Optimal operators for Hartree–Fock exchange from long-range corrected hybrid density functionals

The long-range operators for Hartree–Fock exchange from two recently proposed long-range corrected hybrid functionals, ωB97 and ωB97X [J.-D. Chai, M. Head-Gordon, J. Chem. Phys. 128 (2008) 084106], are discussed. A conserved property is found in the middle-range region of the operator from ωB97X. We argue that the fine details of the Hartree–Fock exchange mixing in this region are responsible for the accuracy of the long-range corrected hybrid functionals in thermochemistry and barrier heights.