[AshleyA]

If you had a simple cubic lattice with d(MgO)=2.10A. How would you calculate the electrostatic energy of a single magnesium in the presence of its first and second nearest neighbour oxygens, and it's nearest neighbour magnesium ions. what equation do you use? I know what the answer but I don't understand it. The solution is E=332(+2)(-2)kcal/mol * ((-6/r) +  (12/(root2)*r)   +(-8/(root 3)*r) ) I know what r is  it's 2.1A but I don't know where they are getting this part of the expression from:                           ((-6/r) +  (12/(root2)*r)   +(-8/(root 3)*r) ) and What equation is being used. Is there a name for it? Thanks

[bodegas]

Again, I don't know if i can help, but I'd be glad to just start some ideas that others could explore further...

What I think the equation means is that you have to take into account the distances to the nearest atoms in the cubic lattice. Consider the atoms displayed in a square like below, blue atoms are magnesium and white are oxygen (I know it's lousy but it was handmade in a hurry). Now, the distance from the atom of magnesium to the oxygen is 2,1 A, and as they are of opposite charges, they attract each other, hence the (-) signal. The distance from the center magnesium to the nearest one, on the corners of the square is given by h²=a²+b², so arises a factor of (root2)*r to the distance. The charges of the atoms are the same so they repel, hence the (+) signal. Now consider the whole cube and consider the distance from the center magnesium atom to the corners of the cube, occupied with, again, oxygen atoms (again a - signal), and you will see that the distance is (root3)*r.
I guess this specific equation has no name as it is just specific to the geometry of the problem (a cubic lattice).

[Borek]

Simple geometry (plus Coulomb's Law) is all needed here.

Check out Madelung constant.

[bodegas]

Exactly...
this is nothing more than an appliction of Coulomb's Law.
Thanks for the reminder, Borek

(Where did all my physics go...? )