Strong-correlation density functionals made simple

Recent work on incorporating strong-correlation (sc) corrections into the scLH22t local hybrid functional [A. Wodyński and M. Kaupp, J. Chem. Theory Comput. 18, 6111-6123 (2022)] used a hybrid procedure, applying a strong-correlation factor derived from the reverse Becke-Roussel machinery of the KP16/B13 and B13 functionals to the nonlocal correlation term of a local hybrid functional. Here, we show that adiabatic-connection factors for strong-correlation-corrected local hybrids (scLHs) can be constructed in a simplified way based on a comparison of semi-local and exact exchange-energy densities only, without recourse to exchange-hole normalization. The simplified procedure is based on a comparative analysis of Becke's B05 real-space treatment of nondynamical correlation and that in LHs, and it allows us to use, in principle, any semi-local exchange-energy density in the variable used to construct local adiabatic connections. The derivation of competitive scLHs is demonstrated based on either a modified Becke-Roussel or a simpler Perdew-Burke-Ernzerhof (PBE) energy density, leading to the scLH23t-mBR and scLH23t-tPBE functionals, which both exhibit low fractional spin errors while retaining good performance for weakly correlated situations. We also report preliminary attempts toward more detailed modeling of the local adiabatic connection, allowing a reduction of unphysical local maxima in spin-restricted bond-dissociation energy curves (scLH23t-mBR-P form). The simplified derivations of sc-factors reported here provide a basis for future constructions and straightforward implementation of exchange-correlation functionals that escape the zero-sum game between low self-interaction and static-correlation errors.