of-freedom when a metal cluster is deposited on an Ar surface[35, 36]. One can define a dipole energy which scales as the square of the dipole amplitudes. Figure 11 shows a typical result for the time evolution of the en- ergy contained in the oscillating dipoles in the case of reflection of Na$_{6}$ deposited on MgO. There is a small initial value which corresponds well to the finite initial distance of the Na cluster to the substrate. There is a large contribution at the time of closest impact. This part is dominated by (instantaneous) static polarization which would also be contained in a Born-Oppenheimer MD. The dipole energy falls back to lower values when the cluster departs from the substrate (see figure 6). But there remains some offset which corresponds to the en- ergy finally transferred to the dipole degrees of freedom. It amounts to about 2% of the impact energy, which is small compared to the other energetic observables, see figure 14 and corresponding discussion in section III D 3. In contrast to the case of Ar substrate, energy transfer to MgO dipoles has actually only a small effect for the overall ionic dynamics. But more subtle properties as optical response and trajectories of free charges (to be discussed in a subsequent publication) will be sensitive to such details. make the process insensitive to the actual cluster which is approaching. That is different for MgO. There is al- ways less energy absorption by the substrate and there is a strong dependence on the cluster configuration. Na$_{6}$ transfers more than twice as much energy as Na$_{8}$. The strong surface corrugation of MgO induces that sensitiv- ity to cluster geometry. Remind that Na$_{6}$ does not match very well to the MgO surface while Na$_{8}$ does (see section II F). 10 2. Energy transfers ”at” impact Notwithstanding asymptotic thermalization, the fast energy transfer to the substrate in the early stages is an interesting observable characterizing the collision pro- cess. Figure 12 shows the kinetic energy of the substrate soon after the collision, i.e. averaged over the first 2 ps after impact, as a function of the initial kinetic energy of the cluster E 0 $_{kin}$. Apparently the energy absorbed by the substrate is proportional to E 0 $_{kin}$. But the slope depends very much on cluster and surface types. The soft Ar sub- strate absorbs much more energy than MgO, typically a bit more than 50% of the initial kinetic energy. The softness and the rather small surface corrugation of Ar More information about what is happening directly around impact time can be obtained by reading off ob- servables at shorter time scales (shorter than the 2 ps used above). Figure 13 shows two such observables as a function of initial kinetic energy. The upper panel shows the energy gain in the approaching phase due to the ac- celeration by the polarization potential. It is defined as the difference of the first maximum of the cluster kinetic energy and the initial energy. Na$_{6}$ acquires slighlty more energy than Na$_{8}$ because it has a non-vanishing dipole moment which, in turn, enhances the polarization attrac- tion. There is a large gain in the low energy range (the regime of soft deposit), while the trend becomes very flat for fast collisions. This is probably due to a move from adiabatic to non-adiabatic relaxation processes in the surface. For very low impact velocities, the sur- face ions have time to follow the forces from the cluster, whereas for very high velocities the surfaces ions do not have enough time to respond before the cluster collides. The lower panel of figure 13 shows an attempt to quantify an “instantaneous energy loss”. To that end, we take dif- ference between the maximum kinetic energy before the impact and the next maximum after the impact. Obvi- ously the instantaneous energy transfer is practically the FIG. 13: Upper panel : The gain in kinetic energy of the clus- ter when approaching the MgO surface; lower panel : Instan- taneous energy loss, defined as the difference between max- imum kinetic energy before the impact and next maximum after impact. FIG. 12: Heating of the MgO or Ar substrate after impact of Na$_{6}$ and Na$_{8}$. The energy transfer to Ar is independent of the cluster structure, whereas the energy transfer to MgO is not. Na$_{6}$ transfers about twice as much energy as the compact Na$_{8}$.  0  1  2  3  4  5  6  0  2  4  6  8  10 inst. energy loss (eV) E 0 kin (eV) Na$_{6}$ Na$_{8}$ 0.55*E 0 kin  0.1  1  10 init. gain: (E kin max -E 0 kin )/E 0 kin Na6 Na8  0  0.5  1  1.5  2  2.5  3  3.5  0  2  4  6  8  10 E kin,substrate  (eV) E 0 $_{kin}$ (eV) Na$_{6}$ @MgO Na$_{8}$ @MgO Na$_{6}$ @Ar Na$_{8}$ @Ar