Examples of hidden numerical tricks in a solid state determination of electronic structure.

The paper focuses on the numerical aspects of the atomistic modelling of materials in the Density Functional formalism. As usual in such a modelling, calculations can be run at various levels of theory and using different numerical options. After a review of the approximations underlying the Local Density Approximation (LDA), the Local Spin Density Approximation (LSDA), etc. the numerical options regarding the size of the basis functions, the use of pseudo-potentials or the selection of k-points are examined in details as well as the subsequent numerical tricks occuring in the calculations, e.g. in geometry optimizations. Finally, results regarding an apatitic mineral are reported and orders of magnitudE' of the expected accuracy are provided.