Electrostatic layer correction with image charges: A linear scaling method to treat slab 2D+h systems with dielectric interfaces

A fast algorithm for dealing with electrostatic interactions in partially periodic systems that are confined along the nonperiodic direction by two planar dielectric interfaces is presented. The method is a generalization of the electrostatic layer correction (ELC) method of Arnold [J. Chem. Phys. 117, 2496 (2002)], and employs an exact relation between the 2D+h system and a three-dimensional (3D) periodic system. The terms connecting the two systems can be evaluated linearly in the number of charges. Thus, the method shows overall the scaling of the underlying method employed to handle the Coulombic 3D case. Moreover, our algorithm can accurately handle multiple polarization image charges due to the dielectric interfaces as well as all the periodic images due to the periodic boundary conditions and has full control over the errors depending on the underlying method used for the 3D periodic case.