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
, 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).