Methane hydrates with the three clathrate structures I, II, and H are studied by quantum-chemical methods. Hybrid density-functional theory B3LYP computations using periodic boundary conditions are combined with force-field methods for the thermal energy effects to calculate energetic, thermodynamic, and structural properties. The pressure dependencies for the crystal structures, lattice energies, and guest molecule interactions are derived. The quantum-chemical geometry optimizations predict too small cell volumes as compared to experimental data, but by including zero-point energy and thermal energy effects, we find the cell volumes increase and the correct densities are obtained. The phase transition from MH-I to ice Ih and methane was computed and found to occur at about 9.7 MPa.