Magnesium is an understudied chemical element that is quite useful in materials science and may be an essential astrochemical building block for grain formation in proto-planetary disks. This work provides quantum chemical prediction for the vibrational and rovibrational spectra of the structurally similar magnesium hydride and magnesium fluoride monomers and dimers. Magnesium fluoride is commonly utilized in infrared-observing windows and is a known terrestrial mineral, sellaite. Magnesium hydride is likely to exist in various astrophysical environments. Comparison of the anharmonic quantum chemical spectral data computed in this work to known gas phase values for MgH2 is excellent with the computed 1584.1 cm(-1) antisymmetric Mg-H stretch less than 5 cm(-1) below experiment for example. The condensed phase vibrational attributions of the dimer, however, are less comparable with the present results potentially indicating that some of the previous assignments may need to be revisited. The magnesium fluoride monomer and dimer have no previous vibrational experimental results reported, and the work here should be solid predictions as to their spectral features for comparison either to laboratory work or potentially even to interstellar observations.