Capping and Decapping Series of Boranes

Whereas many of the capped series of carbonyl clusters of transition metals are known, those of corresponding borane series are unknown. These include the monocapped, bicapped, tricapped, tetracapped and so on. This paper attempts to correlate selected capped series of the carbonyl series with the hypothetical corresponding ones of boranes using 14n and 4n rules. Some selected examples of capped and decapped borane series have been generated and tabulated. The borane clusters are found to follow a precise numerical algorithm. A comparison of selected examples of carbonyl cluster of lower series such as closo, nido and arachno with the corresponding borane clusters has been made. The popularly cited Rudolph system of deducing shapes of clusters is also discussed in terms of decapping series. The use of fragments and their corresponding fragment series enormously simplifies the categorization of molecular formulas into series from which their shapes can be predicted with or without the use of the cluster number (k value). The fragment series vindicates the vital Hoffmann’s isolobal concept very well.

With the above background information, let us illustrate the capping concept with the octahedral carbonyl cluster Os 6 (CO) 18 2− .For the purposes of our illustration, Os 6 (CO) 18 2− may be regarded as Os 6 (CO) 19 (equivalent number of valence electrons).Capping the cluster, simply means successive additions of Os(CO) 2 fragment.Since the fragment Os(CO) 2 belongs to 14n-2 series, its k-value is given by k =2n+1= 2x1+1 = 3.This means when capping or decapping takes place the cluster k value changes by 3.This is shown in Scheme 1.As can be discerned from Scheme 1, the number of osmium atoms increases by one for every step while the number of carbonyl ligands increase by two.When a cluster is decapped, the opposite happens.The Os 6 (CO) 19 carbonyl cluster has a total of 86 valence electrons (V CC ) and belongs to 14n+2 closo series.Since the method of using series to classify a cluster is not common, it is important to briefly demonstrate it.The Os 6 (CO) 19 carbonyl cluster may be expressed in fragments as F = [Os(CO) 3 ] 6 (CO).The corresponding cluster series can then be calculated from the fragments as S =6[Os(CO) 3 ]+ CO.The fragment Os(CO) 3 has a content of 8+3x2 = 14 valence electrons.Applying the 14n rule utilized in our earlier work (Kiremire, 2015b), the fragment belongs to S = 14n (n = 1) series.Hence all the fragments are then converted into valence electron equivalents.Thus, S = 6[8+3x2]+2 = 6[14]+ 2 = 6[14n]+2.The interesting aspect about the algebra of series, it is found that the multiplier does not affect the value of 14n in case of transition carbonyl clusters or 4n in the case of the main group elements.What matters is the value of n of the fragment under consideration.In this regard, 6[14n] = 14n (where n = 6) in this case.Therefore the overall value of the cluster series S =6[14n]+2 = 14n+2.Hence, this cluster is a member of closo series.Its valence content is also obtained from the series S = 14n+2.THUS, when n = 6, S= 14(6) +2 = 86.This value is the same as the valence electrons obtained from the formula F=Os 6 (CO) 19 = 8x6+19x2 = 86.A paper explaining using series to categorize clusters into series and predicting their possible shapes is in press (Kiremire, 2015).Since Os 6 (CO) 19 is a closo cluster of six skeletal elements (6 Os) we can look for its corresponding borane (cousin) closo cluster of 4n+2 series.In order to do that we must convert 14n+2 to 4n+2 by removing 10n electrons.Since we are considering an octahedral cluster of 6 skeletal atoms, n =6.Hence, 10n = 10x6 = 60.Therefore, the borane cluster valence electrons (V BC ) = V CC -60 = 86-60 = 26.The valence electrons of the borane cluster will include those of 6 boron skeletal atoms and the accompanying hydrogen atoms.Let the valence electrons of boron skeletal atoms be V B = 6x3 =18.Hence the remaining valence electrons will be for the hydrogen atoms.Thus, V H =26-18= 8. Hence, the number of the hydrogen atoms expected to combine with the 6 boron atoms will be 8. Therefore the corresponding borane cluster formula will be given by F =B 6 H 8 .We can verify to see if F = B 6 H 8 cluster is also closo as follows F=B 6 H 8 =(BH) 6 H 2 .For this cluster S If we put n = 6 into the cluster formula we get S F =4(6)+2 = 26.Also the k value is given by k = 2n-1 = 2(6)-1 = 11.The number of valence electrons for the cluster B 6 H 8 , V = 3x6+8 = 26.However, we know that the closo boranes occur as negatively charged species and so B 6 H 8 does exist as B 6 H 6 2- (Cotton and Wilkinson, 1980).The addition of Os(CO) 2 capping fragment to Os 6 (CO) 19 carbonyl cluster produces Os 7 (CO) 21 -a mono-capped closo cluster (C 1 C).Its cluster series is readily determined from F = Os 7 (CO) 21 =[Os(CO) 3 ] 7 ; S = 7[14n] = 14n, k = 2n = 2x7 = 14.Clearly the capping of Os 6 (CO) 19 to form Os 7 (CO) 21 the k value has changed from 11 to 14 by a value of 3 as expected.The borane cluster corresponding to Os 7 (CO) 21 is deduced as explained for Os 6 (CO) 19 cluster.The borane cluster deduced is B 7 H 7 .The cluster series for F =B 7 H 7 =(BH) 7 ; S = 7[4n] = 4n, k = 2n = 7x2 =14.The k value for B 7 H 7 is the same as that of Os 7 (CO) 21 carbonyl cluster.What is clearly seen is that the octahedral closo cluster B 6 H 8 has been transformed into a hypothetical mono-capped borane B 7 H 7 .The analysis of the transformation shows clearly that one of the hydrogen atoms in B 6 H 8 has been converted into a boron atom or removed and replaced with a boron atom during the capping process.The successive conversion of hydrogen atoms into B atoms gives the borane products B 7 H 7 (7,7) Ξ Os 7 (CO) 21 , B 8 H 6 (8,6) Ξ Os 8 (CO) 23 , B 9 H 5 (9,5) Ξ Os 9 (CO) 25 , B 10 H 4 (10,4)Ξ Os 10 (CO) 27 , B 11 H 3 (11,3) Ξ Os 11 (CO) 29 , B 12 H 2 (12,2) Ξ Os 12 (CO) 31 , B 13 H 1 (13,1)Ξ Os 13 (CO) 33 and B 14 H 0 (14,0) = B 14 Ξ Os 14 (CO) 35 .
The capping sequence can numerically be expressed as (6,8)→(7,7)→(8,6)→(9,5)→(10,4)→(11,3)→(12,2)→(13,1)→(14,0).We can also work out the k values of the corresponding series of the capped boranes in order to be more familiar with the method of using fragments.Starting with B 8 H 6 as an example, F = B 8 H 6 = (BH) 6 (B) 2 .In this form, we can convert it the series fragments as S=6 4] in terms of valence electrons.Since the fragment has only one skeletal atom, the fragment belongs to the series S = 4n.However the fragment [B] = [3] valence electrons is short of one to become 4n.Hence, its series is given by S=[3]=[4-1]=[4n-1].We can therefore determine the cluster series of the molecular formula B 8 H 6 as S F =6[4n]+2[4n-1] = [4n] + [4n-2].As stated earlier, the multiplier does not change 4n except the integer associated with it.Hence, S F =4n +4n-2=4n-2 (4n+4n is simply =4n).If n=8, then the value of S F =4(8)-2=30 which is the same as the valence electrons given by V=B 8 H 6 =8x3+6=30.This tells us that the series formula makes sense.We can try one more borane cluster B 9 H 5 .The order of formulating fragments to determine molecular formula series does not matter.The borane formula B 9 H 5 can be broken into F = 9[B]+5[H] fragments.By inserting in the respective valence electrons we can derive the series S F =9[3]+5 =9[4-1]+5 = 9[4n-1]+5 =4n-9+5 = 4n-4( again according to the algebra of these series, 9x4n = 4n).To verify that the series formula is correct, insert n=9 into the formula then, S F =4(9)-4=32.The number of valence electrons of B 9 H 5 =9x3+5 =32.Since the series of the cluster is given by S F =4n-4, the k value of the borane cluster is obtained from k=2n+2=2(9)+2=20.The k values for the remaining capped boranes, B 10 H 4 , B 11 H 3 , B 12 H 2 , B 11 H 1 and B 14 can be worked out in the same way.Starting with the k value of B 6 H 8 , they are k = 11,14,17,20, 23,26,29,32 and 35 respectively.The last k value =35 is for the B 14 cluster, the final capping product of the B 6 H 6 2− series.The B 14 cluster belongs to the series S=(B) 14 ; S=14[3]=14[4-1]=14[4n-1] = 4n-14.The k value for B 14 can be calculated from k = 2n+7 = 2(14)+7 =35 .The capping term is given by Cp = C 1 +C 7 = C 8 C[M-6] is shown in Scheme 1.The capping expression is derived from the knowledge of the series.For instance, if we write the series S = 4n-14 as S = 1(4n)+7(-2), then the (4n) represents a mono-capped term while every (-2) after (4n) represents an additional capping.Hence, the total cappings after the inner core octahedral closo cluster will be 1+7 = 8.That is what the symbol C p =C 1 +C 7 =C 8 C[M-6] stands for.The [M-6] means the inner core comprises of six skeletal atoms which constitute an octahedral closo fragment and the C 8 symbol means that eight atoms surround the six atoms as capping elements.This may be viewed as a cluster within a cluster.That is, a nucleus of six surrounded by other eight atoms and the total number of atoms for the whole cluster is 14.The fascinating immense power of fragments and series can be illustrated by deducing the series of the giant carbonyl cluster Ni 38 Pt 6 (CO) 48 (H) 5-complex.We can split the cluster into the following fragments S=38 =14n-88+14 =14n-74.This means the cluster belongs to S=14n-74 series.For S=14n-74=1(14n)+37(-2), C P =C 1 +C 37 =C 38 C[M-6].This symbol implies there are six atoms forming an octahedral cluster nucleus surrounded by 38 other capping atoms.Indeed, it is amazing that the x-ray crystal structure showed six platinum atoms constituting an octahedral nucleus in the center surrounded by 38 nickel atoms in the giant cluster (Rossi and Zanello, 2011) of 44 skeletal atoms.The number of skeletal atoms in the complex is 44.Inserting n =44 into S=14n-74 gives S=14(44)-74=542.The sum of valence electrons of the complex V=44x10+2x48+1+5=542. Therefore, the series can be viewed to represent the valence content of the cluster or fragment.The capping formulation was explained in our earlier work (Kiremire, 2015b).The geometries of the possible isomers of carbonyl clusters Os 6 (CO) 19 (f-1), Os 7 (CO) 21 (f-2), Os 8 (CO) 23 (f-3), Os 9 (CO) 25 (f-4), Os 10 (CO) 27 (f-5), Os 11 (CO) 29 (f-6), and Os 12 (CO) 31 (f-7) are given in Figure 1.On the basis of the capping principle of the boranes, we can deduce the final capping clusters derived from the selected closo boranes as follows and is indicated in brackets: BH 3 (B 4 ), B 2 H 4 (B 6 ), B 3 H 5 (B 8 (B 26 ).Theoretical studies of the cluster B 12 H 6 have recently been conducted (Ohishi,et al., 2009;Szwacki, et al., 2009).This cluster is predicted to be stable with aromatic properties.This cluster may be regarded as a tetracapped derivative of B 8 H 10 (B 8 H 8 2-) closo borane.Also the naturally occuring boron cluster B 12 (Higoshi and Ishii, 2001) may be regarded as the final capping member of the closo series based on B 5 H 7 (B 5 H 5 2-).Furthermore, a fullerene-type boron cluster B 40 has been discovered by laser-vaporization experiments (Zhai et al., 2014).This may be considered to belong to a series given by S = 40 ) closo borane.Among boron clusters which are being studied theoretically (Zhai, et al., 2003)

Decapping Borane Series and the Corresponding Osmium Carbonyl Cluster Series
As mentioned earlier, the fragment Os(CO) 2 with a content of 12 valence electrons and a member of the series 14n-2 was used in the capping series of an octahedral osmium cluster complex,Os 6 (CO) 19 .If we do the reverse, instead of successively adding the capping fragment to the cluster, we can successively remove the fragment from the initial closo cluster.The new cluster species generated constitute the decapping osmium series.The corresponding cousin boranes may be produced in the same manner to generate decapping borane series.For instance, the removal of Os(CO) 2 from Os 6 (CO) 19 produces Os 5 (CO) 17 cluster.Its series can be derived as follows: S=5[Os(CO) 3 ]+2CO=5[8+3x2]+4=5[14]+4=5[14n]+4=14n+4.Hence, this cluster with a valence electron content of 74, is member of nido series (14n+4).In order to get its corresponding borane cousin cluster we must remove the 10n electrons.The corresponding borane cluster will have 5 skeletal atoms and so n = 5.Therefore the number of valence electrons to be removed =10n=10x5 = 50.Thus the required borane cluster will have 74-50=24 valence electrons.These electrons have to be distributed among a borane cluster with 5 boron skeletal toms and the accompanying hydrogen atoms.Thus, applying the same approach used above in the octahedral cluster V BC =24, V B =3x5 =15 and V H = 24-15=9.Therefore the corresponding borane cluster cousin is given by F = B 5 H 9 .The decapping series of Os 6 (CO) 19 are summarized in Scheme 2. The corresponding k value decreases by 3. The negative k values imply that the existence of such species is quite remote.The series are quite precise.Whereas the capping ones terminated at B 14 [with 42 valence electrons]and Os 14 (CO) 35 [182], the decapping process ends at 7(CO)[14] and 14H[14] and the figures in brackets indicate the total valence electron content.The former termination shows the production of 14 borons and the later shows the production of 7 carbonyls with 14 valence electrons and no cluster atom and 14 hydrogen atoms with 14 valence electrons.It is important to note that the capping fragments also follow the law of parallel series.For instance Os(CO) 2 fragment is a member of 14n-2 with 12 electrons, while the (B,-H) fragment with its electron content of 2 follows the 4n-2 rule.There is a difference of 10 (10n = 10x1) valence electrons between 12 and 2.

Capping and Decapping Borane Series
We have demonstrated the concept of numerical generation of capping and decapping borane series for closo B 5 H 5 2-and B 6 H 6 2-clusters.The results of these are given in Schemes 3 and 4. Starting with any member of the closo series B n H n 2-, borane molecules and fragments can be derived by the applying the numerical method illustrated in Schemes 3 and 4.This has been done for the series, n = 1 to n = 12.The results are given in Tables 1 and 2. 1 and 2 It is quite easy to find a given borane molecule or fragment if the sum of the atoms in the given formula including any charge if present add up to the value on the top of Table 1 or 2. Take the following examples for illustrations.First, BH 3 (1+3 = 4), the sum of the atoms is 4. When we look at Table 1 and identify the column headed by 4, it seen that BH 3 is a member of the closo series.Next, B 2 H 6 (2+6 = 8), this is found in the column headed by 8 in Table 2 and belongs to Nido series.Consider B 4 H 10 (4+10 =14).Again, we follow the procedure and check at the column headed by 14.The molecule belongs to arachno series in Table 2. Let us consider B 8 H 12 (8+12 = 20).This is found in Table 2 and is a member of Nido series.It is observed the when B m H n (m=n), the cluster belongs to Mono-capped series 4n.When m <n, the cluster is in Table 2 of Decapping Series and when m>n the cluster is in Table 1 of Capping Series.Consider B 9 H 1 ( 9+1 =10, m>n), the cluster will be found in Table 1 in the column headed by 10.The cluster is a member of penta-capped series.For clusters such as B 4 H 7 (4+7 =11) in which the sum of m and n is an odd number are not considered in this paper as they are not linked to 4n+2 series.Also for m+n (even number)> 26 will lie outside the range of Tables 1 and 2. Just to test the importance of Tables 1 and 2, we looked at some of the boranes mentioned in Lipscomb [26].All these boranes are found in Tables 1 and 2 under the column headed by the number indicated in the bracket after the formula.Tables 1 and 2 may be expanded as required.

Rudolph Decapping Series of Clusters
In order to understand the Rudolph system of correlating shapes of clusters, we need to briefly interpret the numbers in Table 3.Let us take a few examples.Consider the row beginning with the set (6,8).This set represents a borane of formula B 6 H 8 .This borane is a member of the closo series which exist in ionic form in this case B 6 H 6 2-.The next set (5, 9)which is derived by rearranging (6,8) by removing one from 6 leaving 5 and adding it to 8 giving us 9 represents B 5 H 9 which is a nido cluster.Doing the same rearrangement on (5,9) produces the set (4, 10).This set represents the borane B 4 H 10 which is an arachno cluster.The remaining sets of numbers (3,11), (2,12), (1, 13) and (0, 14) represent B 3 H 11 , B 2 H 12 , BH 13 , and H 14 respectively.Some of the fragments represented by numbers are just of academic interest as they may not exist.The first column of numbers represent some members of closo series.These are (1,3) →BH 3 , (2,4)→B 2 H 4 , (3,5)→B 3 H 5 , (4,6)→B 4, H 6 , (5,7)→B 5 H 7 , (6, 8)→B 6 H 8 ,and so on.The next column represents members of the nido series and so on.Rudolph analyzed the structures of boranes and identified the geometrical relationship linking the closo(4n+2) geometry with the corresponding nido(4n+4) and hypho(4n+6) geometries.This relationship is now well known (Rudolph, 1976).However, with our knowledge of series, this geometrical relationship of boranes and other clusters is part of the Decapping Series.The Rudolph decapping series has been represented numerically in Table 3.The numbers shown in Table 3 3 gives the decapped members derived from the corresponding closo series.The set of numbers (5,7)→(4,8)→(3,9) represent B 5 B 7 , B 4 H 8 and B 3 B 9 respectively; (6,8)→(5,9)→(4,10) represent B 6 H 8 (shape Fig. 1: f-1), B 5 H 9 (shape Figure 2: f-2), and B 4 H 10 (shape Figure 2:f-3)respectively.Let us consider the series (7,9)→(6, 10)→(5,11).These numbers correspond to B 7 H 9 (B 7 H 7 2-), B 6 H 10 and B 5 H 11 borane clusters which form part of Rudolph decapping series (Cotton and Wilkinson, 1980).Applying the concept of fragments and their series the k-values corresponding to the formulas of the clusters can be calculated as follows.
The skeletal shapes of the B 7 H 7 2-, B 6 H 10 and B 5 H 11 are shown in Figure 3.The other sets of numbers can be translated into formulas in the same manner.

Applying Isolobal Fragments to Deduce Cluster Series and Predict Possible Cluster Shapes
Take B 5 H 5 2-as an example.The method has been developed for categorization (Kiremire, 2015) of clusters using 4n or 14n rule and will be applied here.We can write the formula as (BH) 5 2-.The series can be derived from S = 5[BH]+2 = 5[3+1]+2 = 5[4]+2 = 5[4n]+2 = 4n+2.Since B 5 H 5 2-belongs to 4n+2 series, it is a closo cluster.The cluster k-value = 2n-1 = 2x5-1 = 9 based on the cluster series (4n+2).This k-value is characteristic of a trigonal bipyramid geometry (Figure 2:f-1).Consider a carborane C 2 B 3 H 5 .We can write the formula as (CH) 2 (BH) 3 .The series of the molecula formula can be derived from S T = 2 . This means that the cluster belongs to the closo series with k-value = 2n-1 = 2x5-1 = 9.This implies the cluster will have an ideal skeletal shape of a trigonal bipyramid (Figure 2:f-1).Another example (C 4 H 4 )Fe(CO) 3 .The cluster formula can be decomposed into the fragments F =[Fe(CO) 3 ]+ 4[CH] and the corresponding cluster series can be derived from the valence electrons of the fragments as follows . Hence, the cluster (C 4 H 4 )Fe(CO) 3 is a member of S = 4n+4 (nido) series.To simplify the analysis of the series for structural identification, 14n has been taken to be similar to 4n and the additions or multiples of 4n do not affect it and it remains as 4n.In other words, in series, y(4n) or y(14n) = 4n or 14n where y = is an integer, 1,2, 3 , and son.Therefore the cluster belongs to nido series (4n+4) with k-value of 2n-2 = 2x5-2 = 8.This k value of 8 is a characteristic of a square pyramid geometry(see Figure 2: f-2).Thus, all the 4 carbon atoms are bonded to Fe and agrees with (η 4 -C 4 H 4 )Fe(CO) 3 formulation.Let us consider the metalloborane B 4 H 8 Fe(CO) 3 .Using the same approach, S T =[Fe(CO . This is also a nido cluster with k = 8.It will have a similar geometry as C 4 H 4 )Fe(CO) 3 .The cobalt complex (B 4 H 8 )Co(η 5 -C 5 H 5 can be analyzed using the same approach.F = B 5 H 9 = (BH) 5 H 4 ; S The equivalence of the cluster k value implies that there is a similarity of the symmetries of the skeletal shapes of the clusters and these are shown in Figure 4.It is found that the cobalt cluster has two isomers (Greenwood and Earnshaw, 1998) ) 3 ] also belong to the 14n series.We also now know that 14n is similar to 4n, meaning that these fragments are isolobal.

Table 1 .
include B 36 and B 42 .The table could be expanded if necessary.