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The Perdew-Zunger's exchange-correlation \cite{Perdew_1992} is used, and the core electrons are represented using norm-conserving Troullier-Martins pseudopotentials\cite{Troullier_1991}.  Periodic boundary conditions were used throughout. The best supercell size was selected so as to reduce the specious effects of the duplication while maintaining controllable computational demands.   The calculations used $(3\times3\times3)$ supercells containing 108 host Copper atoms plus a proton, also represented by a Troullier-Martins pseudopotential (17 ($17$  valence electrons per copper atom are explicitly considered). A single \textit{k} point ($\Gamma$) was used for integrations in the Brillouin zone.   The density is sampled with $130~\mathrm{Ry}$ energy cutoff.