It is not possible to write down a single analytical equation that would relate e.g. elastic material properties or defect formation energies to the threshold displacement energy. Hence theoretical study of the threshold displacement energy is conventionally carried out using either classical or quantum mechanical molecular dynamics computer simulations. Although an analytical description of the displacement is not possible, the "sudden approximation" gives fairly good approximations of the threshold displacement energies at least in covalent materials and low-index crystal directions