To study the application of different potential forms to describe phase equilibrium for Structure I gas hydrates, molecular computations and sensitivity analyses were performed, and results were compared. Using 3-phase monovariant pressure-temperature data, "site-site" and "molecule-molecule" Lennard-Jones and Kihara potential parameters were fit via explicit quadrature calculations for water clathrates with guest molecules of methane (CH4), ethane (C2H6), and cyclopropane (C3H6). Although the Lennard-Jones and Kihara potential forms can be fit satisfactorily to experimental P-T data for ethane and cyclopropane hydrates using the van der Waals and Platteeuw model, they fail to predict accurately cage occupancies of methane hydrates. To correct the inherent inconsistencies of using fitted potentials, an H2O-CH4 bimolecular potential developed and validated in our earlier ab initio study(1) was employed. The intermolecular potential, mapped from first-principles calculations, captures the molecular interaction correctly when compared with experimental 2nd virial coefficient data. Predicted phase equilibria and cage occupancies for methane hydrates using the ab initio potential are in close agreement with experimental P-T data and measured cage occupancies. Moreover, use of this model independent potential helps to validate the van der Waals-Platteeuw statistical model(2), which is used almost exclusively to model the phase behavior of clathrate hydrates. Other potential forms including exp-6 were fit to the ab initio potential to predict phase equilibria, and Optimized Potential for Liquid Simulations (OPLS) was also used to predict cage occupancies. The comparison showed that only the first-principles ab initio potential is able to physically characterize both the microscopic and macroscopic behaviors of methane hydrates. The reasons for this are the following. (1) The ab initio potential is directly related to physical properties, whereas the parameters of pre-chosen potential forms are merely ad hoc fitted quantities. (2) Angular degrees of freedom need to be accurately included in "site-site" interaction potentials, and they are in the ab initio case, but not in the case of most potential forms currently used for calculations of hydrates.