Adiabatic Variational Calculation of the Lattice Relaxation at Metal Surfaces

The relaxation is considered of the top lattice plane on surfaces of simple metals which is determined by a minimum surface energy. A general formulation of the problem is given which allows clear classification of previous theoretical attempts and their comparison with the present model. The latter is based on a variational procedure in terms of the density functional formalism using a parametrized surface model with extended ion cores (Ashcroft model potentials). Especially stressed should be the adiabatic properties of the model consisting in the fact that the electron density changes when the ionic positions are shifted. Numerical results for (100)‐Li, (110)‐Al, and (111)‐Al surfaces are presented. The relaxations have different signs, and they are smaller than 2% of the interlayer spacing even for the case of Al where some LEED interpretations indicate large contractions.