deletions | additions       diff --git a/section_Computational_and_Theoretical_Details__.tex b/section_Computational_and_Theoretical_Details__.tex  index 2036efc..324e395 100644  --- a/section_Computational_and_Theoretical_Details__.tex  +++ b/section_Computational_and_Theoretical_Details__.tex 
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\label{eq:tdks3}  \end{equation}  where the external potential is $\textit{V}_{ext}(\textbf r, t)$ due to ionic core potential, $\textit{V}_{H}(\textbf r, t)$ is the Hartree potential which describes the classical electrostatic interactions between electrons and $\textit{V}_{xc}(\textbf r, t)$ is the exchange-correlation (XC) potential. The spatial coordinate and time are represented by $\textbf r$ and $t$ respectively.  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} with time-dependent modifications \cite{Schleife_2012}.   The Kohn-Sham (KS) orbitals are expanded in a supercell plane-wave basis.  
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