deletions | additions       diff --git a/section_Computational_and_Theoretical_Details__.tex b/section_Computational_and_Theoretical_Details__.tex  index aa1cf97..c413e39 100644  --- a/section_Computational_and_Theoretical_Details__.tex  +++ b/section_Computational_and_Theoretical_Details__.tex 
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The projectile was initially placed in the crystal and the time-independent DFT calculation was implemented to obtain the solutions for the initial condition of the electronic system for the ground state for subsequent evolution. We then perform TDDFT calculations on the electronic system. The projectile is moved with a constant velocity subjected to a straight uniform movement along a [100] channeling trajectory (also called hyper-channeling trajectory). This is done to minimize the collision of the projectile with the host atoms. Also the projectile is subjected to a random trajectory through the host material (also called off-center channeling) in order to assess sensitivity to the ideal hyper-channeling conditions. In this case, there is a stronger interaction between projectile and host atoms because the charge density in the proximity of the host atoms is larger.  The time-dependent KS equation was then solved numerically by explicit time-integration scheme as described in \cite{Schleife_2012}. A time step of $0.121~attoseconds$ $0.121~\mathrm{attoseconds}$  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 $femtoseconds$. 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 
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