Optical response of the sodium alanate system:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">GW</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>-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${}_{3}$AlH${}_{6}$. 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 ${G}_{0}{W}_{0}$ level. Successive improvements consist of including partial self-consistency (so-called ${\mathit{GW}}_{0}$) 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 (${\mathit{GW}}_{0}$-BSE) level of approximation, the shape of the dielectric functions is strongly modified by excitonic effects. Calculations at the ${\mathit{GW}}_{0}$-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.