Predicting structural energies of atomic lattices

The complexity of current ab initio quantum-mechanical calculations of the total energy of given distributions of atoms on a periodic lattice often limits explorations to just a few configurations. We show how such a small number of calculations can be used instead to compute the interaction energies of a generalized Ising model, which then readily provides predicted energies of many more interesting configurations. This is illustrated for AlAs/GaAs systems.