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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,Calvayrac_2000,Mason_2007,Alonso_2008,Andrade_2009} to simulate the collision processes between the target electrons in a solid  and the ion (proton). In TDDFT-EMD method, 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 that it provides a reasonable set of approximations  to calculate the $S_\text{e}$ 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 target ($\mathrm{Cu}$) atom due to 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 TDKS equation can be written as (Hartree atomic units are used here):