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\section{Computational and Theoretical Details}  In this work we employed the formalism of TDDFT coupled with Ehrenfest molecular dynamics (EMD)\cite{Gross_1996}\cite{Calvayrac_2000}\cite{Mason_2007}\cite{Alonso_2008}\cite{Andrade_2009} (EMD) \cite{Gross_1996,Calvayrac_2000,Mason_2007,Alonso_2008,Andrade_2009}  to simulate the collision processes between the target electrons and the ion (proton). In TDDFT-EMD, the dynamics of the electrons are treated quantum mechanically described by TDDFT and the nuclei are point particles treated classically using EMD. The strength of this method is used to calculate the electronic stopping power ($S_\text{e}$) for metals. We compared our results with those contained in \textsc{SRIM} database for the case of proton in $\mathrm{Cu}$. The energy transfered to the electrons of the host atom ($\mathrm{Cu}$) from a constant velocity moving proton is carefully monitored. The energy loss of the proton is negligible hence total energy of the system is not conserved. This is because at the time scales of the simulations, the large mass of the proton guarantees a negligible decline in its velocity. As the proton moves, the time-dependent Kohn-Sham (TDKS) equation\cite{Runge_1984} equation \cite{Runge_1984}  describes electronic density and energy of the system due to the dynamics of effective single particle states under the external potential generated by the proton and the crystal of Cu nuclei. The TDKS equation can be written as (Hartree atomic units are used here): \begin{equation}  \mathrm i\frac\partial{\partial t}\psi_i(\textbf r, t) = \left\{-\frac{\hbar^2\nabla^2}{2m} + V_\text{KS}[n(t)](\{\mathbf R_i(t)\}_i, \mathbf r, t)\right\}\psi_i(\textbf r, t) 
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Exchange-correlation potential is approximated by the LDA (cite PerdewZunger here), the singular (Coulomb) external potential is approximated by a norm-conserving pseudopotential, with $17$ explicit electrons per Cu atom in the valence band.  The simulations of the collisions consist of a well-defined trajectories of the projectile (proton) in the metallic bulk.   The calculations were done using the code \textsc{Qbox}\cite{Gygi_2008} \textsc{Qbox} \cite{Gygi_2008}  with time-dependent modifications \cite{Schleife_2012}. The Kohn-Sham (KS) orbitals are expanded in a supercell plane-wave basis.   These KS orbitals are evolved in time with a self-consistent Hamiltonian that is a functional of the density.   The algorithm for evolution of the orbitals is done using the fourth-order Runge-Kutta scheme (RK4)\cite{Schleife_2012}. (RK4) \cite{Schleife_2012}.  The advantages of using plane-wave approach is that, it conquers basis-size effects which was a drawback for earlier approaches\cite{Pruneda_2007} and finite-size error in the simulations are overcome by considering large simulation cells\cite{Schleife_2015}. The Perdew-Zunger's exchange-correlation \cite{Perdew_1992} is used, and the core electrons are represented using norm-conserving Troullier-Martins pseudopotentials\cite{Troullier_1991}. pseudopotentials \cite{Troullier_1991}.  Periodic boundary conditions were used throughout. The best supercell size was selected so as to reduce the specious effects of the duplication while maintaining controllable computational demands.   The calculations used $(3\times3\times3)$ supercells containing 108 host Copper atoms plus a proton, also represented by a Troullier-Martins pseudopotential ($17$ valence electrons per copper atom are explicitly considered).  
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The projectile was initially placed in the crystal and the time-independent DFT calculation was implemented to obtain the solutions for the initial condition of the electronic system for the ground state for subsequent evolution.   We then perform TDDFT calculations on the electronic system.   The projectile is moved with a constant velocity subjected to a straight uniform movement along a [100] channeling trajectory (also called hyper-channeling trajectory) following the method introduced by Pruneda {\emph  et al.\cite{Pruneda_2005}. al.} \cite{Pruneda_2005}.  This is done to minimize the collision of the projectile with the host atoms. Also the projectile is subjected to a random trajectory through the host material (also called off-channeling) in order to assess sensitivity to the ideal hyper-channeling conditions.   In this case, there is a stronger interaction between projectile and host atoms because the charge density in the proximity of the host atoms is larger. 
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\end{equation}  $S_\text{e}(x)$ has the dimension of a force $(E_\text{h}/a_0)$ and it is the drag force acting on the projectile.%  %