Multi-Modal Foundation · microsoft
Skala 1.0
A neural exchange-correlation functional for DFT delivering hybrid accuracy at semi-local computational cost.
What Skala 1.0 is
Skala 1.0 is a deep-learning exchange-correlation functional for density functional theory (DFT), developed by the OneDFT team at Microsoft Research AI for Science. In standard DFT, achieving high accuracy traditionally requires hand-designed non-local terms higher up Jacob's ladder, such as exact exchange in hybrid functionals, which are computationally demanding. Skala 1.0 instead uses a neural network operating on inexpensive local and semi-local inputs to learn non-local representations directly from high-level reference data.
The model targets common quantum-chemical evaluations, including molecular total energies, reaction thermochemistry, barrier heights, and non-covalent interactions. When tested on the GMTKN55 benchmark set, it achieves accuracy competitive with range-separated hybrid functionals (WTMAD-2 of 3.89 kcal/mol) while exhibiting the asymptotic scaling behaviour of a meta-generalized-gradient approximation (meta-GGA) with a prefactor of roughly three relative to r2SCAN.
Skala 1.0 is intended for self-consistent field (SCF) calculations within quantum chemistry software packages. It serves as an exploratory scientific functional and the predecessor to Skala 1.1, helping researchers compute ground-state electronic properties and reaction energy profiles without the steep scaling of exact-exchange methods.
How it works
Skala 1.0 operates on a 3D atom-centred integration grid, using features derived from the electron density and meta-GGA quantities. Rather than relying on expensive exact exchange, the neural architecture uses shared local layers combined with non-local message-passing between integration points via a secondary, coarser grid. This allows the network to learn both local and non-local electronic representations that map end-to-end to the exchange-correlation energy.
Inputs were generated from converged B3LYP SCF density matrices using def2-QZVP and ma-def2-QZVP basis sets.
Key facts
- Model type
- Neural network DFT exchange-correlation functional
- Input features
- Electron density and meta-GGA quantities on a 3D integration grid
- Computational scaling
- Asymptotic meta-GGA scaling (roughly 3x prefactor over r2SCAN)
- Chemical coverage (trained)
- H–Ar, Br, Kr, I, Xe
- Chemical coverage (tested)
- H–Ca, Ge–Kr, Sn–I, Pb, Bi
- Benchmark accuracy (W4-17)
- ~1 kcal/mol MAE (atomization energies)
- Benchmark accuracy (GMTKN55)
- 3.89 kcal/mol WTMAD-2
What you can use it for
- Reaction thermochemistry
- Evaluating reaction energy differences and barrier heights by calculating the total energy of all reactants and products within a self-consistent field procedure.
- Molecular total energy prediction
- Running SCF calculations to evaluate single-molecule ground-state total energies, particularly where energy differences are needed across conformers or reactions.
- Dipole moment evaluation
- Assessing the quality of self-consistent electron densities and predicted molecular dipole vectors across neutral or polar systems.
- Equilibrium geometry optimization
- Optimizing molecular structures, bond lengths, and bond angles with structural error profiles comparable to standard generalized-gradient approximations.
Run it here
We list this model but cannot run it yet: no pipeline_tag — needs a human.
Everything on this page still applies. Running it needs a loader for this repository, not a bigger machine.
Strengths and limits
Good at
- Attains chemical accuracy (~1 kcal/mol MAE) for atomization energies on the W4-17 benchmark.
- Achieves general thermochemical and non-covalent accuracy on GMTKN55 (3.89 kcal/mol WTMAD-2) on par with range-separated hybrids.
- Maintains meta-GGA computational scaling with only a modest prefactor increase (approximately 3x r2SCAN).
- Generates self-consistent electron densities that yield dipole moment predictions comparable to range-separated hybrids.
Watch out for
- Must be evaluated through an iterative SCF calculation; single-pass evaluation on a fixed density is out of scope.
- Not a production-ready model; researchers are advised to validate performance carefully on their target chemical domains.
- Training coverage is restricted to specific elements (H–Ar, Br, Kr, I, Xe), with testing limited to H–Ca, Ge–Kr, Sn–I, Pb, and Bi.
- The default CPU PySCF implementation can run out of memory on large systems (the largest demonstrated test was 180 atoms with def2-TZVP, around 5,000 orbitals).
Inputs and outputs
You provide
Sequence or text
A protein or nucleotide sequence, or free text — whichever this model was trained on.
You get back
Mean-pooled representation, one vector per input.
Licence
Check the licence before commercial use · mit
The mit licence carries terms worth reading before you depend on it.
Questions
Can I use Skala 1.0 commercially?
Check the licence before commercial use. The mit licence carries terms worth reading before you depend on it.
Can I use Skala 1.0 as a single-shot energy predictor on precomputed densities?
No. Skala 1.0 is designed explicitly to run inside a self-consistent field (SCF) loop. Evaluating it via a single pass on a fixed electron density is considered out of scope.
Which chemical elements does Skala 1.0 support?
The functional was trained on systems containing H–Ar, Br, Kr, I, and Xe. It has been evaluated on tests containing H–Ca, Ge–Kr, Sn–I, Pb, and Bi, but its behaviour outside these spaces is not guaranteed.
What software is needed to run calculations?
The reference implementation runs on CPU via a modified version of PySCF. A traced version is also provided to facilitate integration into GPU-accelerated or alternate SCF software frameworks such as GauXC and Accelerated DFT.
How computationally heavy is Skala 1.0 compared to standard hybrid functionals?
It avoids exact exchange calculations entirely, scaling asymptotically like a meta-GGA functional with an operational runtime prefactor roughly three times that of r2SCAN.
How to cite it
Luise, G., Huang, C.-W., Vogels, T., Kooi, D. P., Ehlert, S., Lanius, S., Giesbertz, K. J. H., Karton, A., Gunceler, D., Stanley, M., Bruinsma, W. P., Huang, L., Wei, X., Garrido Torres, J., Katbashev, A., Chavez Zavaleta, R., Máté, B., Kaba, S.-O., Sordillo, R., Chen, Y., Williams-Young, D. B., Bishop, C. M., Hermann, J., van den Berg, R., & Gori-Giorgi, P. (2025). Accurate and scalable exchange-correlation with deep learning. arXiv:2506.14665v5.
Written from Skala 1.0's own documentation (model card). Statements citing a figure that does not appear there are removed before publication. Licence and running details come from our registry.