The Application of the 4 n Series Method to Categorize Metalloboranes

Metalloboranes have been categorized by using 4n series method. More than one hundred metalloboranes have been analyzed and characterized by the method. The clusters have been found to be centered within the series range S = 4n+6 to 4n-8. According to the classification, the clusters of series S= 4n+0 are mono-capped, S = 4n-2, bi-capped, S = 4n-4, tri-capped, S = 4n-6, tetra-capped and S= 4n-8, penta-capped. Whereas the known stable boranes have almost non-existent capped boranes, such clusters are prevalent within metalloborane complexes. This implies that metal fragments have the potency of stabilizing the fragile capped boranes.


Introduction
The Wade-Mingos rules (Wade, 1971;Mingos, 1972Mingos, , 1984Mingos, , 1991;;Cox, et al, 1981) have widely been utilized to categorize clusters.The 4n series method of categorizing clusters that has recently been developed (Kiremire, 2015a;2015b) complements the PSEPT method.The method is a systematic numerical approach of electron-counting of valence electrons in atoms, fragments, molecules and clusters.The categorization of metalloboranes using the 4n series method is hereby presented in this paper.

Background to the Application of the 4n Series Method
The evolution of the 4n series method for analyzing and categorizing clusters has been discussed extensively (Kiremire, 2015a(Kiremire, , 2015b)).In this paper, the 4n series method is being extended to classification of metallaborane clusters.Adequate examples have been provided to demonstrate the flexibility and the power of the method so as to enable the readers to be more familiar with it.The cluster complexes used have been taken from a wide spectrum of sources but mostly from the work by Fehlner and Grimes (Fehlner, 2002;Callahan, et al, 1974;Grimes, 1974).In addition, the vital isolobal relationship between transition metals and main group elements will be utilized (Hoffmann, 1982;Kiremire, 2015a).The relationship is summarized below.

14n+q 4n+q -10n +10n
This means that the valence electrons from the transition metal fragments have to be lowered to the level of the main group fragments by subtracting 10 unit sets of electrons.If it is one fragment, a numerical value of 10 is subtracted, for two, 2x10, three, 3x10 and so on.It has been found much easier to work with 4n series rather than 14n series.The cluster number k is defined as k = 2n-½ q.In terms of categorization of clusters, S =4n+2 represents the closo cluster, 4n+4(nido), 4n+6 (arachno), 4n+8 (hypho) and 4n+10 (klapo).The capping series start from S =4n+0(mono-capped), 4n-2(bi-capped), 4n-4(tri-capped), 4n-6(tetra-capped) and so on.The proposed capping symbol which was discussed in earlier work is Cp = C 1 C (mono-capped), Cp = C 2 C (bi-capped), Cp = C 3 C (tri-capped) and Cp = C 4 C (tetra-capped) (Kiremire, 2015b).The S = 4n+0 represents a mono-capped cluster and the symbol C 1 is used.For any additional +1(-2), that is, the series S = 4n-2, we get another capping and hence an additional symbol C 1 is added.Thus, the series S = 4n+1(-2), the net capping symbol becomes, Cp = C 1 +C 1 = C 2 , and for S = 4n+3(-2) = 4n-6, Cp = C 1 +C 3 = C 4 .Thus, S = 4n-6 series represents, a tetra-capped cluster.Let us consider the following examples (most of which are known from the application of Mingo-Wades rules) as illustrations of the application of the 4n series method of categorizing clusters.

B 5 H 9
The molecular formula is decomposed into mono-fragments with electron valence content of four.Hence, B 5 H 9 is split into five [BH] fragments.These fragments consist of 5 boron atoms and 5 hydrogen atoms.Since, B 5 H 9 has 5 boron atoms and 9 hydrogen atoms, the remaining 4 hydrogen atoms will be added separately.This is summarized by the work out below.

5[BH]→5[3+1] = 5[4+0] →4n+0(n=5)
Balancing the hydrogen atoms: The skeletal shape of B 5 H 9 is shown in F-1 as a projection and F-2 as square pyramid.A diagram showing the transformation of series into an equivalent hydrocarbon is given in Scheme 1.The skeletal shape of the hydrocarbon analogue C 5 H 4 as an isomer corresponding to B 5 H 9 is shown in F-3.Most of the examples have been taken from an outstanding review by Fehlner (Felner, 2002).
Scheme 1. Converting a series Formula into a corresponding Hydrocarbon molecular formula This means that B5H9 is equivalent to C5H4.
The B5H9 cluster has 5 skeletal atoms M-5 and is a nido type of cluster.Therefore, it is derived from M-6 closo cluster which has an octahedral shape.Hence, the B5H9 cluster has a square pyramid pyramid shape with k value = 8.
The shape will be similar to that of B 5 H 9 discussed above.Again, in this example the molecular formula has been decomposed into mono-fragments each with valence electron content of four in line with 4n series method.
2.5 (C 4 H 4 )Fe(CO) 3 Hence, the skeletal shape is similar to that of B 5 H 9 .
Nido cluster, k =8.Shape is similar to that of B 5 H 9 .

(Cp*Ir
Since this is a nido cluster, its shape is related that of the nearest closo system B 7 H 7 2-.This is in agreement to the Rudolph series (Rudolph, 1976).The cluster B 6 H 10 has a pentagonal pyramid shape (k = 10).The hydrocarbon equivalent is given by F 6)-2 = 10.A sketch of the ideal skeletal shape of B 6 H 10 is given in F-4.This is the expected ideal shape for (Cp*Ir) 2 B 4 H 8 .This is in agreement with the observed shape (Fehlner, 2002).
Two of the skeletal points (enlarged size) refer to the two IrCp* fragments.

(Cp
).This step involves the lowering of [14] valence electron equivalent to [4] valence electron equivalent so as to use 4n series method of categorization.
This cluster is expected to have a shape similar to that of B 5 H 9 .

(Cp
The cluster belongs to mono-capped series. This is a mono-capped cluster with symbol Cp = C I C[M-5].It is a mono-capped trigonal bipyramid (F-8A).This is in agreement with the observed cluster 2.10 in F-8B.
= ReCp* F-8A.Expected ideal skeletal shape of (Cp*Re)2B4H8 The skeletal sketch of (Cp*Cr) 2 B 4 H 8 is shown in F-9A.The observed similar shape (Fehlner, 2002) This means the cluster is a penta-capped octahedral.The predicted skeletal sketch is shown in F-10.This is almost similar to the observed shape (Fehlner, 2002).
Dotted lines denote capping F-10.Sketch of ideal skeletal shape of penta-capped (Cp*W)3(H)B8H8 S= 4n+2(n=6), Closo system.This corresponds to B 6 H 6 2-cluster which has an octahedral shape.The expected shape is sketched in F-11A and the observed one is given in F-11B.
F-11A.Sketch of expected ideal skeletal shape of (Cp*Re)2(H)2B4H8 This means that the cluster is expected to have an inner shape of trigonal bipyramid with three atoms in capping positions.
The expected ideal shape tri-capped trigonal bipyramid skeletal shape is shown in F-12A.This in agreement with the observed shape (Fehlner, 2002) of Cp* 2 Re 2 B 6 H 6 sketched in F-12B.
Thus, Cp* 2 Re 2 B 7 H 7 expected to be a tri-capped octahedral complex.The proposed skeletal sketch is given in F-13A.The shape is similar to the one reported in literature (Fehlner, 2002) and its sketch is shown in F-13B.
F-13A.Sketch of expected ideal skeletal shape of (Cp*Re)2B7H7 F-13B.Sketch of the observed skeletal shape of (Cp*Re)2B7H7

Categorization of Metalloboranes
More than than one hundred metalloborane clusters were categorized using the 4n series method.The results are shown in Tables 1 and 2. Table 2 lists mainly the capped clusters for ease of reference.The clusters form a wide range of series starting with S =4n+6 (arachno) and ending with 4n-8 (penta-capped).The range covers eight families of clusters.This is in contrast to the known stable boranes which comprise only of three main family groups namely, 4n+6 (arachno), 4n+4 (nido) and 4n+2 (closo) with almost no known stable capped boranes (Kiremire, 2015b).According to the 4n series method, the capping series start at 4n+0 and progress to higher capped series.Since capping is prevalent in metalloborane and rare in known borane clusters, it implies that metalloborane clusters indirectly stabilize and promote the existence of fragile capped boranes which are unable to exist on their own.

Conclusion
Capped clusters are relatively common among transition metal carbonyl complexes.On the other hand, such capped clusters are rare in stable borane clusters.In this work, by using the 4n series method, it has been found that capped clusters are prevalent in metalloborane complexes.The capped clusters ranged from 4n+0 to 4n-8 series.This clearly illustrates the fact that metal fragments have a tendency of stabilizing the fragile capped boranes.The 4n series method is extremely useful in categorizing skeletal atoms, molecules, fragments and clusters.

Table 2 .
Display of mainly capped series