9 cluster is not reflected instantaneously, as for MgO, but with a delay of about 500 fs. It requires an additional boost from momentum reflected by the first Ar layer to finally release the cluster. Moreover, so much energy has been deposited in the weakly bound Ar material that the substrate is seriously damaged by that forced “reflec- tion”. These significant differences between Ar and MgO substrate will also be seen in the energy analysis later on. into center-of-mass energy and intrinsic kinetic energy (from the motion relative to the center-of-mass). Let us first consider the case of reflection (upper panel). In the approaching phase, the cluster is accelerated by about 0.68 eV which is small compared to the initial energy 10.9 eV. Dramatic and fast changes emerge at impact time at 200 fs. The cluster kinetic energy exhibits a deep minimum. In that stage, almost all energy is stored in deformation. A large part of that deformation energy is quickly released showing up now as intrinsic kinetic energy of the cluster plus a smaller bit in translational energy. Another small fraction of energy is transferred to the substrate. The translational kinetic energy de- creases further on, because the departing cluster has to work against the attractive polarization interaction. Still, there remains sufficient translational energy to allow the cluster to finally escape, as in a very inelastic collision. Similar results are found for the soft (lower panel in figure 10) and robust deposition (middle panel). Again, only a small fraction of the energy is transferred to the substrate, another small fraction goes to the cluster center-of-mass oscillations, and the major part to intrin- sic energy of the cluster. Particularly interesting is the case of robust deposition (middle panel) where it requires a second bounce to stir up intrinsic cluster motion. Be- fore that, there is still enough energy in translation to allow a lateral hopping from one attractive MgO site to the next (see also figure 4). It is worthnoting that the average trend of the kinetic energy of MgO in figure 10 has a small, but nonvanishing, slope. The cluster con- tinues to exchange energy with the substrate on a very slow pace. That indicates a thermalization process which eventually leads to equidistribution of kinetic energies af- ter long time, however much beyond our simulation ca- pabilities. The present modeling includes an independent dynam- ics of the dipole moments of the oxygen anions in the substrate. It has been shown recently that a signifi- cant amount of energy can be stored in these degrees- A complementing view of the deposition dynamics is given by the kinetic energies. Figure 10 shows the time evolution of the kinetic energies for Na and MgO. The kinetic energy for the Na cluster is furthermore splitted FIG. 10: Time evolution of various contributions to kinetic energy for the collision of Na$_{8}$ with MgO(001) at three differ- ent initial kinetic energies as indicated. Contributions are : Total kinetic energy of the cluster ions (Na, thick curves), con- tributions due to center of mass motion (Na transl., dashes) and relative motion or heat (Na relat., dots), and total kinetic energy of the substrate (MgO, thin curves). FIG. 11: Time evolution of the dipole polarization energy in the MgO(001) substrate for the collision for Na$_{6}$ with MgO(001) at an initial kinetic energy of 8.16 eV (reflection case). D. Energy Transfer 1. Time evolution of energy components  0  0.2  0.4  0.6  0.8  0  0.5  1  1.5  2  2.5  3 E kin  (eV) time (ps) E $^{0}$$_{kin}$=0.109 eV  0  0.4  0.8  1.2  1.6 E kin  (eV) E $^{0}$$_{kin}$=1.09 eV  0  2  4  6  8  10  12 E kin  (eV) Na$_{8}$ leaves box E $^{0}$$_{kin}$=10.9 eV Na Na, transl. Na, relat. MgO  0  0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.8  0  100  200  300  400  500  600 dipole energy [eV] time [fs] Na$_{6}$ with MgO(001) E$_{kin}$ =8.16 eV