deletions | additions       diff --git a/Each_simulation_of_the_ion__.tex b/Each_simulation_of_the_ion__.tex  index 4deb5cb..d5e684e 100644  --- a/Each_simulation_of_the_ion__.tex  +++ b/Each_simulation_of_the_ion__.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.   Since the larger size effects are negligible this calculations 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.