deletions | additions       diff --git a/Each_simulation_of_the_ion__.tex b/Each_simulation_of_the_ion__.tex  index d5e684e..82c6986 100644  --- a/Each_simulation_of_the_ion__.tex  +++ b/Each_simulation_of_the_ion__.tex 
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Since the larger size effects are negligible this calculation used $(3\times3\times3)$ conventional cells containing $108$ host $\mathrm{Cu}$ atoms and $\mathrm{H^+}$.  % also represented by a Troullier-Martins pseudopotential ($17$ valence electrons per copper atom are explicitly considered).   To integrate the Brillouin zone a single $k$-point ($\Gamma$) was used.   The basis set is sampled with a $130~\mathrm{Ry}$ energy cutoff. We tested for k-point convergence in a 3x3x3 Morkost-Pack grid with negligible differences of 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 for subsequent evolution.   We then perform TDDFT calculations on the electronic system with the moving proton.