deletions | additions       diff --git a/Abstract.tex b/Abstract.tex  index a071c4d..cabafef 100644  --- a/Abstract.tex  +++ b/Abstract.tex 
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Time-dependent density functional theory coupled with molecular dynamics is used to study electronic excitations produced by energetic protons %($\mathrm{H^+}$)   in solid copper %$\mathrm{Cu}$   over a wide range of proton velocities. velocities $v = 0.01--10~\mathrm{a.u.}$.  A plane-wave pseudopotential scheme is employed to solve the time-dependent Kohn-Sham equations for a moving ion %$\mathrm{H^+}$ ion   in a periodic %$\mathrm{Cu}$   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 results are in quantitative agreement with experiments, and at low velocity they unveil a crossover region of superlinear velocity dependence (with exponent $\sim 1.5$) in the velocity range $v = 0.1-0.3~\mathrm{a.u.}$ that we associate to the copper crystalline electronic band structure.