Multilayer relaxations at the (0001) surface of Be and Mg

Density functional theory and a plane-wave basis pseudopotential technique is applied to calculate relaxations of the first three interlayer spacings at the (0001) surface of thick Be and Mg slabs. For both metals the calculated outward relaxation of the topmost layer and small relaxations of the deeper layers are in good agreement with experiment and previous calculations. The calculated multilayer relaxations are analysed in terms of the electron charge density profile perpendicular to the surface which shows an oscillatory character with a period consistent with the long-range Friedel oscillations. Our results provide arguments for the generalization of the physical model relating the origin of multilayer relaxation to Friedel oscillations at the bulk truncated surface.