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All models by microsoft →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
The following data is included in our training set:
MSR-ACC : 99% of MSR-ACC/TAE25 (~78k reactions) containing atomization energies for up to five non-hydrogen atoms. This data was generated in collaboration with Prof. Amir Karton, University of New England, with the W1-F12 composite protocol based on CCSD(T) and is released as part of the Microsoft Research Accurate Chemistry Collection (MSR-ACC). Additionally the MSR-ACC subsets for larger TAEs (up to 9 non-hydrogen atoms), conformers, ionization potentials, electron affinities, proton affinities, reaction paths, and distorted equilibrium structures were included. The labels for these data sets are obtained with the W1w method and are part of the currently unpublished subsets of the MSR-ACC.
Atomic Data : Total energies, electron affinities, and ionization potentials (up to triple ionization) for atoms, from H to Ar (excluding Li and Be due to basis-set constraints). This data was produced in-house with CCSD(T) by extrapolating to the complete basis set limit from quadruple zeta (QZ) and pentuple zeta (5Z) calculations. The basis sets used for H and He were aug-cc-pV(Q+d)Z and aug-cc-pV(5+d), while for the remaining elements B--Ar the basis sets were aug-cc-pCVQZ and aug-cc-pCV5Z. All basis sets were obtained from the Basis Set Exchange (BSE). Extrapolation of the correlation energy was performed by fitting a $Z^{-3}$ expression, while the Hartree--Fock energy was extrapolated using the two-point scheme of Karton 2006.
Transition metal properties : Additional data for transition metal atoms and dimers, including ionization potentials, spin splittings, and dissociation energies. The reference energies were obtained from literature.
NCI-Atlas : Five datasets from the NCI-Atlas collection of non-covalent interactions:
GDB9 : The graph data base with up to non-hydrogen atoms computed at W1-F12 level of theory from Karton 2025.
BH9 : Reactions and barrier heights from Prasad et al. 2021 The data set was filtered for systems with up to ten non-hydrogen atoms.
NCIBLIND : Data set of non-covalent dissociation curves from Taylor et al. 2016.
Water2510 : Data set of the potential energy surface of the water dimer from Smith et al. 2016. The data set was fully relabeled with W1w.
DES370k : Subset with CCSD(T)/dCBS(aug-cc-pVQZ) non-covalent interaction energies from Donchev et al. 2021.
MB2061 : Dataset containing decomposition energies of artificial molecules from Gasevic et al. 2025.
W4-CC : Containing atomization energies of carbon clusters from Karton et al. 2009.
For all training data, input density and derived meta-GGA features were computed from density matrices of converged B3LYP SCF calculations (def2-QZVP and ma-def2-QZVP basis sets) using a modified version of PySCF.
The training datapoints are preprocessed as follows.
The training hyperparameter settings are detailed in the supplementary material of Accurate and scalable exchange-correlation with deep learning, Luise et al. 2025. This repository only includes the code to evaluate the provided checkpoints, not the training code.
The training of the functional on the dataset described above took approximately 48 hours for 1M steps on an ND A100 v4 series VM with 8 NVIDIA A100 GPUs (80 GB each), 96 CPU cores, 880 GB RAM, and a 6 TB disk.
The model checkpoints have ~385k trainable parameters.
We have evaluated our functional on several different benchmark sets:
These six benchmark types serve to measure different performance aspects of the functional. Benchmarks 1 and 2 focus on the accuracy of predicted reaction energies. Benchmark 3 evaluates general main-group thermochemistry, kinetics, and noncovalent interactions. Benchmark 4 evaluates geometry optimization and convergence to reference equilibrium structures. Benchmark 5 measures dipole moments, providing a proxy for the quality of the self-consistent electron density produced by the SCF procedure. Finally, benchmark 6 assesses computational cost scaling with respect to system size.
The metrics for the different benchmark sets are:
On W4-17, the Skala-1.1 functional predicts atomization energies at chemical accuracy (~1 kcal/mol MAE). On GMTKN55, which covers general main-group thermochemistry, kinetics, and noncovalent interactions, it achieves a WTMAD-2 of 2.8 kcal/mol, surpassing state-of-the-art range-separated hybrid functionals while only requiring runtimes typical of semi-local DFT.
On the geometry optimization benchmarks, the functional converges to reference equilibrium structures with errors comparable to a range-separated hybrid functional. On the dipole prediction benchmark, the error in dipole moment predictions is better than that of state-of-the-art range-separated hybrid functionals.
Finally, the scaling results show that the Skala-1.1 functional exhibits the asymptotic scaling behavior of a meta-GGA functional, with an approximate prefactor of 3 relative to r2SCAN.
MIT License
Copyright (c) Microsoft Corporation.
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
When using Skala-1.1 in your research, please reference it including the version number as follows:
This work uses the Skala-1.1 functional.
@misc{luise2025, title={Accurate and scalable exchange-correlation with deep learning}, author={Giulia Luise and Chin-Wei Huang and Thijs Vogels and Derk P. Kooi and Sebastian Ehlert and Stephanie Lanius and Klaas J. H. Giesbertz and Amir Karton and Deniz Gunceler and Stefano Battaglia and Gregor N. C. Simm and P. Bernát Szabó and Megan Stanley and Wessel P. Bruinsma and Lin Huang and Xinran Wei and José Garrido Torres and Abylay Katbashev and Rodrigo Chavez Zavaleta and Bálint Máté and Sékou-Oumar Kaba and Roberto Sordillo and Yingrong Chen and David B. Williams-Young and Christopher M. Bishop and Jan Hermann and Rianne van den Berg and Paola Gori-Giorgi}, year={2025}, eprint={2506.14665}, archivePrefix={arXiv}, primaryClass={physics.chem-ph}, url={https://arxiv.org/abs/2506.14665},}