Newest papers

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

Yuhao Chen, Donald G. Truhlar, Xiao He · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.30022 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

Las funciones de intercambio empírico-correlación se instalan en orbitales fijos pero se usan de forma auto-consistente, por lo que las energías mejores a menudo vienen con densidades peores. Mostramos que el residuo de Brillouin de un funcional entrenado en los orbitales de Kohn-Sham de un control de densidad preciso, en primer orden, tanto el cambio de densidad auto-consistente como la brecha entre las energías auto-consistentes. Penalizarlo no requiere una solución de campo auto-consistente durante el entrenamiento. Entrenado en 6 energías y 11 densidades CCSD, un meta-GGA neural supera al SCAN en ambas energías de atomización y densidades de moléculas invisibles.

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Residual, Atomic orbital, Hybrid functional, Physics, Brillouin zone, Density functional theory

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