Clusters electron-precise

The structural principles and reaction chemistry of B-8 compounds have recently been reviewed. This includes not only electron-precise 4-, 5- and 6-membered heterocycles of the types described above, but also electron-deficient polyhedral clusters based on closo-. 

For more electropositive elements, which have an inferior number of valence electrons in the first place, and which in addition have to supply electrons to a more electronegative partner, the number of available electrons is rather small. They can gain electrons in two ways first, as far as possible, by complexation, i.e. by the acquisition of ligands and second, by combining their own atoms with each other. This can result in the formation of clusters. A cluster is an accumulation of three or more atoms of the same element or of similar elements that are directly linked with each other. If the accumulation of atoms yields a sufficient number of electrons to allow for one electron pair for every connecting line between two adjacent atoms, then each of these lines can be taken to be a 2c2e bond just as in a common valence bond (Lewis) formula. Clusters of this kind have been called electron precise. 

Electron precise clusters with exactly one electron pair per polyhedron edge ... 

Molecules such as P4 and the polyanionic clusters such as Si4- or As2- that are discussed in Section 13.2 are representatives of electron precise closo clusters. Organic cage molecules like tetrahedrane (C4R4), prismane (C6H6), cubane (C8H8), and dodecahedrane (C20H20) also belong to this kind of cluster. 

This mode of calculation has been called the EAN rule (effective atomic number rule). It is valid for arbitrary metal clusters (closo and others) if the number of electrons is sufficient to assign one electron pair for every M-M connecting line between adjacent atoms, and if the octet rule or the 18-electron rule is fulfilled for main group elements or for transition group elements, respectively. The number of bonds b calculated in this way is a limiting value the number of polyhedron edges in the cluster can be greater than or equal to b, but never smaller. If it is equal, the cluster is electron precise. 

Mo6 octahedron) the cluster is electron-precise, the valence band is fully occupied and the compounds are semiconductors, as, for example, (Mo4Ru2)Se8 (it has two Mo atoms substituted by Ru atoms in the cluster). In PbMo6Sg there are only 22 electrons per cluster the electron holes facilitate a better electrical conductivity below 14 K it becomes a superconductor. By incorporating other elements in the cluster and by the choice of the electron-donating element A, the number of electrons in the cluster can be varied within certain limits (19 to 24 electrons for the octahedral skeleton). With the lower electron numbers the weakened cluster bonds show up in trigonally elongated octahedra. 

KT1 does not have the NaTl structure because the K+ ions are too large to fit into the interstices of the diamond-like Tl- framework. It is a cluster compound K6T16 with distorted octahedral Tig- ions. A Tig- ion could be formulated as an electron precise octahedral cluster, with 24 skeleton electrons and four 2c2e bonds per octahedron vertex. The thallium atoms then would have no lone electron pairs, the outside of the octahedron would have nearly no valence electron density, and there would be no reason for the distortion of the octahedron. Taken as a closo cluster with one lone electron pair per T1 atom, it should have two more electrons. If we assume bonding as in the B6Hg- ion (Fig. 13.11), but occupy the t2g orbitals with only four instead of six electrons, we can understand the observed compression of the octahedra as a Jahn-Teller distortion. Clusters of this kind, that have less electrons than expected according to the Wade rules, are known with gallium, indium and thallium. They are called hypoelectronic clusters their skeleton electron numbers often are 2n or 2n — 4. 

B8C18 has a dodecahedral Bg c/o.vo-skclclon with 2n = 16 electrons. In this case, the Wade rule neither can be applied, nor can it be interpreted as an electron precise cluster nor as a cluster with 3c2e bonds. B4(BF2)6 has a tetrahedral B4 skeleton with a radially bonded BF2 ligand at each vertex, but it has two more BF2 groups bonded to two tetrahedron edges. In such cases the simple electron counting rules fail. 

State which of the following clusters is electron precise, may have 3c2< bonds or fulfills the Wade rule for closo clusters. 

Just as for group 5, 6, and 7 ( -CsF MCU species, Fehlner has shown that BH3-THF or Li[BH4] react with group 8 and 9 cyclopentadienyl metal halides to result in metallaborane clusters, many of them having a metal boron ratio of 1 3 and 1 4, and much of the synthetic chemistry and reactivity shows close connections with the earlier transition metals. The main difference between the early and later transition metallaboranes that result is that the latter are generally electron precise cluster species, while as has been shown, the former often adopt condensed structures. Indeed, as has been pointed out by King, many of the later transition metallaborane clusters that result from these syntheses have structures closely related to binary boranes and, in some cases, metal carbonyl clusters such as H2Os6(CO)18.159... 

Multicenter bonding is the key to understanding carboranes. Classical multicenter n bonding gives rise to electron-precise structures characteristic of Hiickel aromatics, which are planar and have 4n + 2 n electrons. Clusters are defined here as ensembles of atoms connected by non-classical multicenter bonding , i.e., all... 

Classical aromatics like the electron-rich, cyclobutadiene dianion A or cydo-pentadienyl anion B and electron-precise hydrocarbons (e.g., benzene C, Figure 3.2-1) have pure n multicenter bonds and therefore are generally not regarded as clusters. 

Fig. 3.6-8. Polyhedral cluster frameworks in lithium phosphandiide chemistry. Compound 29 represents an electron-precise cluster, whereas 35 and 36 are electron-deficient,...

Electron-precise, electron-deficient and electron-rich clusters. A cluster classification often adopted in several books, and related to the rules previously presented, corresponds to a subdivision into three categories electron-precise, electron-deficient and electron-rich types. The electron-precise clusters may be considered as reference structures. 

Electron-precise clusters are defined according to the following requirements (Mingos and Wales 1990) ... 

An electron-precise -atom cluster will have 5n (15n) electrons, of which 3n are used to bond the cluster (to form 3 /2 skeleton electron pairs). Notice that the total number of electrons in a cluster is given by the sum of the electrons on cluster vertex atoms plus the electrons, on vertex atoms, from covalent bonds with exocyclic groups. 

A simple, previously mentioned example may be represented by the tetrahedral molecule P4. In this structure there are 4 vertex atoms (n = 4) and there are no exocyclic groups. On the other hand, P has 5 valence electrons, so the number of cluster electrons is 4 X 5 = 20 electrons. This number (20) is therefore related to the number of vertices by the condition 20 = 5n. The cluster is electron-precise. 

Figure 4.27. Valence electron count and vertex count in main group clusters. Notice, according to McGrady (2004), that the different classes of clusters (electron-rich, electron-precise, etc.) simply occupy different domains in a continuum defined by the two variables (electron and vertex counts).

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