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Categorization and Structual Determination of Simple and More Complex Carbonyl Clusters of Rhenium and Osmium Using K-Values and the Cluster Table

Volume 31, Number 1

Enos Masheija Kiremire*

Department of Chemistry and Biochemistry, University of Namibia, Private Bag 13301, Windhoek, Namibia

DOI : http://dx.doi.org/10.13005/ojc/310133

Article Publishing History
Article Received on :
Article Accepted on :
Article Published : 23 Mar 2015
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ABSTRACT:

The shapes of conventional covalent compounds of main group elements and transition metal complexes can usually be deduced from their formulas. However, this is not the case for transition metal carbonyl clusters whose structures more or less resemble those of boranes and carboranes. Tremendous interest in the shapes of metal carbonyl clusters have been kept alive for more than five decades. Polyhedral skeletal theory, Jemmis rules, graph theory, and topological theory among others have been put forward so as to understand the structures of transition metal carbonyl clusters. This paper presents a highly simplified user friendly cluster table based on k-values which can be utilized together with an empirical formula to deduce the symmetries of simple to more complex cluster carbonyl complexes without any background of cluster theories. This approach highly complements the existing theories, in particular, the renowned polyhedral skeletal electron pair theory (PSEPT).

KEYWORDS:

shapes; Categorization; Categorization; Carbonyl Clusters

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Kiremire E. M. Categorization and Structual Determination of Simple and More Complex Carbonyl Clusters of Rhenium and Osmium Using K-Values and the Cluster Table. Orient J Chem 2015;31(1).

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Kiremire E. M. Categorization and Structual Determination of Simple and More Complex Carbonyl Clusters of Rhenium and Osmium Using K-Values and the Cluster Table. Orient J Chem 2015;31(1). Available from: http://www.orientjchem.org/?p=8055

Introduction

Recently, a cluster table for transition metal carbonyls and has been designed to assist in the categorization of clusters and tentative assignment of geometries of clusters1-5. The cluster table has been re-arranged in such way that it has become much more user friendly. In this way, a given cluster can easily be categorized and its geometry tentatively assigned.

The cluster number, k-value for a carbonyl cluster is calculated1-5 using the empirical formula    k = ½ (E-V). By analyzing the cluster numbers, it has been possible to discern the latent infinite world of series of clusters for elements which obey the 18-electron rule or 8-electron rule(octet rule). Some of these series have been organized and are presented in Table 1. In the newly reorganized and simplified table, the columns represent Mx values where x = 2,3, 4, 5, 6, and so on. In this new table,the movement down an Mx column is like driving along a ‘highway’. The movement crosses the columns of different cluster series that vary by ∆k = ± 1.That is, a change of one linkage or bond while the number of skeletal atoms remains the same. It is similar to adding or removing a monodentatelig and (a pair of electrons) step by step. The horizontal movement along the series represents a progressive change in ∆k = ±2 and a change of Mx value by 1. The series comprises of different cluster values( k values) but belong to the same broad category type such as closo, nidoor arachno and so on. In a way each box or square in Table 1 may be regarded to be similar to a ‘clan’ which has many ‘family’ member series. Thus, the box can represent members from, rhenium, ruthenium or osmium ‘families’or any other family and so on. The diagonal movement represent a process in which there is a progressive change by ∆k = ± 3 and Mx by 1 as you shift from one type of ‘cluster clan’series to another. This corresponds to a capping process.

Results and Discussion

A selected range of carbonyl clusters taken mainly from rhenium element have been used as illustrations to categorize the clusters. The results re given in Table 2.In almost all cases categorization of clusters using the empirically calculated k-value and the cluster Table 1 are in agreement with those obtained by the known methods. A few examples are hereby given to illustrate the ease of utilizing the cluster table for categorizing a given cluster from its molecular formula.

  1. Re4(H)4(CO)132-;   E = 4X18 = 72, V = 7×4 +4+ 13×2+2 = 60; k = ½ (E-V) = ½ (72-60) = 6.

‘Raw code’ of the cluster is represented as M-4-6-60:- where M refers to the cluster skeletal element, 4 –the number of skeletal elements, 6-the number of skeletal bonds or linkages, and 60 the total number of valence electrons.  Table 1 has been constructed using a series of raw codes. In order to determine the type of cluster series it belongs to, we look at the cluster Table 1 under ‘M-4 highway’.  The M-4 highway is scanned until the raw code M-4-6-60 is found.  Keeping on the same row, moving to the left, it is found that the raw code is in line with letter N(N = nido). Hence, the cluster is categorized as M-4-6-60-N. Therefore the cluster, Re4(H)4(CO)132- is a member of Nidoclan series of 4 skeletal elements with a total of 60 electrons.The 4 skeletal atoms with 6 linkages are normally found to form an ‘ideal’ tetrahedral (Td ) geometry Fig.1.

Figure 1 Figure 1

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The shape is drawn as a projection looking at it from above.

2. Re5(C)(CO)16(H)2-; E = 90, V = 74, k = ½ (E-V) = ½ ( 90-74) = 8. Raw code = M-5-8-74. As can be seen from Table 1, this cluster also belongs to the Nido family. The cluster category is M-5-8-74-N. The skeletal shape will be a square pyramidC4v. This is shown in Fig. 2.

Figure 2 Figure 2 Click here to View figure

 

3. Re4(CO)162-; E = 72, V = 62, k = 5, raw code = M-4-5-62. Reading from M-4 highway column in table 1, the category code is M-4-5-62-A(arachno, butterfly shape). This shape is given in Fig. 3.

Figure 3 Figure 3
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4. Os5(CO)16; The cluster has the derived category code of M-5-9-72-C. The complex belongs to the closo series. This is a geometry characteristic of regular trigonalbipyramid(D3h) shown in Fig. 4.

Figure 4 Figure 4 

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5. It is interesting to note6 that the cluster complexex RuIr4(CO)152―(M-5-7-76-A),  was found to have elongated trigonalbipyramid shape while on the other hand Os5(CO)16(M-5-9-72-C) was found to have regular trigonalbipyramid shape. The skeletal cluster shape of M-5-7 may be represented as indicated in Fig. 5.

 

Figure 5 Figure 5

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It is not a surprise therefore that the two complexes (M-5-7-76-A) and (M-5-9-72-C) differ in length measurements as they truly belong to different series.

K-Isomerism

In some cluster systems with the same cluster code may exhibit different shapes which may be regarded as isomers. For instance7, Os6(CO)182―(M-6-11-86-C) with k value of 11 has an octahedral shape,

Figure 6 Figure 6 

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while O6(H)2(CO)18 (M-6-11-86-C) with k value of 11 has a mono-capped square pyramid, Fig. 7.

Figure 7 Figure 7

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Also the complexes7 Re4(H)4(CO)152―(E = 72, V = 64, k = ½ (E-V)= 4;from table cluster belongs to the Hypho series and code is M-4-4-64-H. Similarly, the cluster Re4(H)4(CO)16 has a code M-4-4-64-H. However, the cluster shapes are different. The skeletal shapes are given in Fig. 8 and 9.

Figure 8 Figure 8

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Figure 9 Figure 9

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More Examples for Illustration of the Use of Cluster Table.

The osmium cluster Os6(CO)18 great interest6. It is considered as a bi-capped tetrahedron or mono-capped trigonalbipyramid. This observation is readily picked out from Table 1. The cluster category code of the complex is M-6-12-84-C1C. As can be seen from the table, it is a mono-cap of M-5-9-72-C (trigonalbipyramid) which is diagonally below it and diagonally below M-5-9-72-C is M-4-6-60-N (a tetrahedral geometry).This capping process is sketched in Fig.

Figure 10 Figure 10

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Consider the complex Au3Ru4(CO)12L3(H), L = PPh3. It is described as a tri-capped tetrahedron6. Its cluster series category code  from the table is M-7-15-96-C2C. Moving along the diagonal in the table, it is observed that it is a bi-cap of M-5-9-72-C(trigonalbipyramid). But M-5-9-72-C is a mono-cap of M-4-6-60-N(tetrahedral). Hence, in essence, it can be regarded as a tri-capped tetrahedron.

Let us take another example8,9, Os6Pt2(CO)6(COD)2, COD= 4-electron donor. It has a cluster category code M-8-18-108-C3C(M-5, difference between 8 and 3). From Table 1, it is a tri-cap based on trigonalbipyramid (M-5-9-72-C) as you move along M-8 diagonal. The skeletal shape of the cluster is is sketched as shown in Fig. 11.

Figure 11 Figure 11

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The cluster k value can be considered to come from the M-5-9-72-C central unit contributing nine linkages and the three caps donating 3×3 =9 giving a rise of 9+ 9 = 18.

Let us look at another  example10, Os7(CO)19Au2(Ph2CH2PPh2). In this case, E = 9×18=162, V=7×8+19×2+4 = 120. Hence, k = ½ (E-V) = ½ (162-120) =21. The corresponding cluster code for this complex will be M-9-21-120-C4C(based on M-5 , specifically M-5-9-72-C as read from Table 1 diagonal). The sum of the linkages from this is 9 +4×3 =21 in agreement with the calculation. The skeletal sketch of the cluster is given in Fig.12.

Figure 12 Figure 12

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The last example11 we can use to illustrate the power of the empirical formula and cluster table is Hg{Fe5(C)(CO)14}22―. For this complex, E = 11×18=198, V = 12+(5×8+4+14×2)x2+2 = 158, k = ½ (E-V)= ½ (198-158) = 20. Hence, its  code is M-11-20-158-N. Just by inspection of the k value and the formula, the k value can be split up as follows k =20 = 8+4+8. These can be regarded as linkage fragments which can tentatively give rise to the skeletal structure given in Fig. 13.

Figure 13 Figure 13

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The structure indicates two square pyramid units of Fe atoms drawn as seen from above linked to 4 bonds from Hg atom. The carbon atoms are not shown and stereo chemistry not taken into account.

Identifying the Beginning of the Series from the K-Value

There are two approaches in identifying the beginning of a series from a given k value. Consider the complex7, Os9(H)(CO)24―(M-9-20-122-C3C). The complex has a k value of 20. The table shows that the cluster belongs to the clan members of M-9-20-122-C3C series. Also the table shows that the three caps are bestowed onto an octahedral geometry(Oh). Furthermore from the code fragments M-9 and C3, it can readily be deduced that the capping starts at M-6 which is specifically M-6-11-86-C in this case.   The table also shows the beginning cluster clan code  can easily be traced. This will entail the de-capping descent of ∆k =3. This process is illustrated in scheme 1.

Scheme 1 Scheme 1

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This scheme implies that beginning with a hypho cluster of 3 atoms with 2 linkages and 50 valence electrons we can successively generate a butterfly geometry (M-4-5-62-A), followed by a square pyramid geometry (M-5-8-74-N), octahedral geometry (M-6-11-86-C), until we arrive at a tri-capped octahedral geometry of (M-9-20-122-C3C) cluster. The closo series begins with the code M-2-3-30 for two skeletal elements up to M-12-23-170 in the table. The series could be extended as far as possible. Although Table 1 is meant for transition metal carbonyl clusters, it can readily be adapted for use for main group element clusters.

Table 1: Portion of Cluster Series of Transition Metal Carbonyls

M-2 M-3 M-4 M-5 M-6 M-7 M-8 M-9 M-10 M-11 M-12
10 12 14 16 18 20 22 24 26 28 30
C7C M-2-10-16 M-3-12-30 M-4-14-44 M-5-16-58 M-6-18-72 M-7-20-86 M-8-22-100 M-9-24-114 M-10-26-128 M-11-28-142 M-12-30-156
9 11 13 15 17 19 21 23 25 27 29
C6C M-2-9-18 M-3-11-32 M-4-13-46 M-5-15-60 M-6-17-74 M-7-19-88 M-8-21-102 M-9-23-116 M-10-25-130 M-11-27-144 M-12-29-158
  8 10 12 14 16 18 20 22 24 26 28
C5C M-2-8-20 M-3-10-34 M-4-12-48 M-5-14-62 M-6-16-76 M-7-18-90 M-8-20-104 M-9-22-118 M-10-24-132 M-11-26-146 M-12-28-160
  7 9 11 13 15 17 19 21 23 25 27
C4C M-2-7-22 M-3-9-36 M-4-11-50 M-5-13-64 M-6-15-78 M-7-17-92 M-8-19-106 M-9-21-120 M-10-23-134 M-11-25-148 M-12-27-162
  6 8 10 12 14 16 18 20 22 24 26
C3C M-2-6-24 M-3-8-38 M-4-10-52 M-5-12-66 M-6-14-80 M-7-16-94 M-8-18-108 M-9-20-122 M-10-22-136 M-11-24-150 M-12-26-164
  5 7 9 11 13 15 17 19 21 23 25
C2C M-2-5-26 M-3-7-40 M-4-9-54 M-5-11-68 M-6-13-82 M-7-15-96 M-8-17-110 M-9-19-124 M-10-21-138 M-11-23-152 M-12-25-166
  4 6 8 10 12 14 16 18 20 22 24
C1C M-2-4-28 M-3-6-42 M-4-8-56 M-5-10-70 M-6-12-84 M-7-14-98 M-8-16-112 M-9-18-126 M-10-20-140 M-11-22-154 M-12-24-168
  3 5 7 9 11 13 15 17 19 21 23
C M-2-3-30 M-3-5-44 M-4-7-58 M-5-9-72 M-6-11-86 M-7-13-100 M-8-15-114 M-9-17-128 M-10-19-142 M-11-21-156 M-12-23-170
  2 4 6 8 10 12 14 16 18 20 22
N M-2-2-32 M-3-4-46 M-4-6-60 M-5-8-74 M-6-10-88 M-7-12-102 M-8-14-116 M-9-16-130 M-10-18-144 M-11-20-158 M-12-22-172
  1 3 5 7 9 11 13 15 17 19 21
A M-2-1-34 M-3-3-48 M-4-5-62 M-5-7-76 M-6-9-90 M-7-11-104 M-8-13-118 M-9-15-132 M-10-17-146 M-11-19-160 M-12-21-174
  0 2 4 6 8 10 12 14 16 18 20
H   M-3-2-50 M-4-4-64 M-5-6-78 M-6-8-92 M-7-10-106 M-8-12-120 M-9-14-134 M-10-16-148 M-11-18-162 M-12-20-176
  -1 1 3 5 7 9 11 13 14 16 18
H-1   M-3-1-52 M-4-3-66 M-5-5-80 M-6-7-94 M-7-9-108 M-8-11-122 M-9-13-136 M-10-14-150 M-11-16-164 M-12-18-178
  -2 0 2 3 6 8 10 12 13 15 17
H-2     M-4-2-68 M-5-3-82 M-6-6-96 M-7-8-110 M-8-10-124 M-9-12-138 M-10-13-152 M-11-15-166 M-12-17-180

 

Table 1 Continued

  M-11 M-12 M-13 M-14 M-15 M-16 M-17 M-18 M-19 M-20
30 32 34 36 38 40 42 44 46 48
C9C M-11-30-138 M-12-32-152 M-13-34-166 M-14-36-180 M-15-38-194 M-16-40-208 M-17-42-222 M-18-44-236 M-19-46-250 M-20-48-264
29 31 33 35 37 39 41 43 45 47
C8C M-11-29-140 M-12-31-154 M-13-33-168 M-14-35-182 M-15-37-196 M-16-39-210 M-17-41-224 M-18-43-238 M-19-45-252 M-20-47-266
28 30 32 34 36 38 40 42 44 46
C7C M-11-28-142 M-12-30-156 M-13-32-170 M-14-34-184 M-15-36-198 M-16-38-212 M-17-40-226 M-18-42-240 M-19-44-254 M-20-46-268
27 29 31 33 35 37 39 41 43 45
C6C M-11-27-144 M-12-29-158 M-13-31-172 M-14-33-186  M-15-35-200 M-16-37-214 M-17-39-228 M-18-41-242 M-19-43-256 M-20-45-270
26 28 30 32 34 36 38 40 42 44
C5C M-11-26-146 M-12-28-160 M-13-30-174 M-14-32-188 M-15-34-202 M-16-36-216 M-17-38-230 M-18-40-244 M-19-42-258 M-20-44-272
  25 27 29 31 33 35 37 39 41 43
C4C M-11-25-148 M-12-27-162 M-13-29-176 M-14-31-190 M-15-33-204 M-16-35-218 M-17-37-232 M-18-39-246 M-19-41-260 M-20-43-274
  24 26 28 30 32 34 36 38 40 42
C3C M-11-24-150 M-12-26-164 M-13-28-178 M-14-30-192 M-15-32-206 M-16-34-220 M-17-36-234 M-18-38-248 M-19-40-262 M-20-42-276
  23 25 27 29 31 33 35 37 39 41
C2C M-11-23-152 M-12-25-166 M-13-27-180 M-14-29-194 M-15-31-208 M-16-33-222 M-17-35-236 M-18-37-250 M-19-39-264 M-20-41-278
  22 24 26 28 30 32 34 36 38 40
C1C M-11-22-154 M-12-24-168 M-13-26-182 M-14-28-196 M-15-30-210 M-16-32-224 M-17-34-238 M-18-36-252 M-19-38-266 M-20-40-280
  21 23 25 27 29 31 33 35 37 39
C M-11-21-156 M-12-23-170 M-13-25-184 M-14-27-198 M-15-29-212 M-16-31-226 M-17-33-240 M-18-35-254 M-19-37-268 M-20-39-282
  20 22 24 26 28 30 32 34 36 38
N M-11-20-158 M-12-22-172 M-13-24-186 M-14-26-200 M-15-28-214 M-16-30-228 M-17-32-242 M-18-34-256 M-19-36-270 M-20-38-284
  19 21 23 25 27 29 31 33 35 37
A M-11-19-160 M-12-21-174 M-13-23-188 M-14-25-202 M-15-27-216 M-16-29-230 M-17-31-244 M-18-33-258 M-19-35-272 M-20-37-286
  18 20 22 24 26 28 30 32 34 36
H M-11-18-162 M-12-20-176 M-13-22-190 M-14-24-204 M-15-26-218 M-16-28-232 M-17-30-246 M-18-32-260 M-19-34-274 M-20-36-288
  17 19 21 23 25 27 29 31 33 35
H-1 M-11-17-164 M-12-19-178 M-13-21-192 M-14-23-206 M-15-25-220 M-16-27-234 M-17-29-248 M-18-31-262 M-19-33-276 M-20-35-290
  16 18 20 22 24 26 28 30 32 34
H-2 M-11-16-166 M-12-18-180 M-13-20-194 M-14-22-208 M-15-24-222 M-16-26-238 M-17-28-250 M-18-30-264 M-19-32-278 M-20-34-292

 

Table 2: Categorization of Selected Carbonyl Cluster Complexes

Complex E V k Cluster Series *Category Comment
Re2(H)2(CO)8 36 32 2 M-2-2-32-N Linear (double bond)
Re2(CO)10 36 34 1 M-2-1-34-A Linear (single bond)
Re3(H)3(CO)102- 54 46 4 M-3-4-46-N Triangle
Re3(H)2(CO)12― 54 48 3 M-3-3-48-A Triangle
Re4(H)4(CO)152- 72 64 4 M-4-4-64-H Square
Re4(H)4(CO)132- 72 60 6 M-4-6-60-N Tetrahedral (Td)
Re4(H)6(CO)122― 72 60 6 M-4-6-60-N Tetrahedral (Td)
Re4(H)5(CO)12– 72 58 7 M-4-7-58-C
Re4(CO)162- 72 62 5 M-4-5-62-A Butterfly
Re4(H)5(CO)14― 72 62 5 M-4-5-62-A Butterfly
Re4(H)4(CO)12 72 56 8 M-4-8-56-C1C
Re5(C)(CO)16(H)2- 90 74 8 M-5-8-74-N Square pyramid (C4v)
Re6(H)8(CO)182- 108 88 10 M-6-10-88-N
Re6(C)(CO)192- 108 86 11 M-6-11-86-C Octahedral (Oh)
Re6(C)(CO)19(H)― 108 86 11 M-6-11-86-C Octahedral (Oh)
Re6(C)(CO)18(H)22― 108 86 11 M-6-11-86-C Octahedral (Oh)
Re6(C)(CO)18(H)3― 108 86 11 M-6-11-86-C Octahedral (Oh)
Re7(C)(CO)213― 126 98 14 M-7-14-98-C1C Monocap based on Oh(11+3 = 14)
Re7(C)(CO)21(H)2― 126 98 14 M-7-14-98-C1C Monocap based on Oh(11+3 = 14)
Re7(C)(CO)21(H)2― 126 98 14 M-7-14-98-C1C Monocap based on Oh(11+3 = 14)
Re7(C)(CO)22― 126 98 14 M-7-14-98-C1C Monocap based on Oh(11+3 = 14)
Re8(C)(CO)22― 144 110 17 M-8-17-110-C2C Bicap based on Oh(11+3+3 = 17)
Os5(CO)16 90 72 9 M-5-9-72-C Trigonalbipyramid (TBP,D3h)
Os5(CO)15(H)― 90 72 9 M-5-9-72-C Trigonalbipyramid (TBP,D3h)
Os6(CO)18 108 84 12 M-6-12-84-C1C Monocap  based on TBP(9+3 = 12)
Os6(CO)182― 108 86 11 M-6-11-86-C Octahedral (Oh)
(H)Os6(CO)18― 108 86 11 M-6-11-86-C Octahedral (Oh)
(H)2Os6(CO)18 108 86 11 M-6-11-86-C Square pyramid –monocap(8+3 = 11)
Os6(CO)17L4 108 90 9 M-6-9-90-A A triangle on top of
L = P(OMe)3 2 atom linked triangles
H)2Os6(CO)19 108 88 10 M-6-10-88-N
Os7(CO)21 126 98 14 M-7-14-98-C1C Monocap based on Oh(11+3 = 14)
Os7(CO)21(H)2 126 100 13 M-7-13-C

*C = CLOSO, N = NIDO, A = ARACHNO, H = HYPHO, C1C = MONOCAP, C2C = BICAP, etc, H-1 = FIRST SERIES BELOW HYPHO, H-2 = SECOND SERIES BELOW HYPHO, etc.

Os7(CO)22(H)2 126 102 12 M-7-12-N
(H)2Os7(CO)20 126 98 14 M-7-14-98-C1C Bicap Td with a leg linkage(6+3+3+2 =14)
Os8(CO)222― 144 110 17 M-8-17-110-C2C Bicap based on Oh(11+3+3 =17)
(H)Os8(CO)222― 144 110 17 M-8-17-110-C2C 2 Edge-fused Td units each monocapped.
Os9(CO)242― 162 122 20 M-9-20-122-C3C Tricapped  based on Oh(11+3+3+3) =20)
Os9(H)(CO)24― 162 122 20 M-9-20-122-C3C Tricapped  based on Oh(11+3+3+3) =20)
Os10(C)(CO)242― 180 134 23 M-10-23-134-C4C Tetracapped based on Oh(11+3+3+3+3 = 23)
Os10(CO)262― 180 134 23 M-10-23-134-C4C Tetracapped based on Oh(11+3+3+3+3 = 23)


Special Cluster Series

There are special cluster series that are usually encountered in chemistry. Some of these are given in Table 3.

Table 3: Important cluster series normally encountered

Mx k V Category Code Corresponding Code Main Group Element Possible skeletal geometry
2 1 34 M-2-1-34-A M-2-1-14-A Linear, single bond
2 2 32 M-2-2-32-N M-2-2-12-N Linear, double bond
2 3 30 M-2-3-30-C M-2-3-10-C Linear, Triple bond
2 4 28 M-2-4-28-C1C M-2-4-08-C1C Linear, Quadruple bond
3 3 48 M-3-3-48-A M-3-3-18-A Triangle
4 6 60 M-4-4-60-N M-4-4-20-N Td
5 9 72 M-5-9-72-C M-5-9-22-C Trigonalbipyramid
5 8 74 M-5-8-74-N M-5-8-24-N Square pyramid
6 11 86 M-6-11-86-C M-6-11-26-C Oh
6 10 90 M-6-9-90-A M-6-9-30-A Trigonal Prism
7 14 98 M-7-14-98-C1C M-7-14-28-C1C Monocap-Oh
8 17 110 M-8-17-110-C2C M-8-17-300-C2C Bicap-Oh
9 20 122 M-9-20-122-C3C M-9-20-32-C3C Tricap-Oh
10 23 134 M-10-23-134-C4C M-10-23-34-C4C Tetracap-Oh

 

Magic Cluster Ratio (1:2:14)

Consider the cluster category code of the mono-cap series (C1C). The selected ones are given in Table 4.

Table 4: Magic Cluster Ratio

Code: M-x-k-V Magic cluster ratio:-M-x:k:V
M-2-4-28 1:2:14
M-3-6-42 1:2:14
M-4-8-56 1:2:14
M-5-10-70 1:2:14
M-6-12-84 1:2:14
M-7-14-98 1:2:14
M-8-16-112 1:2:14
M-9-18-126 1:2:14
M-10-20-140 1:2:14
M-11-22-154 1:2:14
M-12-24-168 1:2:14
M-13-26-182 1:2:14
M-14-28-196 1:2:14
M-15-30-210 1:2:14
M-16-32-224 1:2:14
M-17-34-238 1:2:14
M-18-36-252 1:2:14
M-19-38-266 1:2:14
M-20-40-280 1:2:14

 

From this table, a constant ratio of 1:2:14 is discerned. The reason for this phenomenon is not clear yet.

Conclusion

Simple and relatively more complex transition metal carbonyl clusters can be analyzed using basic number theory. The cluster number k value is obtained from the empirical formula k = ½ (E-V). The cluster numbers have been utilized to construct a user friendly cluster table for classifying clusters into category series. The cluster number, k value can be used to categorize a given carbonyl cluster. The k value may simply be regarded as the number of bonds or linkages or ‘pillars’ that hold a given cluster system together. Furthermore, from the k value with or without the help of the cluster table the skeletal geometry of the cluster may tentatively derived. By this approach, the skeletal structures of metal carbonyls from simple to relatively more complex can greatly be appreciated without prior knowledge of the polyhedral skeletal electron pair theory12, Jemmis rules13 or topology concepts14. Nevertheless, this work complements the existing knowledge on carbonyl clusters. The author believes method will be enjoyed by a wide spectrum of scholars mainly undergraduate, postgraduate chemistry students as well as chemistry teachers in secondary schoolsor high schools due to its simplicity.

Dedication

This paper is dedicated to Charles Alfred Coulson(1910-1974) who once briefly taught the author in Africa, Gilbert Newton Lewis(1875-1946) and Irving Langmuir(1881-1957).

Acknowledgement

I wish to acknowledge the University of Namibia for provision of facilities and financial assistance, NAMSOV, Namibia for the timely research grant and my wife for the encouragement to write this article.

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