Relaxation at simple metal surfaces is studied via minimization of the total energy of a semi-infinite crystal. The expression for the total energy depends explicitly on the ionic positions, and is based on the use of pseudopotential theory and linear response. Electron screening is treated self-consistently including exchange and correlation effects. From a systematic investigation of the energetics underlying metal surface relaxation, for the low-index surfaces of bcc Na and fcc Al it is concluded that to achieve quantitative surface structural predictions requires the use of the full total-energy expression for the semi-infinite solid. Such an expression must maintain the three-dimensional nature of the system and account properly for the inhomogeneous surface electron density and the self-consistent response of the electron system to the ionic positions (screening). Multilayer relaxation is shown to be essential for quantitative structural predictions and the origins of the phenomena are discussed in detail demonstrating the relative effects of electrostatic terms and band-structure contributions. The results exhibit damped oscillatory multilayer relaxations (the relaxation being particularly pronounced for the open faces) with a period equal to the bulk layer stacking period and agree well with available structural determinations obtained via the analysis of experimental data.

• Received 2 March 1983

DOI:https://doi.org/10.1103/PhysRevB.28.1685