A classical thermodynamic model for the equilibrium pressures of different guests of structure I and II gas hydrates is proposed that removes the need for reference energy parameters used in the van der Waals and Platteeuw (vdWP) type models. The assumption of a constant crystal lattice for different guests within a structure, which is not in agreement with quantum chemistry calculations, is removed. This model uses published Kihara cell potential parameters determined from viscosity and second virial coefficient data, unlike previous models that fit these parameters to hydrate data. Quantum mechanical calculations were used to reduce the number of fitted parameters in the new model. This model greatly improves upon the accuracy of previous models and is applicable over a wide temperature range. Percent absolute average deviations in the predicted equilibrium pressures is 3.27% with two or three guest-hydrate specific parameters compared to more than 11% with three adjustable parameters in the vdWP type models and 8.55% using a recent thermodynamic model that uses five guest-hydrate parameters.