deletions | additions       diff --git a/section_Computational_and_Theoretical_Details__.tex b/section_Computational_and_Theoretical_Details__.tex  index 47af6de..26b7a49 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 $0.121 attoseconds$ 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 $\mathrm(E)$ of the electronic system changes as a function of the projectile position $\mathrm(x)$ since the projectile deposits energy into the electronic system as it moves through the host atoms. The increase of $\mathrm(E)$ as a function of projectile displacement $\mathrm(x)$ enables us to extract the electronic stopping power  \begin{equation}  S(x) = \frac{dE(x)}{dx}  \label{eq:stopping}   \end{equation}