The state of the art in numerical simulation of soft X-ray absorption spectra at the L edge of different elements such zinc and gallium is presented. Significant progress has been achieved recently on the quality of the numerical simulation coming from qualitative agreement to a quantitative one. Moreover, it is possible to obtain the local density of states associated with each element. Works are in progress to take into account the different structural characteristics of materials such the lacunar aspect of solids or the distribution of vacancies inside clusters.