We have studied systems with typical hydrogen bonding and others with interaction involving hydrogen. CH4-CH4, CH4-H2O, CHF3-CH4, and CHF3-H2O dimers were studied using MPWB1K, PBE1PBE, MP2, and QCISD levels of theory with a large number of basis functions. The Pople 6-31+G(2d), 6-311++G(2d,2p), and 6-311++G(3df,3pd) as well as Dunning augmented aug-cc-pVDZ and aug-cc-pVTZ basis sets were used. The dimer geometries were fully optimized. An optimal basis set was determined for these systems to achieve a suitable compromise between accuracy and computational feasibility. A proper strategy was found for the electronic property calculations of dimers studied: the use of aug-cc-pVDZ as the optimal basis set at MP2 level. Dipole moments, polarizabilities, BSSE effects, and Delta ZPE were also analyzed for these dimers.