We extend the Kohn–Sham equations with constrained density (KSCED) to the use of orbital dependent functionals, namely the localized Hartree–Fock (LHF) functional, which is free from the Coulomb self-interaction error. We show that the LHF-KSCED approach yields an accurate description of the embedded density of weakly-bound systems. This performance is rationalized in terms of the reduced importance of the nonadditive kinetic embedding contributions in LHF-KSCED calculations.As a sample application of the LHF-KSCED method we study the ionization potential of solvated thymine.