deletions | additions       diff --git a/Fig_ref_fig_force_on_neighbor_shows__.tex b/Fig_ref_fig_force_on_neighbor_shows__.tex  index 6a650e6..8ddc6a1 100644  --- a/Fig_ref_fig_force_on_neighbor_shows__.tex  +++ b/Fig_ref_fig_force_on_neighbor_shows__.tex 
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The force is obtained by the application of the Hellmann-Feynman theorem \cite{Hellmann_2015,1941,Feynman_1939}.   The adiabatic force is recovered for $v \to 0$ with no oscillations as expected.   The maximum value for the force is obtained at the closest distance between $\mathrm{H^+}$ and neighbor $\mathrm{Cu}$ atom.  As the proton moves away from the $\mathrm{Cu}$ atom, the force decreases significantly and eventually reduces to zero. As the velocity increases the position of the maximum value of the force shifts due to the complex shape-structure of the curves and results oscillations. Oscillations in the force persist for velocities above $1.0 ~\mathrm{a.u.}$, an interpretation in terms of plasmon excitations is given in \cite{Correa_2012}.  %These oscillations becomes persistent as the velocity of the proton increases.%