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(May 16, 2021)

Whereas RSH functionals such as LRC-$\omega $PBE are attempts to add 100% LR Hartree-Fock exchange with minimal perturbation to the original functional (PBE, in this example), other RSH functionals are of a more empirical nature and their range-separation parameters have been carefully parameterized along with all of the other parameters in the functional. These cases are functionals are discussed first, in Section 5.6.1, because their range-separation parameters should be taken as fixed. User-defined values of the range-separation parameter are discussed in Section 5.6.2, and Section 5.6.3 discusses a procedure for which an optimal, system-specific value of this parameter ($\omega $ or $\mu $) can be chosen for functionals such as LRC-$\omega $PBE or LRC-$\mu $PBE.