Ab initio local stress and its application to Al (111) surfaces

A practical way to calculate local quantum stress within the framework of stress density developed by Filippetti and Fiorentini [Phys. Rev. B 61, 8433 (2000)] is proposed and applied to Al (111) surfaces. Through detailed analysis of the gauge-dependent term in the kinetic stress density derived from the kinetic-energy density, it has been shown that the local stress components can be uniquely obtained by defining appropriate local regions where the gauge-dependent term integrates to zero. In Al (111) surface-slab calculations implemented by the projector-augmented-wave method, we have observed Friedel-type oscillation of the layer-by-layer stress, which reveals clear correlation with charge redistribution at the surface.