SALTED: a symmetry-adapted machine-learning program for predicting electron-densities in molecules and materials
Abstract
SALTED provides an open-source Python package for machine learning the quantum-mechanical electron density, n(r), in molecular and condensed-phase systems based on input atomic coordinates and species. The program adopts a linear atom-centered decomposition of the electron density, which makes it highly transferable across diverse atomistic configurations sharing similar chemical environments. Because of this representation choice, SALTED is naturally interfaced with state-of-the-art electronic-structure programs based on atomic orbitals, namely CP2K, FHI-aims, and PySCF, from which reference electron-density data can be generated and used to train a model. The learning algorithm is based on a symmetry-adapted extension of Gaussian process regression, making SALTED especially efficient in small-data regimes. Thanks to the implementation of vector-field kernel functions, SALTED can also learn the first-order response of the electron density to applied electric fields, ∂n(r)/∂E. The application of SALTED within computational workflows has already shown its utility in a wide variety of contexts, including the calculation of polarization vectors and polarizability tensors, the accurate evaluation of Coulomb forces in QM/MM molecular-dynamics simulations, and electronic-structure studies of large-scale 2D materials.
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BibTeX
@misc{lou2026salted,
title = {{SALTED: a symmetry-adapted machine-learning program for predicting electron-densities in molecules and materials}},
author = {Zekun Lou and Alan M Lewis and Théophane Bernhard and Lukas Seifert and Agustin Salcedo and Florian Kleemiss and Mariana Rossi and Andrea Grisafi},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03576},
eprint = {2609.03576},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05834959v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - SALTED: a symmetry-adapted machine-learning program for predicting electron-densities in molecules and materials
AU - Zekun Lou
AU - Alan M Lewis
AU - Théophane Bernhard
AU - Lukas Seifert
AU - Agustin Salcedo
AU - Florian Kleemiss
AU - Mariana Rossi
AU - Andrea Grisafi
PY - 2026
DA - 2026/09/03
PB - HAL
DO - 10.48550/arxiv.2609.03576
UR - https://hal.science/hal-05834959v1
AB - SALTED provides an open-source Python package for machine learning the quantum-mechanical electron density, n(r), in molecular and condensed-phase systems based on input atomic coordinates and species. The program adopts a linear atom-centered decomposition of the electron density, which makes it highly transferable across diverse atomistic configurations sharing similar chemical environments. Because of this representation choice, SALTED is naturally interfaced with state-of-the-art electronic-structure programs based on atomic orbitals, namely CP2K, FHI-aims, and PySCF, from which reference electron-density data can be generated and used to train a model. The learning algorithm is based on a symmetry-adapted extension of Gaussian process regression, making SALTED especially efficient in small-data regimes. Thanks to the implementation of vector-field kernel functions, SALTED can also learn the first-order response of the electron density to applied electric fields, ∂n(r)/∂E. The application of SALTED within computational workflows has already shown its utility in a wide variety of contexts, including the calculation of polarization vectors and polarizability tensors, the accurate evaluation of Coulomb forces in QM/MM molecular-dynamics simulations, and electronic-structure studies of large-scale 2D materials.
ER -