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This paper presents ab initio calculations within the Density Functional Theory (DFT) for the structural and optoelectronic properties of the alkali metal hydrides LiH and NaH in rocksalt structure (B1). This study used the Generalized Gradient Approximation (GGA) of Wu-Cohen to consider the electronic exchange and correlation interactions. In addition, the Tran-Blaha modified Becke-Johnson exchange potential was used with the GGA approach (GGA-TBmBJ) to calculate the band structure with high accuracy. The structural properties, namely the lattice parameter, the bulk modulus, and the pressure derivative of the bulk modulus were determined and found to be generally in good agreement with other research findings. Furthermore, the energy band gaps, the Density Of States (DOS), the static and high-frequency dielectric constant, along the refractive index were addressed and analyzed. These results could be useful for hydrogen storage purposes. [ABSTRACT FROM AUTHOR]