Encyclopedia of Inorganic Chemistry || Coordination Numbers & Geometries

Coordination Numbers & Geometries Brian W. Clare & David L. Kepert University of Western Australia, Nedlands, Australia 1 Introduction 1 2 Five-coordinate Compounds 1 3 Six-coordinate Compounds 3 4 Seven-coordinate Compounds 6 5 Eight-coordinate Compounds 8 6 Nine-coordinate Compounds 9 7 Ten-coordinate Compounds 10 8 Twelve-coordinate Compounds 10 9 Further Reading 11 10 References 11 1 INTRODUCTION A very convenient and widely used method for depicting the 3D structure of molecules AXn is to imagine that the X atoms are situated at the vertices of various polyhedra centered on atom A.1,2 In the two most common geometries (i) the arrangement of four groups about a central atom is tetrahedral, as was independently proposed for carbon by van’t Hoff and Le Bel in 1874,3 and (ii) as Werner proposed some 20 years later in 1893, six groups are commonly arranged about a metal atom at the vertices of an octahedron.4 In some cases, isomers are possible. Thus optical isomers can be obtained when the molecule has no plane of symmetry, for example when four different groups are attached to a tetrahedral carbon atom, [Cabcd], which shows that the molecular rearrangement of such structures must be very slow. Similarly, the ability to isolate optical and geometrical isomers for complexes such as [Co(NH2CH2CH2NH2)2Cl2]+ shows that rearrangement is again very slow. This structural rigidity of the tetrahedron and octahedron arises from the transition states for rearrangement being substantially disfavored relative to the ground state. Steric repulsion between the ligands is an important component. Five-, seven-, eight-, and nine-coordination geometries tend to be substantially less rigid, and different structural isomers of the same composition cannot be isolated. The relative energy required to convert from one polyhedron into another of the same coordination number can be estimated from the ligand–ligand repulsion energies using an empirical force law (Table 1).5 Well-defined rigid stereochemistries may be obtained for all coordination numbers, however, in one of two ways. (i) With the exception of the tetrahedron and octahedron, most polyhedra have different types of vertex, and for complexes of the type [M(unidentate A)x(unidentate B)y] the sorting of the different ligands into the appropriate polyhedral vertices may stabilize a preferred structure. In general, it is found that charged ligands such as halide, and more particularly the more highly charged oxide, sulfide, and nitride, occupy the sterically less crowded vertices, in contrast to uncharged ligands which occupy the remaining sites. It is also found that for complexes of the lighter elements of lower coordination numbers that contain stereochemically active nonbonding pairs of electrons, these lone pairs also occupy the sterically less hindered sites. (ii) Complexes containing chelate groups may also have rigid stereochemistries. For bidentate ligands it is useful to define the geometry of the chelate ring in terms of a ‘normalized bite’ b, defined as the distance between the donor atoms divided by the metal–ligand distance. 2 FIVE-COORDINATE COMPOUNDS The starting point for five-coordination is to consider the trigonal bipyramid and the square pyramid and the relation between them.1,2,6 A twofold axis passes through the metal atom M and the donor atom E, the other four atoms lying on a pair of vertical mirror planes (see Figure 1). The angles between this axis and the metal–ligand bonds to the pairs of atoms AC and BD are defined by φA and φB, respectively. Neither the square pyramid nor the trigonal bipyramid is the same as those defined in classical geometry, which have equal edge lengths. The square pyramid with equal edge lengths is half an octahedron with φA = φB = 90.0◦, but in real molecules the more open space created by the square face relative to the triangular faces is partially closed by increasing φA and φB to ∼100◦. This results in the basal sites becoming more sterically hindered than the axial site. The regular trigonal bipyramid formed from equilateral triangles would have the metal–ligand bond lengths in the triangular plane approximately 30% shorter than the metal–axial ligand bonds. The triangular plane therefore expands, making all bond lengths more nearly equal, with the consequence that the equatorial sites are less sterically crowded with only two close neighbors, compared with three for the axial sites. There is no potential energy barrier between the square pyramid at φA = φB ≈ 100◦ and the two slightly more stable trigonal bipyramids at φA = 90, φB = 120◦ and φA = 120, φB = 90◦. Movement along this ‘reaction coordinate’ connecting the two trigonal bipyramids is usually described as Berry Pseudorotation.7 Any one of the three equatorial site of the trigonal bipyramid can become the apical site of a square pyramid and so repetition of this process scrambles all atom sites. Encyclopedia of Inorganic Chemistry, Online © 2006 John Wiley & Sons, Ltd. This article is © 2006 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Inorganic Chemistry in 2006 by John Wiley & Sons, Ltd. DOI: 10.1002/0470862106.ia049 2 COORDINATION NUMBERS & GEOMETRIES Table 1 Differences in repulsion energy coefficients, 103�X, corresponding to polyhedral rearrangements of [M(ligand)n] n Rearrangement 103�X 4 Tetrahedron Square 215 5 Trigonal bipyramid Square pyramid 13 6 Octahedron Trigonal prism 388 7 Capped octahedron Capped trigonal prism 1 Capped octahedron Pentagonal bipyramid 36 8 Square antiprism Dodecahedron 60 9 Tricapped trigonal prism Capped square antiprism 12 10 Bicapped square antiprism Sphenocorona 25 Bicapped square antiprism Trirhombohedron 26 11 Edge-coalesced icosahedron Capped pentagonal antiprism 9 12 Icosahedron Bicapped pentagonal prism 2397 E C B A M D fA fB Figure 1 General stereochemistry for [M(unidentate)5] Structurally characterized molecules with five identical ligands cover the complete range from the pure trigonal bipyramid (φA = 90, φB = 120◦) to the pure square pyramid (φA = φB ≈ 100◦), some simple examples being shown in Table 2. Whether a compound is near the trigonal bipyramid or near the square pyramid may often be attributed to crystal- packing forces. For example, the structure of SbPh5 is near the square pyramid whereas the solvate SbPh5·0.5C6H12 is near the trigonal bipyramid. In molecules near the trigonal bipyramidal end of the range the axial bonds are about 5% longer than the equatorial bonds, whereas for molecules near the square pyramid the axial bond is about 4% shorter than the four basal bonds. Many five-coordinate molecules exhibit very rapid intramolecular rearrangements, leading to all five ligands being equivalent over the NMR timescale.1,2,5 For example, the 19F NMR spectrum of PF5 shows all fluorine atoms equivalent over the temperature range 60 to −197 ◦C. Proton NMR studies on SbMe5 in carbon disulfide down to about −100 ◦C also show the presence of only one type of methyl group. The 13C NMR spectra of [Fe(CO)5] and [Fe(CNBu)5] Table 2 Stereochemical parameters for examples of [M(unidentate)5] complexes1,2,8 Complex φA (◦) φB (◦) (PhCH2NMe3)[SiF5] 90.3 121.2 [SbPh5]·0.5C6H12 90.3 119.2 (PCl4)[SnCl5] 90.2 117.8 [Sb(C6H4Me)5] 91.1 114.9 [Co(MeC5H4NO)5](ClO4)2 93.0 114.0 [SbPh5] 98.3 105.4 [Mg(Me3AsO)5](ClO4)2 99.8 107.6 [Mg(Me3PO)5](ClO4)2 99.9 106.4 (Et4N)2[InCl5] 103.0 104.7 Table 3 Examples of trigonal bipyramidal molecules with charged ligands, X, occupying trigonal planar sites2 [MX(ligand)4] [MX2(ligand)3] [MX3(ligand)2] [NiBr(PMe3)4](BF4) [NiBr2(PMe3)3] [CoCl3(PEt3)2] [Ni(CH3)(PMe3)4](BPh4) [NiI2{P(OMe)3}3] [AlCl3(thf)2] show only a single resonance at temperatures as low as −170 and −80 ◦C, respectively. Both the 19F NMR and 31P NMR studies of [Fe(PF3)5], [Ru(PF3)5], and [Os(PF3)5] down to −160 ◦C in CHClF2 show all ligands are equivalent. When there is a mixture of different types of ligand, a more well-defined structure is usually observed. In general, charged ligands such as halides require more space about the central atom than do uncharged ligands and occupy the less sterically hindered axial site of a square pyramid or the trigonal planar sites of a trigonal bipyramid, examples being shown in Table 3. The dominant stereochemistry for monooxo complexes is the axially substituted square pyramid, examples including [ReOCl4] and [MOCl4]− (M = Cr, Mo, W) as well as the nitrido complexes [MNCl4]− (M = Mo, Tc, Re, Ru, Os).1 For compounds containing a lone pair, this occupies one of the three trigonal sites of a trigonal bipyramid,2 as in Rb[Bi( •• )(SCN)4] and [Te( •• )Ph4]. The trifluoro complexes ClF3 and XeF3+ are T-shaped but can be considered as trigonal bipyramidal if the two nonbonding lone pairs are considered.2 Likewise, linear trihalide ions such as I3− can be regarded as trigonal bipyramidal with three nonbonding pairs of electrons in the three equatorial sites.2 The edge lengths for a trigonal bipyramid, square pyramid, and intermediate structures vary from 1.73r for the edges linking the equatorial sites of a trigonal bipyramid to 1.39r for the edges linking the basal sites of a square pyramid, where r is the metal–ligand distance. The introduction of chelating ligands of fixed normalized bite influences the structure obtained, the simplest examples being of the type [M(bidentate)2(unidentate)]. Complexes with bidentate ligands of small bite, as in [Fe(S2CNR2)2X] (b = 1.24)9 are close to square pyramidal, whereas complexes with a larger bite, for example [P(O2C6H4)2X] (b ≈ 1.42)1 have stereochemistries intermediate between a square pyramid and Encyclopedia of Inorganic Chemistry, Online © 2006 John Wiley & Sons, Ltd. This article is © 2006 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Inorganic Chemistry in 2006 by John Wiley & Sons, Ltd. DOI: 10.1002/0470862106.ia049 a trigonal bipyramid (X = halide, alkyl, etc.). Superimposed on this effect of normalized bite upon stereochemistry is that due to the unidentate ligand necessarily being different to the bidentate ligands. Thus complexes containing O2− as the unidentate ligand have structures close to square pyramids at all values of the normalized bite, as in [V(MeCOCHCOMe)2O] (b = 1.38)10 and [V(S2CNEt2)2O] (b = 1.21).11 A number of compounds of the p-block elements containing two bidentate ligands can be considered as trigonal bipyramidal if a nonbonding pair of electrons occupies an equatorial site, as in [Pb(RCOCHCOR)2( •• )] and [Sn(S2CNR2)2( •• )].1 3 SIX-COORDINATE COMPOUNDS1,2,12 3.1 [M(unidentate)6] The octahedron is the dominant stereochemistry for com- plexes containing six unidentate ligands. For complexes containing two ligands different from the other four, the rigid nature of the octahedron is illustrated by the ability to separate both cis and trans isomers. When one pair of ligands is grossly different to the other four, the trans structure is more stable. An important example is the dioxo complexes as in the uranyl complexes [UO2X4]2−.2 Other examples of trans-dioxo complexes are [ReO2py4]+, [ReO2(CN)4]3−, and [MoO2(CN)4]4−.2 However, complexes containing two dif- ferent unidentate ligands in addition to O2− may be either cis or trans. Compounds containing two nonbonding pairs of electrons and four unidentate ligands are invariably observed to be square planar, as in [TeII(ligand)4( •• )2]2+, [IIIICl4( •• )2]−, and [XeIVF4( •• )2].2 A second-order Jahn–Teller effect leads to a trigonal prismatic structure being preferred for some d0 ML6 species, such as WMe6. This illustrates the role of electronic effects in determining coordination geometry. 3.2 [M(bidentate)2(unidentate)2] Complexes containing two bidentate and two unidentate ligands may be either cis or trans octahedral, but it is important to note that both structures show very large distortions as the size of the chelate rings is reduced; the trans structure turns into the skew-trapezoidal bipyramidal structure (Figure 2). For a normalized bite of b = 21/2, the cis and trans structures have the same energy, but as the normalized bite is reduced the cis structure becomes more stable. A survey1 of all structurally characterized compounds showed that for b > ∼1.3 there were an approximately equal number of cis and trans structures, but for four-membered chelate rings with b < ∼1.2 there was a strong preference for the cis structure. Reduction in size of the chelate rings in cis- [M(bidentate)2(unidentate)2], as in [Mo(S2CNEt2)2O2],13 is COORDINATION NUMBERS & GEOMETRIES 3 (a) (b) (c) (d) Figure 2 Stereochemistries of [M(bidentate)2(unidentate)2]: (a) cis octahedral; (b) trans octahedral; (c), (d) skew-trapezoidal bipyramidal accompanied by a substantial rotation of the bidentate ligands about the twofold axis of the molecule, relative to the MoO2 plane: θA = 15◦, θB = −60◦ (Figure 3). At the same time the bonding of the bidentate ligand becomes significantly unsym- metrical with the metal ligand bond cis to both unidentate ligands becoming shorter than the metal–sulfur bond to the other end of the bidentate ligand: (M–A)/(M–B) = 0.93. The trans structure of [M(bidentate)2(unidentate)2] with five- or six-membered chelate rings and relatively large normalized bites (b ≈ 1.2–1.5) are normally undistorted. For four-membered chelate rings with b < ∼1.2, however, the plane formed by the two bidentate ligands becomes a trapezoid (Figure 2). The unidentate ligands are simultaneously skewed toward (Figure 2(c)) or even past (Figure 2(d)) the long edge of the trapezoid. The bonding of the bidentate ligand becomes grossly unsymmetrical, the end nearer the unidentate ligands becoming sterically very crowded. Important examples of this skew trapezoidal bipyramid structure are the dialkyltin complexes with four-membered A B C D EF q Figure 3 Distortion in cis-[M(bidentate)2(unidentate)2] as the size of the chelate ring is reduced. The bidentate ligands are rotated in an anticlockwise direction to higher θ relative to the M(unidentate)2 plane Encyclopedia of Inorganic Chemistry, Online © 2006 John Wiley & Sons, Ltd. This article is © 2006 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Inorganic Chemistry in 2006 by John Wiley & Sons, Ltd. DOI: 10.1002/0470862106.ia049 4 COORDINATION NUMBERS & GEOMETRIES chelate rings. Structural parameters for typical examples are given in Figure 4, together with the undistorted [Sn(Me- COCHCOMe)2Me2] for comparison. A notable feature of these structures is the very unsymmetrical bonding of the bidentate ligands, one bond being 20–35% longer than the other. Similar skew-trapezoidal bipyramidal structures are observed for dialkylgermanium14 and -lead15 complexes. Selenium(II) and tellurium(II) xanthates, dithiocarbamates, and related molecules have planar trapezoidal structures with the trans sites apparently occupied by lone pairs of electrons. Detailed parameters for a typical structure, [Te(S2COMe)2( •• )2],16 are shown in Figure 5. 3.3 [M(bidentate)3] The stereochemistries of complexes of the type [M(bidentate)3] occupy an important place in inorganic (a) (b) (c) (d) (e) N 2.70 2.15 2.17 2.42 O O O ON Sn 54 55 75 176 2.48 3.33 P P S S S Sn S 2.48 3.33 69 69 80 142 3.20 2.49 3.23 69 84 137 2.48 P S S P S S Sn 70 2.20 2.18 2.20 O C O O O C C C C C Sn 2.18 86 94 86 94 63 65 83 149 2.51 3.06 2.50 2.95 C C S S S S Sn Figure 4 Geometries, in degrees and A˚, of the Sn(bidentate)2 plane in [Sn(bidentate)2(alkyl)2]. The alkyl groups above and below the plane are skewed towards the long edge of the Sn(bidentate)2 trapezoid: b C–Sn–C(◦) (a) [Sn(NO3)2Me2]14 0.92 144 (b) [Sn(S2CNMe2)2Me2]15 1.06 136 (c) [Sn(S2PMe2)2Me2]16 1.13 123 (d) [Sn{S2P(OEt)2}Ph2]17 1.14 135 (e) [Sn(MeCOCHCOMe)2Me2]18 1.36 180 Encyclopedia of Inorganic Chemistry, Online © 2006 John Wiley & Sons, Ltd. This article is © 2006 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Inorganic Chemistry in 2006 by John Wiley & Sons, Ltd. DOI: 10.1002/0470862106.ia049 S S S S 2.84 2.85 2.51 2.50 66 85 143 66 Te Figure 5 Geometry, in degrees and A˚, of [Te(S2COMe)2( •• )2] FB C A D M q q E Figure 6 General stereochemistry for [M(bidentate)3] chemistry. The general stereochemistry is shown in Figure 6, viewed down the threefold axis. The stereochemistry is defined by the normalized bite b of the bidentate ligands and the angle of twist θ between the upper and lower triangular faces. The regular octahedron corresponds to b = 21/2 and θ = 30◦. The trigonal prism is the eclipsed arrangement with θ = 0. A theoretical dependence of θ upon b is shown by the line in Figure 7. For b = 21/2 the regular octahedron at θ = 30◦ is as expected, but as b is progressively decreased θ also progressively decreases until a trigonal prism is formed. The overwhelming majority of tris(bidentate) complexes have structures intermediate between the octahedron and trigonal prism. The structures are indicated in Figure 7.1 (Dithiolate molecules, [M(S2C2R2)3]x−, are not included in Figure 7 as many have structures much closer to the trigonal prism than would be expected.2) Figure 8 displays some of the data in Figure 7, but is now restricted to complexes of the first-row transition elements from chromium to copper to avoid large variations in the size of the central atom. To a first approximation the ligands divide into three groups. The first group is contained within the limits b = 1.375 to b = 1.50 and consists of those ligands that form six-membered chelate rings, such as acetylacetonate and trimethylenediamine. The second group is contained within the limits b = 1.25 to b = 1.375 and contains the complexes with five-membered chelate rings, such as o-phenanthroline and ethylenediamine. The third group is contained within COORDINATION NUMBERS & GEOMETRIES 5 40 20 30 10 00.8 1.0 1.2 1.4 1.6 b q Figure 7 Angle of twist, θ (degrees), and normalized bite, b, for complexes of the type [M(bidentate)3]. A theoretical curve is also shown b = 1.05 to b = 1.25 and contains the complexes with four-membered rings, such as nitrate and dithiocarbamates. This strikingly simple and important correlation is further illustrated in Figure 9 with three representative examples: [Co(MeCOCHCOMe)3],17 [Co(NH2CH2CH2NH2)3]3+,1 and [Co(NO3)3].18 Further subdivisions can be made according to the size of the nonmetal atoms in the chelate ring. For example, the four-membered chelate ring group may be divided into four subgroups. The subgroup containing ligands of lowest normalized bite (b = 1.05–1.125) consists of (PhN3Ph)− and NO3−, where three small second-row elements complete the chelate ring. There are no known examples of the second subgroup. The third subgroup of normalized bite 1.17–1.25 contains ligands with one second-row element and two larger elements in the chelate ring, such as the dithiocarbamates and xanthates. The fourth subgroup contains the dithiophosphates with three large ring atoms, and this subgroup intrudes into the group containing the five- membered chelate rings. A comparison of the ring geometries of [Co(NO3)3],18 [Co(S2COEt)3],19 and [Co{S2P(OMe)2}3]20 is shown in Figure 10. Unusually large normalized bites may be achieved with five-membered chelate rings by again incorporating large Encyclopedia of Inorganic Chemistry, Online © 2006 John Wiley & Sons, Ltd. This article is © 2006 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Inorganic Chemistry in 2006 by John Wiley & Sons, Ltd. DOI: 10.1002/0470862106.ia049 6 COORDINATION NUMBERS & GEOMETRIES 40 20 30 10 0 0.8 1.0 1.2 1.4 1.6 b q 1.05 1.25 1.375 Figure 8 Angle of twist, θ (degrees), and normalized bite, b, for complexes of the type [M(bidentate)3] (M = Cr, Mn, Fe, Co, Ni, Cu) atoms into the ring. The intrusion of the five-membered ring region into the six-membered ring region in Figure 8 is due to a dithiooxalate complex containing two sulfur atoms in the chelate ring, all other five-membered rings in Figure 8 containing only carbon, nitrogen, and oxygen atoms. Comparative ring geometries in [Co(C2O4)3]3−21 and [Co(S2C2O2)3]3−22 are also shown in Figure 10. The size of the metal atom is also important in determining the normalized bite, the smaller normalized bites being obtained with the larger metal atoms. Thus the lowest normalized bite for a six-membered ring containing a transition metal ion is that observed for [Sc(MeCOCHCOMe)3]23 in which the normalized bite of 1.31 is similar to complexes of the other transition metals containing five-membered chelate rings. Similarly, the lowest normalized bite for a transition metal complex containing a five-membered ring is b = 1.20, observed for the tropolonate complex [Sc(O2C7H5)3].24 4 SEVEN-COORDINATE COMPOUNDS The starting point for the consideration of seven coordination is three structures with very similar stabilities: the pentagonal bipyramid, capped octahedron, and capped 26 .3 33.7 32 .9 27.1 2 0.939 .1 Figure 9 [Co(acac)3], [Co(en)3]3+, and [Co(NO3)3] trigonal prism (Figure 11).1,2,25 There are no potential energy barriers between these polyhedra and a range of structures is expected. For example, moving one of the equatorial atoms of the pentagonal bipyramid (starred in Figure 11) downward forms a capped octahedron with the starred atom as the capping atom. Further movement in the same direction forms a capped trigonal prism. The mirror plane in the plane of the page is retained. Structurally characterized molecules with seven identical ligands are restricted mainly to some fluoro complexes [MF7]x−, aqua complexes [M(H2O)7]2+, isonitrile complexes [M(CNR)7]2+, and cyanide complexes [M(CN)7]x−. The stereochemistries are distorted along the long ‘reaction coordinate’ connecting the capped trigonal prism and the pentagonal bipyramid. The X-ray data on IF72 and [TeF7]−26 are not sufficient to establish the precise stereochemistry. The NMR spectra show rapid intramolecular rearrangement. The anions in K2[NbF7] and K2[TaF7] are intermediate between a capped octahedron and a capped trigonal prism.27 In the calcium polyiodide compound [Ca(H2O)7](I10) the stereochemistry appears to be intermediate between a capped octahedron and a pentagonal bipyramid, whereas Encyclopedia of Inorganic Chemistry, Online © 2006 John Wiley & Sons, Ltd. This article is © 2006 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Inorganic Chemistry in 2006 by John Wiley & Sons, Ltd. DOI: 10.1002/0470862106.ia049 COORDINATION NUMBERS & GEOMETRIES 7 N 1.89 111Co 91 O O 68 1.30 C 2.28 114Co 85 S S 76 1.67 P 2.32 103Co 86 S S 84 1.98 O O C C Co Co S S C C1.93 1.25 1.5384 114 112 2.24 1.70 1.55 118 106 90 Figure 10 Ring geometries, in degrees and A˚, in: [Co(NO3)3], [Co(S2COEt)3], [Co{S2P(OMe)2}3], [Co(C2O4)3]3−, and [Co(S2C2O2)3]3− Figure 11 The pentagonal bipyramid, capped octahedron, and capped trigonal prism [Sr(H2O)7](I12) and [Ca(H2O)7]2[Cd6Cl16(H2O)2]·H2O con- tain capped trigonal prismatic cations.2 A close approximation to a capped trigonal prism is observed for [Mo(CNBu)7](PF6)2. However, the closely related compounds [Cr(CNBu)7](PF6)2, [Mo(CNPh)7](PF6)2, [Mo(CNMe)7](BF4)2, and [W(CNBu)7](W6O19) lie further towards capped octahedra than capped trigonal prisms.2 Solutions of [Mo(CNBu)7]2+ yield only a single 13C NMR signal even down to −135 ◦C, confirming the expected stereochemical nonrigidity.2 The structures of K4[V(CN)7]·2H2O, K5[Mo(CN)7]·H2O, Na5[Mo(CN)7]·10H2O and K4[Re(CN)7]·2H2O are close to pentagonal bipyramids.2 As for five coordination, a mixture of unidentate ligands may lead to more well-defined stereochemistries due to the different types of polyhedral vertices available and the different spatial requirements of the different ligands. For example, the sterically least hindered sites in these structures are the axial sites of a pentagonal bipyramid as these are the only ones with no neighboring ligands having ligand–metal–ligand angles less than 90◦. As expected, the O2− ligand occupies this site and forces this structure in Na3[NbOF6]28 and a range of uranyl complexes such as [UO2(OSMe2)5](ClO4)2.29 Likewise, a planar pentagonal arrangement of fluorine atoms is observed in (Me4N)[XeF5( •• )2] with the pentagonal bipyramidal structure presumably completed by the two lone pairs of electrons.30 Well-defined stereochemistries may also be obtained by replacing the unidentate ligands with chelate groups which have a relatively fixed normalized bite. For example, ligands of very small normalized bite occupy one of the pentagonal edges of the pentagonal bipyramid, these being the short- est edges available among the seven-coordinate polyhedra. Examples include peroxo complexes with three-membered chelate rings, [Ti(O2)F5]3−31 and [Cr(O2)2(CN)3]3−,32 and a number of complexes with four membered chelate rings, [Cd(NO3)2py3]33 and [Hg(O2CCF3)2py3].34 This dependence of structure upon size of the chelate ring is also illus- trated by a group of molybdenum and tungsten carbonyl iodides.35 A complex containing a four-membered chelating phosphine, [W(Ph2PCH2PPh2)I2(CO)3], has the pentagonal bipyramidal structure as above, whereas complexes con- taining larger rings, [Mo(Ph2PCH2CH2PPh2)I2(CO)3] and [Mo(Ph2PCH2CH2CH2PPh2)I2(CO)3], have capped trigonal prismatic structures. For complexes containing larger bidentate ligands which can wrap around the metal atom in a variety of stereo- chemistries, the structure is dependent upon both the size of the chelate ring and the nature of the unidentate lig- ands. A particularly well-studied group of complexes is of Encyclopedia of Inorganic Chemistry, Online © 2006 John Wiley & Sons, Ltd. This article is © 2006 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Inorganic Chemistry in 2006 by John Wiley & Sons, Ltd. DOI: 10.1002/0470862106.ia049 8 COORDINATION NUMBERS & GEOMETRIES the type [M(bidentate)3(unidentate)].2 Uncharged uniden- tate ligands form two types of structure. The first is a capped octahedron with the unidentate ligand in the capping site and the three bidentate ligands forming a three- bladed propeller as in [M(bidentate)3], examples including [Tc(S2COBu)3(PPh3)],36 [Ho(PhCOCH2COPh)3(H2O)],37 and [Y(PhCOCH2COMe)3(H2O)].38 The second structure approximates to a capped trigonal prism and is observed for [Dy(BuCOCH2COBu)3(H2O)], [Lu(C3F7COCH2COBu)3 (H2O)], and [Yb(MeCOCH2COMe)3(H2O)].2 Charged unidentate ligands, on the other hand, form a structure which approximates to a pentagonal bipyramid but is distorted by the constraints of the bidentate ligands to be intermediate between a pentagonal bipyramid and a capped trigonal prism. Examples include [Nb(S2CNEt2)3O],39 [V(S2CNEt2)3O],39 (NH4)3[Nb(C2O4)3O]·H2O,40 and [Zr(MeCOCH COMe)3Cl].41 5 EIGHT-COORDINATE COMPOUNDS The starting point for the consideration of eight coordination is the square antiprism and the triangular dodecahedron (Figure 12).1,2,42 The square antiprism is usually slightly more stable than the dodecahedron and is more commonly observed. The ideal square antiprism has all edge lengths equal but, because the square faces are larger than the triangular faces, the structure distorts slightly by decreasing the size of the square faces, in an analogous way to the distortion observed in square pyramidal molecules. This distortion is measured by a decrease in the angle α, the angle the eight metal–ligand bonds make with the fourfold axis, from the idealized 59.3◦ to about 57◦ (Table 4). The dodecahedron has one set of four donor atoms nec- essarily different from the other set of four, labeled A and B, respectively, in Figure 12. A useful way of viewing the dodecahedron is to consider it as two interpenetrating and mutually orthogonal planar trapezoids, BAAB (Figure 12). Table 4 Square antiprismatic [M(unidentate)8] Molecules2,43,44 Complex α (◦) H4[W(CN)8]·6H2O 57.6 Na3[W(CN)8]·4H2O 59.1 H4[W(CN)8]·4HCl·12H2O 56.1 [Nd(ONC5H5)8](ClO4)3 56.1 [Nd(ONC5H4Me)8](CF3SO3)3 54.4 [NO(NOF)2][IF8] 57.6 [Sr(H2O)8](AgI2)2 58.2 [Cu(H2O)6]2[ZrF8] 57.1 Cs4[U(NCS)8] 56.7 B B B A A A A B Figure 12 The square antiprism and dodecahedron The B–B edges are approximately 25% longer than the A–A and A–B edges so that the B sites, which conse- quently have only three close neighbors, are sterically less crowded than the A sites. Examples of dodecahedral struc- tures include K4[Mo(CN)8]·2H2O,45 (Bu4N)3[Mo(CN)8],46 [Gd(H2O)8]Cl3·2C10H8N2, and [Y(H2O)8]Cl3·2C10H8N2.47 The square antiprism can be converted to the dodecahedron by creasing along a diagonal of each square face so that it becomes the B–B edge of a dodecahedron. Conversely, the dodecahedron in Figure 12 is converted to a square antiprism by forming square faces from two ABAB pairs of triangular faces. There is no potential energy barrier to this interconversion and intermediate structures are also possible, as observed for (Et3NH)2(H3O)2[Mo(CN)8].48 As indicated above, the structures of [M(CN)8]x− (x = 3, 4; M = Mo, W) may be square antiprismatic, dodecahedral, or intermediate. In solution, only a single 13C NMR signal is observed for [Mo(CN)8]4− at temperatures as low as −165 ◦C, consistent with very rapid intramolecular rearrangement.49 For complexes with a mixture of different ligands, the dodecahedron with its two different types of ligand site is generally favored. Charged ligands such as halide preferentially occupy the B sites of a dodecahedron, as observed for [UCl(DMF)7]2[UO2Cl4]3,50 [UCl4(MeCN)4],51 [ThCl4(OSPh2)4],52 and [ThBr4(THF)4].53 On the other hand, [EuCl2(H2O)6]Cl54 and [U(NCS)4{OP(NMe2)3}4]55 retain the square antiprismatic structure. A preference by charged ligands to occupy the B sites of a dodecahedron is also indicated for complexes containing two bidentate ligands, as in [WCl4(Me2PCH2CH2PMe2)2],56 [ThCl4{OP(NMe2)2OP(NMe2)2O}2],57 and a series of diarsine complexes [MX4{C6H4(AsMe2)2}2]x+, where M is TiIV, NbIV, NbV, etc. and X is Cl or Br.58–60 The influence the size of the chelate ring has upon the stereochemistry around the metal atom is clearly shown by complexes of the type [M(bidentate)4]. Bidentate ligands of small normalized bite form dodecahedral structures, in which each of the BAAB trapezoids is formed from a pair of ligands (Figure 13). There are numerous examples of this structure with three- and four-membered chelate rings such as peroxide, nitrate, acetate, xanthate, and dithiocarbamate Encyclopedia of Inorganic Chemistry, Online © 2006 John Wiley & Sons, Ltd. This article is © 2006 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Inorganic Chemistry in 2006 by John Wiley & Sons, Ltd. DOI: 10.1002/0470862106.ia049 (Table 5). Larger rings form an intermediate structure which can be represented as a square antiprism with the bidentate ligands spanning the square edges, but which is frequently distorted due to a creasing of the square faces as has been noted above, and alternative descriptions of the structure may be preferred (Figure 13). This structure is commonly observed for six-membered chelate rings such as the acetylacetonates of the lanthanide and actinide elements (Table 5). Ligands of intermediate size, such as the five-membered chelate rings oxalate and tropolate, and four-membered chelate rings containing large atoms such as dithiophosphate, may have either of the above structures, or an intermediate structure. The largest normalized bites are obtained with a combination of six-membered rings and smaller (than lanthanides or actinides) metal atoms, as in [Nb(BuCOCHCOBu)4], which has a square antiprismatic structure in which the bidentate ligands span the triangular edges to form a four-bladed propeller (Figure 13, Table 5). As for the octahedron–trigonal prism correlation found for [M(bidentate)3], the angle of twist between the two square faces is dependent upon the size of the chelate ring; in this case b = 1.28 and θ = 24◦. A B q q A B B A A B (a) (b) (c) Figure 13 Stereochemistries of [M(bidentate)4]. (a): the dodecahe- dron observed for low values of b. (b): alternative depictions of the intermediate structure observed for intermediate values of b. (c): the square antiprismatic structure observed for large values of b COORDINATION NUMBERS & GEOMETRIES 9 Table 5 Stereochemistries and chelate ring size for examples of complexes of the type [M(bidentate)4]2,61 Ring size Complex Stereochemistry 3 K3[Cr(O2)4] Dodecahedron 3 [Zn(NH3)4][Mo(O2)4] Dodecahedron 4 [Sn(NO3)4] Dodecahedron 4 [Ti(NO3)4] Dodecahedron 4 [Sn(O2CMe)4] Dodecahedron 4 (Et4N)[Bi(S2COEt)4] Dodecahedron 4 [Ti(S2CNEt2)4] Dodecahedron 4 [Mo(S2CNEt2)4]Cl Dodecahedron 4 [Th(S2PMe2)4] Dodecahedron 4 (Ph4P)[Pr(S2PMe2)4] Intermediate 5 [Hf(O2C7H5)4]·DMF Dodecahedron 5 Na4[Zr(C2O4)4]·3H2O Distorted dodecahedron 6 [U(PhCOCHCOPh)4] Intermediate 6 [Zr(MeCOCHCOMe)4] Intermediate 6 [Sm(NH2CONHCONH2)4](NO3)3 Intermediate 6 [Nb(BuCOCHCOBu)4] Square antiprism 6 NINE-COORDINATE COMPOUNDS The two important stereochemistries for nine coordination1,2,62 are the capped square antiprism and the slightly more stable tricapped trigonal prism (Figure 14). The tricapped trigonal prism can be converted to the capped square antiprism by converting two of the capping atoms and the two intervening prism atoms into a square. There is no potential energy barrier to this interconversion and repetition scrambles all nine atoms. The most important structurally characterized compounds containing nine equivalent unidentate ligands are the aqua lanthanoid complexes [Ln(H2O)9]3+.2,63 In these compounds the capping atoms are more sterically hindered than the prism atoms and the metal–capping atom bond lengths are larger than the metal–prismatic atom bond lengths. As the size of the metal atom decreases, all three capping atoms are further squeezed out so that the 9-coordinate structure approaches a (6 + 3)-coordinate structure rather than an 8-coordinate Figure 14 The tricapped trigonal prism and capped square antiprism Encyclopedia of Inorganic Chemistry, Online © 2006 John Wiley & Sons, Ltd. This article is © 2006 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Inorganic Chemistry in 2006 by John Wiley & Sons, Ltd. DOI: 10.1002/0470862106.ia049 10 COORDINATION NUMBERS & GEOMETRIES structure. For example: M–Ocap M–Oprism (M–Ocap)/ (M–Oprism) [La(H2O)9](CF3SO3)3 2.62 A˚ 2.52 A˚ 1.04 [Gd(H2O)9](CF3SO3)3 2.55 2.40 1.06 [Lu(H2O)9](CF3SO3)3 2.50 2.29 1.09 The tricapped trigonal prismatic structure is retained in a series of trinitrato complexes such as [Ln(NO3)3(H2O)3]2,64 in which bidentate nitrates span the capping and prism sites with retention of threefold symmetry. The angle of twist between the two triangles spanned by the three biden- tate ligands is ∼46◦, in good agreement with theory; compare with [M(bidentate)3] and the capped octahedral [M(bidentate)3(unidentate)]. Each bidentate ligand is unsym- metrically bonded as expected, (M–Ocap)/(M–Oprism) ≈ 1.05. The most symmetrical way four equivalent bidentate ligands can be wrapped around a nine-coordinate metal atom is to form a capped square antiprism with the bidentate ligands linking the two square faces of the antiprism to form a four-bladed propeller with the unidentate ligand capping one square face. This structure is observed for [Th(CF3COCHCOCH3)4(H2O)].65 The angle of twist between the two square faces of 42◦ is as expected for the normalized bite of b = 1.15. In the capped square antiprism the four atoms forming the capped face are sterically less crowded than the four atoms forming the uncapped face, and this is reflected in the Th–O bond lengths of 2.39 and 2.46 A˚, respectively. 7 TEN-COORDINATE COMPOUNDS1,2,62 There is, as yet, no structurally characterized compound containing ten unidentate ligands. Nevertheless, the geometry of these hypothetical compounds is a useful introduction to the stereochemistry of known ten-coordinate compounds containing chelate groups, such as [M(bidentate)5]. Three structures can be envisaged for ten coordination: the bicapped square antiprism, sphenocorona, and trirhombohe- dron (Figure 15). The two most important structures for [M(bidentate)5] are shown in Figure 16, drawn as idealized bicapped square antiprisms. Isomer I is possible at all values of the normalized bite whereas isomer II is expected only for larger chelate rings. A number of lanthanoid and actinoid complexes with four-membered nitrate or carbonate rings, [MIII(NO3)5]2− and [MIV(CO3)5]6−, have structure I. The only monomeric molecule in which structure II is observed is [Ba(MeCONHCOMe)5](ClO4)2 with six- membered chelate rings. Figure 15 The bicapped square antiprism, sphenocorona, and trirhombohedron I II Figure 16 Bicapped square antiprismatic isomers of [M(bidentate)5] 8 TWELVE-COORDINATE COMPOUNDS1,2,62 The tetrahedron, octahedron, and icosahedron are the three polyhedra formed from equivalent triangular faces, and these rigid, close packed structures dominate the stereochemistries for coordination numbers four, six, and twelve, respectively. As for ten coordination, there are no twelve-coordinate complexes containing only unidentate ligands. The most common twelve-coordinate molecules are of the type [M(bidentate)6]. Three structural isomers may be formed by wrapping six bidentate ligands along the edges of an icosahedron (Figure 17). Isomer III is less stable than the other two and is not observed. Isomer I is observed for a number of hexanitrato complexes, for example [La(NO3)6]3− and [Th(NO3)6]2−. Isomer II has been observed for the naphthyridine complex [Pr(napy)6]3+. I II III Figure 17 Icosahedral isomers of [M(bidentate)6] Encyclopedia of Inorganic Chemistry, Online © 2006 John Wiley & Sons, Ltd. This article is © 2006 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Inorganic Chemistry in 2006 by John Wiley & Sons, Ltd. DOI: 10.1002/0470862106.ia049 9 FURTHER READING J. Hilton, E. K. Nunn, and S. C. Wallwork, J. Chem. Soc., Dalton Trans., 1973, 173. T. Kimura, N. Yasuoko, N. Kasai, and M. Kukuda, Bull. Chem. Soc. Jpn., 1972, 45, 1649. B. W. Liebich and M. Tomassini, Acta Crystallogr., 1978, B34, 944. G. A. Miller and E. O. Schlemper, Inorg. Chem., 1973, 12, 677. K. C. Mollog, M. B. Hossain, D. van der Helm, J. J. Zuckerman, and F. P. Mullins, Inorg. Chem., 1981, 20, 2172. 10 REFERENCES 1. D. L. Kepert, ‘Inorganic Stereochemistry’, Springer-Verlag, Berlin, 1982. 2. D. L. Kepert, in ‘Comprehensive Coordination Chemistry’, eds. G. Wilkinson, R. D. Gillard, and J. A. 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