Pair potentials and lattice vibrations at simple-metal surfaces

Screened pair potentials and interatomic force constants at simple-metal surfaces are investigated using a semiclassical approach within the infinite barrier model. Reduction in the screening appears to be significant only quite close to the surface. For an electron density corresponding to A1, differences from bulk screening are negligible at distances greater than ∼2.5 Bohr radii from the barrier, and for the lower electron density of Na, at distances greater than $\sim {3.5a}_0$. For surfaces where the reduced screening is significant, models for lattice vibrations or relaxation based on bulk pair potential forms are clearly unreliable. For such surfaces, relaxation and screening effects can each produce force-constant changes of the order of 50% of the largest bulk force constant.