Here rij is the distance between the charges i and j. So there are six boxes at a distance of L form the coordinates given by ( 
L, 0, 0), ( 0, L, 0), ( 0,0, L).We are able to see only four of such boxes as it is 2D in nature.So the contribution of the charge-charge interaction between the charges in the central box and all images of all particles in the six surrounding boxes is given by:
So for a box which positioned at a lattice point n=(nxL,nyL,nzL) we have
It should be noted that the interactions between pairs of charges in the central box are only taken. Thus the total contribution is the interaction of the particles in the central box and the all image boxes. Another resulting interaction is between the spherical array of boxes and the surrounding medium. Equation 27 results in a conditionally convergent series. This implies that the series contains a mixture of positive and negative terms and the sum of each of them is divergent when taken alone.Use of a proper equation allows us to compute the sum of equation 27.Consider the equation
Thus the objective of the equation will be to choose a particular function f(r) in such a manner that it can handle fast variation of 1/r at small values of r and slow variation at long value of r. In the ewald method each charge is is surrounded by a neutralizing charge distribution of of equal magnitude but of opposite sign (see figure 13 below).A commonly uses function is of the from called as Gaussian Distribution[Leach,2001] i.e
