The thermodynamic properties of the hydrogen clathrate hydrate with cubic structure II and hexagonal ice l(h) have been investigated using both lattice dynamics and molecular dynamics methods with the aim of predicting the existence of the self-preservation phenomenon in the hydrogen hydrate. The statistical thermodynamics model with modifications describing host lattice relaxation, guest guest interactions and the quantum nature of guest behavior in clathrate hydrates has been applied to calculate the thermal expansion of the volume for both systems. The calculations show that the hydrate remains in a stable region within the phase diagram because the thermal expansion of the hydrate phase is limited by the thermal expansion of ice. The differences in thermal expansion should lead to the self-preservation effect with the application of additional pressure on the hydrate phase. Molecular dynamics simulations also show that the hydrate phase immersed in the ice phase is stable at ambient pressure, which is below the three-phase ice hydrate gas equilibrium conditions due to the formation of a hydrogen bonding network between the ice and hydrate structures. From a practical point of view this effect can be used for the storage and transport of hydrogen in the hydrate form. (C) 2015 Elsevier B.V. All rights reserved.