Molecular Polyhedra of High Co-ordination Number By E. L. Muetterties and C. M. Wright PONT DE NEMOURS AND COMPANY WILMINGTON DELAWARE 1 9 8 9 8 CENTRAL RESEARCH DEPARTMENT EXPERIMENTAL STATION. E . I . DU U . S . A . A. Introduction This Review is directed to a characterisation of discrete polyhedra in which an atom is within bonding distance of seven or more other atoms. Specifically seven- eight- nine- ten- eleven- and twelve-co-ordinate complexes are described with primary emphasis on structure. Not long ago this area of co-ordination chemistry might have been described as obscure and certainly of limited scope. Advances in synthesis and the classic structural investigations of Hoard and his students1-' have sharply altered the picture in recent years. It is apparent now that the field of higher-co-ordination polyhedra will be quite large in scope touch- ing elements as light as scandium and titanium.Some of the higher-co-ordinate species are chemically and theoretically beguiling; an especially noteworthy one is the nonahydridorhenium d i a n i ~ n ~ ~ ReH:-. From the structural side the general question of geometry particularly relating to the solution state is a subtle difficult yet intriguing problem. Polyhedral isomerisations should be quite easy in these large polyhedra and this complicates definition of the solution or gaseous state. In brief molecular polyhedra of high co-ordination number have scope interesting chemistry and significant research challenge to those interested in synthesis structural and theoretical chemistry. 1 Ligand Classification.-Aside from the obvious classification of the large co- ordination polyhedra into hepta- octa- nona- deca- and dodeca-co-ordinate structures the general class can be differentiated by the nature of the ligands.Within this context there are three major groups (1) complexes with unidentate ligands (2) complexes with multidentate Iigands (3) structures in which there is extensive multicentre bonding generating polyhedra or clusters in which the high- co-ordinate atom (atoms) is a part of a large molecular overstructure. The first class is severely limited in size because the co-ordinating atoms must be small J. L. Hoard and H. H. Nordsieck J . Amer. Chem. SOC. 1939 61 2853. J. L. Hoard J. Amer. Chem. SOC. 1939 61 1252. (a) J. L. Hoard B. Lee and M. D. Lind J . Amer. Chern. SOC. 1965 87 1612; (b) J.M. D. Lind B. Lee and J. L. Hoard J. Amer. Chem. SOC. 1965 87 1611. J. L. Hoard and J. V. Silverton Inorg. Chem. 1963 2,235. ti M. J. Hamor T. A. Hamor M. D. Lind and J. L. Hoard Inorg. Chem. 1964,3 34. S . Richards B. Pedersen J. V. Silverton and J. L. Hoard Inorg. Chem. 1964,3,27. K. Knox and A. P. Ginsberg Inorg. Chem. 1964,3 555. S . C. Abrahams A. P. Ginsberg and K. Knox Inorg. Chem. 1964,3 559. Hoard personal communication. L. 109 Quarterly Re views and electronegative if a relatively stable molecular complex is to result. Primarily this is the ligand chemistry of hydride ion (TcH,2-),1O fluoride ion (TaFs3-),l1 cyanide ion [W(CN)g4-],12 and oxygen complexes INd(OH2),3+].13 There are many ionic lattices of the lanthanide and actinide halides in which halogen atoms bridge metal atoms to yield high-co-ordination spheres about the metal atoms but no simple halogeno-complex of seven- or eight-co-ordination has been described with the exception of those of the fluorides.Class (2) the metal chelates is by far the largest group within high-co-ordina- tion polyhedra. The most common donor atoms for the multidentate ligands are the electronegative oxygen and nitrogen atoms; in fact these are almost the sole donor atoms for higher co-ordinate complexes of d10 metal ions. Ligands of particular note are derived from /3-diketones oxalic acid tropolone NNN’N’- ethylenediaminetetra-acetic acid and nitrilotriacetic acid. Phosphorus and arsenic are excellent donor atoms for the transition elements but not the main- Group elements. A large number14 of hexta- and octa-co-ordinate complexes based on the diarsine ligand (1) and transition metals have been reported.Sulphur should also be a good donor atom in high-co-ordinate chelate structures and some examples have been described e.g. tetrakis(thiatropono)thorium- As a class the chelates dominate the area of higher co-ordination polyhedra in scope numbers and in kinetic and thermodynamic stability. Bidentate ligands can be distinguished by their rigidity coplanarity of ligand atoms or lack of coplanarity and also the ‘bite’ or the preferred separation of the two donor atoms. The more compact the ligand and the smaller the ‘bite’ the more effective is the ligand in generating high-co-ordination structures. The extreme and almost trivial example here is the peroxide ion which has an oxygen-oxygen separation of about 1.41 A in peroxy-complexes.* Another compact ligand is the (Iv) (2).15 * Cotton and BergmadB suggest the structural principle that ‘a polyatomic ligand in which two chemically equivalent atoms are hdd much closer together than such a pair of atoms would be if independent of each other has a tendency to interact through both of the equivalent atoms in such a way that the mean positions of the pairs of atoms lie roughly at the vertices of one of the usual co-ordination polyhedra’.An example is K,Cr(CN)3(Oz)z which has near-trigonal bipyramidal geometry about the chromium.17 lo A. P. Ginsberg Inorg. Chem. 1964 3 567. l1 J. L. Hoard W. J. Martin M. E. Smith and J. F. Whitney J. Amer. Chem. SOC. 1954,76 3820. la 0. 0. Collenberg Z. anorg. Chem. 1922 121 281 298.l3 L. Helmholz J . Amer. Chem. Soc. 1939 61 1544. l4 R. J. H. Clark D. L. Kepert R. S. Nyholm and J. Lewis Nature 1963 199 559. l5 E. L. Muetterties H. Roesky and C. M. Wright J. Amer. Chem. SOC. 1966 87 4856. l6 F. A. Cotton and J. G. Bergman J. Amer. Chem. SOC. 1964,86,2941; J. G. Bergman and F . A. Cotton Inorg. Chem. 1966 5 1208. l7 R. Stomberg Arkiv Kemi 1964 23 401. 110 Muetterties and Wright coplanar nitrate group which has a short oxygen-oxygen separation ca. 2.1 A and forms octa- and dodeca-co-ordinate structures with ease but the stability of the complexes is low; water instantaneously destroys the nitrate co-ordination polyhedron. Intermediate in effectiveness for high-co-ordination structures are the coplanar and compact ions (3) and (4) derived from oxalic acid and tropolone.Chelates derived from these ligands particularly the tropolone ion,18 are much more stable than nitrate complexes. The oxygen-oxygen separation is 2.58 A in bis(tropolono)copper19 and about 2.56 A in oxalato-chelates.20 The ions derived from p-diketone have greater flexibility as far as adjusting to preferred donor atom separations for a given metal atom. However there is a more significant intraligand repulsion factor in the p-diketone chelates than in those obtained from the more compact coplanar ligands such as tropolone or nitrate ion. The more complex multidentate ligands for maximum effectiveness should bridge vertices of preferred co-ordination polyhedra. For example the nitrilo- triacetato-ion easily spans four of the vertices of the octaco-ordinate dodeca- hedral (see Section C.2a) structure.The critical steric point in designing multi- dentate ligands is non-bonding repulsions within the ligand in the conformation required for chelation. Metal clusters or polyhedra are defined as discrete molecules or ions in which the metal atoms describe a polyhedron e.g. octahedron in Mo6C11,2- or a fragment of a polyhedron e.g. triangle in Re,C1123-. Co-ordination numbers of seven (Re,C1123-) eight (Pt&ll,) and nine ~a6Cl12(OH2>~+] have been found for individual metal atoms in these cluster species. Metal clusteis or polyhedra are properly treated as a distinct structural class since these species are explicable only on consideration of the structure as a whole i.e. molecular orbital theory and not in terms of individual atom co-ordination spheres.In the latter context valence-bond representations generally require invoking bent bonds. For more detailed information on metal clusters the reader is directed to a recent review by Schafter.21 Certain classes of ligand will be excluded from this discussion because there is some ambiguity regarding their co-ordinacy and because their chemistry is so extensive. In particular the huge areas of cyclopentadienyl-metal and olefin- metal complexes in which co-ordination numbers of three and two respectively might be invoked for the organic ligand will not be discussed. [For example l8 E. L. Muetterties J. Amer. Chem. SOC. 1966 88 305. l9 W. M. Macintyre J. M. Robertson and R. J. Zahrobsky Proc. Roy. SOC. 1966 A 289 161. 2o G. L. Glenn J. V. Silverton and J. L. Hoard Inorg.Chem. 1963 2 250. 21 H. Schafer Angew. Chem. 1964,76 833. 111 Quarterly Reviews (T-C~H,),T~H,~~ may be considered as a nonaco-ordinate tantalum structure. J Similarly aromatic hydrocarbon and ~-allyl complexes are excluded. Non- bonding electron pairs which are by inference stereochemically active will be considered quasi-ligands. No attempt will be made to treat ionic or metallic structures in detail however reference will be made to structural types within these two classes. Wells’s treati~e~~a on structural inorganic chemistry provides a more exhaustive assay of ionic and metallic lattices. 2 Metal-Ion Requirements.-Unfortunately present theories of chemical bond- ing are not sufficiently advanced to treat definitively molecules its large as hepta (or higher)-co-ordinate compounds.An attempt even to rationalise the existing knowledge of high-co-ordination structures must be mechanistic and rather empirical. Molecular orbital theory in even its extended forms is quite incapable today of predicting geometries for higher-co-ordination polyhedra. With valence bond approximations the best that can be done is qualitatively to assay orbital over-laps from purely symmetry arguments. For example in octaco-ordination the cube is not an attractive co-ordination polyhedron since only seven hybrid orbitals of proper symmetry can be generated unlessforbitals are used and this is consistent with observation. The stability of the cube versus say the square antiprism is however one of the few relatively dear distinctions that can be made on purely symmetry grounds for idealised geometries in higher-co-ordinate structures.Ground-state geometries are most simply rationalised by using the non-bonding repulsion model first introduced by Sidgwick and PoweU,=b later extended by Gillespie and Nyholm.24 There have been a number of attempts principally by Hoard and Silverton to lend some quantitative aspects to this simple approximation and mention will be made of the results of such calculations for each of the higher-co-ordinate systems. For ionic structures (see ‘Pauling’s rules’25) there is a rather good correlation between cation-anion radius-ratio and the co-ordination number of the metal ion. Further the co-ordination polyhedra in these instances are regular or highly symmetrical polyhedra. For example in AB compositions the relations are as shown in Table 1.However there are exceptions to this generalisation particularly among simple ionic structures where packing of twelve atoms of like charge is not possible and octaco-ordination is the largest co-ordination polyhedron for ionic lattices of the AB type. Co-ordination numbers of nine or more are however found in AB and AB salts or polymeric lattices and in intermetallic compounds. Cation-anion ratio is also an important consideration in molecular polyhedra but by itself it is of no predictive value with respect to idealised geometries. 22 M. L. Green J. A. McCleverty L. Pratt and G. Wilkinson J. Chern. SOC. 1961 4854. 23a A. F. Wells ‘Structural Inorganic Chemistry’ 3rd edn. Oxford University Press London 1961. 23b N. v. Sidgwick and H. M. Powell Proc. Roy. SOC.1940 A 176 153. 24 R. J. Gillespie and R. S. Nyholrn Quart. Rev. 1957 11 339. 25 L. Pallling ‘Nature of the Chemical Bond’ 3rd edn. Cornell Univ. Press Ithaca N.Y. 1960 p. 524; J . Amer. Chern. SOC. 1929,51 1010; 1933,55,1895. 112 Muetterties and Wright Table 1 Minimum radius-ratio 0.225 0.414 0.592 0.732 0.732 0.902 1-OOO Co-ordination number 4 6 7 9 12 12 a Co-ordination polyhedron Examples Tetrahedron LiCl Octahedron NaCl Capped octahedron Cube CSCl Tricapped trigonal prism Icosahedron Cube octahedron For molecular compounds or complexes metal-ion size is obviously an important factor in the formation of high-co-ordination structures. A table of ionic radii will quickly identify the important large ions (see Figure 1) such as I I 1 I I I I 1 1111 I I 1 I I 1 I 4 P fl f2 f3 f 4 f5 f 6 f7 re'* fI f2 f3 P f 5 P Metal ion electronic configuration Fig.1 Plot of metal-ion electronic configuration against ionic radius. the lanthanide and actinide ions. However size alone is insufficient since there is no authentic example of a discrete high-co-ordination complex of for exampIe the large alkali-metal ions. Hydration numbers of the large caesium and potassium ions appear to be less than six whereas the smaller but bivalent magnesium cation has a co-ordination number greater than six. Obviously metal-ion charge is also important. Thus more properly the facility with which an ion can form higher-co-ordination structures is some function of metal-ion size and charge. The filling of the d-electron level also has some impact on ease of formation of high-co-ordination structures.Metal ions of do or low d" electronic configura- tion generally form more stable high-co-ordinate structures than do metal ions of high dx cofiguration. The latter point is explicable on a basis of d-eIectron- 113 Quarterly Reviews ligand repulsions; or as alternatively characterised by Clark et all4 there are fewer low-energy orbitals available for bonding in the high dx configurations. Discrete high-co-ordination structures have been observed for metal ions of high dx electronic configurations although only with chelate ligands. Moreover these have been limited to high-spin species such as Mn2+ (d5) and F e s (d6). Heptaco-ordination has never been established for a low-spin species of for example a ds ion. Here the crystal-field stabilisation is significant and should raise the reorganisation energy for conversion of the octahedron into a heptaco- ordinate structure.It is interesting that studies of substitution reactions of low-spin d6 ions do not appear to be s'2 reactions; i.e. a heptaco-ordinate intermediate or transition state is not implied. In metal clusters where there is significant metal-metal bonding high co-ordination numbers have been observed for metal ions of high d" configuration and low spin e.g. Co,(CO), and Pt,Cl,,. Clark et all4 also consider formation of high-co-ordinate specifically octaco- ordinate structures in the early transition series to be more favourable than with post-transition-metal ions and suggest that this also reflects the greater avail- ability of low-energy s p and d orbitals for the low dx configurations.There is of course a significant metal-ion size decrease between do and d10 configurations in the same periodic series e.g. titanium(1v) has an ionic radius of 0.68 A com- pared with gallium(III) 0-62 A and germanium(Iv) 0.54 A. Hepta- and octa- co-ordinate structures are known for titanium but not for gallium or germanium. On the other hand tin(1v) (0-71 A) which is more comparable in size with titanium(Iv) does form hepta- and octa-co-ordinate species. In fact metal ions of do and d10 configuration of the same size and charge display comparable tendencies toward formation of high co-ordination structures although there exists some dichotomy in behaviour with respect to the nature of the ligand a not unexpected result. 3 Geometry.-For a given co-ordination number the differences between idealised geometries are surprisingly small for the high-co-ordination species and for real 'slightly distorted' structures discussion in terms of idealised geo- metries may become a matter of semantics.Establishment of ground-state structure for the crystalline state demands in many cases in the words of Pro- fessor Hoard 'the full power of three-dimensional X-ray data'. Much of the early work based on powder or two-dimensional results does not meet the necessary conditions. Of all the co-ordination numbers seven is in the most primitive state of structural characterisation. Octa- and nona-co-ordinate geometries are rather well established for the solid state. Few of the higher-co-ordinate structures are sufficiently stable to exist in the gaseous state. Gaseous species appear to be limited to IF, ReF, :XeF, and a number of tropolone and /&diketone derivatives e.g.(tropolono),Th and (acetylacetonato),Zr. Of these only the fluoro-derivatives are sufficiently simple for a meaningful structural analysis of the gaseous ground state by electron diffraction and even these present major problems because of the large heavy- 114 Muet terties and Wright atom scattering. No really rigorous study of the gaseous state has been made although preliminary electron-diffraction studies on IF and :XeF have been reported. It is unfortunate that so few high-co-ordinate species can be examined as gases for this is the only state that will provide an unperturbed environment and answer the question of the preferred ground-state structure. Because there is little difference between idealised geometries for any given co- ordination number there is no assurance that the same geometry for a given species will prevail in all the physical states.The energy differences between isomers is small; smaller than or comparable with packing forces in the solid state solvation energies in the solution state and association energies in the liquid state. The latter forces may in some cases stabilise a geometry that is not the ground-state geometry for the gaseous state. As is invariably the case solution- or liquid-state geometry the state of most general interest to chemists is the most difficult to define. Because of the com- plexity of the species there is no spectroscopic or diffraction technique that will establish geometry for this physical state with a high degree of rigour.Further ionisation ligand dissociation and solvation phenomena must be considered in the solution process of any high-co-ordinate species. For example NbF,2- is well established for the crystalline state. However dissolution of an NbF,2- salt in an aqueous medium even those of high fluoride and hydrogen ion con- centration gives a solution state in which NbF,- predominates and spectro- scopic studies have failed to detect the presence of the NbF,2- ion in s o l ~ t i o n . ~ ~ J ~ Dissolution of chelates may be quite complex. Because the reorganisation energy in going from seven- to eight- or eight- to nine- or nine- to ten-co-ordinate structures is very small there is a distinct possibility that an octaco-ordinate chelate for example may solvate to a nona- or deca-co-ordinate species (e.g.see Plate 1). This is especially true for the larger lanthanide tervalent ions and thorium(1v) complexes. Alternatively dissociation may prevail. A tris-chelate of the type (chel),MX may tend to ionise in polar media to give either (chel),Mf or (chel),M(solvent)+ ions. This type of process is known in titanium chemistry.28 Another type of ligand dissociation partial or complete dissociation of a chelate ligand may be common to chelates and especially to anionic complexes. Partial dissociation may or may not be followed by solvation Species like (5) and (6) may be important intermediates or transition states in chelate exchange reactions of the type M' = H+ or a metal ion 26 0. L. Keller jun. Znorg. Chem. 1963 2 783. 28 M. Cox J.Lewis and R. S . Nyholm J. Chem. SOC. 1964 61 13. K. J. Packer and E. L. Muetterties J . Amer. Chem. SOC. 1963 85 3035. 115 Quarterly Reviews Polar and nucleophilic solvents should favour processes like (1) and (2). Alterna- tively ligand dissociation may be complete and may or may not be followed by solvation Intermediates (7) and (8) could also be important in chelate exchange. Complete dissociation of the chelating ligand unaccompanied by solvation is observed with the octaco-ordinate bisdiarsine complex TiCl,,[diars],* on dissolution in benzene to give a hexaco-ordinate titanium complex TiCl,,[diars]. Characterisation of solution-state geometries and the dynamic processes of solution is the major research challenge in high-co-ordination structures. 4 Stereochemistry.-There are insufficient data to comment meaningfully about stereochemistry in the higher-co-ordinate structures.Characterisation of the more complex mixed-ligand species is necessary before any correlations can be made. There are however qualitative predictions to be derived from some of the mechanistic approaches to the question of bonding and structure. For most of the idealised geometries in any given co-ordination number the differences in geometry are comparable with the distortion imposed by vibra- tionally excited states.29 Thus for the long-term observation or description (> 10-l2 sec.) the high-co-ordination structures must be considered as potential stereochemically non-rigid species. Optical activity which has its origin in asym- metry at the metal atom centre may be very short-lived in solution for the higher-co-ordination species (see particularly Section C for a discussion of this stereochemical aspect) and geometrical isomerisation is also a potentially low- energy process in these structures.B. Heptaco-ordination Heptaco-ordinate structures once presumed to be limited to heavy-metal ions are now known for metal ions ranging from titanium to uranium with electronic configurations of doy P dlO andf” and even for boron in a complex cage struc- ture. The geometry problem for heptaco-ordinate species is far from resolved even for the solid state. Generally discussions of heptaco-ordinate geometry have been based on three idealised? structures which are the pentagonal bi- pyramid (D,J capped trigonal prism (C,,) and capped octahedron(C3y). These are presented in conventional perspectives in Plate 2.None of these has been established for a non-chelate heptaco-ordinate species with the precision of modern three-dimensional X-ray analysis and nothing less will suffice because of the subtle differences between these idealised models. There is a fourth basic * diars is ligand (1) on p. 109. t The term idealised is used in this Review loosely to denote limiting symmetry forms and does necessarily imply an energetically favoured geometry. 29 E. L. Muetterties Inorg. Chem. 1965.4 769. 116 Muet terties and Wright geometry the tetragonal base-trigonal base (Cs) rigorously established for complexes metal clusters and polymeric oxides. There are two idealised forms and one of these is depicted in Plate 2. (The second form has the same symmetry but differs in the relative orientation of the tetragonal and trigonal bases.There is an infinite number of forms intermediate in orientation of the base8 between the two boundary models.) It should be noted that this geom- etry for actual molecules is a refkction of constraints placed on the complex by the ligand the cluster or the solid lattice. This geometry has never been observed in a heptaco-ordinate species with unidentate ligands. The tetragonal base-trigonal base model is only very slightly distorted from the C, capped tri- gonal prism. In fact none of these seven-co-ordinate geometries differs signifi- cantly from another as can be seen from the alternative perspectives in Plate 3. Conformational interconversions require relatively slight bending modes and lifetimes of ground-state geometries may be quite short.29 Furthermore the energy difference between these various idealised states should be small with respect to intermolecular forces generated by ordering or solvation phenomena in the solid liquid or solution states.There have been several attempts*O,al to evaluate the relative stabilities of the idealised heptaco-ordinate MX models simply by considering repulsive forces generated from interactions of like ligand atoms. Considering the repulsive force as an inverse power n of distance the pentagonal bipyramid appears most stable for small values of n the C, model for intermediate values and the C, model for large values to the limit of the hard-sphere model. The energy differences are however very small; and because attractive forces are ignored and because calculations are limited to spherical models i.e.equivalent bond distances within each model the analyses have no predictive value. Another treatment32 of heptaco-ordinate geometries similar to the above but based on a different mathematical approach not limited to preconceived geometries con- firmed the earlier comparisons of the Dbk CZv and C, structures. However the force analyses minimised at a model not previously considered (or so far observed in actual systems). This model has only visualised in the spherical representation (9). *- - - - - - e C2 symmetry and is most easily (9 ) Configurationally the C model is easily generated from the other idealised heptaco-ordinate models by minor bending modes. It will be interesting to see 98 R. J. Gillespie Canad.J. Chem. 1960 38 818. 31 D. Britton Canud. J . Chern. 1963,41 1632. 3a T. A. Claxton and G. C. Benson Canad. J. Chem. 1966,44 157. 117 QuarterZy Reviews whether any actual MX species possess this geometry. Professor J. L. Hoard (personal communication) has noted that the iron(m) derivative of 1 ,Zdiamino- cyclohexane-NN’-tetra-acetic acid (Figure 7 vide infra) approximates the geom- etry of the C model. The most significant result of these analyses of repulsive forces in MX species is that the energy differences between idealised models are probably quite small. None of these analyses is applicable to heptaco-ordinate species in which the ligands are not identical. For such mixed species it is intuitively reasonable that energy minimisation is most favourable in D5h for MX,Y species in C, or C, for MX,Y and in the 4-3 trigonal base-square base for MX4Y3 particularly if X and Y differ significantly in steric or electronic properties.1 Pentagonal Bipyramid.-Pentagonal bipyramidal geometry is reported for the U0,F,3- (ref. 33) ion in the crystalline lattice of the potassium salt on the basis of a two-dimensional X-ray analysis. The U-0 bonds are axial with a 1.76 A separation and the equatorial U-F bond distances are 2.24 A. There is an ordered (tetragonal) and a disordered (cubic) form of K,UF,.= The disordered form appears to be isostructural with K3U0,F and the U-F bond distances are 2.26 A. Powder diffraction data35 suggest that in P-UF each uranium atom is within bonding distance of seven fluorine atoms; the positions of the fluorine atoms were not established.It would be extremely valuable to have precision neutron and X-ray diffraction data for a UF:- salt to fix geometry and bond parameters (will the axial bond distances be shorter than the equatorial dis- tances?). Puckering of the pentagonal ring may be observed for solid-state pentagonal bipyramidal molecules or ions. In the solution state pseudorotation analogous to that characterised for cyclopentane may be a low-energy process for the bonding atoms in the pentagonal ring (10). This has been postulated for iodine heptafluoride.% Hampson and P a ~ l i n g ~ ~ have characterised the ZrF,& ion in the ammonium and potassium salts as C, (capped octahedron) ; however their two-dimensional analysis is not definitive. Zachariasen has argued that 2rF:- is in fact a pen- tagonal bipyramid.= The basic crystallographic problem is complicated by thermal disorder in these salts.Hoppe and Rodder38 report TbF,% (Cs3TbF,) as probably isostructural with ZrF,3-. Other possible heptafluoro-anions include 33 W. H. Zachariasen Acta Cryst. 1954 7 783. 34 W. H. Zachariasen Acta Cryst. 1954 7 792. a5 W. H. Zachariasen Acta Cryst. 1949 2 296. 36 R. E. Lavilla and S. H. Bauer J . Chem. Phys. 1960 33 182. 37 G. C. Hampson and L. Pauling J . Amer. Chem. SOC. 1938 60 2702. 38 (a) R. Hoppe and K. M. Rodder 2. anorg. Chem. 1961 313 154; (6) R. D. Peacock H. Selig and I. Sheft Proc. Chem. SOC. 1964 285; Inorg. Chem. 1967 in the press. 118 Muetterties and Wright XeF,-,38b CeF,* PrF?- NdF?- and DyF,3-?941 A vibrational analysis of iodine heptafluoride implicated Dbh symmetry for this volatile An electron-diffraction of gaseous IF suggests neaf symmetry but with a non-coplanar equatorial belt of five fluorine atoms; the average I-F distance is 1.825 A.Single-crystal X-ray data have also been presented for this molecule43 but are not sufficient to differentiate between the D5h and C, Nuclear magnetic resonance (n.m.r.) results for liquid IF and ReF have been used to argue for a ground-state geometry of very short life.45,46 A preliminary report of a two-dimensional X-ray analysis of K2Mo0,F4,0H indicated that the molybdenum atom is heptaco-ordinate with three fluorine atoms and a peroxide group coplanar with the molybdenum and the remaining fluorine and oxygen (water) atoms on the axis normal to the plane.47 A high- pressure form of U03 has puckered pentagonal bipyramidal geometry for the oxygen atoms about each uranium The collinear uranyl bonds are short ranging between 1.80 and 1.85 A.In Cs,(UO&,(S04) the uranyl group is co- ordinated to five sulphate oxygen atoms to give a near-pentagonal bi~yramid.**~ A near-pentagonal bipyramidal co-ordination sphere is present for three of the cobalt atoms in the metal polyhedron of CO~(CO)~~ vide i1zfra.4~ In Zr(OH),(Cr0,)5(H,0)2 there are infinite chains of zirconium atoms bonded to hydroxide and chromate oxygens?Oa The zirconium atoms are co-ordinated to seven oxygen atoms in the shape of an almost regular pentagonal bipyramid. In K,Cr(O,),(CN) there is near-pentagonal bipyramid geometry with two apical and one equatorial cyano-group (Figure 2).17 The co-ordination polyhe- dron of Cr(O&,(NH& is described as a distorted pentagonal bipyramid?Ob 2 Capped Trigonal Prism (C,,).-The potassium salts of NbF,2- and TaF:- possess nearly identical monoclinic cell units.Analysis of two-dimensional X-ray data2 pointed to a slightly distorted C, capped trigonal prism model for NbF,2- with an average Nb-F separation of 1.97 A. A similar analysis of Na,Zr,F, suggested a linking of trigonal prism polyhedra (ZrFt-) through the square faces with a bridging fluorine atom.5l The Zr-F separations fall in the aB R. Hoppe and K. M. Rodder Z. anorg. Chem. 1961,312,277. 4 1 L. Asprey Rare Earth Research 1961 58. 42 R. C. Lord M. A. Lynch jun. W. C. Schumb and E. J. Slowiski jun. J. Amer. Chem. SOC. 1950,72,522. 43 R. D. Burbank and F. N. Bensey jun. J. Chem.Phys. 1957 27 981. 4p J. Donohue Acta Cryst. 1965 18 1018. 45 E. L. Muetterties and K. J. Packer J. Amer. Chem. SOC. 1964 86 293. 46 R. J. Gillespie and J. W. Quail Cunnd. J. Chem. 1964 42 2671. 47 D. Grandjean and R. Weiss Compr. rend. 1965 261 448. (a) S. Siegel H. Hoekstra and E. Sherry Acta Cryst. 1966 20 295; (b) M. Ross and H. T. Evan jun. J. Znorg. Nuclear Chem. 1960 15 338. 49 P. Corradini J. Chem. Phys. 1959 31 1676. 5* (a) G. Lundgren Arkiv Kemi 1958,13,59; (b) E. H. McLaren and L. Helmholz. J. Phys. Chem. 1959 63 1279. 51 R. M. Herak S. S. Malcic and L. M. Manojlovic Acta Cryst. 1965 18 520. R. Hoppe and W. Liebe Z. anorg. Chem. 1961,313,221. 119 Qluarterly Reviews i C R Fig. 2 Structure of Cr(O,)&N)Ss- in K,Cr(O&,(CN) (ref. 17). range 2.00 A to 2.10 A. Salts of PuF7-5s and WF7-63 ions have been isolated but there are no definitive structural data.The K,PaF salt is not isostructural with K,NbF7 but is nonaco-ordinate. The NbF,O- structure has been recently con- firmed by three-dimensional neutron-diffraction analysis.64 Refined values of the Nb-F separations vary between 1.940 and 1.978 A. The slight distortion from C, symmetry and the exceptionally large vibrational distortions of two of the fluorine atoms are explicable in terms of the packing in the crystal. The monoclinic or B form of the rare-earth oxides (Sm,O,-Gd,Od contains MO units of three types two of which are essentially capped trigonal prisms and the third is octahedral with an additional very long M-O distance of 3.12 A.6595s The two heptaco-ordinate capped trigonal prisms differ only in dimensions with each one having one long Sm-0 distance (2.71 and 2.76 A).The hexagonal form ( A modification) of lanthanum cerium praseodymium neodymium and americium(II1) oxides apparently (X-ray and neutron powder diffraction data) has polyhedra of MO units for which the capped octahe- dron (C3J is a fair approximation of geometry for these ~ n i t s . ~ ' ~ ~ There are three metal-oxygen distances of 2.38 A three of 2-72 A and one of 2.45 A. Reportedly isostructural with A-La,O are La,O,S Ce,O$ and Pu202S59 with four oxygen and three sulphur atoms bonded to the metal atom. 3 Capped Octahedron (C3,).-This geometry has been suggesteds7 for ZrF,'- although challenged by Zachariasei~.~~ Williams and Hoard prescribed the cap- ped octahedron for the NbOFs3- ion from analysis of two-dimensional X-ray measurements.60~61 The Nb-0 bond was placed on the threefold axis although the data were not sufficient to establish this.Metal-ligand separations averaged 2.0 A but the Nb-0 bond should be significantly shorter than the Nb-F bond. 52 R. A. Penneman G. D. Sturgeon L. B. Asprey and F. H. Kruse J. Amer. Chem. SOC. 1965,87. 5803. 53 G. B. Hargreaves and R. D. Peacock J . Chenz. Sac. 1958 2170. 54 G. M. Brown and L. A. Walker Acta Cryst. 1966,20 220. 55 W. H. Zachariasen Acta Cryst. 1949 2 60. 56 D. J. Cromer J . Phys. Chem. 1957 61 753. 57 L. Pauling 2. Krist. 1929 69 415. 58 W. C. Koehler and E. 0. Wollan Acta Cryst. 1953 6 741. 59 0. J. Guentert and R. L. Mozzi Acta Cryst. 1958 11 746. 6o M. B. Williams and J. L. Hoard J . Amer. Chem. SOC. 1942 64 1139.61 J. L. Hoard and W. J. Martin J . Amer. G e m . SOC. 1941 63 11. 120 Muetterties and Wright Both K,ZrF and K3NbOF give closely similar X-ray diffraction patterns. A series of salts based on TaOF,& are isomorphous by diffraction criterion with the NbOFt- salts.g2 In the A form of the rareearth oxides the metal atom has a distorted C, arrangement of seven nearest oxygen a t o r n ~ ~ ~ ~ * (see Section B.2). 4 Tetragomi Base-Trigonal Base.-Two configurations of this polyhedron that possess a plane of symmetry are (1 1) and (12). These conformers are inter-related by a rather trivial twisting mode of the trigonal face and are both very similar to the capped trigonal prism (see Plate 3). Conformation (11) is found for the iron atoms in the cyclobutadiene complex (C6H5)&Fe(CO)3 (Figure 3.6' The structures of the parent cyclobutadiene complex H4C4Fe(C0)3,M,65 has not been established.Conformation (12) is reported66 for a cyclobutadienenickel- (III) chloride solvate with benzene (Figure 4). The monoclinic forms of Zr0267968 0 CI CH3 Fig. 3 Structure of (C,H,),C,Fe(CO) (ref. 63). Fig. 4 Structure of (CH,),C4NiC13 in the (CH$,C,NiCI3,C6H crystal (ref. 66). and HfO,Sg show configuration (12) for the oxygen co-ordination sphere about the metal atoms. In ZrO the metal-oxygen bond distances are 2-07 for the trigonal base and 2-21 A for the square base. A similar configuration is reported 62 A. E. Baker and H. M. Haendler Znorg. Chem. 1962 1 127. 63 R. P. Dodge and V. Schomaker Nafure 1960 186 798. 6p G. F. Emerson L. Watts and R. Pettit J. Amer.Chern. SOC. 1965 87 131. J. D. Fitzpatrick L. Watts G. F. Emerson and R. Pettit J . Amer. Chcrn. Soc. 1965 87 3254. 66 J. D. Dunitz H. C. Mez 0. S. Mills and H. M. M. Shearer Helv. Chim. Acta 1962 45 647. 67 J. D. McCullough and K. N. Trueblood Actu Crysf. 1959 12 507. 6* D. K. Smith and H. W. Newkirk Acru Cryst. 1@65,18,983. 69 J. Adam and M. D. Rogers Acfu Cryst. 1959 12 951. 121 Quarterly Reviews for ZrOS.'O There are four basal sulphur atoms at ca. 2-62 A and three oxygen atoms at 2.13 A. Metal atoms in metal polyhedra or clusters sometimes have co- ordination polyhedra similar to (12) vide infra. 5 Chelate Structures.-Certain metal derivatives of ethylenediaminetetra-acetic acid display a tendency to retain a molecule of solvent. Two of these analysed in the solid state by three-dimensional X-ray methods have been shown to have heptaco-ordinate metal atoms with a strongly bound water molecule.(The heptaco-ordinate ion is probably the dominant species in solution.) In the iron- (111) chelate6 the bonding atoms closely approximate a pentagonal bipyramid whereas in the manganese(@ derivative' the co-ordination polyhedron more closely approximates a capped trigonal prism (Figures 5 and 6). Heptaco-ordina- tion has also been rigorously established for a calcium salt of a hydrated iron(ru) derivative of 1,2-diaminocyclohexane-NN'-tetra-acetic acid. The idealised model is shown in Figure 7. Cohen and Hoard7I describe the co-ordination polyhedron as approximating a capped trigonal prism and alternatively* as a close approxi- mation of the C model (9). The calcium ion in this crystalline iron complex has OH2 Fig.5 Structure of the iron(nr) complex with ethylenediaminetetra-acetic acid in LiFe(OH,)- (ethylenediaminetetra-acetute),2H20 (ref. 6). Fig. 6 Structure of the heptuco-ordinate mangunese(I1) ion Mn(OH,)(ethylenedianrinetetra- in Mn3(H30),(ethylenediuminetetru-ucetate),,8H20. There are also hexaco-ordin- ate manganese ions in this crystal lattice (ref. 7). Fig. 7 Structure of the iron(rr1) complex with 1,2-diaminocyclohexune-NN'-tetru-acetic acid in Ca[Fe(OH~(chelate)],,9H2O (ref. 71). * Personal communication from Professor Hoard. 'O J. D. McCullough L. Brewer and L. A. Bromley Acta Cryst. 1948,1 287. 71 a. H. Cohen and J. L. Hoard J. Amer. Chem. SOC. 1964,86,2749; 1966,88 3228. 122 Muetterties and Wright a virtually perfect C, capped trigonal prismatic co-ordination polyhedron.Cohen and Hoard7 note that in heptaco-ordinate complexes based on ethylenediaminetetra-acetic acid either the pentagonal bipyramid or the capped trigonal prism is a favourable geometry but with the diaminocyclohexanetetra- acetic acid ligand the ring constraints favour the capped trigonal prism (or C,) geometry. In heptaco-ordination one of the most common chelate structures has the composition ( ~ h e l ) M X . ~ ~ s ~ ~ ~ ~ Even in those cases where the chelating ligand is symmetrical there is a large number of possible isomers for each of the four idealised geometries with the exception of the pentagonal bipyramid which has only three isomers. If the ‘bite’ of the chelating ligand is relatively rigid then matching of ‘bite’ with polyhedral edges will be a geometry-determining factor.On the other hand if the ‘bite’ is flexible and if X the unidentate ligand differs significantly from the chelating donor atoms in electronic or steric features energy minimisation will be most favourable in such models as the capped octahedron and the capped trigonal prism where the unidentate ligand can occupy a unique site. Using these models two capped octahedral isomers and three capped prisms to define the minimum set of reasonable isomeric structures in (chel),MX and their closely related isomers in the other geometries we have drawn Figure 8 to represent easy polyhedral isomerisation paths. The vertical columns represent geometries closely related in the sense that small distortions suffice to interconvert structures.6 Metal Polyhedra or Clusters.-Heptaco-ordination is quite often present in polynuclear metal carbonyls and their derivatives. For example analysis of two- and three-dimensional X-ray results for CO,(CO), established a tetra- hedron of cobalt atoms (Figure 9) with three basal cobalt atoms that are bonded to three other cobalt atoms two bridging CO groups and two terminal CO g r o ~ p s . ~ ~ ~ ~ The co-ordination polyhedron for the basal heptaco-ordinate cobalt atoms approximates to a pentagonal bipyramid. Presumably the isoelectronic ion F~CO,(CO),~- is isostructural with c0,(co),,.75 A diethylacetylenederiva- t i ~ e ~ ~ of Co,(CO),, Co,(CO),,(C,H,~C z CC,H,) has been precisely analysed with three-dimensional measurements (Figure 10) and the two basal cobalt atoms are heptaco-ordinate.The two other cobalt atoms can be considered as hexa- or heptaco-ordinate depending on whether the C = C interaction with these two cobalt atoms is taken as unidentate or bidentate. A 4 3 type metal- atom co-ordination sphere is found for the apical iron atom in S2Fe3(C0)z7 and Se,Fe,(C0),78a (Figure 11) which both have tetragonal pyramids of iron 72 G. T. Morgan and A. R. Bowen J. Chem. Soc. 1924,125 1252. 7s E. L. Muetterties and C. M. Wright J. Amer. Chem. SOC. 1964 86 5132. 74 C. H. Wei and L. F. Dahl J . Amer. Chem. SOC. 1966 88 1821. 76 P. Chini L. Colli and M. Peraldo Gazzetfu 1960 90 1005. 7g L. F. Dahl and D. L. Smith J. Amer. Chem. Soc. 1962 84,2450. 77 C. H. Wei and L. F. Dahl Znorg. Chem. 1965 4,493. 78 (a) L. F. Dahl and P. W. Sutton Inorg. Chem. 1963 2 1067; (b) U.Anders and W. A. G. Graham Chem. Comm. 1966,291. 123 Quarterly Reviews c3 Cl c2 c2 c2 c2v c2v c2 Fig. 8 Some of the possible geometrical isomers for the various heptaco-ordinate models in a (chel),MX structure (see text). Each column comprises structural isomers configurationally related by small distortions. oc ko/" -0 Fig. 9 Structure of Co,(CO),,. The three basal cobalt atoms are heptaco-ordinate. The slx cobalr-cobalt distances are identical within experimental error (refs. 49 74). Fig. 10 Structure of Co,(CO),,(CBH,C = CC,H,) (ref. 76). and chalcogenide atoms as the basic metal cluster. The heptaco-ordinate poly- hedron approximates that of (12). The exact geometry in Fe3(C0),2 has now been unequivocally e~tablished'~ as depicted in Figure 12 and two of the iron atoms are heptaco-ordinate ; the co-ordination polyhedron approximates the capped octahedron.The new MnFez(CO),2- anion7a is probably isostructural with Fe,(CO)12. Two of the iron atoms in [C,H,C,C,H,]FQ(CO)~ are heptaco-ordinate 124 MPrcttertim and Wright Q 0 0. c' \ /C/O c I / Fig. 11 Structures of S,Fe,(CO)B and Se,Fe,(CO)o. The structures differ only in the orientdon of the (CO) triangle over the Fe,S and Fe,Se base. In the former a CO group is directly over an iron atom and in the latter over a selenium atom (refs. 77 78a). 0 OC\- i /co Fig. 12 Structure of Fe,(C0),2 (ref. 74). (Figure 13); one of the acetylenic carbon atoms is equidistant from all three iron whereas the second acetylenic carbon atom is bonded to only two iron atoms. Heptaco-ordination is also observed in a related diphenylacetylene-iron derivative [ C6H,C2C,HJ,Fe,( CO)880 which exists in two structural modifications.In the violet metastable form two iron atoms are within bonding distance of two other iron atoms four carbon atoms and three terminal carbonyl groups (Figure 14). The unique iron atom is hexa- or octa-co-ordinate depending on whether the olefhic linkage is considered a mono- or bi-functional moiety. In Fe,(CO),,C (Figure 15) the five iron atoms describe a square pyramid and the basal iron atoms are heptaco-ordinate.81 Heptaco-ordination is found in the rhenium(r1r) halide clusters. The prototype is RqCllZS- which has been rigorously characterised as an equilateral triangle of chlorine atoms with rhenium atoms at the mid-edge points; the remaining nine chlorine atoms are terminally attached in groups of three to each rhenium atom (Figure 1 6).82,83 The co-ordination polyhedron about the rhenium atoms approximates to a pentagonal bipyramid.A similar arrangement is found in the 79 J. F. Blount L. F. Dahl C. Hoogzand and W. Hiibel .J. Amer. Chem. SOC. 1966,88,292. 8o R. P. Dodge and V. Schomaker J . Organornetallic Chem. 1965,3,279. E. H. Braye L. F. Dahl W. Hubel and D. L. Wampler J. Amer. Chem. SOC. 1962,84 4633. 82 J. A. Bertrand F. A. Cotton and W. A. Dollase Znorg. Chem. 1963,2 1166. 83 W. T. Robinson J. E. Ferguson and B. R. Penfold Proc. Chern. SOC. 1963 116. 125 Quarterly Reviews TH5 Fig. 13 Structure of [C6H,.C2.C6H,]Fe,(CO) (ref. 79). Fig. 14 Structure of [C,H,.C2.C,H,],Fe,(C0) in the violet metastable crystal form. See Figure 28 for the isomeric structure (ref.80). The terminal carbon atoms represent one of the carbon atoms of the phenyl substituents. 0 Fig. 15 Structure of Fe,(CO)15C (ref. 81). CI CI Cl Fig. 16 Structure of Re3C1,,3- in CF,R~,CI, (ref. 82). Fig. 17 Structure of Re3C1,[P(C2H5),C,H J9 (ref. 85). /I\\ CL 126 Muetterties and Wright parent trichloride and tribromide; Re3Xg groups are in double layers and are joined together by chlorine-atom bridges to create a q~asi-Re,X,~~ ~ t r u c t u r e . ~ ~ ~ A derivative of the trichloride Re3C19[P(C2H,),C6H5]3 is isostructural with Re,CI,,* (Figure 17),85 and there are related complexes of Re,CI and Re3Br with a number of donor molecule^.^^^^^ Additionally there are Re,CI,,Z- Re,Br,,,- and Re3Brll2- anions in which one or two terminal halogens are missing from the Re3X123- ~ t ~ ~ t ~ r e .~ ~ - ~ ~ ~ ~ ~ ~ ~ For a sulphide (and a selenide) derivative of rhenium carbonyl Re3(CO),(SC,H,), it has been suggested that the C,H,S(C,H,Se) group serves as the bridging ligand as chlorine is in Re3CI ,:-. 90a A heptaco-ordinate polyhedron that is significantly different from the four idealised models discussed above exists in a series of tetrameric copper@) iodide complexes with phosphines arsines e t ~ . ~ l [The analogous silver(1) halide com- plexes are also tetrameric and may be isostru~tural.~~] These have tetrahedra of copper atoms with iodine atoms above the faces and donor ligands at the vertices (Figure 18).92 Each copper atom is within bonding distance of three iodine atoms three copper atoms and one donor atom (of the donor ligar~d).~~ Six atoms of the co-ordination sphere are below the central copper atom (13).This geometry is simply a reflection of the entire structure rather than any As \ As Fig. 18 Structure of [(C,H,),AsCuI] (ref. 92). 84 (a) F. A. Cotton and J. T. Mague Inorg. Chem. 1964 3 1402; (b) F. A. Cotton and S. J. Lippard ibid. 1965 4 59; (c) B. R. Penfold and W. T. Robinson ibid. 1966 5 1758; (d) M. Elder and B. R. Penfold ibid. 1966 5 1763. 85 F. A. Cotton and J. T. Mague Inorg. Chem. 1964 3 1094. 86 F. A. Cotton S. J. Lippard and J. T. Mague Znorg. Chem. 1965 4 508. F. A. Cotton N. F. Curtis C. B. Harris B. F. G. Johnson S. J. Lippard J. T. Mague W. R. Robinson and J. S. Wood Science 1964 145 1305. J. E. Ferguson B. R. Penfold and W. T. Robinson Nature 1964,201 181 ; Inorg.Chem. 1966 5 1763. M. Elder and B. R. Penfold Nature 1965 205 276. * O (a) A. G. Osborne and F. G. A. Stone Chem. Comm. 1965 361 ; (6) E. W. Abel B. C. Crosse and G. V. Hutson Chem. and Ind. 1966 238. O1 F. G. Mann D. Purdie and A. F. Wells J. Chem. Suc. 1936 1503. BzA. F. Wells 2. Krist. 1936 94 447. 127 Quarterly Reviews indication of preferred stereochemistry for heptaco-ordinate copper. A closely related configuration is foundgS for one of the iron atoms in Roussin's Black Salt CsFe,S,(NO),,H,O. The apical iron atom (Figure 19) is within bonding Fig. 19 Structure of the iron-sulphur polyhedron in Roussin's Black Salt CsFe,S,(NO),,OH (ref. 93). distance of three irons three sulphurs and a nitrogen of a nitrosyl group. The interaction of the unique iron atom with the three other iron atoms may be accounted for with a single delocalised molecular orbital.There are two isomeric boron hydrides of the composition B,,H, which have heptaco-ordinate boron atom^.^*^^^^^ The centrosymmetric species may be described as two B, units from decaborane (B,,H,J sharing a pair of boron atoms with the latter atoms each within bonding distance of six other boron atoms and a bridge hydrogen atom (Figure 20).Q40 The iso-B,,H, s t r u ~ t u r e ~ ~ ~ is formally analogous in that two B, units from decaborane are joined by sharing two boron atoms but the points of fusion are different from that in the normal structure (Figure 21). The 'shared' boron atoms again are the heptaco-ordinate ones; one is within bonding distance of the five boron and two hydrogen atoms and the other is near seven boron atoms.There are a number of solid-state structures derived from the early transition elements in which metal-metal interactions occur and heptaco-ordination is found for the transition element. Niobium(1v) iodide is a polymeric chain with two cis-bridging Nb-I-N b bondsg5 The niobium-niobium separation is only 3.3 1 A indicating metal-metal bonding and establishing heptaco-ordinate G. Johansson and W. N. Lipscomb Acta Cryst. 1958,11 594. 9g (a) P. G. Simpson and W. N. Lipscomb J. Chem. Phys. 1963 39,26; ( b ) P. 0. Simpson K. Folting R. D. Dobrott and W. N. Lipscomb ibid. p. 2339; (c) P. G. Simpson K. Folting and W. N. Lipscomb J. Amer. Chem. SOC. 1963 85 1879. 95 L. F. Dahl and D. L. Wampler Acta Cryst. 1962 15 903. 128 Muetterties and Wright Fig.20 Structure of n-B,,H,,. The two heptaco-ordinate boron atoms are represented by circles. The black dots represent boron atoms each of which has a terminal hydrogen atom (not depicted) (ref. 94a). Fig. 21 Structure of iso-B,,H,,. The notations are those of Figure 20 (refs. 94b 94c). niobium atoms (Figure 22). Tantalum(1v) iodide is isomorphous95~gs and niobium(1v) chlorides7 is structurally analogous with niobium iodide. Other niobium compounds which have Nb-Nb interactions and are heptaco-ordinate include NbOC1,Q8 and NbO,,QQ and a formally related species is M O C I . ~ ~ ~ In the W,C1,3- ion the two tungsten atoms are within bonding distance and are bridged by three chlorine atoms.lo1 The remaining halogens are terminally bonded three to each tungsten atom. Fig 22 Structure of i L NbI (ref.95). 7 Quasi-heptaco-ordinate Polyhedra.-Zenon hexafluoride unlike all other known neutral metal hexafluorides does not possess 0 symmetry.lo4 The precise geometry is as yet uncharacterised but the distortion from Ok symmetry 96 L. F. Dahl and D. L. Wampler J. Amer. Chem. SOC. 1959 81 3150. 97 H. G. Schnering H. Wohrle and H . Schiifer see ref. 21 p. 842. 98 H. G. Schnering and H . Wohrle see ref. 21 p. 1841. 99 B. 0. Marinder Arkiv Kemi 1962, 19 435. loo H. G. Schnering and H. Wohrle Naturwiss. 1963 50 91. lol W. H. Watson jun. and J. Waser Acta Cryst. 1958.11 689. loe L. S. Bartell R. M. Gavin jun. and H. B. Thompson J. Chem. Phys. 1965 43 2547. Quarterly Reviews is presumed by some103 to reflect the presence of a non-bonding pair of electrons in a directed orbital.Accepting such a non-bonding electron pair as a quasi- ligand we can enlarge the definition of heptaco-ordination to encompass such molecules ions and complexes as XeF6,103 IF6- BrF, IF5,NC,H5 and IF,,0CHN(CH,),.104 It should be noted that in some isoelectronic species such as TeC1,2- the non-bonding electrons must be in an s orbital because regular octahedral geometry pre~ai1s.l~~ Thus structural data are required to define precisely this class of quasi-heptaco-ordinate structures. 8 Solution Data.-There is no definitive structural datum for heptaco-ordinate species in solution. Nuclear magnetic resonance results for a number of these species in solution have been equivocal in a structural sense because invariably there was spectroscopic equivalence of ligand atoms. This has been true for ReH,p(C,H,),] (‘H resonance of ReH atoms is a triplet due to HP coupling),los as well as ReF7,4 IF,- BrF6- and IF5 complexes (19F spectra).lo4 The spectroscopic ligand-atom equivalence in IF and ReF has been ascribed to fast intramolecular is0merism.4~,~~ A similar explanation might be suggested for ReH,p(C,H,)a,* but the remaining species are labile and fast intermolecular ligand exchange may provide the fast averaging process.More recently Professor L. S . Bartell (personal communication) has suggested for XeF, which is dis- torted from Oh symmetry and is a quasi-heptaco-ordinate structure with the non-bonding electron pairs in a directed orbital a rapid intramolecular re- arrangement formally analogous to the ammonia inversion. 7 The polyhedral rearrangement is estimated to be very fast possibly faster than that for ammonia.There are a number of unimolecular tris-chelates of the type (chel),MX that are most certainly heptaco-ordinate but the geometries are as yet undefined. Examples from the tropolone and substituted tropolone ions are (tropolono),- SnC6H5,73 (tropol0no),TiC1,~~~ and (y-isopropyltropolono),Nb015 which are all non-ionic and monomeric in organic solvents. Analogous acetylacetone derivates of Zr and HfN e.g. (acac),HfCI are monomeric and give no evidence of ionisation to the tris-chelate metal cation which is established for titanium (a~ac),Ti+.,~ However the hafnium and zirconium derivatives based on the bulky anion derived from dibenzoylmethane although non-ionic themselves react with ferric chloride to give the salt (bzbz),M+FeC1,-.28 Catechol forms an apparent hept aco-ordinate s tructurelo8 with t ant alum(v) methoxide [(cat),- TaOCH,I2-.Reactions of niobates and tantalates with catechol in aqueous media give species of the type (cat),Nb03- and [(cat)3TaOTa(cat),]*-.109 pyramidal geometry if the hydrogen atoms are all in the pentagonal plane. Io3 R. J. Gillespie ‘Noble Gas Compounds’ Chicago University Press Chicago 1963 p. 333. lo* E. L. Muetterties ‘Advances in The Chemistry of The Co-ordination Compounds’ The MacMillan Co. New York 1961 p. 509. lo5 E. E. Aynsley and A. C. Hazell Chem. and Ind. 1963,611. lo6 L. Malatesta M. Freni and V. Valenti Gazzetfa 1964 94 1278. lo7 E. L. Muetterties and C. M. Wright J . Amer. Chem. SOC. 1965 87 4706. lo* R. Gut H. Buser and E. Schmid Helv. Chim. Acta 1965 48 878.lo9 A. Rosenheim and E. Roehrich 2. anorg. Chem. 1932,204 342. * All five metal-hydrogen atoms would be environmentally equivalent in pentagonal bi- t See also Trans. Amer. Crysf. ASSOC. 1966,’ 2 149. 130 Muetterttes and Wright Halogen oxidation of halogenopentacarbonylmetallate anions X(CO),M- gives rise to a series of heptaco-ordinate anionic species:l1° The solid products are salts which function as typical 1 1 electrolytes in nitro- benzene. This oxidation route to heptaco-ordinate anions is general to XW(CO)5- and XMo(CO) where X and halogen oxidant is bromine or iodine. This pro- procedure has also been applied to a series of diarsine (0-phenylenebis-di- methylarsine) complexes:111,112 1 2 Mo(CO),(diars) - [Mo(CO),(diars),I]+I- Analogous triarsine [bis-(0-dimethylarsinophenyl)methylarsine] chemistry1lsU pc exists xs M(CO),(triars) - [M(CO),(triars)W+X- (M = Cr Mo W; X = Br I) A [M(CO),(triars)xl+X- -+ M(CO)2(triars)X Molecularity and ionicity were established by molecular-weight and conductivity studies as well as metathetical ion-exchange reactions.Similar chemistry pervades bis-phosphine chelate chemistry of molybdenum and tungsten c a r b o n y l ~ . ~ ~ ~ For example iodination or bromination of the 1,2-bisdiphenyIphosphinoethane derivative Mo(CO),(diphos) yields Mo(CO),(diphos)X which is diamagnetic and a non-electrolyte. 1 ,2-Dithian complexes of molybdenum and tungsten carbonyls are oxidised by iodine to give non-ionic unimolecular species of the type [W(CO),(dith)I,] that are probably heptaco-ordinate with bridging dithian groups.ll5 M.C. Ganorkar and M. H. B. Stiddard J . Chem. SOC. 1965 3494. ll1 W. J. Kirkham A. G. Osborne R. S. Nyholm and M. H. B. Stiddard J. Chem. SOC. 1965 550. llx H. L. Nigam R. S. Nyholm and M. H. B. Stiddard J. Chem. Soc. 1960 1806. l13(a) C. D. Cook R. S. Nyholm and M. L. Tobe J. Chem. SOC. 1965 4194; (6) R. S. Nyholm M. R. Snow and M. H. B. Stiddard ibid. p. 6570; (c) M. R. Snow and M. H. B. Stiddard Chem. Comm. 1965 580. 116 H. C. E. McFarlane and W. McFarlane J. Znorg. Nuclear Chem. 1965 27 1059. J. Lewis and R. Whyman J. Chem. SOC. 1965,5486. 131 Quarter& Reviews An interesting type of heptaco-ordinate complex comprises the metal deriva- tives of v(co) in that there is metal-metal bonding e.g. (C,H,),PAU-V(CO)~ and (triars)Cu-V(CO),.l16 These complexes are monomeric and non-ionic.A related V-V complex is [V(CO)B(diars)], derived from V(CO) and the diarsine.l16 Niobium and tantalum pentahalides react with some donor molecules to give bis-adducts that may be heptaco-~rdinate.ll~-~~* The fluoride adducts are quite insoluble.120 Complexes of the pentachlorides or pentabromides with two molecules of donors such as tetramethylene sulphide pyridine trimethylamine and triphenyl-phosphines -arsines and -stibines have been reported but there is no measurement on molecularity. The sulphide adducts have rather high thermal ~tabi1ity.l~~ Well characterised are the 1 1 diarsine (1) complexes of NbCl and TaCl,; the complexes are monomeric and non-conducting.lZ3 There is a recent review of complexes formed by Group V metal halides.124 Conditions for synthe~is'~~J*~ have been characterised for the isolation of salts of the NbF,2- TaF:- and TaF,& ions from acidic aqueous media but the nature of the solution species has only recently been studied.It appears that the con- centration of ions like NbF72- is very small in aqueous media; the major solution species are NbF,- and NbOF,2-.26,27 On the other hand the tantalum system indicates a much higher stability for TaF,2- in aqueous media.127 This ion and the TaF,- ion are the major ions present in hydrofluoric acid solutions of tan- taluni(v); addition of NH,F to such solutions favours TaF,2- ion formation at the expense of the TaF,- ion. In KF-LiF melts tantalum(v) and niobium(v) are present predominantly as the heptafluorornetallate a n i ~ n s . ~ ~ * J ~ ~ Sodium ion favours formation of the hexafluorometallate ion; both TaF6- and TaF?- ions are present in NaF-LiF melts.Zirconium and hafnium tetrachlorides react with pyridine in benzene to give tris-adducts.130 Molecularity in solution is unknown on warming the adducts lose one molecule of pyridine at ca. 70". Tris-chelates of rare-earth ions particularly those exemplified by the ,8- diketone derivatives separate from protonic solvents with one to three molecules 116 A. S. Kasenally R. S. Nyholm R. J. O'Brien and M. H. B. Stiddard Nature 1964 204 871. 117 G. W. A. Fowles and C. M. Pleass J. Chem. SOC. 1957 2078. 11* P. J. H. Carnell and G. W. A. Fowles J. Chem. SOC. 1959,4113. 119 (a) F. Fairbrother and J. F. Nixon J. Chem. SOC. 1962 150; (6) F. Fairbrother K. H. Grundy and A. Thomson J . Less Common Metals 1966 10 38.120 (a) H. C. Clark and H. J. Emelbus J. Chem. SOC. 1958 190; (b) R. G . Cave11 and H. C. Clark J . Znorg. Nuclear Chem. 1961 17 257. lal J. Desnoyers and R. Rivest Canad. J. Chem. 1965 43 1879. lZ2 K. Lindner and H. Feit 2. anorg. Chern. 1924,132 10. lZ3 R. J. H. Clark D. L. Kepert and R. S. Nyholm J . Chem. SOC. 1965 2877. lZp M. Webster Chcm. Rev. 1966 66 87. 121 A. W. Laubengayer and C. G . Polzer J. Amer. Chem. SOC. 1941 63 3264. lZ6 0. Hahn and K. E. Piitter 2. anorg. Chcm. 1923 127 153. lP7 0. L. Keller jun. and A. Chetham-Strode jun. Inorg. Chem. 1966 5 367. 128 J. S. Fordyce and R. L. Baum J. Chent. Plzys. 1966 44 1 1 59. J. S. Fordyce and R. L. Baum J . Chem. Plzys. 1966,44 1166. I3O T. C. Ray and A. D. Westland Inorg. Chern. 1965 4 1501. 132 Plate 1 Perspectives of tlze idealised octaco-ordinate D4d square antiprism and nonaco-ordinate Dan symmetrically tricapped trigonal prism models illustrating the small distortion required in increasing co-ordination number.Plate 2 Conventional perspectives of the idealised heptaco-ordinate models. From left to right are the C, capped trigonal prism Cs tetragonal base-trigonal base D5h pentagonal bipyra- mid and C, capped octahedron. Plate 3 Perspectives illustrating structural similarities in the idealised heptaco-ordinate models. From left to right are the CaV capped trigonal prism Cs tetragonal base-trigonal base D5h pentagonal bipyramid and C, capped octahedron. Plate 4 Idealised octaco-ordinate geometries. From left to right are the square antiprism (D4d) dodecahedron (D2& undecahedron or bicapped trigonal prism (C2v) s-bicapped trigonal anti- prism (&& and hexagonal bipyramid (D6h).Plate 5 Perspective illustrating similarities in the cube s-bicapped trigonal antiprism and hexagonal bipyramid. Plate 6 Perspective illustrating the similarities in the square antiprismatic dodecahedral and undecahedral models. Muetterties and Wright of s o l ~ e n t . ~ ~ - ~ ~ ~ The solvate molecules cannot (with several exceptions) be removed without solvolysis and decomposition of the tris-chelate strongly suggesting a significant bonding interaction between the metal atoms and the donor atom of the solvent. The monosolvate phases may well contain heptaco- ordinate metal atoms. In solution the co-ordination number of these chelates is not established.Eight or nine may be the average co-ordination number for the large ions such as lanthanum but this probably falls to a limiting value of seven at lutetium. In the tropolone system a dihydrate of tris(tropo1ono)erbium has been isolated but in general the tris(tropo1onates) of the Ianthanides separate from water in anhydrous ~OI-III.~O~ These anhydrous forms are very intractable and are believed to be polymeric through bridging oxygen atoms.lo7 Metal-ion co-ordination numbers in the polymeric structures could be seven or eight.lo7 A tetracyanotrihydroxytechnetium anion Tc(OH),(CN),~ has been described on the basis of isolation and analysis of a thallium salt; the salt was obtained by dissolution of hydrated technetium(rv) oxide in aqueous hydrocyanic acid.140 Protactinyl sulphates PaO(SO& and selenates may be heptaco-ordinate with bidentate sulphate gr0ups.1~~ Arguments142 have been presented for a heptaco-ordinate iridium intermediate IrH,(CO)[P(C,H&l, which is formally related to the well-establishedlo6 ReH,[P(C,H,)& and to ReHs[P(C,H5)J4?43 This class of high-co-ordinate phosphino-metal hydrides may prove to be fairly large.C. Octaco-ordination Octaco-ordination is rather common in complexes of the larger metal ions. The ‘larger metal’ ions begin about scandium so the span of octaco-ordinate structures is really quite large.lo7 (In lattices octaco-ordination has been established for atoms as small as boron e.g. CO,,V,B,.~~) These co-ordination polyhedra seem more pervasive in the chemistry of the lanthanide and actinide ions and the early transition-metal ions particularly those of do dl and d2 configuration although there are apparent octaco-ordinate structures based on metal ions of d10 configuration such as Pb4+ Sn4+ and In%.It remains to be established how extensive octaco-ordination is for metal ions of d10 configuration; only recently 131 G. W. Pope J. F. Steinbach and W. F. Wagner J . Znorg. Nuclear Chem. 1961 20 304. lsa L. C. Thompson and J. A. braas Znorg. Chem. 1963 2 89. lS3 J. G. Stites C. N. McCarty and L. L. Quill J . Amer. Chem. SOC. 1948 70 3142. 130 R. C. Ohlmann and R. G. Charles J . Chem. Phys. 1964,40 3131. lSs L. R. Melby N. J. Rose E. Abramson and J. C. Caris J . Amer. Chem. Soc. 1964 86 5117. 138 (a) C. Brecher H. Samuelson and A. Lempicki J. Chem. Phys. 1965 42 1081; (b) C. Brecher A. Lempicki and H.Samuelson J . Chem. Phys. 1964 41,279. 13’ R. G. Charles and A. Perrotto J . Inorg. Nuclear Chem. 1964,26,373. 138 F. Halverson J. S. Brinen and J. R. Leto J . Chem. Phys. 1964 40 2790. 139 J. R. Ferraro and T. V. Healy J. Inorg. Nuclear Chem. 1962,24 1449. la0 W. Herr and K. Schwochau Angew Chem. 1961,73,492. lol K. W. Bagnall D. Brown and P. J. Jones J. Chem. Soc. 1965 176. la* L. Vaska Inorg. Nuclear Chem. Letters 1965 1 89. 143 M. Freni and V. Valenti Gazzetra 1961 91 1357. H. D. Stadelmaim and J. G. Avery 2. Metall. 1964,56,508. 133 Qwrterly Reviews has this aspect of d1* metal-ion chemistry come under serious investigation A number of idealised geometries have been established or suggested for octaco-ordination. Simplest and most symmetrical of these is the cube which is found in ionic lattices like caesium chloride and calcium fluoride but it has never been observed in a molecular species.Non-bonding repulsions are at a maximum in this regular polyhedron; moreover only seven s p and d orbitals possess proper symmetry for bonding. Although an unfavourable model for most cases the cube is not out of the question for a metal ion offz configuration where there are sufficient orbitals of proper symmetry but the non-bonding repulsions would not of course be relieved in this case. Actually a variant of the cube has been suggested for some uranyl compounds. The variant the symmetrically bicapped trigonal antiprism or puckered hexagonal bipyramid (&) is derived from a cube by a trigonal distortion. One of the uranyl structures 01U03 is purpor- t e d l ~ l ~ ~ only slightly distorted from a cubic array but most uranyl compounds appear to be closer to hexagonal bipyramidal geometry (see Plates 4 and 5).The next most symmetrical of the octaco-ordinate polyhedra is the square antiprism (D4d) (Plate 4). Non-bonding repulsions are significantly lower in the antiprism relative to the cube and there is no symmetry problem for utilisation of eight orbitals with a dx electronic configuration. The square antiprism con- formation is commonly found in the solid state for MX8"- ions and for octaco- ordinate chelate structures. Very closely related to the square antiprism is the D2d dodecahedral structure which is based on two interpenetrating trapezoids. The similarity of the D4d antiprism and geometries is illustrated in Plate 6.In the dodecahedral model there are two types of ligand environment each equally populated. The dode- cahedral structure has been observed in a number of octaco-ordinate chelates and ions; the classic example is the dodecahedral Mo(CN)$- ion.' In one sense the dodecahedral structure bridges the gap between the cube and the square anti- prism; any slight distortion of the cube in the manner outlined in Figure 23 brings it into the Dza point-group. Fig. 23 Distortion of the cube to dodecahedral geometry. Another possible idealised geometry and least symmetrical of the polyhedra l4ti W. H. Zachariasen Actu Cryst. 1948,1,281. 134 Muetterties and Wright is the C, hendecahedron derived from a trigonal prism by the capping of two square faces (Plate 4). This geometry first accorded theoretical status by Kimbal114s from symmetry arguments has not been established for a molecular octaco-ordinate structure but has been defined for some lanthanide and actinide halide lattices.This geometry is a hybrid of the D2d and geometries; the striking similarities of these three geometries are shown in Plate 6. A special case of octaco-ordination is found in metal polyhedra. For example in Pt&2 the octahedral Pt6 group describes the faces of a cube whose edges are defined by the twelve chlorine atoms.147 Each platinum atom is nearly coplanar with four chlorine atoms and is bonded to four other platinum atoms. The geometry for individual metal atoms in these metal polyhedra or clusters is not really relevant to the question of ground-state geometry in molecular species.Moreover Pt,CIl2 can be considered isostructural with Ta,CI,,(OH,)~~ if filled non-bonding platinum orbitals are directed out from the cube faces thus yielding a quasi-nonaco-ordinate platinum atom analogous to the nonaco- ordinate tantalum atoms [Ta(Ta),Cl,OH,] (see Section D). Some rather unusual octaco-ordinate geometries are also found in other metal polyhedra e.g. Fe6(CO),,C,148 but these are defined by the overall metal cluster arrangement. 1 Structural Relationships.-(a) Unidentate Zigands. It is of interest to draw some qualitative energy relationships among the various possible octaco-ordinate structures by considering such factors as steric interactions and promotional energies. Of the octaco-ordinate geometries only three D4d D2d and C2, have proper symmetry to use eight metal orbitals derived solely from s p and d levels.Since these three models are very closely related in geometry (Plate 6) it is not unreasonable to presume that the energy levels for these structures should be comparable. The C, model which is of significantly lower symmetry than the other two may be slightly higher in energy particularly if all eight ligands are identical. These three models differ electronically in that the lowest-energy d orbital is d,a for d for D2d and dxs-,,B for C,,. The cube should be the highest-energy species on the basis of promotional energy and repulsion con- siderations. The repulsion term is relieved to some degree in the D3d and DBd models. Another possible model is the symmetrically bicapped trigonal prism which should be less attractive than the DSd model on purely steric grounds (this DSh structure has never been observed).The lowest-energy d orbitals in the Oh and D systems are a degenerate set d,* and dxa-,, for Oh dxa-ut and d, for D3a d, and d for D6h and dxa-,,a and d, for D3h. A speculative outline of energy relationships for the octaco-ordinate models is depicted in the potential-energy diagram of Figure 24. This diagram is only schematic and no meaning should be read into the finer details of line shapes. The energy barriers for conformational isomerisation should be relatively small. 146 G. E. Kimball J. Chem. Phys. 1940 8 188. 14' K. Brodersen G. Thiele and H. G. Schnering Z. anorg. Chem. 1965 337 120. lC8 E. H. Braye L. F. Dahl W. Hubel and D. L. Wampler J . Amer. Chem. Soc. 1962 84 4633. 135 Quarterly Reviews Beginning at the left only slight distortions are required to isomerise D4& to C2, C2 to D2d to Oh Oh to D3d and D3d to Dan.Unfortunately there is no physical measurement relevant to isomerisation processes and this concept of potential stereochemical non-rigidity cannot be quantitatively delineated at this stage. These comments should not be taken as a generalisation for all octaco- ordinate structures. There should be complexes where a given geometry is signi- ficantly stabilised with respect to the other geometries by.rr bonding or by very low coulombic or non-bonding repulsions. In such cases the barrier to con- formational isomerisation may become quite large and the isomerisation rates may be very low except at high temperatures. E Qi Fig. 24 Possible energy diagram for octaco-ordinate species as a function of configuration.Qi is a shape function relating to interbond angles which describes a continuous path for configuration conversions. Except for the cited uranyl complexes all octaco-ordinate molecular species have either the square antiprismatic or the dodecahedral structure. Since a large number of such structures have been determined one may ask if there are any evident correlations between the configuration adopted and properties asso- ciated with metal ions or the ligands. The answer is no at least with respect to any simple correlation. Clark Kepert Nyholm and Lewis1* note that the more polarisable ligands like cyanide tend to yield a dodecahedral array about a metal atom ; however they emphasise that this correlation is ‘purely tentative’.The only real attempt to elaborate and make the parameters favouring either the prism or the dodecahedron quantitative is that of Hoard and Silvertons and an extension of this treatment by K e ~ e r t . l ~ ~ Hoard and Silvertons consider the direct bonding interaction to be essentially equivalent for the D4d and DZd co-ordination polyhedra and assign stabilisation of either polyhedron to effects arising from (1) non-bonding repulsions in the lQ9 D. L. Kepert J. Chem. SOC. 1965 4736. 136 Muetterties and Wright primary co-ordination sphere (2) coulombic repulsions and (3) geometrical restrictions from ligand stereochemistry. It must be emphasised that the attrac- tion forces are not taken into account and this could severely affect the con- clusions. Hoard and Silvertons conclude that for octaco-ordinate complexes where the ligands are alike and unidentate (1) Calculated angles for the two polyhedra closely approximate those experi- mentally observed.(Hybridisation schemes for metal s p and d orbitals in square antipri~maticl~~~ and d~decahedrall~~~ geometries also yield bond angle values in good agreement with those experimentally observed.) However this is not necessarily a justification of the repulsion model since the basic geometry is assumed for each polyhedron. (2) Energetically the DZd and models are equivalent within the meaning- ful limits of the arguments and assumptions. These two models are preferred to the cube and the hexagonal bipyramid. (3) The intrinsic ligand non-equivalence i.e. environmental as well as metal- ligand bond distance logically provides an operator for energy minimisation of the dodecahedral model relative to a square antiprism for MX4Y4 species in which X and Y are significantly different ligands electronically or sterically.If size is the distinguishing feature the smaller donor atoms should go to the A (Figure 25) sites. This important prediction should be examined experi- Fig. 25 The dodecahedron ( D z d ) with edge and vertex notations following the Hoard and Silverton6 convention. Only two of the eight “g” edges are labelled. mentally. The chelate TiC14,2(diars) a special case of MX4Y4 does in fact have the dodecahedral configuration.151 To speak of stabilisation of a hexagonal bipyramid is conceptually misleading. The hexagonal bipyramid is not a particularly attractive polyhedron for MX or MX,Y species.If however octaco-ordination is to be considered for an MX,Y2 compound where YMY is a rigid collinear array (resonance or n-bond stabilisation) the hexagonal bipyramid the bicapped trigonal antiprism or the cube are the only reasonable models. This is to say that a cylindrical system such as uranyl deformed to adjust to a or D4d polyhedron would represent a very unstable high-energy state. For such systems the dodecahedron and the square antiprism are destabilised. lao(a) G. H. Duffey J. Chem. Phys. 1950 18 746; (b) G. Racah ibid. 1943 11 214. lS1 R. J. H. Clark J. Lewis R. S. Nyholm P. Pauling and G. B. Robertson Nature 1961 192 222. 137 Quarterly Reviews (b) Chelates. The isomer possibilities in dodecahedral or square antiprismatic geometry where the ligands are multidentate is obviously quite large.152 For example consider the possible stereoisomers in a M(chel) structure in which the ligands are identical bidentate and symmetrical? For the square antiprism there are three isomers of plane of symmetry.D, and C symmetry none of which possesses a There are twice as many stereoisomers in the less symmetrical dodecahedron; these have DZd S4 D (two isomers) C, and C symmetries; none except the @@@@ *2d D2 s4 D2 c2 Cl DZd isomer has a plane of symmetry. Generation of these isomers may be more readily visualised from Figure 25 and Table 2 which identify the isomers by the polyhedral edges employed. There are close interrelationships between all nine stereoisomers; that is to say relatively slight distortions can convert a dode- cahedral isomer into a square antiprismatic isomer.Two isomer relationships are outlined for conversion of dodecahedral into square antiprismatic geometry; the fist group is generated by relatively slight distortions and the second group requires much larger distortions (Table 2). Motions required by conversion of the first order are so small that vibronic excitation may suffice for traversing the energy barrier. There are important consequences to this inherent stereochemical non-rigidity namely that two or more geometrical isomers related by one or more first-order conversions should be substantially present in the solution liquid or gaseous state of an octaco-ordinate species if the states of the 152 L. E. Marchi W. C . Fernelius and J. P. McReynolds J. Amer. Chem. SOC.1943,65,329. 138 Muetterties and Wright Table 2 Dodecahedron isomer (dodecahedral edge notation*) Related square antiprism isomers First order Second order D2d (mmmm) D2 D4 c2 s 4 (gggg) c2 D2? 0 4 D,’ (aabb) 0 4 D2 c2 c (mmgg) C and D2 D4 c (abmg) c2 D2 0 4 D2 (gggg) D4and D2 C2 This precisely follows the notations of Hoard and Silverton.’ isomers are comparable. Moreover the racemisation of an optically active form (+) or (-) forms exist for all isomers except D2d) should proceed quite rapidly particularly for the D square antiprism which is the only geometry other than D2d observed for the crystalline state of tetrakis-bidentate ~helates.2~ An estimate for the ground-state lifetime of a (+) or (-) form of the D2 isomer is 10-1 to lo-* second. That is not to say that a single crystal of a (+) or (-) form will not be isolated but that optical activity will not be generally observed for solutions of a D2 square antiprismatic isomer.The longest-lived optical isomers appear to be those with D,’ dodecahedral geometry. This type of argument can easily be extended to unidentate structures of the type MA,B,,. Hoard and Silverton5 have analysed relative stabilities of ground-state geo- metries for chelates and presented several conclusions based on the nature of the chelate and the overall charge on the complex. (1) If the ligand is coplanar and if the complex is charged minimisation of the coulombic interaction occurs with dodecahedral geometry and D2d symmetry. This class is exemplified by Zr(C204)44- and Cr(02)43-. (2) For neutral tetrakis-complexes in which the metal-oxygen bond is long e.g.> 2.30 A for acetylacetonates the shorter polyhedral edges (e.g. a b in Figure 25) are clearly preferred to minimise ring strain. This argument uniquely identifies the DZdDOD and D2S* models as the low-energy species as is observed for the cerium thorium and uranium tetrakis(acety1acetonates). We note an extension of this point. Matching of polyhedral edges to the oxygen-oxygen separation in the highly rigid tropolone ligand (4) should be the critical factor in determining ground-state geometry for tetrakis(tropol~nates).~~~ On this basis the D2 square antiprismatic and the DZd dodecahedral isomers should be the more stable isomers for all tetrakis(tropo1onates) except possibly those based on very small metal ions such as tin(rv).S Any departure from these predictions may reflect a contraction or elongation of the metal-oxygen bonds generated by coulombic repulsions in charged complexes.Since the range of tetrakis- (tropo1ono)-chelates is large Sc3+ to U4+ this series is worth detailed structural investigation. (3) Neutral M(chel) molecules in which the metal-oxygen bond distance is $ Molecular mDdels for (tropolono),Zr support this proposal. Ease of connectivity goes D < C < D in square anti-prismatic geometry and D,’ < C < C f D < S c Datl in dodecohedral geometry. 139 QuarterIy Reviews less than 2-30 A may have D or D symmetry in square antiprismatic geometry or D2d S, or D symmetry in dodecahedral geometry. It is rather difficult to present a more detailed energy differentiation among these five models without considering specific metal ions and specific ligands.So far all determined structures have essentially D square antiprismatic or D2d dodecahedral geometry. More detailed analyses of this class of chelates is in the paper by Hoard and Sil~erton.~ (4) Constraints imposed upon geometry by ter- quadri- quinque-dentate etc. chelates are severe and generalisations for this class are not significant. Any conclusions must be based on a specific multidentate ligand. In the ethylene- diaminetetra-acetate anion the six donor ligands readily conform to six of the eight general positions for the dodecahedron namely the two nitrogen atoms at adjacent A vertices and four oxygen atoms at B vertices (Figure 25). In the nitrilotriacetato-anion with the nitrogen atom at an A vertex the glycinate rings span a rn and g edges and a twofold rotation will generate the other half of a quasi-dodecahedral complex as found for bisnitrilotriacetatozirconate(1v) (-2).2 Structural Data for the Crystalline State.-(a) Dodecahedron (Table 3). The dodecahedron can be visualised as two structurally equivalent mutually per- pendicular trapezoids. Alternatively the structure can be visualised by dividing the eight ligands into two sets of four that form an elongated tetrahedron and a flattened tetrahedron which are interlocked. Figure 23 shows the distortion of the cube leading to the dodecahedral structure. This structure was first estab- lished by Hoard and Nordsieck in 1939 as the co-ordination polyhedron of the eight cyanide groups about molybdenum in K,Mo(CN),,~H,O.~ This analysis based on two-dimensional data has been reexamined with three-dimensional data to obtain more highly refined values for bond angles and distances.Within experimental error there is no difference in bond distance between the A and B type (Figure 25) Mo-C bonds (personal communication from Professor J. L. Hoard). Dodecahedra1 geometry has also been established for ‘chelate’ structures based on the compact peroxy and nitrate ligands. In K3Cr0, the chromium ion is surrounded by eight oxygen atoms as first shown by Stomberg and Brosset from two- and three-dimensional X-ray re~u1ts.l~~ A refinement of this structure by SwaIen and I b e r ~ I ~ ~ with the three-dimensional data established the oxygen- oxygen bond length in the peroxide group to be 1.405 f 0.039 A which is shorter than a normal peroxy-separation and the chromium-oxygen separations to be 1-846 f 0-022 A and 1.944 f 0.024 A.Isomorphous with K,CrO are K3Nb0, K,TaO, and K3V08>55,156 The nitrate ion is bidentate in [As(C,H,),],- [Co(NO,)J with an oxygen-oxygen separation of 2-1 A.16 The co-ordinated lS3 R. Stomberg and C. Brosset Acra Chem. Scand. 1960 14 441. lS4 J. D. Swalen and J. A. Ibers J. Chem. Phys. 1962 37 17. lS5 J. E. Fergusson C. J. Wilkins and J. F. Young J. Chem. Soc. 1962 2136. lS6 G. Boehm 2. Krist. 1926 63 319. 140 Muett ert ies and Wr&h t oxygen atoms form a distorted dodecahedron around cobalt so that the observed symmetry is only C,,,. Four metal-ligand distances are 24-2.11 A and four are 2.36-2.54 A which define an elongated and severely flattened tetrahedron respectively.The nitrogen atoms (centre of the nitrate group) are at vertices of a flattened tetrahedron. The two N-Co-N angles bisected by the molecular C axis are 152" and 144" compared with 109" for a regular tetrahedron. Cotton and Bergman have synthesised an analogous compound [As(C,H,),],- [Co(O,CCF,)J which has virtually the same electronic spectrum as the nitrate complex.l6 A three-dimensional structural determination20 of tetrasodium tetrakis- oxalatozirconate(rv) trihydrate established the co-ordination polyhedron around zirconium as dodecahedral and thus fixed the structure of the isomorphous hafnium complex. The average zirconium-oxygen distances are 2.1 68 8 (form- ing the flattened tetrahedron) and 2.230 8 (forming the elongated tetrahedron) and the average intra-ring oxygen separation is 2.563 A with essentially planar rings.The angle at zirconium in the ring is 71.3" and the average 0-Zr-0 angle between adjacent rings in the same plane is 70.4" and 147". The tetrakisdibenzyol- methane derivative of cerium(rv) also has the dodecahedral geometry with Ce-0 distances of 2.4&2.44 A and the thorium and uranium(1v) analogues are isomorphous by diffraction ~riteri0n.l~' A structural determination by three-dimensional X-ray analysis of the dipo- tassium salt of bis(nitrilotriacetato)zirconate(Iv) monohydrate established the [N(OAc),I3- ligand as quadridentate. The co-ordination polyhedron adheres to the constraints of the dode~ahedrall~~ model although the Zr-N distance is abnormally long (Figures 25 and 26). Two oxygens and two nitrogens lie in *-- 0 Zr -0 =2.13A Zr -0 = 2.25 Zr-N =2.75 Fig.26 The dodecahedral co-ordination of the nitrilotriacetato-ligands about W,. in K,Zr- (nitrilotriacetate)2,0H2. The broken lines represent the bridging groups of the chelate ligand (ref. 158). one tetrahedron with bond lengths of 2-251 and 2.439 A respectively and the zirconium-oxygen bonds in the other tetrahedron are 2.124 and 2.136 A which is in agreement with those found for unidentate ligands. Isomorphous with Zr[N(OAc),],2- is H~[N(OAC),],~-.~~~ 15' L. Wolf and H. Barnighausen Acta Cryst. 1960 13 778. 158 J. L. Hoard E. Willstadter and J. V. Silverton J . Amer. Chem. SOC. 1965 87 1610. lS9 J. L. Hoard J. V. Silverton G. L. Glen and E. Willstadter Proc. Seventh ICCC Stock- holm Uppsala (June 1962). 141 Quarterly Reviews A number of diarsine (1) complexes of the type MCI4,2(diars) have been pre- pared by Clark Lewis Kepert and Nyholm.14Jso The crystal structure has been established for TiC14,2(diars) by P.Pauling et aZ.151 and is octaco-ordinate with the diarsine rings bridging edge a and a (Figure 25) of the two interpenetrating trapezoids. The titanium-arsenic distance is 2-71 f 0.02 A the titanium- chlorine distance is 2-46 & 0.02 & and the separation between adjacent arsenic atoms is 3.21 A. Isomorphous with TiCI4,2(diars) are MX4,2(diars) where M = Zr Ti Hf Nb or V and X = Br or CI.l5l The dodecahedron is also found in polymeric octaco-ordinate units. The zirconium and hafnium atoms in K2ZrF6 and K2HfF6 respectively are sur- rounded by eight fluorine atoms four of which are shared. The polyhedra are connected in a chain-like fashion by sharing two opposite edges of the MF polyhedron.The crystal-structure determination of potassium hexafluorozir- conium(1v) gave 2-1 2-2-26 A as the zirconium-fluorine separation.161 The zirconium atom in Li,BeF,ZrF is also surrounded by eight fluorine atoms; four at 2-05 A (forming the flattened tetrahedron) and four at 2.16 A from the zirconium.162 An X-ray powder study of thorium tetrachloride and uranium tetrachloride suggests that the structures are isomorph~us.~~~ Each metal appears to be surrounded by eight chlorine atoms. In ThCI four chlorines are apparently at a distance of 2.46 A and four at 3.11 8 from the metal. The corresponding distances in UCI are 2.41 A and 3.09 A. Isomorphous with UC14 are NpC14 and PaC14.1aa The lattice of gallium dichloride is based on an array of Ga+ and GaC14- ions.ls5 The tetrachlorogallate anion is tetrahedral with gallium-chlorine distances of 2.19 A.Each Ga+ ion is surrounded by eight chlorine atoms from six different tetrahedra. The chlorine atoms occupy positions at comers of an irregular dodecahedron with four at 3-18 A and four at 3.27 A from the Ga+ ion. The dodecahedron is also found in zircon (ZrSi04)166 in which zirconium is bound by four oxygen atoms at 2-15 A and four at 2.29 A. The same oxygen polyhedron is found in yttrium phosphate (YPo4)186~u7 In addition the oxygen dodecahedra1 co-ordination polyhedron is found in the garnet structure. The garnets are a group of orthosilicates of which grossularite Ca3AI,(Si04), uvarovite Ca,Cr,(SiO,), and andradite Ca,Fe,(SiO,), are exampIes.168,16B The general formula is R311 RZII1 (SO,) with packing of the SiO tetrahedron such that the RII ions are eight- and the RII1 ions are six-co-ordinate.Structurally related to these silicates are the fluoroaluminates e.g. Na3A12(LiF4)3.170 The lanthanum cerium and neodymium phosphates exist in the monoclinic 1 6 0 R. J. H. Clark D. L. Kepert and R. S. Nyholm Nature 1963 199 559. 161 H. Bode and G. Teufer Acta Cryst. 1956 9 929. lci2 D. R. Sears and J. H. Burns J. Clzem. Phys. 1961 41 3478. 163 R. C. L. Mooney Acta Cryst. 1949 2 189. 164 W. H. Zachariasen Acfu Cryst. 1949 2 388. 165 G. Garton and H. M. Powell f. Inorg. Nuclear Chem. 1957 4 84. 166 I. R. Kirstanovic Actu Cryst. 1958 11 896 167 M. K. Carron M. E. Mrose and K. J. Murata Amer. Min. 1958 43,985.168 A. L. Gentile and R. Roy Amer. Min. 1960 45 701. 1-59 A. Durif Electron Telecomm. Internat. Conf. Brussels vol. 3 part 1 500 (1958). 1'0 G. Menzer Z. Krist. 1930 75 265. 142 Muetterties and Wright or hexagonal structure. The monoclink form is isomorphous with the mineral monazite. In the hexagonal structure the metal is octaco-ordinate.171 In CeP04 the cerium is surrounded by four oxygens at 2.34 8 and four at 2.66 A and the co-ordination polyhedron approximates dodecahedra1 geometry. In a sulphate of zirconium Zr,(OH),(S04),(H20)4 the zirconium is octaco-ordinate and the oxygen co-ordination polyhedron approximates the dodecahedron.172 Each Table 3 Dodecahedra1 octaco-ordinate structures NdPO4 Y PO Ce(DBM)4j Ga+[GaCI,l- ThC14 UCl NPC4 PaCI /3-ThBr4 Hard-sphere model Hoard-Silverton model d4sp3 Hybrid orbitals M-Aa(av.) Bond distance (A) 6~"(av.)Q 2.71 2.202 2-22 2.29 2-16 2.21 2-25(0) 2*44(N) 2.230 1.846 2.15 2.11 2.03 2.34 2-42 3.18 3.1 1 3.09 2-86 1.00 1 -03 36 43 35.3 35.2 43.4 36.0 47 36 36-85 35.2 34.55 M-Ba(av.) Bond distance (A) SBo(av.)a Ref.* 2.46 2.185 2.22 2.15 2.05 2.16 2.13 2.1 68 1 -944 2.1 5 2.36 2.54 2.66k 2.42 3.27k 2.46 2.41 2-61 1.00 1 -00 73 65.5 71-8 73.5 86-8 71.8 81 75 69.46 73.5 72.78 151 160 172 173 166 162 161 161 158 159 20 20 153 154 155 156 155 156 155 156 192 1 1 16 171 171 171 166 167 157 165 163 163 164 164 1 149 5 150b aSee Figure 25 for bond distance edge and angle notation; bdiars = o-phenylenebisdi- methylarsine; clsomorphous with TiCI4,2diars are M = Zr Hf V Nb; X = C1 and M - Ti Nb Zr Hf; X = Br.Probably also isomorphous with TiCI4,2diars are M = W Tc Re; X = Ci; M = Re; X = Br and M = Nb X = I; da = 2.78 b = 3.00-3.42 g = 2.62- 2.82 m = 2-34-2.63 A; ea = 2.42 g = 2.85 m = 2-54 A; fa = 2.52 g = 2-68 m = 2.47 A; QN(OAC),~- = nitrilotriacetic acid ion a = 2.68 g = 2.785 m = 2.62 A; ha = 2-57 b = 3.19,g = 2-735,m = 2*563A;tK3Cr0,,a = 2-57 b = 2.75,g = 2.74.m = 1*49A;jDBM= dibenzoylmethane ion a = 2.667 m = 2.866 A; kSpecific assignments of distance to the M-A and M-B bonds were not made by the authors; L D.E. Scaife Inorg. Chem. 1966 5 162. * For references see Text. 171 R. C. L. Mooney Acra Cryst. 1950 3 337. 172 D. B. McWhan and G. Lundgren Inorg. Chem. 1966 5,284. 143 Quarterly Reviews zirconium atom has two hydroxide oxygens four sulphate oxygens and two water oxygens at a mean distance of 2.19 A.Dodecahedra1 geometry is also found in Zr(OH),(N03),(H20) with a Zr-0 distance of 2-22 A.173 In other zirconium salts there is a near-square antiprismatic geometry (see Section C.2b). Lanthanum telluride La2Te3 described as a Th3P4 type structure has a lanthanum co-ordination sphere of eight tellurium atoms with La-Te distances of 3-244 and 3-418 A?74 A number of heavy-metal phosphides arsenides anti- monides and tellurides have this structure e.g. U3As4 and U,Te, as well as some rare-earth sulphides selenides and tellurides e.g. Ce2S3.175J76 The poly- hedron might be described as a highly distorted dodecahedron or square anti- prism; however any description in terms of idealised geometries is unrealistic for this particular polyhedron. (6) Square antiprism (Table 4).The square antiprismatic geometry is well established by X-ray analysis for discrete octaco-ordinate unidentate and bidentate compounds and for polymeric or ionic lattices. The only discrete complexes with unidentate ligands are the octafluorometallate ions. Sodium octafluorotantalate exists in the crystalline state with near D4d symmetry for the TaFS3- complex ion at least within the accuracy of the two-dimensional X-ray analyskll There is however a high probability that some distortion from full D4d symmetry arises from packing forces. The Ta-F bond distance ranges from 1.93-2.01 A with an average length of 1.98 A and the average F-F separation is about 2.41 8 and 2.42 A for square edges and triangular edges respectively. A similar structure apparently obtains in the K2ReF8 lattice (two-dimensional X-ray The Re-F distance varies in the range 1437-1.93 A.The struc- tures of such fluro-complexes as R u F ~ - ) ~ ~ WF 8 9 2- 179 M o F ~ - - ~ ~ ~ ~ ~ ~ XeF8”;38b the apparently isostructural UFSs and PaFss,lsl and TeF,2-ls2 have not been determined. Preliminary analysis of X-ray measurements for Na,UF indicates the uranium atom is octaco-ordinate (U-F = 2-29 A).183 The tetrakis(acety1acetonates) of zirconium cerium(Iv) and thorium are reported to use the square antiprism co-ordination polyhedron. The zirconium- (IV) acetylacetonate whose structure was determined by Silverton and HoardlS4 with three-dimensional X-ray data is of nearly D symmetry with an average zirconium-oxygen bond length of 2.198 A and a 0-Zr-0 ring angle of 75’. The intra-ring oxygen-oxygen distance is 2.674 A and the acetylacetonate ring 173 D.B. McWhan and G. Lun‘dgren Acfa Cryst. 1963 16 36. 174W. L. Cox H. Steinfink and W. F. Bradley Znorg. Chem. 1966 5 318. 175 J. Flahaut M. Guittard M. Patrie M. P. Pardo S. M. Golabi and L. Domange Acfa Cryst. 1965 19 14. 176 W. H. Zachariasen Acta Cryst. 1949 2 57. 177 P. A. Koz’min J. Struct. Chem. (U.S.S.R.) 1964 5 60. 178 E. E. Aynsley R. D. Peacock and P. L. Robinson Chem. and Znd. 1952 1002. 179 B. Cox D. W. A. Sharp and A. G. Sharpe J. Chem. SOC. 1956 1242. 180 G. B. Hargreaves and R. D. Peacock J . Chem. SOC. 1958 4390. l e a E. L. Muetterties J . Amer. Chem. SOC. 1957 79 1004. 1e3 J. G. Malm H. Selig and S . Siegel Inorg. Chem. 1966 5 130. 1e4 J. V. Silverton and J. L. Hoard Inorg. Chem. 1963 2,243. D. Brown and J.F. Easey J. Chem. SOC. ( A ) 1966 254. 144 M uetterties and Wright folds out about this edge of the antiprismatic square face by an angle of 22.6f7". The inter-ring square edge distances average 2.590 A. The distortion of the structure from square antiprismatic geometry is toward D dodecahedral. Hafnium(1v) acetylacetonate is isomorphous with the zirconium chelate by diffraction criterion. An isomorphous p-thorium(Iv) acetylacetonate of D point-group symmetry has been reported by Grdenid and MatkovidlS5 although the structure was not sufficiently refined unequivocally to establish stereo- chemistry. The average thorium-oxygen distance is 2.41 A with an 0-Th-0 angle of 70"; the oxygen-oxygen separation within acetylacetonate rings is 2.74 A; between adjacent rings it is 3-05 A and 3.10 A along the square and tri- angular face edges respectively.Tetrakis(acety1acetonato)plutonium is reportedlse to be isomorphous with P-thorium(rv) acetylacetonate. From a two-dimensional X-ray analysis of cerium(1v) tetrakis(acetylacetonate) square antiprismatic geometry has been suggested with an 0-Ce-0 angle of 72" and a cerium-oxygen bond distance of 2.40 Within the ring the oxygen-oxygen separation is 2.81 A and the distance between adjacent rings is 2-97 A and 2.95 8 along square faces and triangular faces respectively. Isomorphous with t e t rakis(acety1acet 0nato)cerium are the a-ur anium(1v) and a-thorium(1v) acetylacetonate~.~~~~ The crystalline 01 form of the thorium(1v) tetrakis(acety1acetonate) is formed spontaneously at room temperature from the /? Grdenid and M a t k o ~ i i l ~ ~ ~ attribute the two modifications of the thorium chelate to differences in packing arrangements but the structures of the two forms are not sufficiently well established to preclude alternative explana- tions such as changes in stereochemistry.A polyhedron of eight oxygens in a distorted square antiprismatic arrange- ment surrounds yttrium in yttrium(rr1) tris(acety1acetonate) trihydrate.ls8 The yttrium is co-ordinated to the six oxygens of the acetylacetonate ligands which bridge square edges and to two water oxygens which are at vicinal positions. The average Y-Oacac distance is 2.367 A the Y-Owater distance is 2-41 A and the average 0-Y-0 angle formed with the acetylacetonate ring is 72.5". Co-ordination polyhedra approximating that of the square antiprism have been suggested for a number of ionic or polymeric lattices.In all cases there is distortion of the polyhedron and the distortion is reportedly high in some of the polyhedra. Unfortunately the rigour of the analysis in most of the X-ray structural determinations of these 'polymeric lattices' falls short of establishing unequivocally the geometry of the co-ordination polyhedron. Therefore the assignments cited below might possibly be changed upon full three-dimensional analysis to dodecahedral or hendecahedral geometry. The lattice structures of a-ZrF,189a (the structure of the /? form has not been lE5 D. Grdenit and B. MatkoviC Nature 1958 182 465. lS6 A. E. Comyns Actu Cryst. 1960 13 278. lS7 (a) B. MatkoviC and D. Grdenic Acta Crysf. 1963 16 456; (6) D. Grdenic and B.Matkovii Acta Cryst. 1959 12 817. lE8 D. E. Sands J. A. Cunningham and W. F. Wagner; D. E. Sands personal communi- cation 1966. (a) R. D. Burbank and F. N. Bensey jun. U.S. Atomic Energy Corn. K-1280 (1956); (b) A. C. Larson R. B. Roof jun. and D. T. Cromer Actu Cryst. 1964,17,555. 145 Quarterly Reviews deterrninedlgoa) and UF,1S4JsQb are essentially identical. The heavy-metal atoms are within bonding distance of eight fluorine atoms which describe a slightly dis- torted square antiprism. Metal-fluorine distances range from 2-23-2.35 A in UF and 2-03-2-18 8 in a-ZrF,. The tetrafluorides of hafnium thorium neptunium plutonium cerium,lU praseodymium,190b terbium,lgoc americi~m,lgO~ and curium1goe are isomorphous with a-ZrF by diffraction criterion. In HfF,,- 3H20 there is a polymeric chain of hafnium atoms bridged by fluorine atom~.l~l The co-ordination polyhedron is described as a distorted square antiprism.For the compositionally related ZrF4,3H201g2 there are dimers instead of polymers and the zirconium co-ordination polyhedron apparently more closely resembles the dodecahedra1 geometry. An X-ray analysis of Eu(H,O),C& established a lattice of EU(H20),C12+ and Cl- The geometry of the europium co-ordination sphere was described as a highly distorted square antiprism with europium-oxygen and -chlorine distances of 2-44 and 2.77 A respe~tive1y.l~~ Acceptable alternative descriptions of the geometry are a distorted dodecahedron and a distorted hendecahedron. There are a number of isomorphous hydrated lanthanide and actinide chlorides (Nd Sm Er Gd and Pu).lg4 Analysis of the gadolinium salt gave a geometry quite comparable with the europium case.lg4 The average bond lengths are 2.77 and 2-40 A for the Gd-CI and Gd-0 bonds.Barium hydroxide octahydrate has based on a two-dimensional X-ray analysis a slightly distorted square antiprismatic array of eight water molecules about the barium atom at a distance of 2.69-2.77 A?95 The same metal-ion co- ordination polyhedron is suggested for the strontiumlg6 analogue and for Ca02,8H20.1g7 These analyses are based on two-dimensional data. Octaco-ordination is found for iodine in a number of iodates e.g. the iso- morphous Ce(I0,)4 and h(Io3)4,1g8 Ce(103)p,H20,199 Zr(10,)4,200 and NaIO,) ;201 and the co-ordination polyhedron is described as a ‘crude antiprism’. Five non- bonded oxygen atoms plus the three associated with the iodate complete the polyhedron.In Ce(IO,) the cerium atom has seven oxygen atoms at 2.18- 2.41 A and one at 2-82 8 to form a ‘much distorted Archimedean antiprism’.lg8 Each of two oxygen atoms per iodate group is shared with the cerium atom. Less lgo (a) V. Amirthalingam and K. V. Muralidharan J. Inorg. Nuclear Chem. 1964 26 2038; (b) J. Soriano M. Givon and J. Shamir Znorg. Nuclear Chem. Letters 1966,2 13; (c) B. B. Cunningham D. C. Feay and M. A. Rollier J. Amer. Chem. SOC. 1954,76 3361; ( d ) L. B. Asprey ibid. p. 2019; (e) L. B. Asprey F. H. Ellinger S. Fried and W. H. Zachariasen ibid. 1957 79 5825. lgl D. Hall C. E. F. Richard and T. N. Waters Nature 1965 207 405. lg2 T. N. Waters Chem. and Ind. 1964 713. lg3 N. K. Bel’skii and Yu. T. Struchkov KristallograJ’iya 1965 10 16.lgP M. Marezio H. A. Plettinger and W. H. Zachariasen Acta Cryst. 1961 14 234. lg5 H. Manohar and S. Ramaseshan Z . Krist. 1964 119 357. lg6 H. G. Smith Acta Cryst. 1953 6 604. lg7 R. S. Shineman and A. J. King Acta Cryst. 1951 4 67. lg8 D. T. Cromer and A. C. Larson Acta Cryst. 1956 9 1015. lg9 J. A. Ibers Acta Cryst. 1956 9 225. A. C. Larson and D. T. Cromer Acta Cryst. 1961 14 128. 201 C. H. MacGillavry and C. L. P. Van Eck Rec. Truv. chim. 1943 62,729. 146 Muetterties and Wright distorted is the antiprismatic arrangement of oxygen atoms about cerium in Ce(I0,)4,H20.199 The average Ce-0 distance in the hydrate is 2.33 A. Three- dimensional X-ray studies of Zr(XOJ4 show a nearly perfect antiprism of oxygen atoms about the zirconium with an average Zr-0 distance of 2.210 A.2oo Octaco-ordination has been suggested for zirconium cerium thorium and uranium in a number of oxygen derivatives and a discussion of this class of basic salt is given by Lundgren.202 Zirconium sulphate tetrahydrate has a layer lattice of Zr(SOk),,4H20 composition.203 Each zirconium atom is within bonding distance of four oxygen atoms from water molecules and four oxygen atoms from individual sulphate ions.The average Zr-0 distance is 2.18 A. This structure is closely related to U(S04)2,4H20.204 The zirconyl halide octahydrates ZrOCl,,- 8H,O and ZrOBr2,8H20 are isomorphous and have a near-antiprismatic co- ordination sphere of eight oxygen a t ~ m ~ . ~ ~ ~ ~ ~ ~ ~ Lundgren has suggested octaco- ordination with a near-square antiprismatic arrangement of oxygen atoms in Zr(OH)2S0,,172 Th(OH)2S04,207 U(OH)2S04,208 Th(OH)2Cr04,H20,209 A recent crystal-structure detemination2l3 of RbLiF and isostructural CsLiF shows that rubidium is surrounded by eight fluorines in a square anti- prismatic arrangement at distances of 2.78-3.16 A (average 2.95 A).In CsLiF, casium is surrounded by six fluorines at 2.96-3.15 A and two at 3.50 and CeOSO4,H2O,2l0 U(SOp),,4H2OY U604(0H),(S0~)6,211 and Ce604(OH)4(S0~)6.212 3.53 A. Table 4 Square antiprismatic octaco-ordinate structuresa Compound NaIOs RbLiP2 CsLiF Ca02,8Hz0 Sr02,8 H20 Ba02,8H,0 SrCI2,2H,O BaC1,,2H20 Sr(OH),,8 Ha0 MOW23 Ha0 HfF, 3 H2O a-ZrF4b UF HfF* C e F I M-X Squar 8" Bond distance (A) edge (A) 2.78-3.1 6 2.96-3-15 3.50-3.53 3.1 3-3.36 2-60 2.74 209 2.12 2.28 3.23 57 202 G. Lundgren Svensk Kem.Tidskr. 1959 71 200. J. Singer and D. T. Cromer Acra Cryst. 1959 12 719. 204 P. Kierkegaard Acra Chem. Scand. 1956 10 599. A. Clearfield and P. A. Vaughan Acra Cryst. 1956 9 555. 206 G. M. Muha and P. A. Vaughan J. Chem. Phys. 1960,33 194. 207 G. Lundgren Arkiv Kemi 1950 2 535. 208 G. Lundgren Arkiv Kemi 1952 4 421. 209 G. Lundgren and L. G. SillCn Arkiv Kemi 1949 1,277. *lo G. Lundgren Arkiv Kemi 1953 6 59. 212 G. Lundgren Arkiv Kemi 1956 10 183. 213 J. H. Burns and W. R. Busing Znorg. Chern. 1965.4 1510. G. Lundgren Arkiv Kemi 1953 5 349. TriangIe edge (4 2oyf.* Y e 21 3 21 3 197 e 197 e g 196 3.50 195 191 189a 189b 164 164 147 Quarterly Reviews Table &continued Compound ThF4 NPF4 PuF4 Zr ( a ~ a c ) ~ Rf( a ~ a c ) ~ flh(ac44 Pu(acac) Ce(acac) a-U(a~ac)~ ~x-Th(acac)~ ZrO C12,8H20 ZrOBr2,8H20 Zr(IOd4 Zr(S04)8,4&0 Th(0H j~Cr04,H20 U(S04)2,4HzO U(OHhSO4 u 60doH)4(so4) 6 Hard-sphere model Hoard-Silverton dSp3 Hybrid orbitals d4sp3 Hybrid orbitals model eo 57.3 58.2 58.5 58 57 59 58 58 54 59-25 57.3 60.9 57.6 M-X Bond distance (A) 2.198 2-41 2.40 2.24 2.21 2.178 2.19 1.98 1.87-1.93 2.41 2.33 2.18-2'41 2.82 2-44(0) 2*77(C1) 2*41(0) 2-77(C1) 3-20 2-4 2.5 2.3 2.3 2-3 1.000 1.000 Square Triangle edge (A) edge (A) 164Ref .* 164 164 2.59,2.676 2.74 184 184 3.05 2-74d 3.10 185 186 2.97 2.81 2.95 187 187 187 205 205 2.65 2.73 200 2531,2623 2719 203 2859.2648- 172 2.41 2.42 11 177 212 210 2.83 2.75 199 198 198 2.91 3.33 2864.19 193 194 194 194 194 194 207 209 204 208 21 1 1.215 1.215 149 1.190 1.258 5 3.85 4.02 223a b 150a 150a aThe groups indicate isomorphous series; 6There are two kinds of zirconium atom one with a metal-fluorine distance of 2.09 the other with a metal-fluorine distance of 2.12 A.All Zr-F distances within a given polyhedron are equal; Cacac = acetylacetonate ion; dThe length of the edge the acac ring spans; * For references see Text except as follows eR. W. G. Wyckoff 'Crystal Structures' Interscience New York 1965 2nd edn. vol. 3 p. 842; PA. T. Jensen Kg1. danske Videnskab Selskab Mat.-fys. Medd. 1943 20 No. 5; gldem ibid. 1945 22 NO. 5. (c) Hexagonal bipyramid (Table 5). Although not yet subjected to the test of a three-dimensional X-ray analysis the existence of hexagonal bipyramidal geometry in uranyl compounds seems fairly well established. First the collinear or very nearly collinear nature of the uranyl (UO,) group appears to be on a moderately sound basis.In RbUO,(NO& the best fit of two-dimensional X-ray and neutron diffraction data is with an arrangement in which the collinear 148 Muetterties and Wright OUO group (U-0 distance 1.78 A) is bisected by a plane of three nitrate groups.214,216 The hexagon of oxygen atoms is slightly puckered; oxygen atoms are alternately 0.09 A above and below the plane. Each nitrate group is effectively bidentate with respect to the uranium atom yielding a non-regular (threefold symmetry) hexagonal co-ordination. A similar arrangement has been found consistent with two-dimensional X-ray measurements for NaU02(0COCH& with three acetato-groups providing the threefold symmetry of hexaco-ordina- tion in the plane perpendicular to the OUO group,2lS and an analogous three- dimensional variant in U02C03 with bidentate carbonato-gr~ups?~~ Powder data for U02(N03)2,6H20218 and U02(N03)2,20P(OC2H,),219 have been interpreted in a formally similar fashion with two nitrate and two 'para' oxygen atoms from the solvate molecules describing the hexagonal co-ordination sphere.Recently the U02(N03),,6H20 structure was reexamined with three- dimensional neutron diffraction The uranyl group (U-0 distance 1.76 A) is surrounded by a near-planar hexagon of four oxygen atoms from two bidentate nitrate groups and two equivalent water oxygen atoms. Table 5 D3d and Dan Octaco-ordinate structures Compound Bonda distance (A) Ref.* Compound Bond" distance (A) Re/.* CaUOaOa 2U-01= 1-92 145 RbUOz(N03)s 2U-01 = 1.78 215 6U-011 = 2-29 8Ca-O = 2-45 [UO,(NO*),.2U-01 = 1.76 220 Bicapped trigonal antiprism Planar hexagonal bipyramid 6U-011 = 2.48 2HaOI.4HaO 2U-011 = 2.397 SrUOaOa 2u-011= 1-91 145 2U-011 = 2.504 2U-011 = 2.547 6U-Or1 = 2.33 8Sr-0 = 2.58 UO~COI 2U-01= 1-67 UO,F 2U-01 = (1-91)b e 4U-011 = 2.52 217 6U-F = 2.50 2U-011 = 2,44 6Am-F = 2.47 ~Pu-OII= 2.55 KAmOaFz 2Am-01 = (1*93)b f KpuOaCOs 2Pu-01 = (1*94)b g RbAmO&O3' g or-U03 2U-01= 2-08 222 6U-011 = 2.39 145 NaUOa(O,CCHa) 2U-01= 1.71 216 6U-011 = 2.49 NaMOa(OsCCH3),C M = Np Pu Am 164 216 uo z(N03)~f(c~H 60)3POI*d 219 "The uranyl oxygens are designated 01 and the other six oxygens 011; m e s e distances are estimated; "This compound is isomorphous with the one directly above; NO parameter is available; * For references see Text except as follows eW.H. Zachariasen Acta Cryst. 1948,1 277; Idem ibid. 1954,7 795; OF. Ellinger and W. H. Zachariasen J. Phys. Chem. 1954 58 405. 214 J. L. Hoard and J. D. Stroupe National Nuclear Energy Series Div. 111 2 13 McGraw Hill Book Co. New York 1949. 215 G. A. Barclay T. M. Sabine and J. C. Taylor Act@ Cryst. 1965 19 205. alb W. H. Zachariasen and H. A. Plettinger Acta Cryst. 1959 12 526. 217 D. T. Cromer and P. E. Harper Acta Cryst. 1955 8 847. 218 J. E. Fleming and H. Lynton Chem. and Ind. 1960 1416. 219 J. E. Fleming and H. Lynton Chem. and Znd. 1959 1409. 2zo (a) J. C . Taylor and M. H. Mueller Acta Cryst. 1965 19 536; (6) B. 0. Loopstra and E. H. P. Cordfunke Rec. Trav. chim. 1966,85 135. 149 Quarterly Reviews Like the cube the hexagonal bipyramid is not an attractive model on purely symmetry grounds for metal ions that do not utilisef orbitals.( d ) Bicapped trigonal antiprism (puckered hexagonal bipyramid) (Table 5). There are insufficient structural data to place the symmetrically bicapped trigonal antiprism (0 d ) among the established octaco-ordinate geometries. Such a geometry has been suggested for the layer lattices found in a-U03 CaUO, SrU04 and UO,F but the X-ray data consisted solely of powder diffraction patterns.145 A recent neutron diffraction study of the hexagonal a-U03 suggests that this form is an imperfectly crystalline form of rhombohedral 01-U03?20b (e) Undecahedron or bicapped trigonal prism (Table 6). Experimental evidence definitive for the C, undecahedron is now available from the single-crystal X-ray analysis of terbium trichloride.221 The chlorine atoms at trigonal vertices are at 2.70 and 2.79 A from the terbium atom; the two chlorine atoms at the square pyramidal vertices are at 2-95 A.A ninth chlorine atom is at a distant approach of about 4.0 A and is non-bonding. This type of structure was first suggested by Zachariasen222 for several lanthanide and actinide halides e.g. PuBr and NdBr, on the basis of X-ray powder diffraction data. The undeca- hedral species may be considered as frustrated nonaco-ordinate structures in that close approach of the ninth halogen is inhibited by the steric hindrance of the other eight halogen atoms. Table 6 Undecahedral octaco-ordinate structures Compound Re$ * Compound YF3a 224 PLIB~,~ SmF 224 TbC136 EuFB 224 NbBr GdFs 224 SmBr TbFs 224 EuBr HoFS 224 AmBrs ErFs 224 mF3 224 PrIs DYF3 224 P-NPBr TmF 224 CeI BiF 224 f UI Th,SUb g NPI ThI,C 2236 PUI m 3 LuF 224 NdIs Ref.* 222 221 222 222 h 222 222 222 h h h 222 222 222 222 W3y-F = 2.3 A; b8ThII-S = 2.94 A (See also Table 10); C8Th-I = 3.20 A (See also Table 4); dSPu-Br = 3.08 A; e2Tb-C1 = 2-74,4Tb-CI = 2-79 2Tb-CI = 2.95 A; * For references see Text except as follows fW. H. Zachariasen U.S. Atomic Energy Commission Argonne National Laboratory Report ANL-4400 (January 1950); O W . H. Zachariasen Acta Cryst. 1949,2,288 ; hF. H. Spedding and A. H. Daane Ames Laboratory Report IS-350 (September 1961). 921 J. D. Forrester A. Zalkin D. H. Templeton and J. C. Wallmann Inurg. Chem. 1964 3 185. 222 W. H. Zachariasen Acfu Cryst. 1948 1,265. 150 Muetterties and Wright Thorium tetraiodide has been described in terms of a distorted square anti- prism.223a Because of the close similarity of the antiprism and the undecahedron the thorium tetraiodide structure can equally well be described as a distorted unde~ahedron.,~,~ The yttrium atom in yttrium t r i f l ~ o r i d e ~ ~ ~ has essentially the same geometry about it as does terbium in terbium trichloride except that the ninth distant halogen atom is closer in YF than in TbCl,.This is essentially a compromise between an octa- and a nonaco-ordinate structure. The yttrium-fluorine dis- tances are 2.3 A with the ‘distant’ ninth fluorine atom at 2.6 A. Isostructural with YF are the orthorhombic lanthanide trifluorides samarium to lutetium inclusive. In a second (hexagonal) lanthanide fluoride structure formed by lanthanum to europium inclusive and also holmium and thulium there is nonaco-ordination by fluorine about the metal atom.cf) Cube. As noted earlier a co-ordination cube has not been observed for any molecular metal complex. It is found extensively in ionic lattices exemplified by the czsium chloride and calcium fluoride structures. (8) Metal polyhedra. Hexadecacarbonyl hexarhodium has a basic octahedral array225 of rhodium atoms each attached to two terminal carbonyl groups with an interpenetrating tetrahedron of bridging carbonyl groups (Figure 27). The co-ordination sphere about each rhodium atom is a hybrid of the square anti- prism and the dodecahedron. Four rhodium atoms describe a square face and four carbonyl groups form a near-trapezoidal array about a single rhodium atom. ? s C Fig. 27 Structure of Rh,(CO)l, (ref.225). Fig. 28 Srructure of[C,H,.CII.C,H JzFe,(CO)8 in the black stable crystal. See Figure 14for the isomeric structure (ref. 80). In the black stable form of [C6H5C,C6H5],Fe3(CO), one iron atom is un- ambiguously octaco-ordinate.80 This unique iron atom is bonded to two terminal carbonyl groups two bridging carbonyl groups two iron and two carbon atoms. The other two iron atoms may be described as hexa- or octaco-ordinate depend- 223 (a) A. Zalkin J. D. Forrester and D. H. Templeton Znorg. Chem. 1965 3 639; (b) D. H. Templeton personal communication. 424 A. Zalkin and D. H. Templeton J . Amer. Chem. SOC. 1953 75 2453. 2p5 E. R. Corey L. F. Dahl and W. Beck J. Amer. Chem. SOC. 1963 85 1202. 151 Quarter Iy Reviews ing upon the definition of co-ordination number for the olefin-iron interaction (Figure 28).The apical iron atom in Fes(CO),,C is octaco-ordinate.sl This iron atom has an unique geometry with three terminal carbonyl groups in half the co-ordina- tion sphere and a square pyramidal Fe4C arrangement in the other half (Figure 15). The remaining four iron atoms are heptaco-ordinate. Crystalline PtCl contains discrete Pt&1,2 units in which there is an octa- hedron of platinum atoms and nearly coplanar with each platinum atom are four chlorine atoms which in sum total describe the twelve edges of a cube.147 Each platinum atom is thus bonded to four chlorine atoms and four platinum atoms (Figure 29). An analogous structure is apparently present226 in the solu- tion state for Bi,(OH)126+. There may be octaco-ordination in [Re(CO),H] with an Re triangle bridged by hydrogen U Fig.29 Structure of Pt,Cl, (ref. 147). Fig. 30 The structure of discrete Zr4(OH)8(OH2)1,8+ in ZrOCI2,8H20. The eight oxygen atoms oj'the hydroxyl groups describe the basic cube. Each cube face is capped with a zirconium atom which is bonded to four oxygen atoms from water molecules as illustrated for one face in the diagram (refs. 205 206). Eight oxygen atoms form a square antiprism about each uranium atom in [U604(OH)J12+6S042-. The six uranium atoms describe an octahedron with a uranium-uranium distance of 3-84 A and the U-0 separation is 2-3 A.212 If the uranium atoms were considered to be within bonding distance each uranium atom would be dodecaco-ordinate. This structure is based on a two-dimensional X-ray analysis and may be subject to significant refinement or change.The zirconyl halide octahydrates mentioned above as having square antiprismatic co-ordination about the zirconium atoms exist in the solid state and apparently also in solution as discrete Zr4(0H),(OH~,,s+,8C1- groups (Figure 30).205*20s The zirconium atoms are in a square configuration with bridging hydroxyl groups and each zirconium atom has four terminal water groups. Apparently bound by coulombic forces the eight halogen atoms occupy specific sites about the polyhedron. Octaco-ordinate metal atoms are found in the eicosahedral metallo-boranes. For example rhenium is octaco-ordinate in B,C2HllRe(CO),-. The rhenium atom completes the carborane eicosahedron and is bonded to three boron and a26 V. A. Maroni and T. G. Spiro J. Amer. Chem.SOC. 1966,88 1410. (a) D. K. Huggins W. Fellmann J. M. Smith and H. D. Kaesz J. Amer. Chem. SOC. 1964 86 4841; (6) A. Zalkin T . E. Hopkins and D. H. Templeton Inorg. Chem. 1966 5 1189. 1 52 Muetterties and Wright two carbon atoms in the adjacent pentagonal plane. Three carbonyl groups are terminally bonded to the rhenium atom.227b 3 Solution State.-There are no measurements that provide any significant information concerning the geometry of octaco-ordinate complexes in solution. With the recent interest in laser materials a number of publications have ap- peared claiming structural definition of tetrakis-chelates of rare-earth ions a very extensive class of octaco-ordinate compounds by analysis of electronic or fluorescence ~ p e ~ t r a . ~ ~ ~ ~ ~ ~ - ~ ~ ~ Although the conclusions may be correct the analyses possess little rigour.Unfortunately there is no physical technique that will provide sufficient data for an unequivocal structural determination for such complex molecules in solution. For special cases a technique such as nuclear magnetic resonance (n.m.r.) may provide information regarding non-equivalence that will unambiguously eliminate some of the possible stereoisomers from con- sideration; however in all cases examined so far only spectroscopic equivalence of magnetic nuclei in the ligands has been observed. These include Mo(CN),4- (13C),29 ReH,[P(C,H&] (lH),loS and a number of chelate struc- t u r e ~ . ~ ~ ~ ~ ~ ~ ~ Intermolecular exchange can be rigorously excluded as the origin of the equivalence for the fist two examples and for a few of the chelate structures.The octacyanometallate ions are a particularly interesting case for solution studies. It has been argued on the basis of Raman and infrared data that in solution Mo(CN):- has D4d square antiprism geometry rather than the D2d dodecahedra1 geometry established for the solid potassium salt.233 The optical spectrum has been interpreted in terms of D4d as well as D 2 d symmetry but these analyses are far from definiti~e.~%-~~' As noted above the cyano-complex in solution shows a single sharp 13C n.m.r. resonance which is consistent withD,d symmetry but attention is called to the potentially short ground-state lifetimes of an octaco-ordinate structure which can disqualify any physical observation of a relatively long time scale for the determination of point-group ~ymmetry.2~ The closely analogous paramagnetic ions Mo(CN),3- and W(CN)t- have been examined by electron spin resonance t e c h n i q ~ e s .~ ~ ~ ~ ~ ~ Analysis of spectra at 25" in aqueous solution and at -196" in frozen glycerol solution indicates a similarity in structure in these two states and the results are consistent only with a D4d ground state (with the reasonable assumption that configurational exchange at -196" is slow relative to the e.s.r. time scale).237 The spectra of 228 J. Blanc and D. L. Ross J. Chem. Phys. 1965 43 1286. 23s H. Bauer J. Blanc and D. L. Ross J. Amer. Chem. SOC. 1964 86 5125. 230 N. J. Rose and E. Abramson J . Chem. Phys. 1965 42 1849. aslT. J. Pinnavaia and R. C. Fay Inorg. Chem. 1966,5 233. 232 A. C. Adams and E. M. Larsen Inorg. Chem.1966 5 228. a33 H. Stammreich and 0. Sala Z. Efektrochem. 1960 64 741 ; 1961 65 149. 234 R. M. Golding and A. Carrington Mol. Phys. 1962,S 37 I . 235 E. Konig Theor. Chim. Acta. 1962 1 23. 236 G. Gliemann Theor. Chim. Acta 1962 1 14. 237 B. R. McGarvey Inorg. Chem. 1966,5,476. 238 R. G. Hayes J . Chem. Phys. 1966,44,2210. 153 Quarterly Reviews dilute concentrations of K,Mo(CN) in &MO(CN) are consistent with D2d symmetry.237 This is the only well-defined example of a high-co-ordinate struc- ture which has different ground-state geometries in the solid and the solution state. The nature of octaco-ordinate species in solution is not well characterised in terms of solvation phenomena dissociation and ligand exchange. These extremely important considerations are probably inter-related and should certainly be more extensively examined.There is good evidence that lanthanide and actinide tetrakis-chelates interact significantly with strong donor molecules such as amides and sulphoxides. For example the electronic spectrum of the tetrakis(acetylacetonato)europium(m) anion in alcohol is grossly altered on addition of dimethylformamide suggestive of complex f0rmati0n.l~~ Variational concentration studies indicate that the complex is highly dissociated in solu- t i ~ n . l ~ ~ An analogous chelate anion derived from dibenzoylmethane reacts with dimethylformamide to give a crystalline 1 1 add~ct.l,~ Tetrakis(tropo1ono)- thorium(1v) forms 1 1 crystalline complexes with donor molecules like dimethyl sulphoxide.l* On the other hand the related neutral tropolone derivatives of zirconium and hafnium(1v) give no evidence of complex formation; and this is true also for cationic species such as tetrakis(tropolono)tantalum(v)+.18 Clearly steric factors must control formation of nonaco-ordinate complexes significantly.Ligand dissociation in octaco-ordinate species is generally a relatively easy process although there is one notable exception the non-labile Mo(CN):- ion. The stability of the cyanides probably reflects the much more effective delocalisa- tion of charge possible with cyano-groups; this is a critical point for these highly charged (-3 to -5) anionic complexes. In contrast to the cyanides the octa- fluorometallate ions are completely or nearly completely dissociated in aqueous media e.g. there is no evidence of the TaF,& ion in HF or NH,F-HF solu- t i o n ~ .~ ~ ~ In chelates many of the acetylacetonate complexes exhibit tendencies to dissociate in solution and this is quite well documented for the anionic tetrakis- /hikctone derivatives of europium;136 one or two molecules of solvent un- doubtedly take up co-ordination sites in the chelate x Solvent + E~(acac)~- + acac- + Eu(acac),(solvent). In the tropolone chelates stability of the tetrakis-derivatives is a function of the formal charge on the complex and the size of the metal ion.lo7 Here the cationic derivatives are more stable than the neutral ones which are in turn more stable than the anionic complexes. The hydrolysis rates of the tetrakis(tropo1onates) of niobium(v) and tantalum(v) are strikingly different although the ionic radii of these metal congeners differ only slightly (Ta5+ = 0.73 A; Nb5+ = 0.70 A).In neutral solutions the tantalum chelate is not significantly hydrolysed but the niobium derivative rapidly hydrolyses with the separation of tris(tropo1ono)- oxyniobium(v).107~239 The theimodynamic stabilities of the niobium and tantalum tropolonates may be more similar than is apparent for the case of neutral solu- E. L. Muetterties and C. M. Wright J . Amer. Chem. Soc. 1965 87 21. 1 54 Muetterties and Wright tions because of the very low solubility of T3Nb0 a species that has no analogue in the tantalum system. Quantitative soholytic data for octaco-ordinate species are lacking except for a series of europium acetylacetonates. The degree of dissociation of the tetrakis- anions in alcohol is 24 37 43 and lOO% respectively for the acetylacetone benzoylacetone dibenzoylmethane and benzoyltrifluoroacetone derivatives.13s A cation effect upon dissociation has been observed for tetrakis(benzoy1tri- fluoroacetonato)europium and is ascribed to ion-pair formation with the benzoyltrifluoroacetonato-anion.240 Lability of ligands in octaco-ordinate structures has been demonstrated in a number of systems.For example dissolution of tetrakis(acety1acetonato)- zirconium(1v) and tetrakis(trifluoroacetylacetonato)zirconium(Iv) in benzene yields a solution in which all possible isomers are The mixed complexes Zr(tfac),(acac) Zr(tfac),(acac), and Zr(tfac)(acac) are favoured at the expense of Zr(tfac) and Z r ( a ~ a c ) ? ~ ~ * ~ ~ The deviation from a purely statis- tical distribution of ligands is ascribed to entropy changes; enthalpy changes are nearly zero.A similar exchange is observed in the analogous Hf Ce and Th systems. Exchange rate is lowest in the hafnium case and highest for thorium. All of the fluorine n.m.r. resonances in the mixed thorium system coalesce at ca. 43"; lifetimes are less than a second at such temperatures. It is interesting that the thorium chelates are the most labile. Thorium unlike Zr Hf and Ce shows a tendency to be nonaco-ordinate i.e. the tetrakis-chelates tend to solvate in strongly basic media. The exchange studies were however done in non-basic media such as benzene. Perhaps nonaco-ordinate binuclear species like (14) are important intermediates for the thorium system in benzene whereas unassisted ligand dissociation may prevail with the smaller metal chelates.Rate of exchange of tropolone with tetrakis(tropolono)tantalum(v)f cation is estimated to be less than lo3 sec.-l from n.m.r. data; tracer studies have shown the exchange is 94 "/ complete in 30 minutes.lo7 Rate of ligand exchange increases in going to neutral and again in going to anionic tetrakis(tropo1ono)metallates. This ligand lability makes the outlook for isolation of optical isomers in octaco- ordinate chelates rather p00r?99107 Nuclear magnetic resonance studies of octaco-ordinate p-diketone or tropolone chelates have as yet failed to discern the environmental non-equival- ence of ligand atoms (e.g. methyl groups in acetylacetonates) expected for D (square antiprism) or D2 (dodecahedral) ~ymmetry.2~~ No evidence of geo- metrical isomers was obtained by n.m.r.studies of the tetrakis(trifluoroacety1ace- tonato) derivatives of Zr Hf Ce and Th even at temperatures as low as - 105". z40 E. P. Riedel and R. G. Charles J. Appl. Phys. 1965 36 3954. 155 Quarterly Reviews These studies point to but do not define the stereochemical non-rigidity of octaco-ordinate structures.231 Some of the chelates particularly those based on tropolone and related oxo- bidentate ligands are readily degraded by hydroxide ion. Interestingly as shown by tracer studies in the case of cationic tetrakis(tropolonates) a significant part of the hydrolysis comprises hydroxide ion attack of the chelate structure at a ligand po~ition.2~~ There have been extensive syntheses and physical studies of actinide com- plexes and this enormous area of chemistry cannot be treated in detail in this Review.A review of the co-ordination chemistry of the actinides by C ~ m p ~ and a spectroscopic review by Rabinovitch and B e l f ~ r d ~ ~ ~ provide considerable detail (584 references). In any case there is a large number of actinide complexes particularly uranyl complexes of the type UO,(chel),- that are undoubtedly Table 7 Possible octaco-ordinate uranyl compounds Compound Ligand Ref. ~ ~ ~ 3 ~ ~ 6 H 7 ~ 3 ~ 3 1 3 Acetylacetonate a *M+UOz(CSH70&- Acetylacetonate b c UOZ(C~H$OZF~)%,~HZO (4,4,4-Trifluoro-1-(2-thienyl)-l,3- d Hfruo,(c,o~lloz)31- 3-Tsopropyltropolonate UO2(CpH6NOSO3)3- 5-Sulphonato-8-quinolinolate * M+UOz(HOC 8H4C00)3- Salicylate i NH4UOZ(C 6H 5N202)3 N-Nitrosophenylhydroxylamine ion j KU~Z(CSH~OSZ)~ Ethyl xanthate k KU02(C4H7OS2)3 Tsopropyl xanthate k K[UOP(C~H~~N~,),~,HZO Diethyl dithiocarbamate k rUOz(Cl4Hlo~2N)Pl5 Benzoylnicotinoylmethane ion I U O Z ( C ~ ~ H I ~ ~ Z N ) ~ ( N ~ ~ ) ~ Benzoylnicotinoylmethane ion I UO,(C,,H,z0,),,2.5HzO Dibenzoylmethane ion m U ~ ~ ( N ~ ~ ) Z ~ C S H ~ N O N-Meth ylacet anilide P P ~ O ~ ( N O ~ ) ~ ~ ( C ~ H S O ) ~ O Tributyl phosphate 4 butanedionate] *M+[UOz(CpH,N0)31- 8-Quinolinolate g U0,~(C7Hl,0),POOl,[(C,H,,o),PooHl~ 2-Ethylhexylphosphoric acid h UO,(NO3),,2CH3CN n UOZ(N~~)Z,~CSHCTN 0 HP02(C9H6NO)3 8-Quinolinolate r *M = K NH4 CHaNH, CsHsNH3 H =A.E. Comyns B. M. Gatehouse and E. Wait J . Chern. SOC. 1958,4655; bA. E. Comyns ref. 241 p. 125 132; eK. Hager 2. unorg. Chem. 1927 162 82; dA. E. Comyns ref. 241 p. 125; eD. Dyrssen Acra Chem. Scund. 1956,10 353;fC.F. Richard R. L. Gustafson and A. E. Martell J . Amer. Chem. SOC. 1959 81 1033; eE. P. Bullwinkel and P. Noble jun. ibid. 1958 80 2955; hC. F. Baes jun. R. A. Zingaro and C. F. Coleman J . Phys. Chem. 1958 62 129; {J. T. Barr and C. A. Horton J . Amer. Chem. SOC. 1952 74 4430; 5W. S. Horton J. Amer. Chem. SOC. 1956,78 897; "R. A. Zingaro ibid. p. 3568; ZL. Sacconi and G. Giannoni J . Chem. SOC. 1954 2368; mL. Sacconi G. Caroti and P. Paoletti ibid. 1958 4257; nG. I. Kobyshev and D. N. Suglobov Proc. Acad. Sci. U.S.S.R. Sec. Phys. Chem. 1958 120 325; oJ. T. Barr and C. A. Horton J . Amer. Chem. SOC. 1952 74 4430; PR. Rascanu Ann. Sci. Univ. Jussy 1931,17,70; Chem. Abs. 1933,27,2647; QG. F. Best H. A. C. McKay and P. R. Woodgate J . Znorg. Nuclear Chem. 1957 4 315; rB. G. Harvey H. G.Heal A. G. Maddock and E. L. Rowley J. Chem. SOC. 1947 1010. 341 A. E. Comyns Chem. Rev. 1960,60 115. 943 E. Rabinovitch and R. L. Belford 'Spectroscopy and Photochemistry of Uranyl Com- pounds' Macmillan New York 1964. 156 Muetterties and Wright octaco-ordinate although the data are not definitive. A representative list of these complexes is in Table 7. Possible octaco-ordinate structures are listed in Tables 8 and 9. Table 8 Possible octaco-ordinate compounds with unidentate ligands Compound * ZrCI4,4RNH2 ZrC14,4NH ZrC1,,8NH3 TaC13[NHR],,3NH2R (R = CH, C2Hd PbCI4,4RNH (R = CH n-GH,) TeF,,2N( CHa La13,8DMF Ce(C104),,8DMA Pr(ClO&,,8DMA Pr13,8DMF Nd(C104),,8DMA Nd13,8DMF Sm13,8DMF (R = CH3 CGHJ La( ClO,&,8DMA Gdl,,8DMF ThCl4,4ROH (R = C2H6 n-C4H,) ThC14,4CH3.COC6H6 ThBr4,2CH3COOC2H6 ThBr4,4C6H,CH0 ThBr4,4CH,CN ThCl4,4RNH (R = CH, C,H& Th14,4CH3CN ThC14,4DMA ThT4,4DMA Th(SCN),,4DMA UC1,,4n-C3H,.NH UC14,6N2H2 UC1,,4NMA U12CI,,5DMA U13Cl,5DMA wC14,2.5DMA] [U(NOLJ~,~-~DMAI~ rITh(N03)4,2.5DMAI2 UId,4DMA &At C C C 118 C d 288 e 288 288 e 288 e e 293 f g h h h d i j k 264 k k I 1 k 264 264 264 289 264 6 157 Quarterly Reviews Table Qontinued Compound* Ref3 U(SCN)4,4DMA rn K4Mo(CN)7,2H20 n K3M0(CN)8 237,238 K3W(CN)8 237,238 KS[M~(OH)~(~N)~I,~H~O 0 K4[M o(OH)4(CN)d,4H@ P K3W(OH)4(CN)J Q KdMo(OH)dCN)5(NO)] 0 KdMo(CN)5(OH),] t MOC14,4(C,H&ASO P 4 r [Mo(CN),(CH,CN),(H20)~,4H20 8 Na,MoF 179 u K3MoF 180 K3WF8 179 u [WCO)&I3 227 v Rb,WF 53 K2Re(CN) 8 W K3Re(CN)8 W Ag,[Re(CN),NOI X ReH,l?(C,H5)3l3 106 K,RuF 178 c1(C0)[(C6H5)3P130sHD2a 142 [(c6H,)4As12[c0(02ccFd~ 16 Pd(N03) Y Am03 z Cs2TeF 182 Cs2XeF8 386 K4Th(NCS)8 aa lTh(OCHdJ bb K,PaF 181 IN(CH,)J,PaC1 cc Rb4UWCS) dd K,U(CNS)JH,O dd K4U(CNS)8 rn Na2UFSb 183 Li,UF 181 K2UCIg ee * NMA = N-Methylacetamide; DMA = A"'-dimethylacetamide; DMF = "'-dimethyl- formamide.QSuggested intermediate. *From an analysis of X-ray data; UF co-ordination (U-F = 2.29 A) was established but the geometry is as yet undefined. t For references see Text except as follows CJ. M. Matthews J . Amer. Chem. SOC. 1898 20 815; dE. L. Muetterties and W. D. Phillips ibid. 1957 79 2975; CT. Moeller and V. Galasyn J . Znorg. Nuclear Chem. l960,12,259;fD. C. Bradley M. A. Saad and W. Wardlaw 1 58 Muetterties and Wright J. Chem. SOC. 1954 109; gG. Jantsch and W. Urbach Helv. Chim. Acta 1919 2 490; hR.C. Young J. Amer. Chem. SOC. 1934 56 29; tK. W. Bagnall D. Brown P. J. Jones and J. G. H. du Preeze J. Chem. SOC. 1965 350; jT. Moeller and D. S. Smith U.S. Report Air Force Office of Scientific Research TN-58-559 (1958); kK. W. Bagnall D. Brown P. J. Jones and P. S. Robinson J. Chem. SOC. 1964 2531; 11. Kalnins and G. Gibson J. Inorg. Nuclear Chem. 1958,7 5 5 ; "K. W. Bagnall D. Brown and R. Colton J. Chem. SOC. 1964 2527; nP. C. H. Mitchell and R. J. P. Williams ibid. 1965 4570; OW. P. Griffith J. Lewis and G. Wilkinson ibid. 1959 872; PW. R. Bucknall and W. Wardlaw ibid. 1927 2981 ; qK. N. Mikhalevich and V. M. Litvinchuk J. Znorg. Chem. (U.S.S.R.) 1964,9,1293; X. N. Mikhalevich and V. M. Litvinchuk ibid. 1959 4 800; 8F. Holzl Monatsh. 1927 48 689; tS. M. Horner and S .Y. Tyree Znorg. Chem. 1962 1 947; S. UKatz Zbid. 1964 3 1598; uJ. M. Smith. W. Fellmann and L. H. Jones ibid. 1965,4,1361; WR. Colton R. D. Peacock and G. Wilkinson Nature 1958,182,393; %R. L. Colton R. D. Peacock and G. Wilkinson J. Chem. SOC. 1960 1374; YC. C. Addison and B. G. Ward Chem. Comm. 1966,155; "P. F. Lindley and P. Woodward J. Chem. SOC. ( A ) 1966 123;aaY. Y. Kharitonov A. K. Molodkin and A. V. Babaeva Bull. Acad. Sci. (U.S.S.R.) Div. Chem. Sci. 1964 No. 4 578; bbD. C. Bradley Nature 1958 182 121 1 ; C C D . Brown Colloques Internationaux du Centre National de la Recherche Scientifique Orsay France No. 154 (1965); d d ( a ) V. P. Markov and E. N. Traggeim Zhur. neorg. Khim. 1961 6 2316; (b) V. I. Belova Y. K. Syrkin and E. N. Traggeim Zhur. neorg. Khim. 1964 9,2673; eeK.W. Bagnall D. Brown and J. G. H. du Preeze J. Chem. SOC. 1964,2603. Table 9 Possible octaco-ordinate compounds with multidentate ligands *ZrQ- *Zr(edta)(PDS)2- *Zr(edta)(L)a- bZr(edta)(acac)2- bZr(edta)(L)2- bZr(L)(L')a- Zr(tftac) Zr(tfa~)~ bZr(aca~)~-,(tfac)~ Hf( t fac) *Hf(aca~),-~(tfac)~ T4Ta+ N~(~C~C)~(OC~HD)B TANb+ Ta(acac)3(OC2H6)!4 Ligand (L) Ref. d e Dimethyldithiocarbamate ion 290 107 Dimethyldithiocarbamate ion 290 f f NN-Dihydroxyethylglycinate f N-Hydroxyethyliminodiacetic f Diethylenetriaminepenta-acetic f acid ion acid ion 3,ddisulphonate ion g Disodium 1,8-dihydroxynaphthaIene- g g Citrate ion g N-Hydroxyethylethylenediamine- g h triacetic acid ion oxalate ion 23 1 231.232 231 231,232 i 107 i 107 Dimethyldithiocarbamate ion 290 Oxalate ion i k 1 Oxalate ion m Oxalate ion n 73 0 159 Quarterly Reviews RE(acac),- Na+RE(T,)- b[RE(L)(L')ls- RE(CH,CO,),(o-phen) RE(N03)3(o-~hen)2 bPm(L),- bPm(L),- bE~(L)4- Eu(acac) ,2 H20 ELI( tfac),- Eu(tftac),- Eu( tftac),(o-phen) 'Eu(L)~- Eu(L),- Eu(L),,2pyridine Gd( t ft ac),- Gd(L),- Tb(tftac),- Tb(tftac),(o phen) Tb(L)4- 'M( EDTA),SHZO "m(L),- bTmf Lh- EW)dPFd3 Eu(L)3,2H,O Th(02CC6H5)r bTh(L)4 Th(tftac) Ligand (L) Ref.P 73 73 15 4 r a-Hydroxyisobutyrate ion S t Glycolate S Lactate S t-Butylpenta-lY3-dione ion t 23 1 107 136 229 240 t u v 107 N-Hydroxyethylethylenediamine- triacetic acid ion iminodiacetic acid ion Glycolate Lactate Glycolate 4-Picoline N-oxide ion Hexafluoroacetylacetonate ion Lactate Dibenzoylmethane ion Dibenzoylmethane ion Dibenzoylmethane ion Dibenzoylmethane ion Glycolate a-Hydroxyisobutyrate ion or-Hydroxyisobutyrate ion Oxalate ion y-Isopropyltropolone ion Thiotropone ion 5 Sulphonato-8-quinolinolate ion Diethylenetriaminepenta-acetic acid ion Diethylenetriaminepenta-acetic acid ion trans- 1,2-Diarninocyclohexane- NNN"'-tetra-acetic acid ion l-(o-Arsonophenylazo)-2-naphthol- 3,6-disulphonic acid ion 132 W W S S S 135 136a 138 229 135 135 135 134 229 229 135 229 229 3 S S S X S 261 YY 284 Z aa 107 bb 18 cc 15 dd ee 3- 8- gg hh ii Muetterties and Wright Table 9-continued Comuounda Ligand (L) Ref.ThCj,(o-phen)p ii Pa( t f t a ~ ) ~ 285 kk kk U(==) U( t f a ~ ) ~ KbU(L)4,5H,O Oxalate ion U(edta),ZH,O Np( oxine)4 11 Pu(oxine) 11 Am(oxine) 11 if) UAbbreviations are as follows 1,lO-Phenanthroline (o-phen) disodium-l,2-dihydroxy- benzene-3,5-disulphonate ion (PDS) ethylenediaminetetra-acetic acid ion (edta) acetyl- acetonate ion (acac) 1,l ,l-trifluoropentane-2,4-dione ion (tfac) o-phenylenebisdimethylarsine (diars) phthalocyanine (pc) 8-quinolinolate ion (oxine) thenoyltrifluoroacetone ion (tftac) Rare Earth metal ion (RE) tropolone ion 0; bThese compounds were not isolated.These formulations are based on spectroscopic or potentiometric titration data; = Tb-Lu; * For references see Text except as follows dJ. D. Miller and R. H. Prince J. Chem. SOC. 1965,3185; eD. Dyrssen J. Inorg. Nuclear Chem. 1958,8,291 ;fB. I. IntorreandA. E. Martell J. Amer. Chem. SOC. 1960 82 358; UIdem ibid. 1961,83 3618; hR. E. Connick and W. H. McVey ibid. 1949 71 3182; ‘P. N. Kapoor and R. C. Mehrotra J. Less Common Metals 1965,8 339; jM. C. Steele Austral.J. Chem. 1957,10 368; kJ. E. Fergusson W. Kirkham and R. S. Nyholm ‘Rhenium’ Elsevier Amsterdam 1962 pp. 36-44; U. E. Fergusson and R. S . Nyholm Chem. and 2nd.. 1958 1555; mR. Charonnat Ann. Chem. 1931 16 186; nM. Platsch 2. anorg. Chem. 1899 20 308; OW. J. Kroenke and M. E. Kenney Inorg. Chem. 1964,3,251; PK. Ramaiah and D. F. Martin Chem. Comm. 1965 130; QL. Pokras and P. M. Bernays J. Amer. Chem. SOC. 1951,73 7; rL. Pokras M. Kilpatrick and P. M. Bemays ibid. 1953 75 1254; 8L. W. Holm G. R. Choppin and D. Moy J. Inorg. Nuclear Chem. 1961 19,251 ; tJ. S. Brinen F. Halverson and J. R. Leto J. Chem. Phys. 1965,42 4213; uM. L. Bhaumik ibid. 1964,40,3711; 1964,41,574; WG. H. Dieke H.M. Crosswhite and B. Dunn J. Opt. SOC. Amer. 1961 51 820; wF. A. Hart and F. P. Laming J. Inorg. Nuclear Chem.1965 27 1605; ZW. W. Wendlandt Analyt. Chem. 1957 29 800; VJ. P. Phillips J. F. Emery and H. P. Price ibid. 1952 24 1033; “(a) G. N. Wyrouboff and A. Verneuil Ann. Chim. phys. 1905,6,441; (6) F. A. Johnson and E. M. Larson Inorg. Chem. 1962 1 159; aaD. C. Madigan J. Appl. Chem. 1959 9 252; bbD. Dyrssen Acta Chem. Scand. 1955 9 1567; CcH. Iinuma J. Chem. SOC. Japan 1943 64 742; ddRef. f Table 7; eeG. H. Carey R. F. Bogucki and A. E. Martell Inorg. Chem. l964,3,1288;ffR. F. Bogucki and A. E. Martell J. Amer. Chem. SOC. 1958,80,4170; Sfl. H. Seu S. Wu and T . Chuang J. Inorg. Nuclear Chem. 1965 27 1655; hhH. Brintzinger H. Thiele and U. Muller Z. anorg. Chem. 1943 251 285; a‘A. R. Palmer Analyt Chim. Acta 1958 19 458; jjB. W. Fitzsimmons P. Gans B. C. Smith and M. A. Wassef Chem.and Ind. 1965 1698; kkH. Gilman R. G. Jones E. Bindschadler D. Blume G. Karmas G. A. Martin jun. J. F. Nobis J. R. Thirtle H. L. Yale and F. A. Yoeman J. Amer. Chem. SOC. 1956 78 2790; 43. H. Eberle and C. Keller Angew. Chern. Internat. Edn. 1965 4 971. D. Nonaco-ordination Nonaco-ordinate structures are fairly common in molecular complexes and in ionic lattices of the larger lanthanide and actinide ions. There are a number of idealised ground-state geometries for hepta- and octaco-ordinate structures but only one polyhedron has been reported for nonaco-ordinate molecular com- plexes. The polyhedron is the symmetrically tricapped trigonal prism (D3 J. (This polyhedron devoid of a central atom may be present inBiSS+.243) Interestingly this geometry is uniquely defmed by hybridisation of one s three p and five d orbitals.The only other reasonable polyhedron and one observed in metal cage compounds and in certain metal tellurides and arsenides is the monocapped a48 A. Hershaft and J. D. Corbett Inorg. Chem. 1963,2,979. 161 Quarterly Reviews square antiprism (C,,) which can be generated from the trigonal prism by rela- tively small distortions (Plates 7 and 8). The monocapped square antiprism should also be observed for some molecular nonaco-ordinate species in the solid state because packing forces may favour this less symmetrical polyhedron in some instances. Reorganisation energy for going from an octaco-ordinate square antiprism or dodecahedron to a nonaco-ordinate trigonal prism or monocapped square antiprism should be very small (see Plate 1).There are data that bear on the ease of distortion of nonaco-ordinate geo- metries. In the polyhedral B,H:- ion the nine boron atoms describe a Dsh tricapped trigonal prism in the solid state. For the solution state of B9H:- the llB n.m.r. data rigorously rule out the C, model and are wholly con- sistent with the D3h tricapped trigonal prism.244 Since the B polyhedron lacking a central atom is generated primarily by B-B attractive forces it is intrinsically a stereochemically more rigid structure than an MX co-ordination structure. Two of the most extraordinary nonaco-ordinate molecular species are TcH,2- and ReH,2-. Three-dimensional X-ray analysis and neutron diffraction studies*~ established the capped trigonal prismatic structure for ReH2- (Re-H = 1-68 A). This ion had previously been characterised as Re* then ReHZ- and then ReH,2-.The technetium ionlo is isostructural with ReH,2-. It will be interesting to see if this heavy-metal hydride chemistry extends to other metals in the transition group. Nonahydration is quite common for the tervalent rare-earth ions. Ketelaar245 first suspected a trigonal prismatic arrangement for M(OH&,3+ after an X-ray examination of the nonahydrated ethyl sulphates of yttrium and several rare earths including lanthanum and dysprosium. Later H e l m h ~ l z ~ ~ ~ in a now classic X-ray study established such a polyhedron for Nd(OH2),3+ in Nd(OH,),(BrO,),. The Nd-0 bond distances were 2.51 8 for the three central bonds and 2.47 for the outer six; the difference in bond distances was within experimental error. The trigonal prism of M(OH&?+ in the erbium yttrium and scandium ethyl sulphates [M(C,H,S0,)3,9H,0] was confirmed by Fitzwater and R ~ n d l e .~ ~ In the erbium compound the six M-O distances to the corners of the prism are 2-37 A and the remaining three are 2.52 A. Not all hydrated rare-earth ions are necessarily nonaco-ordinate; Hoard Lee and Lind3 point out that there is probably an equilibrium between M(OH,),3+ and M(OH2),3+ ions in solution and that the average hydration number is closer to nine for La3+ and probably closer to eight for the last member of the series Lu3+Fb which is significantly smaller (by 0.213 A). Lanthanide hydration numbers have not been rigorously established for the solution state. Some of the large bivalent metal cations are also nonahydrated at least in the crystalline state.Strontium chloride hexahydrate which is typical of the alkaline earth halide hydrates has a columnar structure (two-dimensional X-ray 244 F. Klanberg and E. L. Muetterties Inorg. Chem. 1966 5 1955. 246 J. A. A. Ketelaar Physica 1937 4 619. 246 L. Helmholz J . Amer. Chem. Soc. 1939 61 1544. a47 D. R. Fitzwater and R. E. Rundle Z. Krist. 1959 112 362. 162 Muetterties and Wright with strontium atoms coplanar with three water-oxygen atoms at 2.80 A and the strontium atom are connected through trigonally arranged bridging oxygen atoms of water molecules at 2.62 A. The co-ordination polyhe- dron is the tricapped trigonal prism. Lanthanide trihydroxides also have a trigonal prismatic grouping; in this case the nonaco-ordinate unit is M(OH),6-. The isostructural series includes the trihydroxides of La Pr Nd Sm Gd and Dy.Surprisingly the very small lanthanide ions E?+ and Ybw are also reported to be nonaco-ordinate in the hydroxide lattices.MQ Nonaco-ordination with symmetrically tricapped trigonal prismatic geometry is found in a large number of ionic lattices of the lanthanide and actinide as well as large bivalent metal halides. A partial list of these nonaco- ordinate structures is in Table 10. The rubidium ion in RbCdC1 is nonaco- ordinate.250 The capped trigonal prism is also found in complex metal fluorides. In hexagonal NaNdF, there are two Nd3+ sites and in each site the Ndw ions are co-ordinated to nine fluorine atoms with near D3h symmetry for the poly- h e d r ~ n . ~ ~ ~ One prism is smaller than the other; the average Nd-F distances are 2.377 A and 2.426 A for the twe sites.NaLaF and NaCeF are probably iso- structural.261 X-Ray data also indicate an isostructural relationship of NaCaMF (M = rare earth or yttrium tervalent ion) and NaYF to NaNdF,.251-253 The hexagonal rare-earth trifluoride lattices (Tysonite) have nine fluorine atoms within bonding distance of the metal atoms; the space-group is P’3 ~ 1 . ~ ~ The co- ordination polyhedron is quite irregular. Zachariasen presents arguments (intensity calculations or consideration of interatomic distances) for nonaco- ordination in the lattices of the following actinide halides UC13(U-9CI = 2.96 A) /3,-Na,ThF6(Th-9F = 2-41 A) p2-K2UF6 p2-Na2UF, Pl-K2UF (U-9F = 2.73 A) and U2F,(U-9F = 2.31 A).2229255 In K,PaF each protac- tinium atom is surrounded by nine fluorine atoms which approximate the vertex positions of a tricapped trigonal prism; the Pa-F distances range from 2.19- 2.46 A?5s Nonaco-ordination has also been established3 in a rare-earth chelate KLa(OH&[(OCCH&2NCH2CH2N(CH2CO)J,5H20.(Isomorphous with this complex are the potassium salts of the La Nd and Gd chelates the sodium salts of La Nd Tb Gd and Er and the ammonium salts of Nd and Gd.3 The co-ordination polyhedron in the terbium complex is isostructural with the lan- thanum complex. The distances are Tb-N 2.665 A Tb-0 2.377 A and Tb-Owater 2.481 The co-ordination polyhedron is defined by the six 248 A. T. Jensen Kgl. danske Videnskab. Selskab Mat.-fys. Medd. 1940,17 No. 9 1. 249 K. Schubert and A. Seitz Z. anorg. Chem. 1947 254 116. 193. 251 J. H. Burns Inorg. Chem.1965 4. 881. a52 B. P. Sobolev D. A. Mineev and V. P. Pashutin Kristallografiya 1963 8 545. 253 A. A. Voronkov N. G. Shumyatskaya and Yu. A. Pyatenko J. Struct. Chem. (U.S.S.R.) 1962 3 665. 254 A. Zalkin D. H. Templeton and T. E. Hopkins Inorg. Chem. 1966 5 1466. 255 W. H. Zachariasen Acta Cryst. 1949 2 390. 256 D. Brown and A. J. Smith Chem. Comm. 1965 554. C. H. MacGuillavry H. Nijveld S. Dierdorf and J. Karsten Rec. Trav. chim. 1939,58 163 Table 10 Non-molecular structures with nonaco-ordinate metal atoms Co-ordination Co-ordinationa 5 Class Compound group polyhedron Bond distance (A) UCls M(z)@ TCTP UCIs 9U-C1= 2-96 MC18 MBr M(OH)s MFs (M = La-Gd Ac U Np Pu Am) (M = La Ce Pry Ac U a-Np) (M = La Pry Nd Sm Gd Dy Er) (M = La-Nd Sm Eu Ho Tm Ac ma MOO TCTP Pbcl TCXP U-Am) PbCls 9Pb-CI = 2.8-3.5 Pb(O€l)Cl Pb(OH)4(C1) 5 2Pb-OR = 2.67,2Pb-OH = 2.93 PbBr SPb-Cl = 3.23 PbFa BaXt' EuCl SmCl ThSt 9Th-S = 2.95 ThSe US BiOCl BiOBr 4Bi-0 = 2.31 4Bi-Cl = 3.07 4Bi-0 = 2.32.4Bi-Br = 3.18. Bi-Cl = 3.49 NaCa(RE)Fl* NaNdF NaMF SrC1,,6H20 SrCI,,GH,O TCTP TCTP TCTP P 8 Ref.* 5 222 i3 249 s 222 222 e 224 164 f g h h h h h i k 4 4 i Bi-Br = 3-92 6(RE,Ca-F) = 2.39 3(RE,Ca-F) = 2.30253 6Nd-F = 2.426,3Nd-F = 2.377 25 1 (M = La-Nd Eu-Er Y Sm Tm Dy) 251 6Er-0 = 237 3Er-0 = 2-52 247 6Y-0 = 2.37 3Y-0 = 2.55 247 6Pr-O = 2.47 3Pr-0 = 2.65 247 M = La-Sm Gd Dy 245 Sr-0 = 2.62 Sr-0 = 2.80 248 252 Table 10 Non-molecular structures with nonaco-ordinate metal atoms Co-ordination Co-ordinationa 5 Class Compound group polyhedron Bond distance (A) UCls M(z)@ TCTP UCIs 9U-C1= 2-96 MC18 MBr M(OH)s MFs (M = La-Gd Ac U Np Pu Am) (M = La Ce Pry Ac U a-Np) (M = La Pry Nd Sm Gd Dy Er) (M = La-Nd Sm Eu Ho Tm Ac ma MOO TCTP Pbcl TCXP U-Am) PbCls 9Pb-CI = 2.8-3.5 Pb(O€l)Cl Pb(OH)4(C1) 5 2Pb-OR = 2.67,2Pb-OH = 2.93 PbBr SPb-Cl = 3.23 PbFa BaXt' EuCl SmCl ThSt 9Th-S = 2.95 ThSe US BiOCl BiOBr 4Bi-0 = 2.31 4Bi-Cl = 3.07 4Bi-0 = 2.32.4Bi-Br = 3.18. Bi-Cl = 3.49 NaCa(RE)Fl* NaNdF NaMF SrC1,,6H20 SrCI,,GH,O TCTP TCTP TCTP P 8 Ref.* 5 222 i3 249 s 222 222 e 224 164 f g h h h h h i k 4 4 i Bi-Br = 3-92 6(RE,Ca-F) = 2.39 3(RE,Ca-F) = 2.30253 6Nd-F = 2.426,3Nd-F = 2.377 25 1 (M = La-Nd Eu-Er Y Sm Tm Dy) 251 6Er-0 = 237 3Er-0 = 2-52 247 6Y-0 = 2.37 3Y-0 = 2.55 247 6Pr-O = 2.47 3Pr-0 = 2.65 247 M = La-Sm Gd Dy 245 Sr-0 = 2.62 Sr-0 = 2.80 248 252 Table 10 Non-molecular structures with nonaco-ordinate metal atoms Co-ordination Co-ordinationa 5 Class Compound group polyhedron Bond distance (A) UCls M(z)@ TCTP UCIs 9U-C1= 2-96 MC18 MBr M(OH)s MFs (M = La-Gd Ac U Np Pu Am) (M = La Ce Pry Ac U a-Np) (M = La Pry Nd Sm Gd Dy Er) (M = La-Nd Sm Eu Ho Tm Ac ma MOO TCTP Pbcl TCXP U-Am) PbCls 9Pb-CI = 2.8-3.5 Pb(O€l)Cl Pb(OH)4(C1) 5 2Pb-OR = 2.67,2Pb-OH = 2.93 PbBr SPb-Cl = 3.23 PbFa BaXt' EuCl SmCl ThSt 9Th-S = 2.95 ThSe US BiOCl BiOBr 4Bi-0 = 2.31 4Bi-Cl = 3.07 4Bi-0 = 2.32.4Bi-Br = 3.18. Bi-Cl = 3.49 NaCa(RE)Fl* NaNdF NaMF SrC1,,6H20 SrCI,,GH,O TCTP TCTP TCTP P 8 Ref.* 5 222 i3 249 s 222 222 e 224 164 f g h h h h h i k 4 4 i Bi-Br = 3-92 6(RE,Ca-F) = 2.39 3(RE,Ca-F) = 2.30253 6Nd-F = 2.426,3Nd-F = 2.377 25 1 (M = La-Nd Eu-Er Y Sm Tm Dy) 251 6Er-0 = 237 3Er-0 = 2-52 247 6Y-0 = 2.37 3Y-0 = 2.55 247 6Pr-O = 2.47 3Pr-0 = 2.65 247 M = La-Sm Gd Dy 245 Sr-0 = 2.62 Sr-0 = 2.80 248 252 OI Table 10-continued Class BaCIz,H20 Nd(Br03),9Ha0 PbFCl Compound SrXz b,6H20 CaXsb,6HZO Ba12,6H20 BaC12,Hz0 Nd(Br03),9H20 NdCla99H2O Co-ordination Co-ordinationa polyhedron Bond distance (A) group 7Ba-Cl = 3-25,2Ba-OH = 2-76 Ba(C1),(OH2)2 MOI20)0 TCTP 6Nd-0 = 2-47 3Nd-0 = 2.51 TCTP 9K-F = 2.73 9Th-F = 2.38 9K-F = 2.73 9U-F = 2.36 9U-F = 2.31 9Th-F = 2-40 6ThI-S = 3.07 3ThI-S = 2.82 TCTP m1(s)6(s)3 M(Z)4(Z')5 CSPA Pb(F),(Cl),Cl Th(O),(S)5 4Th-0 = 2.40 5Th-S = 3.00 Ref.* 248 248 248 t 246 246 5 t t 293 U 222 255 255 40 38 222,255 222 V 222,255 c; 2 255 9' -Y 2 182 1 1 m 1 - w 8 Table 10-continued class Compound uos NpOS AcOCl AcOBr PUOCl PuOBr YOCl YOBr LaOCl LaOBr SmOCl HoOCl REOClb REOBrb Co-ordination Co-ordination" group polyhedron Bond distance (A) 4NpO = 232,SNp-S = 2.91 4U-0 = 2.34 5U-S = 2.93 4La-O = 2-39 4La-Cl = 3-18 4La-O = 2.40 4La-Br = 3.28 4Sm-0 = 2.30,4Sm-C1 = 3.11 4Ho-0 = 2.25,4Ho-C1 = 3.05 L a 4 = 3-14 La-Br = 3.49 Sm-Cl = 3.09 Ho-Cl = 3.04 Ref.* ki i 2 i 2 164 s 164 164 164 164 n 0 0 P P 164 n 164 n "Tricapped trigonal prism (TCTP) monocapped square antiprism (CSPA); bX = C1 Br I; CRare Earth metal ion (RE); dPossibly iso- morphous with ,B,-Na,ThF,; * For references see Text except as follows eD. H. Templeton and C. H. Dauben J. Amer. Chem. SOC. 1954 76 5237; fH. Braekken 2. Krist. 1932 83 222; BH. Brasseur Bull. SOC. Roy. Sci. LiZge 1940,9,166; hW. Doll and W. Klemm Z. anorg. Chem. 1939,241,239; tW. H. Zachariasen Actu Cryst.l949,2,291;jR. W. M. D'Eye P. G. Sellman and J. R. Murray J. Chem. SOC. 1952 2555; kE. D. Eastman L. Brewer L. A. Bromley P. W. Gilles and N. L. Lofgren J. Amer. Chem. SOC. 1950 72 4019 ZW. H. Zachariasen Actu Cryst. 1949 2 288; mW. Nieuwenkamp and J. M. Bijvoet 2. Krist. 1932 81 469; "1. Mayer S. Zolotov and F. Kassierer Inorg. Chem. 1965 4 1637; OL. G. Sille'n and A. L. Nylander Svensk kem. Tidskr. 1941,53 367; PD. H. Templeton and C. H. Dauben J. Amer. Chem. SOC. 1953 75 6069; gL. G. Sill6n Svensk kern. Tidskr. 1941,53,39; rB. K. Veinstein and Z. G. Pinsker Zhur. fiz. Khim. 1949 23 1058; SR. Fitzwater and R. E. Rundle U.S. Atomic Energy Commission Report ISC-241 (1952); W. I. Iverovna V. P. Tarasova and M. M. Umanskii Izvest. Akad. Nauk S.S.S.R. Ser. Fiz. 1951 15 164; *H.Lambot Bull. SOC. Roy. Sci. Lie'ge 1943 12 439; VL. A. Harris Actu Cryst. 1960 13 502. Muetterties and Wright donor atoms of the ethylenediaminetetra-acetate ion and three water oxygen atoms. Because of the spatial limitations imposed by the ligand the geometry does not closely approximate the trigonal prism; Figure 3 1 illustrates geometry and relevant bond distances. Hoard Lind and Lee3b suggest that in this anionic lanthanum complex decaco-ordination will prevail in solution and that decaco- ordination will extend to analogous complexes of Ce3+ to Gd3+ inclusive. Bohigian and M~te11~~' suggest that the triethylenetetraminehexa-acetic acid derivative of thorium(rv) is either a nona- or deca-co-ordinate complex. There is a tris- (tetrahydrofuran) solvate of tris(dipyridy1)yttrium that might be a nonaco- ordinate structure.258 Fig.31 Structure of lanthanum(rrr) trihydrate ethylenediaminetetra-acetate complex in KLa(ethylenediaminetetra-acefate),(OH~,,5H,O (ref. 3). It has been suggested that in sodium guanidinium trisulphatothorium hexa- hydrate the thorium is nona~o-ordinate~~~ with three water molecules at the square pyramidal vertices and six sulphato-groups (which bridge co-ordination polyhedra) at the trigonal vertices of a tricapped trigonal prism. In K2Th(S04)4,2H20 the thorium is surrounded by two water oxygen atoms and seven sulphato-oxygen atoms of which two come from the same sulphato- Octaco-ordinate thorium chelates clearly show acceptor character and there are specific reports of a dimethyl sulphoxide adduct of tetrakis(tropo1ono)- thorium1* and an acetic acid adduct of tetrakis(thenoyltrifluoroaceto)thorium.261 There is also a series of thorium and uranium(rv) halide or perchlorate complexes with donor molecules such as amides but there is no definitive datum as to the molecularity of these species.262-264 Thorium(1v) nitrate forms a complex with two tributylphosphine l i g a n d ~ .~ ~ ~ Since the nitrate groups appear to be bidentate this could be another example of decaco-ordinate thorium. Nonaco-ordination is also found in complex intermetallic structures. An group -259 260 257 T. A. Bohigian jun. and A. E. Martell Znorg. Chem. 1965,4 1264. 258 S. Herzog and K. Gustav Z. Naturforsch. 1962 17b 62. 25D A. K. Molodkin G. A. Skotnikova and E. G. Arutyunyan J . Znorg. Chem. (U.S.S.R.) 1964 9 1458.260 E. G. Arutyunyan and M. A Porai-Koshits J. Struct. Chem. (U.S.S.R.) to be published. 262 K. W. Bagnall D. Brown and A. M. Deane J. Chem. SOC. 1962 1655. 263 K. W. Bagnall A. M. Deane T. L. Markin P. S. Robinson and M. A. A. Stewart J. Chem. SOC. 1961 1611. 264 K. W. Bagnall D. Brown P. J. Jones and J. G. H. DuPreez J . Chem. SOC. 1965,3594. 265 J. R. Ferraro A. Walker and C. Cristallini Inorg. Nuclear Chem. Letters 1965 1 25. G. Goldstein 0. Menis and D. L. Manning Analyt. Chem. 1960 32 400. 167 Quarterly Re views example is NiBi which Zhdanov266 claims from analysis of diffraction data has an Ni(Ni,Bi,) co-ordination polyhedron approximating the tricapped trigonal prism. A preliminary report of the structure of NbS,Br and NbS,Cl indicates nonaco-ordination for the niobium atoms (Figure 32).267 There may be nonaco- ordinate thorium atoms in some of the thorium-sulphur (e.g.Th,S,,) and thorium-selenide phases. In LaTe and NdTe, each metal atom is surrounded by nine tellurium atoms which roughly describe a monocapped square anti- prism.2sg The La-Te distances in LaTe range from 3.26-3.38 A. Isostructural with the tellurides is Fe2As.269 Fig. 32 Niobium co-ordination polyhedron in NbS2C1 (ref. 267). Fig. 33 The Mo,,CI,~+ polyhedron in the Mo,CI,,~- anion; each molybdenum atom has a terminal chlorine atom within bonding distance (ref. 270). Two other kinds of nonaco-ordinate geometry are found in metal cages or clusters. These geometries are defined by the complex polyhedron of metal atoms and ligands. One is represented by the Mo6CI,G+ framework in which the metal atoms describe an octahedron and the chlorine atoms which bridge these metals describe a cube (Figure 33).270 To this framework six relatively labile ligands take terminal bonding positions to the metal atoms.These terminal ligands are of the type halide ions (as in Mo6Cl,2- and MO6ClgBr;-) hydroxide ion water and organic donor molecules such as pyridine and triethy- lamine.271-253 In these polyhedra the metal atom is within bonding distance of 3 8 0 Cl Mo Cl cr 288 G. S. Zhdanov Academy Sciences (U.S.S.R.) 1954 10 99; Chem. Abs. 1956 SO 2234d. 287 H. G. Schnering W. Beckmann and H. Schafer see ref 21 p. 842. 268 R. Wang H. Steinfink and W. F. Bradley Inorg. Chem. 1965,5 142. 269 A. F. Wells ‘Structural Inorganic Chemistry’ 3rd edn. Oxford University Press London 1961 p.520. 270 C. Brosset Arkiv Kemi. Min. Geol. 1946 22 A 1. 271 J. C. Sheldon J . Chem. SOC. 1960 3106. 272 J. C. Sheldon J. Chem. SOC. 1960 1007. 279 C. Brosset Arkiv Kemi 1949 1 3 5 3 . 168 Muetterties and Wright four other metal atoms four cage halide ions and one terminal ligand to give a monocapped square antiprismatic co-ordination polyhedron as in (1 5 ) with a ninth site directed up out of the plane of the paper from the central position. This polyhedron devoid of a central atom may prevail in B,CI,H or B,C1,H2-.274 Other metal (e.g. tungsten)-halogen systems may have analogous cage struc- tures. Moreover the curious (n-C6H6)6Mn6(NO)B is isoelectronic with MO,CI,,~- and probably has Mn6 octahedra with a cubic array of bridging 3 NO groups.276* The second class of metal cage structure with nonaco-ordinate metal atoms is typified by the Ta6C1,;+ structure in which the metal atoms again form an octahedron (edges are - 2.9 A) but the halogen atoms are at the mid-edges of a cube (Figure 34).276 Again a labile ligand site is probably tangential to the cube Fig.34 The Ta6Cl12a+ polyhedron. In solution each tantalum atom is probably terminally attached to a water molecule (ref. 276). Four of the chlorine atoms are omitted for clarity. faces as in Ta6C1,,(OH2)~+ and Nb,CI12(OH2)62+. The co-ordination poly- hedron for the metal atoms is a monocapped cube (16). This type of structure is found in (Nb6Ts)I,, (the %,I polyhedron is distorted from Oh to Ci sym- metry through shifts of two apical niobium atoms away from the line normal to the plane of the four other niobium atoms277) (Nb6CI12)C12 ("a6112)12 Ta6Br12(OH2)62+ va6c112)cI, (Ta6Br12)Br2~ fl@r12)Br3 and (Ta6Br12) Recent X-ray and molecular weight data by F.A. Cotton et. al. show a composition 274 J. A. Forstner T. E. Haas and E. L. Muetterties Inorg. Chem. 1964 3 155. 276 R. B. King and M. B. Bisnette Inorg. Chem. 1964 3 791. 276 P. A. Vaughan J. H. Sturdivant and L. Pauling J. Amer. Chem. Soc. 1950 72 5477. L. R. Bateman J. F. Blount and L. F. Dahl J. Amer. Chem. Soc. 1966 88 1082. (n-C,HJSMn,(NO),. 1 69 Quarterly Reviews Br6?1,277-280 The tantalum and niobium polyhedral cations appear to undergo two-electron oxidations.281 The reported Ir6114 may be isostructural with (Ta611& and contain nonaco- ordinate iridium atoms.282 E. Decaco-ordination Decaco-ordination in molecular complexes is found or seriously suspected only for lanthanide or actinide-metal complexes.This may be fortuitous but only for these metal ions can$-orbital overlap be reasonably considered and a valence- bond representation of decaco-ordination would utilise f orbitals. On the other hand a multicentre-bond molecular orbital approximation would obviate invocation of f-orbital participation. Actually f-orbital overlap in decaco- ordinate complexes is necessarily real on symmetry grounds alone; however the magnitude of the overlap integral is at this stage simply a matter of conjecture. Size of the metal ion as well as compactness of ligands is obviously important if a high-co-ordination polyhedron is to be generated. Accordingly the earlier members of the lanthanide and actinide series are the most favourable candidates for decaco-ordination because of the severe ion contractions with increasing numbers off electrons.This is illustrated in Figure 1 in which ionic radii are plotted against atomic number; a few other large metal ions particularly the alkaline earth bivalent ions are included for reference. High oxidation state also favours maximum co-ordination number but this must often be compromised because of the tremendous decrease in ionic radius with ionic charge e.g. compare Ce4+ with Ces+ in Figure 1. Decaco-ordination has been rigorously established for only one complex. A three-dimensional X-ray analysis4 of La[(02CCH2),NCH2~CH2N(CH,C0,H)- CH2C0],4H,0 shows two nitrogen atoms four carboxylic-oxygen atoms and four water-oxygen atoms within bonding distance of the lanthanum atom.Geometry is defined primarily by the constraints of the sexadentate ligand. The lanthanum atom is slightly above the six donor atoms of the chelate leaving adequate room for co-ordination of the four water molecules. The structure is presented in Figure 35 with pertinent bond distances. This lanthanum example provides no information about preferred ground-state geometry for decaco- ordination because of distortion arising from the chelate moiety. A decaco- ordinate complex with all ligands identical is required and none is known. Possible models for such polyhedra are the symmetrically bicapped square antiprism (D4 d) (established for the B,,H1,2- polyhedron which has no central atom) and a bicapped dodecahedron (C,) which are generated from the two common polyhedra for octaco-ordinate structures and are of proper symmetry 278 R.E. McCarley and J. C. Boatman Znorg. Chem. 1965,4 1486. 279 P. J. Kuhn and R. E. McCarley Znorg. Chem. 1965 4 1482. 280 A. Simon H. G. Schnering H. Wohrle and H. Schiifer Z. anorg. Chem. 1965 339 155. R. E. McCarley B. G. Hughes F. A. Cotton and R. Zimmerman Inorg. Chern. 1965 4 1491. 282 S. F. A. Kettle Nature 1965 207 1384. 1 70 Muetterties and Wright Fig. 35 Structure of the decaco-ordinate lanthanum atom in La[(O,CCHz),NCH,CHz*N- (CH&OZH)CH,COe],4Ho0 (ref. 4). for an sp3d5fhybrid model. The disparities and similarities of these two poly- hedra are reflected in Plates 9 and 10. Both polyhedra are easily generated from the tricapped trigonal prism the idealised model for nonaco-ordination.Re- organisation energy for either conversion should be small. Professor Hoard in a personal communication has noted that the D4d bicapped square antiprism is not an unreasonable model on steric grounds but it is definitely less favourable than the D3h nonaco-ordinate and Ih dodecaco-ordinate models. With a bond distance of 2.40 A the eight pyramidal edges and eight zig-zag edges are 2.60 A and the square edges are long 3.09 A. The radius-ratio is 0-848 which is two- thirds of the way from the value of 0-732 for the D3h nonaco-ordinate model and 0.905 for the eicosahedron. In a pentakis-bidentate chelate such as the Th(trop01onate)~- ion described below the preferred stereoisomers for the chelate based on a bicapped square antiprism model and the 2-58 A ‘bite’ of the tropolone ion would have no square edges bridged by a tropolone ion.The tropolone anion (4) forms decaco-ordinate complexes18 with Th4+ and U4+. Stability of the anionic complexes M(0,C7H5)5- is only modest outside of the crystalline state of the alkali-metal salts. The anionic complex dissociates in polar media but not in non-polar solvents. Even in the solid state packing considerations loom significant and crystalline salts are obtained only with the smaller alkali-metal ions. This is most apparent for U(02C,H,),- where only lithium salts have been isolated. Multivalent ions of do configuration e.g. Hf4+ and Taw do not complex tropolone ion beyond the tetrakis stage. Another apparent decaco-ordinate chelate is the thorium derivative of tri- ethylenetetraminehexa-acetic a ~ i d . 2 ~ ~ Some of the octaco-ordinate thorium chelates tend to be complexed with solvent e.g.the bis-acetic acid complex of tetrakis(thenoyltrifluoroaceto)thorium(Iv),261 and these may be decaco-ordinate. Additionally some of the tetrakis-bidentate chelates of thorium separate from solution with an extra molecule of the parent ligand in the protonated form. This is particularly characteristic of the chelates derived from 8-hydroxyquinoline and its derivatives. The additional molecule of 8-hydroxyquinoline can be removed at high temperature in a These complexes may be decaco-ordinate in the solid state; however they appear to dissociate in solution but here the solvent may be displacing 8-hydroxyquinoline to give either a p83 T. Moeller and M. V. Ramaniah I . Amer. Chem. SOC. 1954,76 2022.2a4 W. W . Wendlandt Analyt. Chem. 1956,28,499. 171 Quarterly Reviews nona- or deca-co-ordinate species f.e. Th(~hel)~(solvent) or a. There is also a report of a pentakis(thenoy1trifluoroacetone) derivative of protactinium(~v).~*~ Salts of the pentakis(carbonato)thorium ion Th(C03),g- and of MO(CO,),~- have been isolated and these may have five chelating carbonato-groups arrayed about a central metal atom.286,287 There are many reports of lanthanide and actinide complexes that might be decaco-ordinate at least in the solid state but no definitive structural data are available. For example there is a large number of amide and phosphine oxide complexes of the type La(C104)3,8CH,CON(CH3)2 Er(C104),,7- and Th14,6CH,CON(CH3)2.262-2M~288~289 The actinide complexes have been shown to ionise in polar organic solvents like acetonitrile and nitromethane; degree of ionisation is often a function of concentration and of time.There is a preliminary report of a curious pentakis(dimethyldithiocarbonamato)tantalum(v) compound but no structural or spectral data were presented.290 It has been reported that in the presence of hexamethylenetetramine the salts of many bivalent ions tend to separate from aqueous solution with ten molecules of water. The formation of these complexes e.g. BaC12,[(CH~,N~,,10H20 has been ascribed to stabilisation by hexamethylenetetramine of high-hydration forms of the inorganic salts. An X-ray examination291 of the calcium salt how- ever established that the calcium ion is simply octahedrally co-ordinated to six oxygen (water) atoms. CH,*CON(CHJ, U(C104)4,6CH3CON(CH& U(NOJ4,2.5CH3CON(CH& F.Undecaco-ordination Eleven-atom polyhedra are not to our knowledge very common in inorganic chemistry and this probably reflects the fact that there are no particularly good idealised models for an eleven-atom polyhedron. The lower stabilities of idealised undecaco-ordinate polyhedra relative to the more favourable polyhedra for deca- and dodeca-co-ordination contribute to the dearth of eleven-atom co- ordination complexes. Recently Ueki Zalkin and T e m p l e t ~ n ~ ~ ~ ~ concluded from a three-dimensional X-ray analysis of Th(NO3),,5H2O that the crystals are orthorhombic and that the thorium atom is within bonding distance of eleven oxygen atoms three from water molecules and eight from four nitrate groups which function as bidentate ligands.The light-atom positions were also charac- terised in a neutron diffraction study;292b the average bond distances are 2-46 for thorium to oxygen in the bound water molecules and 2.57 for the thorium- 285 G. Bouissitres and J. Vernois Compt. rend. 1957 244 2508. x86 I. I. Chernyaev V. A. Golovnya and A. K. Molodkin J. Inorg. Chem. (U.S.S.R.) 1958 3 100. 287 M. C. Steele Austral. J. Chem. 1957 10 367. 289 K. W. Bagnall P. S. Robinson and M. A. A. Stewart J. Chem. Suc. 1961,4060. ego S. E. Rasmussen and N. C. Broch Chem. Comm. 1965 289. 291 P. DeSantis A. L. Kovacs A. M. Liquori and L. Mazzarella J. Amer. Chem. SOC. 1965 87 4965. 292 (a) T. Ueki A. Zalkin and D. H. Templeton Actu Cryst. 1966 20 836; (b) J. C. Taylor M. H. Mueller and R. L. Hitterman ibid. p. 842.T. Moeller and G. Vicenti J. Inorg. Nuclear Chem. 1965 27 1477. 1 72 Muetterties and Wright oxygen distances in the nitrate interactions. The polyhedron itself cannot readily be described as any particular polyhedron but Taylor Mueller and H i t t e m ~ a n ~ ~ ~ ~ point out that if the nitrate interactions are considered as single entities rather than bidentate functions the geometry approximates the NbF,2- mono-capped trigonal prism (C2w). The low symmetry (C& of ligand atoms about the thorium atom may reflect distortions due to packing effects or to the very short ‘bites’ of the nitrate group. Multidentate ligands can impose serious distortions on an idealised geometry in co-ordination chemistry Eleven-atom polyhedra are found extensively among boron hydrides. Examples of these are B,C2HI1 and its derivatives wherein nine boron atoms and two carbon atoms comprise the polyhedron with exopolyhedral BH bonds.The crystal structure of this ‘carborane’ series has been determined for the bis-dimethyl (C substitution) derivative (personal communication from Professor Hawthorne) and in Plate 11 the B,C2 polyhedral array is compared with a stick model of the thorium eleven-atom co-ordination complex. The B,,HIl2- ion of Klanberg and Muet- terties may be isostructural with the B9C2 carboranes. As pointed out above when the possible constraints of the bidentate nitrate ligands are considered the distortion of the thorium complex from the C, geometry observed in the BgC carborane is really not very severe. The only other idealised geometry that might be seriously considered in eleven-atom metal co-ordination compounds would be derived directly from the eicosahedron by removing one of the eicosa- hedral ligands leaving an open-faced structure of C, symmetry.This particular geometry has not been rigorously established either in metal co-ordination chemistry or in boron chemistry. However a modified version of it might be observed in a periodic lattice if packing arrangements were such that the eicosa- hedron could not be completed owing to strong non-bonding repulsions from large or bulky ligands and that the twelfth ligand position would be absent or else there might be another ligand at a very long distance on the unique fivefold axis. G. Dodeca- and Higher Co-ordination The eicosahedron (Figure 36) is established for the co-ordination sphere of a lanthanum cation complex; twelve sulphate oxygen atoms are within 2.60- 173 Quarterly Reviews 2.74 A of type I lanthanum ions in the crystal lattice of La,(S0,)3,9H,0.293u The eicosahedron is slightly distorted possibly owing to packing factors.Because the other smaller lanthanide ions failed to crystallise in this form it was sug- gested that lanthanum(1u) is just barely able to support the co-ordination of twelve oxygen atoms. There is a hexasulphatothorium ion Th(S04)6*- isolated in the form of salts that may be analogous to the lanthanum There are reports of dodecaco-ordination in other structures and these also involve bidentate ligands which have very short ‘bites’. Especially noteworthy are nitrate and oxalate complexes. Cerium in Ce2Mg,(NO3),,,24H2O is sur- rounded by twelve oxygen atoms at an average distance of 2.64 A.294 These oxygen atoms belong to six nitrate ions and are at the vertices of a slightly irregular eicosahedron.The oxygen-nitrogen-oxygen bond angle of the bidentate nitrate function is smaller than in free nitrate ion; apparently some distortion of the nitrate is necessary to generate a stable eicosahedral co-ordination poly- hedron about cerium(II1). In a polyhedron such as Ce(NO3),& the bridging nitrate groups are symmetrically arranged as the handles in the Argentine ‘pato ball’ (see Figure 37). This arrangement appears to be the most favourable for Fig. 37 The structure (Th) of Ce(N03)ss- in Ce,Mg3(NO.&,24H,O (ref. 294). any eicosahedron with six bidentate ligands. The idealised geometry of a discrete polyhedron of this type has the unusual Th point-group symmetry.In Mg(H2O),Th(N0,),,2H2O there is an eicosahedral arrangement of six nitrate groups about thorium with near Th symmetry for the Th(NO,),Z- polyhedron.295 The Th-0 separation is 2-63 A. There is an eicosahedral arrangement of six water and six perchlorate oxygen atoms about the barium ion in Ba(C10,),,3HZO with Ba-0 distances ranging from 2.96-3.18 A similar arrangement is found in Ba(N03)2296,297 with six bidentate nitrate ions arranged as in ce(NoJt+; and in BaSiF and BaGeF each barium atom is nearly equidistant from twelve fluorine atoms from eight 193(a) E. B. Hunt jun. R. E. Rundle and A. J. Stosick Acta Cryst. 1954 7 106; (b) A. Rosenheim V. Samter and J. Davidsohn Z . anorg. Chem. 1903,35,424. 294 A. Zalkin J.D. Forester and D. H. Templeton J. Chem. Phys. 1963 39 2881. 295 S. Scavnicar and B. Prodic 1965 Acta Cryst. 18 698. z96 N. V. Mani and S. Ramasesham Z. Krist. 1960 114 200. 297 F. M. Jaeger and F. A. van Melle Proc. Acad. Sci. (Amsterdam) 1928.31 651. 174 Muetterties and Wright neighbouring hexafluorometallate ani0ns,2~* which form a nearly regular eicosahedron. Dodecaco-ordination thus appears to be limited to the almost trivial cases where the 'chelating ligand' has a very short bite as in the nitrate ion. Alternatively such polyhedra as La(NO,),& can be considered as octahedral with a preferred LaW-NO3- orientation in which La-0 interactions are maximal (or in which the La-N separation is minimised). Inorganic oxides which are based on close-packed XO layers tend to have the heavy X atoms surrounded by twelve oxygen atoms as in the BaNi0,,299 perov- skite,30° and hexagonal BaTi0Zo1 structures.In the idealised perovskite the twelve oxygen atoms described a cube octahedron (Figure 38) about the heavy atom. The hydrogen-atom positions in 6-uranium hydride UH, have been deter- mined by neutron diffractionFo2 There are two types of uranium atoms. One is surrounded by twelve hydrogen atoms at the corners of an eicosahedron of Th symmetry (faces composed of isosceles triangles). The second type of uranium atom is also dodeca~o-ordinate~~~ but the hydrogen atoms are in sets of three; the configuration approximates the truncated tetrahedron (Figure 39). Fig. 38 The cube octahedron. Fig. 39 The truncated tetrahedron. Very high co-ordination numbers are commonly found in close-packed structures such as the heavy-metal silicides and in complex alloy structures particularly those derived from the heavy metals.Co-ordination numbers of ten twelve fourteen fifteen and sixteen have been reported. Decaco-ordination is found in three structural classes of heavy metal silicide TiSi,,304 CrSi,,305 and MoSi,Fo6 The isomorphous series ThSi,,307 LaSi2,308 CeSi,,309 a-USi, NpSi, e9* J. L. Hoard and W. B. Vincent J. Amer. Chem. Soc. 1940 62,3126. 299 J. J. Lander Acta Cryst. 1951 4 148. 300 R. S. Roth J. Res. Nut. Bur. Stand. 1957 58 75. 301 R. D. Burbank and H. T. Evans jun. Acta Cryst. 1948 1 330. 302 R. E. Rundle J. Amer. Chem. Soc. 1951 73 4172. 303 R. N. R. Mulford F. H. Ellinger and W. H. Zachariasen J. Amer. Chem. Sue. 1954,76 297. 304 F.Laves and H. J. Wallbaum 2. Krist. 1939 101 78. 305 B. BorCn Arkiv Kemi Min. Geol. 1933 11 A No. 10. 306 W. H. Zachariasen Z. phys. Chem. 1927 128 39. 307 G. Brauer and A. Mitius 2. anorg. Chem. 1942 249 325. 308 F. Bertaut and P. Blum Acta Cryst. 1950,3 319. 309 W. H. Zachariasen Acta Cryst. 1949 2 94. 175 Quarterly Reviews PuSi, and the uranium silicides U3Si and U3Si:O7 contain dodecaco-ordinate metal atoms. Tetradecaco-ordination is found in the metal-rich silicide Mo3Si305 where molybdenum has two molybdenum four silicon and eight molybdenum atoms at distances of 2-44 A 2-73 A and 2.99 A respectively. The data are not sufficiently precise to define the geometry about the metal or silicon atoms. Further even the matter of co-ordination number becomes a bit of a semantic point in these close-packed structures.Frank and Kasper310 define the co- ordination sphere of an atom as encompassing all other atoms whose centres are nearer the atom in question than any other; alternatively co-ordination number is the number of nearest neighbours. The former definition unam- biguously assigns twelve and fourteen to the co-ordination numbers for hexagonal close-packed metals and body-centered cubic metals respectively. In complex intermetallic phases the co-ordination number is fourteen although the nearest-neighbour rule sets the number as one or two. Four idealised co- ordination polyhedra for complex alloy structures are shown in Figures 36 and 40-42. All four have triangular faces a reflection of the fact that there is tetra- hedral grouping of atoms throughout these structures thus requiring triangulated co-ordination polyhedra.In contrast for cubic close packing there are square as well as triangular faces and the co-ordination polyhedron for twelve in this system is the cube octahedron (Figure 38). Fig. 40 Idealised geometry for tetradecaco-ordination. There is an example of eicosaco-ordinate uranium in uranium dib~ride.~ll Each metal atom in a position of D,h symmetry is close to twelve boron atoms at the vertices of a hexagonal prism and to an additional eight others through the faces of the B, prisms at a distance comparable with the metallic diameter. slo F. C . Frank and J. S . Kasper Acra Cryst. 1958,11 184. m1 B. W. Howlett J. Inst. Metals 1959 88 91. 176 A Muetterties and Wright Fig. 41 Idealised geometry for pentadecaco-ordination.Fig. 42 Idealised geometry for hexadecaco-ordination. H. Comments on Lanthanide and Actinide Chemistry There is an apparent complexity in the solid-state chemistry of lanthanide and actinide compounds. Compositions or stoicheiometries which are quite diverse provide few clues to the underlying structural principles. Moreover poly- morphism is very common. Especially noteworthy in this context is the fluoro- complex chemistry of uranium(@ and (IV). The stoicheiometries of the reactions of alkali-metal fluoride with uranium@) and uranium(1v) are quite varied. This complexity in lanthanide and actinide chemistry is explicable in the light of the 177 Quarterly Reviews structural considerations presented in the preceding sections. There is the pos- sibility of co-ordination numbers for the metal atom of six seven eight and nine as well as some intermediate cases that may be described as 6+ 7+ and 8 f (see Sm,O in Section B.2 and YF and TbCI in Section C.2e).If one uses a trigonal prism as the hypothetical base model then as shown in Figure 43 it is quite easy to go from 6+ to nonaco-ordination. All of the geometries illustrated in Figure 43 have been established in rare-earth compounds. The difference in 1 I AH:tok other idea I i zed geometries Fiz. 43 Hypothetical transformation mechanisms for changes in co-ordination number. energy levels for these various co-ordination models should not be gross and will be very sensitive to the radius-ratio of metal atom to ligand atom and to the polarising power and the size of other cations that may be present in the lattice.Moreover the barrier for polyhedral rearrangements to other idealised geo- metries (for any given co-ordination number) will not be very large. The differ- ences in energy levels and the barriers to changes in co-ordination number or geometry should be the same order of magnitude as foices generated by packing and ordering factors in the solid state. Thus the extraordinary range of stoicheio- metries in the MF-UF or UF systems may simply reflect very subtle differences in the actual arrangement of fluorine atoms about the uranium atom or in some cases to changes in co-ordination number. Polymorphism reflecting again changes in the co-ordination number or in the geometry of the polyhedron is also expected in the solid state because of the relatively small energy differences among the co-ordination polyhedra.The rare-earth oxides (see Section B) are an excellent example of the subtle structural changes that can occur. In the cubic C form the metal atoms are hexaco-ordinate with distorted octahedra of two types C, and C,, which share a vertex whereas in the hexagonal A form they are heptaco-ordinate with near C, symmetry (monocapped octahedron). There are three distinct co-ordination polyhedra in the monoclinic B form with two of these having heptaco-ordinate metal atoms and near C, symmetry (mono- capped trigonal prism) and one polyhedron that is essentially an octahedron although there is a seventh oxygen atom on a threefold axis at a non-bonding distance of 3.12 A. The two heptaco-ordinate polyhedra differ only in the dimen- sions of the capped t r i g o d prisms.178 Muetterties and Wright I. Suggested Numbering Rules for Co-ordination Polyhedra 1 Discrete Polyhedra.-To provide a consistent system for the specification of stereochemistry in all co-ordination polyhedra it is important that a universal numbering procedure be adopted. This is particularly critical for the description of metal co-ordination polyhedra that have multidentate ligands. Several types of convention can be visualised that would label identical vertices and identical edges would simply identify vertices or would label identical vertices and identify all vertices with a combination of letters and numbers. We have con- sidered in detail a number of alternative procedures and would like to suggest the following numbering rules.This suggestion conforms to previously adopted rules set forth for octahedral complexes,312 and for borane and carborane :a C4y-SOUARE PYRAMID 6 { 4 1 0' -OCTAHEDRON j !!- -7? 4 3 I uh-cueE 4 @ d - T ~ ~ ~ ~ ~ ~ ~ ANTIPRISM & -TRIGONAL PRISM $ 3 3 7 - 6 ,a SF[ SF[ 4 7 4 7 CS c s 4 MONOCAPPED OCTAHEDRON 3 CLV MONOCAPPED SQUARE BASE-TRIGONAL CAP c3v TRIGONAL PRISM 8fjj6 4 3 7 0,ySOUARE' ANTIPRISM 4 bH-8lCAPPED TRIGONAL PRISM pv -MONOCAPPED SOUARE ANTIPRISM b 6 h - ~ ~ ~ ~ ~ ~ ~ ~ ~ EIPYRAMID I 4 0 56 BICAPPEO TRIGONAL ANTIPRISM 8 Cpv-BICAPPED TRIGONAL PRISM 9 4 h - I-TRICAPPED TRIGONAL PRISM 31p W. C. Fernelius 'Advances in Chemistry' Series No. 8 Amer. Chem. SOC. 1951. 179 Quarterly Reviews 8 SQUARE ANTIPRISM I 7 C~V-MONOCAPPED PENTAGONAL ANTIPRISM 1 I~-ICOSAHEDRON 1 04 -OMNICAPPED CUBE 6 c2 I ( E s C ~ H I ~ STRUCTURE ) rd -TRUNCATED TETRAHEDRON oh-cueE OCTAHEDRON 6 1,@14 1 1 10 Og,j- S-EICAPPED H EXAGO I4 AL ANT I PR ISM 4 9 74 -DISTORTED ICOSAHEDRON; " PATOHEDRON 1 Ih -PENTAGONAL DODECAHEDRON Fig.44 Numbering convention for the more common co-ordination polyhedra. poIyhedra31S (this is not strictly true for the borane and carborane polyhedra in that the directions given by Adams recommend initiation of the numbering system at an apex position). Illustrations of the suggested numbering for poly- hedra are given in Figure 44 and a procedure for numbering any polyhedron is given below. Numbering Rules.-(1) Do not number the central atom in co-ordination com- plexes. (24 Select the proper axis of highest order (or one from a degenerate set of 313 R .Adams Inorg. Chem. 1963 2 1087. 180 Muetterties and Wright highest order). If there are one or two polyhedral vertices on the axis then begin numbering with one of these vertices. (If there are two vertices on the principal axis and if there is no plane of symmetry perpendicular to this principal axis begin the numbering at the vertex which is nearer to the largest number of other poly- hedral vertices This qualification is necessary for some of the less regular polyhedra.) If there are no vertices on the principal axis of symmetry follow directions in (3) below. If there is no symmetry axis follow directions in (4). (2b) Drop down from vertex number (1) until one or more other vertices lie in a plane ‘A’ perpendicular to the highest symmetry axis. (2c) Number the vertices in plane ‘A’ identified in (2b) in a clockwise fashion.(If the vertices are non-equivalent in this plane ‘A’ begin by numbering the first two vertices whose connecting line is parallel to the element generating non- equivalence of symmetry in plane ‘A’. This qualification is necessary for poly- hedra such as the C, monocapped trigonal prism. If there is still an ambiguity with the above qualification then select the element generating the asymmetry whose vertices are nearest plane ‘A’. This problem arises for poly- hedra such as the C, bicapped trigonal prism whose numbering is illustrated in Figure 44.) Continue down to the next plane ‘B’ of vertices and again number in a clockwise fashion. Pick up the numbering at a vertex that is in a plane ‘X’ which includes the vertex with the lowest number in the top plane ‘A’ and the principal symmetry axis identified in (24.If no vertex is in the intersection of planes ‘B’ and ‘X‘ then rotate plane ‘X’ about the principal axis in a clockwise fashion to the first polyhedral vertex then pick up the numbering at this vertex and continue in a clockwise fashion. Continue this procedure until all planes encompassing polyhedral vertices are numbered. The vertex of lowest number in plane ‘A’ remains the reference point throughout. (3) If no vertices lie on the axis of highest symmetry then go to the plane perpendicular to this axis and begin numbering as in (2b) and (24. [For poly- hedra which do not have a plane of symmetry perpendicular to the principal axis of symmetry begin numbering at the end which has the largest number of vertices in the first plane perpendicular to the principal axis.There remains an ambiguity as to the vertex which is identified as (1) in some truncated polyhedra e.g. the axially truncated square pyramid. In these cases start with the polygon of smaller dimensions.] (4) If the polyhedron possesses only a plane of symmetry select if possible a unique vertex and identify this as vertex (1). (It is very difficult to state a general unambiguous procedure for polyhedra of such low symmetry.) Number the remaining vertices in a fashion formally analogous to the procedures above. (See the numbering convention for the two square base-trigonal capped poly- hedra in Figure 44.) With these rules other polyhedra not illustrated in Figure 44 can be numbered in a consistent fashion. As noted above there are alternative systems for number- ing of certain polyhedra which would be specific to these polyhedra and would at the very least be aesthetically more pleasing.A case in point is the problem en- countered with our suggested system for all of the polyhedra based on the tri- 181 Quarterly Reviews gonal prism in particular the various capped trigonal prismatic polyhedra. In these cases the trigonal prismatic vertices have different numbers for all the capped derivative polyhedra. Alternatively the trigonal prismatic vertices might have been given a non-varying set of numbers one to six and the capped apices numbers seven to nine. However we recommend sacrifice of aesthetics in favour of a wholly consistent set of rules. Attention is called to the Hoard and Silverton labelling system6 for numbering the octaco-ordinate dodecahedron which is particularly attractive for this polyhedron in that like vertices and like edges are immediately apparent from the labelling procedure.However this procedure does not uniquely identify edges and vertices and does present some problems in chelate structures for uniquely specifying isomers. Our suggested numbering system provides ready identification of isomers in chelate structures. For example the possible eight-co-ordinate chelate (17) based on the thiatropone chelate ligand would be identified as 1,2 (S 0); 3 4 (S 0); 5 6 (0 S); 7 8 (S 0) square antiprism and the isomer (18) as 1 5 (0 S); 2,6 (S 0); 3 7 (S 0); 4 8 (S 0) square antiprism. 2 Linked and Fused Polyhedra.-Polyhedra which are linked at one or more sites should be numbered as they would be (1.1 above) if not linked.Numbers are employed as subscripts to distinguish polyhedra. If these polyhedra have a plane of symmetry perpendicular to the principal proper axis of symmetry the poly- hedra should be numbered so that the vertices which are linked have the lower numbers i.e. numbering should commence at the end at or nearest the linkage site. Examples for linked s-bicapped square antiprisms are (19) (20) and (21). This system is applicable to metal co-ordination polyhedra and to polyhedra lacking a central atom such as the polyhedral boranes and carboranes. If polyhedra are fused at a vertex edge or face and if these polyhedra lack a central atom (e.g. polyhedral boranes) the whole structure should be con- sidered as a new polyhedron subject to rules (1) to (4) in paragraph (1) above.Fused polyhedra which individually contain central metal atoms are members of the broad class of compounds commonly described as metal clusters. Because the metal atoms may be environmentally non-equivalent and additionally may actually be different nuclei the metal atoms in these condensed polyhedra must be numbered. With this modification of rule (1) in the procedure above the 1 82 M uetterties and Wright 9 6 9 71 suggested numbering procedure is applicable to metal clusters. However it may not be generally necessary to apply a numbering convention to metal clusters (unless an extensive chelate chemistry develops at the terminal or exopolyhedral positions). Words alone should provide a simple and straightforward descrip- tion for metal clusters.It is suggested that resolution of this issue be postponed until metal cluster chemistry is more highly elaborated. Appendix The following information relevant to the subject of high co-ordination structures has come to our attention since the submission of the original manuscript. Ligand.-The adaptability of the non-rigid chelating ligand acetylacetone is quite systematically documented in an article by Lingafelter and Braun3I4 in which interatomic distances and angles in published and some unpublished complexes with acetylacetone chelates have been compared. In complexes rang- ing from pentaco-ordinate to octaco-ordinate species the oxygen-metal-oxygen angle varies from about 70" up to 98". In the tetrakis-derivatives of zirconium(Iv) and cerium(1v) the bond angles are nearly the same 75" and 73" respectively.Metal-oxygen distances in these two specific tetrakis-complexes are about 2-20 A in zirconium and vary in the cerium case from 2.37-2.43 .$; the latter distances are based on two-dimensional data whereas the zirconium was deter- mined with three-dimensional data. 314 E. C. Lingafelter and R. L. Braun. J. Amer. Chern. Suc. 1966 88,2951. 189 Quarterly Re views Heptaco-ordination.-Antimony(m) and selenium(rv) have a potential for quasi- heptaco-ordinate geometry in the hexahalogeno-anions. However analysis of crystals of (NH,)4Sbr~rSbVBr,2 has shown that in this lattice the SbBr63- ions have strict Oh symmetry and are he~aco-ordinate.~~~ An infrared study of salts of TeC1,2- TeBre2- Te162- and the related selenium species was made and it was concluded that although the extra pair of electrons in the tellurium and selenium complexes does not distort the individual octahedra it does affect the position of the stretching and bending modes.These results however even in comparison with the related tin complexes are not definitive because they are based solely on the solid state either as Nujol mulls or as pressed disks.31g Bartlett et al. have presented a preliminary analysis of the crystal structure of [XeF,]+ (PtF6]-. This structure is presented as an ionic lattice with square pyramidal XeF,+ groups. However the xenon atom is almost within bonding distance of one of the fluorine atoms associated with the hexafluoroplatinate atom. If this is accepted as a bonding interaction an alternative description of the species is a xenon- fluorine-platinum bridge structure in which xenon then may have the quasi- heptaco-ordinate structure with a non-bonding pair of electrons residing in a directed orbital .317 Numerous new fluoro-complexes have been reported in recent months by a number of workers.These include such species as nitrosyl salts of transition- metal fluoro-complexes e.g. NOWF, (NO),WF, (NO),ReF, and N00sF,?l8 as well as alkali fluoride complexes of quinquevalent neptunium319 and similar complex fluorides of ter- and quadrivalent uranium.320 No structural information is available for the nitrosyl salts so the actual co-ordination number in the solid- state species has not been established although co-ordination numbers of at least seven are not unrealistic for these particular metals.In the case of the neptunium complex it has been shown that Rb,NpF is monoclinic and iso- structural with K2TaF, which is apparently heptaco-ordinate and presumably has the capped trigonal prismatic geometry. The new work on the ter- quadri- and quinque-valent uranium complexes has not progressed to a stage such that the actual co-ordination number has been definitely established but again co-ordination numbers of at least seven are reasonable for the relatively large U3+ U4+ and U5+ ions. In work by K a t ~ ~ ~ l it has been shown that the hexa- fluorides of uranium tungsten and molybdenum react with sodium fluoride to achieve stoicheio-metric ratios of 1 2 and 1 1 at high rates if the sodium fluoride has been preformed by decomposition of Na2UF8. Equilibrium pres- sures are reported.Definitive structural information is as yet unavailable. Potential heptaco-ordinate fluoride complexes of hafnium(1v) with NH,F 315 S. L. Lawton and R. A. Jacobson Inorg. Chem. 1966,5 743. 316 N. N. Greenwood and B. P. Straughan J. Chem. SOC. (A) 1966 962. 317 N. Bartlett F. Einstein D. F. Stewart and J. Trotter Chem. Comm. 1966 550. 318 N. Bartlett and S. P. Beaton Chem. Comm. 1966 167. 319 L. B. Asprey T. K. Keenan R. A. Penneman and G. D. Sturgeon Inorg. Nuclear Chem. Letters 1966 2 19. 320 R. E. Thoma H. A. Friedman and R. A. Penneman J . Amer. Chem. SOC. 1966,88,2046. 321 S. Katz Inorg. Chem. 1966 5 666. 184 Muet t ert ies and Wright HF and H20 have been reported?, A series of neptunium plutonium ameri- cium and curium complex fluorides have been prepared e.g.Na,Np,F,, Na7fi&1 Na,h,F,, and Na,Cm,F,,. The structures have not been estab- lished and co-ordination numbers may be anything from seven to nine.323 In NaNb6015F there is a periodic lattice which contains a pentagonal bipyramidal NbO,F group as a repeating structural unit which shares edges with a ring of octahedra. The mean metal-oxygen distance is 2-03 A. Isostructural with the fluoride complex is NaNb60,50H?24 Relative to the capped trigonal prism as an idealised model in heptaco- ordination RandiC and Mak~iC,~ have calculated the splittings of d orbitals for heptaco-ordinate complexes of the type NbP,2- using a point-charge model and find the results very sensitive to assumed geometrical angles of the molecule. In a review by J. L. Hoard326 on some aspects of haem stereochemistry structural data for pure iron porphyrins are presented and it is pointed out that a substantial displacement of the iron atom from the plane of the porphine nitrogen atoms is a normal structural property of all high-spin iron porphyrins and that significant alterations in the conformation about the co-ordination group are expected to accompany transition to the low-spin state.It has been suggested that heptaco-ordination exists about the iron atom of the haem and in oxymyoglobin in which the oxygen molecule is symmetrically attached to the iron. If this is the case Hoard has suggested that the capped trigonal prism is the more probable geometry but Hoard favours the standard octahedron as the model for this particular complex. In chelate chemistry Clark Greenfield and Nyh~lrn,~' have shown that terdentate arsines such as tris-l,l,l-(dimethylarsinomethy1)ethane react with the trihalides of titanium and vanadium to give monomeric species of 1 1 stoicheiometry which display no evidence of electrical conductivity in solution.Nuclear magnetic resonance suggests that all three arsine atoms of each ligand are co-ordinated to the metal and therefore it appears that the titanium and vanadium atoms are heptaco-ordinate in these complexes. There have been a number of recent developments in cluster chemistry in which the metal atoms are in fact heptaco-ordinate. Most of these are deriva- tives of the Re,CI,,* ion its analogues or derivatives of dodecacarbonyltri-iron. Cotton and L i ~ p a r d ~ ~ have prepared a rather intriguing cluster retaining the basic geometry of the Re,Br,,% ion by reaction of the bromide with silver arsenate followed by treatment with dimethyl sulphoxide.The composition of the compound is Re,Br3(As0,),[(CH3),SO],. The dimethyl sulphoxide groups probably occupy terminally co-ordinating sites in the plane of the three rhenium atoms with the two terdentate arsenate groups at terminal positions normal to 322 M. B. Gaudreau Compt. rend. 1966 263 67. 323 T. K. Keenan Inorg. Nuclear Chem. Letters 1966 2,211. 325 M. RandiC and Z. MaksiC Theor. Chim. Acta 1966 4 145. 326 J. L. Hoard to be published. 327 R. J. H. Clark M. L. Greenfield and R. S. Nyholm J. Chem. SOC. (A) 1966 1254. 328 F. A. Cotton and S. J. Lippard J. Amer. Chem. Soc. 1966,88 1882. S. Ar,derson Acta Chem. Scand. 1965 19 2285. 185 Quarterly Reviews the planes described by the three rhenium atoms.In two independent studies carbonyl analogues of the Re3Br,,3- structure have been obtained. These species have a composition [M(CO),SR] where M represents manganese or rhenium and R an organic group such as ethyl or phenyl. Structurally these complexes have not been defined but by analogy with the rhenium case it is presumed that the thiol groups serve as bridging groups and that the carbonyl groups are all terminally b0nded.3~~*~~* Stewart and O'Donnell~l suggested that the core of the Mo,C1,3+ cation is similar to that found in Re3C1,23- and Re3CI,. In this particular case unless molybdenum were solvated in solution molybdenum would only be hexaco-ordinate. A phosphine derivative of dodecacarbonyltri-iron has recently been described which has the same structure as the parent compound with the phosphine group at a terminal positio11.3~~ A crystal-structure determinationw of this phosphine derivative has established that there are two isomeric structures in the single crystal one with the phosphine terminally bonded to the unique hexaco-ordinate iron atom and one with the phosphine terminally bonded to a heptaco-ordinate iron atom (see Figure 12).Notably the two bridging carbonyl groups appear to be asymmetric in both isomers. A complete three-dimensional structural analysis of the complex oxide UO3,3Y,O has been completed and shows that the distribution of metal ions in the structure is not fixed by symmetry. Rhombohedra1 uranium atoms are octahedrally co-ordinated with all uranium-oxygen distances equal; however reduction of this rhombohedral phase followed by oxidation leads to a uranium co-ordination number of seven.The existence of a rhombohedral structure in the range of U02+z,Y203 compositions is apparently made possible by the partial substitution of uranium at yttrium positions. With the uranium atoms at the cell origin the co-ordination number increases to seven or eight with the extra U-0 bonds being perpendicular to opposite faces of the octahedron at a distance of 2.46 A. At temperatures above lOOO" the structure rearranges to the normal fluorite structure with octaco-ordinate (cubic polyhedron) uranium.= Octaco-ordination.-A review specific to eight-atom co-ordination polyhedra will appear shortly by S. J. Li~pard.3,~ Chelate chemistry still dominates most of the recent advances.Most significant of these is the discovery of the volatile CS+Y(CF~-CO-CHCOCF,)~- salt which sublimes in vacuo or in air at 180-230". Structural analysis by X-ray diffraction * More recently it has been established that :the manganese derivative is a tetramer not a trimer (A. Wojcicki and J. Lewis personal communication). 3z9 E. W. Abel and B. C. Crosse J . Chem. SOC. (A) 1966 1141. 330 A. G. Osborne and F. G. A. Stone J . Chem. SOC. ( A ) 1966 1143. 331 D. F. Stewart and T. A. O'Donnell Nature 1966 210 836. 332 R. J. Angelici and E. E. Siefert Znarg. Chem. 1966 5 1457. 333 D. J. Dahm and R. A. Jacobson Chem. Comm. 1966,496. 334 S . F. Bartram Inarg. Chem. 1966 5 749. 385 S. J. Lippard 'Progress in Inorganic Chemistry' ed. F. A. Cotton Interscience New York 1966.186 Muetterties and Wright is in progress.ssg The structure of calcium dipicolinate trihydrate has been deter- minedB7 by a three-dimensional X-ray structural analysis. The co-ordination poly- hedron is an irregular dodecahedron consisting of the planar terdentate dipicol- inate ligand (Ca-0 = 2-406 2.524 A; Ca-N = 2.491 A) a bridging ligand oxygen atom (Ca-0 = 2.363 A) and four water molecules (Ca-0 = 2-405-2.567 A). Two calcium dipicolinate units form a dimer by sharing a ligand oxygen. The co-ordination polyhedra are linked through the oxygen atom of a combined water molecule to give a three-dimensional network in the solid state. Sulphito- complexes of thorium(1v) have been described with unit-cell compositions of Na,8Th(S0,)l,,CO(NH2)2,1 8H20 in which the sulphite moiety may be bifunc- tional to give octa(or higher)co-ordinate thorium polyhedra.B8 Further work with the unique diarsine (o-phenylenebisdimethylarsine) has shown that TiF4and TiI do not behave like TiCI,.The fluoride gives a polymeric presumably fluorine bridged structure of the composition (TiF,),,diarsine in contrast to the molecular dodecahedral TiC142diarsine complex.161 Behaviour of the iodide also departs from that of the chloride and Clark et aZ.339 suggest an ionic formulation (TiI,,2diar~ine)~+21-. Qualitative observations of the reaction of diarsine with ZrC1 and HfCI show a significantly higher rate of precipitation of ZrC14,- 2diarsine; conjecture on this observation is tempting; but as the authors note in the absence of detailed kinetic data speculation is ~ n r e a l i s t i c .~ ~ Extension of the work with diarsine to the analogous phosphineaO suggests that high-co- ordinate structures can also be achieved with the diphosphine and the early transition elements. With titanium tetrachloride and the diphosphine a very reactive 1 2 complex is formed which is isomorphous with dodecahedral TiCI, 2diarsine. The authors conclude that stereochemistry rather than intrinsic elec- tronic properties associated with the donor atom is a dominating parameter.=O Anhydrous tetrakisnitrate complexes of tin@) titaiium(Iv) and zirconium(1v) have been reported. Preliminary X-ray analysis of Ti(NOa4 suggests D2d dodecahedral geometry.341,342 Thorium (IV) complexes with pyrocatechol-3,5- disulphonic acid may be eight (or higher) co-ordinate species.343 Differentiation between the lanthanides and actinides (periodic analogues) is apparent in the stability of the complexes of americium to fermium with 1,2-diaminocyclohexane- tetra-acetic acid.This suggests diminution of the chelate functionality and in- creasing hydration with increasing atomic number possibly owing to the sharp decrease in atomic radius going from americium to fermium.344 Lead(1v) acetate is octaco-ordinate with basic dodecahedral geometry although 336 S. J. Lippard J. Amer. Chem. SOC. 1966 88 4300. a37 G. Strahs and R. E. Dickerson Spore Newsletter 1965 2 30. 338 V. A. Golovnya A. K. Molodkin and V. N. Tverdokhlebov Rum. J. Inorg. Chem. 1965 10 1195. 339 R. J. H. Clark W. Errington J. Lewis and R. S. Nyholm J . Chem. Soc. (A) 1966 989. 340 R. J. H. Clark R. H. U. Negrotti and R.S. Nyholm Chem. Comm. 1966,486. 341 C. C. Addison C. D. Garner W. P. Simpson D. Sutton and S. C. Wallwork Proc. Chem. SOC. 1964 367. 342 B. 0. Field and C. J. Hardy Proc. Chem. SOC. 1962 76. 343 Y. Murakami and A. E. Martell Bull. Chem. SOC. Japan 1966,39 1077. 344 R. D. Baybarz J. Inorg. Nuclear Chem. 1966 28 1055. 187 Quarterly Reviews there is some distortion.345 Carbonate complexes of the lanthanides may also be octaco-ordinate ; complexes of the type M(CO,),& have been describeds46 (M = Cd Pr Nd Sm and Eul*I). Tetrakis-oxalates of Cew and PrN are possibly o~taco-ordinate.~~ Further evidence of ligand lability in octaco-ordinate acetylacetonate-type derivatives comes from studies by Adams and L a r ~ e n ~ ~ * and by Cotton Legzdins and L i p ~ a r d . ~ ~ In mixtures of the neutral Zr HfW or anionic YIII tetrakis- complexes with a given metal ion ligand exchange with various substituted acetylacetonates is rapid and non-random.Mixed complexes are preferentially formed. Equilibrium constants for some of these systems have been e v a l ~ a t e d . ~ ~ ~ ~ ~ A number of new lanthanide and actinide periodic lattices and complex salts have been reported all of which may have octaco-ordinate metal atoms. These include PaBr (which is isomorphous with dodecahedra1 ThBr,) Pax,,- salts PaX4,2(and 4)-ligand complexe~,3~~ an isomorphous series of NpF,- PI,#,- AmF6- and CmF,- saltss1 (with the compact fluoride ion the co-ordination number may exceed eight) hexachloro- and hexabromo-complexes of Th U and Nprv,s2 as well as chloro-complexes of the lanthanides e.g.Na,EuCI, Na,EuCl, Na,HoCl, and Na,ErC1,.55S Probable octaco-ordinate thorium(rv) uranyl and neptunyl complexes recently described are UO,(NO,), Th(NO,) (see below for possible decaco- ordination),354 Np(N03),,2H20 and related degradation phosphite uranyl complexes e.g. U0,(N03),[OP(C6H,)3],356 (see octaco-ordination). Preliminary X-ray analysis of U02(02)3 diffraction data indicates near-hexagonal bipyramidal geometry with coplanar 0 groups in the hexagonal plane with a linear UO group [a long uranyl-oxygen distance of 1.88 A (normally about 1.77 A) and a 2.27 A U-0 peroxide ~eparation1.3~~ In UO,(NO,),(H,O) and in UO,(NO,),(H,O),,H,O the uranyl grouping retains the characteristic linear array. The two nitrate groups are trans and bidentate and significantly bent from the equatorial UO plane to give essentially a chain conformation.The uranyl U-0 separations are long (1.9 A) the U-O(H,O) separations are 2-0& and the U-O(NO,) separations are 2.1 and 2.4 A in the dihydrate and trihydrate respec ti vel y .35 8335 345 B. Kamenar Acta Cryv. 1963 16 A 34. 346 H. S. Sherry and J. A. Marinsky Inorg. Chem. 1963,2,957. 347 S . W. Pajahoff Monatsh. 1963 94 526. s4* A. C. Adams and E. M. Larsen Inorg. Chem. 1966,5 814. 349 F. A. Cotton P. Legzdins and S. J. Lippard to be published. 350 D. Brown and P. J. Jones Chem. Comm. 1966,279. 351 T. K. Keenan Inorg. Nuclear Chem. Letters 1966 2 153. 352 D. Brown J. Chem. SOC. (A) 1966 766. 353 B. G. Korshunov and D. V. Drobot Russ. J Inorg. Chem. 1965,10 1256. 354 J. R. Ferraro and A. Walker J. Chem. Phys. 1966 45 550.355 J. B. Laidler J. Chem. SOC. (A) 1966 780. 356 F. A. Hart and J. E. Newberry J. Inorg. Nuclear Chem. 1966 28 1334. 357 N. W. Allcock Chem. Comm. 1966 536. a5* V. M. Vdovenko E. V. Stroganov A. P. Sokolov and G. Lungu Radiokhimiya 1962 4 59. 359 V. M. Vdovenko E. V. Stroganov and A. P. Sokolov Radiokhimiya 1963,5,97. 188 Muetterties and Wright Analysis of the three-dimensional X-ray measurements for the tetrapheny- larsonium salt of Co(0,CCF3),2- established near S4 symmetry. The co-ordina- tion polyhedron more nearly approximates to a tetrahedron than a dodecahedron and the authors prefer a characterisation of this anion as a tetrahedral Co2+ complex.ssO The high-temperature tetragonal form of ZrO in contrast to the heptaco- ordinate zirconium in normal ZrO has octaco-ordinate zirconium atoms with near dodecahedra1 geometry (four Zr-0 separations at 2-07 8 and four at 2.45 A)?a1 In cluster chemistry the niobium atom cluster in the fl-Nb3Br periodic lattice is analogous to the Re,ClIz3- cluster but additionally has a centrally located bromine atom to give effectively octaco-ordinate niobium Specific directions for the preparation of metal-atom cores for the square antiprism and dodecahedron models for Fischer-Taylor-Hirschfelder atomic models have been recently reported by Homeier and Larsen.363 Nonaco-ordination.-Dimethyl sulphoxide complexes of thorium(1v) chlorides of the type ThCl,,S(CH&$O are monomeric in acetonitrile and non-conducting in nitromethane suggestive of a nonaco-ordinate complex provided these basic solvents are not entering the co-ordination sphere.The uranium complex UCl4,3(CH,),SO is on this count heptaco-ordinate. Although uranium(W) is smaller than thorium(Iv) it is somewhat surprising that there appears to be a significant drop in co-ordination numbers in these related systems.364 Perhaps the authors’364 suggestion of solvent participation is the answer and actual co- ordination numbers in the two systems are the same or differ by only one. Complexes of lanthanide nitrates with dimethyl formamide M(DMF),(NO,), have been prepared and nonaco-ordination suggested.365 In nitromethane the complexes do not behave as electrolytes but in dimethyl formamide there is a displacement reaction apparently to give the cation [M(DMF),(NO,),]+ which also may be nonaco-ordinate provided that the nitrate groups are bidentate.Similarly the oxonitrate anionic complexes of niobium and tantalum OM(NO,) have been isolated as tetramethylammonium salts and may be nonaco-ordinate.ss6 The volatile casium salt of Y(CF3COCHCOCF3)4- noted above shows a parent mass ion corresponding to CSY[CF,COCHCOCF,]~+ although this is very weak.33s A strong peak assignable to CsY[CF3CO-CHCOCFJ3+ suggests that the caesium is very tightly bound. The site of binding is unknown and it seems unlikely that there is a close Cs-Y interaction to give nonaco- ordination. Lippard suggests that the caesium ion may either be bound to the 360 J. A. Bergman jun. and F. A. Cotton Inorg. Chem. 1966,5 1420. 361 G. Teufer Acta Cryst. 1962 15 1187. 362 A. Simon and H. G. von Schnering J. Less Common Metals 1966 11 31. 363 E. Homeier and E.M. Larsen J. Chem. Educ. 1966,43 376. 364 K. W. Bagnall D. Brown P. J. Jones and J. G. H. du Preez J. Chem. SOC. (A) 1966,737. 365 S. S. Krishnamurthy and S. Soundarajan J . Inorg. Nuclear Chem. 1966 28 1689. 366 D. Brown and P. J. Jones J. Chern. SOC. (A) 1966,733. 189 Quarterly Reviews 'sheath of negative fluorine atoms which surround the yttrium atom' or may be bound to the methylene (= CH-) carbon atom. Nonaco-ordination has been suggested for the lanthanide(rI1) complexes with 1 -hydroxycyclopentanecarboxylic acid.367 In optical studies of europium and neodymium complexes with nitrilotriacetic ethylenediaminetetra-acetic and diethylenetriaminopenta-acetic acids the species have been analysed in terms of metal co-ordination numbers of six to eight.3s8 These estimates seem abnormally low and octa- to at least nona-co-ordination is more reasonable for these chelate derivatives of these large tervalent ions.The structural investigation of LaF by Zalkin Templeton and HopkinsMs have characterised the lanthanum polyhedron as irregular with a nonaco- ordinate lanthanum atom. Man~mann~~O also reported an X-ray analysis of LaF and gave the same space-group P&l as Zalkin et al. However Mansmann describes the lanthanum co-ordination polyhedron as did Ofteda13'l who had the incorrect space group as undecaco-ordinate with nine LaF separations of 2.42-2.61 8 and two at 3.10 A. These separations agree closely with those found by Zalkin et al. We prefer the characterisation as nonaco-ordinate since a separation of 3-01 8 is greater than the sum of the van der Waals radii and these two long La-F separations may be only weakly bonding.Lanthanide fluoride complexes of the type NaMF where M = YIIl and lanthanide("I) excepting Yb and Lu are isomorphous with NaLaF,372 which has nonaco- ordinate lanthanum atoms.70 The oxyfluoride Pa20F8 is isomorphous with U2F (body-centred cubic) and may have a nonaco-ordinate protactinium at0m.3~~ The Pa20CI analogues may be nonaco-ordinate but steric factors may effect a significant change from the fluoride lattice and in the protactinium co- ordination ~phere.3~~ Analysis of the X-ray diffraction data375 for a single-crystal of NdTe (periodic lattice) shows the neodymium to be surrounded by nine tellurium atoms with the basic geometry of monocapped square antiprism (Nb-Te distances are 3.21 (4 Te) 3.36 (1 Te) and 3.35 A (4 Te).In new cluster chemistry developments B~rbank,~ has analysed the Ta6C1,,,7H20 structure by X-ray diffraction. The crystals are trigonal with a probable space-group P31 rn. Burbank describes the structure as distorted and subject to faulting. The basic tantalum co-ordination polyhedron is the previously described Ta,C1,22+ unit with two chlorine atoms and four water molecules filling the terminal tantalum sites to give nonaco-ordination. The Ta 'octa- hedron' is elongated on the four-fold axis. Other new and presumably costruc- 367 J. E. Powell and D. L. G. Rowlands Inurg. Chem. 1966 5 819. 388 T. V. Ternovaya and N. A. Kostromina Russ. J. Znorg. Chem. 1965 10 1100. 369 A. Zalkin D. H. Templeton and T. E. Hopkins Inorg. Chem. 1966 5 1466. 370 V. M.Mansmann 2. Krist. 1965 122 375. 371 I. Oftedal 2. phys. Chem. 1931 B 13 190. 372 R. E. Thoma H. Insley and G. M. Hebert Inorg. Chem. 1966,5 1222. 373 L. Stein Znorg. Chem. 1964 3 995. 374 D. Brown and P. J. Jones J. Chem. SOC. (A) 1966 874. 375 B. K. Norling and H. Steinfink Znorg. Chem. 1966 5 1488. 376 R. D. Burbank Inorg. Chem. 1966 5 1491. 190 Muetterties and Wright tural clusters of this type are W,Br,* W6Br16,377 Nb,Br14,8H,0 Ta,Br,4,8H20S78 Nb,C116,3C2H,0H379 and Nb,Fl,.380 Deca- and Dodeca-co-ordination.-Tetrakisacetatouranium(w) a fibrous mole- cule has been characteri~ed~~l by X-ray analysis as consisting of linear arrays of bicapped square antiprisms (with co-ordinated oxygen atoms serving as bridging groups). This type of structure may be found in other very large quadrivalent metal acetates or nitrates e.g.Th(N03)4 although the analogous lead(1v) derivative has a molecular lattice with octaco-ordination. Brown and Jones382 have prepared a series of nitrate complexes with protac- tinium. Depending upon the functionality of the nitrate ligands co-ordination may range from ten in CH,CN,Pa(NO&OPa(No,),NCCH to twelve in CsPa(NOJ,. In the ytterbium-antimony phase diagram YbSb is one of the most stable phases present. Preliminary X-ray analysis383 of this phase indicates that the ytterbium atom is decaco-ordinate with a near-square antiprismatic arrangement with eight antimony atoms at distances of 3.19-3-30 A with two more antimony atoms at relatively long distances of 3.57 A but these two are over one of the square faces. This significant departure from idealised symmetrically bicapped square antiprismatic geometry is not disconcerting in that YbSb is a periodic lattice.Line Notation for Co-ordination Compounds.-McDonnell and Pa~ternack,3~~ using a reference-structure approach developed a notation system for represen- tation of inorganic structures in co-ordination compounds based on considera- tion of compatibility with systems formulated for organic structures.385387 Their suggested notation system is based384 on letters and closely follows the H a y ~ a r d ~ ~ rules. The lettering system differs from ours only in the matter of where the numbering starts in successive planes reflecting the minor conflict between I.U.P.A.C. recommendations and the usage in the United States partic- ularly for polyhedral boranes.McDonnell and Pasternack’s system is not compre- hensive for established co-ordination polyhedra and is arbitrary if not mislead- 377 H. Schafer and R. Siepmann J. Less Common Metals 1966 11 76. 378 H. Schafer and B. Spreckelmeyer J. Less Common Metals 1966 11 73. 379 B. Spreckelmeyer and H. Schafer J . Less Common Metals 1966 11 74. 380 H. Schafer H. G. von Schnering A. Simon D. Giegling D. Bauer R. Siepmann and B. Spreckelmeyer J. Less Common Metals 1965 10 154. 381 I. Jelenic D. GrdeniC and A. Bezjak Acra Cryst. 1964 17 758. 382 D. Brown and P. J. Jones J. Chern. SOC. (A) 1966 733. 383 R. Wang R. Bodnar and H. Steinfink Inorg. Chem. 1966 5 1468. 384 P. M. McDonnell and R. F. Pasternack J . Chem. SOC. 1965 56. 385 ‘Rules for I.U.P.A.C. Notation for Organic Compounds’ John Wiley and Sons Inc.New York N.Y. 1961. 386 H. W. Hayward ‘A New Sequential Enumeration and Line Formula Notation System for Organic Compounds’ Patent Office Research and Development Report No. 21 Depart- ment of Commerce Washington D.C. 1961. 387 W. J. Wiswesser ‘A Line-Formula Chemical Notation’ Thomas Y. Crowell Co. New York N.Y. 1954. 191 Quarterly Reviews ing in the capital-letter notation for the specific polyhedron in any given polyatom system ‘The symmetry designators although assigned somewhat arbitrarily reflect frequency of occurrence of individual configuration.’ The latter qualifi- cation was not correctly applied to the seven- and eight-atom polyhedra con- sidered by them. Polyhedral Holes.-Many minerals and also synthetic periodic lattices have a network of holes that may be described as polyhedral.These polyhedra for the most part do not correlate with the polyhedra that dominate in high-co-ordina- tion structures and in polyhedral boranes. The pores or holes in silicate minerals may be generated by the incorporation or inclusion of polyhedral ions during the condensation polymerisation of the silicate chains or nets.38s The types of polyhedral holes include the cube octahedron in faujasite and s0dalite,3~~ hexagonal prisms in certain and very large ones such as the hexacosahedron found in Linde Sieve A,389,392 and the triacontrahedral (30) and dotetracontahedral (42) cavities in synthetic ana1~ites.s~~ New Structural Data.-The crystal structure of Cs+Y(CF,COCHCOCF,),- which was previously is c0mplete.3~~ The yttrium atom is co- ordinated to eight oxygens (Y-0 = 2-33 A) in a dodecahedral co&guration with the chelate groups spanning “g” edges (see Figure 25) rather than the “m” edges resulting in the first known example of idealized D symmetry for the dodecahedral configuration.The D dodecahedral structure could possibly result from a slight distortion of the D square antiprism. A cause of such distortion might be the observed close association of the Cs+ cation with the Y(CF,COCHCOCF,),- anion in the solid state.394 The previously known dodecahedral configurations have D2d symmetIy (m edge span). Based on a crystal structure determination the ligands in NH,[Pr(CH,.SCCHCOCF,),] are reported 395 to also span “g” edges but the symmetry is lowered by the reversed attachment of one of the asymmetric ligands. A recent three dimensional single crystal study of [Fe(C,H,N),]2+[Fe4(CO),,]2- establishes the configuration of the [Fe4(C0),,I2- anion as a tetrahedron of iron atoms396 (Feb-Fea = 2-58 A Feb-Feb = 2.50 A) with the same general structure as Co,(CO), (Figure 9) and the thirteenth CO group on the three-fold axis triply bridging the three basal iron atoms aver.Feb-COb = 2-00 A. The three carbonyl groups in the basal plane of the iron atoms are not symmetrically placed between the two iron atoms (Fe-CO = 2.24 2.28 2-33; Fe-VO = 1.80 388 R. M. Barrer Chem. in Britain 1966 2 380. 389 R. M. Barrer Endeavour 1964 23 122. 390 L. S. Dent and J. V. Smith Nature 1965 181 1794. 391 L. Broussard and D. P. Shoemaker J. Amer. Chem. SOC. 1960,82 1041. 392 W. M. Meier and G. T. Kokotailo 2. Krist. 1965 121 14.393 R. M. Barrer and I. S. Kerr J . Chem. SOC. 1963 434. 394 S. J. Lippard F. A. Cotton and P. Legzdins J. Amer. Chem. SOC. 1966,88,5930. 395 M. Cefola W. Hamilton R. Lalancette and S. Laplaca reference 394 footnote 11. 396 R. J. Doedens and L. F. Dahl J . Amer. Chem. SOC. 1966,88,4847. 192 Muetterties and Wright 1-81 1-85) and do not bridge as in CO,(CO)~~ but a weak interaction exists. Considering the nine carbonyls in the Fe,CO fragments as terminal (aver. Fe-CO = 1-72 A) the basal iron atoms are seven co-ordinate with a distorted version of a 4 3 orientation of ligands. The apical iron atom is six-co-ordinate. The results of the structure determination of [(C,H5)aAs]2Re3C11~97 and Cs2Re3Br11398 are now published. The basic structure is the R%X,23- structure (Figure 16) with one terminal halogen atom missing.A significant structural change is the shortening of the two Re-Re bonds to the halogen deficient rhenium atom to 2.435 A vs. 2.483 A in the chloride and 2.43 A vs. 2-49 A in the bromide. The two terminal halogen rhenium bonds on the halogen-deficient rhenium atom are also significantly shorter than the others. In the Cs2Re3Brll structure the Re-Br bonds on the bromine-deficient rhenium are bent towards each other 133" vs. 159" for the angle subtended by a pair of off-plane bromine atoms at a non-bromine deficient rhenium. on IF is presented using the rotating sector microphotometer method; the previous study employed the visual methodF6 Preliminary analysis indicates that the structure is close to a penta- gonal bi-pyramid and that the axial bonds are shorter than the equatorial bonds.A three dimensional single crystal X-ray study of anhydrous Ti(N03),400 established co-ordination of eight oxygen atoms to the titanium atoms from four bidentate nitrate groups. The basic geometry approximates the dode- cahedron (DZd symmetry). The nitrate groups in K3[Hg(N02)4]N03401 are bidentate by a three-dimensional crystal structure analysis and arranged around the mercury atom in roughly a tetrahedral orientation with the eight oxygen atoms 2.4 A from the mercury. The structure of a-Gd,S3 was solved by a three dimensional single crystal X-ray study402 and is found to contain two nonequivalent gadolinium atoms. One gadolinium site is co-ordinated to seven sulphur atoms at an average distance of 2.81 A and the co-ordination polyhedron is a slightly distorted square-capped trigonal prism.The co-ordination polyhedron of the other gadolinium site is a bicapped trigonal prism with eight sulphur atoms at an average distance of 2.90 A. Within each polyhedron the gadolinium-sulphur distances are approxi- mately equivalent. This rare-earth a-sesquisulphide structure may exist for Ce to Dy?03 A neutron powder diffraction study of HoDtM indicates a structure in which holmium has nine nearest hydrogen neighbours at a distance of 2-10 to 2-29 A and two hydrogen neighbours at 2.48 A. The holmium atom is nine co-ordinate and the co-ordination polyhedron is the tricapped trigonal prism with distortion 897 B. R. Penfold and W. T. Robinson Inorg. Chem. 1966,5,1758. s98 M. Elder and B. R. Penfold Inorg. Chern. 1966,5 1763. s99 H.B. Thompson jun. and L. S. Bartell Trans. Amer. Cryst. Ass. 1966,2 190. 400 C. D. Garner and S. C. Wallwork J. Chem. SOC. (A) 1966,1496. 401 D. Hall and R. V. Holland Proc. Chem. Soc. 1963,204. 402 C. T. Prewitt and A. W. Sleight Amer. Cryst. ASSOC. Jan. 25 (1967) Atlanta Georgia. Cryst. 1965,19 14. 404 D. Mansmann and W. E. Wallace J . Phys. (France) 1964.25,454. A second electron diffraction J. F. Lahaut M. Gutlard M. Patrie M. P. Pardo S. M. Golabi and L. Domange Acta. 193 Quarterly Reviews in the capping so as to lower the point group symnietry about holmium to C,. The other hexagonal rare-earth trihydrides SmH, GdH, TbH, DyH, ErH, TmH, LuH, HoH and YH probably have the same crystal structure as We thank Professor J. L. Hoard for critical comments. HOD^ 194