  Adsorbed transition metal atoms can have partially filled $d$- or $f$-shells
due to strong on-site Coulomb interaction. Capturing all effects originating
from electron correlation in such strongly correlated systems is a challenge
for electronic structure methods. It requires a sufficiently accurate
description of the atomistic structure (in particular bond distances and
angles), which is usually obtained from Kohn-Sham density functional theory
(DFT), which due to the approximate nature of the exchange-correlation
functional may provide an unreliable description of strongly correlated
systems. To elucidate the consequences of this popular procedure, we apply a
combination of DFT with the Anderson impurity model (AIM), as well as DFT+U for
a calculation of the potential energy surface along the Co/Cu(001) adsorption
coordinate, and compare the results with those obtained from DFT. The
adsorption minimum is shifted towards larger distances by applying DFT+AIM, or
the much cheaper DFT+U method, compared to the corresponding spin-polarized DFT
results, by a magnitude comparable to variations between different approximate
exchange-correlation functionals (0.08 to 0.12 Angstrom). This shift originates
from an increasing correlation energy at larger adsorption distances, which can
be traced back to the Co 3$d_{xy}$ and 3$d_{z2}$ orbitals being more correlated
as the adsorption distance is increased.
