5.6.1 Semi-Empirical RSH Functionals

Semi-empirical RSH functionals for which the range-separation parameter should be considered fixed include the $\omega$B97, $\omega$B97X, and $\omega$B97X-D functionals developed by Chai and Head-Gordon;^{159, 160} $\omega$B97X-V and $\omega$B97M-V from Mardirossian and Head-Gordon;^{610, 612} M11 from Peverati and Truhlar;⁷²³ $\omega$B97X-D3, $\omega$M05-D, and $\omega$M06-D3 from Chai and coworkers;^{576, 575} and the screened exchange functionals N12-SX and MN12-SX from Truhlar and co-workers.⁷²⁷ More recently, Mardirossian and Head-Gordon developed two RSH functionals, $\omega$B97X-V and $\omega$B97M-V, via a combinatorial approach by screening over 100,000 possible functionals in the first case and over 10 billion possible functionals in the second case. Both of the latter functionals use the VV10 non-local correlation functional in order to improve the description of non-covalent interactions and isomerization energies. $\omega$B97M-V is a 12-parameter meta-GGA with 15% short-range exact exchange and 100% long-range exact exchange and is one of the most accurate functionals available through rung 4 of Jacob’s Ladder, across a wide variety of applications. This has been verified by benchmarking the functional on nearly 5000 data points against over 200 alternative functionals available in Q-Chem.⁶¹²