Total valence electron counting schemes

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. 

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. 

The assumption of resemblance reveals a second, subtler, presupposition. The periodic chart places elements in columns, or groups, based on the numbers of their valence electrons. Thus, nitrogen is placed in group 5 (15 in the IUPAC scheme) even though it frequently expresses a valence of three. Fixed-period molecules with the same total number of atomic valence-shell electrons ( isoelectronic, horizontally isoelectronic, or isosteric molecules such as N2 and CO) usually have properties more similar than do molecules selected at random. Molecules whose atoms come from different periods but have the same numbers of valence electrons ( vertically isoelectronic or isovalenf molecules such as the salts LiF, Nal, and CsCl), often have somewhat similar properties. So, the sum of the atomic valence electron counts, i.e., the sum of the atomic group numbers, is important. Thus, it appears that using... 

Weak covalent interactions with the d atomic orbitals are also present, leading to the electronic energy level scheme as shown in Fig. 4.4b. The total number of valence electrons is 18. The complex is stable at this electron count because of the large energy gap between highest occupied d levels and the antibonding a orbitals. This corresponds to the so-called 18 electron rule. 

The third weighting scheme is related to vertex valence and takes into account the number of bonds incident to a vertex and its pairs of unshared electrons. Each electron pair present counts one, each missing electron pair contributes —1 to the total valence of atoms, and in the case of free radicals the unique electron present in the outer valence shell contributes half a bond to the total valence. The vertex weight Wj is then defined as... 

The tetrahedral —> butterfly rearrangement is quite common in cluster chemistry but few examples are reversible. One example of a reversible process involves the interconversion of Pd4(CO)5(PBu 3)4 to Pd4(CO)6(PBu 3)4 (Scheme What is perhaps surprising about this reaction is that Pd4(CO)5(PBu"3)4 has a butterfly geometry whereas the cluster with the additional CO ligand has a tetrahedral palladium skeleton. This is clearly in contrast with the usual observation that tetrahedral clusters have two fewer valence electrons than butterfly clusters i.e. 60 and 62 cluster valence electrons (CVE), respectively). This anomaly is a consequence of the capacity of the palladium atom to form stable compounds with 14 and 16 valence electrons and as such Pd4(CO)s(PBu 3)4 and Pd4(CO)e(PBu"3)4 do not conform to the usual total electron counts for compounds that obey the EAN rule but have 54 and 56 electrons, respectively. 

The effectiveness of this electron counting method can be illustrated by looking at Scheme 2.6, which shows carbon and two of its other 4A family members, silicon (Si) and germanium (Ge). As can be seen, their total electron counts are very different (6,14, and 32), but nevertheless, all the three atoms have four electrons in their valence shells. Since the valence shell in main group elements can contain a maximum of eight electrons, the connectivity of all these atoms will be four. 

Let us now turn to discuss the total electron count on the TM. The complexes in parts (a) and (b) of Scheme 9.6 involve two early TM cations, Ti and Sc +. The Ti ion has no electrons in the valence shell, and therefore to achieve Nirvana, the ion must bind nine single-connector ligands This is obviously too crowded, and the H " in Scheme 9.6a takes up two C5H5 ligands, which are three-fold connectors, and two Cl hgands, thus acquiring only 16e. This complex is by the way one of the Ziegler-Natta catalysts that performs polymerization of olefins (e.g., of H2C=CH2). 

The structures of some of the simpler boranes are shown in Figure 14.17. Once these structures were well-established, chemists quickly realized that the bonding in them could not be explained by the normal types of schemes. A Httle electron counting reveals the problem. Take diborane as the prototype. Each of the two boron atoms provides 3 valence electrons, and the six hydrogens provide 1 each. This yields a total of 12 electrons, 2 short of the number needed for conventional 2c-2e bonds. In other words, we need 14 electrons for a structure such as that found in Figure 14.18a, and we do not have enough. The compound is electron-deficient. How is this problem to be solved ... 

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