Atomic level simulations on a million particles: The cell multipole method for Coulomb and London nonbond interactions

The N² computations implicit in the Coulomb and other long range interactions remain the critical bottleneck in atomic-level simulations of the structure and dynamics of large systems. We report here the cell multipole method which scales linearly with N and requires only modest memory. To demonstrate the feasibility of this approach, we report systematic calculations on realistic polymer systems with up to 1.2 million atoms on a laboratory workstation. The method becomes faster than the exact method for systems of 300 atoms, and for a 1.2 million-atom polymer, it is 2377 times faster. The method treats a class of interactions of the form q_iq_j/r _ij^p, which includes Coulomb (p=1), London dispersion (p=6), or shielded Coulomb (p=2) interactions. This method is well suited for highly parallel and vector computers.