Molecular beam scattering experiments are used to investigate the extent of thermal accommodation of Ne, CD4, ND3, and D2O in collisions with long chain CH3, NH2, and OH terminated self-assembled monolayers (SAMs) on gold. Surface rigidity, internal degrees of freedom of the impinging gas, and potential energy surface well depths have been explored as a way to predict the outcome of a gas-surface collision. Ne is used to assess the mechanical rigidity of the SAMs. The order of rigidity is CH3 < NH2 ~ OH. The NH2 and OH terminated SAMs are more rigid due to the intermolecular hydrogen bonding structure at the gas-surface interface. Despite the hydrogen bonding nature of the NH2 and OH terminated SAMs CD4, ND3, and D2O are extensively thermally accommodated on the surfaces, therefore surface rigidity is no solely responsible for energy transfer dynamics. It was found that the number of degrees of freedom do not predict how extensively a gas will thermally accommodate on a surface capable of hydrogen bonding. A qualitative correlation between increasing potential energy well depths and the extent of thermal accommodation has been established as a result of these scattering experiments.