Sulfur contaminants in industrial gas streams, such as hydrogen sulfide and mercaptans, must be eliminated due to safety and environmental considerations. Ionic liquids, as a new class of chemical compounds, are an alternative to conventional aqueous alkanolamine solutions currently used in absorption gas treatment processes. In this work, the solubilities of methyl mercaptan (CH3SH) and hydrogen sulfide gases in 1-butyl-3-methylimidazolium-based ionic liquids with tetrafluoroborate ([C4mim][BF4]), hexafluorophosphate ([C4mim][PF6]), trifluoromethanesulfonate ([C4mim][OTf]), and bis(trifluoromethylsulfonyl)imide ([C4mim][Tf2N]) anions have been studied using molecular dynamics (MD) simulation and a recently developed OPLS all-atom (OPLS-AA-0.8) force field. A new concept, the induced free volume, has been introduced in this work, which provides a realistic and precise connection between the thermodynamic entropic contributions to the dissolution process of CH3SH and H2S in the ionic liquids, on one hand, and the microscopic free/void volume induced as a result of the entrance of a gas solute molecule into the liquid structure, on the other hand. The thermodynamic energetic contributions were correlated to the CH3SH/H2S interaction with the ionic species of the ionic liquids. Quantum chemical energy decomposition analysis (EDA) was employed to calculate and analyze the binding interaction and nature of CH3SH/H2S interactions with the ionic species of ionic liquids. It was found that the van der Waals contributions to the interaction of CH3SH with ionic liquids are more significant compared to that of H2S, while the opposite conclusion could be deduced for the corresponding electrostatic contributions. Both CH3SH and H2S established equivalent hydrogen bonding interactions with the ionic liquids studied in this work. The diffusion coefficients of the ionic species, as well as the excess chemical potentials and Henry’s constants for the dissolution of CH3SH and H2S in the ionic liquids, were calculated by free energy perturbation technique (FEP) and compared with the MD simulated and experimental data, reported in the literature. It was concluded that the OPLS-AA-0.8 force field yields Henry’s constants and diffusivities that are in better agreement with the reliable experimental data corresponding to other OPLS versions reported to date.