ML26: New Ingredients for an Integral-Features Density Functional with Broad Chemical Accuracy

Abstract

Integral-features density functional theory (IF-DFT) replaces the conventional integration over local ingredients with a nonlinear mapping from global integral descriptors, enabling machine-learned density functionals with broad transferability. Here we report ML26@MN15, a new IF functional that extends the earlier ML25@MN15 model by incorporating 12 additional correlation features─including overlap-projected rung-3.5 terms, CS1 dynamic-correlation ingredients, and VV10 nonlocal correlation─and by treating Hartree–Fock exchange as an integral feature rather than as a fixed hybrid percentage. ML26@MN15 employs 79 integral features evaluated on MN15 ingredients and a single-hidden-layer neural network with 5000 nodes to produce a size-extensive exchange–correlation energy. Trained on 185 databases comprising 7242 reference data, ML26@MN15 achieves a data-averaged energetic mean unsigned error of 0.89 kcal/mol, improving upon ML25@MN15 by 15% and outperforming a group of previous leading functionals across all eight chemical partitions examined. For the widely used MDB2019S, MGCDB84, and GMTKN55 data sets, ML26@MN15 yields the lowest averaged errors among all tested functionals, including the results for GMTKN55 by ML-based Skala-1.1 and DM21 density functional approximations. The new functional also maintains strong performance for systems containing heavy elements and exhibits improved behavior on a challenging self-interaction benchmark. These results show that expanding the integral-feature space with physically motivated nonlocal ingredients yields a density functional with unprecedented accuracy across diverse chemical benchmarks. The broad and consistent accuracy of ML26@MN15 highlights the promise of integral-features density functional approximations as a scalable framework for incorporating additional nonlocal physics into future functional development.