Model sources

• Repository: https://github.com/microsoft/skala
• Paper: https://arxiv.org/abs/2506.14665

Quickstart

Uses

Direct intended uses

1. The Skala functional is being shared with the research community to facilitate reproduction of evaluations with our model.
2. Evaluating the energy difference of a reaction by computing the total energy of all compounds in the reaction using a Self-Consistent-Field (SCF) evaluation with the Skala exchange correlation functional.
3. Evaluating the total energy of a molecule using a Self-Consistent-Field (SCF) evaluation with the Skala exchange correlation functional. Note that like all density functionals, energy differences are predicted much more reliably than total energies of single molecules.
4. The SCF evaluation we provide is implemented using Accelerated DFT and GauXC , which runs the functional inference on GPU.

Risks and limitations

1. The Skala inference server currently supports only single-instance endpoints.
2. Interpretation of results requires expertise in quantum chemistry.
3. The Skala functional is trained on atomization energies, conformers, proton affinities, ionization potentials, elementary reaction pathways, non-covalent interactions, as well as a small amount of electron affinities and total energies of atoms. We have benchmarked the performance on the public benchmark W4-17 for atomization energies, as well as the public benchmark set GMTKN55, which covers general-main group thermochemistry, kinetics and noncovalent interactions, to provide an indication of how it generalizes outside of the training set. We have also measured robustness on dipole moment predictions and geometry optimization
4. The Skala functional has been trained on data that contains the following elements of the periodic table: H-Ar, Br, Kr, I, Xe. We have tested it on data containing the elements H-Ca, Ge-Kr, Sn-I, Pb, Bi.
5. When used with A100 80GB, the GPU memory currently limits the molecular size to up to approximately 100 atoms when used with the "fine" grid.
6. Given the above point 3 to 5, we remind the user that this is not a production model. Therefore, we advise testing the functional further before applying it to your research. We welcome any feedback!

Training details

Training data

• 99% of MSR-ACC:TAE (±78k reactions) containing atomization energies. 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).
• Total energies, electron affinities and ionization potentials (up to triple ionization) for atoms, from H to Ar (excluding Li and Be because of 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) basis set calculations. The basis sets used for H and He were aug-cc-pV(Q+d)Z, aug-cc-pV(5+d), while for the remaining elements B-Ar the basis sets used 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 simple Z⁻³ expression, while extrapolation of the Hartree-Fock energy was performed using the two-point extrapolation suggested in Comment on: “Estimating the Hartree–Fock limit from finite basis set calculations” [Jensen F (2005) Theor Chem Acc 113:267], Karton et al., Theor. Chem. Acc. 2005 .
• Four datasets from the ATLAS collection of non-covalent interactions :
  • D442x10 , dissociation curves for dispersion bound van-der-Waals complexes
  • SH250x10 , dissociation curves for sigma-hole bound van-der-Waals complexes
  • R739x5 , compressed van-der-Waals complexes
  • HB300SPXx10 , dissociation curves for hydrogen bound van-der-Waals complexes
• W4-CC, containing atomization energies of carbon clusters provided in Atomization energies of the carbon clusters Cn (n = 2−10) revisited by means of W4 theory as well as density functional, Gn, and CBS methods, Karton et al., Mol. Phys. 2009 .

Training procedure

Preprocessing

• For each molecule the density and derived meta-GGA features are computed based on the density matrix of converged SCF calculations with the B3LYP functional using a def2-QZVP or ma-def2-QZVP basis set using a modified version of the PySCF software package.
• Density fitting was not applied for the SCF calculation.
• The density features were evaluated on an atom centered integration grid of level 2 or level 3.
• The radial integral was performed with the Treutler-Ahlrichs, Gauss-Chebychev, Delley, or Mura-Knowles based on Bragg atomic radii with Treutler based radii adjustment.
• The angular grid points were pruned using the NWChem scheme.
• No density based cutoff was applied and all grid points were retained for training.

Training hyperparameters

Speeds, sizes, times