deletions | additions       diff --git a/section_Computational_and_Theoretical_Details__.tex b/section_Computational_and_Theoretical_Details__.tex  index 07f8722..b28b50e 100644  --- a/section_Computational_and_Theoretical_Details__.tex  +++ b/section_Computational_and_Theoretical_Details__.tex 
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The Kohn-Sham (KS) effective potential $V_{KS}[n](\textbf R, \textbf r, t)$ is given as  \begin{equation}  V_\text{KS}[n](\{\textbf R_i(t)\}_i, \textbf r, t) = \textit{V}_{ext}(\{\textbf \textit{V}_\text{ext}(\{\textbf  R_i(t)\}_i, \textbf r, t) + \textit{V}_\text{H}[n](\textbf r, t) + \textit{V}_{XC}[n](\textbf \textit{V}_\text{XC}[n](\textbf  r, t) \label{eq:tdks3}  \end{equation}  where the external potential is $V_\text{ext}(\{\textbf R_i(t)\}_i, \textbf r, t)$ due to ionic core potential (with ions at positions $\mathbf R_i(t)$), $V_{H}(\textbf r, t)$ 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 and time coordinates are represented by $\mathbf r$ and $t$ respectively. The instantaneous density at time $t$ is denoted by $n(=n(t))$. $n(t)$.  Exchange-correlation potential is approximated by the LDA (cite PerdewZunger here), the singular (Coulomb) external potential is approximated by a norm-conserving pseudopotential, with $XX$ 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.