Simple route to lattice energies in the presence of complex ions.

Lattice energies for ionic materials which separate into independent gaseous ions can be calculated by standard Born-Haber-Fajans thermochemical cycle procedures, based on the energies of formation of those ions. However, if complex ions (such as sulfates) occur in the material, then a sophisticated calculation procedure must be invoked which requires allocation of the total ion charge among the atom components of the complex ion and evaluation of the attractive and repulsive energy terms. If, instead, the total ion charge is allocated to the central atom of the complex ion (with zero charge on the coordinated atoms), to create a "condensed charge ion" (having zero self-energy), then a straightforward calculation of the electrostatic (Madelung) energy, E(M)', correlates well with published lattice energies: U(POT)/kJ mol(-1) = 0.963E(M)', with a correlation coefficient, R(2) = 0.976. E(M)' is here termed the "condensed charge" electrostatic (Madelung) energy. Thus, using the condensed charge ion model, we observe that a roughly constant proportion (∼96%) of the corresponding lattice energy arises from the electrostatic interaction terms. The above equation permits ready evaluation of lattice energies for ionic crystal structures containing complex ions, without the necessity to estimate any of the problematic nonelectrostatic interaction terms. A commentary by Prof. H. D. B. Jenkins substantiating this analysis is appended.