We apply the optimized effective potential method (OPM) to the multivalent 3dn (n = 2, …, 8) ions; Mν+ (ν = 2, …, 8). The total energy functional is approximated by the single-configuration Hartree–Fock. The exchange potential for the average energy configuration is decomposed into the potentials derived from F2(3d, 3d) and F4(3d, 3d) Slater integrals. To investigate properties of the density-functional potential, we have checked the scaling properties of several physical quantities such as the density, the 3d orbital and these potentials. We find that the potentials of the Slater integrals do not have the scaling property. Instead, the weighted potential of an ion i, which is the potential of the Slater integrals times the 3d-orbital density, satisfies the scaling property where qi3d is the occupation number of the 3d-orbital R3d(r) for ion i. Furthermore, the weighted potential can be approximated by the ion-independent functional of the 3d-orbital density ckR8/33d(r)/q3d where c2 = 0.366 and c4 = 0.223. This suggests that the weighted potential can be expressed as a functional of the 3d-orbital density.