Lekner type method for summing the dipole-dipole interactions in computer simulations of one- and two-dimensionally periodic systems

The Lekner type summations of the interaction energies for polar systems with periodicity in one and two directions are presented. In the derivation of the energy expressions we used the integral representation of the gamma function and Poisson summation formula-the approach developed by us in calculations of the Coulomb interaction energy. The worked out methods are compared with the Ewald type summations, and the formula for two-dimensional periodicity is applied in the molecular dynamics simulations of two systems composed of polar ellipsoidal particles.