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

A dual-channel framework for range-separated local hybrid functionals (RS2LH framework) has been developed. It uses two local mixing functions (LMFs) for the coordinate-space mixing of semi-local and exact exchange-energy densities, one for the short-range, one for the long-range contributions. It is shown that previous range-separated local hybrids with strong-correlation corrections (scRSLH) can also be understood within this framework. As an intermediate step towards training of explicit RS2LH functionals with neural-network LMFs (n-LMFs), we start from an existing scRSLH, retain the human-designed Padé-form strong-correlation contributions but replace the human-designed t-LMF by an n-LMF. This gives the ωLH26nP functional, which in contrast to previous scRSLH functionals does not require a so-called calibration function to deal with the gauge ambiguity of exchange-energy densities. We then proceed to the first explicit RS2LH construction, ωLH26n, where both short-range and long-range LMFs are explicitly trained as neural networks 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 measure for strong correlations, but also on diverse quasiparticle energies, i.e., Koopmans-based computations of ionization potentials, electron affinities, and band gaps. Both RS2LH functionals perform well for many 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, the explicit ωLH26n RS2LH shows larger deviations. It is shown that the available energy data used currently for LMF training are good for the short-range LMF but insufficient for a full and stable training of the long-range LMF required to recover the correct asymptotic potential. Here the composite approach of ωLH26nP benefits from the pre-designed strong-correlation features and gives a more stable long-range LMF suitable also for quasiparticle energies. The deep-neural-network DM21 functional exhibits even larger deviations for quasiparticle energies than ωLH26n. Analyses strongly suggest that fractionalcharge data alone are insufficient to enforce the correct asymptotic potential and that quasiparticle-energy data should be included in the training of highly flexible functionals for which the correct behavior is not built into their physical structure.