This dissertation focuses on the computational chemistry predictions of the mechanisms and products of Lewis acid gases with materials of interest to understand the chemistry of these systems and to aid in the design of practical sorbents for acid gas separations and conversions. A detailed computational investigation of the species present prior to the introduction of a sorbent was performed. The barriers and overall thermodynamics of H2SO4, H2SO3, H2S2O3, and H2S2O2 formation from the reactions of SOx (x = 2 or 3) with H2O and H2S in both gas phase and in aqueous solution as well as the resulting acidities of these Brønsted acids were predicted. These calculations were performed using the Feller-Peterson-Dixon (FPD) methodology with implicit MP2/aug-cc-pVTZ/COSMO corrections included for predicting energies in aqueous solution and predict favorable formation of strongly acidic H2SO4 and the experimentally elusive H2S2O3. The thermodynamics of a novel type of NO2 adsorption to Groups IV and VI transition metal oxide clusters, calculated at the CCSD(T)//B3LYP level, are compared directly to the previously predicted binding energies of CO2, SO2, and H2O to these oxides and correlated with the M-O bond dissociation enthalpy, vertical excitation energy, electron affinity, and ionization potential trends of the bare metal oxides themselves. The results provide key insight into the importance of band gaps and M-O bond strengths for the selection of metal oxides for NOx separations. The role of 4f electrons and the surrounding ligand environment on the acid gas interactions of H2O, NO2, and SO2 with a promising class of metal-organic frameworks (MOFs), the rare-earth 2,5-dihydroxyterephthalic acid frameworks, was studied using DFT for both a cluster model which explicitly treats the lanthanide 4f electrons and a periodic model to predict bulk interactions without the inclusion of active 4f electrons. Insight into the reaction mechanisms of the promising post-combustion capture of CO2 by aqueous and solid-state amines was studied primarily using the composite G3(MP2) methodology. As a whole, these studies provide a detailed understanding of the chemical thermodynamics and kinetics relevant to acid gas capture by promising materials of interest.