A fast multipole method for periodic systems with arbitrary unit cell geometries

The point-charge fast multipole method (FMM) for periodic boundary conditions is generalized from cubic to rectangular simulation cells. This development let us treat lattices with orthogonal (rectangular) unit cells. The lattice of non-orthogonal systems can be transformed to yield a rectangular simulation cell. Thus, our periodic FMM algorithm can be applied to lattices with arbitrary unit cells. We also discuss in detail our proposed solutions for problems arising from the accuracy of the infinite summation contribution and the dipole moment of the simulation cell. Benchmark results of our periodic FMM show linear-scaling properties.