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

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Abstract
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 qiqj/rijp, 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.