Native implementation of the machine-learned Skala exchange-correlation functional in CP2K: Unified one-centre reconstruction for molecular and condensed-phase calculations
Abstract
We implement the machine-learned Skala exchange-correlation (XC) functional natively in CP2K using its Gaussian and plane-wave (GPW) and Gaussian and augmented-plane-wave (GAPW) methods. A joint one-centre reconstruction of density, density gradients, and kinetic-energy density before functional evaluation preserves mixed gradient terms and nonlocal couplings between smooth and atom-local contributions in all-electron and pseudopotential calculations. An XC-specific GAPW representation resolves rapidly varying local contributions on atom-centred grids, reducing plane-wave requirements for pseudopotential calculations. The implementation includes Brillouin-zone sampling and point-group symmetry reduction. With sufficiently flexible orbital bases, it retains the molecular benchmark accuracy of our earlier GauXC formulation. All-electron Skala-D3(BJ) calculations yield a mean absolute error (MAE) of 1.54 kJ mol−1 against diffusion Monte Carlo for crystalline CO2, NH3, and urea, spanning dispersion, quadrupolar electrostatics, and hydrogen bonding. For all thirteen DMC-ICE13 phases, the MAEs are 1.16 kJ mol−1 for absolute lattice energies and 0.82 kJ mol−1 for the twelve relative energies to ice Ih. At fixed experimental geometries, all-electron/mixed-core calculations give a band-gap MAE of 0.43 eV on a 15-material set, substantially below commonly used semilocal functionals and comparable to widely used hybrid functionals. The LC10 benchmark nevertheless reveals systematically underestimated equilibrium lattice constants, indicating structural overbinding. This framework connects molecular Skala to condensed-phase electronic structure and enables future development using periodic many-body reference data.
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BibTeX
@misc{pototschnig2026native,
title = {{Native implementation of the machine-learned Skala exchange-correlation functional in CP2K: Unified one-centre reconstruction for molecular and condensed-phase calculations}},
author = {Johann Pototschnig and Franz Pöschel and Jürg Hutter and Thomas D. Kühne},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34055},
eprint = {2609.34055},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34055},
}
RIS
TY - UNPB
TI - Native implementation of the machine-learned Skala exchange-correlation functional in CP2K: Unified one-centre reconstruction for molecular and condensed-phase calculations
AU - Johann Pototschnig
AU - Franz Pöschel
AU - Jürg Hutter
AU - Thomas D. Kühne
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34055
UR - https://arxiv.org/abs/2609.34055
AB - We implement the machine-learned Skala exchange-correlation (XC) functional natively in CP2K using its Gaussian and plane-wave (GPW) and Gaussian and augmented-plane-wave (GAPW) methods. A joint one-centre reconstruction of density, density gradients, and kinetic-energy density before functional evaluation preserves mixed gradient terms and nonlocal couplings between smooth and atom-local contributions in all-electron and pseudopotential calculations. An XC-specific GAPW representation resolves rapidly varying local contributions on atom-centred grids, reducing plane-wave requirements for pseudopotential calculations. The implementation includes Brillouin-zone sampling and point-group symmetry reduction. With sufficiently flexible orbital bases, it retains the molecular benchmark accuracy of our earlier GauXC formulation. All-electron Skala-D3(BJ) calculations yield a mean absolute error (MAE) of 1.54 kJ mol^−1 against diffusion Monte Carlo for crystalline CO_2, NH_3, and urea, spanning dispersion, quadrupolar electrostatics, and hydrogen bonding. For all thirteen DMC-ICE13 phases, the MAEs are 1.16 kJ mol^−1 for absolute lattice energies and 0.82 kJ mol^−1 for the twelve relative energies to ice Ih. At fixed experimental geometries, all-electron/mixed-core calculations give a band-gap MAE of 0.43 eV on a 15-material set, substantially below commonly used semilocal functionals and comparable to widely used hybrid functionals. The LC10 benchmark nevertheless reveals systematically underestimated equilibrium lattice constants, indicating structural overbinding. This framework connects molecular Skala to condensed-phase electronic structure and enables future development using periodic many-body reference data.
ER -