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CHAPTER 10, Metal Clusters:,  Structure and Bonding in Higher Boranes, Boron hydrides or simply boranes are a class of compounds that have the generic formula BxHy., Though the boron does not react with hydrogen directly to form any of the boron hydrides, yet many of these, compounds can easily be synthesized under special reaction conditions. However, because of the high affinity, of boron for oxygen, these compounds readily oxidize on contact with air (lighter boranes even explode); and, therefore, do not occur in nature. This class is derived from the borane (BH3) itself, which exists only as a, transient intermediate and dimerizes to form diborane (B2H6) immediately. The higher boranes are all consisted, of boron clusters that are actually polyhedral in nature. Besides the neutral boranes, a large number of anionic, boron hydrides also exist. The general formula for single-cluster boron hydrides is BnHn2−, BnHn+4, BnHn+6,, BnHn+8 and BnHn+10 (n is the number of boron atoms) for closo-, nido-, arachno-, hypho- and klado- type,, respectively. There also exists a series of substituted neutral hypercloso-boranes that have the theoretical, formulae of BnHn., The naming of neutral boranes is done with a Greek prefix showing the number of boron atoms and, the number of hydrogen atoms in brackets. In the naming of anions, the hydrogen count is specified first, followed by the boron count and the overall charge in the bracket in the last. Furthermore, the prefix closonido- etc. can also be added. For example:, Formula, , B5H9, , B4H10, , B6H62−, , Name (IUPAC), , Pentaborane(9), , Tetraborane(10), , hexahydridohexaborate(2−), , Type, , Nido-, , Arachno-, , Closo-, , Understandably many of the compounds have abbreviated common names. The prefix like closo-, nido are, actually related to geometry and the number of framework electrons of a particular cluster. Now because the, boron hydrides are electron-deficient compounds, the structure and bonding in higher boranes can be, understood only after rationalizing the 3-center-2-electron bond involved.,  Valence Bond Treatment of Three-Centre Two-Electron Bond, The simplest example of boron hydride containing 3-center-2-electron bond is diborane; and, therefore, the first orbital based approach we can use to study the diborane structure is valence bond theory., The B2H6 or diborane can be considered as a dimeric unit of two BH3 molecules. Now, as all the three halffilled sp3 hybrid orbitals of boron are already used to bind hydrogens, the dimerization seems to be impossible., However, the valence bond theory still suggests a mode of dimerization through sp3-hybridization. The, electronic configuration of boron in its ground state and excited state are:, , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, ↑↓, , 387, ↑, , 2s2, ↑, 2s1, , Ground state boron, 2p1, , ↑, , ↑, , Excited-state boron, , 2p2, , The mixing of one s and three p orbitals generate four sp3 hybrid orbitals; three half-filled and one empty. Each, boron atom in the diborane structure can use two of its sp3 hybrid orbitals half-filled to bind two hydrogen, atoms (terminal-H). The remaining two hybrid orbitals (one half-filled and one empty) are then used to bind, bridging-H atoms as given below., , (a), , (b), , Figure 1. The (a) orbital overlap of hybrid atomic orbital of boron with hydrogens and (b) the resulting, banana-shaped 3-center-2-electron bond., , It can be clearly seen that the valence electron in each bridging hydrogen must get delocalize over all three, atoms (B–H–B) to bond to both of the B atoms simultaneously. This is pretty much contradictory for the, valence bond theory, which likes to bound the valence electrons into regions of space that are localized between, two participating nuclei only. Additionally, the molecular geometry of diborane cannot be explained using, valence shell electron pair repulsion (VSEPR) theory as far as bridging hydrogens are concerned. According, to VSEPR model, two bonds around each bridging hydrogen should be linear i.e. the B–H–B bond angle should, be equal 180° with straight-line coordination around.,  Molecular Orbital Treatment of Three-Centre Two-Electron Bond, The rationalization of the 3-centre-2-electron bond is much more convincing from the molecular, orbital approach, which considers the delocalization of electron density in bonding as a common phenomenon., Now because we only want to understand the nature of bonding involved in B–H–B bridges, we need to focus, on just the part of the molecule. Before the formation of molecular orbitals, we need to identify the basis, function required. Owing to the partial success of the valance bond theory in the rationalization of the 3-center2-electron bond, we can make the use of four equivalent sp3 hybrid orbitals and two s orbitals of hydrogen, atoms to construct the symmetry adapted linear combinations (SALCs) of atomic orbitals., Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 389, 1, 𝜓𝑏2𝑢 (B) = (𝜙1 − 𝜙2 − 𝜙3 + 𝜙4 ), 2, , (5), , 1, 𝜓𝑏3𝑢 (B) = (𝜙1 + 𝜙2 − 𝜙3 − 𝜙4 ), 2, , (6), , The single-electron wave functions and corresponding molecular orbital shapes for B–H–B portion of diborane, are shown in Figure 3. For simplicity, only the largest lobes of the four sp3 hybrid orbitals are depicted., Nevertheless, the smaller lobes on the opposite side also have a good possibility to overlap, which makes the, energies two nonbonding molecular orbitals unequal. The mixing of two SALCs of a1g symmetry generates, two molecular orbitals; one bonding and other antibonding shown by a1g and a1g*, respectively. Similarly, the, mixing of two SALCs of b3u symmetry yields two molecular orbitals of b3u and b3u* symmetry., , Figure 3. Partial one-electron molecular orbital energy level diagram for the B–H–B part of B2H6., , The shapes of molecular orbital with a1g and b3u symmetry evidently show that the electron density present in, them is actually delocalized over all three nuclei involved in B–H–B unit of diborane. A certain amount of, direct B–B bonding in diborane is also present which helps to stabilize the molecule geometry; which is, attributed to small-sized H-groups., Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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390, , A Textbook of Inorganic Chemistry – Volume I, ,  Classification of Bonds Present in Higher Boranes, The explanation of overall bonding in higher boranes needs the calculation of electrons involved in, the skeletal structure of Bn cluster and these electrons are generally referred as the “framework electrons”., Moreover, the B–H–B bridges are considered as part of the Bn framework while the terminal B–H are, discarded. Though the electrons involved in the framework construction of Bn cluster are very much, delocalized, yet the localized 3-centre 2-electron and 2-centre 2-electron orbital approach can be used to, explain the main features of the boranes. Each B atom uses one electron in the normal 2-center-2-electron, terminal B–H bond and the remaining two electrons are used in Bn framework. The structure of higher boranes, may or may not have all of the following kinds of bonds i.e. they may possess few or all types., 1. Terminal B–H bond: This is a normal 2-center-2-electron covalent bond and is generally shown as B–H., , 2. Direct B–B bond: This is a 2-center-2-electron bond and is able to connect to two boron atoms. These, bonds are generally represented as B–B., , 3. Bridging or open B–H–B bond: This is a 3-center-2-electron bond and is able to connect two boron and, one hydrogen atoms. These bonds are generally represented as B–H–B., , 4. Closed B–B–B bond: This is a 3-center-2-electron bond and is able to connect three boron atoms that are, at the corners of an equilateral triangle. These bonds are generally represented as B–B–B., , 5. Open bridging B–B–B bond: This is a 3-center-2-electron bond and is able to connect three boron atoms, to form a B–H–B like bridge found in diborane. These bonds are represented as B–B–B., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 391, ,  Geometry Prediction in Higher Boranes Using Lipscomb’s Model Involving STYX Numbers, The main initial approach to understand the structures of boranes and related species was Lipscomb’s, topological model involving STYX numbers and rules. W. N. Lipscomb was an American chemist who, developed a method to find the key combinations of bonding profile that are actually possible for a specific, boron hydride formula. Each boron atom in neutral boranes or hydroborate anions has at least one H attached, by a normal 2-center-2-electron sigma bond; therefore, it can be assumed that one B–H bond is present per, boron atom. Besides, Lipscomb also proposed that every other bond present in the cluster must belong to any, of the following categories., i) 3-centre-2-electrons B–H–B bond, labeled as “S”., ii) Closed, open, or a mixture of both 3-centre 2-electrons B–B–B bond, labeled as “T”., iii) 2-center-2-electrons B–B bond, labeled as “Y”., iv) 2-center-2-electrons B–H terminal bond (simply no. of BH2 groups), labeled as “X”., The structure prediction of borane clusters using the Lipscomb model involves the three major, components which are discussed in detail below., 1. The relationship between STYX code and valence electrons: The correlation between the boranes, formula and the number and types of bonds in the cluster is given by simple equations of balance. These, equations relate all kinds of sigma bonds to the number of valence electrons available., i) Three centers orbital balance: The electron deficiency in a borane cluster can be removed only if one 3center-2-electron bond is created by each boron atom. Thus, the sum of the number of 3-centre 2-electron B–, H–B bonds and the number of 3-centre 2-electron B–B–B bonds must be equal the number of B–H units (n)., 𝑛 = S+T, , (7), , ii) The hydrogen balance: Supposing that one terminal hydrogen is attached to each boron atom, the number, of hydrogen atoms leftover (m), must be distributed among bridges and additional B–H terminal bonds., 𝑚 = S+X, , (8), , iii) The electron balance: Now, if each BH unit contributes one pair of electrons to the skeleton and each of, the extra hydrogens gives one electron; the number of electron pairs contributed by additional hydrogens must, be calculated by halving their number. All of these electron pairs must be participating in bonding; and, therefore, the total number of bond pairs can be given as:, 𝑛 + (𝑚/2) = S + T + Y + X, , (9), , 1, Y = (S − X), 2, , (10), , From equation (7) and (8) we get, , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 392, , 2. The calculation of various STYX possibilities: After knowing the correlation between various kinds of, bonds with framework electron pairs in boron hydrides, we need to follow the following steps to write various, STYX possibilities., i) Write down the general formula of given borane cluster in form like BnHn+m to fix the value of n and m., ii) Calculate the number of B–H–B bridges which are represented by S. The value of S must lie within the, range of m/2 to m. In other words, the value of S must satisfy the following condition., 𝑚, ≤ S ≥𝑚, 2, , (11), , The validation of the higher limit comes from the fact that m represents the total additional hydrogens out of, which some are present in B–H–B bond and some are present in B–H terminal bond. Therefore, if all the, additional hydrogens are present in B–H–B bond, the value of “S” at its maximum can just be equal to m. The, validation of the lower limit can be derived equation (8) and equation (9) as:, 𝑛 + (𝑚/2) = (𝑚 − X) + T + Y + X, , (12), , 𝑚, 𝑛 = ( )+T+Y, 2, , (13), , 𝑚, S+T = ( )+T+Y, 2, , (14), , 𝑚, S = ( )+Y, 2, , (15), , From equation (7), we get, , Thus, the value of S is always equal to or greater than m/2., iii) For different values of S obtained in 2nd step, we have to calculate the equally possible solutions for the, values of T, Y and X., iv) There are many sets of STYX numbers for a given borane cluster and thus many possible topologies., 3. The shortlisting of STYX codes using empirical rules: In order to select the correct STYX code among, several possibilities, empirical rules have been developed which follow as:, i) The STYX number sets with negative value are not considered as they have no physical meaning., ii) All boranes have at least a 2-fold symmetry, so it is assumed that any new hydride probably would have at, least one plane, center, or two-fold axis of symmetry. Low symmetry seems to activate the center of reactivity., iii) Only one terminal hydrogen and no bridging hydrogen may be attached to boron that is bound to five, neighboring borons. This restricts B–H–B bridges and BH2 groups to the open edges of boron frameworks., iv) If a boron atom is bound to four other boron, it will probably not make use of more than one B–H–B bridge., v) A boron atom that is bound to only two other boron atoms will be involved in at least one B–H–B bridge., Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 393, , The whole concept can be exemplified using the diborane structure. The general formula for diborane, can be written in the form of B2H2+4; which gives the values of n and m as 2 and 4, respectively. From equation, (11), we get, (16), , 4, ≤ S ≥4, 2, The possible values of S = 2, 3, 4. By using S = 2 in equation (7), we get, 2=2+T, , (17), , T=0, , (18), , 4=2+X, , (19), , X=2, , (20), , Similarly, putting S = 2 in equation (8), we get, , Now putting the values of T and X from equation (18) and equation (20) in equation (9), we get, 2 + (4/2) = 2 + 0 + Y + 2, , (21), , Y=0, , (22), , Similarly, by taking the value of S as 3 and 4, one can get two another set of possible STYX numbers as, tabulated as given below., Table 2. Three possible sets of STYX numbers for B2H6., Number of B–H–B, bonds (S), , Number of B–B–B, bonds (T), , Number of B–B bonds, (Y), , Number of BH2 groups, (X), , 2, , 0, , 0, , 2, , 3, , −1, , 1, , 1, , 4, , −2, , 2, , 0, , It can clearly be seen that out of three sets of STYX numbers, only the first one is physically reasonable since, the latter two involve negative values. Besides, this also confirmed by the experimental geometrical structure, of the diborane that the STYX number of 2002 is, of course, seems to be correct; because there are two B–H–, B bridges, no three-center B–B–B bonds or two-center B–B bonds and two B–H terminal bonds in addition to, those already considered i.e. two BH2 groups. A similar procedure can be applied to find out the topological, structures of other borane clusters like B4H10, B5H9, B10H14., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 394, ,  Structure and Bonding Profile of Some Typical Higher Borane Clusters, As we have already discussed the fundamentals of structure and bonding in higher borane systems,, now we will implement those ideas to explain some typical examples., 1. Tetraborane-10 (B4H10): The bonding in B4H10 can easily be explained by drawing the plane projections, of its three-dimensional structure as shown below., , Figure 4. Planar view for the structure of B4H10., , It can be clearly seen that there are four B–H–B bridges, no closed or bridging B–B–B unit, one B–, B bond and two terminal BH2 groups. Hence, the overall STYX code for B4H10 molecule is 4012. Now, considering the electron requirement of various kinds of bonds present, the individual contribution of boron, and hydrogen atoms can easily be tabulated., Table 3. Nature and number of bonds (along with electrons required) present in B4H10., Nature of the, Bond, , Number of, Bonds, , Total electron, required, , Contribution from 4 B, atoms, , Contribution from 10, H atoms, , B–H–B, , 4, , 8, , 4, , 4, , B–B–B, , 0, , 0, , 0, , 0, , B–B, , 1, , 2, , 2, , 0, , B–H, , 6, , 12, , 6, , 6, , Hence, four 3-centre 2-electron and seven 2-centre 2-electron bonds require a total 4×2 + 7×2 = 22 electrons., Four boron atoms have 12 valence electrons while 10 electrons are actually contributed by ten hydrogen groups, that participating in both types of bonds., Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 395, , 2. Pentaborane-9 (B5H9): The pentaborane-9 (commonly called pentaborane) is an inorganic compound with, the formula B5H9, and is different from pentaborane-11 (B5H11). It is one of the most common cluster hydrides, of boron, though it is a highly reactive compound. Owing to its high reactivity toward oxygen, it was once, evaluated as rocket or jet fuel. Like many of the smaller boron hydrides, pentaborane is colorless, diamagnetic,, and volatile. The bonding in B5H9 can easily be explained by drawing the plane projections of its threedimensional structure as shown below., , Figure 5. Structure of B5H9., , Its structure is that of five atoms of boron arranged in a square pyramid. Each boron has a terminal, hydride ligand and four hydrides span the edges of the base of the pyramid. It can be clearly seen that there, are four B–H–B bridges, one closed or triply bridged B–B–B unit, two B–B bond and no terminal BH2 groups., Hence, the overall STYX code B5H9 molecule is 4120. Now considering the electron requirement of various, kinds of bonds present, the individual contribution of boron and hydrogen atoms can easily be tabulated., Table 4. Nature and number of bonds (along with electrons required) present in B5H9., Nature of the, Bond, , Number of, Bonds, , Total electron, required, , Contribution from 5 B, atoms, , Contribution from 9, H atoms, , B–H–B, , 4, , 8, , 4, , 4, , B–B–B, , 1, , 2, , 2, , 0, , B–B, , 2, , 4, , 4, , 0, , B–H, , 5, , 10, , 5, , 5, , Hence, five 3-centre 2-electron and seven 2-centre 2-electron bonds require a total 5×2 + 7×2 = 24 electrons., Five boron atoms have 15 valence electrons while 9 electrons are actually contributed by nine hydrogen groups, that are participating in both types of bonds., Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 396, , 3. Pentaborane-11 (B5H11): The pentaborane-11 is a compound with the general formula B5H11. It is a, colorless liquid at room temperature with a boiling point of 63°C. The bonding in B5H11 can easily be explained, by drawing the plane projections of its three-dimensional structure as shown below., , Figure 6. Structure of B5H11., , The pentaborane-11 is having unsymmetrical square-pyramidal and five boron atoms are present at, the five corners of a square pyramid, just like in the case B5H9 molecule. Three out of five boron atoms have, a terminal hydride ligand while two adjacent boron on the base of the pyramid has two hydride group each,, and four hydrides span the edges of the base of the pyramid. It can be clearly seen that there are three B–H–B, bridges, two closed or triply bridged B–B–B unit, zero B–B bond and three-terminal BH2 groups. Hence, the, overall STYX code B5H11 molecule is 3203. Now considering the electron requirement of various kinds of, bonds present, the individual contribution of boron and hydrogen atoms can easily be tabulated., Table 5. Nature and number of bonds (along with electrons required) present in B5H11., Nature of the, Bond, , Number of, Bonds, , Total electron, required, , Contribution from 5 B, atoms, , Contribution from 11, H atoms, , B–H–B, , 3, , 6, , 3, , 3, , B–B–B, , 2, , 4, , 4, , 0, , B–B, , 0, , 0, , 0, , 0, , B–H, , 8, , 16, , 8, , 8, , Hence, five 3-centre 2-electron and eight 2-centre 2-electron bonds require a total 5×2 + 8×2 = 26 electrons., Five boron atoms have 15 valence electrons while 11 electrons are actually contributed by eleven hydrogen, groups that are participating in both types of bonds., Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 397, , 4. Hexaborane-10 (B6H10): The bonding in B6H10 can easily be explained by drawing the plane projections of, its three-dimensional structure as shown below., , Figure 7. Structure of B6H10., , It can be clearly seen that there are four B–H–B bridges, two closed or triply bridged B–B–B unit,, two B–B bond and no terminal BH2 groups. Hence, the overall STYX code B6H10 molecule is 4220. Now, considering the electron requirement of various kinds of bonds present, the individual contribution of boron, and hydrogen atoms can easily be tabulated., Table 6. Nature and number of bonds (along with electrons required) present in B6H10., Nature of the, Bond, , Number of, Bonds, , Total electron, required, , Contribution from 6 B, atoms, , Contribution from 10, H atoms, , B–H–B, , 4, , 8, , 4, , 4, , B–B–B, , 2, , 4, , 4, , 0, , B–B, , 2, , 4, , 4, , 0, , B–H, , 6, , 12, , 6, , 6, , Hence, six 3-centre 2-electron and eight 2-centre 2-electron bonds require a total 6×2 + 8×2 = 28 electrons., Six boron atoms have 18 valence electrons while 10 electrons are actually contributed by ten hydrogen groups, that are participating in both types of bonds., Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 398, , 5. Decaborane-14 (B10H14): The bonding in B10H14 can easily be explained by drawing the plane projections, of its three-dimensional structure as shown below., , Figure 8. Structure of B10H14., , In decaborane, the B10 framework resembles an incomplete octadecahedron. Each boron has one, radial hydride, and four boron atoms near the open part of the cluster feature extra hydrides. It can be clearly, seen that there are four B–H–B bridges, six B–B–B unit (four B-B-B triple bridge bonds and two B-B-B bent, bridge), two B–B bond and zero terminal BH2 groups. Hence, the overall STYX code B10H14 molecule is 4620., Now considering the electron requirement of various kinds of bonds present, the individual contribution of, boron and hydrogen atoms can easily be tabulated., Table 7. Nature and number of bonds (along with electrons required) present in B10H14., Nature of the, Bond, , Number of, Bonds, , Total electron, required, , Contribution from 10, B atoms, , Contribution from 14, H atoms, , B–H–B, , 4, , 8, , 4, , 4, , B–B–B, , 6, , 12, , 12, , 0, , B–B, , 2, , 4, , 4, , 0, , B–H, , 10, , 20, , 10, , 10, , Hence, ten 3-centre 2-electron and twelve 2-centre 2-electron bonds require a total 10×2 + 12×2 = 44 electrons., Ten boron atoms have 30 valence electrons while 14 electrons are actually contributed by fourteen hydrogen, groups which are participating in both types of bonds., Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 399, ,  Structural Relationship Between Closo, Nido and Arachno Boranes, The structural relationship between closo, nido and arachno boranes is shown by the diagonal, connecting species having the same number of skeletal electron pairs. Hydrogen atoms are omitted for clarity., , Figure 9. Continued on the next page…, , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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400, , A Textbook of Inorganic Chemistry – Volume I, , Figure 9. The structural relationship between closo, nido, and arachno boranes; the diagonal lines connect, species that have the same number of skeletal electron pairs (SEP)., , The structural relationships shown above explain various geometrical aspects of borane clusters; and, provides a somewhat conceptual way to think about these systems. For instance, the structure of dodecahydrocloso-dodecaborate anion (B12H122−) is a regular icosahedron. Similarly, the structure of nido-B10H14 can easily, be obtained just by removing a six-degree vertex from closo-decaborate (B10H102−) anion. The removal of one, B–H unit and the addition of two H atoms converts nido-B5H9 into a butterfly-shaped arachno-B4H10 borane., Nevertheless, it should also be noted that the interconversion of these structures may or may not be possible, chemically; and the same statement can be made for their chemical formula., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 401, ,  Wade’s Rules, Though the Lipscomb’s topological model involving STYX numbers and rules was good in the, rationalization of structures of some of the boranes and related species, it was not enough to higher boranes, and carbonyl clusters. Therefore, a more sophisticated and comprehensive method was needed. In 1971, a, British chemist, Kenneth Wade, published a revolutionary paper in the field of cluster chemistry. The main, outlines of this communication were later to be called as Wade’s rules, which provided a straightforward and, elegant explanation of the geometries of ‘‘electron-deficient’’ cluster compounds in terms of the number of, skeletal electron pairs (SEPs) available. The main focus of this paper was on boranes, carboranes and lowvalent transition-metal clusters; whose structures could not be explained by the normal 2-center-2-electron, bond. After Wade’s initial report, another British chemist, Michael Mingos, extended the principles of counting, skeletal electron pairs to electron-precise and electron-rich clusters and gave a more generalized way of, calculating the skeletal electron contribution of a wide range of transition-metal. Thereafter, the rules became, known as the Wade-Mingos rules or, more formally, the polyhedral skeletal electron pair theory (PSEPT)., The structure prediction is based on different sets of rules (4n, 5n, or 6n), which are developed on the, basis of the number of electrons present per vertex. The 4n rules are pretty much accurate in predicting the, structures of clusters with 4 electrons per vertex, as is the case for many carboranes or boranes. The clusters, following 4n rule are generally classified as closo-, nido-, arachno- or hypho-, depending on whether they, represent a complete (closo-) deltahedron, or a deltahedron that is missing one (nido-), two (arachno-) or three, (hypho-) vertices. However, if the count of electrons is near to 5 electrons per vertex, the structure changes, occur and are governed by the 5n rules (based on 3-connected polyhedrons). Moreover, if the electron count, is increased further, the clusters with 5n electron counts become very unstable, and the 6n rules find their role., The cluster compounds following 6n rule have structures that are dependent on rings.,  4n Rule, The basis closo-polyhedra for the 4n rules are composed of triangular faces. The number of vertices, in the cluster prediction and the corresponding basis polyhedron is given below., Table 8. Base polyhedrons for structure prediction using 4n rule., No. of Vertex, , Polyhedron, , No. of Vertex, , Polyhedron, , 4, , Tetrahedron, , 9, , Tricapped trigonal prism, , 5, , Trigonal bipyramid, , 10, , Bicapped square antiprism, , 6, , Octahedron, , 11, , Octadecahedron, , 7, , Pentagonal bipyramid, , 12, , Icosahedron, , 8, , D2d (trigonal) dodecahedron, , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 402, , Using the electron count, the predicted structure can be found. n is the number of vertices in the cluster. The, 4n rules are enumerated in the following table., Table 9. Electron count and predicted structure using 4n rule., Electron count, , Name, , Predicted structure, , 4n − 2, , Bicapped closo, , n − 2 vertex closo polyhedron with 2 capped faces, , 4n, , Capped closo, , n − 1 vertex closo polyhedron with 1 face capped, , 4n + 2, , Closo, , Closo polyhedron with n vertices, , 4n + 4, , Nido, , n + 1 vertex closo polyhedron with 1 missing vertex, , 4n + 6, , Arachno, , n + 2 vertex closo polyhedron with 2 missing vertex, , 4n + 8, , Hypho, , n + 3 vertex closo polyhedron with 3 missing vertex, , 4n + 10, , Klado, , n + 4 vertex closo polyhedron with 4 missing vertex, , The valence electrons are enumerated when the counting of electrons for each cluster is carried out. For each, transition metal atom or ion present, ten electrons are subtracted from the total number of electrons. For, example, in Rh6(CO)16 the total number of electrons would be 6 × 9 + 16 × 2 − 6 × 10 = 86 – 6 × 10 = 26., Therefore, the cluster is a closo polyhedron because n = 6, with 4n + 2 = 26. When structure prediction is, carried out, other postulates may be given as:, i) For clusters that are comprised mainly of transition metals, any main group atoms are generally counted as, ligands or interstitial atoms, and not vertices., ii) Larger atoms or more electropositive groups have the tendency to occupy vertices of higher connectivity;, while the smaller or more electronegative atoms tend to fill vertices of low connectivity., iii) In some special boron hydride clusters, every boron connected to 3 or more vertices has one terminal H,, while a boron connected to two other vertices has two terminal H. Any extra hydrogens left are placed in openface positions to even out the coordination number of different vertices., iv) In some special cases of transition metal clusters, ligands are added to the metal centers to impart the metals, a reasonable coordination numbers, and if any H atoms are present, they should be placed in bridging sites to, even out the coordination numbers of different vertices., Generally speaking, closo clusters with n vertices are n-vertex polyhedral structures. To find the nidocluster structure, a closo cluster with n + 1 vertices is exploited as a starting point; if the cluster is consisted of, small atoms, a vertex with high connectivity is removed; while if the cluster is consisted of large atoms, a, vertex with low-connectivity is removed. To find the structure of arachno clusters, a closo polyhedron with, n+2 vertices is exploited as the starting point, and a nido complex with n+1 vertex is created by the rule, Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 403, , discussed above. However, if the cluster is of small atoms, a second vertex which adjacent to the first is, removed; and if the cluster is of large atoms mainly, the second vertex removed is not adjacent to the first one., Examples: i) P4: Electron count = 4 × number of valence electron of P = 4 × 5 = 20 electrons. Since n = 4, 4n, + 4 = 20, so the cluster is a nido borane. Starting from base polyhedron of n + 1 vertex, one vertex has to be, removed. Here, starting from trigonal bipyramid and removing one axial vertex gives the tetrahedral cluster., , Figure 10. Structure of P4., , ii) S42+: Electron count = 4 × number of valence electron of S = 4 × 6 −2 (for charge) = 22 electrons. Since n, = 4, 4n + 6 = 22, so the cluster is an arachno borane. Starting from base polyhedron of n + 2 vertex, two, vertexes have to be removed. In this case, it will start from octahedron and then the removal of two nonadjacent vertexes will give square cluster., , Figure 11. Structure of S42+., , iii) B5H54−: Electron count = 5 × 3 + 1 × 5 + 4 = 24 electrons. Since n = 5, 4n + 4 = 24, so the cluster is a nido, borane. In this case, will start from octahedron and then the removal of one vertexes will give square pyramidal., The hydrogens have been omitted for clarity., , Figure 12. Structure of B5H54−., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 404, , iv) Os6(CO)18: Electron count: 6 × Os + 18 × CO – 60 (for 6 osmium atoms) = 6 × 8 + 18 × 2 – 60 = 24. Since, n = 6, 4n = 24, so the cluster is capped closo. Starting from a trigonal bipyramid, a face is capped. The carbonyls, have been omitted for clarity., , Figure 13. Structure of Os6(CO)18., , v) C2B5H7: Electron count = 2 × C + 5 × B + 7 × H = 2 × 4 + 3 × 5 + 7 × 1 = 30. Since n in this case is 7, 4n +, 2 = 30, the cluster is closo. The hydrogens have been omitted for clarity., , Figure 14. Structure of C2B5H7., , The bookkeeping for deltahedral clusters is sometimes carried out by counting skeletal electrons pairs, instead of the total number of electrons. The CH and BH units are considered as 3 and 2 electron donor,, respectively. Additional hydrogen contributes 1 electron and charge is considered as it is. m is the sum of the, number of boron and carbon atoms., No. of e pair, , m−1, , m, , m+1, , m+2, , m+3, , m+4, , m+5, , Structure, , Bicapped closo, , Capped closo, , Closo, , Nido, , Arachno, , Hypho, , Klado, , For example, in C2B7H13, m is 9, while electron pairs are 2 × CH + 7 × BH + 4 × H = 6 + 14 + 4 = 24 or 12, pairs. The number of framework electron pairs are 9 + 3 = 12; hence the structure is arachno., Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 405, ,  5n Rule, If electrons per vertex are approaches 5, the 5n rule is used based on a different series of polyhedra, known as the 3-connected polyhedra, in which each vertex is connected to 3 other vertices., Table 10. Base polyhedrons for structure prediction using 5n rule., No. of Vertex, , Polyhedron, , No. of Vertex, , Polyhedron, , 4, , Tetrahedron, , 14, , Dual of triaugmented triangular, , 6, , Trigonal prism, , 16, , Square truncated trapezohedron, , 8, , Cube, , 18, , Dual of edge-contracted icosahedron, , 10, , Pentagonal prism, , 20, , Dodecahedron, , 12, , D2d pseudo-octahedron, , The 5n rules are as follows:, Table 11. Electron count and predicted structure using 5n rule., Electron count, , Predicted structure, , 5n, , n-vertex 3-connected polyhedron, , 5n + 1, , n – 1 vertex 3-connected polyhedron with one vertex inserted into an edge, , 5n + 2, , n – 2 vertex 3-connected polyhedron with two vertexes inserted into an edge, , 5n + k, , n – k vertex 3-connected polyhedron with k vertex inserted into an edge, , Examples: i) P4S3: Electron count = 4 × number of valence electron of P + 3 × number of valence electrons, of S = 4 × 5 + 3 × 6 = 38 electrons. Since n = 7, 5n + 3 = 38. Three vertices are inserted into edges., , Figure 15. Structure of P4S3., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 406, , ii) P4O6: Electron count = 4 × number of valence electron of P + 6 × number of valence electrons of O = 4 × 5, + 6 × 6 = 56 electrons. Since n = 10, 5n + 6 = 56. Six vertices are inserted into edges., , Figure 16. Structure of P4O6., ,  6n Rule, If the electron count per vertex is about 6, a 6n rule is used for structure prediction. This is because, structures based on 4n or 5n rules would become unstable if the number of electron approaches 6, and clusters, tend to give structures governed by the 6n rules. The rules for the 6n structures are as follows:, Table 12. Electron count and predicted structure using 6n rule., Electron count, , Predicted structure, , 6n − k, , n-membered ring with k⁄2 transannular bonds, , 6n − 4, , n-membered ring with 2 transannular bonds, , 6n − 2, , n-membered ring with 1 transannular bond, , 6n, , n-membered ring, , 6n + 2, , n-membered chain (n-membered ring with 1 broken bond), , Examples: i) S8: Electron count = 8 × number of valence electron of S = 48 electrons. Since n = 8, 6n = 48., Therefore, the cluster is an 8-membered ring., , Figure 17. Structure of S8., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 407, , ii) C6H14: Electron count = 6 × number of valence electron of C + 14 × number of valence electrons of H = 6, × 4 + 14 × 1 = 38 electrons. Since n = 6, 6n + 2 = 38. Therefore, the cluster is a 6-membered chain., , Figure 18. Structure of C6H14., , It is also worth mentioning that Wade’s rules not only rationalized the structures of a vast number of, cluster compounds but they have also stimulated further research in cluster chemistry., ,  Carboranes, Carboranes are the cluster composed of carbon, boron and hydrogen atoms; and just like boranes, can, be classified as closo-, nido-, arachno-, hypho-, or -klado based on whether they represent a complete (closo), polyhedron, or a polyhedron that is missing one (nido-), two (arachno-), or more vertices. Carboranes are the, most common examples of heteroboranes. The electronic structure of carboranes has been described by WadeMingos rules. Three main categories of carboranes are discussed below.,  Closo-(Closed) Carboranes, These are closed triangular polyhedral structures in which all the vertices of the triangular polyhedral, geometries are occupied mainly by boron and some sites by carbon atoms. There are n+1 electron pairs (or, 4n+2 skeletal electrons) involved in multicentre bonding in closo-carborane; where n represents the total, number of B and C atoms. Some of the common examples of closo-carboranes are:, 1. C2B10H12: In C2B10H12, n = 12; according to Wade’s rule, the two CH units contribute 2×3 = 6 electrons and, ten BH units contribute 10×2 = 20 electrons to the bonding molecular orbitals or to the skeletal structure. Thus,, there are 13 electron pairs (n+1 = 13) present in the multicentre bonding orbitals of C2B10H12, confirming this, as a closo kind. Three isomers (ortho-, meta- and para-) are possible., , Figure 19. Structure and isomerism in C2B10H12 (dicarba-closo-dodecaborane)., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 408, , 2. C2B3H5: In C2B3H5, n = 5; according to Wade’s rule, the two CH units contribute 2×3 = 6 electrons and, three BH units contribute 3×2 = 6 electrons to the bonding molecular orbitals or the skeletal structure. Thus, there are 6 electron pairs (n+1 = 6) present in the multicentre bonding orbitals of C2B3H5, confirming this as, closo kind. Three isomers are possible which are given below., , Figure 20. Structure and isomerism in C2B3H5., ,  Nido-(Nestlike) Carboranes, These are nest-like geometries and can be assumed as the derivatives of closed triangular polyhedral, structures in which one vertex is removed. Most of the sites in these clusters are occupied by boron atoms, while some sites by carbons. There are n+2 electron pairs (or 4n+4 skeletal electrons) involved in multicentre, bonding in nido-carboranes; where n represents the total number of B and C atoms. Common examples are:, 1. C2B9H13: In C2B9H13, n = 11; and according to Wade’s rule, the two CH units contribute 2×3 = 6 electrons,, nine BH units contribute 9×2 = 18 electrons, and two additional hydrogens contribute 2×1 = 2 electrons to the, bonding molecular orbitals or the skeletal structure. Thus there are total 26 electrons or 13 electron pairs (n+2, = 13) present in the multicentre bonding orbitals of C2B9H13, confirming this as nido kind. The structure of, some of the possible isomers that can be obtained experimentally are given below., , Figure 21. Structure and isomerism in C2B9H13., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 409, , 2. C2B4H8: In C2B4H8, n = 6; according to Wade’s rule, the two CH units contribute 2×3 = 6 electrons and, three BH units contribute 4×2 = 8 electrons and two additional hydrogens contribute 2×1 = 2 electrons to the, bonding molecular orbitals or the skeletal structure. Thus there are total 16 electrons or 8 electron pairs (n+2, = 8) present in the multicentre bonding orbitals of C2B4H8, confirming this as a nido kind. The structure of, some of the possible isomers that can be obtained experimentally are given below., , Figure 22. Structure and isomerism in C2B4H8., ,  Arachno-(Weblike) Carboranes, These are web-like geometries and can be assumed as the derivatives of closed triangular polyhedral, structures in which two vertices are removed. Most of the sites in these clusters are occupied by boron atoms, while some sites by carbons. There are n+3 electron pairs (or 4n+6 skeletal electrons) involved in multicentre, bonding in arachno-carboranes; where n represents the total number of B and C atoms. Some of the common, examples of arachno-carboranes are:, 1. C2B6H12: In C2B6H12, n = 8; according to Wade’s rule, the two CH units contribute 2×3 = 6 electrons and, six BH units contribute 6×2 = 12 electrons and four additional hydrogens contribute 4×1 = 4 electrons to the, bonding molecular orbitals or the skeletal structure. Thus there are total 22 electrons or 11 electron pairs (n+3, = 11) present in the multicentre bonding orbitals of C2B6H12, confirming this as an arachno kind. The structure, of some of the possible isomers that can be obtained experimentally are given below., , Figure 23. Structure and isomerism in C2B6H12., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 410, , 2. C2B7H13: In C2B7H13, n = 9; according to Wade’s rule, the two CH units contribute 2×3 = 6 electrons and, seven BH units contribute 7×2 = 14 electrons and four additional hydrogens contribute 4×1 = 4 electrons to, the bonding molecular orbitals or the skeletal structure. Thus there are total 24 electrons or 12 electron pairs, (n+3 = 12) present in the multicentre bonding orbitals of C2B7H13, confirming this as an arachno-kind. The, structure of some the possible isomers that can be obtained experimentally are given below., , Figure 24. Structure and isomerism in C2B7H13., ,  Structural Pattern Correlation Between Closo, Nido and Arachno Carboranes, The structural pattern in closo, nido and arachno carboranes for different vertexes and skeletal, electron pairs is very much important to to theoretical as well experimental analysis. Hs are omitted for clarity., , Figure 25. Continued on the next page…, Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 411, , Figure 25. Continued on the next page…, , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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412, , A Textbook of Inorganic Chemistry – Volume I, , Figure 25. The structural relationship between closo, nido, and arachno carboranes., , Some hypho-carboranes (C2Bn−2Hn+6) also do exist in which three vertices from the parent deltahedron are, missing. Furthermore, carboranes are also formed by joining two or more preceding types; called as conjunctocarboranes., ,  Metal Carbonyl Clusters- Low Nuclearity Carbonyl Clusters, Metal carbonyl clusters are the metal clusters (two or more metal centers directly bonded to each, other) having carbonyl groups as the ligand species. The metal centers in these cluster geometries are actually, present in low oxidation state (+1, 0, −1) that can be stabilized by carbonyl ligands. Metal carbonyl clusters, are mainly formed by some end-group metal (Fe, Co, Ni, Ru, Rh, Pd, Os, Ir, Pt) of the d-block elements. The, primary domain of carbonyl clusters is composed of neutral carbonyls, carbonyl anions, metal carbonyl, hydrides. The carbonyl hydride clusters can be obtained from neutral carbonyls by replacing one of the CO, groups with two H-groups; while carbonyl anions are derived by replacing CO with one H-atom and one, negative charge, or with two negative charge. Metal carbonyl clusters can be classified into two types; low, nuclearity carbonyl clusters (LNCC) and high nuclearity carbonyl clusters (HNCC), depending upon the, number of metal centers involved in the skeletal framework. If the number of metal centers is in the range of, 2–4, they are generally labeled as low nuclearity; while on the other hand, a metal-center number of 5 and, Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 413, , above makes them designable as high nuclearity carbonyl cluster system. Owing to the difference of electron, counting scheme from high nuclearity carbonyl clusters, this section will exclusively deal with low nuclearity, carbonyl clusters. The rationalization of bonding and structural profile of some important low nuclearity, carbonyls clusters on the basis 18-electron scheme is discussed below.,  Dinuclear Carbonyl Clusters:, The structural framework of dinuclear metal carbonyl clusters is comprised of two metal centers, connected by 1 metal-metal bond, and therefore, linear in geometry. The CO groups can be terminal, bridging, or both. The most common examples of these are Co2(CO)8, Fe2(CO)9, Mn2CO10, Tc2CO10, and Re2CO10., 1. Co2(CO)8: This cluster is known to exist in two isomers; the first one has a D3d symmetry with one metalmetal bond with zero bridging carbonyl, the second one is of C2v symmetry and has two bridging CO ligands, along with one metal-metal bond. The 18-electron count for Co2(CO)8 is 2×9 + 8×2 = 34. Hence, one metalbond (2 electrons) is needed to fulfill the requirement of two metal centers (36 electrons)., , Figure 26. Structures and bonding in Co2(CO)8., , 2. Fe2(CO)9: The structure of Fe2(CO)9 exist with D3h symmetry, and contains three bridging CO ligands and, six terminal CO groups attached. The 18-electron count for Fe2(CO)9 is 2×8 + 9×2 = 34. Hence, one metalbond (2 electrons) is needed to fulfill the requirement of two metal centers (36 electrons)., , Figure 27. Structures and bonding in Fe2(CO)9., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 414, , 3. M2(CO)10: M2CO10 (M = Mn, Tc, Re) exists with D4d symmetry with one metal-metal bond and four CO, ligands attached to each of the metal centre. The 18-electron count for M2CO10 (M = Mn, Tc, Re) is 2×7 +, 10×2 = 34. Hence, one metal-bond (2 electrons) is needed to fulfill the requirement of two metal centers (36, electrons)., , Figure 28. Structures and bonding in M2CO10 (M = Mn, Tc, Re)., ,  Trinuclear Metal Carbonyls, The structural framework of trinuclear metal carbonyl clusters is comprised of three metal centers, connected by three metal-metal bonds, and therefore, usually trigonal in geometry. The CO groups can be, terminal, bridging or both. The most common examples of trinuclear carbonyl clusters are Fe3CO12, Ru3(CO)12, and Os3(CO)12 systems., 1. Fe3CO12: Fe3(CO)12 is different, with two bridging CO ligands, resulting in C2v symmetry. The 18-electron, count for Fe3(CO)12 is 3×8 + 12×2 = 48. Hence, three metal-metal bonds (6 electrons) are needed to fulfill the, requirement of three metal centers (54 electrons)., , Figure 29. Structures and bonding in Fe3(CO)12., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 415, , 2. M3(CO)12 (M = Os, Ru): For example, the Ru3(CO)12 cluster has D3h symmetry, consisting of an equilateral, triangle of Ru atoms, each of which has two axial and two equatorial CO ligands. Os3(CO)12 has the same, structure. The 18-electron count for M3(CO)12 (M = Os, Ru) is 3×8 + 12×2 = 48. Hence, three metal-metal, bonds (6 electrons) are needed to fulfill the requirement of three metal centers (54 electrons)., , Figure 30. Structures and bonding in M3(CO)12 (M = Os, Ru)., ,  Tetranuclear Metal Carbonyls, The structural framework of tetranuclear metal carbonyl clusters is comprised of four metal centers, connected by four to six metal-metal bonds, and therefore, usually tetrahedral in geometry. The CO groups, can be terminal, bridging or both. The most common examples of tetranuclear carbonyl clusters are Ir4(CO)12,, Co4(CO)12, Rh4(CO)12, Re4CO162−, Ru3(CO)12 and Os4(CO)16 systems., 1. Ir4(CO)12: The Ir4(CO)12 has perfect Td symmetry with no bridging CO ligands groups. The 18-electron, count for Ir4(CO)12 is 4×9 + 12×2 = 60. Hence, six metal-metal bonds (12 electrons) are needed to fulfill the, requirement of four metal centers (72 electrons)., , Figure 31. Structures and bonding in Ir4(CO)12., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 416, , 2. M4CO12 (M = Co, Rh): M4CO12 (M = Co, Rh) is consisted of a tetrahedral M4 core, but the molecular, symmetry is C3v. Three carbonyl ligands are bridging ligands and nine are terminal. The 18-electron count for, M4(CO)12 (M = Co, Rh) is 4×9 + 12×2 = 60. Hence, six metal-metal bonds (12 electrons) are needed to fulfill, the requirement of four metal centers (72 electrons)., , Figure 32. Structures and bonding in M4(CO)12 (M = Co, Rh)., , 3. [Re4(CO)16]2−: [Re4(CO)16]2− has D2h symmetry with no bridging carbonyl. The 18-electron count for, [Re4(CO)16]2− is 4×7 + 16×2 + 2 (charge) = 62. Hence, five metal-metal bonds (10 electrons) are needed to, fulfil the requirement of four metal centres (72 electrons)., , Figure 33. Structures and bonding in [Re4(CO)16]2−., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 417, , 4. Os4(CO)16: The tetranuclear Os4(CO)16 is analogs to the cyclobutane with a puckered structure. The X-ray, diffraction analysis of Os4(CO)14 unveiled an irregular tetrahedral Os4 skeleton with four weakly semi-bridging, CO groups and four different Os–Os bond lengths. The 18-electron count for Os4(CO)16 is 4×8 + 16×2 = 64., Hence, four metal-metal bonds (8 electrons) are needed to fulfill the requirement of four metal centers (72, electrons)., , Figure 34. Structures and bonding in Os4(CO)16., , It is worthy to note that the electron counting scheme in low nuclearity carbonyl clusters is the same, as that is used in mononuclear metal carbonyl complexes., ,  Total Electron Count (TEC), The simple 18-electron rule has been proven of great significance in the case of structural, rationalization of low nuclearity carbonyl clusters. However, if the number of metal centers per cluster is equal, or greater than five; then the conventional approach is not significant, and does not provide any satisfactory, results. For example, the 18-electron count for Rh6(CO)16 is 6×9 + 16×2 = 86; which means that eleven metalmetal bonds (108 − 86 = 22) are needed to fulfil the requirement of six metal centres. But the actual structure, of Rh6(CO)16 is consisted of an octahedral Rh6 core with twelve metal-metal bonds. Moreover, simple 18electron treatment for high nuclearity carbonyl clusters (HNCC) does not provide any information regarding, the overall geometry. The situation also becomes more and more complex if some encapsulated heteroatom, like carbon is also present. Therefore, because of the lacking of any rational solution for the electronic structure, of high nuclearity carbonyl clusters, most of the efforts have been devoted to find a correlation between their, structure and the number of electrons available for cluster binding. It is worthy to mention that high-nuclearity, carbonyl clusters are also considered as electron-deficient compounds; which is obviously due to the, inadequate number of electrons to allow the assignment of all bonds as 2-centre 2-electron in nature., Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 418, ,  Isolobal Analogy Between M(CO)3 And BH Fragments, A British chemist, Kenneth Wade, solved the unexplained problem of structure and bonding, predictions in high nuclearity carbonyl clusters by developing a new scheme of electron counting, total electron, count (TEC). This new proposal was actually the extension of his previously used scheme for boranes and, carboranes, in which he had correlated the structure of boranes and their derivatives with the number of, electrons involved in the skeletal framework. The idea behind this extension was that the M(CO)3 unit is, actually isolobal with the BH unit. This can be better explained by taking the example of Ru(CO)3 fragment., , Figure 35. Structures and bonding in the isolobal pair of BH and Ru(CO)3., , The BH unit uses one of four valence orbitals of boron and two electrons, one from boron and one from, hydrogen. Hence, the spare valence orbitals and corresponding electrons left on boron are three and two, respectively. These spare orbitals and electrons are then used in cluster bonding. Similarly, the Ru(CO)3 unit, uses six of nine valence orbitals of ruthenium and twelve electrons, six from ruthenium and six from three, carbonyl ligands. Therefore, the spare valence orbitals and corresponding electrons left on ruthenium are three, and two respectively., Therefore, 3n valence orbitals and 2n electrons should be available in any BnHn cluster system. The, overlap of 2n valence orbitals oriented towards the surface of the polyhedron generates n bonding and n, antibonding molecular orbitals. The overlap of n valence orbitals oriented towards the core of the polyhedron, generates 1 strongly bonding and n–1 weakly bonding, nonbonding or antibonding molecular orbitals. Thus, we can say that a total of n+1 bonding molecular orbitals are generated in the process of cluster formation, and, the number of electrons required to fill these bonding molecular orbitals is 2n+2. However, in n BH units of, BnHn cluster can supply only 2n electron, explain why BnHn2− or cluster is more stable than simple BnHn. The, same argument holds true about Run(CO)3n cluster system, i.e. 2n+2 electrons are needed to fill all the bonding, molecular orbitals. Hence, [Ru6(CO)18]2− anion would be more stable than Ru6(CO)18 cluster system.,  Electron Counting Scheme for High Nuclearity Carbonyl Clusters, The isolobal analogy of M(CO)3 fragment with B–H (or C–H) unit inspired Kenneth Wade to explore, this field further; and he of course then came with a new set of rules for electron counting in high nuclearity, carbonyl cluster systems. He suggested that the total electron count of these clusters can be correlated to, Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 419, , skeletal electron count participating in the cluster bonding in a similar way adopted in boranes or carboranes., The total electron count can be calculated by adding the following contributions:, i) The number of valence electrons of all metal-centers., ii) Two electrons for each carbonyl group irrespective of the fact whether it is terminal or bridged., iii) One electron for each unit of negative charge., iv) The number of valence electrons of each hetero or interstitial atoms like carbon or nitrogen., This total electron count then can be used to predict the structure and bonding of carbonyl cluster, systems by extracting the skeletal electron count. Now, as we know that 2n+2, 2n+4, 2n+6 skeletal electrons, are required for closo, nido and arachno boranes, respectively; the same is true for metal carbonyl clusters., However, in addition to the 2 valance electrons to be used in the skeletal framework, each M(CO)3 also contains, 12 non-skeletal electrons. The theoretical basis of this claim comes from the fact that each M–CO bond, contains 4 electrons; 2 σ-electrons donated by CO ligand to the metal, and 2 π-electrons donated by the metal, back to the lowest unoccupied antibonding molecular orbital of CO ligand. This gives a total electron count, for closo polyhedron as 12n + 2(n +1). Hence, the predictions of structure and bonding in high nuclearity, carbonyl cluster with n vertexes can be summed up only after considering these twelve non-skeletal electrons., Table 9. Total electron count (TEC) and predicted structure., Total electron count, , Name, , Predicted structure, , 12n + 2(n − 1), , Bicapped closo, , n − 2 vertex closo polyhedron with 2 capped faces, , 12n + 2n, , Capped closo, , n − 1 vertex closo polyhedron with 1 face capped, , 12n + 2(n + 1), , Closo, , Closo polyhedron with n vertices, , 12n + 2(n + 2), , Nido, , n + 1 vertex closo polyhedron with 1 missing vertex, , 12n + 2(n + 3), , Arachno, , n + 2 vertex closo polyhedron with 2 missing vertex, , 12n + 2(n + 4), , Hypho, , n + 3 vertex closo polyhedron with 3 missing vertex, , 12n + 2(n + 5), , Klado, , n + 4 vertex closo polyhedron with 4 missing vertex, , It should also be noted that Wade’s predictions based on total electron count are also applicable to, low nuclearity carbonyl cluster systems in which the number of metal centers present is three or four. For, example, the total electron count for Ir4(CO)12 is 4 × Ir + 12 × CO = 4 × 9 + 12 × 2 = 60. Since n = 4, 12n +, 2(n + 2) = 60, so the cluster is nido. Starting from a trigonal bipyramid, a vertex is removed. Similarly, the, total electron count for Fe3(CO)12 is 3 × Fe + 12 × CO = 3 × 8 + 12 × 2 = 48. Since n = 3, 12n + 2(n + 3) = 48,, so the cluster is arachno. Therefore, the structure prediction Starts from a trigonal bipyramid, and then two, axially opposite vertexes are removed., Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 420, ,  Structure and Bonding Profile of Some Typical High Nuclearity Carbonyl Clusters Using TEC, As we have already discussed the fundamentals of structure and bonding in high nuclearity carbonyl, clusters systems, now we will implement those ideas to explain some typical examples., 1. M6(CO)16 (M = Co, Rh): The total electron count for Rh6(CO)16 is 6×Rh + 16×CO = 6×9 + 16×2 = 86., Since n = 6, 12n + 2(n + 1) = 86, so the cluster is closo. Therefore, the structure prediction starts from an, idealized octahedron. The predicted structure for Rh6(CO)16 cluster system is shown below., , Figure 36. Structure of M6(CO)16 (M = Co, Rh)., , 2. Os5(CO)16: The total electron count for Os5(CO)16 is 5×Os + 16×CO = 5×8 + 16×2 = 72. Since n = 5, 12n, + 2(n + 1) = 72, so the cluster is closo. Therefore, the structure prediction starts from an idealized trigonal, bipyramid. The predicted structure for Os5(CO)16 cluster system is shown below., , Figure 37. Structure of Os5(CO)16., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 421, , 3. [Os6(CO)18]2−: The total electron count for [Os6(CO)18]2− is 6×Os + 18×CO + 2 (for negative charge) = 6×8, + 18×2 +2 = 86. Since n = 6, 12n + 2(n + 1) = 86, so the cluster is closo. Therefore, the structure prediction, starts from an idealized octahedron. The predicted structure for [Os6(CO)18]2− cluster system is shown below., , Figure 38. Structure of [Os6(CO)18]2−., , 4. Os5C(CO)15: The total electron count for Os5C(CO)15 is 5×Os + 15×CO + 1×C = 5×8 + 15×2 + 4×1 = 74., Since n = 5, 12n + 2(n + 2) = 74, so the cluster is nido. Therefore, the structure prediction starts from an, idealized octahedron, and then one vertex is removed. The predicted structure for Os5C(CO)15 cluster system, is shown below., , Figure 39. Structure of Os5C(CO)15., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 422, , 5. [Ru6N(CO)16]−: The total electron count for [Ru6N(CO)16]− is 6×Ru + 16×CO + 1×N + 1 (for negative, charge) = 6×8 + 16×2 + 1×5 + 1 = 86. Since n = 6, 12n + 2(n + 1) = 86, so the cluster is closo. Therefore, the, structure prediction starts from an idealized octahedron. The predicted structure for [Ru6N(CO)16]− cluster, system is shown below., , Figure 40. Structure of [Ru6N(CO)16]−., , 6. [Fe4N(CO)12]−: The total electron count for [Fe4N(CO)12]− is 4×Fe + 12×CO + 1×N + 1 (for negative charge), = 4×8 + 12×2 + 1×5 + 1 = 62. Since n = 4, 12n + 2(n + 3) = 62, so the cluster is arachno. Therefore, the, structure prediction starts from an idealized octahedron, then two adjacent vertexes are removed. The predicted, structure for [Fe4N(CO)12]− cluster system is shown below., , Figure 41. Structure of [Fe4N(CO)12]−., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 423, ,  Correlation Between TEC and SEP, The implementation of the rules listed in ‘Table 9’ is more often carried out in reverse gear, i.e. 12, electrons for each metal center are subtracted from the total electron count. The number of electrons thus, obtained is then divided by 2 to get skeletal electron pairs. The number of skeletal electron pairs (SEP) can be, calculated using equation (23) as described below:, (23), , 1, SEP = (TEC − 12 electrons per metal center), 2, , Now the structure prediction of some common high nuclearity carbonyl cluster systems on the correlative basis, of total electron count (TEC) and skeletal electron pairs (SEP) can be summed up as:, Table 10. Structure prediction of some common clusters on the correlative basis of TEC and SEP., Carbonyl, cluster, , Total electron count, (TEC), , Skeletal electron pairs, (SEP), , Vertex in parent, polyhedron, , Predicted, structure, , Rh6(CO)16, , (6 × 9) + (16 × 2) = 86, , 0.5 × [86 – (6 × 12)] = 7, , 6, , Closo, , Os5(CO)16, , (5 × 8) + (16 × 2) = 72, , 0.5 × [72 – (5 × 12)] = 6, , 5, , Closo, , Os5C(CO)15, , (5 × 8) + (15 × 2) + (4), = 74, , 0.5 × [74 – (5 × 12)] = 7, , 5, , Nido, , [Fe4C(CO)12]2−, , (4 × 8) + (12 × 2) + (4), + (2) = 62, , 0.5 × [62 – (4 × 12)] = 7, , 6, , Arachno, , [H3Ru4(CO)12]−, , (4 × 8) + (12 × 2) + (3), + (1) = 60, , 0.5 × [60 – (4 × 12)] = 6, , 5, , Nido, , [Ru5N(CO)14]−, , (5 × 8) + (14 × 2) + (5), + (1) = 74, , 0.5 × [74 – (5 × 12)] = 7, , 7, , Nido, , [Fe4N(CO)12]−, , (4 × 8) + (12 × 2) + (5), + (1) = 62, , 0.5 × [62 – (4 × 12)] = 7, , 6, , Arachno, , Finally, it should also be noted that the total electron counting scheme is applicable to most of the, high nuclearity carbonyl cluster systems, yet the exceptions like [Ni5(CO)12]2− do exist., , Buy the complete book with TOC navigation,, high resolution images and, no watermark., , Copyright © Mandeep Dalal

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A Textbook of Inorganic Chemistry – Volume I, , 424, ,  Problems, Q 1. Discuss the molecular orbital treatment of three-center two-electron bond in detail., Q 2. What are the STYX numbers? How would you use the Lipscomb’s model to find out the STYX code for, B4H10 cluster system?, Q 3. Draw and discuss the structure and bonding in B5H9 and B5H11., Q 4. How many B–H–B and B–B–B bonds are present in B10H14 cluster?, Q 5. Discuss the structural relationship between closo, nido and arachno type boranes., Q 6. What are Wade’s rules? How can we use these rules to predict the structures of B5H54− and P4 clusters?, Q 7. What are carboranes? Explain with suitable examples., Q 8. Draw and discuss the structural pattern correlation between closo, nido and arachno type carboranes., Q 9. What are the low nuclearity carbonyl clusters? How do they differ from the high nuclearity ones?, Q 10. How would you calculate the number of metal-metal bonds in Fe3(CO)12 and Ir4(CO)12?, Q 11. Define total electron count (TEC)., Q 12. Explain the electron counting scheme for high nuclearity carbonyl clusters in detail., Q 13. How would you explain the isolobal Analogy Between Ru(CO)3 And BH units?, Q 14. Using total electron count (TEC), explain the structure of Rh6(CO)16 and Os5C(CO)15., Q 15. Describe the correlation between total electron count (TEC) and skeletal electron pairs (SEP), and use, same to predict the structures of [Fe4N(CO)12]− and [H3Ru4(CO)12]−., , Copyright © Mandeep Dalal

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CHAPTER 10 Metal Clusters:, , 425, ,  Bibliography, [1] B. W. Pfennig, Principles of Inorganic Chemistry, John Wiley & Sons, New Jersey, USA, 2015., [2] G. Raj, Advanced Inorganic Chemistry Vol-1, Krishna Prakashan Media, Uttar Pradesh, India, 2008., [3] A. J. Welch, The significance and impact of Wade’s rules, Chem. Commun., 49, 2013, 3615., [4] K. Wade, The Structural Significance of the Number of Skeletal Bonding Electron-pairs in Carboranes,, the Higher Boranes and Borane Anions, and Various Transition-metal Carbonyl Cluster Compounds, Chem., Commun., 1971, 792., [5] D. M. P. Mingos, A General Theory for Cluster and Ring Compounds of the Main Group and Transition, Elements, Nature Physical Science, 236, 1972, 99., [6] R. N. Grimes, Carboranes, Academic Press, London, UK, 2011., [7] B. R. Puri, L. R. Sharma, K. C. Kalia, Principals of Inorganic Chemistry, Milestone Publishers, Delhi,, India, 2012., [8] F. A. Cotton, G. Wilkinson, C. A. Murillo, M. Bochmann, Advanced Inorganic Chemistry, John Wiley &, Sons, New Jersey, USA, 1999., [9] M. McPartlin, C. R. Eady, B. F. G. Johnson, J. Lewis, X-Ray structures of the hexanuclear cluster, complexes [Os6(CO)18] 2–, [HOs6(CO)18] –, and [H2Os6(CO)18], Chem. Commun., 1976, 884., [10] C. R. Eady, B. F. G. Johnson, J. Lewis, B. E. Reichert, G. M. Sheldrick, [Os5(CO)16]: X-Ray Crystal and, Molecular Structure, Chem. Commun., 1976, 271., [11] A. Taheri, L. A. Berben, Making C-H Bonds with CO2: Production of Formate by Molecular, Electrocatalysts, Chem. Commun., 52, 2015, 1768., [12] B. M. Gimarc, J. J. Ott, Isomers of C2B3H5 and the Diamond-Square-Diamond Rearrangement, Mechanism, Inorg. Chem., 25, 1986, 83., [13] A. A. A. Attia, A. Lupan, R. B. King, Tetracarbaboranes: Nido Structures Without Bridging Hydrogens,, Dalton Trans, 45, 2016, 18541., [14] B. D. Gupta, A. J. Elias, Basic Organometallic Chemistry: Concepts, Synthesises and Applications,, Universities Press (India) Private Limited, Andhra Pradesh, India, 2010., [15] J. E. Huheey, E. A. Keiter, R. L. Keiter, Inorganic Chemistry: Principals of Structure and Reactivity,, HarperCollins College Publishers, New York, USA, 1993., , Copyright © Mandeep Dalal

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Table of Contents, CHAPTER 1 ..................................................................................................................................... 11, Stereochemistry and Bonding in Main Group Compounds: ........................................................ 11, , , VSEPR Theory ................................................................................................................................ 11, , , , dπ–pπ Bonds .................................................................................................................................... 23, , , , Bent Rule and Energetic of Hybridization....................................................................................... 28, , , , Problems .......................................................................................................................................... 42, , , , Bibliography .................................................................................................................................... 43, , CHAPTER 2 ..................................................................................................................................... 44, Metal-Ligand Equilibria in Solution:................................................................................................. 44, , , Stepwise and Overall Formation Constants and Their Interactions ................................................ 44, , , , Trends in Stepwise Constants .......................................................................................................... 46, , , , Factors Affecting Stability of Metal Complexes with Reference to the Nature of Metal Ion and, Ligand .............................................................................................................................................. 49, , , , Chelate Effect and Its Thermodynamic Origin................................................................................ 56, , , , Determination of Binary Formation Constants by pH-metry and Spectrophotometry .................... 63, , , , Problems .......................................................................................................................................... 68, , , , Bibliography .................................................................................................................................... 69, , CHAPTER 3 ..................................................................................................................................... 70, Reaction Mechanism of Transition Metal Complexes – I: ............................................................ 70, , , Inert and Labile Complexes............................................................................................................. 70, , , , Mechanisms for Ligand Replacement Reactions ............................................................................ 77, , , , Formation of Complexes from Aquo Ions ....................................................................................... 82, , , , Ligand Displacement Reactions in Octahedral Complexes- Acid Hydrolysis, Base Hydrolysis .... 86, , , , Racemization of Tris Chelate Complexes ....................................................................................... 89, , , , Electrophilic Attack on Ligands ...................................................................................................... 92, , , , Problems .......................................................................................................................................... 94, , , , Bibliography .................................................................................................................................... 95

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CHAPTER 4 ..................................................................................................................................... 96, Reaction Mechanism of Transition Metal Complexes – II:...................................................... 96, , , Mechanism of Ligand Displacement Reactions in Square Planar Complexes ................................ 96, , , , The Trans Effect .............................................................................................................................. 98, , , , Theories of Trans Effect ................................................................................................................ 103, , , , Mechanism of Electron Transfer Reactions – Types; Outer Sphere Electron Transfer Mechanism and, Inner Sphere Electron Transfer Mechanism .................................................................................. 106, , , , Electron Exchange ......................................................................................................................... 117, , , , Problems ........................................................................................................................................ 121, , , , Bibliography .................................................................................................................................. 122, , CHAPTER 5 ................................................................................................................................... 123, Isopoly and Heteropoly Acids and Salts: ........................................................................................ 123, , , Isopoly and Heteropoly Acids and Salts of Mo and W: Structures of Isopoly and Heteropoly, Anions ............................................................................................................................................123, , , , Problems ........................................................................................................................................ 152, , , , Bibliography .................................................................................................................................. 153, , CHAPTER 6 ................................................................................................................................... 154, Crystal Structures: ............................................................................................................................... 154, , , Structures of Some Binary and Ternary Compounds Such as Fluorite, Antifluorite, Rutile, Antirutile,, Crystobalite, Layer Lattices - CdI2, BiI3; ReO3, Mn2O3, Corundum, Pervoskite, Ilmenite and, Calcite.............................................................................................................................................154, , , , Problems ........................................................................................................................................ 178, , , , Bibliography .................................................................................................................................. 179, , CHAPTER 7 ................................................................................................................................... 180, Metal-Ligand Bonding: ....................................................................................................................... 180, , , Limitation of Crystal Field Theory ................................................................................................ 180, , , , Molecular Orbital Theory – Octahedral, Tetrahedral or Square Planar Complexes...................... 184, , , , π-Bonding and Molecular Orbital Theory ..................................................................................... 198, , , , Problems ........................................................................................................................................ 212, , , , Bibliography .................................................................................................................................. 213

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CHAPTER 8 ................................................................................................................................... 214, Electronic Spectra of Transition Metal Complexes: .................................................................... 214, , , Spectroscopic Ground States ......................................................................................................... 214, , , , Correlation and Spin-Orbit Coupling in Free Ions for 1st Series of Transition Metals ................. 243, , , , Orgel and Tanabe-Sugano Diagrams for Transition Metal Complexes (d1 – d9 States) ................ 248, , , , Calculation of Dq, B and β Parameters ......................................................................................... 280, , , , Effect of Distortion on the d-Orbital Energy Levels ..................................................................... 300, , , , Structural Evidence from Electronic Spectrum ............................................................................. 307, , , , Jahn-Tellar Effect .......................................................................................................................... 312, , , , Spectrochemical and Nephelauxetic Series ................................................................................... 324, , , , Charge Transfer Spectra ................................................................................................................ 328, , , , Electronic Spectra of Molecular Addition Compounds................................................................. 336, , , , Problems ........................................................................................................................................ 340, , , , Bibliography .................................................................................................................................. 341, , CHAPTER 9 ................................................................................................................................... 342, Magnetic Properties of Transition Metal Complexes: ................................................................. 342, , , Elementary Theory of Magneto-Chemistry ................................................................................... 342, , , , Guoy’s Method for Determination of Magnetic Susceptibility ..................................................... 351, , , , Calculation of Magnetic Moments ................................................................................................ 354, , , , Magnetic Properties of Free Ions ................................................................................................... 359, , , , Orbital Contribution: Effect of Ligand-Field ................................................................................ 362, , , , Application of Magneto-Chemistry in Structure Determination ................................................... 370, , , , Magnetic Exchange Coupling and Spin State Cross Over ............................................................ 375, , , , Problems ........................................................................................................................................ 384, , , , Bibliography .................................................................................................................................. 385, , CHAPTER 10 ................................................................................................................................. 386, Metal Clusters: ...................................................................................................................................... 386, , , Structure and Bonding in Higher Boranes ..................................................................................... 386, , , , Wade’s Rules ................................................................................................................................. 401