The Kapustinskii equation calculates the lattice energy U<sub>L</sub> for an ionic crystal, which is experimentally difficult to determine. It is named after Anatoli Fedorovich Kapustinskii who published the formula in 1956.
The calculated lattice energy gives a good estimation for the BornâÂÂLandé equation; the real value differs in most cases by less than 5%.
Furthermore, one is able to determine the ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known. This is useful for rather complex ions like sulfate (SO) or phosphate (PO).
Kapustinskii originally proposed the following simpler form, which he faulted as "associated with antiquated concepts of the character of repulsion forces".
Here, K<nowiki/>' = 1.079 J÷m÷mol<sup>âÂÂ1</sup>. This form of the Kapustinskii equation may be derived as an approximation of the BornâÂÂLandé equation, below.
Kapustinskii replaced r<sub>0</sub>, the measured distance between ions, with the sum of the corresponding ionic radii. In addition, the Born exponent, n, was assumed to have a mean value of 9. Finally, Kapustinskii noted that the Madelung constant, M, was approximately 0.88 times the number of ions in the empirical formula. The derivation of the later form of the Kapustinskii equation followed similar logic, starting from the quantum chemical treatment in which the final term is where d is as defined above. Replacing r<sub>0</sub> as before yields the full Kapustinskii equation.