Comprehension of the basic concepts for the design of CO2-philic molecules is important due to the possibility for "green" chemistry in supercritical CO2 of substitute solvent systems. Lewis acid-base interactions and C-H center dot center dot center dot O weak hydrogen bonding were suggested as two key factors in the solubility of CO2-philic molecules. To isolate the stabilization energy of weak hydrogen bonding from the overall binding energy, high-level quantum mechanical calculations were performed for the van der Waals complexes of CO2 with methane, methylacetate, dimethylether, acetaldehyde, and 1,2-dimethoxyethane. Structures and energies were calculated at the MP2 level of theory using the 6-31+G(d) and aug-cc-pVDZ basis sets with basis set superposition error corrections. In addition, the single-point energies were calculated using recently developed multilevel methods. This study shows that the Lewis acid-base interaction has a significant impact on the complex stability compared to the C-H center dot center dot center dot O weak hydrogen bond. The additional stabilization energy of the cooperative weak hydrogen bond with alpha-proton of the carbonyl group was negligible on the enhancement of supercritical CO2 solubility. However, the stabilization energy was larger for the ether group, such that it may have an important role in increasing the supercritical CO2 solubility. Additional formation of cooperative weak hydrogen bonds may not further increase the solubility due to the stability reduction by steric hindrance.