Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.30022

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

Yuhao Chen·Donald G. Truhlar·Xiao He
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

physics.chem-phcs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yuhao Chen, Donald G. Truhlar, Xiao He. 2026-10-21. Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals. https://arxiv.org/abs/2610.30022

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Near Chemical Accuracy From Size-Consistent Padé Resummed Møller-Plesset Perturbation Theory

Padé resummation of the correlation energy from Møller-Plesset (MP) perturbation theory is not size-consistent and is therefore seldom used. We present an orbital-based Padé resummation of the MP2 and MP3 self-energy operators, whose trace yields a size-consistent correlation energy. We find that damping the third-order same-spin contribution leads to substantially increased accuracy, with the resulting same-spin damped orbital Padé resummed (SSD-OPMP3) approach attaining near-chemical accuracy (mean absolute error $\sim$ 1 kcal/mol) for total atomization energies of non-multireference molecules in the W4-17 dataset against the gold standard CCSD(T) method. Excellent performance surpassing CCSD is also obtained for other molecular datasets such as those containing barrier heights, noncovalent interactions, dipole moments, static polarizabilities, and transition-metal chemistry. SSD-OPMP3 is thus a highly accurate electronic structure method with the same noniterative $O(N^6)$ cost as MP3, filling a gap in the cost/accuracy hierarchy of wavefunction methods.

physics.chem-ph↗
arXiv2026

What Rate Theories Compute: Chemical kinetics from Arrhenius to machine-learned potentials

Chemical rate theories have advanced by changing how a reaction is represented and which molecular quantities are calculated. Several advances also supplied controlled corrections to earlier theories. I connect this history, from Arrhenius to machine-learned potentials, to tests of the assumptions behind a calculated rate. Original sources clarify Marcelin's treatment of incomplete transmission and reactive-population depletion, and Christiansen's descriptions of orientation and collisional deactivation. Five numerical comparisons distinguish tests against experiment from tests using the same molecular model and from calibration. For hydrogen desorption from platinum, a published barrier adjustment improves absolute rate agreement but increases the spread of calculated-to-experimental ratios across temperatures; the source supplies no rate uncertainties. For triosephosphate isomerase, changing the prior on microscopic rates shifts the median inferred intermediate energy from 7.3 to 17.2 kJ/mol with the same inputs, likelihood, and bounds. This sensitivity calculation does not determine a preferred physical energy. I also examine how later molecular information can change the interpretation of older measurements. Hydrogen-oxygen chain branching provides a published reconciliation involving revised thermochemistry and dynamics. For pyrophosphate hydrolysis, conditional speciation identifies a potentially important complex containing two magnesium ions whose hydrolysis rate is not supplied by the recent calculations. Proposed tests use independent species populations, a later optical calibration of Criegee intermediates, and controlled temperature histories and local recession measurements in diamond dissolution.

physics.chem-ph↗
arXiv2026

Unconstrained learning of equivariant atomistic properties

Machine-learned interatomic potentials based on graph neural networks (GNNs) have made first-principles accuracy routine for the potential energy surface (PES). Their backbones, often O(3)-equivariant by design, are increasingly used to learn other atomistic properties. Many of these are of high angular order or pseudotensorial character, defined per atom, or expanded on large atom-centered basis sets. Such targets strain equivariant GNNs, whose tensor products grow steeply in cost with angular order and can fail to represent the target if truncated, forcing difficult trade-offs between hyperparameters. Unconstrained models like the Point-Edge Transformer (PET) instead replace explicit O(3) algebra with edge-to-edge attention and learn equivariance from data, so that the same backbone can in principle learn any equivariant property. We demonstrate how to use PET to learn molecular dipoles and polarizabilities, NMR chemical shielding tensors, and auxiliary-basis expansions of the electron density. Increasing the backbone size systematically improves both accuracy and equivariance error, and targeted architectural and training choices reduce the symmetry breaking further. PET matches or improves on the released reference models at lower inference cost and, compared with equivariant models, a smaller memory footprint. The predictions give accurate IR and Raman spectra and isotropic shieldings; the predicted densities accelerate self-consistent field calculations and give one-shot ground-state properties, and pretrained density models transfer to higher levels of theory by fine-tuning on little data. The impact of approximate equivariance is small for most observables, further validating this approach to train fast, accurate, and useful surrogate models for properties beyond the PES.

physics.chem-ph↗