Electron counting rule cluster valence electrons

The location of electrons linking more than three atoms cannot be illustrated as easily. The simple, descriptive models must give way to the theoretical treatment by molecular orbital theory. With its aid, however, certain electron counting rules have been deduced for cluster compounds that set up relations between the structure and the number of valence electrons. A bridge between molecular-orbital theory and vividness is offered by the electron-localization function (cf p. 89). 

When the number of metal atoms in a cluster increases, the geometries of the clusters become more complex, and some are often structurally better described in terms of capped or decapped polyhedra and condensed polyhedra. For example, the first and second clusters listed in Table 19.4.3 are a capped octahedron and a bicapped octahedron, respectively. Consequently, capping or decapping with a transition-metal fragment to a deltapolyhedral cluster leads to an increase or decrease in the cluster valence electron count of 12. When a transition-metal atom caps a triangular face of the cluster, it forms three M-M bonds with the vertex atoms, so according to the 18-electron rule, the cluster needs an additional 18 - 6 = 12 electrons. The parent octahedron of [Os6(CO)is]2- has g = 86, the monocapped octahedron Osy(CO)2i has g = 98, and the bicapped octahedron [Oss(CO)22]2- hasg = 110. 

The complex [PbsfMofCOA I4 has been recently reported (Yong el al., 2005) and exhibits the structure shown below. Does the compound obey the electron-counting rules for clusters If not, where might one seek an explanation of its behavior Consider explicitly tripledecker complexes as well as complications caused by separating the external cluster lone pairs from cluster bonding pairs (see Chapter 2, Problem 12). For your information, the measured distance between the Mo atoms is 3.216 A, whereas twice the covalent radius of Mo is 2.90 A, the Mo-Mo distance in [Mo2(CO)h> 2 is 3.123 A and the Mo-Mo distance in the 27-valence electron tripledecker complex CpMo(r 5-As5)MoCp is 2.764 A. 

According to normal electron counting rules , these complexes are isoelectronic all have 48 cluster valence electrons (CVE). 

According to the 18-electron rule, a valence electron count of 120 would be required for clusters with a cubic shape and this condition is fulfilled by e. g. [Ni8(CO)8(PPh)6]. [20] The aforementioned compounds, however, often display appreciable deviations from this criterion if PPhj and Q are considered as 2e donors and jU4-PPh as a 4e donor, then 2 and 3 contain 116 and 112 valence electrons respectively. 

Examples of the application of the mentioned rules to a few naked metal clusters according to Mingos and Wales (1990) are reported in Table 4.4. For each species the valence electron (s and p) count is made both on the basis of the component valences by adding/subtracting one electron for each negative/positive charge, and on the basis of the geometry and the number of vertices. 

A transition element has 5 additional valence orbitals, the 5d orbitals, and therefore 10 additional electrons are required per atom to fill the valence shell of each metal atom. A closo cluster consisting only of transition metal atoms should have a total of 14/i + 2 valence electrons. A capped cluster should have 14n, a nido cluster 14/i + 4, and an arachno cluster 14n+6. The combined formula 4/i+2 + 10m would represent the total electron count for a closo cluster, A mMm, of n atoms that contains m transition metal atoms and n -m main group atoms.Table 8.2 summarizes the main rules, and the following examples show how the total electron counting scheme is applied. 

In both [Fe4X4(N0)4](X = S or Se) and [Fe4S2(NO)4(NCMe3)2] the total valence electron count is 60. This is the number characteristic of tetrahedral tetranuclear metal clusters, such as [Ir4(CO)12], in the Wade and Mingos skeletal-electron counting schemes (76, 77) and, furthermore, each iron atom in these clusters obeys the 18-electron rule, provided that it forms single Fe-Fe bonds to each of the other iron atoms in the tetrahedron. 

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