  I propose a method to calculate logarithmic interaction in two dimensions and
coulomb interaction in three dimensions under periodic boundary conditions.
This paper considers the case of a rectangular cell in two dimensions and an
orthorhombic cell in three dimensions. Unlike the Ewald method, there is no
parameter to be optimized, nor does it involve error functions, thus leading to
the accuracy obtained. This method is similar in approach to that of Sperb [R.
Sperb, Mol. Simulation, 22, 199 (1999).], but the derivation is considerably
simpler and physically appealing. An important aspect of the proposed method is
the faster convergence of the Green function for a particular case as compared
to Sperb's work. The convergence of the sums for the most part of unit cell is
exponential, and hence requires the calculation of only a few dozen terms. In a
very simple way, we also obtain expressions for interaction for systems with
slab geometries. Expressions for the Madelung constant of CsCl and NaCl are
also obtained.
