In 1918 Born and Landé proposed that the lattice energy could be derived from the electric potential of the ionic lattice and a repulsive potential energy term.
where
:N is the Avogadro constant;
:M is the Madelung constant, relating to the geometry of the crystal;
:z is the charge number of the cation;
:z is the charge number of the anion;
:e is the elementary charge, equal to ;
:ε is the permittivity of free space, equal to ;
:r is the nearest-neighbor distance between ions; and
:n is the Born exponent (a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically).
The Born–Landé equation above shows that the lattice energy of a compound depends principally on two factors:
* as the charges on the ions increase, the lattice energy increases (becomes more negative),
* when ions are closer together the lattice energy increases (becomes more negative)
Barium oxide (BaO), for instance, which has the NaCl structure and therefore the same Madelung constant, has a bond radius of 275 picometers and a lattice energy of −3054 kJ/mol, while sodium chloride (NaCl) has a bond radius of 283 picometers and a lattice energy of −786 kJ/mol. The bond radii are similar but the charge numbers are not, with BaO having charge numbers of (+2,−2) and NaCl having (+1,−1); the Born–Landé equation predicts that the difference in charge numbers is the principal reason for the large difference in lattice energies.
Closely related to this widely used formula is the Kapustinskii equation, which can be used as a simpler way of estimating lattice energies where high precision is not required.