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We observe in Figure~\ref{fig:log_stopping_power} is not as particularly simple.  In order to interpret the results we also  calculated the linear response stopping $S_\text{L}(n, v)$ \cite{Lindhard_1964} based on the Linhard RPA dielectric function $\epsilon_\text{RPA}$ for different effective densities $\rho$ \cite{Giuliani_2005}. \begin{equation}  S_\text{L}(n, v) = \frac{2 e^2}{\pi v^2} \int_0^\infty \frac{\mathrm{d}k}{k} \int_0^{k v} \mathrm{d}\omega\omega \Im {\varepsilon^{-1}_\text{RPA}(\rho, k, \omega)}  \end{equation}  (which assumes a proton effective charge of $Z_1 = 1$).  As shown in Fig.~\ref{fig:log_stopping_power}, for $v < 0.1~\mathrm{a.u.}$ the results mimics the response of an effective  electron gas with one electron per $\mathrm{Cu}$ atom. The resulting curves shown in Fig.~\label{fig:} agree with the shows that for $v > 0.3~\mathrm{a.u.}$ at least the 11 electrons per atom (full valence) behaves as the stopping electron gas.  We observe $S_\text{e}$ kink around $v \sim 0.1 ~\mathrm{a.u.}$ due to a mixture of $d$-band in the electronic density of states.   For energy loss our new results for $v \leq 0.06~\mathrm{a.u.}$, are primarily due to $s$-band electrons.   In the simulation we directly show a crossover region between the two linear regimes, and we find that the friction in direct proportion to the velocity with a power law of with exponent $1.455$.  The kink we found at $v = 0.1~\mathrm{a.u.}$ can be explained by conservation laws in the effective  homogeneous electron gas and general properties of electronic density of states in crystalline $\mathrm{Cu}$. The minimum energy loss with maximum momentum transfer from an electron to an ion moving with velocity $v$ are respectively $2\hbar k_\text{F}$ and $2\hbar k_\text{F} v$ (plus corrections of order $m_\text{e}/m_\text{p}$).   Therefore Due to Pauli exclusion only  electrons in the energy  range $E_\text{F} \pm 2\hbar k_\text{F} v$ can participate in the stopping process. Taking into account that DFT band structure predicts that the $\mathrm{d}$-band is $\Delta = 1.5~\mathrm{eV}$ below the Fermi energy, energy (see for example, Fig. 3(a) in Ref.~\cite{Lin_2008}),  that electron (band) effective mass are close to $1$ for and $k_\text{F} = 0.72$ for $\mathrm{s}$-electrons.   Based in this DFT ground state density of states  plus conservation laws we obtain an estimate of $v_\text{kink} = \Delta/\hbar/k_\text{F} = 0.081~\mathrm{a.u.}$ in qualitative agreement with the TDDFT prediction. The second (negative) kink at $v = 0.3~\mathrm{a.u.}$ is more difficult to explain precisely as the qualitative description in terms of $k_\text{F}$ become more ambiguous, but it is related to the point at which the whole conduction band (11 electrons) starts participating in the process.