deletions | additions       diff --git a/Each_simulation_of_the_ion__.tex b/Each_simulation_of_the_ion__.tex  index 1757746..f1bdcb4 100644  --- a/Each_simulation_of_the_ion__.tex  +++ b/Each_simulation_of_the_ion__.tex 
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Finite size effects are studied between 108 and 256 atoms in a supercell of $(3\times3\times3)$ and $(4\times4\times4)$ respectively in this simulation, the errors remain within 3\% in conformity with the earlier observation \cite{Schleife_2015}.  The plane-wave basis set is sampled with a $130~\mathrm{Ry}$ energy cutoff.   We also tested for k-point convergence in a $(3\times3\times3)$ Morkost-Pack grid (for the cubic  108-supercell), that which  would be equivalent to a 2916 ($108\times 27$ simulation cell of an hypothetical periodic system, including replicas of the proton), for selected velocities with negligible differences within 0.08\%.  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 as the initial condition for subsequent evolution with the moving projectile.