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 9adb3e4..7c76af2 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}\cite{Eugen_Schwarz_1991}\cite{Tang_2009}\cite{Sanville_2007}\cite{Henkelman_2006}\cite{Yu_2011}. As the proton gets closer to the $Cu$ atom, the fraction of charges increases tremendous showing back and forth movement of charges between the proton and $Cu$ atom. As 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.%