deletions | additions       diff --git a/Each_simulation_of_the_ion__.tex b/Each_simulation_of_the_ion__.tex  index 92f117c..6017b2c 100644  --- a/Each_simulation_of_the_ion__.tex  +++ b/Each_simulation_of_the_ion__.tex 
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The projectile $\mathrm{H^+}$ is initially placed in the crystal and a time-\emph{independent} DFT calculation was completed to obtain the converged ground state results that are required for subsequent evolution.   We then perform TDDFT calculations on the electronic system with the moving proton.  Following the method introduced by Pruneda \emph{et al.} \cite{Pruneda_2005} the projectile is then allowed to move with a constant velocity subjected to a straight uniform movement along a $\langle 100\rangle$ channeling trajectory (also called hyper-channeling) which minimizes the collision of the projectile with the host atoms. atoms~\cite{Correa_2012,Schleife_2015,Pruneda_2007}.  In the off-channeling case the projectile takes random trajectories through the host crystal yielding a stronger interaction between the projectile and the core of the host atom due to the larger proximity.   The need to take into account off-channeling trajectories was described in Ref.~\cite{Schleife_2015}.