All-electron machine-learned orbital-free density functional for periodic CHNO systems
Abstract
We introduce STRUCTURES-P, a machine-learned all-electron orbital-free density functional for periodic CHNO systems. Electrostatics are evaluated analytically in an atom-centered Gaussian basis, while an equivariant network learns the kinetic and exchange-correlation energy from energies and gradients of non-ground-state densities. Minimizing the functional from a superposition of atomic densities recovers the Kohn-Sham ground state: on held-out crystals, the density error falls from 6.7% to 0.4% of the electron count and the energy error reaches 0.25 mHa per atom, half that of a same-architecture interatomic potential. A single functional can be trained for both isolated molecules and periodic systems, and the model generalizes to larger unit cells. It largely preserves relative-energy rankings and reproduces convex-hull vertices on the tested H-N composition slice. Together, these results demonstrate the viability of machine-learned all-electron orbital-free DFT for variational density optimization and energy evaluation in fixed-geometry solids.
Related
- Transformer-inspired architectures make machine-learned electron densities accurate and transferable enough to bypass self-consistency
- Machine-learned Laplacian-level density functional from exact exchange-correlation potentials and energies
- Molecular Implementation of the Machine-Learned Skala Exchange-Correlation Functional in CP2K through GauXC
- Native implementation of the machine-learned Skala exchange-correlation functional in CP2K: Unified one-centre reconstruction for molecular and condensed-phase calculations
- Influence of Exchange–Correlation Functional on Machine-Learned Interatomic Potentials’ Accuracy: A Systematic Study of Borosilicate Glasses
BibTeX
@misc{ickler2026allelectron,
title = {{All-electron machine-learned orbital-free density functional for periodic CHNO systems}},
author = {Marc K. Ickler and Andreas Hermann and Fred A. Hamprecht},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17975},
eprint = {2610.17975},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17975},
}
RIS
TY - UNPB
TI - All-electron machine-learned orbital-free density functional for periodic CHNO systems
AU - Marc K. Ickler
AU - Andreas Hermann
AU - Fred A. Hamprecht
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17975
UR - https://arxiv.org/abs/2610.17975
AB - We introduce STRUCTURES-P, a machine-learned all-electron orbital-free density functional for periodic CHNO systems. Electrostatics are evaluated analytically in an atom-centered Gaussian basis, while an equivariant network learns the kinetic and exchange-correlation energy from energies and gradients of non-ground-state densities. Minimizing the functional from a superposition of atomic densities recovers the Kohn-Sham ground state: on held-out crystals, the density error falls from 6.7% to 0.4% of the electron count and the energy error reaches 0.25 mHa per atom, half that of a same-architecture interatomic potential. A single functional can be trained for both isolated molecules and periodic systems, and the model generalizes to larger unit cells. It largely preserves relative-energy rankings and reproduces convex-hull vertices on the tested H-N composition slice. Together, these results demonstrate the viability of machine-learned all-electron orbital-free DFT for variational density optimization and energy evaluation in fixed-geometry solids.
ER -