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We investigate electrical properties of anhydrous and hydrous forsterite crystalwith 3.2 wt% water by using firstprinciples calculations.The calculation results indicate that the pressure weakly affects the electrical properties of anhydrous forsterite.Two types of defect configurations involving the two hydrogen atoms in different positions are considered.Type 1 involves the entrapment of two hydrogen atoms in a Mg vacancy,which demonstrates little effect on the electronic density of states(DoS) of the forsterite crystal.Type 2 corresponds to the replacement of one hydrogen atom into the Mg vacancy with the other one located in different orientations(free proton model).It is this configuration that can significantly change the DoS of the forsterite crystal.The gap energy of the free proton model derived at different orientations is in the range of 0.693-1.007eV.