M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 20
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Polyhedral Molecular Geometries123Figure 3-18. A few members of the fullerene family. Buckminsterfullerene, C60 , is“the roundest, most symmetrical large molecule found so far” [35].3.7.1. Boron Hydride CagesThe boron hydrides are one of most beautiful classes of polyhedralcompounds whose representatives range from simple to rathercomplicated systems. Our description here is purely phenomenological. Only in passing is reference made to the relationship of thecharacteristic polyhedral cage arrangements of the boron hydrides andthe peculiarities of multicenter bonding that has special importancefor their structures.All faces of the boron hydride polyhedra are equilateral or nearlyequilateral triangles.
Those boron hydrides that have a complete polyhedral shape are called closo boranes (the Greek closo meaningclosed). One of the most symmetrical, and, accordingly, most stablepolyhedral boranes is the B12 H12 2– ion. Its regular icosahedral configuration is shown in Figure 3-19. The structural systematics of Bn Hn 2–closo boranes and related C2 Bn-2 Hn closo carboranes, are presented inTable 3-2 after Muetterties [36]. In carboranes some of the boron sitesare taken by carbon atoms. In the icosahedral ion [Pt@Pb12 ]2– , theplatinum atom is inclosed in a regular icosahedral lead cluster [37],analogous to B12 H12 2– .Another structural class of the boron hydrides is the so-called quasicloso boranes.
They are related to the closo boranes by removinga framework atom from the latter and adding in its stead a pair ofelectrons. Thus one of the polyhedron framework sites is taken by anelectron pair.1243 Molecular Shape and GeometryFigure 3-19. Boron skeletons of boron hydrides. Left: Regular icosahedral boronskeleton of B12 H12 2– ; Right: Closo, nido, and arachno boranes after Williams [38]and Rudolph [39]. The genetic relationships are indicated by diagonal lines. Usedwith permission, copyright (1976) American Chemical Society.There are boron hydrides in which one or more of the polyhedral sites are truly removed. Figure 3-19 shows the systematics ofborane polyhedral fragments as obtained from closo boranes, afterR. E.
Williams [40] and R. W. Rudolph [41]. All the faces of the polyhedral skeletons are triangular, and thus the polyhedra may be termeddeltahedra and the derived fragments deltahedral. The starting deltahedra are the tetrahedron, the trigonal bipyramid, the octahedron, thepentagonal bipyramid, the bisdisphenoid, the symmetrically tricapped3.7. Polyhedral Molecular Geometries125Table 3-2. Structural Systematics of Bn Hn 2– closo Boranes and C2 Bn–2 Hn closoCarboranesaPolyhedron, point groupBoraneDicarbaboraneTetrahedron, Td(B4 Cl4 )b––C2 B3 H5Trigonal bipyramid, D3hOctahedron, OhB6 H6 2–C2 B4 H6Pentagonal bipyramid, D5hB7 H7 2–C2 B5 H7Dodecahedron (triangulated), D2dB8 H8 2–C2 B6 H8Tricapped trigonal prism, D3hB9 H9 2–C2 B7 H9Bicapped square antiprism, D4dB10 H10 2–C2 B8 H10Octadecahedron, C2vB11 H11 2–C2 B9 H11Icosahedron, IhB12 H12 2–C2 B10 H12aAfter E.
L. Muetterties, ed., Boron Hydride Chemistry. Academic Press,New York, 1975.bB4 H4 not known.trigonal prism, the bicapped square antiprism, the octadecahedron,and the icosahedron [42].A nido (nest-like) boron hydride is derived from a closo boraneby the removal of one skeleton atom. If the starting closo boraneis not a regular polyhedron, then the atom removed is the one at avertex with the highest connectivity. An arachno (web-like) boronhydride is derived from a closo borane by the removal of two adjacentskeleton atoms. If the starting closo borane is not a regular polyhedron, then again, one of the two atoms removed is at a vertex with thehighest connectivity.
Complete nido and arachno structures are shownin Figure 3-20 together with the starting boranes [43]. The fragmentedstructures are completed by a number of bridging and terminal hydrogens. The above examples are from among the simplest boranes andtheir derivatives.3.7.2. Polycyclic HydrocarbonsSome fundamental polyhedral shapes are realized among polycyclichydrocarbons.
The bond arrangements around the carbon atoms insuch configurations may be far from the energetically most advantageous, causing strain in these structures. The strain may be so largeas to render particular arrangements too unstable to exist under anyreasonable conditions. On the other hand, the fundamental characterof these shapes, their high symmetry, and aesthetic appeal make them1263 Molecular Shape and GeometryFigure 3-20.
Examples of closo/nido and closo/arachno structural relationshipsafter Muetterties [44]. Top: Closo-B6 H6 2– and nido-B5 H9 ; Bottom: Closo-B7 H7 2–and arachno-B5 H11 .an attractive and challenging “playground” to the organic chemist[45]. Incidentally, these substances are often building blocks for suchimportant natural products as steroids, alkaloids, vitamins, carbohydrides, antibiotics, etc.Tetrahedrane, (CH)4 , would be the simplest regular polyhedralpolycyclic hydrocarbon (Figure 3-21a).
However, since it has sucha high strain energy, it has not (yet?) been prepared in spite of considerable efforts [46]. By now, over 10 different derivatives of tetrahedrane have been prepared, for example, tetra-tert-butyltetrahedrane(Figure 3-21b) [47]. It is amazingly stable, perhaps because thesubstituents help “clasp” the molecule together.The next Platonic solid is the cube, and the corresponding polycyclic hydrocarbon, cubane, (CH)8 (Figure 3-21c), has been knownfor some time [49]. The strain energy of the CC bonds in cubane isamong the highest known. It is unstable thermodynamically but stablekinetically, “like a rock” [50].
Referring to its instability, Marchand3.7. Polyhedral Molecular Geometries127Figure 3-21. Polyhedral molecular models. (a) Tetrahedrane, (CH)4 ; (b) Tetra-tertbutyltetrahedrane, {C[C(CH3 )3 ]}4 [48]; (c) Cubane, (CH)8 ; (d) Dodecahedrane,(CH)20 ; (e) C60 H60 ; (f) Triprismane, C6 H6 ; pentaprismane, C10 H10 ; and hexaprismane, C12 H12 .1283 Molecular Shape and Geometryconsidered cubane as a physical organic chemist’s “subject/patient”by analogy with the clinical psychologists studying deviants to learnmore about normal behavior [51].
He also demonstrated the riches ofthe chemistry developed from the cubane base.The preparation of dodecahedrane, (CH)20 , (Figure 3-21d) byPaquette et al. [52] followed Schultz’s prediction almost two decadesbefore, concerning possible hydrocarbon polyhedranes [53]:Dodecahedrane is the one substance of theseries with almost ideal geometry, physically themolecule is practically a miniature ball bearing!One would expect the substance to have a lowviscosity, a high melting point, but low boilingpoint, high thermal stability, a very simple infraredspectrum and perhaps an aromatic-like p.m.r.spectrum. Chemically one might expect a relatively easy (for an aliphatic hydrocarbon) removalof a tertiary proton from the molecule, for thenegative charge thus deposited on the moleculecould be accommodated on any one of the twentycompletely equivalent carbon atoms, the carbanionbeing stabilized by a ’rolling charge’ effect thatdelocalizes the extra electron.In the (CH)n convex polyhedral hydrocarbon series each carbonatom is bonded to three other carbon atoms.
The fourth bond isdirected externally to a hydrogen atom. Around the all-carbon polyhedron, there is thus a similar polyhedron whose vertices are protons.The edges of the all-carbon polyhedron are carbon–carbon chemicalbonds, while the edges of the larger all-proton polyhedron do notcorrespond to any chemical bonds. This kind of arrangement of thepolycyclic hydrocarbons is not possible for the remaining two Platonicsolids.
There are four bonds meeting at the vertices of the octahedron and five at the vertices of the icosahedron. For similar reasons,only seven of the 13 Archimedian polyhedra can be considered in the(CH)n polyhedral series. One of them is the so-called “fuzzyball,” orC60 H60 , a predicted form of fully hydrogenated buckminsterfullerene(Figure 3-21e) [54].
Table 3-3 presents some characteristics of thepolyhedranes.Face anglesTetrahedrane(CH)4Triangle, 460◦Cubane(CH)8Square, 690◦Dodecahedrane(CH)20Pentagon, 12108◦Truncated tetrahedrane(CH)12Triangle, 4; Hexagon, 460◦Truncated octahedrane(CH)24Square, 6; Hexagon, 890◦ ; 120◦Truncated cubane(CH)24Triangle, 8; Octagon, 660◦ ; 135◦Truncated cuboctahedrane(CH)48Square, 12; Hexagon, 8; Octagon, 690◦ ; 120◦ ; 135◦Truncated icosahedrane(CH)60Pentagon, 12; Hexagon, 20108◦ ; 120◦Truncated dodecahedrane(CH)60Triangle, 20; Decagon, 1260◦ ; 144◦Truncated icosidodecahedrane(CH)120Square, 30; Hexagon, 20; Decagon, 1290◦ ; 120◦ ; 144◦aAfter H.
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