Lekner summation of long range interactions in periodic systems

We present a complete set of practical expressions for fast and accurate evaluation of Coulomb interactions, forces and energies, in any rectangular periodic medium. This analysis also includes explicit expressions for energy constants and self-energies of charged particles in periodic lattices. Energy constants and self-energies are further evaluated for logarithmic interactions in two-dimensional rectangular systems with periodic boundary conditions. The expressions are optimized for computational speed and tested by direct numerical implementation.