0000000000269568
AUTHOR
J. Mansikka-aho
Level-spacing distribution in the tight-binding model of fcc clusters.
A lattice-gas Monte Carlo method is used to simulate metallic fcc clusters at finite temperatures. A tight-binding model including s and p electrons has been derived for reproducing the free-electron-like energy band for the bulk metal and this model is used for calculating the electronic structures of the fcc cluster. The resulting level-spacing distribution at the Fermi energy is a Wigner distribution. The width of the distribution in small clusters is smaller than that calculated from the bulk density of states. In the lattice gas clusters the energy gaps related to the electronic magic numbers do not show up at the Fermi level. The energy between the last occupied and the first unoccupi…
Effects of Crystal Field Splitting and Surface Faceting on the Electronic Shell Structure
The shell structure of the valence electrons is clearly observed in all alkali and noble metal clusters containing up to hundreds of atoms[1 – 4]. It is seen in the abundances of the clusters, in the ionization potential and in the polarizability. The shell structure of the valence electrons is closely related to the shell model of nuclei, but is simpler owing to the negligibly small spin-orbit interaction. The ability to produce all sizes of metal clusters has made the metal clusters a test ground for the super-shell structure[5].
Shell structure in large nonspherical metal clusters.
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.
Effects of the cluster surface on the electronic shell structure: faceting, roughness and softness
Several simple models have been used to study the effects of the surface on the electronic shell structure in metal clusters. The main results are as follows: The icosahedral clusters have the same electronic shell structure as the sphere up to about 1000 atoms. The surface roughness causes the distribution of the level spacings to be a Wigner distribution. By varying the softness of the potential we can obtain potentials where the simplest classical orbits are the ‘five-point star’ or even ‘the three-point star’.
Star orbits in metal clusters
A possibility that classical five-point star orbits play a dominant role for shell structures of large metal clusters is investigated quantum mechanically. With a soft Woods-Saxon spherical potential a signature of the five-point star orbit is found in the level densities. Quantum numbers of degenerate levels in the soft Woods-Saxon potential differ by 2 and 5 in radial nodes and angular momenta, respectively. Unlike the experimental observation the peaks in the mass spectrum are not equally spaced as a function of N 1/3 . The self-consistent jellium model does not reproduce the degeneracy associated with the five-point star orbits. It is demonstrated that by covering high-density metal clu…
Odd-even staggering in simple models of metal clusters
The odd-even staggering of free-electron metal clusters is studied using several simple models: Noninter-acting electrons in a rectangular box, triaxial harmonic oscillator, and Huckel model. Finite temperature effects are studied using the Monte Carlo method. All the models show qualitatively similar odd-even staggering. In the ground state the HOMO-LUMO gap is larger than the neighbouring energy gaps. The reduction of the odd-even staggering due to exchange and correlation is studied using the local-spin-density approximation.
Electronic Shell Structure in Icosahedral Metal Clusters
The shell structure of valence electrons in icosahedral and cuboctahedral simple metal clusters is studied using the free electron model and the Huckel model. The shell structure in a 1415 atom icosahedral cluster has still similarities with that of a spherical cluster. The effect of the finite temperature on the shell structure in liquid clusters is discussed.
Shell structure and level spacing distribution in metallic clusters
The lattice gas Monte Carlo and tight binding method is used to study the electronic shell structure in large metallic clusters. The average density of states of a large ensemble of deformed clusters shows the same shell structure as the most spherical geometry. The level spacing distribution at the Fermi level is a Wigner distribution.