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In these calculations, we fix the coordinates of two C atoms, away from the absorbed Zr atom, in the graphene surface with the previously calculated and relaxed distances. The two fixed atoms neglect the movement of the graphene center-of-mass during relaxations. We relax all the other C atoms. We nullify the forces of the Zr atom in the x and y axes at every step while the z coordinate is relaxed. The total-energy mapping of the Zr atom on a graphene surface is shown in Fig. 5.
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