Although it may appear straightforward, the previous paragraph described Friedel oscillations (FOs) around a single perturbation (adsorbate). However, what happens when there are multiple perturbations or the presence of external fields or inhomogeneity in the electron gas? Analyzing adsorbate self-assembly, catalytic activity, on-surface reactions, and electronic and magnetic structures would be incomplete without incorporating the interaction term into the system's Hamiltonian. Apart from the simplified approximate expression for the FOs detailed in the previous paragraph, there is also a second popular description of the FOs devised by Hyldgaard and Persson in the experimental literature. Authors started out with the Shockleytype surface-state bands, and by using the scattering T -matrix, they obtained some approximate results for the two-and threebody interactions between the adsorbates on the metallic surface. Below, we dive deeper into the possible interactions they published.