Electronic Shell Effects Research Articles

An ab initio study of cluster–surface interaction: Na clusters on the NaCl(001) surface

Structure, stability, dynamics, and the electronic structure of small sodium clusters with 2 to 12 atoms adsorbed on the NaCl(001) surface are studied using an ab initio total energy method. The interaction between the ideal surface and the metal cluster is found to be weak due to a large energy gap between the surface and the cluster single-electron states. As a result, the geometry and the electronic structure of the smallest clusters (N⩽6) is distorted only slightly if compared to the free clusters. For larger sizes it seems possible to have both 2D and 3D structure isomers with a notable interisomeric energy barrier. The cluster binding energy to the surface has a local maximum at N=6 which we interpret to be caused by electronic shell effects in 2D. The weak cluster–surface interactions are modified dramatically in the presence of surface F centers (missing chlorine atoms). The F center increases the adsorption energy of sodium adatom by 1 eV and changes the nature of adsorption from physisorption to chemisorption. Similarly, the binding of small sodium clusters to the surface is enhanced by F centers.

Electron Distribution and Collective Resonances in Sodium Clusters11The project supported by National Natural Science Foundation of China

Electron distribution and collective resonances of sodium metallic clusters, with the inhomogeneous jellium model, are studied by means of the Thomas-Fermi statistical method with a Wood-Saxon charge distribution for positive charge background and the sum-rule formalism. The density distribution of the valence electrons has been calculated for small sodium clusters and the “redshift” effect of collective resonances is found in agreement with the experimental results. The characteristic electronic shell effects of sodium clusters are found, which cannot be obtained by using homogeneous jellium model. The collective resonances in medium sized sodium clusters are predicted and the “redshift” effect decreases as cluster size increases.

Shell effects in planar electron clusters

We investigate the electronic shell structure of planar metal clusters, having in mind clusters on insulating surfaces with an interface energy such that the cluster covers the surface in a monolayer. In this first survey we concentrate on the shell effects of such a planar electron cloud using the Ultimate Jellium Model where the structural effects of the positive background are completely eliminated. An axially symmetric electron cloud shows shell effects which are, however, somewhat smaller than those of fully free threedimensional clusters. The free variation of the shape for planar clusters on surfaces, leading to many triaxial clusters, diminishes the shell effects even further, leading to the existence of hybrid-deformed clusters and a lack of energetically favored “magic” clusters in an intermediate size range N ≈ 10.30. In contrary to the situation for free clusters the small shell energies have a minor effect on the energetics of the groundstate. As a consequence, electronic shell effects are only one ingredient amongst others to determine the kinetics of cluster growth on (insulating) substrates. With a bold rescaling assumption, we can relate axially symmetric planar clusters to the planar electron cloud in a neutral quantum dot, having the consequence that shell effects persist to play a role in these systems.

Barriers and Deformation in Fission of Charged Metal Clusters

The influence of electronic shell effects on the barriers and channels pertaining to metal-cluster fission is studied using a shell correction method in connection with an asymmetric two-center-oscillator model potential. This approach has the advantage that the ensuing shape parametrization allows for an independent variation of the deformations of parent and daughter clusters. Results for both symmetric and asymmetric channels associated with the parent clusters Na{sub 10}{sup 2+} and Na{sub 18}{sup +} are presented. We find that barriers, which separate the parent configuration from molecular-type configurations associated with preformation of the fragments, are most important and must be considered, together with the subsequent separation process, for proper elucidation of metal-cluster fission phenomena. 23 refs., 3 figs.

Symmetric and asymmetric fission of charged sodium clusters

A deformed-jellium model is used to calculate the fission barrier height of Na242+ → Na21++Na3+ and Na422+ → 2Na21+ within the Kohn—Sham Density Functional Theory (i.e., including shell effects). Although the shape of the barrier obviously depends on the parametrization of the fission path, we have found that the barrier maximum corresponds to a configuration in which the emerging fragments are already formed and rather well apart. The two examples chosen serve to illustrate the influence of the electronic shell effects.

Electronic shell effects in triaxially deformed metal clusters: A systematic interpretation of experimental observations.

We develop and apply a semiempirical shell-correction method to calculate the binding energies of open-shell, neutral and charged, simple-metal clusters, which can be modeled as triaxially deformed jellium droplets. Systematics of ground-state properties of clusters with sizes up to 100 atoms, such as ionization potentials and electron affinities, are studied and compared to available experimental measurements on sodium, potassium, and copper clusters. We also report on systematics of the energetics of fission channels for doubly charged cationic and anionic species, as well as the energetics of monomer and dimer separation channels, and compare them to experimental data. Pertaining to characteristic patterns as a function of cluster size in the above quantities, triaxial shell effects exhibit a rich structure, yielding overall substantial improvement in the agreement between theory and experiment. In particular, we show that the lifting of the degeneracies in the electron spectra via cluster triaxial-shape deformations underlies the appearance of odd-even alternations in such patterns. Furthermore, our analysis of ground-state properties can lead to unambiguous assignments of equilibrium cluster shapes, as well as shape isomers.

Electronic and atomic structure of Cs N and Cs N O clusters

The electronic and atomic structure of CsN and CsNO clusters up toN=70 is studied using both the spherical jellium model and a spherical average pseudopotential (SAPS) method. Due to shortcomings in the Aufbauprinciple of one-electron shells the spherical jellium model fails to give a consistent description of CsN and CsNO. These problems do not occur in the SAPS scheme, which allows to take into account structural aspects beyond the electronic shell effects. Due to the existence of ionic bonding these structural effects are more evident in CsNO clusters than in the pure metallic CsN clusters. The embedding energy of oxygen in CsN is negative for allN, showing a strong affinity of CsN clusters for oxygen. The embedding energy exhibits large size oszillations, since for certain values ofN the oxygen atom must displace a central Cs atom to the cluster surface.

Electronic-shell effects in small doubly charged lead clusters.

Lead-cluster mass spectra, the lead clusters being generated by the gas aggregation technique and ionized by electron impact, reveal, besides the well-known relative abundance maxima for singly charged species, relative concentration maxima for the doubly charged ones. Among the most intense peaks the following ones for ${\mathrm{Pb}}_{\mathrm{n}}^{2+}$: n=9, 15, 23, 27, and 35 were found. Since lead is tetravalent, the total numbers of valence electrons for the above-mentioned ions are 34, 58, 90, 106, and 138 per cluster (i.e., 4n-2), respectively. These numbers are exactly those for which the shell closing of the valence electrons within a spherically symmetric potential is achieved. This result demonstrates the importance of electronic effects on the stability, not only for neutral and singly charged metal clusters, but also for doubly charged ones.

Electronic and atomic structure of Na, Mg, Al and Pb clusters

Density functional theory is used to study the electronic and atomic structure of small clusters of Na, Mg, Al and Pb. We study the quantityEN−1–EN, which has relevance to the processes of cluster growth and evaporation (EN is the total energy of the cluster withN atoms). By comparing the results of the jellium model with those of a more realistic model (although still simple) we are able to appreciate “structural” effects beyond the “electronic-shell effects” which form the essence of the predictions of the jellium model. The calculations predict formation of atomic shells and appreciable reconstruction as the cluster grows.

Z1 oscillations in low energy heavy ion ranges

Following the observation in an earlier paper of systematic deviations from a universal range-energy relationship, the ranges of a series of elements from 53I to 92U, implanted at a reduced energy of ϵ = 0.09 in amorphised Si, have been measured and the dimensionless range, ϱ, has been found to exhibit a distinct oscillatory behaviour as a function of Z 1 rather than the constant dependence predicted by any theory based on a Thomas-Fermi model of the atom. These oscillations are believed to result from the modification to the scattering cross section caused by electron shell effects and some evidence for this conclusion arises from a marked difference in trends between the range and the straggling measurements which should be sensitive to the form of the interatomic potential.