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same for Na$_{6}$ and Na$_{8}$ independent of their differences in structure; and the energy loss is approximately propor- tional to E 0 $_{kin}$. About half (more precisely around 55%) of the impact energy is withdrawn from the cluster in that first round. 

It is, furthermore, interesting to see how the ini- tially available energy is distributed over the various con- stituents. Such energy balance is shown in figure 14 as a function of E 0 $_{kin}$. All energies have been averaged over 2 ps after impact time. They are drawn relative to the maximum kinetic energy of the cluster before impact. The energy terms do not necessarily sum up to one be- cause the interaction between substrate and cluster is omitted, as well as the intrinsic potential energy of the cluster. Low energies ( < 2 . 72 eV for Na$_{8}$ and < 2 . 18 eV for Na$_{6}$) represent the regime of deposition. The largest amount of energy is used up here for intrinsic cluster motion combined with potential energy of the substrate. The latter is responsible for the attachment of the clus- ter to the surface. The higher energies represent the regime of reflection. The share of energies depends here on the cluster geometry. For Na$_{6}$, the translational mo- tion takes the lead, whereas the intrinsic motion shrinks to almost zero. That complies with the trajectories in figure 6 which show that the cluster is repelled from the surface with opposite orientation but only weakly per- 

## 3. Redistribution of initial kinetic energy 

<img src='content_image/376569.jpg'>

turbed structure. The reflection of the top ion seems to proceed independently from the five-fold ring. The ring hits first and departs first while the top ion is reflected later thus departing behind the ring. 

For both clusters, kinetic and potential energies of the MgO behave similar. For high E 0 kin in the reflection regime, potential and kinetic energy are equal. The clus- ter quickly transfers some momentum to the substrate at impact and then disappears. This leaves the sub- strate ions oscillating around their equilibrium positions in harmonic motion, associated to equipartition between kinetic and potential energy. For high E 0 kin in the soft landing domain, the situation is different. The poten- tial energy becomes the dominant contribution because the cluster is adsorbed and remains in contact with the surface. This distorts the surface and leads to a large po- tential energy. Polarization energy is dominating in the potential energy. But the isolated contribution from the oxygen dipoles, also shown in figure 14, is comparatively small. The polarization within the oxygen ions in fact remains small as compared to the polarization caused by the displacement of O versus Mg, each one carrying a net charge of ± 2 e . 

We have analyzed the dynamics of deposition of small Na clusters on an MgO surface taking up a well tested hi- erachical QM/MM modeling where the cluster electrons are treated quantum mechanically by time-dependent local-density approximation and the cluster ions as well as the substrate atoms by classical molecular mechanics. The dynamical polarizability of the substrate atoms is taken into account to describe correctly the strong po- larization effects in the cluster–material interaction. The results are compared to deposition on Ar surface which is much softer than MgO. 

Test cases were Na$_{6}$, which is a strongly oblate cluster with a finite dipole momentum, and the well bound and highly symmetrical Na$_{8}$. The general pattern are simi- lar : The clusters are very quickly stopped by the sub- strate, they transfer a rather small amount of energy to the substrate while acquiring strong internal excitation. For larger impact energies, the clusters are reflected from the surface. This reflection is, of course, inelastic and leaves the clusters departing in highly excited intrinsic motion. There are, on the other hand, significant differ- ences between the two cases, since the cluster geometry has a large influence on the dynamics. The main effects come from the strong surface corrugation of MgO(001). Na$_{6}$ does not match the surface structure and thus ac- quires significant lateral motion in contrast to Na$_{8}$ which keeps better on a vertical track. Moreover, Na$_{6}$ transfers more energy to the substrate than Na$_{8}$. 

In comparison to Ar(001) surface, we find a simi- lar energy range for deposition and reflection. The de- tails, however, differ dramatically. Deposition on Ar(001) 

## IV. CONCLUSIONS 

