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This paper addresses a known weakness of machine-learned density functionals: a functional fitted to fixed orbitals can gain accuracy in energies while losing accuracy in self-consistent densities. The authors tie both problems to a single quantity, the Brillouin residual, and show it can be penalized during training without running self-consistent-field solutions. Results are limited to a small training set (6 energies, 11 CCSD densities) and a neural meta-GGA compared against SCAN, so readers should treat the gains as promising but not yet broadly validated.
Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals
arXiv:2610.30022v1 Announce Type: cross Abstract: Empirical exchange-correlation functionals are fitted on fixed orbitals but used self-consistently, so better energies often come with worse densities. We show that the Brillouin residual of a trained functional on the Kohn-Sham orbitals of an accurate density controls, to first order, both the self-consistent density shift and the gap between fitted and self-consistent energies. Penalizing it requires no self-consistent-field solution during training. Trained on 6 energies and 11 CCSD densities, a neural meta-GGA surpasses SCAN in both atomization energies and densities of unseen molecules.
Abstract:Empirical exchange-correlation functionals are fitted on fixed orbitals but used self-consistently, so better energies often come with worse densities. We show that the Brillouin residual of a trained functional on the Kohn-Sham orbitals of an accurate density controls, to first order, both the self-consistent density shift and the gap between fitted and self-consistent energies. Penalizing it requires no self-consistent-field solution during training. Trained on 6 energies and 11 CCSD densities, a neural meta-GGA surpasses SCAN in both atomization energies and densities of unseen molecules.
Chemical Physics (physics.chem-ph); Artificial Intelligence (cs.AI)
arXiv:2610.30022 [physics.chem-ph]
(or arXiv:2610.30022v1 [physics.chem-ph] for this version)
https://doi.org/10.48550/arXiv.2610.30022 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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