If one wants to go beyond the finger print method to interpret spectroscopic data and existing phases, in depth use of DFT can be quite relevant. This will be illustrated via some recent results, many involving Electron Energy Loss Spectroscopy in the low loss region.  The materials considered will be essentially a sodium battery compound Na_2/3FePO₄, the silicon alloy with lithium to be used as negative electrode in a lithium battery and  α-­‐MoO₃, in view of explaining the photochromic properties of related compounds.