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, $n(\mathbf{r})$, 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, $\partial n(\mathbf{r})/\partial \mathbf{E}$. 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.