5.6 Range-Separated Hybrid Density Functionals

5.6.1 Semi-Empirical RSH Functionals

Semi-empirical RSH functionals for which the range-separation parameter should be considered fixed include the ωB97, ωB97X, and ωB97X-D functionals developed by Chai and Head-Gordon;146, 147 ωB97X-V and ωB97M-V from Mardirossian and Head-Gordon;626, 628 M11 from Peverati and Truhlar;749 ωB97X-D3, ωM05-D, and ωM06-D3 from Chai and coworkers;586, 585 and the screened exchange functionals N12-SX and MN12-SX from Truhlar and co-workers.753 More recently, Mardirossian and Head-Gordon developed two RSH functionals, ωB97X-V and ωB97M-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. ωB97M-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.628