sketch. The active cell is continued by an outer region of MgO material (“zone IIa”) where the ionic centers of Mg and O are kept fixed, while oxygen dipoles still remain ac- tive degrees-of-freedom. Thus zone I together with zone IIa constitute the “active cell”. Anything farther out (“zone IIb”) is totally frozen at crystalline configuration and only its Madelung potential is considered. The ef- fect of the outer region on the active part is given by a time-independent shell-model potential [51]; the actual parameters of this force field were adopted from [45]. The active cell consists of three layers, each containing square arrangements of 242 Mg 2+ cations and 242 O 2 − anions. The ions in the lowest layer are fixed at the bulk structure to prevent them from relaxing and forming an artificial second surface. The volume where ions and electrons are mobile (zone I) has a diameter of 24 a$_{0}$ , all layers together (zone I+IIa) extend to 42 a$_{0}$ from the surface. Bulk structure farther out is modeled by the Madelung potential. Checks with models of a larger number of lay- ers showed that three layers provide an adequate descrip- tion of the very inert MgO material. (The soft Ar(001) substrate, used for comparison later on, is more critical and requires at least four active layers plus two frozen ones.) The total energy is composed as E = E$_{Na}$ + E$_{MgO}$ + E$_{coupl}$ where E$_{Na}$ describes an isolated Na cluster, E$_{MgO}$ the MgO(001) substrate, and E$_{coupl}$ the coupling be- tween the two subsystems. For E$_{Na}$ , we take the stan- dard TDLDA-MD functional as in previous studies of free clusters [49, 50] including an average self-interaction correction [52]. The energy of the substrate and the cou- pling to the Na cluster consist of long-range Coulomb energy and some short-range repulsion which is modeled through effective local core-potentials [45]. To avoid the Coulomb singularity and to simulate the finite extension of Mg 2+ and O 2 − ions, we associate a smooth charge distribution ρ ( ⃗ r ) ∝ exp ( − ⃗ r $^{2}$/σ$^{2}$) with each of these ionic The hierarchical QM/MM model has been detailed in [37]. We review that here briefly. The various con- stituents and their degrees-of-freedom are summarized in table I. The Na cluster is treated in standard fash- ion [49, 50]. Valence electrons are described in terms of single-particle wavefunctions ϕ$_{n}$ ( ⃗ r ) and the complement- ing Na + ions are handled as charged classical point par- ticles characterized by their positions R$_{i}$$_{(Na)}$ , see upper block of table I. The electrons are described by TDDFT at the level of the local density approximation (LDA) The substrate is composed of two species: Mg 2+ cations and O 2 − anions. The cations are electrically inert and can be treated as charged point particles; they are labeled by i ( k $^{)}$. The anions are easily polarizable, an aspect which is described by allowing for two constituents: a valence elec- tron distribution (labeled by i ( v $^{)}$) and the complementing core (labeled by i ( c $^{)}$). Each of these three types of con- stituents is described as a classical degree-of-freedom in terms of positions ⃗ R$_{i}$ (type) , see the lower block of table I. The difference R ( c ) − R ( v ) represents the electrical dipole moment of the O 2 − anion and is thus allowed, by con- struction, to explicitly evolve in time, as a function of the local electric field due to all constituents of the system at a given instant. The combined system is sorted in four stages of de- creasing activity, as sketched in figure 1. The Na cluster is treated at the highest level of theory with full TDLDA- MD. The Mg and O ions of the substrate are arranged in fcc crystalline order corresponding to bulk MgO, with a lattice parameter of 7.94 a$_{0}$ . All dynamical degrees- of-freedom for Mg and O, as listed in table I, are taken into account in an active cell of the MgO(001) surface re- gion underneath the Na cluster, denoted “zone I” in the B. The energy A. The degrees-of-freedom II. BRIEF SUMMARY OF THE MODEL FIG. 1: Schematic view of the hierarchical model for Na N on MgO(001) surface. TABLE I: The dynamical degrees-of-freedom of the model. Upper block : Na cluster. Lower block : Active cell of the MgO substrate. See text for details. to explore qualitatively the impact of cluster properties on the deposition process. The paper is organized as follows: In section II, we summarize the QM/MM model for Na clusters on MgO. Section III presents results tracking the detailed dynam- ics in terms of trajectories and analyzing the processes with respect to energy transfer and energy balance. Con- clusions are summarized in section IV. 2 ϕ n ( ⃗ r ) , n = 1 , ...N$_{el}$ valence electrons of the Na cluster ⃗ R$_{i}$ (Na) , i (Na) = 1 ...N$_{i}$ positions of the Na + ions ⃗ R$_{i}$ ( c ) , i ( c ) = 1 ...M positions of the O cores ⃗ R$_{i}$$_{(}$ v ) , i ( v ) = 1 ...M center of the O valence cloud ⃗ R$_{i}$ ( k ) , i ( k ) = 1 ...M positions of the Mg 2+ cations surface Na cluster shell model zone I zone IIa zone IIb (frozen cores, free shells) Gaussian charge densities (free cores & shells) point charges Madelung potential only QM active