Clusters metallic, shell structure

In order to investigate the characteristic of large precious metal cluster systems by using small model clusters, the shell structures, such as cubo-octahedral or icosahedral clusters, are adopted as the M (M = Au, Pd, Pt, n= 13, 55) cluster model systems. 

Such a simple model, without the barrier due to the Qo at the center, has been used to calculate the electronic shell structure of pure alkali metal clusters[9]. 

Controlled decomposition of pre-formed [(COD)Pt(CH3)2] in the presence of triorganoaluminium led to the preparation of the first Pt cluster (size 0.75 + 0.1 nm). The one-shell structure and the metallic state were confirmed by XPS and XANES [352]. 

Our first attempt of a successive reduction method was utilized to PVP-protected Au/Pd bimetallic nanoparticles [125]. An alcohol reduction of Pd ions in the presence of Au nanoparticles did not provide the bimetallic nanoparticles but the mixtures of distinct Au and Pd monometallic nanoparticles, while an alcohol reduction of Au ions in the presence of Pd nanoparticles can provide AuPd bimetallic nanoparticles. Unexpectedly, these bimetallic nanoparticles did not have a core/shell structure, which was obtained from a simultaneous reduction of the corresponding two metal ions. This difference in the structure may be derived from the redox potentials of Pd and Au ions. When Au ions are added in the solution of enough small Pd nanoparticles, some Pd atoms on the particles reduce the Au ions to Au atoms. The oxidized Pd ions are then reduced again by an alcohol to deposit on the particles. This process may form with the particles a cluster-in-cluster structure, and does not produce Pd-core/ Au-shell bimetallic nanoparticles. On the other hand, the formation of PVP-protected Pd-core/Ni-shell bimetallic nanoparticles proceeded by a successive alcohol reduction [126]. 

Kan et al. reported preparation of Au-core/Pd-shell bimetallic nanoparticles by successive or simultaneous sonochemical irradiation of their metal precursors in ethylene glycol, respectively. In the successive method, Pd clusters or nanoparticles are first formed by reduction of Pd(N03)2, followed by adding HAUCI4 solution. As a result, Au-core/Pd-shell structured particles are formed, although Pd-core/Au-shell had been expected. In their investigations, the successive method was more effective than the simultaneous one in terms of the formation of the Au-core/Pd-shell nanoparticles [143]. 

The jellium model of the free-electron gas can account for the increased abundance of alkali metal clusters of a certain size which are observed in mass spectroscopy experiments. This occurrence of so-called magic numbers is related directly to the electronic shell structure of the atomic clusters. Rather than solving the Schrodinger equation self-consistently for jellium clusters, we first consider the two simpler problems of a free-electron gas that is confined either within a sphere of radius, R, or within a cubic box of edge length, L (cf. problem 28 of Sutton (1993)). This corresponds to imposing hard-wall boundary conditions on the electrons, namely... 

It has been long known that for a given transition-metal cluster the open-shell and the closed-shell species may differ. Typically, metal-ligand bond lengths are elongated for the open-shell structures, where the metal centers carry local spins and electrons occupy antibonding orbitals, in comparison to their closed-shell... 

The metal clusters in HFeCo3(CO)g(P(OMe)3)3 and H3Ni4(Cp)4 contain different numbers of electrons. The former cluster is a closed-shell structure (60 electrons) while the latter contains 63 electrons and is paramagnetic with S... 

In the case of metal clusters, for example, valence electrons show the shell structure which is characteristic of the system consisting of a finite number of fermions confined in a spherical potential well [2]. This electronic shell structure, in turn, motivated some theorists to study clusters as atomlike building blocks of materials [3]. The electronic structure of the metallofullerenes La C60 [4] and K C60 [5] was investigated from this viewpoint. This theorists dream of using clusters as atomlike building blocks was first realized by the macroscopic production of C60 and simultaneous discovery of crystalline solid C60, where C60 fullerenes form a close-packed crystalline lattice [6]. 

Exercise 3.15. Using metal cluster ideas, try various electron counts on [AI77R20]2 with an Al Ali2 Al44 (AlR)2o shell structure (consult Chapter 2). 

Trinuclear dusters are nearly always triangular, often heteronuclear, and very numerous. The M3(CO)i2 clusters of Fe, Ru, and Os have been much studied and can be used to illustrate some typical cluster chemistry. The Os3(CO)i2 cluster with the structure (16-XIII), where CO groups are denoted simply by lines, are electronically precise, namely, they have exactly the right number of electrons to provide each metal atom with an 18-electron, closed shell configuration. In such systems there is a total of 48 electrons, and each M—M bond is of order 1. As... 

Various refinements of the above model have been proposed for example, using alternative spherical potentials or allowing for nonspherical perturbations,and these can improve the agreement of the model with the abundance peaks observed in different experimental spectra. For small alkali metal clusters, the results are essentially equivalent to those obtained by TSH theory, for the simple reason that both approaches start from an assumption of zeroth-order spherical symmetry. This connection has been emphasized in two reviews,and also holds to some extent when considerations of symmetry breaking are applied. This aspect is discussed further below. The same shell structure is also observed in simple Hiickel calculations for alkali metals, again basically due to the symmetry of the systems considered. However, the developments of TSH theory, below, and the assumptions made in the jellium model itself, should make it clear that the latter approach is only likely to be successful for alkali and perhaps alkali earth metals. For example, recent results for aluminium clusters have led to the suggestion that symmetry-breaking effects are more important in these systems. ... 

The other kind of general behavior observed for both metallic and non-metallic clusters, is that A.fi cohj I and A all change in a non-uniform way consistent with the existence of shell structure within the cluster. That is, there is evidence for extra stability for certain values of N, called magic numbers. The evidence often comprises increased intensity in the mass spectra for the magic numbers. This has been seen for the alkali metals and the noble metals of Group 11. 

Although less stackable than the other systems considered here, fullerenes, in other respects, also qualify as clusters, for several reasons. First, they do so because of their large size and symmetrical shapes. Second, there can exist similarly formed groupings of C atoms with diverse numbers (70, 120, etc) and related properties. Third the p bonds of C give rise to a delocalised electronic shell structure similar in many respects to the closed shells of metallic clusters each carbon atom donates four electrons to a shell whose precise shape is determined by the fullerene structure, but which is closed, has a thickness of about one atom, and is very similar to the closed shells of metallic clusters. 

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