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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} 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}. \textsc{Qbox}\cite{Gygi_2008} with time-dependent modifications \cite{Schleife_2012}.  The Kohn-Sham (KS) orbitals are expanded in the a supercell  plane-wave basis around the atoms and the projectile. 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}. The advantages of using plane-wave approach is that, it conquers basis-size effects which was a drawback for earlier approaches 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 pseudopotentials from Troullier and Martins\cite{Troullier_1991}. Troullier-Martins 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). A single \textit{k} point ($\Gamma$) was used for integrations in the Brillouin zone. The density is sampled with 130 Ry mesh $130~\mathrm{Ry}$ energy  cutoff. 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). trajectory) following the method introduced by Pruneda et 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-center channeling) 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. 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 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 ($E$) of the electronic system changes as a function of the projectile position ($x$) since the projectile (forced to maintain its velocity)  deposits energy into the electronic system as it moves through the host atoms. The increase of $E$ as a function of projectile displacement $x$ enables us to extract the electronic stopping power power.  \begin{equation}  S_\text{e}(x) = \frac{\mathrm{d}E(x)}{\mathrm{d}x}