Local-Hybrid Functional With a Composite Local Mixing Function Built From a Neural Network and a Strong-Correlation Model.

Due to their position-dependent admixture of the exact-exchange (EXX) energy density, local hybrid functionals (LHs) enable a flexible balance between reduced self-interaction errors and smaller static-correlation errors, allowing an escape from the usual zero-sum game between these two central aspects of the development of density functional approximations. Recent LHs with strong-correlation factors incorporated into their local mixing functions (LMFs) governing the position-dependence of EXX admixtures have been particularly successful in this context. As only few exact constraints for LMFs are known regarding valence-space behavior, some recent efforts have used machine learning in this context, and the recent LH24n functional with a "neural-network LMF" (n-LMF, DOI: 10.1021/acs.jctc.4c01503) has shown excellent performance for the large GMTKN55 test suite of main-group energetics. However, so far the construction of n-LMFs that also cover strong-correlation effects has not been successful. Here we report the LH25nP functional that has an n-LMF optimized in the presence of a fixed strong-correlation factor. LH25nP-D4 achieves a remarkable self-consistent WTMAD-2 value of 2.47 kcal/mol for the GMTKN55 set, the so far lowest value for a rung 4 functional. Mean absolute deviations of 2.4 kcal/mol for the large W4-11RE reaction-energy set are also the lowest known currently for rung 4. At the same time, very low fractional-spin errors and excellent performance for the spin-restricted dissociation of covalent bonds, as well as a curing of spin-contamination problems in open-shell transition-metal complexes has been found, suggesting a clear deviation from the usual zero-sum behavior. Transferability to organometallic transition-metal energetics is so far less favorable, suggesting the need for a wider training of n-LMFs that includes data for transition-metal systems.