Machine learning helps improve accuracy and efficiency of small-molecule calculations

When experiments are impractical, density functional theory (DFT) calculations can give researchers accurate approximations of chemical properties. The mathematical equations that underpin the calculations are carefully tailored to the molecules and materials to which they’re applied. But each equation comes with a trade-off between accuracy and demand for computing time.

Microsoft researchers believe they have found a way to use machine learning to push those limits for small molecules (arXiv 2025, DOI: 10.48550/arXiv.2506.14665). The preprint publication has not been peer-reviewed.

DFT is based on molecules’ electron density and in theory can be used to determine properties exactly. In practice, it is impossible to calculate the subtle interactions between numerous electrons. Computational chemists have instead come up with different approximations of the exchange-correlation (XC) functional, the term in DFT equations that captures those interactions.

As an alternative to using these hand-crafted functionals, Microsoft’s Paola Gori-Giorgi, Jan Hermann, Rianne van den Berg, and colleagues built a deep learning model that inferred an XC functional from a database they created with about 150,000 reaction energies for molecules with five or fewer noncarbon atoms.

They are not the first group to apply machine learning to the challenge of coming up with an ideal XC functional. But the Microsoft team used a more complex algorithm than others, incorporating the latest tools borrowed from large language models. And their training data are roughly two orders of magnitude larger than the datasets that others have used.

The group calls the functional Skala, from the Greek word for ladder. It’s a nod to the increasingly complex mathematical “rungs” that computational scientists add to their models to reach greater accuracy, sometimes called the Jacob’s Ladder approach.

The researchers report that their functional’s prediction error in calculating small-molecule energies is half that of ωB97M-V, which is considered one of the better functionals available today. It was in the middle of the pack for calculations involving metal atoms, which Skala XC wasn’t trained on. They say ωB97M-V computes molecular properties in the same or less computer time than other functionals.

While she hasn’t tested Skala herself, computational scientist Marivi Fernández-Serra of Stony Brook University says, “I have the impression that this is going to be a very good functional.” Fernández-Serra, who has also been working on machine learning approaches to DFT functionals, says the way Microsoft incorporated various deep learning tools makes Skala XC efficient at inferring from large amounts of data. She and others also say the group had the advantage of Microsoft’s enormous resources to generate its training data—something many academic scientists do not have and current US policy is shrinking further.

For other DFT researchers, the advantages of Skala are less clear. “For people who work on metals, this won’t work,” says A.J. Medford, a chemical engineer at the Georgia Institute of Technology who has used machine learning for DFT. The functionals that work well for metals and solids are particularly valuable in materials science because they can accelerate the exploration of chemical space.

Medford is skeptical that the Microsoft team will be able to generate similarly high-quality training data for atoms with more electrons. And he says researchers using DFT on small molecules may not see the need for a new functional when existing ones work well enough.

Gori-Giorgi, the senior research manager for the Skala XC team, disagrees. She says that in collaboration with external experts, her group has already identified computational techniques that they believe the team could use to expand its training database to include larger atoms.

Another researcher in the field, Ryo Nagai of Preferred Networks, says in an email to C&EN that he is impressed with how Skala XC was able to learn and that it will help move research forward. But like Medford, he is skeptical about how it will fare with metals and solids. He questioned the group’s tests of Skala’s performance and says he wants to see it challenged with more-complex calculations.

Microsoft’s efforts have some echoes of forays into DFT by Google DeepMind, which released a machinelearning functional (Science 2021, DOI: 10.1126/science.abj6511) to significant fanfare (Science 2021, DOI: 10.1126/science.abm2445). But it ultimately proved too computer intensive to be useful.

DeepMind’s James Kirkpatrick, who led the 2021 research, would not comment on Microsoft’s efforts but tells C&EN in an email that the company “is working on related approaches.”