deletions | additions       diff --git a/Figure_ref_fig_charge_on_copper_bader_voronoi_shows__.tex b/Figure_ref_fig_charge_on_copper_bader_voronoi_shows__.tex  index 9e198e3..a89aaff 100644  --- a/Figure_ref_fig_charge_on_copper_bader_voronoi_shows__.tex  +++ b/Figure_ref_fig_charge_on_copper_bader_voronoi_shows__.tex 
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Figure \ref{fig:charge_on_copper_bader_voronoi} shows the values of the charge on a particular neighboring copper atom relative to its initial state due to proton with $v = 1.8 ~\mathrm{a.u.}$ as a function of proton position along the channeling trajectory. The bader analysis program is used to extract the charges on the $Cu$ atom from the time-dependent electronic charge density. Details of the bader analysis program can be found in \cite{Bader_Site,Eugen_Schwarz_1991,Tang_2009,Sanville_2007,Henkelman_2006,Yu_2011}. As the proton gets closer to the neighboring $Cu$ atom, the fraction of charges decreases gradually showing that the $Cu$ atom loosing charges to the proton. In the range $2.0 \text{to} 4.0~a_0$, ~\text{to} ~4.0~a_0$,  the $Cu$ atom loses the maximum fraction of charges which is the range where the proton is closest in the vicinity of the $Cu$ atom. As the proton gradually passes the $Cu$ atom, there is a back and forth movement of charges between the proton and $Cu$ atom. From $8.0~a_0$, where the proton is further away from the $Cu$ atom, the fraction of charges stabilizes since at that time there is less interaction. The decrease is seen again when the proton approaches the same $Cu$ atom by reentering the supercell.% %  %back and forth movement of charges between the proton and $Cu$ atom. When the proton gradually passes the $Cu$ atom, the fraction of charges stabilizes since at that time there is less interaction. The spike is seen again when the proton approaches the same $Cu$ atom by reentering the supercell.%