The electrostatic potential energy, E, between a pair of ions of equal and opposite charge is:
where
:z = magnitude of charge on one ion
:e = elementary charge, 1.6022 C
:ε = permittivity of free space
::4ε = 1.112 C/(J·m)
:r = distance separating the ion centers
For a simple lattice consisting ions with equal and opposite charge in a 1:1 ratio, interactions between one ion and all other lattice ions need to be summed to calculate E, sometimes called the Madelung or lattice energy:
where
:M = Madelung constant, which is related to the geometry of the crystal
:r = closest distance between two ions of opposite charge