Four-atom clusters, reactivity

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. 

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. 

We count the N2 + O2—>N + N+ 0 + 0 channel as a reactive one because all the trajectories we examined yielded a four atom final state only when it was preceded by the formation of NO, however briefly. In addition, this channei has a dynamical energy threshold significantly higher than the endoergicity. The total yield is shown vs. the impact velocity for N2 + O2 molecules embedded in a cluster of 125 rare gas atoms, One can replot this figure in terms of a reduced variable, see Fig. 13. 

Os.3H2(CO)io behaves as an unsaturated cluster in that it is much more reactive than Os3(CO)i2. One way of looking at this is to say that, as a 46e cluster, it lacks 2e from the EAN count of 48e. It is often viewed as containing an Os=Os double bond because the EAN count for a system with four M—M bonds in a three-atom cluster is 46e. We would then regard an Os=Os double bond, like a C=C double bond, as being unsaturated. Structure 13.5 shows that there are two Os—H—Os bridges. 

Figure 1 The spatial distribution of 14 nitrogen atoms (black) and oxygen atoms (white) inside a Ne cluster (not shown), 70 fs after surface impact at 12 km/sec. A tube connects those atoms which are within their equilibrium bond distance. The box is the smallest hypothetical enclosure drawn about all the reactive atoms in the cold cluster, prior to impact. Note the considerable compression and the chemical implication there are several examples where three or four atoms are within the range of the chemical forces. 

Figure 3 The hyperradius for the four atoms during the N2 + O2 2NO reactive collision vs. time (in fs), for the bottom panel of Fig. 2. The time 185 fs is indicated. The position of the four reactive atoms and of three cluster atoms (cf. Fig. 4 for an identification of the serial number) at that time is shown. 

Four-nuclear cluster species Sc/ obtained under the similar conditions indicate the highest reactivity [54]. In contrast to monoatomic ions Ln", Sc/ reacts with methane. The primary process in this case is also the dehydrogenation of alkane resulting in the formation of Sc/R ions, in which R is dehydrogenated initial hydrocarbon. When the number of carbon atoms in the hydrocarbon is more than three the secondary processes lead to the Sc/ insertion into C-C bonds, for example ... 

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.

Iron is so far unique in that it alone forms carbidocarbonyl clusters containing only four metal atoms, and the discovery of this class of compounds and the reactivity of its members has provided one of the most... 

The 30th anniversary of the modem DFT was celebrated in June 1994 in Cracow, where about two hundred scientists gathered at the ancient Jagiellonian University Robert G. Parr were the honorary chairmen of the conference. Most of the reviewers of these four volumes include the plenary lecturers of this symposium other leading contributors to the field, physicists and chemists, were also invited to take part in this DFT survey. The fifteen chapters of this DFT series cover both the basic theory (Parts I, II, and the first article of Part III), applications to atoms, molecules and clusters (Part III), as well as the chemical reactions and the DFT rooted theory of chemical reactivity (Part IV). This arrangement has emerged as a compromise between the volume size limitations and the requirements of the maximum thematic unity of each part. 

The reactions catalyzed by laccases proceed by the monoelectronic oxidation of a suitable substrate molecule (phenols and aromatic or aliphatic amines) to the corresponding reactive radical (Riva, 2006). The redox process takes place with the assistance of a cluster of four copper atoms that form the catalytic core of the enzyme they also confer the typical blue color to these enzymes because of the intense electronic absorption of the Cu-Cu linkages (Piontek et al., 2002). The overall outcome of the catalytic cycle is the reduction of one molecule of oxygen to two molecules of water and the concomitant oxidation of four substrate molecules to produce four... 

In virtually all its stable compounds carbon forms four bonds and has coordination numbers of 2 (=C— or =C=), 3 (=CQ, or 4, with linear, triangular (planar), and tetrahedral geometries, respectively CO has coordination number 1. In interstitial carbides (Section 7-3), certain metal cluster compounds1 (Section 7-9), and very stable trigonal bipyramidal and octahedral penta- and hexa(aurio)methanium cations of the type (LAu)5C+ and (LAu)6C2+, where L is a phosphine,2 carbon atoms are found with coordination numbers of 4, 5, or 6. Coordination number 5 is also found in compounds with bridging alkyls such as Al2Me6, in some carboranes (Section 5-12), and in reactive carbocations.3... 

The efficiency of cluster impact in driving four-center reactions is due to a matching between what the cluster can do to the reactants or products and the very selective energy requirements and the specific energy disposal in a concerted reactive collision, as discussed in details in Sec. 3.2. The cluster serves to provide both the steric and energetic conditions necessary for this reaction. In terms of the impact parameter of the relative motion of the two reactants, their confinement by the cluster keeps it low, so that they do not miss one another. This confinement within the cluster favoring low impact parameter collisions is a key ingredient in why such processes are so efficient. Furthermore, both the activation of the reactants before the reaction and the stabilization of the hot product after it, are due to the cluster atoms. 

The high reactivity of the four-center reactions inside the cluster is due to a matching between the energetic and steric requirements of the reaction and the actions of the cluster s atoms on the reactive system. A very essential feature of the four-center reactions in impact heated clusters is the importance of the remarkable timing of the sequence of events that takes place. Unlike the simpler case of dissociation of diatomics embedded in the cluster, the concerted four-center reactions require a fine tuned coordination of many degrees of freedom. The timing is more crucial in the case of the four-center reactions since the whole scenario is richer. 

Matrix isolation experiments showed that small clusters of magnesium and calcium are more reactive than atoms " . Thus, codeposition of CH3Br and magnesium, monitored by IR and UV visible spectra, indicated that Mg2 and Mgs were consumed while Mg atoms were not. It was proposed that Mg clusters reacted in a four-center transition state, and this is the first example of cr-bond breaking on a cluster but not an atom under the same experimental conditions. 

---