deletions | additions       diff --git a/Figure_ref_fig_charge_on_proton_bader_voronoi_shows__.tex b/Figure_ref_fig_charge_on_proton_bader_voronoi_shows__.tex  index c92868b..b0d7843 100644  --- a/Figure_ref_fig_charge_on_proton_bader_voronoi_shows__.tex  +++ b/Figure_ref_fig_charge_on_proton_bader_voronoi_shows__.tex 
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Figure \ref{fig:charge_on_proton_bader_voronoi} shows the electronic charge transfer values relative to the initial state during the proton trajectory as a function of its position in the crystal moving with velocity, $v = 1.8 ~\mathrm{a.u.}$. The charges (bader and voronoi) gain by the proton are extracted from the time-dependent electronic charge density by using a bader analysis program explained in details in \cite{Eugen_Schwarz_1991,Tang_2009,Sanville_2007,Henkelman_2006,Yu_2011}. The fraction of charges gained by the proton oscillates throughout its trajectory and more charges are gained when its closest to a neighboring $Cu$ atom. Before the proton reenters the periodic supercell ($\gtrsim 20.46~a_0$) the maximum charges gained remains relatively constant but gradually starts increasing after reentering showing that the proton is picking up more charges from the target atoms.%  %Since the proton is placed in the crystal before the ground state calculation, it has obtained a charge of $1.2292$ which is expected just before it starts moving in the crystal. Each time the proton crosses a unit cell the value of the charge oscillate per unit cell traversed.%  %