  We present a reciprocal space technique for the calculation of the Coulomb
integral in two dimensions in systems with reduced periodicity, i.e., finite
systems, or systems that are periodic only in one dimension. The technique
consists in cutting off the long-range part of the interaction by modifying the
expression for the Coulomb operator in reciprocal space. The physical result
amounts in an effective screening of the spurious interactions originated by
the presence of ghost periodic replicas of the system. This work extends a
previous report [C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006)], where
three-dimensional systems were considered. We show that the use of the cutoffs
dramatically enhances the accuracy of the calculations for a given supercell
size, and it allows to describe two-dimensional systems of reduced periodicity
with substantially less computational effort. In particular, we consider
semiconductor quantum-dot arrays having potential applications in quantum
information technology.
