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Seven-Coordination. a Molecular Orbital Exploration of Structure, Stereochemistry, and Reaction Dynamics ROALD HOFFMANN,’ BARBARA F

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Seven-Coordination. a Molecular Orbital Exploration of Structure, Stereochemistry, and Reaction Dynamics ROALD HOFFMANN,’ BARBARA F Seven-Coordination Inorganic Chemistry, Vol. 16, No. 3, 1977 511 S. F. A. Kettle, Inorg. Chem., 4, 1661 (1965). K. N. Raymond, J. Chem. Soc., Chem. Commun., 470 (1974)l was later For a perceptive analysis of the u- and r-bonding capabilities of CO, revised to a 153O bent structure [L. D. Brown and K. N. Raymond, Inorg. N2, and CN- see (a) K. G. Caulton, R. L. DeKock, and R. F. Fenske, Chem., 14, 2595 (1975)l. J. Am. Chem. SOC..92. 515 (1970): (b) R. L. DeKock. A. C. SaraDu. (43) J. P. Collman, R. R. Gagne, C. A. Reed, W. T. Robinson, and G. A. and R. F. Fenske, Inorg. Chem., IO, 38(1971); (c) A. C. Sarapu and Rodley, Proc. Natl. Acad. Sci. U.S.A.,71, 1326 (1974). R. F. Fenske, ibid., 14, 247 (1975). (44) B. M. Hoffman, D. L. Diemente, and F. Basolo, J. Am. Chem. SOC., 92. 61 11970). G. Herzberg, “Spectra of Diatomic Molecules”, Van Nastrand, Princeton, --.-- ,---I N.J., 1950, pp 522, 553. (45) E.-I. Ochiai, J. Inorg. Nucl. Chem., 35, 1727, 3389 (1973). J. Chatt, D. P. Melville, and R. L. Richards, J. Chem. Soc. A, 2841 (1969). (46) (a) G.A. Rodley and W. T. Robinson, Nature (London),235,438 (1972); (a) D. Cullen, E. Meyer, Jr., T. S.Srivastava, and M. Tsutsui, J. Chem. (b) G. A. Rodley and W. T. Robinson, Synth. Inorg. Met.-Org. Chem., Soc.. Chem. Commun.. 584 (1972): (b) J. J. Bonnet, S. S. Eaton, G. 3, 387 (1973); J. P. Collman, H. Takaya, B. Winkler, L. Libit, S. K. R. Eaton, R. H. Holm, and J. A. Ibers, J. Am. Chem. SOC.,95, 2141 Seah, G. A. Rodley, and W. T. Robinson, J. Am. Chem. SOC.,95, 1656 (1973). (1973). V. L. Goedken and S.-M. Peng, J. Chem. Soc., Chem. Commun., 914 (47) R. S. Gall, J. F. Rogers, W. P. Schaefer, and G. G. Christoph, J. Am. (1974). Chem. Soc., 98, 5135 (1976). (a) E. J. Heidner, R. C. Ladner, and M. F. Perutz, J. Mol. Bid, 104, (48) We might note here again that the general Walsh diagram of Figure 707 (1976); (b) J. C. Norvell, A. C. Nunes, and B. P. Schoenbm, Science, 7 is uncertain with respect to level spacings. For instance in 190,568 (1975); (c) R. Huber, 0. Epp, and H. Formanek, J. Mol. Biol., one might suspect a linear geometry and a low-spin ground state, yet 52, 349 (1970). Cr(OJ(py)(TPP) has two unpaired electrons: C. A. Reed, Abstracts, (a) P. A. Bretscher, Ph.D. Dissertation, University of Cambridge, 1968; 172nd National Meeting of the American Chemical Society, San (b) W. A. Hendrickson and W. E. Love, Narure (London),New Biol., Francisco, Calif., 1976, No. INOR 125. 232, 197 (1971); (c) J. F. Deatherage, R. S. Loe, C. M. Anderson, and (49) D. M. P. Mingos, W. T. Robinson, and J. A. Ibers, Inorg. Chem., 10, K. Moffat, J. Mol. Biol., 104, 687 (1976). 1043 (1971). A calculation on the mode of attack of alkyl halides on Co(CN)t- yields (50) W. R. Scheidt and J. L. Hoard, J. Am. Chem. SOC.,95,8281 (1973). a similar nonlinear reaction path: K. Ohkubo, H. Kanaeda, and T. (51) G.Broden, T. N. Rhodin, C. Brucker, R. Benbow, and Z. Hurych, Surf. Tsuchihashi, Bull. Chem. Soc. Jpn., 46, 3095 (1973). Sei., in press. This excludes bridging 02as well as those complexes containing more (52) R. Hoffmann, J. Chem. Phys., 39, 1397 (1963); R. Hoffmann and W. than one O2 per metal center. N. Lipscomb, ibid., 36, 2179, 3489 (1962); 37, 2872 (1962). An initial report of a linear Co-0-0 in Co(CN)502)- [L. D. Brown and (53) J. W. Lauher and R. Hoffmann, J. Am. Chem. SOC.,98, 1729 (1976). Contribution from the Departments of Chemistry, Cornel1 University, Ithaca, New York 14853, and University of Connecticut, Storrs, Connecticut 06268 Seven-Coordination. A Molecular Orbital Exploration of Structure, Stereochemistry, and Reaction Dynamics ROALD HOFFMANN,’ BARBARA F. BEIER, EARL L. MUETTERTIES,’ and ANGEL0 R. ROSS1 Received October 7, 1976 AIC601311 A systematic molecular orbital analysis of seven-coordinatemolecules is presented, with an emphasis on the basic electronic structure, substituent site preferences, and pathways for interconversion of various geometries. Conformations studied in detail include the pentagonal bipyramid (PB), capped octahedron (CO), and capped trigonal prism (CTP). With respect to u or electronegativity effects the following conclusions are reached for the optimum site of substitution in a d4complex by a better u donor: PB equatorial (eq), CO capping site (c), CTP edge (e). For ?r effects the following preferences are deduced for d4 systems substituted by an acceptor and do by a donor (> means preferred): PB ax > eq, eqll > eq,; CO (cf = capped face, uf = uncapped face, c = capping site) cf > c > uf, cf, > cfll, uf, > ufll; CTP (qf = quadrilateral face, e = edge, c = capping site) qf - e > c, qf, > qfil, e, > ell, cy > c,. These preferences are reversed for the d4donor substituent case. The agreement with information available from structural studies is good, though often the same conclusions would be reached from steric arguments. All pathways of polytopal rearrangement in seven-coordination are of low energy. In the seemingly complex yet quite simply ordered’ complexes of high coordination number. The role of seven- structural scheme for inorganic chemistry, seven-coordination coordination is significant when viewed in the light of reaction occupies a niche that is formally analogous to fivecoordination. intermediates or transition states in associative reactions of Neither five- nor seven-coordinate complexes can achieve as six-coordinate complexes, oxidative addition reactions of meritorious a structural form as their nearest coordination five-coordinate complexes, and, most importantly, dissociative neighbors, four, six, and eight; and consistently, each is a less reactions of eight-coordinate complexes. An understanding common coordination form than their nearest neighbors. A of mechanism in these reaction regimes requires delineation partial explanation for the “discontinuties” at five- and of the electronic and steric factors that direct structural and seven-coordination may be derived from the graph shown in stereochemical trends in seven-coordination. This paper is Figure 1. There is a much less effective packing arrangement addressed to the issue of electrsnic controls. in progressing from four- to five- or from six- to seven-co- Structural studies**6and calculation^^-^^ suggest that sev- ordination and a quite modest penalty in ligand repulsion en-coordination has in the general’ case a potential surface effects for a return to a more uniform spatial array of ligands that is not distinguished by a deep minimum corresponding in a further progression from five- to six- (essentially no to one polytopal” form. This situation, analogous to that penalty) or seven- to eight-coordination.* Nevertheless, established for the five-coordination family, in part reflects and ~even-coordinate~,~complexes are isolable and well-defined the simple geometric fact that seven points cannot be arranged molecular entities, although seven-coordination forms are by so as to describe a regular polyhedron. The number of far the less common of the two presumably because of steric nonisomorphic polyhedra with seven vertices is large, 34. Each as well as electronic penalties incurred in the construction of of these polyhedra has been illustrated by Britton and Dunitz.13 Within this complete set, just three high-symmetry * To whom correspondence should be addressed at Cornell University. p~lyhedra~,~,’~suffice to describe the established elements of 512 Inorganic Chemistry, Vol. 16, No. 3, 1977 Hoffmann, Beier, Muetterties, and Rossi IOO- - 0 95- 0 90- 0 85- 0 80- 070- - - A Figure 2. The two most common polyhedra in eight-coordination, On the left is the D4d Archimedean square antiprism and on the right the DZddodecahedron. All vertices are equivalent in the former polyhedron whereas there are two types of vertices (A and B), 055 I 1 ’ ’ I I I I 1 4 56 78 91Oll12 distinguished by symmetry and connexity, in the dodecahedron. Coordination Number which has been discussed as one possible ~ay-point’~~’~in an Figure 1. A plot of the ratio of polyhedron radius (M-L) to polyhedron edge length (L-L) vs. coordination number, N (ML,), for the various associative ML6 substitution reaction-the other possible types of polyhedra, following the Day and Hoard discussion.2a The transition state in a concerted reaction is the pentagonal solid line representing optimal packing joins the points for the three bipyramid.’6b regular polyhedra that have all faces triangular. Identification of Alternatively, the idealized seven-coordinate forms 2-4 may specific polyhedra reading up for increasing ratio, Le., less effective be conceptually generated by vertex removal from the favored packing: N = 4, the regular tetrahedron and the square; N = 5, the or most common’* eight-coordinate geometries (see Figure 2). trigonal bipyramid and (coincidentally) the tetragonal pyramid; N Although this approach is not readily envisaged nor readily = 6, the regular octahedron and the trigonal prism; N = 7, the C,, illustrated by drawings (a careful inspection of models is monocapped octahedron, the C, monocapped trigonal prism, and the required), there is a cogent reason for considering such a DSbpentagonalbipyramid; N = 8, the D4dsquare antiprism, the DZd generation scheme. Seven-coordinate intermediates will be dodecahedron, and the cube; N = 9, the Djh tricapped trigonal prism and the C,, monocapped square antiprism; N = 10, the DPdbicapped much more common in substitution reactions of eight-coor- square antiprism; N = 12, the regular icosahedron and the Oh cu- dinate than of six-coordinate complexes. Starting from the boctahedron. D2d dodecahedral eight-coordinate form, there are two possible degradative processes because of the two different types of structure5s6in seven-coordination although minor polyhedral vertices (Figure 3).
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