The range separating parameter (μ) in the long-range corrected spin-unrestricted BLYP (LC-UBLYP) method is tuned so as to reproduce the second hyperpolarizabilities (γ) of several open-shell singlet metal–metal bonded systems calculated using the strongly electron-correlated spin-unrestricted coupled cluster singles, doubles and perturbative triples [UCCSD(T)] method. For these systems, μ values ranging between 0.7 and 0.9 bohr−1 provide a reliable description of the bond length dependence of γ in the bond length region where γ is enhanced by the contribution of dσ electrons with an intermediate open-shell character.