A computational laboratory experiment is described, which involves the advanced study of an atomic system. The students use concepts and techniques typically covered in a physical chemistry course but extend those concepts and techniques to more complex situations. The students get a chance to explore the study of atomic states and perform calculations at a high enough level to provide predicted emission lines in good agreement with literature results. The specific exercise described applies these methods to fifth period transition metals (ground-state systems) and to various configurations of several period two representative elements (both ground and excited states). The computations are performed with programs written by Froese Fisher and co-workers, which perform Hartree-Fock (HF), multiconfiguration HF, and configuration interaction calculations. Since these are atomic systems, the angular dependence of the orbital functions can be described by spherical harmonics (or combinations thereof), which leaves a differential equation in the radial coordinate that can be solved by numerical methods. The details involved in this exercise are presented along with some typical results.