Greater understanding and accurate predictions of structural, thermochemical, and spectroscopic properties of chemical compounds is critical for the advancements of not only basic science, but also in applications needed for the growth and health of the U.S. economy. This dissertation includes new ab initio composite approaches to predict accurate energetics of lanthanide-containing compounds including relativistic effects, and optimization of parameters for semi-empirical methods for transition metals. Studies of properties and energetics of chemical compounds through various computational methods are also the focus of this research, including the C-O bond cleavage of dimethyl ether by transition metal ions, the study of thermochemical and structural properties of small silicon containing compounds with the Multi-Reference correlation consistent Composite Approach, the development of a composite method for heavy element systems, spectroscopic of compounds containing noble gases and metals (ArxZn and ArxAg+ where x = 1, 2), and the effects due to Basis Set Superposition Error (BSSE) on these van der Waals complexes.