# Is this the correct way to calculate the Madelung constant?

I'm trying to compute the Madelung constant of the ZnS lattice. The method is as follows: The lattice is a face-centered-cubic with basis $S^-: (0,0,0)$ and $Zn^+: (1/4,1/4,1/4)$. The Madelung constant is $$\alpha=\sum_j \frac{q_j}{r_j}$$ where $q_j$ is the charge (in this case divided by the number of neighboring blocks) of $j$ and $r_j$ the distance to a fixed ion. Evjen's method tells us that we need to form blocks of neutral charge to obtain a good convergence.

I've chosen to start with two cubes and the origin is placed in the center of the face that is common to both cubes (so I have a block of size 1x1x2). Then, two get more precision I add two cubes in each direction (so in the second iteration I have a block of size 3x3x4).

The problem is that this method converges to $\alpha\approx 5.35$, when it should be $\alpha\approx 1.64$. Is this the correct block expansion? I've tried with other block and I get the same value.

I haven't included the code, because I think that the problem is in the block chosen.

• This question is a possible duplicate of scicomp.stackexchange.com/q/19780/15 – Juan M. Bello-Rivas Jan 2 '16 at 16:43
• @JuanM.Bello-Rivas I don't think so, because the ZnS has different structure than NaCl. For example the CsCl blocks have to be dodecahedron, not cubes. – jinawee Jan 2 '16 at 16:52