Introducing Open Boundary Conditions in Modeling Nonperiodic Materials and Interfaces: The Impact of the Periodicity Assumption

Simulations are essential to accelerate the discovery of new materials and to gain full understanding of known ones. Although hard to realize experimentally, periodic boundary conditions are omnipresent in material simulations. In this work, we introduce ROBIN (recursive open boundary and interfaces), the first method allowing open boundary conditions in material and interface modeling. The computational costs are limited to solving quantum properties in a focus area that allows explicitly discretizing millions of atoms in real space and to consider virtually any type of environment (be it periodic, regular, or random). The impact of the periodicity assumption is assessed in detail with silicon dopants in graphene. Graphene was confirmed to produce a band gap with periodic substitution of 3% carbon with silicon in agreement with published periodic boundary condition calculations. Instead, 3% randomly distributed silicon in graphene only shifts the energy spectrum. The predicted shift agrees quantitatively with published experimental data. Key insight of this assessment is, assuming periodicity elevates a small perturbation of a periodic cell into a strong impact on the material property prediction. Periodic boundary conditions can be applied on truly periodic systems only. More general systems should apply an open boundary method for reliable predictions.