Periodic boundary conditions in ab initio calculations. II. Brillouin-zone sampling for aperiodic systems

Brillouin-zone sampling in total-energy calculations of aperiodic systems using periodic boundary conditions is considered. Although the energies converge to the exact result in the limit of large supercells for any k-point sampling scheme, they do not converge at the same rate. In particular, it is shown that the use of a single sampling point at the origin of reciprocal space is especially inefficient. A k-point sampling scheme is proposed, which is computationally efficient and its efficacy relative to other common approaches is demonstrated.