The Categorization and Structural Prediction of Transition Metal Carbonyl Clusters Using 14 n Series Numerical Matrix

A matrix table of valence electron content of carbonyl clusters has been created using the 14n-based series. The numbers so generated form an array of series which conform precisely with valence electron contents of carbonyl clusters. The renowned 18 electron rule is a special case of 14n+4 series. Similarly, the 16 electron rule is another special case of the 14n+2 series. Categorization of the carbonyl clusters using the matrix table of series has been demonstrated. The table is so organized that clusters numerically represented can easily be compared and analyzed. The numbers that are diagonally arranged from right to left represent capping series. The row from right to left represents a decrease in valence electron content with increase in cluster linkages. The variation of cluster shapes of constant number of skeletal elements especially four or more may be monitored or compared with the variation with the valence electron content.


Introduction
The borane and transition metal carbonyl clusters have been of great interest to chemists for considerable long time due to the special geometries, unusual bonding framework and promising wide range of industrial applications (Stock, 1933;Kobayashi, 2007).The Wade-Mingos rules have been extremely helpful in deducing the cluster geometries (Mingos, 1984;Wade, 1976;Jemmis, 1984Jemmis, , 2001Jemmis, ,2002Jemmis, ,2003Jemmis, ,2005Jemmis, ,2006Jemmis, ,2008;;King, 2002;Welch, 2013).Furthermore, it has been found that carbonyl clusters and some main group clusters can be categorized using 4n and 14n series (Kiremire, 2014(Kiremire, , 2015)).Since the 14n series (14n±q) run parallel to 4n series (4n±q), the 4n series can be used instead of the 14n series.This is because it is easier to use 4n rather than 14n series.We have also demonstrated that the 14n and 4n series can be used to categorize and predict shapes of clusters of carbonyls, boranes and heteroboranes (Kiremire, 2014(Kiremire, ,2015)).In this paper, a numerical sequences based on 14n series that give precise valence contents of clusters and their arrangements into series is presented.In this way, using the valence content of a cluster formula, the cluster can readily be categorized and its possible geometry predicted.

The Extraction of Carbonyl Clusters from the Table
We can use Table 1 to extract carbonyl clusters as needed.Furthermore, it is quite interesting to discover that the table gives precise valence content of the cluster skeletal fragments including the stable mono-skeletal carbonyl complexes that obey the famous 18-electron rule.For instance, when n = 1, and S = 14n+0 = 14.This means the valence content is 14 for a single skeletal element.Suitable transition metal fragments are [Os(CO) 3 ], [ReH(CO) 3 ] and [RhH(CO) 2 ].For n = 1 and V = 18, suitable fragments could be Ni(CO) 4 , Fe(CO) 5 , Cr(CO) 6 , HCo(CO) 4 , HMn(CO) 5 , and H 2 Fe(CO) 4 .Clearly, the widely used and long-standing 18-electron rule of mono-skeletal element clusters is part and parcel of the entire cluster series universe of the transition metal carbonyl complexes.Let us take another example of n = 6 and S = 86.This refers to a valence electron content of 86 for 6 skeletal elements.When we look at the table, this corresponds to series S = 14n+2.The cluster formula corresponding to this will be given by F = 14n+2 = [Os(CO) 3 ](6)+ CO = Os 6 (CO) 18 +CO = Os 6 (CO) 19 .However, we know that the cluster exists as Os 6 (CO) 18 2-and has an octahedral shape (O h ).The special number [14] represents a vital building block for carbonyl series.Other transition metal carbonyl fragments of one skeletal element with 14 valence electron content include RhH(CO) 2 , and ReH(CO) 3 .We can construct carbonyl clusters of these fragments that correspond to S = V = 86 and n = 6 where S means series and V valence electron content.Let us proceed with rhodium, F = 14n+2 = [Rh(H)(CO) 2 ](6)+CO = Rh 6 (H) 6 (CO) 12 +CO = Rh 6 (CO) 3 (CO) 12 +CO = Rh 6 (CO) 16 .This rhodium cluster is well known and is the first one to be found to have an octahedral symmetry (Cotton and Wilkinson, 1980).In these simple operations in terms of valence electrons, [14] in the formula represents the series building block for transition metal carbonyl clusters and for the main group elements the building block is [4].But if we use the 4n series for transition metal carbonyl clusters, [4] should be interpreted as [14] in order to generate cluster formulas.It can be seen that the [2H] = [CO] in terms of valence electron contribution to a cluster fragment or formula.Also [2] in F =14n+2 can be replaced by [CO] or a negative charge of (-2) in terms of valence electron content.That is why the osmium cluster Os 6 (CO) 19 may be written as Os 6 (CO) 18 2-in terms of the series.The rhenium cluster can be derived in the same manner, F = 14n+2 = [Re(H)(CO)3]( 6)+CO = Re 6 (H) 6 (CO) 18 +CO = Re 6 (CO) 3 (CO) 19 = Re 6 (CO) 22 .The following known octahedral rhenium carbonyls , Re 6 (C)(CO) 19 2-, Re 6 (C)(CO) 19 (H) -, Re 6 (C)(CO) 18 (H) 3-, Re 6 (C)(CO) 18 (H) 2 2-,and Re 6 (H) 7 (CO) 18 -, all are electronically equivalent in terms of valence electron content of 86.Let us determine an osmium cluster of the series S = 14n+4 when n = 1.For n = 1 means we will be focusing on one skeletal atom of a fragment.Such a fragment will have S = 14(1)+4 = 18 valence electrons surrounding it.Suppose we assume such fragment has an osmium atom, then the [14] building block will be [Os(CO) 3 , V = 8+3x2 = 14].Therefore the formula fragment of the series S = 14n+4 when n =1 will be given by F = 14n+4 = [Os(CO) 3 ](1)+2CO = Os(CO) 5 .Consider another element say, chromium.The building block of [14] will have the corresponding fragment of [Cr(CO) 4 , V = 6+4x2 = 14].Hence the formula of the carbonyl complex corresponding to 14n+4 for one skeletal atom, n =1 will be given by F = [Cr(CO) 4 ](1)+2CO = Cr(CO) 4 +2CO = Cr(CO) 6 .Thus, a carbonyl cluster of a number of given fragments of a known transition metal can be derived in the same manner.

Categorization of carbonyl Clusters Using the 14n Series Matrix Table
The use of Table 1 to categorize a given cluster is straight forward.First of all, the valence content(S or V) of the cluster is calculated.Then the number (n) of the skeletal elements is noted.Finally you identify on the matrix where the value V corresponding to a given n is.The corresponding cluster series is read off on the top of the matrix table .A few examples will be used to illustrate this.Take Os 3 (CO) 12 cluster, n = 3, V = 48.Moving along n = 3 axis and reaching 48, the vertical movement arrives at the series S = 14n+6.This means the cluster belongs to ARACHNO series.The clusters,Os 4 (CO) 14 ; n = 4, V = 60,S = 14n+4, NIDO; Os 5 (CO) 16 , n = 5, V = 72, S = 14n+2, CLOSO;Os 6 (CO) 18 ; n = 6, V = 84, S = 14n+0, mono-capped, C 1 C[M-5] on trigonal bipyramid cluster;Os 6 (CO) 18 2-cluster, n = 6, V = 86, S = 14n+2, CLOSO;Os 8 (CO) 22 2-, n = 8, V = 110, S = 14n-2, bi-capped cluster, C 2 C[M-6] on an octahedral geometry;Os 10 (CO) 26 2-, n = 10, V= 134, S = 14n-6, C 4 C[M-6] is a tetra-capped octahedral cluster; and Pd 23 (CO) 20 L 10 , n = 23, S = 14n-32, C 17 C[M-6]-has 17 capped atoms and 6 nuclear cluster atoms possibly forming an octahedral shape.In the case of this palladium cluster, its valence content of 290 for n = 23 does not appear in Table 1.However its cluster series can be obtained by simple extrapolation.For n = 23, V= 310 when S = 14n -12.Now when n = 23 and V = 290 along the n = 23 row, V undergoes a decrease of 310-290 = 20.Therefore S value has to decrease by the same amount.This means the required S = 14n-12-20 = S = 14n-32, and Cp = C 17 C [M-6].This means that the cluster has a closo octahedral complex surrounded by 17 atoms.A closo cluster refers to S = 14n+2 series.For [M-6] closo nuclear cluster, n = 6 and V = 86 as shown in Table 1.A collection of known carbonyl clusters categorized in this manner are given in Table 2.The matrix table was also utilized to categorize a number of ruthenium carbonyl clusters generated using UV Laser Desorption Mass Spectroscopy (Critchey, et al 1999).The results are shown in Tables 3 and 4.
The next set of cluster set for the S = 14n+4 series is (3,46) The cluster number k can be calculated from the series formula.For S = 14n+4, k =2n-2.Therefore, 5)-2 = 10-2 = 8.The metal-metal skeletal linkages is related to geometrical skeletal structures for clusters of low nuclearity.For the 14n+4 series k = 0 for n = 0 and k = 2 for n = 2.In the case of k =2 for n =2 two metal atoms joined together by two linkages.Thus, there is a metal-metal bonding of bond order 2. That is, MM, and hence the following complexes(C 5 H 5 ) 2 Rh 2 (CO) 2 , Re 2 (C 5 H 5 ) 2 (CO) 4 , Re 2 H 2 (CO) 8 and Os 2 (CO) 8 are expected to have metal-metal double bond.For n =3, k = 4 implies that there 4 linkages within the 3 metal atoms.The possible linkages are of the skeletal elements M-2 to M-5 for 14n+4 series are shown in Figure 1.

Correlation between Transition Metal Carbonyl Clusters with Main Group Clusters
Let us consider S = 14n+6 for n =2, and k =2n-3 = 1 The value of S = 14(2)+6 = 34.This in agreement with the valence content of Mn 2 (CO) 10 and the presence of single metal-metal bond in the complexes.Let us consider the complex Co 6 (C)(CO) 15 2-.We can code the complex as (6, 90).This means that the 6 skeletal elements are surrounded by 90 valence electrons.It also belongs to 14n+6 series with k = 2n-3 = 2(6)-3 = 9.From the series, we can deduce that the parallel main group series is S = 4n+6.For n = 6, we can also derive the corresponding hydrocarbon formula as F = 4n+6 = [C](6)+6H = C 6 H 6 .The carbon atom with a valence content of 4 can be used as a building block replacing [4] in the formula and replacing n by 6 and the last 6 in the formula substituting it with 6 H atoms which are assumed to supply six electrons.If we were considering carbonyl clusters, 6 could be replaced by 3 CO molecules.In summary Co 6 (C)(CO) 15 2-⥈C 6 H 6 .For both clusters, k = 2n-3 = 9.The shape of Co 6 (C)(CO) 15 2-is trgonal prism (see F-9 Figure 3).One of the isomers of C 6 H 6 is sketched in Figure 6, F-12 for benzene and F-13 for prismane.The structure of F-13 is similar to that of F-11.However, in case of C 6 H 6 , many more isomers can be generated which can satisfy the requirement of k =9.Some selected known fragments and complexes for CLOSO, NIDO and ARACHNO series respectively are indicated in trees T-1, T-2 and T-3.

2+
(1,20), Ni(CN) 4 2-(1,20), (C 5 H 5 ) 2 TiCl 2 (16), RhCl(PPh 3 ) 3 (1,16), MR 2 (M = Zn, Cd, Hg) (1,14),TiCl 4 (1,8) as first members of the respective series in Table 1.Clearly, the 18-electron rule of 14n+4 series that has a wide range of complexes has enjoyed the attention of science for a long time (Langmuir, 1921;Miessler,2014).The prevalence of 18-electron based complexes could imply that the 18-electron system (island of chemical stability)is more stable than 16, 14 or any other valence electron systems.The valence electron content around a cluster of skeletal elements has great influence on the shape of the skeletal elements regardless of their origin.That is, (6, 86) has a tendency to form an octahedral shape (O h ).For example, [M-6, 86, M= Os, Rh, Re ) of S = 14n+2 closo series are all expected to have an octahedral geometry.The valence electron table as written (Table 1) presents capping series along the diagonal from right to left.However, the capping series as defined by 14n+0 column-begins with mono-capping [C 1 C] series with the very series 14n+0 column.The horizontal movement from right to the left in Table 1 results in the successive increase of k value by 1.On the other hand the movement along the diagonal gives a stepwise change in cluster k value by 3. The movement along the column involves the successive variation of k value by 2. The series matrix(Table 1) implies that the clusters especially the transition metal carbonyls are all interrelated via series.Thus, the 18-electron rule complexes (1,18) of 14n+4 are interrelated with those of (2,32), (3,46), (4,60) and so on which belong to the S =14n+4 series.There is also an interesting correlation

Figure 8 .
Figure 6.Sketches of some of the capping series based on Octahedral cluster

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. The cluster examples include Os 3 H 2 (CO) 12 , Re 3 H 3 (CO) 10 It has been shown that 14n-based series of transition metal carbonyl clusters and fragments run parallel to the 4n-based series of main group clusters and fragments.Hence, 14n +6 will correspond to 4n+6 of the main group elements.While the [14] electron content is utilized to form a backbone of transition metal carbonyl clusters, the [4] electron content can be used to construct the backbone of main group clusters.A natural suitable fragment is carbon [C] or boron hydrogen[BH].The complex (C 5 H 5 ) 2 Rh 2 (CO) 2 belongs to 14n+4 series with k = 2.The series 14n+4⥈ 4n+4.The hydrocarbon corresponding to this for n =2 is given by F = 4n+4 = [C](2)+4H = C 2 H 4 .For k = 2 for n = 2, means that both the rhodium complex and C 2 H 4 have double bonds.Their shapes are sketched in Figure5.The structure of related diborane is added comparison.
That is, 14n+2 ⥈ 4n+2.In order to find its equivalent hydrocarbon we must derive it from the series F = 4n+2 for n = 2, this means F = [C](2)+2H = C 2 H 2 .As we know well,C 2 H 2 has a carbon-carbon triple bond, C≡C.Similarly, Mo 2 (C 5 H 5 ) 2 (CO) 4 is expected to have a triple bond around which the supporting ligands congregate.Its possible structure is shown in Figure4and that of C 2 H 2 is inserted in the background for comparison.It is readily deduced that CH fragment is isolobal to (C 5 H 5 )Mo(CO) 2 fragment.

Table 2 .
Known Carbonyl Clusters Categorized Using the Cluster Matrix Table

Table 3 .
Carbonyl Clusters from Research Paper Categorized Using the Cluster Matrix Table

Table 4 .
Further Categorization of Carbonyl Clusters from Research Paper Using the Cluster Matrix Table