This thesis examines the ground and excited electronic states of the uranyl (UO22+) and uranate (UO42-) ions using Hartree-Fock self-consistent field (HF SCF), multi-configuration self-consistent field (MCSCF), and multi-reference single and double excitation configuration interaction (MR-CISD) methods. The MR-CISD calculation included spin-orbit operators. Molecular geometries were obtained from self-consistent field (SCF), second-order perturbation theory (MP2), and density functional theory (DFT) geometry optimizations using the NWChem 4.01 massively parallel ab initio software package. COLUMBUS version 5.8.1 was used to perform in-depth analysis on the HF SCF, MCSCF, and MR-CISD potential energy surfaces. Excited state calculations for the uranyl ion were performed using both a large- and small core relativistic effective core potential (RECP) in order to calibrate the method. This calibration included comparison to previous theoretical and experimental work on the uranyl ion. Uranate excited states were performed using the small-core RECP as well as the methodology developed using the uranyl ion.