Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals

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.

Source: arXiv:2610.30022v1 - http://arxiv.org/abs/2610.30022v1 PDF: https://arxiv.org/pdf/2610.30022v1 Original Link: http://arxiv.org/abs/2610.30022v1