Optical response of the sodium alanate system: $GW_0$-BSE calculations and thin film measurements

We calculate from first principles the optical spectra of the hydrides in the sodium alanate hydrogen storage system: NaH, $NaAlH_4$, and $Na_3AlH_6$. In particular we study the effects of systematic improvements of the theoretical description. To benchmark the calculations we also measure the optical response of a thin film of NaH. The simplest calculated dielectric functions are based upon independent electrons and holes, whose spectrum is obtained at the $G_0W_0$ level. Successive improvements consist of including partial self-consistency (so-called $GW_0$) and account for excitonic effects, using the Bethe-Salpeter equation (BSE). Each improvement gives a sizable blue shift or red shift of the dielectric functions, but conserves the trend in the optical gap among different materials. Whereas these shifts partially cancel at the highest ($GW_0$-BSE) level of approximation, the shape of the dielectric functions is strongly modified by excitonic effects. Calculations at the $GW_0$-BSE level give a good agreement with the dielectric function of NaH extracted from the measurements. It demonstrates that the approach can be used for a quantitative interpretation of spectra in novel hydrogen storage materials obtained via, e.g., hydrogenography