  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 intro-duce 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 which allows explicitly discretizing millions of atoms in real space and
to consider virtually any type of environment (be it periodic, regular, or
ran-dom). The impact of the periodicity assumption is assessed in detail with
silicon dopants in graphene. Graphene was con-firmed 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 periodici-ty 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.
