The weak hydrogen bond is an important type of noncovalent interaction, which has been shown to contribute to stability and conformation of proteins and large biochemical membranes, stereoselectivity, crystal packing, and effective gas storage in porous materials. In this work, we systematically explore the interaction of methane with a series of functionalized organic molecules specifically selected to exhibit a weak hydrogen bond with methane molecules. To enhance the strength of hydrogen bond interactions, the functional groups include electron-enriched sites to allow sufficient polarization of the C-H bond of methane. The binding between nine functionalized benzene molecules and methane has been studied using the second order Moller-Plesset perturbation theory to reveal that benzenesulfonic acid (C6H5-SO3H) and phenylphosphonic acid (C6H5-PO3H2) have the greatest potential for efficient methane capture through hydrogen bonding interactions. Both acids exhibit efficient binding potential with up to three methane molecules. For additional insight, the atomic charge distribution associated with each binding site is presented.