The interplay between strong correlation and adsorption distances

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.