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\textbf{Abstract}   We use The  time-dependent density functional theory coupled with molecular dynamics is used  to study electronic excitations produced by energetic protons ($\mathrm{H^+}$) in solid $\mathrm{Cu}$ over a wide range of proton velocities. A plane-wave pseudopotential scheme is employed to solve the time-dependent Kohn-Sham equations for a moving $\mathrm{H^+}$  ion in the $Cu$  crystal. These electronic excitations determine the stopping power of the material and alter the interatomic forces for both channeling and off-channeling trajectories.   Our off-channeling trajectories  results are in quantitative agreement with experiments (for off-channeling trajectories) the channeling nature of our simulations. experiments.  Also these present  results unveil a region of superlinear velocity dependence related to copper crystalline band structure.