A study of reactions of laser-ablated thorium atoms and O2 using matrix isolation infrared spectroscopy has been conducted using electronic structure calculations to interpret the infrared spectra of three new thorium oxide species, ThO2-, Th2O2, and Th2O4 obtained in argon and neon matrixes. The potential energy surface for the reaction of matrix isolated ThO with CH4 to give the CH3Th(O)H intermediate has been calculated at the CCSD(T) level, it reveals that the CH3Th(O)H molecule possesses a pyramidal structure with a closed shell singlet ground state. Formation of the CH3Th-(O)H molecule from the reaction of ThO and methane has an energy barrier of 30 kcal/mol, which is consistent with the appearance of the 1CH3Th(O)H absorptions under broad band mercury arc UV irradiation. The 3Th + 1CH3OH asymptote is predicted to be 119 kcal/mol above the reactant asymptote, 1ThO + CH4, utilizing the spin orbit correction to the 3Th atom which is in excellent agreement with the value of 118.7 ± 3.8 kcal/mol. The first reliable predictions of the frequencies of the isolated uranyl ion have been made to develop new techniques to determine how this important form of uranium is being complexed in the environment. A comprehensive computational study of UO22+ complexed with the phosphate anions H2PO4-, HPO42-, and PO43- and water ligands has been performed at the density functional theory (DFT) and correlated molecular orbital theory levels in the gas phase and in aqueous solution. This study was done to aid the effort in developing solutions to the in situ remediation challenge posed by the nuclear waste stored in the tanks at the Hanford and Savannah River nuclear weapons production sites. This information can be used to provide a better understanding of the speciation of such species and to better our understanding of mobility issues of tank waste as well as stability concerns for waste matrices.