Borane Clusters Hiding Inside Carbonyl Clusters

Introduction    

The existence of series in boranes and carbonyl clusters were discovered by Wade and Mingos^1-2. Their studies were supported by Molecular Orbital Theory. Recently, it has been found that the carbonyl and borane clusters in fact do encompass a wide  spectrum of series^3-4. These series which are interrelated and are based on 14n and 4n rules^3-4. If the carbonyl series are given by ST = 14n+q and the corresponding main group elements are given by SG= 4n+q where q can take up multiple integers of 2, positive or negative, then it became clear that ST = (14n+q)-10n = SG = 4n+q.  This implies that if we remove 10n value electrons from the valence electrons (V) of a carbonyl cluster we will have the remaining electrons (V_T) available for conversion into a corresponding  formula of a compound of the main group element. With this in mind, the correlation was focused  mainly on converting carbonyl clusters into borane clusters. These findings are presented in Table 1.

Results and Discussion   

The removal of 10n electrons from carbonyl clusters clearly revealed the close relationship between the 14n series for the transition metal carbonyl clusters and the 4n series of main group elements especially the boranes. The method involves first calculating the valence electrons(V) of the carbonyl cluster. Then subtracting the equivalent 10n electrons. The remaining electrons (V_T) are distributed between equivalent valence electrons of boron skeletal atoms (V_B) and the valence electrons of the hydrogen atoms (V_B) assumed to be associated with boron skeletal atoms. For example, Os₅(CO)₁₆, V = 8X5+16X2 = 72, V_T = 72-50 = 22, V_B = 5X3 = 15, V_H = V_T-V_B = 22-15 = 7. Hence, the borane cluster formula (F_B) corresponding to Os₅(CO)₁₆ cluster = B₅H₇ = B₅H₅^2-. Other borane clusters have been derived in the same way. More examples are illustrated in Schemes 1 and 2.

Table 1: Equivalence Relationship of Carbonyl and Borane Clusters  Click here to View table

 

Scheme 1  Click here to View scheme

 

Scheme 2  Click here to View scheme

 

Equivalence Relationship In Series   

hen the carbonyl series of transition metals and that of the main group elements are scrutinized, then the equivalence relationship between them is clearly discerned. That is if the carbonyl series of the transition metal are given by ST = 14n + α and that of the main group elements by SG = 4n+ β such that α = β including the sign before it, then equivalence relationship between the series does exist. For instance, 14n Ξ 4n (Monocapped series) as α = β = 0. Similarly 14n +2 Ξ 4n +2( Closo series), 14n+4 Ξ 4n+4(Nido series), 14n+6 Ξ 4n+6 (Arachno), 14n+8 Ξ 4n+8 (Hypho),14n +10 Ξ 4n+10(Klapo), 14n-2 Ξ 4n-2 (Bicapped),14n-4 Ξ4n-4(Tricapped), 14n-6 Ξ 4n-6(Tetracappe),14n-8 Ξ4n-8(Pentacapped), 14n-10 Ξ4n-10(Hexacapped) and so on. Therefore, the removal of 10n electrons from a transition metal carbonyl series converts it into an equivalent series of the main group element. This is the principle underlying the clusters presented in Table 1. Many examples other than those presented in the table can be derived.

Structural Relationship of the Cluster Series  

Closo, Nido and Arachno

It is important to briefly explain the terms closo, nido and arachno before touching on equivalence relationship between boranes and carbonyl clusters. These are terms that evolved with the discovery of boranes. They are actually series of compounds which were found to possess structural relationship that was observed within them and reported by Rudolph^2a. The closo ones have the ideal geometries with all the atoms linked with triangular sides. An example is the octahedral B₆H₆²⁻with six skeletal atoms[M-6]. When one atom is removed an ideal square pyramid shape is produced such as B₅H₉ (M-5). The result shape is that of a nido cluster regarded as derived from the octahedral closo system [M-6]. The removal of another atom from  B₅H₉ (M-5) gives a 4-skeletal atom cluster B₄H₁₀(M-4). This is regarded as arachno with two atoms missing from the shape of the original closo octahedral geometry. As we have observed, the spectrum of series especially the carbonyls is wide.

Consider Os₅(CO)₁₆  and  B₅H₅^2- clusters. For the carbonyl cluster, n = 5, 14n = 14×5 = 70 and number of valence electrons(V) =5×8+16×2 = 72 and hence its series (ST = 14n +2 = 72). Also its corresponding cluster number k = 2n-1 = 2×5-1 = 9. This means the carbonyl cluster belongs to 14n+2 series. In the case of the borane cluster, n =5 as well, 4n =4×5 =20 and V =5×3+5+2 = 22 and so SG = 4n+2 = V and likewise it belongs to 4n +2

series. Its k value = 2n-1 = 2×5-1 =9. This implies that Os₅(CO)₁₆ and B₅H₅^2― clusters are equivalent  and their cluster number k values are equal. Hence, it is likely that their skeletal atom geometries will be similar. Indeed, the skeletal atoms of the two clusters portray a trigonal bipyramid⁵ shape as sketched in Figure 1.

Figure 1  Click here to View figure

 

Figure 2 Click here to View figure

 

The clusters Rh₆(CO)₁₆ (V = 86) and B₆H₆^2-(26) are equivalent⁵ since the former belongs to 14n+2 while the later 4n+2. Furthermore, their cluster number values k = 11 are equal and they also have an octahedral skeletal geometry as sketched in Figure 2. Just to familiarize ourselves with the method of establishing the equivalence relationship, let us work on this example. This is well illustrated in Scheme 3.

Scheme 3  Click here to View scheme

 

In exploring the equivalence relationship further, let us focus on diatomic skeletal systems further. The cluster system Rh₂(Cp)₂(CO)₂⁶ is equivalent to B₂H₆, C₂H₄, and O₂. The rhodium cluster belongs to the nido series 14n+4 and with k- value of k = 2n-2 = 2. This means that the two atoms are linked with a double bond, Rh=Rh. Similarly, in the diatomic atoms O₂, and C₂ in  C₂H₄ will be doubly linked, O=O, and C=C.

However in the case of B₂H₆ the double bond is represented by two banana bonds⁵ as sketched in Figure 3.

Figure 3  Click here to View figure

 

The carbonyl complex⁶, Cr₂(Cp)₂(CO)₄ belongs to closo series (14n+2) with k = 2n-1 = 2×2-1 =3. This means that the two chromium atoms are triply linked, that is, CrΞCr. As can be seen from Table 1,this complex is equivalent to C₂H₂(4n+2), with k=2n-1 =3. The C₂H₂ diatomic skeletal molecule indeed has a triple bond, CΞC.  The Mn₂(CO)₁₀ belongs to the Arachno series(14n+6) with k =2n-3 =2×2-3=1. Therefore the manganese carbonyl has a

single bond Mn-Mn. It is equivalent to C₂H₆ (C-C) and F₂(F-F) which belong to 4n+6 series and do have single bonds. What is fascinating is what the shape of B₂H₈(4n+6) will be. What is also interesting is that theoretical studies⁷ which have been done on BH₅(4n+4) and B₂H₈(4n+6) molecules which unlike their hydrocarbon counterparts CH₄ (4n+4) and C₂H₆ (4n+6) are unstable. On the basis of the work done by Olah, etal⁷, the possible structures of the hypothetical molecules BH₅ and B₂H₈ are sketched in Figure 4. Also according to the series, the B₂H₈(4n+6) molecule is expected to have a single bond k = 2n-3 = 2×2-3 = 1. As can be deduced from the series, the counterparts for BH₅  are CH₄ and its analogues such as SiH₄, GeH₄, SnH4 and PbH₄ belong to 4n+4 series as well as carbonyls such as Fe(CO)₅, Ru(CO)₅, and Os(CO)₅ which   belong to 14n+4 series. The bond between the H₂ and B atom is a simplified form of a three-centered bond.

Figure 4  Click here to View figure

 

Capping Series 

The capping carbonyl series give rise to corresponding capped boranes. Many of the hypothetical capped borane series equivalents are useful in categorization of carbonyl clusters.  For instance Os₁₀(C )(CO)₂₄^2-  is equivalent to B₁₀H₄. The series for B₁₀H₄ can be determined as n = 10, 4n = 40 and V = 10×3+4 = 34 and hence SG = 4n-6 =34 = V. This series can be written as 4n +3(-2). We know from the knowledge of series that 4n represents the first capping C¹ and that every (-2) multiple after the 4n represents an additional capping, this means that the series 4n-6, has Cp = C¹ +C³ = C⁴C. By extrapolating B₁₀H₄ to Os₁₀(C )(CO)₂₄^2- complex, then it can be deduced that the carbonyl cluster is tetra-capped octahedral C⁴C[M-6] as it known to be the case⁸. This code is also important as it indicates that the cluster is in the row number six[M-6] beginning from M-1 of the column in which the closo [M-6] is found and then the cluster capped based on [M-6] is in column number six from the closo system [M-6] in the capping series^3-4.

 

The derivation of main group compound equivalent to a carbonyl cluster could easily be reflected in Table 2 of closo series. For instance in case of Os(CO)₄ (V =16) if 10 (n =1)valence electrons are removed then 6 valence electrons will remain. This corresponds to the elements of group 6(or 16) such O, S, Se, and Te, or a combination of fragments such as CH₂ or CR₂. This clearly is in full agreement with Hoffman’s isolobal concept⁹. In the case of Os₂(CO)₇, the valence electrons of 10 for n = 2, could correspond to species such as N₂ and C₂H₂.

Conclusion         

The results obtained and displayed in Tables 1and 2 strongly support of power of the 14n and 4n series and their applications to categorize carbonyl and main group element clusters. They are also in agreement with  the Hoffmann’s isolobal concept. The assumption is that the skeletal elements in transition metal carbonyl clusters must obey the 18 electron rule while those in the main group elements must obey the octet rule. This work greatly complements what has been published elsewhere in literature on carbonyl and borane clusters^1-2,10-13.

Acknowledgement

The author wishes to acknowledge the University of Namibia for financial and material support, NAMSOV, Namibia for generous funding and my wife, Merab Kambamu Kiremire for her encouragement to write up this paper.

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