Interaction energies between the guests CH4, C2H6, C3H8, and CO2 with hydrate cages are calculated using ab initio quantum mechanics (QM), and then fit to a Lennard-Jones (LJ) potential plus an electrostatic term to predict guest occupancies in the hydrate cavities. This procedure differs from that commonly used with the van der Waals and Platteeuw (vdWP) model in which the intermolecular potential parameters are fit to hydrate equilibrium pressures. The procedure here is seen to improve upon the vdWP model with Sloan's Kihara potential parameters when compared to Raman spectroscopy and NMR data for guest compositions in the hydrate cavities. The LJ potential fit to QM interaction energies is also used in our recently developed fugacity based model to predict hydrate equilibrium pressures. For the ethane hydrate below 287.4 K and the ethane-carbon dioxide mixed hydrate, the percent absolute average deviation (%AAD) from experimental hydrate equilibrium pressures is only 3.4 and 3.5, respectively. This is an improvement upon Sloan's vdWP model that has a 10.8 and 4.8%AAD, respectively for these systems.