Categorization and Structual Determination of Simple and More Complex Carbonyl Clusters of Rhenium and Osmium using K-values and the Cluster Table ENOS

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 kvalues 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).

The cluster number, k-value for a carbonyl cluster is calculated [1][2][3][4][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 M x values where x = 2,3, 4, 5, 6, and so on.In this new table,the movement down an M x column is like driving along a 'highway'.The movement crosses the columns ofdifferent 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 monodentateligand (a pair of electrons) step by step.The horizontal movement along the series represents a progressive change in "k = ±2 and a change of M x 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 familyand so on.The diagonal movement represent a process in which there is a progressive change by "k = ± 3 and M x 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.Theresults re given inTable 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.
Re 4 (H) 4 (CO) 13 2- '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, Re 4 (H) 4 (CO) 13 2-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 (T d ) geometry Fig. 1.The shape is drawn as a projection looking at it from above.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 pyramidC 4v .This is shown in Fig. 2.

4.
Os 5 (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(D 3h )shown in Fig. 4.

More examples for illustration of the use of cluster table.
The osmium cluster Os 6 (CO) 18 great interest 6 .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-C 1 C.As can be seen from the table, it is a monocap 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 tetrahedralgeometry).This capping process is sketched in Fig. 10.It is interesting to note 6 that the cluster complexex RuIr 4 (CO) 15 2¯( M-5-7-76-A), was found to have elongated trigonalbipyramid shape while on the other hand Os 5 (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.
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 3x3 =9 giving a rise of 9+ 9 = 18.
The last example 11 we can use to illustrate the power of the empirical formula and cluster table is Hg{Fe 5 (C)(CO) 14 } 2 2¯.For this complex, E = 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 stereochemistry not taken into account.

Identifying the beginning of the series from the kvalue
There are two approaches in identifying the beginning of a series from a given k value.Consider the complex 7 , Os 9 (H)(CO) 24 ¯(M-9-20-122-C 3 C).The complex has a k value of 20.The table shows that the cluster belongs to the clan members of M-9-20-122-C 3 Cseries.Also the table shows that the three caps are bestowed onto an octahedral geometry(O h ).Furthermore from the code fragments M-9 and C 3 , 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      This will entail the de-capping descent of "k =3.This process is illustrated in scheme 1.
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 tricapped octahedral geometry of (M-9-20-122-C 3 C) 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.

Special cluster series
There are special cluster series that are usually encountered in chemistry.Some of these are given in Table 3.
(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 theory 12 , Jemmis rules 13 or topology concepts 14 .Nevertheless, this work complements the existing knowledge on carbonyl clusters.Theauthor believes method will be enjoyed by a wide spectrum of scholars mainly undergraduate, postgraduate chemistry students as well as chemistry teachersin secondary schoolsor high schools due to its simplicity.

Scheme 1 :
Scheme 1: Shows the diagonal descent of k=20 to the

Table 1 :
Portion of Cluster Series of Transition Metal Carbonyls