  A linear-response method to calculate the effective Coulomb interaction ($U$)
between closed-shell localized electrons is suggested and applied to the $3d$
closed-shell systems (Cu, Zn, and ZnO) based on plane-wave basis
density-functional theory calculations. Since the closed-shell localized states
are far below the Fermi level, large local perturbation potential ($\alpha$)
projected to the localized states is applied to induce purposeful density
response ($\Delta n$). From the $\alpha$, the perturbation potential cost for
density response onset, by which the $\Delta n$ begins to be induced, is
removed. The main screening channel for the effective Coulomb interaction is
the itinerant electrons deoccupied from the perturbed localized states. The Cu,
Zn, and ZnO $3d$ electron binding energies are calculated based on the local
density approximation plus $U$ with the $U$ values calculated from the
linear-response, which are found to be in good agreement with experiments.
