We present a comparison between accurate textit{ab initio} calculations and a high-quality experimental data set (1986-2002) of electric-field gradients and magnetic hyperfine fields of Cd at different sites on Ni, Cu, Pd and Ag surfaces. Experiments found a systematic rule to assign surface sites on (100) and (111) surfaces based on the main component of the electric-field gradient, a rule that does not work for (110) surfaces. Our calculations show that this particular rule is a manifestation of a more general underlying systematic behavior. When looked upon from this point of view, (100), (111) emph{and} (110) surfaces behave in precisely the same way. The experimentally observed parabolic coordination number dependence of the Cd magnetic hyperfine field at Ni surfaces is verified as a general trend, but we demonstrate that individual cases can significantly deviate from it. It is shown that the hyperfine fields of other 5sp impurities at Ni surfaces have their own, typical coordination number dependence. A microscopic explanation for the different dependencies is given in terms of the details of the s-DOS near the Fermi level.
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