In this paragraph, we try to give some indication of what can be done with an ab initio code and how it is done in practice. The calculation starts with the posi­tioning of atoms of given types in a calculation cell of a certain shape. That would be all if the calculations were truly ab initio. Unfortunately, a few more pieces of information should be passed to the code; the most important ones are described in the final section. The first section introduces the basic outputs of the code, and the second one deals with the possible cell sizes and the associated CPU times.

1.08.2.3.1 Output

We describe in this section the output of ab initio calculations in general terms. The possible applica­tions in the nuclear materials field are given below. The basic output of a standard ab initio calculation is the complete description of the electronic ground state for the considered atomic configuration. From this, one can extract electronic as well as energetic information.

On the electronic side, one has access to the elec­tronic density of states, which will indicate whether the material is metallic, semiconducting, or insulating (or at least what the code predicts it to be), its possi­ble magnetic structure, and so on. Additional calcula­tions are able to provide additional information on the electronic excitation spectra: optical absorption, X-ray spectra, and so on.

On the energetic side, the main output is the total energy of the system for the given atomic configura­tion. Most codes are also able to calculate the forces acting on the ions as well as the stress tensor acting on the cell. Knowing these forces and stress, it is possible to chain ground-state calculations to perform various calculations:

• Atomic relaxations to the local minimum for the

atomic positions.

• From the relaxed positions (where forces are zero), one can calculate second derivatives of the energy to deduce, among other things, the phonon spec­trum. This can be done either directly, by the so — called frozen phonon approach, or by first-order perturbation theory (if such feature is implemen­ted in the code). In this last case, the third-order derivative of the energy (Raman spectrum, phonon lifetimes) can also be computed.

• Starting from two relaxed configurations close in space, one can calculate the energetic path in space joining these two configurations, thus allowing the calculation of saddle points.

• The integration of the forces in a Molecular Dynamics scheme leads to so-called ab initio molecular dynamics (see Chapter 1.09, Molecu­lar Dynamics). Car-Parrinello molecular dynam­ics18 calculations, which pertain to this class of calculations, introduce fictitious dynamics on the electrons to solve the minimization problem on the electrons simultaneously with the real ion dynamics.