Natural gas mixtures are inclusion compounds composed of major light hydrocarbon gaseous molecules (CH4, C2H6, C3H6, and C3H8). Previous ab initio calculations were mainly limited by the cluster models. For the first time, we report first-principles calculations on the stability and vibrational properties of the gas molecules inside the crystalline lattice of type II clathrate. In accordance with our calculations, the larger the size of guest molecule, the more stable the clathrate hydrate for small-sized alkane guest molecules (CnHm, n <= 3, m <= 8). The interaction energy per guest molecule gradually increases as the number of guest molecules increase for both sII pure and sII mixed hydrates. In addition, the vibrational frequencies of guest molecules trapped in sII hydrate are also simulated. The C-C stretching frequency shows a blue shift as the amount of guest molecules increase. Our theoretical results prove to be valuable insight for identifying the types of guest molecules from experimental spectroscopic data.