  We have extended the validity of the correlation between the surface
3d-core-level shift (SCLS) and the surface d band shift (SDBS) to the entire 4d
transition metal series and to the neighboring elements Sr and Ag via accurate
first-principles calculations. We find that the correlation is quasilinear and
robust with respect to the differencies both between initial and final-state
calculations of the SCLS's and two distinct measures of the SDBS's. We show
that despite the complex spatial dependence of the surface potential shift
(SPS) and the location of the 3d and 4d orbitals in different regions of space,
the correlation exists because the sampling of the SPS by the 3d and 4d
orbitals remains similar. We show further that the sign change of the SCLS's
across the transition series does indeed arise from the d band-narrowing
mechanism previously proposed. However, while in the heavier transition metals
the predicted increase of d electrons in the surface layer relative to the bulk
arises primarily from transfers from s and p states to d states within the
surface layer, in the lighter transition metals the predicted decrease of
surface d electrons arises primarily from flow out into the vacuum.
