Ab initio calculations are often compared to and sometimes confused with empirical potential calcu­lations. We will now try to clarify the differences between these two approaches and highlight their point of contacts. The main difference is of course that ab initio calculations deal with atomic and elec­tronic degrees of freedom. Empirical potentials depend only on the relative positions of the consid­ered atoms and ions. They do not explicitly consider electrons. Thus, roughly speaking, ab initio calcula­tions deal with electronic structure and give access to good energetics, whereas empirical potentials are not concerned with electrons and give approximate energetics but allow much larger scale calculations (in space and time).

Going into some details, we have shown that ab initio gives access to very diverse phenomena. Some can be modeled with empirical potentials, at least partly; others are completely outside the scope of such potentials.

In the latter category, one will find the phenomena that are really related to the electronic structure itself. For instance, the calculations of electronic excitations (e. g., optical or X-ray spectra) are concep­tually impossible with empirical potentials. In the same way, for insulating materials, the calculation of the relative stability of various charge states of a given defect is impossible with empirical potentials.

Other phenomena that are intrinsically electronic in nature can be very crudely accounted for in empir­ical potentials. The electronic stopping power of an accelerated particle is an example. As indicated above, it can be calculated ab initio. Conversely, from the empirical potential perspective one can add an ad hoc slowing term to the dynamics of fast mov­ing particles in solids whose intensity has to be estab­lished by fitting experimental (or ab initio) data. In a related way, some forms of empirical potentials rely on electronic information; for instance, the Finnis-Sinclair36 or Rosato et a/.37 forms. In the same spirit, a recent empirical potential has been designed to reproduce the local ferromagnetic order of iron.38 However, this potential assumes a tendency for ferromagnetic order, while ab initio calculation can (in principle) predict what the magnetic order will be.

Therefore, ab initio is very often used as a way to get accurate energies for a given atomic arrangement. This is the case for the formation and migration energies of defects, the vibration spectra, and so on. These phenomena are conceptually within reach of empirical potentials (except the ones that reincorpo­rate electronic degrees of freedom such as charged defects). Ab initio is then just a way to get proper and quantitative energetics. Their results are often used as reference for fitting empirical potentials. However, the fit of a correct empirical remains a tremendous task especially with the complex forms of potentials nowadays and when one wants to correctly predict subtle, out of equilibrium, properties.

Finally, one should always keep in mind that cohesion in solids is quantum in nature, so classical interatomic potentials dealing only with atoms or ions can never fully reproduce all the aspects of bonding in a material.