  The effective on-site Coulomb interaction (Hubbard $U$) between localized
electrons at crystal surfaces is expected to be enhanced due to the reduced
coordination number and reduced subsequent screening. By means of first
principles calculations employing the constrained random-phase approximation
(cRPA) we show that this is indeed the case for simple metals and insulators
but not necessarily for transition metals and insulators that exhibit
pronounced surface states. In the latter case, the screening contribution from
surface states as well as the influence of the band narrowing increases the
electron polarization to such an extent as to overcompensate the decrease
resulting from the reduced effective screening volume. The Hubbard $U$
parameter is thus substantially reduced in some cases, e.g., by around 30% for
the (100) surface of bcc Cr.
