Cell multipole method for molecular simulations in bulk and confined systems

One of the bottlenecks in molecular simulations is to treat large systems involving electrostatic interactions. Computational time in conventional molecular simulation methods scales with O(N{sup 2}), where N is the number of atoms. With the emergence of the cell multipole method (CMM) and massively parallel supercomputers, simulations of 10 million atoms have been performed. In this work, the optimal hierarchy cell level and the algorithm for Taylor expansion were recommended for fast and accurate molecular dynamics (MD) simulations of three-dimensional (3D) systems. CMM was then extended to treat quasi-two-dimensional (2D) systems, which is very important for condensed matter physics problems. In addition, CMM was applied to grand canonical ensemble Monte Carlo (GCMC) simulations for both 3D and 2D systems. Under the optimal conditions, the results show that computational time is approximately linear with N for large systems, average error in total potential energy is less than {approx}1%, and RMS force is about 0.015 for 3D and 2D systems when compared with the Ewald summation