High-level quantum chemical methods play an important role in our understanding of chemical mechanisms underlying catalytic/biochemistry reactions. This thesis focuses on applications of quantum chemical methods to investigate catalytic reaction mechanisms relevant to biochemistry and atmospheric chemistry. In addition, I use composite ab initio procedures for designing bio-inspired antioxidants based on the endogenous antioxidant carnosine. In particular, I focus on catalytic processes involving proton transfers in biologically relevant species and atmospherically relevant species. The combination of these approaches gives us the depth understanding reaction mechanism and thermochemical properties of the compounds using high-level quantum chemical methods.