The formalism of the Kohn–Sham equations with constrained electron density is extended to the spin-polarized case. The isotropic hyperfine coupling constants (Aiso(Mg)) of Mg+ embedded in a Ne or Ar matrix represented using a cluster are calculated and compared to that of free Mg+. For the largest basis set used, the calculated values (222.9 and 210.4 gauss for Ar and Ne, respectively) agree with experimental measurements (222.4 and 211.6). The shifts of Aiso(Mg) relative to the values for free Mg+ are rather basis-set-independent.