Source-linked AI summary
Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals
Yuhao Chen, Donald G. Truhlar, Xiao He
TL;DR
Empirical exchange-correlation functionals are fitted on fixed orbitals but used self-consistently, leaving the resulting density shift and energy gap unconstrained. The paper penalizes the Brillouin residual on accurate-density orbitals without solving the SCF equations during training. Trained on six energies and 11 CCSD densities, its neural meta-GGA outperforms SCAN in atomization energies and densities.
Problem
Energy-only fitting evaluates functionals on reference-density orbitals but does not constrain whether their self-consistent solutions remain on those orbitals.
Source: p. 1Method
The method penalizes the Brillouin residual on accurate-density Kohn-Sham orbitals, using one Fock build per system without solving or differentiating through SCF.
Source: pp. 1, 3Results
NN-mGGA(EGD) has an atomization-energy MAE of 3.3 kcal/mol (SCAN 3.7, r2SCAN 3.8) and a density error of 0.29, versus 0.57–0.64 for SCAN and r2SCAN.
Source: p. 5Takeaways & Limitations
Stationarity at the reference solution offers a general, inexpensive constraint for learned models used inside self-consistent or variational solvers.
Source: p. 5The energy-relaxation upper bound relies on a positive-definite Hartree-XC kernel, which is usually dominated by the Hartree part.
Source: p. 2
Abstract
from arXiv · showhide
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.