# Deposition of Na Clusters on MgO(001) 

M. B¨ ar $^{1}$, P. M. Dinh2 , $^{3}$, L. V. Moskaleva$^{4}$, P.-G. Reinhard$^{1}$, N. R¨ osch $^{4}$, and E. Suraud2 , 3 

1) Institut f¨ ur Theoretische Physik, Universit¨ at Erlangen, Staudtstrasse 7, 91058 Erlangen, Germany 

2) Universit´e de Toulouse; UPS; Laboratoire de Physique Th´eorique (IRSAMC); F-31062 Toulouse, France 

3) CNRS; LPT (IRSAMC); F-31062 Toulouse, France 

4) Technische Universit¨ at M¨ unchen, Department Chemie and Catalysis Research Center, 85747 Garching, Germany 

(Dated: November 7, 2018) 

We investigate the dynamics of deposition of small Na clusters on MgO(001) surface. A hier- archical modeling is used combining Quantum Mechanical with Molecular Mechanical (QM/MM) description. Full time-dependent density-functional theory is used for the cluster electrons while the substrate atoms are treated at a classical level. We consider Na$_{6}$ and Na$_{8}$ at various impact energies. We analyze the dependence on cluster geometry, trends with impact energy, and energy balance. We compare the results with deposit on the much softer Ar(001) surface. 

A major branch of present-days cluster research com- prises clusters in contact with solid surfaces, for an overview see, e.g., [1–4]. The interaction of these two entities gives rise to a rich scenery of effects such as, e.g., chemical reactions at surfaces [5–7], particu- larly, catalytic applications [8–10], or modified optical response[11–13]. One crucial aspect here is the process of cluster deposition which is relevant for synthesis and for analysis of clusters in contact with surfaces. More- over, the deposition dynamics as such is an interesting and demanding process due to the subtle interplay of the impact of interface energy, electronic band struc- ture of the substrate, and surface corrugation. Accord- ingly, there is a wealth of investigations on cluster deposi- tion, experimentally oriented [14–21], theoretically with molecular dynamics (MD) techniques [22–26] or more de- tailed quantum mechanical methods [27–33], for reviews see [2, 8, 34]. Although addressing the same physical processes, these various theoretical approaches, relying on different approximations, often provide useful com- plementary information. Recently, we have investi- gated deposition dynamics of Na clusters on Ar(001) sur- face [33, 35, 36]. The aim of this paper is to continue these theoretical studies now considering deposition dy- namics of Na clusters on a much ”harder” surface than Ar, namely MgO(001) insulator surfaces. The struc- tural properties and optical response of Na$_{n}$ on MgO have already been studied in great detail in using the present computational approach [37]. Both Ar and MgO are similar in that they are both insulators with a large band gap, but they differ significantly in other important properties. There are, however, large differences in other properties. Ar is a Van-der-Waals bound material, thus very soft with little surface corrugation. On the other hand, MgO is an ionic crystal, well bound and with large surface corrugation. It is thus most interesting to see how deposition dynamics proceeds in that case, as such, and at variance with the Ar case. 

The theoretical description of clusters on surfaces is 

PACS numbers: 34.50.Lf, 36.40.Sx, 68.49.Fg 

## I. INTRODUCTION 

very involved due to the huge number of degrees-of- freedom of these systems. This holds the more so for dynamics. The vast majority of theoretical studies thus resorts to MD simulations using effective force fields be- tween the atoms, as mentioned above [22–26, 34]. These are comparatively inexpensive and can provide a perti- nent picture of the leading atomic transport processes. Metal clusters are more than an ensemble of atoms be- cause they held together by delocalized bonds (due to a common electron cloud); in consequence they show pro- nounced shell effects [38–40]. This makes a quantum me- chanical description of cluster dynamics advisable. Most of the fully quantum mechanical pictures make compro- mises in concluding on dynamical features from a series of static calculations. A true Born-Oppenheimer MD for deposition of Pd clusters on MgO substrate can be found in [29]. The enormous expense of such high level cal- culations limits the size of the systems, particularly the size of the representative for the substrate. On the other hand, there are many situations in which the substrate is much more inert than the cluster. Our test case of Na clusters on MgO(001) belongs to that class. This sug- gests to use a hierarchical description where the cluster electrons are treated quantum-mechanically by full Time- Dependent Density-Functional theory (TDDFT) while the substrate atoms are handled at a lower level of refine- ment by classical motion. This modeling belongs to the family of coupled Quantum-Mechanical with Molecular- Mechanical methods (QM/MM) which are often used in other fields as, e.g., bio-chemistry [41–43] or surface physics [44, 45]. In earlier studies, we developed and ap- plied a QM/MM model for Na clusters in contact with Ar [35, 36, 46–48]. We have shown that it was most cru- cial to include properly the dynamical polarizability of the substrate when exploring truly dynamical processes as we aim at. Recently, we extended the modeling to Na clusters on MgO surfaces, again including dynamical po- larizability [37]. Here we take up that model and apply it to a study of deposition dynamics. We will consider Na$_{6}$ and Na$_{8}$ as test cases. These two clusters have very different geometries and binding properties which allows 

