deletions | additions       diff --git a/Figure_ref_fig_fit_graph_shows__.tex b/Figure_ref_fig_fit_graph_shows__.tex  index 570e0bc..5e5cee7 100644  --- a/Figure_ref_fig_fit_graph_shows__.tex  +++ b/Figure_ref_fig_fit_graph_shows__.tex 
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Figure \ref{fig:fit_graph} shows how we obtained the slopes of Figure \ref{fig:energy_distance}. In Figure \ref{fig:fit_graph}, the magenta curve shows the adiabatic potential energy surface (APES) curve at $v = 0 ~\mathrm{a.u.}$; which is obtained due to the Born-Oppenheimer approximation. The oscillations in the curves reflect the periodicity of the $\mathrm{Cu}$ lattice. At $v = 0 ~\mathrm{a.u.}$, there is no transfer of energy, just oscillations of the total energy with a zero slope. To obtain the slope for $v = 0.06 ~\mathrm{a.u.}$ which represents the $S_\text{e}$ at this velocity, we subtract the oscillations of the $v adiabatic curve ($v  = 0 ~\mathrm{a.u.}$ curve ~\mathrm{a.u.}$)  from $v = 0.06$ curve due to the non-adiabatic effect at velocities greater than $0 ~\mathrm{a.u.}$ to obtain the red line curve with little oscillations. This subtraction is done to remove the oscillations that result from the periodic lattice. A linear fit , $y = a + bx$ (blue line) gives a slope of $0.00714015~E_\text{h}/a_0$ $0.00698913~E_\text{h}/a_0$  with an error of $\pm 4.781 6.936  \times 10^{-6}~E_\text{h}/a_0$. 10^{-5}~E_\text{h}/a_0$.  We then proceed to do a linear fit in addition to an oscillatory function $y = a + bx + A\cos(k x + \phi)$ (black line) to capture any remnant oscillation. This oscillation fit gives a slope of $0.00743442~E_\text{h}/a_0$ $0.00743456~E_\text{h}/a_0$  with an error of $\pm 8.517 8.52  \times 10^{-7}~E_\text{h}/a_0$. For higher velocities, a linear fit alone is enough to obtain reasonable error values. values.%