The reduced cell multipole method for Coulomb interactions in periodic systems with million-atom unit cells

Standard methods for calculating Coulomb interactions of periodic systems use Ewald-type formulations or minimum image approximations, neither of which is practical for large (million-atom) systems. We describe the reduced cell multipole method which is 38 times faster than the Ewald method for a 4816-atom (unit cell) system. The method scales linearly with the number of atoms in the cell, making simulations of million-atom systems practical, as demonstrated in a series of applications on a laboratory workstation.