A layer summation for electrostatic surface problems. Application to the classical cleavage energy

A rather general method is given for calculating the electrostatic potential due to a half‐infinite 2D‐lattice periodic charge distribution. Such kind of potentials arises in the Coulomb integrals of the classical cleavage energy (a contribution to the surface energy) or in calculating ionic lattice relaxation near metal surfaces. For the former quantity numerical results are presented here. It is found that the contribution due to bulk electron density oscillations must be taken into account even for simple metals to get results for the total surface energy comparable with experimental ones (rather than with experimental surface tensions). Taking into account these density oscillations the anisotropy ratios are markedly improved, too. The calculation is made for all simple metals in terms of pseudopotential theory.