Ab initio calculations are performed to investigate the host guest interactions and multiple occupancies of some sulfur-(H2S, CS2) and nitrogen -containing (N-2, NO, and NH3) molecules in dodecahedral, tetrakaidecahedral, and hexakaidecahedral water cages in this work. Five functionals in the framework of density functional theory are compared, and the M06-2X method appears to be the best to predict the binding energies as well as the geometries. Results show that N-2 and NO molecules are more stable in the 51264 cage, while NH3 and H2S prefer to stabilize in the 51262 cage. This suggests that the sI hydrates of NH3 and H2S exhibit higher stability than the sII structures and that sII NO hydrate is more stable than sI NO hydrate. N-2 is found to be more stable in type II structure with single occupancy and to form type I hydrate with multiple occupancy, which is consistent with the experimental observations. As to the guest molecule CS, it may undergo severe structural deformation in the 512 and 51262 cage. For multiple occupancies, the 512, 51262, and 51264 water cages can trap up to two N-2 molecules, and the 51264 water cage can accommodate two H2S molecules. This work is expected to provide new insight into the formation mechanism of clathrate hydrates for atmospherically important molecules.