Metallic clusters on an ionic surface

EUROPHYSICS LETTERS

20 April 1996

Europhys. Lett., 34 (3), pp. 177-182 (1996)

Metallic clusters on an ionic surface ¨ kkinen and M. Manninen H. Ha Department of Physics, University of Jyv¨ askyl¨ a P.O. Box 35, FIN-40351 Jyv¨ askyl¨ a, Finland (received 4 December 1995; accepted in final form 11 March 1996) PACS. 36.40Cg – Electronic and magnetic properties of clusters. PACS. 36.40Qv – Stability and fragmentation of clusters. PACS. 73.20Hb – Impurity and defect levels; energy states of adsorbed species.

Abstract. – A total-energy method based on ab initio pseudopotentials and Kohn-Sham formulation of the density functional theory is used to study the geometry and the electronic structure of small sodium clusters up to Na8 deposited on an ionic NaCl(001) surface. The surface induces very small changes to the structure of the adsorbed cluster as compared to the free cluster, due to the large gap which separates the single-electron states associated with the cluster from those belonging to the substrate. The binding energy of the cluster to the surface has local maxima for Na2 and Na6 . The characteristics of the surface diffusion of a single sodium adatom are predicted.

Recent progress in cluster science has extended the focus of interest from the study of free clusters [1] to supported nanostructures, composite clusters, and cluster-assembled materials [2]. Each of these areas hold promises to technologically important applications, as well as contain major new challenges to theoretical understanding of the underlying physics. Understanding the interaction of clusters with surfaces is crucial for a better control of processes such as deposition of energetic clusters for growing thin films of good quality [3], or low-energy deposition with soft-landing techniques [4] which opens up new tools to measure fundamental properties of size-selected substrate-supported clusters. While most of the theoretical work done so far is based on atomistic simulations using classical empirical or semiempirical models for the interatomic interactions, proper first-principles quantum-mechanical methods are required to study small metal clusters, the physics of which is known to be governed by their electronic structure. Here we report on ab initio calculations aimed at providing insight into basic interactions between small metal (sodium) clusters and insulating surfaces, in our case the ionic NaCl(001) surface. We choose to study the Na/NaCl(001) system primarily for two reasons. First, there exist a number of investigations on metal-rich alkali-halide clusters [5] providing evidence on the phase segregation into metallic and non-metallic parts, and demonstrating that a surfacesegregated metallic overlayer in these small systems can be thermally quite stable [6]. Second, the results obtained here for the deposited clusters can be directly compared to well-known properties of free sodium clusters in the same size range. c Les Editions de Physique °

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Fig. 1. – The energy landscape seen by a single sodium adatom on the NaCl(001) surface: (left) change in the total energy and (right) corrugation of the optimal adsorption height on a route A → B → C → A, shown by the inset in the panel on the right. The nearest-neighbour distance in the substrate AB = 2.82 ˚ A. A is the position of the substrate Cl− ion.

The calculations are done using the BO-LSD-MD (Born-Oppenheimer Local-Spin-Density Molecular Dynamics) method, described in detail by Barnett and Landman [7]. The original method was modified [8] to include the supercell technique in the electronic-structure calculation. The BO-LSD-MD method has proven to be a versatile and effective method for calculating the total energy and interatomic forces of an arbitrary ionic configuration on the Born-Oppenheimer potential energy surface, making it possible to do fast structural optimization and relatively long molecular-dynamics simulations for a number of systems [7]. The supercell for the NaCl(001) surface consists of a one-layer slab in the (x, y)-plane with (6 × 6) lattice sites for ions of alternating charge (18 sites both for the Na+ and Cl− ions). In the surface plane the lattice parameter is 5.64 ˚ A [9]. The supercell dimension in the z-direction (thickness of the vacuum region) is 13.2 ˚ A. For the Brillouin zone sampling we use only the Γ -point of the supercell, which is a reasonable approximation due to the fact that the bands in alkali halides are relatively narrow and flat. We have also checked that increasing the number of substrate layers or the dimensions of the supercell does not significantly change our results. The pseudopotentials [10] for sodium 3s1 and chlorine 3s2 3p5 electrons have been tested in previous studies of sodium chloride clusters [6]. Sodium clusters are initially placed within the vacuum region 3.5–4 ˚ A from the slab, and the total energy of the system is then minimized by allowing only the coordinates of the cluster atoms to relax by a conjugate-gradient method. Energy minimizations are started mainly from the known geometries of the free clusters [5], [6], but in some cases for N ≥ 5 variations to the initial geometry are done in repeated minimization procedures. We begin to discuss our results by studying the substrate potential landscape seen by a single sodium adatom. To this end we have optimized the height of the adatom position and calculated the corresponding total energy at a number of locations within the irreducible part of the surface unit cell (see fig. 1). The optimal adsorption site is found to be on top of a A above the surface plane. The largest corrugation of the substrate substrate Cl− ion 2.80 ˚ potential occurs atop the substrate Na+ ion. The optimal diffusion path for the adatom goes along the diagonal of the surface unit cell, essentially parallel to the surface plane, and with the diffusion barrier of 0.08 eV. The curvature of the potential atop the substrate Cl − ion leads to the vibration energies of 2.6 meV and 8.8 meV for in-plane and out-of-plane modes, respectively. Using a simple thermally activated hopping model with the calculated values for the in-plane vibration frequency and the diffusion barrier, we find that at room temperature the adatom self-diffusion constant should be of the order of 2 × 10−5 cm2 /s. The calculated value for the adsorption energy is about 0.6 eV. We see no charge transfer (chemical bond) between

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Fig. 2. – Optimized geometries of Na3 (top, left) to Na8 (bottom, right) on NaCl(001) compared to the geometries of the corresponding free clusters. Cluster atoms are shaded black, and white large and small circles depict substrate Cl− and Na+ ions, respectively. For Na8 we show both a 2D and a 3D structure. In order to aid visualization, “bonds” between cluster atoms are drawn using a cut-off value of 3.7 ˚ A.

the adatom and the surface. If the gradient corrections to the LSD result are included [7], the adsorption energy shifts to 0.4 eV. We have not been able to find any experimental data on the characteristics of sodium adatoms on sodium chloride surfaces, hence our results serve as first theoretical predictions. The optimized geometries for NaN /NaCl(100), 3 ≤ N ≤ 8, are shown in fig. 2 in comparison with known geometries of the corresponding free clusters, calculated with the same pseudopotential [5], [6]. On average, the adsorbed clusters lie 3.0–3.1 ˚ A above the surface plane, which is slightly more than the adsorption height of a single Na adatom (2.80 ˚ A). It is obvious from fig. 2 that Na atoms tend to locate themselves on top of substrate Cl− ions. However, the Cl− –Cl− distance (3.99 ˚ A) is slightly more than the typical bond length in the free sodium cluster, and the geometry the cluster takes on the surface is a result of the competition between the energy cost paid to the corrugations in the substrate potential and the interactions within the cluster. We note that for N ≤ 4 the symmetry of the surface cluster follows that of the free cluster (1 ): Na3 /NaCl(100) is a deformed triangle (C2v ) with the Na–Na bond length of 3.24 ˚ A (3.15 ˚ A for the free cluster) and the opening angle 95.0◦ (84.6◦ ), and Na4 /NaCl(100) is a rhombus (D2h ) with the Na–Na bond length of 3.48 ˚ A (3.42 ˚ A) and the sharp angle 57.1◦ ◦ ˚ ˚ (52.2 ). The bond length of the adsorbed dimer is 3.18 A (2.99 A). For N = 5, 6 the geometry of the adsorbed cluster is still close to that of the free cluster, but the corrugation of the substrate potential starts to play a greater role and the exact symmetries of the free cluster (C2v and C5v , respectively) are broken. Beyond N = 6, the 2D nature of the adsorbed cluster makes it drastically different from the free cluster. For the Na8 we show both a 2D (C2v ) and a 3D adsorbed structure. We compare the electronic structure of the adsorbed clusters to the free ones by showing the Kohn-Sham (KS) single-electron levels in fig. 3. We remark that in the Na N /NaCl(100) system there is a gap (not shown) of 2–3 eV between the lowest occupied cluster state and the highest occupied substrate state. Due to this gap, there is no considerable mixing between the cluster and the substrate states. It is seen from fig. 3 that up to N = 5 the KS electronic structure changes very little in the process of adsorption, which correlates with the findings in fig. 2 for the geometric structure. For N = 6, the lowering of symmetry (C5v → C2v ) splits off the two-fold degenerate HOMO level, although the splitting is hardly visible in fig. 3. (1 ) When discussing the symmetry of the adsorbed 2D clusters we ignore the fact that the substrate induces small distortions in the z-direction, i.e. the clusters beyond Na3 are not strictly planar.

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Fig. 3. – KS one-electron energy levels (top) for NaN /NaCl(001) at the Γ -point and (bottom) for the free sodium clusters. For NaN /NaCl(001) we do not show the substrate levels, the highest of which are located at about −6 eV. For each set of levels both spin orientations are shown, the up-spin on the left and the down-spin on the right (when these are degenerate a long horizontal line is drawn). The shortest lines correspond to unoccupied levels and the longer ones to occupied levels.

Clear differences become evident for N = 7, 8: i) The free Na7 (pentagonal bipyramid, D5h ) has degenerate p-states in the plane of the pentagon (separately for both spin polarizations), which split off for the 2D structure due to the reduced symmetry. ii) The HOMO of the free Na8 (dodecahedron, D2d ) has two-fold degeneracy, which splits off for the 3D adsorbed cluster, correlating with the finding that the initially slightly prolate cluster deforms towards an oblate shape upon adsorption. To complete our discussion on the static properties of the adsorbed clusters we show in fig. 4 the calculated energy (per cluster atom) to dissociate the adsorbed cluster into non-interacting neutral atoms, E b = (E s +N E a −E s+c )/N , where E s is the total energy of the supercell having only the substrate, E a is the total energy of the neutral sodium atom, and E s+c is the total energy of the supercell having the adsorbed cluster on the substrate. The most interesting feature in fig. 4 is the local maximum of E b at N = 6. We interpret this as an electronic-shell effect in 2D. Considering the 2D adsorbed Na7 it is clear that the seventh valence electron has to occupy an orbital parallel to the surface having d-character, whence in the free 3D Na7 cluster a p-type orbital is occupied. Six valence electrons thereby close a p-like shell in the 2D shell structure. In this context we want to remark that very recent 2D-jellium calculations on both free [11] and adsorbed [12] alkali clusters yield N = 6 as a “magic number”. The difference in the shell structures of the adsorbed and free Na7 clusters is naturally closely connected to the significant changes in the geometry taking place upon adsorption. We further remark that the 2D Na8 /NaCl(100) is now an open-shell cluster and, indeed, is strongly deformed from the spherical (or “circular”) symmetry, in analogy with open-shell 3D clusters, such as Na14 [13]. We note that in our calculations the 2D and 3D structures of Na8 /NaCl(100) are energetically very close to each other (within 0.05 eV). More accurate calculations would be needed to judge their relative energetic order, furthermore, also other orientations for the adsorbed cluster as well as other known 3D low-energy structures [14] should be studied before one can draw a conclusion on which is the dimensionality of the ground state of Na8 /NaCl(100) structures. Finally, we note that also for other free sodium clusters than Na8 there exist almost isoenergetic isomers, perhaps most notably the triangular geometry for Na6 [14]. We have checked that when deposited on the surface the energy of this isomer indeed is very close (0.01 eV) to the

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Fig. 4. – Calculated binding energy E b to the surface per cluster atom.

structure shown in fig. 2. The energetics of the different isomers, finite-temperature dynamics and diffusion are currently under investigation and will be discussed elsewhere [15]. In conclusion, ab initio total-energy calculations show that the ionic NaCl(001) surface induces only minor changes to the geometry and the electronic structure of small adsorbed sodium clusters as compared to the properties of the free clusters up to Na 6 . The main reason for the result is a large gap (at least 2 eV) between the highest occupied substrate level and the lowest occupied cluster level. The most notable change induced by the surface is the enhanced relative stability of Na6 due to the reduced dimensionality. For larger sizes, both a 2D and a 3D adsorbed structure seem to be possible, and more work is needed to clarify their relative stability. *** We gratefully acknowledge R. N. Barnett and U. Landman at Georgia Institute of Technology, Atlanta, for numerous discussions on the BO-LSD-MD method. This study is supported by the Academy of Finland. Calculations have been performed at the Center for Scientific Computing, Espoo, Finland. REFERENCES [1] de Heer W. A., Rev. Mod. Phys., 65 (1993) 611. [2] Jena P., Khanna S. N. and Rao B. K. (Editors), Physics and Chemistry of Finite Systems: From Clusters to Crystals, Vol. I-II (Kluwer, Dordrecht) 1992. [3] Haberland H., Insepov Z. and Moseler M., Z. Phys. D, 26 (1993) 229, and references therein. [4] Cheng H.-P. and Landman U., Science, 260 (1993) 1304, and references therein. ¨ kkinen H. and Landman U., J. Phys. Chem., 99 (1995) [5] Barnett R. N., Cheng H.-P., Ha 7731, and references therein. ¨ kkinen H., Barnett R. N. and Landman U., Europhys. Lett., 28 (1994) 263; Chem. Phys. [6] Ha Lett., 232 (1995) 79. [7] Barnett R. N. and Landman U., Phys. Rev. B, 48 (1993) 2081; for recent applications of the method, see ref. 28-31 therein and ref. [5], [6] of this paper. ¨ kkinen H. and Landman U., unpublished. [8] Barnett R. N., Ha [9] Ashcroft N. W. and Mermin N. D., Solid State Physics (Holt, Rinehart and Winston) 1976. [10] Troullier N. and Martins J. L., Phys. Rev. B, 43 (1991) 1993. [11] Kohl C., private communication. [12] Kolehmainen J., private communication.

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¨ kkinen H. and Manninen M., Phys. Rev. B, 52 (1995) 1540. [13] Ha ˇ ic ˇ-Koutecky ´ V., Fantucci P. and Koutecky ´ J., Chem. Rev., 91 (1991) 1035; [14] Bonac ¨ thlisberger U. and Andreoni W., J. Chem. Phys., 94 (1991) 8129. Ro ¨ kkinen H. and Manninen M., unpublished. [15] Ha