Shell structure in large nonspherical metal clusters

Abstract

Electronic shell structure of icosahedral and cuboctahedral sodium clusters with 300 to 1500 atoms has been studied using a potential-well approximation for the effective one-electron potential. The results show that icosahedral clusters yield the same shell structure as spherical clusters up to the cluster size of about 500 atoms and that similarities persist until the cluster has about 1000 atoms. The shell structure of a cuboctahedral geometry begins to deviate from that of a sphere when the cluster size is about 100. A study on quadrupole deformations of large clusters shows that surface fluctuations in liquid clusters cannot destroy the shell structure even in the largest clusters.ters, the radius is determined by ro =N' r"where N is the number of atoms in the cluster and r, the Wigner-Seitz radius. All calculations in this paper have been done with the parameters for sodium: Vo= -0.205 a.u. and r, =3.93 a.u. 46 12 649

On the metallic droplet model for successive ionization potentials of metal clusters ‐ relativistic electronic structure investigations of the icosahedral gold cluster Au55

“…Also the jellium HOMO (-3.36 eV) lies too high in energy by about 1.8 eV as compared to the HOMO of Auss ( -5.19 eV) which agrees quite well with the experimental value of the polycrystalline work function of bulk gold, W, = 5.1 eV [7]. On the other hand, the ordering of the occupied s-type levels is correctly predicted if one takes into account that jellium levels with angular momentum 1 2 3 split under I, symmetry [5]. The part of the 6s manifold that falls outside the 5d manifold is clearly discernible whereas some of the s-type levels in the energy range of the 5d band cannot be resolved since they are mixed into many d-type states.…”

Electronic shell structure and chemisorption on gold nanoparticles

“…44 Our results show that the inclusion of a d band, as well as the inclusion of an atomic lattice with various irregularies as per the different cluster generation procedures used here, have limited effect on the shell structure in this size range.…”

Hückel model for metal clusters: Ground states and low energy isomers

“…The model has no adjustable parameters. Surprisingly, the ground state geometries of the Hiickel clusters (within the limitation of the constant bond length) are in agreement with the ground states, or the low-energy isomers, obtained with ab initio' quantum chemistry methods ?-4,lO Moreover, the small Hiickel clusters 6 ,7 seem to show similar shell structure as the simple jellium model: or ab initio calculations,1O and even in large spherical Hiickel clusters consisting of hundreds of atoms the shell structure is clearly seen in the energy levels: Il.12 The Huckel model has also been used in studying'the faceting of large clusters 13 and the level spacing statistics. 14 - 16 Previously, the ground states of alkali clusters were investigated in the HiickeImodel~y Wang et al 6 by application of graph theory up to 9 atoms.…”

“…In the case of large Huckel clusters the icosahedral structures have lower total energies than the cubic structures. 13 For this reason and in order to make the Huckel calculations somewhat more realistic we have also considered a model where the nearest neighbor distance is allowed to vary, in most calculations ±5.5%.…”

“…12, 13 We will now examine the, shell, structure in the low energy isomers, which are generally nonspherical, Instead of looking each isomers separately we take a average of the density of states of the ensemble made of the 20 low energy isomers.-The integrated density of states for four cluster sizes is shown in Fig. 8.…”