deletions | additions       diff --git a/section_Computational_and_Theoretical_Details__.tex b/section_Computational_and_Theoretical_Details__.tex  index 086a623..eaf3a0f 100644  --- a/section_Computational_and_Theoretical_Details__.tex  +++ b/section_Computational_and_Theoretical_Details__.tex 
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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 ($E$) of the electronic system changes as a function of the projectile position $\mathrm(x)$ ($x$)  since the projectile 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 \begin{equation}  S_e(x) = \frac{dE(x)}{dx}  \label{eq:stopping}   \end{equation}  $S_e(x)$ $S_\text{e}(x)$  has the dimension of a force $(E_h/a_0)$ $(E_\text{h}/a_0)$  and it is the drag force acting on the projectile.