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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} 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 $\mathrm(S_e)$ for metals. We compared our results with those contained in \textit{SRIM} database for the case of proton in Cu.   The energy transfered to the electrons of the host atom (Cu) ($\mathrm{Cu}$)  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} 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 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 package \textsc{Qbox}\cite{Gygi_2008}. The Kohn-Sham (KS) orbitals are expanded in the plane-wave basis around the atoms and the projectile. 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}. The advantages of using plane-wave approach is that, it conquers basis-size effects which was a drawback for earlier approaches 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 pseudopotentials from Troullier and Martins\cite{Troullier_1991}. 
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The time-dependent KS equation was then solved numerically by explicit time-integration scheme as described in \cite{Schleife_2012}. A time step of $0.121~\mathrm{attoseconds}$ was used which is below the stability limit for the numerical explicit time-integration scheme for these type of basis set. The wave functions were then propagated for several femtoseconds.  The total electronic energy $\mathrm(E)$ ($E$)  of the electronic system changes as a function of the projectile position $\mathrm(x)$ since the projectile deposits energy into the electronic system as it moves through the host atoms. The increase of $\mathrm{E}$ $E$  as a function of projectile displacement $\mathrm {x} $ $x$  enables us to extract the electronic stopping power \begin{equation}  S_e(x) = \frac{dE(x)}{dx} 
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\end{equation}  $S_e(x)$ has the dimension of a force $(E_h/a_0)$ and it is the drag force acting on the projectile.