Total electron count

The dispersion forces that act between atoms of the noble gases depend on the polarizabilities of their electron clouds. The total electron counts for these atoms are 10 for neon and 54 for xenon. When two atoms approach each other, the smaller electron cloud of neon distorts less than the larger electron cloud of xenon, as a molecular picture illustrates ... 

As a simple example of non-d coordination, let us consider the hexaammine-zinc(II) cation [Zn(NH3)6]2+, whose optimized structure is shown in Fig. 4.51. Each ammine ligand serves as a formal two-electron sigma donor, and the total electron count atZn therefore corresponds to a 22e system, again violating the 18-electron rule. Each ammine ligand is bound to the Zn2+ cation by about 60.7 kcal mol-1, which is in part attributable to classical electrostatic interactions of ion-dipole type. 

In addition to the rules reported, a relation between the total electron count (TEC) and the number of skeletal electrons (SE) may be mentioned. This may be summarized as follows (Wade 1976) ... 

A classic example of the application of the above-mentioned rules is given by the borane series B6H62 (octahedron, closo), B5H9 (square pyramid, nido) and B4H10 (butterfly, that is two triangles joined by sharing an edge, arachno). The total electron counts (TEC) result in the three clusters 26, 24 and 22 whereas the skeletal electron... 

Reductive elimination is simply the reverse reaction of oxidative addition the formal valence state of the metal is reduced by two (or one in a bimetallic reaction), and the total electron count of the complex is reduced by two. While oxidative addition can also be observed for main group elements, this reaction is more typical of the transition elements in particular the electronegative, noble metals. In a catalytic cycle the two reactions always occur pair-wise. In one step the oxidative addition occurs, followed for example by insertion reactions, and then the cycle is completed by a reductive elimination of the product. 

All the systems considered in Table I feature a main-group fragment electron count of three, only one electron of which is involved in interstitial bonding. We now explore the consequences of increasing the total electron count of the main-group fragment to five electrons. Two examples of this electron count are represented by C5H5MH2 (M=B, Al). For both molecules the minimum... 

A difference of two orders of magnitude has been measured in the DC conductivity of AU55 and Aufj at 100 K [29,30]. From this, and the MES observation [46] that the total electron count in the metal core of Au s may be about 2 less than in AU55, it would appear that there is a very nonuniform distribution of levels, with a much larger energy splitting for the HOMO level of Au j than for AU55. Furthermore, the density of states in these levels must be very low. 

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. 

TABLE 8.2 Formulas Representing the Total Electron Count for Polyhedra Consisting of Main Group Elements, A, and Transition Metals, M... 

Fig. 16.56 Structures of osmium complexes which hove seven pairs of skeletul electrons. Each copped triangular face adds twelve electrons to the total electron count, but the number of skeletal pairs remains seven. Likewise removing OstCOlj deletes twelve electrons without changing the number of skeletal pairs. The diagonal lines show alternate geometries with the same total number of electrons [From McPanlm. M Poh-kednm IWM.J. 2 9 Reproduced with permission.)...

An important consequence of the nonutilization of tangential orbitals is that platinum clusters often do not obey the normal electron counting rules and appear to be electron deficient (19,21,29,58,75,76). Electron counts are usually intermediate between those found in normal transition metal clusters (58-68) and those observed in gold clusters (58,78), but no satisfactory general electron counting theory has been developed for Pt-containing clusters. In small Pt clusters constructed from PtL2 units, theoretical studies have shown that the total electron count depends on the relative orientation of the... 

Number of electrons in ferrocene 1 can be counted in the following way. In ferrocene, Fe is Fe(II) and has six d-electrons. The cyclopentadienyl anion donates six electrons (2x2 from two double bonds and two electrons from the anion), and 6 + (4 x 2) + (2 x 2) = 18 electrons satisfy the rule. In another calculation Fe, regarded as Fe(0), offers eight electrons and the cycloptendienyl radical supplies one electron. Therefore, total electron count is 8 + (4 x 2) + (1 x 2) = 18. 

Add the number of valence shell electrons for each atom. If the compound is an anion, add the charge of the ion to the total electron count because anions have "extra" electrons. If the compound is a cation, subtract the charge of the ion (an easy way to remember is that the number of valence electrons for groups 1 7 2 is the group number, e.g.,, H-1,Ca-2,etc. and for groups 13-18 it is group number minus 1, e.g AI-13, valence electron number is 3). 

A few examples of special relevance to homogeneous catalytic systems are given in Fig. 2.1, along with total electron counts. The rationales behind the schemes that are used to arrive at the electron counts are described in the following. 

Cp2Zr(CH3)(THF)]+ The zirconium oxidation state is 4+ and each Cp ligand donates six electrons. The ligand CTC donates two electrons. The solvent molecule, THF, also donates two electrons, and the total electron count is 12 + 0 + 2 + 2=16. With the covalent model zirconium is in the zero oxidation state and has four electrons Ad2,5s2) in the valence shell. Both Cp and CH3 are considered as radicals and therefore donate five and one electron, respectively. The valence electron count is therefore 4 + 2x5 + 1+ 2-1 = 16. Notice that because of the positive charge, we subtract one electron. 

The migration reaction diminishes the total electron count of the complex by two, and creates a vacant site at the metal P-elimination does the opposite. P-Elimination requires a vacant site at the metal centre, and the electron count of the complex increases by two electrons during the process. The reaction resembles the P-elimination reaction occurring in many organic processes, but the difference lies in the intramolecular nature of the present process, as the eliminated alkene may be retained in the complex. In organic chemistry the reaction may well be a two-step process, e.g. proton elimination with a base followed by the leaving of the anion. In transition metal chemistry, however, it is the availability of d orbitals that greatly facilitates a concerted cis P-elimination. 

To summarize, we now have two ways by which the degeneracy at the Fermi level found for the C atom chain can be removed. Bond alternation along the chain is one way and substitution of the C atoms by two different alternating atoms, keeping the total electron count constant, is the other. Both require a doubling of the elementary translation (or unit cell). 

Four-atom clusters are also very numerous, particularly in heteronuclear form. The majority of them display tetrahedral structures and the best known homonuclear prototypes are the M CO) (M = Co, Rh, and Ir) molecules. In these the 18-electron rule is satisfied for each metal atom through the formation of six M—M single bonds and the total electron count is 60. Some representative heteronuclear analogues are shown as (16-XV) and (16-XVI) these are also 60 electron systems. 

While the number of skeletal electron pairs, denoted 5, is at the root of the correlation procedures, discussions found in the literature are often couched in terms of other, related parameters, particularly the total electron count (TEC). The TEC is obtained from the formula by adding the following contributions ... 

The number of valence electrons for each hetero and/or interstitial atom. For example, 1 for H, 4 for C, 5 for P. Column 2 of Table 16-2 presents some examples of total electron counts. 

Table 16-2 Examples of Correlating Structures with Total Electron Count on a Wade s Rules Basis...

Cluster Total electron count (TEC) No. of skeletal electron pairs (S) Vertices of parent polyhedron Structural conclusion... 

Let us now ask how we could predict the correct total electron count, as just defined, for a stable cluster of known structure (i.e., closo, nido, or arachno). To do this for metal carbonyl clusters, it is postulated that in addition to the electrons necessary for skeletal bonding each metal atom will also have 12 nonskeletal electrons. The basis for this assumption is that in the pyramidal M(CO)3 unit each M—CO bond will comprise two formally carbon tr electrons that are donated to the metal atom and two formally metal it electrons that backbond, at least partially, to the CO ligand. Thus, in predicting the total electron count for a closo polyhedral cluster of n vertices, the result would be 12n + 2 n + 1). Similarly, for nido and arachno clusters that are derived from an n-vertex polyhedron (their parent polyhedron) by removal of one or two vertices, respectively, there will be 12 and 24 fewer total electrons, respectively. 

Many carbonyl-type clusters consist of a central polyhedron to which one or more additional metal atoms are appended by placement over a triangular face. These appended metal atoms are called capping atoms. The electron counting rules we have discussed can be extended to cover such structures by the rule that the addition of a capping atom does not change the skeletal electron requirement for the central cluster. Thus, the addition of a capping atom simply increases the total electron count by 12 electrons. 

Figure 18-F-6 Structures and total electron counts for osmium clusters with seven skeletal electron pairs. Structures related by the diagonal arrows are alternatives for the same total electron count.

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