6 -5  0  5  10  15  20  0  0.5  1  1.5  2  2.5 ionic z-coord. (a 0 ) time (ps) Na$_{8}$ leaves box E $^{0}$$_{kin}$=10.9 eV Na O Mg -5  0  5  10  15  20 ionic z-coord. (a 0 ) E $^{0}$$_{kin}$=1.09 eV -5  0  5  10  15  20 ionic z-coord. (a 0 ) E $^{0}$$_{kin}$=0.109 eV -10 -5  0  5  10 -10 -5  0  5  10 ionic y-coord. (a 0 ) ionic x-coord. (a$_{0}$) -10 -5  0  5  10 ionic y-coord. (a 0 ) -10 -5  0  5  10 ionic y-coord. (a 0 ) FIG. 4: Left : Time evolution of the ionic z -coordinates of Na$_{8}$ approaching MgO(001). Right : Projection of the Na and MgO trajectories into the x - y plane; the figures are vertically sorted by increasing initial kinetic energy : Soft deposition (top), robust deposition (center), reflection (bottom). mixed situation because the ions of the cluster will nec- essarily be placed above different sites. In the following, we will discuss deposition of Na$_{8}$ and Na$_{6}$ which have very different structures and so promise to show different deposition scenarios. As a first step in the analysis, we shall consider detailed ionic trajectories both perpendic- ular and parallel to the surface. The case of Na$_{8}$ is shown in figure 4. The cluster was injected with its symmetry axis pointing through a hollow site and with the lower ring facing closer to bridge sites. The top panels show a soft deposition where the initial kinetic energy is 0 . 109 eV (0 . 0136 eV per Na ion). The left upper panel shows that the cluster is slightly accelerated in the initial phase, due to the attraction from the surface. But that acceleration differs for the different ions on the lower ring because they approach different sites on the surface. At the same time, the cluster rotates in the x - y plane to bring the four ions of the lower ring closer to the attractive oxy- gen sites. One may spot that from the top view in the right upper panel. At the point of closest impact around 900 fs, the cluster transfers some momentum to the sur- face. The substrate ions are slightly displaced from their equilibrium positions and oscillate around their new po- sitions. The disturbance quickly decreases from layer to layer. The perturbation is negligible already in the fourth layer. The complicated detailed dynamics of the Na ions indicates that a major part of the translational kinetic energy is converted into heat, i.e. kinetic energy of the motion relative to the center of mass, as will be confirmed Figure 5 complements the view within showing a se- quence of snapshots of the detailed structure for each of the three cases discussed above. The uppermost panel for soft deposition nicely shows the initial rotation of the cluster to match the attractive oxygen sites. The further snapshots indicate the sizeable internal excita- tion, however remaining small enough to see at all times clearly the two-ring structure of Na$_{8}$. The middle panel for more robust deposition also presents the much larger cluster oscillations where the original cluster structure is often blurred, but reappears shortly at other times. That demonstrates the surprisingly good binding of Na clus- ters, particularly the Na$_{8}$ cluster with its magic electron configuration. The lowest panel shows the case of re- flection. Obviously, some ions would like to stick to the surface, but are finally caught back by the cluster which departs in a highly excited state. The bottom panels of figure 4 show a hard collision with initial kinetic energy E 0 kin = 10 . 9 eV. Internal clus- ter and excitation and surface perturbation are, of course, again larger. The new feature is that the cluster is re- flected from the surface and leaves the numerical box at about 1 ps, however with huge internal excitation. It is not clear whether the departing cluster will stay asymp- totically stable. That is beyond our simulation capacity. The middle panels of figure 4 show a more robust deposition dynamics with initial kinetic energy E 0 kin = 1 . 09 eV. The initial velocity is higher and the impact time comes earlier, now at 450 fs. The pattern remains, in principle, similar to the softer deposition. There is lit- tle momentum transfer to the substrate, strong internal excitation of the cluster, and the cluster is not departing too far from the impact point. However, perturbations are much larger, yielding larger amplitudes in vertical and lateral motion. As a consequence, the two rings of Na$_{8}$ are now not always clearly separated. Nevertheless the typical structure of Na$_{8}$ reappears from time to time as we will see later. The top-down projection of the tra- jectories (middle right panel of figure 4) indicates a new effect, a sideward drift from one adsorption site to the next equivalent site. This sideward drift is again induced by the interplay between attractive O and repulsive Mg sites. The chaotically moving Na ions explore a strongly corrugated surface which leads to occasional side kicks from the repulsive Mg sites. in section III D. Nevertheless, the cluster basically keeps its original structure during the whole simulation period of 9 ps. In particular the two rings, each made of four ions, always stay clearly separated from each other. The top-down projection of the trajectories (see right-hand side of figure 4) shows that the cluster as a whole (or its center of mass) remains oscillating around the point of impact. The remaining kinetic energy of the cluster does apparently not suffice to overcome the surface cor- rugation barriers. This is related to the fact that the Na$_{8}$ structure fits approximately well to the structure and binding distance of MgO, see section II F.