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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 $m_\text{e}/m_\text{p}$).   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 $\Delta_\text{DFT}  = 1.5~\mathrm{eV}$ 1.6~\mathrm{eV}$  below the Fermi 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. $\mathrm{Cu}$ $\mathrm{s}$-electrons \cite{Ashcroft_2003}.  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. In reality, the $\mathrm{d}$-band is about $\Delta_\text{exp} = 2~\mathrm{eV}$ below the Fermi energy, that means that both the DFT-based estimate and the TDDFT result should be giving an underestimation of \%25 of the kink location.