Seven-atom clusters

Figure 11 Character of the arrangement of the spin magnetic moments, and average magnetic moment, in seven-atom clusters with a pentagonal bipyramid structure and interatomic distances ranging from <4ulk to 80% <4ulk- Reproduced with permission from Ref. 79.

By analyzing the density matrix composition of planar and 3D structures of seven atom clusters (II and IV of Fig 1), calculated using scalar relativistic pseudo-potential at the GGA theory level, Fernandez and coworkers conclude that the planarity of An clusters is driven by the hybridization of the half-filled 6s orbital with the fully occupied 5d 2 orbital, which is favored by relativistic effects. Thus, the three valence electrons in the orbitals 6s and 5d 2, form a sticky-waist cylinder , where the cylinder is due to the almost filled s + d 2 hybrid, and the sticky-waist is due to the nearly half-filled s — d 2 hybrid orbital. 

Wc will first examplify the above principles on a six atom and a seven atom cluster. These two clusters are the most striking examples of the differences beween nickel and cobalt clusters. These cobalt clusters are the two least reactive of all the cobalt clusters, whereas for nickel these two clusters are as reactive as clusters of other sizes. In the final subsection we will discuss also the four, five, eight, nine and ten atom clusters of which in particular the eight and nine atom clusters have a markedly lower reactivity for cobalt than for nickel. All calculations described in this section used a one- or two- electron ECP level description of the metal atoms. No all-electron atoms were included. 

Quantitative calculations of the electronic structure for ternary systems have been reported in a relatively small number of papers. The first series of the calculations was performed by the simple cluster MWH method. Small [TiC Ng ] and [TiC Oi ] (n = 0,1,..., 6) clusters simulating the structure of corresponding carbonitrides and oxycarbides have been studied by Ivanovsky et al (1979a,b). It was found that with an increase of the N/C or 0/C ratio N(0)2s and N(0)2p-bands get broader while the similar bands for C get narrower. Calculated TiL ,-(0, N, C)K emission spectra of TiC,Ni, and TiC,Oi jt appear to be in reasonable agreement with the experimental data obtained by Brytov et al (1974) and Nikitin (1982). Similar cluster calculations have been carried out for ZrC jOi, VC Ni VC,Oi (, VN,Oi jj and NbN,jNi, systems by Ivanovsky (1988) and Ivanovsky et al (1984). Along with seven-atom clusters, [MX6 X ,Mi2] clusters were considered which took into account M-M interactions and all possible arrangements of different ligands in the central metal atom polyhedron. 

A chemical formula describes the composition of a substance by giving the relative numbers of atoms of each element. When a substance contains discrete molecules, a chemical formula is also a molecular formula. A chemical formula contains elemental symbols to represent atoms and subscripted numbers to indicate the number of atoms of each type. The simplest chemical formulas describe pure elements. The chemical formulas of most elements are their elemental symbols helium is He, silicon is Si, copper is Cu. However, seven elements occur naturally as diatomic molecules (Figure 3-lT so their chemical formulas take the form X2 A few other elements occur as atomic clusters, notably P4 and Sg. ... 

Figure 23. Plot of experimental ( ) and theoretical three-body rate constants as a function of cluster size for the clustering of one CO molecule to copper clusters, Cun. Note the dramatic increase in reactivity (almost four orders of magnitude) within the first seven atom additions to the clusters. The overall trend represents a transition from termolecular to effective bimolecular behavior. The solid line (theory) was obtained assuming a loose transition state while the dotted line shows the results for a tight transition state for monomer and dimer only (upper limit). Taken with permission from ref. 155.

Even though qualitative bonding descriptions of metal atom clusters up to six or seven atoms can be derived and in some cases correlated with structural detail, it is clear that most structures observed for higher clusters cannot be treated thus. Nor do the structures observed correlate with those observed for borane derivatives with the same number of vertices. Much of borane chemistry is dominated by the tendency to form structures derived from the icosahedron found in elemental boron. However, elemental transition metals possess either a close-packed or body-centered cubic arrangement. In this connection, one can find the vast majority of metal polyhedra in carbonyl cluster compounds within close-packed geometries, particularly hexagonal close-packing. 

Metal oligomers are stabilized at quite small nuclearity when formed at low dose in the presence of polyacrylate PA [85]. From pulse radiolysis of Ag" -PA solutions, it appears that the very slow (10 1 mol sec ) dimerization of Agi" silver oligomers [39,89] (275 and 350 nm) results into a blue-silver clusters ( = 4) absorbing at 292 and 800 nm [90], and stable in air for years (Fig. 3). The 800-nm absorption band is assigned to a cluster-ligand PA interaction [86,91]. Clear images by STM show flat clusters of 0.7 nm with atoms spaced by 0.25 nm (Fig. 3) [85]. Each cluster contains seven atoms (possibly with an eighth atom in the central position). Because only four atoms were reduced, they correspond to the stoichiometry Ag7 (or Agg ). 

Theoretical quantum-chemical study of pyridine adsorption at Hg electrode (including its charged surface) has been described by Man ko et al. [137,138]. An ab initio Hartree-Fock-Roothaan method has been employed. The electrode was modeled as a planar seven-atomic Hg-7 cluster. The deepest minimum of the total energy of the adsorption system was found for positive charge density and Py interacting with the metal through the lone electron... 

In summary, there are several conceivable ways in which a seven-Mo-atom cluster having octahedral Co or Mo linked to the periphery by three -S- bonds could exhibit two different behaviors. The following lists the suggestions discussed in this section and some additional suggestions ... 

The applicability of the dimensional model to Ionic and nonlonlc molecules containing as many as seven atoms Is gratifying. This demonstrates the Insensitivity of the entropy (as determined by the configurational Integral) to the exact form of the pair potential. This encouraged us to attempt similar correlations with homonuclear clusters. We will test whether the Xq species follow the prescriptions of the dimensional model for the corresponding MXjj species. For convenience, we will restrict ourselves to the entropy at 1000 K. The correlations at other temperatures and for the free energy functions are similar. 

Figure 7. The DFT calculated interaction of I-epoxy-3-butene (EpB) with a seven-atom silver cluster. [Adapted from (46)].

Other Clusters. The cobalt clusters with six and seven atoms are the ones which differ most dramatically from the corresponding nickel clusters. The eight and nine atom clusters are also much less reactive for cobalt than for nickel, while the Co g cluster is as strongly reactive as the Ni.g cluster. The experimental result for the four and five atom cobalt clusters is not completely clear to us. For the five atom cluster it is on the one hand claimed that it has reacted almost completely but on the other hand the relative reactivity is given in a figure as smaller than for the unreactive COg cluster (1). For all these clusters we have obtained some preliminary results, which are described below. 

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