As we could see earlier, the Friedel oscillations depend on the dimensionality of the system. In general the surface oscillations due to the fact that e.g. the (111) surfaces of noble metals do form the nearly-free electron gas (NFEG), meaning that the surfacestate electrons are restricted to quite a narrow layer at the surface. Henceforth, one, in principle, could expect, to some extent, the 1/r 2 decay asymptotic of the Friedel oscillations. In 1999, Hyldgaard and Persson derived the adsorbate-adsorbate interaction mediated by the Shockley-type surface state , which may be expressed as (between two adsorbates i and j being apart at distance dij) ∆E pair (dij) ≈ -EF sin 2 (δF )