3 centers. We associate a similar smooth charge distribu- tion to the O 2 − valence cloud as well. This altogether yields a soft Coulomb potential to be used for all active particles. pared to electronic motion. True electronic excitations are thus extremely small. For example, ionization stays safely below a fraction of 0.001 electrons. It would then be well justified to use Born-Oppenheimer-MD rather than full TDLDA-MD, as long as one carefully main- tains the crucial dipole polarizability of the substrate. But the TDLDA-MD scheme is so efficient that it is still preferable for reasons of computing time. Remind that the dipole response of the substrate needs to be propa- gated at electronic time scale and dipole stepping is more economic than fully relaxing the dipoles in each Born- Oppenheimer step. The calibration of the whole model has to address three issues: The cluster as such, the environment as such, and the coupling between both. The modeling for the cluster is taken over from work on free clusters [49, 50]. The model parameters for the pure environment are the same as in previous studies of MgO(001) [45, 53]. The parameters for the coupling between environment and Na cluster were calibrated from scratch. The tuning for Na@MgO(001) was performed using fully quantum- mechanically computed Born-Oppenheimer surfaces for Na atoms and Na + ions on MgO(001) from [53]. These surfaces were computed at four different substrate sites (O 2 − , Mg $^{2+}$, hollow, bridge) down to close distances where the full substrate repulsion was felt. For further details and the actual model parameters, see [37]. Two quantitative points are worth to be mentioned. The modeling achieves a barrier for penetration of clus- ter electrons into the substrate which reproduces nicely the large band gap of 6.9 eV for MgO. The fully quantum mechanical calculations show that electron transfer from the substrates O 2 − anions to a Na atom remains below 0.1 charge units down to the closest distances consid- ered (where the repulsive energy comes about the band gap). Transfer from the Na atom to the Mg 2+ cation is totally ignorable. This nice decoupling of ad-atoms and substrate is probably a feature of simple metals. Noble metals, e.g., can develop a more involved surface chem- istry due to the closeness of the d shell [29]. First, the ground state structures of the pure MgO surface and of the free Na cluster are determined for the given model by simulated annealing. The Na cluster is then placed at a certain distance from the surface of the substrate. A distance of about 15 a$_{0}$ has turned out to be sufficient. After that a Galilean transformation is applied to the cluster. This means that each of the cluster ions is given a momentum ⃗ P$_{0}$ in the direction towards the surface and the electronic wave functions are boosted by an equivalent momentum as where ⃗ p$_{0}$ = m e M ⃗ P$_{0}$ , m$_{e}$ and M are the electron and Na ion mass, respectively. This provides the initial state from which on the system propagates in a straightforward manner according to the TDLDA-MD equations. From the energy functional, once established, one de- rives the static and dynamical equations variationally in a standard manner. The numerical solution of the coupled quantum-classical system proceeds as described in [37, 54, 55]. The electronic wavefunctions and spa- tial fields are represented on a Cartesian grid in three- dimensional coordinate space. The numerical box em- ployed here has a size of (64 a$_{0}$ ) $^{3}$. The spatial derivatives are evaluated via fast Fourier transform. The ground state configurations were found by interlaced accelerated gradient iterations for the electronic wavefunctions [56] and simulated annealing for the ions in the cluster and the substrate. Propagation is done by the time-splitting method for the electronic wavefunctions [57] and by the velocity Verlet algorithm for the classical coordinates of Na + ions and MgO constituents. All the collisional processes studied in the current pa- per proceed on an ionic time scale, i.e. slow as com- The starting point of deposition dynamics are well re- laxed structures for the clusters and pure MgO(001) sur- face. These had been discussed extensively in [37]. The MgO surface is a cut through cubic crystal structure. From the top, one sees a chess-board structure with al- ternating Mg and O ions. For the Na clusters, we will use here Na$_{6}$ and Na$_{8}$ as examples. The initial state starts F. Structure of the test cases D. Solution scheme FIG. 2: The structures of free Na$_{6}$ (left) and Na$_{8}$ (right). The bond distance along the five-fold ring of Na$_{6}$ is 6.5 a$_{0}$ and the top ion resides 3.1 a$_{0}$ above the ring. The bond distance in the two four-fold rings of Na$_{8}$ is 6.2 a$_{0}$ and the distance between the two rings is 5.8 a$_{0}$ . ϕ$_{i}$ ( ⃗ r ) → exp( ı⃗ p$_{0}$ · ⃗ r ) ϕ$_{i}$ ( ⃗ r ) (1) E. Preparation of the system C. Calibration of the QM/MM model