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Time-dependent density functional theory coupled with molecular dynamics is used to study electronic excitations produced by energetic protons.  A plane-wave pseudopotential scheme is employed to solve the time-dependent Kohn-Sham equations for a moving ion in a periodic crystal.  The electronic excitations and the band structure determine the stopping power of the material and alter the interatomic forces for both channeling and off-channeling trajectories.   Our off-channeling results are in quantitative agreement with experiments, and at low velocity they unveil a crossover region of superlinear velocity dependence (with a power of $\sim 1.5$) in the velocity range $v = 0.1-0.3~\mathrm{a.u.}$, 0.07-0.3~\mathrm{a.u.}$,  which we associate to the copper crystalline electronic band structure. The results are rationalized by simple band models in connecting two  separate regimes. We find that the limit of electronic stopping $v\to 0$ is not as simple as phenomenological models suggest and it plagued by band-structureand non-linear  effects.