We extend the recent formulation of the Ewald sum for electrostatics in a two-dimensionally periodic three-dimensional multiatom layer or two-dimensional single-atom layer system with a rectangular periodic boundary condition(J Chem Theory Comput, 2014, 10: 534–542) to that with a parallelogrammic periodic boundary condition in general. Following the discussion of an efficient implementation of the formula, we suggest a simple setup of parameters using a relatively smaller screening factor and the associated larger real space cutoff distance to reach an optimized algorithm of an order N computational cost. The connection between the previous application of the Ewald sum to ionic crystal systems and the future application to molecular self-assembly or disassembly systems on solid surfaces or at liquid-liquid interfaces are illustrated to demonstrate the applicability of the present work to simulate the self-assembly process and to produce dynamical, structural and thermodynamic properties of experimental self-assembly systems of interest.
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