How to calculate the lattice sums of BCC?

[ilovecubes]

How do I calculate the lattice sums A12 and A6 for a BCC structure?

I have calculated the following so far:

A12 = 8(1/1)^12 + 6(1/root2)^12 + 12(1/2)^12 + 16(1/root5.5)^12 + 8(1/root6)^12 = 8.097.

Have i made any mistakes? Are my nearest neighbour values correct? Please help!

 

[nasu]

How do I calculate the lattice sums A12 and A6 for a BCC structure?

I have calculated the following so far:

A12 = 8(1/1)^12 + 6(1/root2)^12 + 12(1/2)^12 + 16(1/root5.5)^12 + 8(1/root6)^12 = 8.097.

Have i made any mistakes? Are my nearest neighbour values correct? Please help!

Second nearest neighbors distance is a (lattice constant).
First n.n. distance is a*sqrt(3)/2 (half body diagonal)
So the coefficient in the second term should be (sqrt(3)/2)^12.