Unusual underground Capping Carbonyl Clusters of Palladium

Transition metal carbonyls form unlike boranes a wide range of clusters. High nuclearity carbonyl clusters have a tendency to form capped clusters. Using the method of series explained in this paper, many capped carbonyl clusters have been identified for group 7, 8, 9 and 10 transition metals such as rhenium, osmium, rhodium and palladium. The series have discovered that palladium form exclusively capped carbonyl clusters. Furthermore, it has been discovered that some of the capped clusters have negative nuclear closo function. Such carbonyls have been regarded as capping underground. This paper presents the unique characteristic of high nuclearity capping carbonyl clusters of palladium.


Introduction
The polyhedral skeletal electron pair theory (PSEPT) has been exceedingly useful in categorizing clusters especially boranes and carbonys for many years (Mingos, 1972;Wade, 1976;Cox, 1981;Mingos, 1984;Lee, et al, 1989;Jemmis, et al, 1984;Jemmis et al, 2001;2002;2003;Balakrishnarajan and Hoffmann, 2004;Jemmis, 2005;2005;Wales, 2005;Jemmis, et al., 2008;Welch, 2013).In our previous extensive work on clusters we found that the 4n and 14n rules could also be utilized to categorize the clusters and predict the shapes carbonyl cluster series (Kiremire, 2014;Kiremire, 2015a;Kiremire, 2015b) especially those of small to medium size level.Furthermore, we found that using 4n series cluster molecular formulas could be decomposed into fragments from which cluster series can be derived and their geometrical shapes predicted (Kiremire, E. M. R., 2015c).Unlike the PSEPT which was derived from molecular orbital theory, the 14n±q and 4n±q (where q is an integer) rules were empirically derived by analysis of carbonyl, hydrocarbons and borane cluster formulas and known shapes.

Authenticity of the 4n And 14n Series
Since the use of series categorize clusters is not well known, it is extremely important to explain this approach to cluster analysis.Recently, it has been found that Hoffmann"s isolobal fragments (Hoffmann, 1982) could assigned series (Kiremire,2015d).For a given cluster formula, skeletal elements of the cluster are identified.The formula is then decomposed into suitable mono-skeletal fragments.If a selected skeletal element is a main group element of the periodic table, then the 4n rule is applied, if it is a transition metal, the 14n rule is applied.For example, if carbon (C) is taken as a fragment, it has [4] valence electrons.According to the series approach used in this paper, it will be classified as belonging to 4n(n = 1) series .If the fragment is [CH], then the electron content will be [4+1] and this will be categorized as being a member of 4n+1 series.A phosphorus atom P with a valence electron content of five will be categorized in the same way.That is, [5] = [4+1] = 4n+1.Thus, the four electrons must be separated first to form the backbone of the series and the rest will be used in the categorization of the series and the cluster.The fragment [BH] = [3+1] = [4] will belong to 4n +0 series.In the case of transition metal carbonyl clusters, the classification is based upon 14n rule.Take the case of the fragment F = [Os(CO) 3 ], the valence electron content is [8+3x2] = [14].This means we can classify the fragment as belonging to 14n+0 series.It has been found that the 14n is isolobal to 4n.Therefore it is easier to use 4n instead of 14n for classification.If we get a fragment F = [Os(CO) 4 ], then the valence content is [16], then we can split this into [14+2] = 14n+2 series.This is the same as 4n+2 due to isolobal relationship.In case of the fragment F = [Rh(CO) 3 ], the valence content is . This means we can classify the fragment as belonging to 14n+1 series or to 4n+1 due to isolobal relationship.If a fragment has less than 14, then its valence content can be transformed into a form consistent with 14n series.For instance, the fragment, such as F= [Pd(CO)] has [10+2] valence electron content.This is then transformed into [10+2] = [14-2] = 14n -2 which equivalent to 4n-2 due to isolobal relationship.In fact, the fragment F= [Pd(CO)] is equivalent to F = Os(CO) 2 fragment.The isolobal relationship may simply be represented as given here 14n±q is isolobal to or simply 14n±q = 4n±q.

Results and Discussion
Using the series approach, a large number of known carbonyl clusters have been categorized and the results came out precisely as the ones obtained from literature (Hughes and Wade,2000).These findings are given In Table 1.Using the same method, a good collection of different 19 examples have been analyzed using fragments and series and the results are given in the following section so as to expose the reader to a variety of applying series for categorization of clusters.

Capping Clusters
In our earlier work (Kiremire, 2015a, Kiremire 2015b), a capping symbol C n C (n = 1, 2, 3,.) was proposed.The capping symbol of clusters has been covered in previous work.But will briefly be repeated here for the purpose of getting readers be more familiar with it.For mono-capped closo, series S = 14n+0, the capping symbol C 1 C, n has a value of 1 signifying one cap.In the case of bi-capped cluster, S = 14n-2, the capping symbol is Cp = C 2 C( n = 2).This means, if S = 14n-2 = 14n+1(-2), then the capping is Cp = C 1 +C 1 = C 2 C. The first C 1 comes from the 14n component of the series as it implies a mono-cap.The second C 1 comes from 1(-2) component of the series.According to the series, for every negative integer of two (-2), there is an additional capping.Thus, S = 14n-4 = 14n+2(-2), the capping symbol is Cp = C 1 +C 2 = C 3 C ( tri-capped).Similarly, for S = 14n-6 = 14n+3(-2), the capping symbol is Cp = C 1 +C 3 = C 4 C(tetra-capped).Some of the capped carbonyl clusters are given in Table 1.They include among others, Re 4 H 4 (CO) 12 ,S = 14n, If we analyze Re 4 H 4 (CO) 12 S = 14n, C 1 C[M-3] cluster system closely, C 1 means that one skeletal atom is capping on three others which constitute an inner core closo cluster that obeys the 14n+2 or simply 4n+2 rule.The building block of the rhenium cluster must have a content of [14] electrons according to the series while the capping cluster must have a valence electron content of [12].The suitable fragments of rhenium will be [Re(H)(CO) 3 ] and [Re(H)(CO) 2 ] respectively.The [M-3] symbol means that the inner core cluster is a member of S = 4n+2 series and n = 3.We can construct the formula of the inner core as follows: F = 4n+2 = [Re(H)(CO) 3 ] (3)+CO = Re 3 (H) 3 (CO) 9 + CO = Re 3 (H) 3 (CO) 10 .This is the inner closo cluster.In order to derive the entire cluster formula, we must add the mono-cap, that is, Re 3 (H) 3 (CO) 10 + [Re(H)(CO) 2 ] = Re 4 (H) 4 (CO) 12 .Let us discuss a few more examples to illustrate how fragments are utilized to generate series.Consider Os 4 (CO) 16 cluster.There are 4 skeletal osmium atoms.Hence, we can decompose this into 4[Os(CO) 3 ] fragments and 4CO ligands.The valence electron content of [Os(CO) 3 ] fragment = 8+3x2 = 14.In using the series method, it makes the work easier to create fragments whole valence electron content are [14] for transition metals or [5] for main group elements.If not the values must be close to these values less or above.The fragment F = [Os(CO) 3 ] belongs to 14n series.Therefore, 4 [14n] = 14n just as carbon fragment [C] fragment S = 4n+0 series (n = 1) and C 4 = 4[C] = 4[4n] = S = 4n+0 series (n = 4).Each of the CO ligand donates 2 valence electrons and therefore 4CO ligands will contribute 8 valence electrons.Therefore the net cluster series S = (14n+0)+8 = 14n+8.This cluster belongs to the HYPHO series.Since 14n is isolobal to 4n, then the series can be regarded to be the same as S = 4n+8.The simplicity of working with 4n rather than 14n, makes 4n more user friendly.Take another example, Os 9 (CO) 24 2-cluster.This cluster has 9 skeletal osmium atoms.It is easier to aim to decompose the cluster into nine [14] valence electron fragments.This is done as follows, Os 9 (CO) 24 2-= 9[Os(CO) 3 ]-3CO+2.This gives us 27CO ligands.Since we have only 24CO ligands in the cluster, we need to subtract 3CO ligands to balance the ligands.This gives rise to subtracting 3x2 = 6 valence electrons.The cluster has a charge, q of -2.This means that q also supplies 2 more electrons to the valence electron content.To sum up, 9[Os(CO) 3 ] = 9[14] = 9[14n] = 14n+0 which is the same as 4n+0.We need to remove the valence electrons of 3CO and add 2 electrons from the charge.This gives us S= (4n+0)-( 6 . This is a tri-capped cluster.This means that three of the nine osmium atoms are capped and the 6 comprise of nuclear octahedral closo cluster.The complex is a tri-capped octahedral cluster.The symbol {M-6] means this belongs to 14n+2 or 4n+2 series.We can generate the formula of this inner cluster using the electron building block [14] of the carbonyl clusters and the n =6 value of the closo cluster as follows F = [Os(CO) 3 ] (6)+2 = Os 6 (CO) 18 2 .We could also have used CO ligand instead of converting +2 into a charge of (2-).-The complex Os 6 (CO) 18 2-as is found is indeed an octahedral closo complex (Cotton and Wilkinson,1980).Let us consider a few members of S = 14n+0 series starting with Os(CO) 3 fragment.Since F = Os(CO) 3 then S = 4n+0 and Cp = C 1 C[M-0].According to series, the building block of the series is based upon the [14] valence electron content.The capping fragment is based upon the [12] valence electron content.The capping is centered upon the closo inner nucleus.This means [M-0] = 4n+2 and F = 4n+2 = [Os(CO) 3 (0)+CO since n = 0.This gives F = CO for the first member of 14n+2 or 4n+2 series.In order to get the formula of the 14n or 4n series we have to add the value of the inner core [M-0] to the value of the capping fragment.That is, F = [M-0] +C 1 .The value of C 1 = [Os(CO) 2 ].Hence, F = CO + [Os(CO) 2 ] = Os(CO) 3 .This means that CO is the closo nucleus of Os(CO) 3 while Os(CO) 2 is the capping component of Os(CO) 3 .The combination of the two generates the first member of the fragment of the 4n series.The fragment Os 2 (CO) 6 is the second member of S = 4n+0 series.This means that it is also a mono-capped cluster.That is, Cp = C 1 C[M-1] meaning that there is one skeletal capping atom while the other forms the inner closo core.We need to define what [M-1] means in terms of the series.The closo symbol [M-1] = 4n+2 = [Os(CO) 3 (1)+CO = Os(CO) 3 + CO = Os(CO) 4 .Let us recall that for osmium, C 1 = Os(CO) 2 .Hence, F = C 1 + [M-1] = Os(CO) 2 + Os(CO) 4 = Os 2 (CO) 6 .It is quite clear that the series easily explain why Os(CO) 3 and Os 2 (CO) 6 are members of the first mono-capping series.The third member of the 4n series is Os 3 (CO) 9 .The corresponding capping symbol for this is Cp Therefore the cluster formula is generated by adding the capping fragment to the closo nuclear component C 1 + [M-2] = [Os(CO) 2 ]+ [Os 2 (CO) 7 ] = Os 3 (CO) 9 .In the same manner, it can easily be shown that Os 4 (CO) 16 is a member of S = 4n series and Cp = C 1 C[M-3] where C 1 = Os(CO) 2 and [M-3] = Os 3 (CO) 10 .The clusters, Os 6 (CO) 18 and Os 7 (CO) 21 which are also members of the C 1 C series have already been discussed.

Palladium Underground Capping Carbonyl Clusters
From the discussion presented above, it is quite clear that series are have the power to analyze clusters of all types based on fragments and series derived from them using the valence electron content.An analysis on palladium carbonyl clusters was made on a large collection of carbonyl clusters using series.The results are given in Table 2.A large number of these palladium carbonyls have been produced by Dahl research team (Mednikov, Dahl, 2010).It is quite amazing that palladium forms a wide range of capped carbonyl clusters.They range from closo [M-11] to closo [M -76 ].What was found interesting according to series is that for palladium there are clusters which cap using negative closo nuclear clusters.It is proposed that such capping clusters with negative closo values such as [M -76 ] be regarded as undergoing clapping underground.This is similar to highways which are constructed for underground traffic travel.Consider capping at [M-0].This means capping at base level high way.The symbol [M-0] for palladium carbonyl means [M-0] = 4n+2 = [Pd(CO) 2 ](0)+CO = CO.That is, the cluster has a closo nucleus with no skeletal atom (n = 0) and the skeletal building block is based on [14] valence electrons.In the case of palladium a suitable fragment is F = [Pd(CO) 2 ]and a capping fragment of twelve valence electrons [12], [is F =Pd(CO)].The integer (+2) means two valence electrons added to 14n or 4n series.Likewise, capping at [M -1 ] means = 4n+2 = [Pd(CO)2(-1)+CO = -Pd(CO) 2 +CO = -Pd(CO).That is, capping at underground highway level n = -1.The negative sign means that closo value function will have a negative value since n = -1.This negative value must be added to the value of the capping function to generate the cluster molecular formula.Since [M -1 ] has a negative power, n = -1, as in the case of Pd 54 (CO)  Therefore the molecular formula is obtained by adding the two functions as F = Pd 55 (CO) 55 -[Pd(CO)] = Pd 54 (CO) 54 .This cluster is equivalent to Pd 54 (CO) 40 L 14 in terms of valence electron content as CO and L each donate two electrons.

Capping carbonyl Clusters above the Ground and Underground
An X-Y type of axis has been designed to explain the impression derived from the capping cluster carbonyls of palladium.This is shown in Figure 1.As can be seen from Table 2, there are clusters whose closo nucleus starts from [M-0] to [M-11].The closo [M-0] may be regarded as the beginning of being above the ground and those below the [M-0] similar to the X-axis may be taken as capping below the ground (underground).Those capping above the ground include The capping image here is similar to that of athletics where runners in lanes compete in jumping series of huddles.In the example of [M-6] lane or highway, one cluster is at C 17 huddle or series, another at C 23 , another at C 24 , and the last at C 36 .From the capping symbol of a cluster, its molecular formula may be derived.The palladium cluster with a capping code C 36 C[M-6] is Pd 33 Ni 9 (CO) 41 L 6 4-and this can be readily be converted into its equivalent cluster.The capping fragment has an electron content of [12] and in the case of palladium carbonyl clusters this corresponds to [Pd(CO)] and in for skeletal building block contains [14] skeletal electrons.Therefore,C 36 = 36[Pd(CO)] = Pd 36 (CO) 36 .The closo inner core [M-6] = 4n+2 = [Pd(CO) 2 ](6)+CO = Pd 6 (CO) 12 +CO = Pd 6 (CO) 13 .The formula of the cluster will be the sum of the capping value and that of the inner core cluster Pd 36 (CO) 36 +Pd 6 (CO) 13 = Pd 42 (CO) 49 .In the cluster Pd 33 Ni 9 (CO) 41 L 6 4-,Pd = Ni in terms of valence electron content.Also the ligand CO = L in terms of electron content.The charge of (-4) has electron content of 2CO ligands.Hence, the cluster Pd 33 Ni 9 (CO) 41 L 6 4-= 33Pd+9Pd+41CO +6CO +2CO = Pd 42 (CO) 49 .The underground capping cluster is also readily identified by the series.Take the case of Pd 59 (CO) 36 L 14 ,S = 4n-136, Cp = C 69 C[M -10 ].According to the series the symbol, C 69 means that there 69 capping fragments each of 12 electrons.That is, C 69 = 69[Pd(CO)] = Pd 69 (CO) 69 .The closo inner core [M -10 ] cluster means that it belongs to the closo series S = 4n+2.Therefore [M -10 ] = 4n+2 = [Pd(CO) 2 ](-10)+CO = -Pd 10 (CO) 20 +CO = -Pd 10 (CO) 19 .In terms of the series, this means that in order to generate the observed cluster formula of the carbonyl complex, we must the value of the inner core from the value of the capping function.This leads us to the following formula of the complex F = Pd 69 (CO) 69 -Pd 10 (CO) 19 = Pd 59 (CO) 50 .In terms of valence electron content Pd 59 (CO) 36 L 14 , L = CO and hence the cluster is the same as Pd 59 (CO) 36 (CO) 14 = Pd 59 (CO) 50 .Just as in developed nations complex road system, this cluster could be viewed as having been formed (capping) along the high way 10 [M -10 ] underground.Let us consider the next underground capping cluster Pd 69 (CO) 36 L 18 , 4n-168, and Cp = C 85 C[M -16 ].The capping formula can be utilized to recreate the cluster formula of the carbonyl complex.Following the same procedure as in the above example, C 85 = 85[Pd(CO)] = Pd 85 (CO) 85 .The closo inner core [M -16 ] = 4n+2 = [Pd(CO) 2 ](-16)+ CO = -Pd 16 (CO) 32 +CO = -Pd 16 (CO) 31 .In order to get the formula of the cluster complex we have to subtract the inner core from the capping function.This gives us F = Pd 85 (CO) 85 -Pd 16 (CO)  .This is the same as Pd 165 (CO) 60 L 30 .The cluster series formula such as 4n-480 can also be used to calculate the molar mass.If we put n = 241 into the series, we get S = 4(165)-480 =180.Since 14n is isolobal to 4n, then the difference is 10n.This means for transition metal we must add 10n electrons we will get the value of valence electron cluster of the palladium cluster.That is, to the 165x10 = 1650 we must add 180 =1830.The valence electron content of the cluster Pd 165 (CO) 60 L 30 is 165x10+90x2 = 1860.What is fascinating is the discovery by use of series that the cluster, Ni 38 Pt 6 (CO) 48 (H) 5-, S= 4n-74; Cp = C 38 C[M-6] has an octahedral closo nuclear cluster comprising of six platinum atoms (Rossi, 2011) at the centre of a large cluster.The rhodium cluster ( Hughes and Wade, 2000), Rh 22 (CO) 37 4-, S = 4n-38, Cp = C 20 C[M-2], has two atoms in the centre of the cluster of 22 skeletal atoms.For the cluster (Hughes and Wade, 2000), Os 17 (CO) 36 2-, S = 4n-28, Cp = C 15 C[M-2].According to the series, this cluster has 2 atoms at the centre of a cluster of 17 skeletal elements.Thus, both the rhodium and osmium clusters are placed on [M-2] highway above the ground.The osmium is at "city" number 15 along the [M-2] highway while the rhodium is at city number 20( C 20 ) along the [M-2] highway above the ground.Clearly, the palladium element mainly form unique carbonyl clusters, those which do capping above the ground and those which cap underground.

The Generating Function of the Palladium Carbonyl Clusters
It has been found that one of the best way of generating the molecular formulas of known and unknown carbonyl clusters is to use the [4] or [14] function and multiples.That is, the multiples of 4n or 14n series generate the backbone of the series.The addition of CO ligands to the backbone members gives the clusters series with positive integers such as 4n+2 closo, 4n+4 nido, and 4n+6 arachno.The capping clusters begin with digit zero (0) after 4n, that is, S = 4n+0( mono-capped), the next capping has the series S = 4n-2( bi-capped), 4n-6( tri-capped) and so on.These have negative integers after 4n.Using 4n instead of 14n is much easier and faster.This is the approach that has been used to categorize the clusters from main group and transition metals.Since palladium forms exclusively capping clusters, generating functions that give capping clusters have been designed for palladium.A selected number of these clusters and fragments have been created and are given in Table 3.A number of known and hypothetical clusters were identified in the table.Among others, these include Pd 12 (CO) 15 L 7 ,Pd 10 (CO) 14 L 4 , Pd 3 (CO) 3 L, Pd 8 (CO) 14 , Pd 10 (CO) 16 , Pd 10 (CO) 12 L 6 , and Pd 16 (CO) 13 L 9 .The shape will be a pentagonal bipyramid.The shape will be a pentagonal bipyramid.4n+0 6.
The ideal shape of the cluster is that B5H9 which is a delivative of CLOSO B6H6 2-.
The cluster will have a square pyramid shape.

Conclusion
Palladium forms a wide range of capping carbonyl clusters.The revelation by series method indicate that palladium forms two types of capping clusters -those which undergo capping "above the ground" and those which do so "underground".The difference between the above the ground and underground capping clusters is that the closo nucleus of the above the ground capping cluster is a positive function or has a positive value and when added to the capping function produces the molecular formula of the cluster with an enhanced molar mass.On the other hand the closo nucleus of the underground capping cluster is negative function and when subtracted from the capping cluster function gives rise to a molecular formula of the cluster with a reduced molar mass.The examples with [M -q ] closo nuclear decapping clusters are given above.By using the capping generating series, some known palladium clusters can be generated as indicated in Table 3.A given molecular formula of a cluster of any size can be decomposed into mono-skeletal fragments from which the cluster series can be derived.The simple series such as bicapped, monocapped, closo, nido, arachno, hypho and klapo can readily be utilized to predict the borane-type of geometrical structures or related ones.The discovery of underground capping clusters has introduced a new dimension in the chemistry of carbonyl clusters.Each cap represents a class of series.For instance, C 1 indicates mono-capped series and C 10 shows series with 10 caps.Clearly palladium portraying a series of C 241 capping in Pd 165 (CO) 60 L 30 is perhaps one of the largest carbonyl cluster containing a large number of skeletal metal atoms.The series method used in the above examples indicate that it gives the same result of categorizing clusters as PSEPT method.A large variety of examples categorized by the series method used in this paper have been provided to indicate the viability and flexibility of the method as well as to make it more familiar to the reader.Since 14n series are isolobal to 4n series, it is much easier and faster to work with 4n series for categorization and structure prediction of clusters.This series method can easily be taught at both undergraduate and postgraduate levels.

Figure
Figure 1.Underground High ways of Capping Carbonyl Clusters

Table 1 .
Comparison of Categorization of Clusters Using 4n Series and the known Literature results

Table 2 .
Derived Series of some Palladium carbonyl Clusters