The detection of more than 100 giant planets orbiting nearby stars and 40 brown dwarfs (substellar objects) has invigorated the stellar and planetary modeling communities. While spectroscopic investigations of brown dwarfs (BD) have been performed, only one spectral feature, that due to atomic sodium, has been seen in only one extrasolar giant planet (EGP). Spectroscopic studies are necessary for characterizing these unique stellar and planetary systems. However, current BD and EGP atmospheric models are insufficient largely due to the lack of complete and accurate data for a number of molecules. To help address this problem, we propose that an undergraduate student investigate two relevant molecules. Specifically, the student, using existing codes based on state-of-the-art quantum-mechanical techniques, will calculate complete molecular line lists, with associated oscillator strengths, for NaH and NaCl. Following atomic Na, these are believe to be the next most abundant sodium species in BDs and EGPs and their detection would allow for a full accounting of the sodium elemental abundance for the first time in a BD or EGP. In this project, the student will get an introduction to the physics of diatomic molecules, will learn about the computational approach of the Numerov technique for solving a second-order differential equation and apply it in a practical problem, and will be exposed to the astrophysics of BDs and EGPs. The resulting data will be provided to atmospheric modelers and used to predict spectra of BDs and EGPs which can be compared to future observations from the next generations of space- and ground-based far infrared telescopes.