deletions | additions       diff --git a/Each_simulation_of_the_ion__.tex b/Each_simulation_of_the_ion__.tex  index c141845..56a9226 100644  --- a/Each_simulation_of_the_ion__.tex  +++ b/Each_simulation_of_the_ion__.tex 
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To integrate the Brillouin zone a single $k$-point ($\Gamma$) was used.   The basis set is sampled with a $130~\mathrm{Ry}$ energy cutoff.  The projectile $\mathrm{H^+}$ is initially placed in the crystal and a time-independent 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.