The present study focuses on the impact of the vibrational frequencies on the thermodynamic behavior of hydrides, deuterides and tritides, using high scale harmonic phonon calculations based on first-principle calculations. 115 M H y hydrides were considered, for y={0.5, 1, 2} with M among 30 metallic elements. The results were found in excellent agreement with the available experimental data and pointed out trends on the evolution of the hydride zero point energy as a function of the crystal structure and the host metal nature. Based on these information, the vibration contribution to the formation enthalpy was deduced. This contribution is responsible for the differences between the enthalpies and therefore pressures of formation of the hydride, deuteride and tritide compounds. This so-called "isotope effect" is experimentally observed but has never been studied by large scale calculations. A straightforward method has been developed allowing to quantify the isotope effect at non zero temperature. It explains the experimentally observed relative stability of hydride, deuteride and tritide compounds. As a major achievement, a new phenomenon was highlighted, which has never been anticipated, consisting in an inversion of the isotope effect when the temperature increases.