When compressed with water or ice under high pressure and low temperature conditions, some gases form solid gas hydrate inclusion compounds which have higher melting points than ice under those pressures. In this work, we study the balance of the guest-water and water-water interaction energies that lead to the formation of the clathrate hydrate phases. In particular, molecular dynamics simulations with accurate water potentials are used to study the energetics of the formation of structure I (sI) and II (sII) clathrate hydrates of methane, ethane, and propane. The dissociation enthalpy of the clathrate hydrate phases, the encapsulation enthalpy of methane, ethane, and propane guests in the corresponding phases, and the average bonding enthalpy of water molecules are calculated and compared with accurate calorimetric measurements and previous classical and quantum mechanical calculations, when available. The encapsulation energies of methane, ethane, and propane guests stabilize the small and large sI and sII hydrate cages, with the larger molecules giving larger encapsulation energies. The average water-water interactions are weakened in the sI and sII phases compared to ice. The relative magnitudes of the van der Waals potential energy in ice and the hydrate phases are similar, but in the ice phase, the electrostatic interactions are stronger. The stabilizing guest-water "hydrophobic" interactions compensate for the weaker water-water interactions and stabilize the hydrate phases. A number of common assumptions regarding the guest-cage water interactions are used in the van der Waals-Platteeuw statistical mechanical theory to predict the clathrate hydrate phase stability under different pressure-temperature conditions. The present calculations show that some of these assumptions may not accurately reflect the physical nature of the interactions between guest molecules and the lattice waters.