For what concerns the basis sets we briefly present plane wave codes, codes with atomic-like localized basis sets, and all-electron codes.

All-electron codes involve no pseudoization scheme as all electrons are treated explicitly, though not always on the same footing. In these codes, a spatial distinction between spheres close to the nuclei and interstitial regions is introduced. Wave functions are expressed in a rather complex basis set made of different functions for the spheres and the interstitial regions. In the spheres, spherical harmonics asso­ciated with some kind of radial functions (usually Bessel functions) are used, while in the interstitial regions wave functions are decomposed in plane waves. All electron codes are very computationally demanding but provide very accurate results. As an example one can mention the Wien2k5 code, which implements the FLAPW (full potential linearized augmented plane wave) formalism.6

At the other end of the spectrum are the codes using localized basis sets. The wave functions are then expressed as combinations of atomic-like orbi­tals. This choice of basis allows the calculations to be quite fast since the basis set size is quite small (typi­cally, 10-20 functions per atom). The exact determi­nation of the correct basis set, however, is a rather complicated task. Indeed, for each occupied valence orbital one should choose the number of associated radial Z basis functions with possibly an empty polar­ization orbital. The shape of each of these basis functions should be determined for each atomic type present in the calculations. Such codes usually involve a norm-conserving scheme for pseudoization (see the next section) though nothing forbids the use of more advanced schemes. Among this family of codes, SIESTA7,8 is often used in nuclear material studies.

Finally, many important codes use plane waves as their basis set.9 This choice is based on the ease of performing fast Fourier transform between direct and reciprocal space, which allows rather fast calcula­tions. However, dealing with plane waves means using pseudopotentials of some kind as plane waves are inappropriate for describing the fast oscillation of the wave functions close to the nuclei. Thanks to pseudopotentials, the number of plane waves is typi­cally reduced to 100 per atom.

Finally, we should mention that other basis sets exist, for instance Gaussians as in the eponymous chemistry code10 and wavelets in the BigDft project,11 but their use is at present rather limited in the nuclear materials community.