First-principles calculations of metal surfaces. I. Slab-consistent bulk reference for convergent surface properties

The first-principles computation of the surfaces of metals is typically accomplished through slab calculations of finite thickness. The extraction of a convergent surface formation energy from slab calculations is dependent upon defining an appropriate bulk reference energy. I describe a method for an independently computed, slab-consistent bulk reference that leads to convergent surface formation energies from slab calculations that also provides realistic uncertainties for the magnitude of unavoidable nonlinear divergence in the surface formation energy with slab thickness. The accuracy is demonstrated on relaxed, unreconstructed low-index aluminum surfaces with slabs with up to 35 layers.