deletions | additions       diff --git a/The_simulations_of_the_collisions__.tex b/The_simulations_of_the_collisions__.tex  index 103d303..5f12e33 100644  --- a/The_simulations_of_the_collisions__.tex  +++ b/The_simulations_of_the_collisions__.tex 
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Periodic boundary conditions are used throughout this study.   The supercell size was chosen so as to reduce the specious size effects while maintaining controllable computational demands.   The calculations used $(3\times3\times3)$ conventional cells containing 108 $108$  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.