setup. That run recorded 900 candidates and accepted 44 improvements, and its final champion, AutoSella-G, was obtained at cycle 897 with mean relative force-call cost of 97.79% on training and 98.14% on validation. On the held-out GFN2-xTB benchmarks it provides little benefit on single-molecule systems and performs substantially worse on the intermolecular datasets, which is a useful contrast: a run can look successful on its own training and validation splits while delivering almost nothing on the held-out sets.

What the Sella baseline actually buys

The paper's own panel analysis puts the AutoSella gains in context. On single-fragment molecules, Sella's margin over a well-configured generic optimizer is small: pysisyphus with delocalized internal coordinates needs 105.4% of Sella's force calls on Test and 103.6% on Dipeptides, and with redundant internals and the Fischer–Almlöf initial Hessian it needs 110.5% and 106.0%. Almost all of the 5–6.5× advantage Sella holds over Cartesian methods comes from its choice of internal coordinates and a model initial Hessian rather than from its step algorithm.

The paper isolates the two factors inside a single program. In geomeTRIC, changing only the coordinate system moves the cost on Test from 129.6% with TRIC and 130.4% with delocalized internals, through 145.9% with primitive internals and 327.2% with HDLC, to 572.2% with Cartesian coordinates, a factor of 4.4. In pysisyphus, changing only the initial Hessian moves the cost from 110.5% with the Fischer–Almlöf model, through 110.8% with Lindh's and 130.5% with Swart's, to 193.2% with a simple diagonal guess and 444.9% with the unit matrix, a factor of 4.0.

These averages are taken over molecules that both the method and Sella converged, so the paper treats them as lower bounds: the worst settings also fail on more molecules, with geomeTRIC in Cartesian coordinates leaving 141 of the 500 Test molecules unconverged and pysisyphus with the unit Hessian leaving 56. This is the context in which AutoSella's savings should be read. The search did not start from a weak baseline; it started from the fastest open-source optimizer in the panel and still found consistent reductions.

Where these optimizers do and do not transfer

The practical split is between AutoSella-F and AutoSella-A, and between single-fragment and multi-fragment systems. AutoSella-F delivers consistent force-call reductions relative to Sella across all four held-out datasets on GFN2-xTB, GFN-FF, and r2SCAN-3c, with mean energy recovery at or above the baseline. AutoSella-A is competitive on the first three datasets but regresses on Solvated PubChem on every potential tested, requiring more force calls than Sella while recovering less energy.

The paper's own conclusion is that inexpensive surrogate potentials can enable automated algorithm development when direct search at the target level is too costly. That is the transferable claim: the search ran entirely on GFN2-xTB, never evaluated a DFT gradient, and still produced an optimizer whose savings persist at the r2SCAN-3c level. The paper is a preprint under review, so the reported numbers should be read as the authors' measurements rather than as independently replicated results.

For a reader deciding what to take from this, the decision-relevant comparison is not whether an LLM can write optimizer code, but which variant to trust and on what system. If the target is single-fragment organic molecules, both variants reduce force calls relative to Sella on the held-out sets. If the target is solvated or otherwise multi-fragment systems, the evidence points to AutoSella-F and away from AutoSella-A, whose regression on Solvated PubChem appears under GFN2-xTB, GFN-FF, and r2SCAN-3c alike. The most notable result remains the DFT case: 40.24% of Sella's force calls on Solvated PubChem with greater mean energy recovery, obtained without the search ever seeing a DFT gradient.

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