Dispersion corrected r²SCAN based global hybrid functionals: r²SCANh, r²SCAN0, and r²SCAN50

The regularized and restored semilocal meta-generalized gradient approximation (meta-GGA) exchange-correlation functional r²SCAN [Furness et al., J. Phys. Chem. Lett. 11, 8208-8215 (2020)] is used to create three global hybrid functionals with varying admixtures of Hartree-Fock "exact" exchange (HFX). The resulting functionals r²SCANh (10% HFX), r²SCAN0 (25% HFX), and r²SCAN50 (50% HFX) are combined with the semi-classical D4 London dispersion correction. The new functionals are assessed for the calculation of molecular geometries, main-group, and metalorganic thermochemistry at 26 comprehensive benchmark sets. These include the extensive GMTKN55 database, ROST61, and IONPI19 sets. It is shown that a moderate admixture of HFX leads to relative improvements of the mean absolute deviations for thermochemistry of 11% (r²SCANh-D4), 16% (r²SCAN0-D4), and 1% (r²SCAN50-D4) compared to the parental semi-local meta-GGA. For organometallic reaction energies and barriers, r²SCAN0-D4 yields an even larger mean improvement of 35%. The computation of structural parameters (geometry optimization) does not systematically profit from the HFX admixture. Overall, the best variant r²SCAN0-D4 performs well for both main-group and organometallic thermochemistry and is better or on par with well-established global hybrid functionals, such as PW6B95-D4 or PBE0-D4. Regarding systems prone to self-interaction errors (SIE4x4), r²SCAN0-D4 shows reasonable performance, reaching the quality of the range-separated ωB97X-V functional. Accordingly, r²SCAN0-D4 in combination with a sufficiently converged basis set [def2-QZVP(P)] represents a robust and reliable choice for general use in the calculation of thermochemical properties of both main-group and organometallic chemistry.