microsoft/skala-1.1

Skala 1.1 model

Model details

In pursuit of the universal functional for density functional theory (DFT), the OneDFT team from Microsoft Research AI for Science has developed the Skala-1.1 exchange-correlation functional, as introduced in Accurate and scalable exchange-correlation with deep learning, Luise et al. 2025. This approach departs from the traditional route of incorporating increasingly expensive hand-designed non-local features from Jacob\'s ladder into functional forms to improve their accuracy. Instead, we employ a deep learning approach with a scalable neural network that uses only inexpensive input features to learn the necessary non-local representations.

The functional is based on a neural network architecture that takes as input features on a 3D grid describing the electron density and derived meta-generalized-gradient (meta-GGA) quantities. The architecture performs scalable non-local message-passing on the integration grid via a second, coarser grid, combined with shared local layers that enable representation learning of both local and non-local features. These representations are then used to predict the exchange-correlation energy in an end-to-end data-driven manner.

To facilitate this learning, the model is trained on a dataset of unprecedented size, containing highly accurate energy labels from coupled cluster theory. The largest subset focuses on atomization energies and was generated in collaboration with the University of New England. This subset is released as part of the Microsoft Research Accurate Chemistry Collection (MSR-ACC, Accurate Chemistry Collection: Coupled cluster atomization energies for broad chemical space, Ehlert et al. 2025). To broaden coverage of other types of chemistry, the training dataset is further complemented with in-house generated datasets covering conformers, ionization potentials, electron affinities, proton affinities, noncovalent interactions, distorted equilibrium geometries, and elementary reactions, as well as a small amount of publicly available high-accuracy data.

We demonstrate that departure from the historical trade-off between accuracy and efficiency is enabled by learning non-local representations of electronic structure directly from data, bypassing the need for increasingly costly hand-engineered features. The Skala-1.1 functional surpasses state-of-the-art hybrid functionals in accuracy across the main-group chemistry benchmark set GMTKN55, which covers general main-group thermochemistry, kinetics, and noncovalent interactions, with an error of 2.8 kcal/mol, while retaining the lower computational cost characteristic of semi-local DFT. With this work, we demonstrate the viability of our approach toward the universal density functional across all of chemistry.

Users of this model are expected to have a basic understanding of the field of quantum chemistry and density functional theory.

Developed by : Chin-Wei Huang, Deniz Gunceler, Derk Kooi, Gregor Simm, Klaas Giesbertz, Giulia Luise, Jan Hermann, Megan Stanley, Paola Gori Giorgi, P. Bernát Szabó, Rianne van den Berg, Sebastian Ehlert, Stefano Battaglia, Stephanie Lanius, Thijs Vogels, Wessel Bruinsma

Shared by : Microsoft Research AI for Science

Model type : Neural Network Density Functional Theory Exchange Correlation Functional

License : MIT

Direct intended uses

1. The Skala-1.1 functional is shared with the research community to facilitate reproduction of the evaluations presented in our paper. 2. Evaluating reaction energy differences by computing the total energy of all compounds in a reaction using a self-consistent field (SCF) calculation with the Skala-1.1 exchange-correlation functional. 3. Evaluating the total energy of a molecule using an SCF calculation with the Skala-1.1 exchange-correlation functional. Note that, as with all density functionals, energy differences are predicted much more reliably than total energies of individual molecules. 4. The SCF implementation provided uses PySCF and GPU4PySCF, which runs the functional on CPU and GPU. We also provide a traced version of the Skala-1.1 functional so that other, more optimized open-source SCF codes—including GPU-enabled ones—can integrate it into their pipelines, for instance through GauXC. A compatible fork of GauXC is included in this repository.

Out-of-scope uses

1. Evaluating the functional with a single pass given a fixed density as input is not the intended way to evaluate the model. The model\'s predictions should always be made by using it as part of an SCF procedure. 2. We do not include a training pipeline for the Skala-1.1 functional in this code base.

Risks and limitations

1. Interpretation of results requires expertise in quantum chemistry. 2. The Skala-1.1 functional is trained on atomization energies, conformers, proton affinities, ionization potentials, electron affinities, elementary reaction pathways, distorted equilibrium geometries, and non-covalent interactions, as well as a small amount of total energies of atoms and transition metal atoms and dimer properties. We have benchmarked performance on W4-17 for atomization energies and on GMTKN55, which covers general main-group thermochemistry, kinetics, and noncovalent interactions, to provide an indication of generalization beyond the training set. We have also evaluated robustness on dipole moment predictions and geometry optimization. 3. The Skala-1.1 functional has been trained on data containing the following elements: H–Xe. It has been tested on data containing H–Xe, Pb, and Bi. 4. Given points 2 and 3 above, this is not a production model. We advise testing the functional further before applying it to your research and welcome any feedback.

Recommendations

1. In our PySCF-based SCF implementation, the largest system tested contained 180 atoms using the def2-TZVP basis set (~5000 orbitals) on Eadsv5 series virtual machines. Larger systems may run out of memory. 2. For implementations optimized for memory, speed, or GPU support, we recommend integrating the functional with other open-source SCF packages, for instance through GauXC. A compatible fork of GauXC is included in this repository. 3. Skala-1.1 will also be available through [Azure AI…