Categorization of surface polarity from a crystallographic approach

With ab initio codes that employ three-dimensional periodic boundary conditions, the slab-and-vacuum model has proven invaluable for the derivation of energetic, atomistic, and electronic properties of materials. Within this approach, polar and nonpolar slabs require different levels of treatment, as any polar instability must be compensated on a case-by-case basis in the former. This article proposes an efficient algorithm based on isometries to identify whether a slab with the given surface orientation would be intrinsically polar, and if not, to obtain information on where to cleave the bulk crystal to obtain a stoichiometric nonpolar slab and whether reconstruction is necessary to generate a stoichiometric slab that is not polar.