AI agents find a compact chemistry formula—but not a universal winner

The work targets exchange–correlation functionals, approximations at the heart of density functional theory. This approach makes electronic-structure calculations practical by working with electron density, rather than explicitly tracking the full many-electron problem. The functional supplies contributions that remain difficult to describe exactly. Improving it can improve calculated chemical energies without abandoning that practical framework.

Instead of asking a language model to predict energies directly, the researchers asked AI agents to propose executable mathematical expressions. A shared GPU evaluator fitted their adjustable coefficients to 870 training reactions, measured performance on 2,963 validation reactions, and returned numerical feedback. Agents kept plans, candidate lineages and summaries so subsequent proposals could build on earlier experiments.

Four screening checks covered spin interchange, the uniform-electron-gas exchange limit, exchange-factor scaling and sensitivity to numerical integration grids. Passing these checks was a filter, not proof that a candidate satisfied every physical requirement.

The principal result, O159, has 13 fitted parameters. Its distinctive ingredient is a smooth “density window” multiplying the same-spin correlation factor, which describes one contribution associated with electrons sharing a spin orientation. The multiplier approaches one at both density extremes but reduces the factor’s magnitude by roughly 15–30% at its intermediate-density peak.

That description alone does not explain why it helps. The researchers therefore compared separately refitted alternatives: removing the window, changing its shape, moving it to opposite-spin correlation or switching it off in certain orbital environments. These controls favored applying the window to the entire same-spin factor. Analysis localized much of its reaction-energy effect to low-gradient regions with relatively single-orbital character. This remains an empirical rule for the tested functional framework, not a general law of electron correlation.

The crucial next step was self-consistency. Rapid search evaluations used fixed electron densities from an established functional, ωB97M-V. In a self-consistent calculation, the candidate instead influences the orbitals and density, which in turn influence its energy. A formula that succeeds only on borrowed densities might fail this feedback loop.

O159 converged for all 5,930 molecular systems in the MGCDB84 campaign. Its weighted root-mean-square error on 1,152 held-out test reactions fell from ωB97M-V’s 4.309 to 3.805 kilocalories per mole, an 11.7% reduction. However, the established GAS22 functional remained better on that test, at 3.589. Much of O159’s improvement over ωB97M-V was also already present in the refitted architecture without its new window.

External evaluation supplied a more restrained result. Computational cost limited testing to 36 of GSCDB137’s 137 datasets. O159’s mean normalized error ratio was 1.139, versus 1.144 for the local ωB97M-V reference; the paired comparison did not establish a statistically significant difference. O159 improved some properties and worsened others, including evaluated vibrational, electric-field-response and transition-metal categories.

Against the refitted no-window control, heavy-atom total-energy error fell by about 29%. That is a different comparison from the 11.7% held-out gain. Across the 20 external datasets without MGCDB84 antecedents, the aggregate window benefit was not significant and disappeared when the heavy-atom dataset was excluded.

The agent comparisons need similar care. Opus-5.5 agents first passed the screening-and-validation gate using about 40 times fewer assigned tokens than Codex agents using GPT-6-Astra. But more than 97% of both runs’ totals were cache reads: this is not a demonstrated 40-fold advantage in speed or monetary cost.

At roughly 400 fits per workflow, agents found lower validation errors than a SyFES evolutionary baseline. Yet agents could introduce an explicit density scale absent from the baseline’s representation, received relevant suggestions and used different fitting procedures. Their advantage therefore compares complete workflows, not language-model reasoning in isolation. The strongest result is narrower: agents produced an inspectable candidate and useful controls, and its improvement over one reference survived self-consistency without becoming a universal benchmark victory.