from free clusters. Their structures are shown in figure 2. Note that the vertical axis in the figure will represent the direction perpendicular to the surface in the forthcom- ing deposition processes ( z axis). Na$_{6}$ is strongly oblate consisting out of a ring of five ions topped by one sin- gle ion. Na$_{8}$ has a highly symmetric configuration out of two rings of each four ions tilted relative to each other by 45 ◦ to minimize Coulomb energy. The electronic cloud of Na$_{8}$ is close to spherical shape because N = 8 electrons correspond to a strong shell closure for Na clusters [40]. It is important to note that the bond distances for Na$_{8}$ (6.2 a$_{0}$ ) are not far from the diagonal distance between oxygen sites in the MgO(001) surface (5.7 a$_{0}$ ) while the dimensions of the fivefold ring in Na$_{6}$ do not fit well to the surface. That will play a role in the dynamical evo- lution studied later on. The equilibrium distance of the lower cluster plane (facing towards the surface) and the first surface layer is 5 a$_{0}$ . 

## A. Na monomer on MgO – the influence of sites 

A two component system like MgO has more possible adsorption sites than a homogeneous material like an ar- gon substrate. The properties of an oxygen site are much different from those of the magnesium site because of the much larger polarizability of oxygen. We will thus con- sider four positions with respect to the surface : O site, Mg site, hollow and bridge. The structure calculations of [37] have shown that O, due to its large polarizability, is the most attractive site while Mg acts like a repulsive site on the cluster. This is in agreement with quantum chemical ground state calculations of transition metals on MgO [58]. 

In order to check the adsorption properties of the var- ious sites, we first study the deposition dynamics of a Na monomer. We briefly remind the static properties of Na@MgO(001). The O site is most attractive, bind- ing Na 5 a$_{0}$ above the surface with energy 0.25 eV. The Mg site is dominantly repulsive. The hollow and bridge sites lie in between these extremes. For deposition dy- namics, the atom was initialized 15 a$_{0}$ away from the substrate above an O site, Mg site or hollow site respec- tively, each with an initial momentum along z direction, pointing perpendicular towards the surface with a mag- nitude corresponding to a kinetic energy E 0 kin = 0 . 136 eV. Figure 3 shows the results of the simulation. The z -coordinates are chosen such that the (average) MgO surface layer resides at z = 0. The simplest case is the impact on the O site. The atom approaches the surface up to a distance of 4 . 5 a$_{0}$ which is reached at about 500 fs and transfers part of its momentum to the substrate ions. The transfer proceeds at a very short time scale. The surface itself is excited mainly by the first collision which initially only affects the ions in the immediate vicinity of the atom at closest impact. The perturbation quickly 

## III. RESULTS AND DISCUSSION 

spreads over the surface, but the associated sound wave does not penetrate very deep into the surface. The os- cillations in the third layer are already almost negligible. After the instant of closest contact, the atom bounces back, but it has already lost so much energy that it can- not escape from the surface anymore. Thus it performs damped oscillations, with each bounce transferring some momentum to the surface and being practically adsorbed within the first 2 ps. The final distance approaches nicely the equilibrium distance of 5 a$_{0}$ . The right upper column of figure 3 shows the corresponding kinetic energy con- tributions. In the first 400 fs, the attraction from the MgO substrate leads to a rapid increase of the kinetic energy of the atom up to 0 . 45 eV. At the point of clos- est contact, the repulsive part of the interface potential stops the atom abruptly. That first collision transfers by far the largest amount of energy to MgO, whereas at all subsequent collisions the energy decreases more slowly. In order to check that the oscillations proceed only per- pendicular to the surface, the kinetic energy of the Na atom has been split into contributions from perpendicu- lar (or vertical) and parallel (or transverse) motion. The latter is too small to be visible in figure 3 and practi- cally negligible. Thus the motion of Na proceeds strictly perpendicular to the surface. The kinetic energy trans- ferred to the MgO can also be read off from figure 3 (see right upper panel). The contributions from oxygen and magnesium are given separately. Oxygen ions are the lighter species and therefore react first being quickly accelerated. About 100 fs later, the energy has already been distributed almost equally over both ion types. 

The dynamics behaves totally different if the atom im- pinges on the (repulsive) Mg site, see middle panels of figure 3. At first glance, the z -component of the Na tra- jectory looks quite similar to the case before. But one notes that the motion is not damped after the first re- flection. The kinetic energies (middle right panel) give a clue on the process. There is much less energy transfer at first impact which is related to the fact that the Mg 2+ ion is more inert. And there is a significant amount of lateral kinetic energy for the Na atom creeping up after impact time at 500 fs. In fact, most of the kinetic energy is now in lateral motion. The atom is deflected by the Mg 2+ ion. It is to be noted that the annealing of the substrate configuration leaves a small amount of symme- try breaking with fluctuations of the atomic positions of about 0.05 a$_{0}$. This small symmetry breaking allows the atom to acquire sidewards momentum and so it bounces away in sideward direction, hops over the surface sev- eral times changing direction whenever it comes close to another surface ion. The motion is almost undamped be- cause little energy is transferred to the surface after the first collision. The atom has thus still too much energy to be caught by a certain site of the surface. But as the atom cannot escape the surface as a whole, it will con- tinue to lose slowly energy and finally be attached to an oxygen site, long after the simulation time of 3 ps. 

The bottom panels of figure 3 show the case of impact 

