Fig. \ref{fig:stopping_power} shows a comparison of our calculated \(S_\text{e}\) with Srim-based model and experimental data. In the channeling case, the maximum of our calculated stopping is lower in value and velocity compared to the Srim database and the off-channeling case, and it decreases faster after the maximum.

For the off-channeling case, there is a better agreement between our \(S_\text{e}\) results with the Srim data in most of the range. In experiments, where trajectories are not necessarily finely controlled, the projectile does indeed explore core regions of the host atoms, and that is presumably why off-channeling simulations are a better representation for the most common experiments \cite{Dorado_1993}. At higher velocities (\(v > 4 ~\mathrm{a.u.}\)) further disagreement stems from combined effect of the lack of explicit deeper core electrons in the simulation and also size effects, as excitations of long wavelength plasma oscillations are artificially constrained by the simulation supercell \cite{Schleife_2015}. It is clear that a larger cell and eventually the inclusion of more core electrons would be necessary to obtain better agreement in this high velocity region that is out the of scope of this article.

Although experimental values have considerable vertical spread, our calculated stopping power is on the low side for most of the points and also below the fitted by Srim model \cite{Ziegler_2010}. While this was partially explained by taking into account off-channeling trajectories near the maximum of stopping, there are other possible intrinsic limitations of the approximations to the density functional theory used. Along this line, we would like to note that more sophisticated approaches, based on the dielectric and current-density response but including the exact many-body and dynamic exchange-correlation treatment, are available in the literature \cite{Nazarov_2007}. This type of advanced approaches which are beyond the current scope contain explicitly additional channels of dissipation not taken into account in our adiabatic exchange and correlation functionals, which can be relatively important. Given the aforementioned limitations of the orbital based method and the exchange and correlation used it is still reassuring to see agreement up to a few times the velocity of the maximum stopping and gives us confidence to make predictions in the lower velocity regime.

At low velocity we observe that the off-channeling and channeling simulated results collapse into a common curve, this effect has been seen in the simulations before \cite{Correa_2012,Schleife_2015,Ullah_2015}. The effect is that the computed quantity less sensitive to the precise geometry of the trajectory, as the geometric cross section increases. We speculate that this is because the effective binary cross section increases beyond the interatomic separation making the energy loss less sensitive the precise geometry of the environment.