Dual-channel range-separated local hybrid functionals beyond the zero-sum game

A dual-channel range-separated local hybrid (RS2LH) framework has been developed. It uses two local mixing functions (LMFs) for the coordinate-space mixing of short- and long-range semi-local and exact exchange-energy densities. Previous range-separated local hybrids with strong-correlation corrections (scRSLH) can be reformulated as RS2LH. We start from an existing scRSLH, retain the human-designed Padé-form sc-contributions, but replace a t-LMF by a neural network (n-LMF). This gives the ωLH26nP composite model which, in contrast to previous scRSLH functionals, does not require a calibration function to deal with the gauge issue. We then proceed to the first explicit RS2LH, ωLH26n, where two n-LMFs are explicitly trained on weak- and strong-correlation as well as fractional-charge training data. ωLH26nP and ωLH26n are evaluated on a wide range of data, including GMTKN55 and W4-17RE main-group energetics, organometallic transition-metal test sets, spin-restricted covalent bond dissociation as a measure for strong correlation, but also on diverse quasiparticle energies. Both functionals perform excellently for main-group energy benchmarks but show limited transferability to transition-metal energetics. While ωLH26nP also performs excellently for molecular quasiparticle energies comparable to previous RSLH functionals, and also for spin-restricted bond dissociation, the explicit ωLH26n RS2LH shows larger deviations. It is shown that the available training energy data are adequate for the SR-LMF but insufficient to give the correct asymptotic potential via the LR-LMF. The composite approach of ωLH26nP benefits from the pre-designed strong-correlation features and the resulting excellent quasiparticle energies. The deep-neural-network DM21 functional performs worse than ωLH26n; its fractional-charge training data alone are clearly insufficient to obtain accurate quasiparticle energies.