Hydrogen desorption from hydride matrix is still an open field of research. Extensive abinitio molecular dynamics simulations are performed to characterize the desorption process at the interface MgH2-Mg. The numerical model succesfully repoduces the experimental desorption temperature for the hydride with and without Fe catalyst. Formation energies and work of adhesion are computed and linked to the desorption mechanism. Moreover a detailed analysis of the structural data reveals the role played by the catalysts in the lowering the desorption temperature.