We studied structural and dynamical properties of H (super -) absorbed in Mg 2 SiO 4 by ab-initio molecular dynamics. We first calculated the T = 0 equation of state of pure forsterite as a function of pressure, and we determined the relative stabilities of the olivine, beta -spinel, and spinel polymorphs. The results show that the ab-initio model successfully reproduces the known structural properties of the system. In the protonated phases, in agreement with experimental evidence, our computations show that H (super -) is absorbed preferentially in the beta -spinel phase. The most stable absorption site is located close to the O1 atom, which is coordinated by five Mg (super 2+) cations and not directly bound to Si. In addition to this stable absorption site, the computation reveals other low-energy positions, forming an extended network of hydrogen bonds, that could play an important role in the diffusion of H (super -) in beta -spinel. We analyze the dependence of structure and dynamics of the pure and protonated phases as a function of temperature and pressure.