M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 21
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P. Schultz, “Topological Organic Chemistry: Polyhedranes and Prismanes.” J. Org. Chem. 1965, 30, 1361–1364.3.7. Polyhedral Molecular GeometriesNameTable 3-3. Characterization of Polyhedrane MoleculesaFormulaGeometry and number of faces (all regular)1291303 Molecular Shape and GeometryThe cubane molecule may also be considered and called tetraprismane (vide infra). It may be described as composed of eight identical methine units arranged at the corners of a regular tetragonalprism with Oh symmetry and bound into two parallel four-memberedrings conjoined by four four-membered rings. Triprismane, (CH)6[55], has D3h symmetry and pentaprismane, (CH)10 [56], has D5hsymmetry.
Triprismane, pentaprismane, and hexaprismane, C12 H12(not yet prepared), are shown in Figure 3-21f. The quest for asynthesis of pentaprismane is a long story with a happy ending [57].Hexaprismane, (CH)12 , which is the face-to-face dimer of benzene hasnot yet been prepared.
A recent study showed that this dimerizationwould not only be symmetry-forbidden (see, Chapter 7), but wouldalso be hindered by a high energy barrier [58]. Table 3-4 presentssome characteristic geometric information on the hydrocarbon prismane molecules. The description of the general n-prismane is that itis composed of 2n identical methine units arranged at the corners ofa regular prism with Dnh symmetry and bound into two parallel nmembered rings conjoined by n four-membered rings.Incidentally, the regular prisms and the regular antiprisms are alsosemiregular, i.e., Archimedian, solids. Moreover, the second prism, inits most symmetrical configuration, is a regular solid, the cube; and thefirst antiprism, in its most symmetrical configuration, is also a regularsolid, the octahedron.Only a few highly symmetrical structures have been mentionedabove.
The varieties become virtually endless if one reaches beyondNameTable 3-4. Characterization of Prismane MoleculesaFormulaGeometry and number offaces (all regular)Face anglesTriprismaneC6 H6Triangle, 2; Square, 360◦ ; 90◦TetraprismaneC8 H8Square, 690◦(cubane)PentaprismaneC10 H10Pentagon, 2; Square, 5108◦ ; 90◦HexaprismaneC12 H12Hexagon, 2; Square, 6120◦ ; 90◦HeptaprismaneC14 H14Heptagon, 2; Square, 7128◦ 34 ; 90◦n-PrismaneC2n H2nn-gon, 2; Square, n–b ; 90◦aAfter H. P. Schultz, “Topological Organic Chemistry: Polyhedranes andPrismanes.” J.
Org. Chem. 1965, 30, 1361–1364.bApproaches 180◦ as n increases.3.7. Polyhedral Molecular Geometries131Figure 3-22. Left: Ice crystal structure; Right: the iceane hydrocarbon molecule.the most symmetrical convex polyhedral shapes. For example, thenumber of possible isomers is 5,291 for the tetracyclic structures ofthe C12 H18 hydrocarbons with 12 skeletal carbon atoms [59]. Of allthese geometric possibilities, however, only a few are stable [60].One is iceane shown in Figure 3-22.
The molecule may be visualized as two chair cyclohexanes connected to each other by threeaxial bonds. Alternatively, the molecule may be viewed as consistingof three fused boat cyclohexanes. The trivial name iceane had beenproposed for this molecule by Fieser [61] almost a decade beforeits preparation [62]. As Fieser was considering the arrangement ofthe water molecules in the ice crystal (Figure 3-22), he noticedthree vertical hexagons with boat conformations.
The emerging horizontal (H2 O)6 units possess three equatorial hydrogen atoms and threeequatorial hydrogen bonds available for horizontal building. Fieserfurther noted that this structure “suggests the possible existence ofa hydrocarbon of analogous conformation of the formula C12 H18 ,which might be named ‘iceane.’ The model indicates a stable strainfree structure analogous to adamantane and twistane.
‘Iceane’ thuspresents a challenging target for synthesis” [63]. Within a decade thechallenge was met.There is a close relationship between the adamantane, C10 H16 ,molecule and the diamond crystal. The Greek word adamant meansdiamond and diamond has been termed the “infinite adamantylogue toadamantane” [64]. While iceane has D3h symmetry, adamantane hasTd .
This high symmetry can be clearly seen when the configuration ofadamantane is described by four imaginary cubes packed one insidethe other, two of which are shown in Figure 3-23. Similar structures1323 Molecular Shape and GeometryFigure 3-23. Adamantane and its analogs. Left: Adamantane, C10 H16 or(CH)4 (CH2 )6 ; in two representations; Right: P4 O6 (top) and (PO)4 O6 (bottom).are found among inorganic compounds where, by analogy to adamantane, (CH)4 (CH2 )6 , the general formula is A4 B6 . Here A may be, e.g.,P, As, Sb, or PO, as illustrated in Figure 3-23.Adamantane molecules may be imagined to join at vertices, edges,or even at faces. Examples are shown in Figure 3-24; most of them,however, have not yet been synthesized [65].Figure 3-24. Joined adamantanes. Top, left: joined at vertices, [1]diadamantane[66]; Top, right: joined at edges, [2]diadamantane [67]; Bottom: joined at faces,diamantane (congressane) [68], triamantane [69], and three isomers of tetramantane:“iso” C3v ; “anti”, C2h ; and “skew”, C2 [70].3.7.
Polyhedral Molecular Geometries1333.7.3. Structures with Central AtomAdamantane is sometimes regarded as the cage analog of methanewhile diamantane and triamantane as the analogs of ethane andpropane. Methane has, of course, a tetrahedral structure with thepoint group of the regular tetrahedron, Td . Important structures maybe derived by joining two tetrahedra, or, for example, two octahedra, at a common vertex, edge, or face as shown in Figure 3-25.Ethane, H3 C–CH3 , ethylene, H2 C=CH2 , and acetylene, HC≡CH, maybe derived formally from joined tetrahedra in such a way. The analogywith the joining tetrahedra is even more obvious in some metal halidestructures with halogen bridges [71]. Thus, e.g., the Al2 Cl7 – ion maybe considered as two aluminum tetrachloride tetrahedra joined at acommon vertex, or the Al2 Cl6 molecule may be looked at as two suchtetrahedra joined at a common edge.
These examples are shown inFigure 3-26.Figure 3-25. Joined tetrahedra and octahedra.In mixed-halogen complexes, such as potassium tetrafluoroaluminate, KAlF4 [72], there is also a tetrahedral metal coordination. Infact, the regular or nearly regular tetrahedral tetrafluoroaluminate partof the molecule is an especially well defined structural unit.
It isrelatively rigid, whereas the position of the potassium atom aroundthe AlF4 tetrahedron is rather loose. The most plausible model forthis molecule is also shown in Figure 3-26. The KAlF4 moleculeis merely a representative from a large class of compounds with134Figure 3-26.molecules.3 Molecular Shape and GeometryThe configurations of the Al2 Cl7 – ion and Al2 Cl6 and KAlF4great practical importance: the mixed halides have greatly enhancedvolatility compared with the individual metal halides.For tetralithiotetrahedrane, (CLi)4 , the structure with the lithiumatoms above the faces of the carbon tetrahedron was found in thecalculations to be more stable than with the lithium atoms above thevertices (Figure 3-27) [73].The prismatic cyclopentadienyl and benzene complexes of transition metals are reminiscent of the polycyclic hydrocarbon prismanes. Figure 3-28 shows ferrocene, (C5 H5 )2 Fe, for which both thebarrier to rotation and the free energy difference between the prismatic(eclipsed) and antiprismatic (staggered) conformations are very small[75].
Figure 3-28 also presents a prismatic model with D6h symmetryfor dibenzene chromium, (C6 H6 )2 Cr.Molecules with multiple bonds between metal atoms often havestructures with beautiful and highly symmetrical polyhedral shapes.The square prismatic [Re2 Cl8 ]2– ion, shown in Figure 3-29, playedan important role in the history of the discovery of metal–metalFigure 3-27. Model of the (CLi)4 molecule [74].3.7. Polyhedral Molecular Geometries135Figure 3-28. Prismatic molecular models. Ferrocene: prismatic (D5h ) and antiprismatic (D5d ); dibenzene chromium: prismatic (D6h ).Figure 3-29.
The square prismatic structure of the [Re2 Cl8 ]2– ion which played ahistoric role in the discovery of metal–metal multiple bonds (see, text) and a Sovietstamp with the same structure. The building in the background is the research institute in Moscow where the first such structure was prepared.multiple bonds [76]. The first report of the very short Re–Re bondappeared in 1958, in Russian, from the Inorganic Chemistry Institute of the Soviet Academy of Sciences in Moscow [77]. The authors,Ada Kotel’nikova and V. G. Tronev, recognized the presence of directmetal–metal bonding, but failed to suspect that it might be multiplebonding. The bond was so short that it was suspect.
A few years laterF. Albert Cotton reinvestigated the structure, confirmed the findings ofthe Moscow scientists, and introduced the notion of Re–Re quadruplebonding [78]. The original study by Kotel’nikova and Tronev wascommemorated on a postage stamp issued for the fiftieth anniversaryof their Institute (Figure 3-29).Figure 3-30 shows another molecule with metal–metal multiplebond. Its shape is similar to the paddles that propel riverboats. Thereis then a whole class of hydrocarbons called paddlanes [79] and oneof their representatives is also shown in Figure 3-30.1363 Molecular Shape and GeometryFigure 3-30. Left: Dimolybdenum tetraacetate, Mo2 (O2 CCH3 )4 [80]; Right:[2.2.2.2]Paddlane.3.7.4. Regularities in Nonbonded DistancesThe structure of the ONF3 molecule is depicted in Figure 3-31 withthe bond lengths, bond angles, and nonbonded distances.
The shape ofthe molecule well approximates a regular tetrahedron formed by threefluorines and one oxygen. The nonbonded F···F and F···O distancesrepresenting the lengths of the edges of a tetrahedron are equal withinthe experimental errors of their determination [81]. The molecule hasC3v symmetry, and the central nitrogen atom is obviously not in thecenter of the tetrahedron of the four ligands.In some molecular geometries, the so-called intramolecular 1,3separations are remarkably constant.
The “1,3” label refers to theinteractions between two atoms in the molecule which are separatedby a third atom. The near equality of the nonbonded distances in theONF3 molecule is a special case. What is more commonly observed isthe constancy of a certain 1,3 nonbonded distance throughout a seriesof related molecules. Significantly, this constancy of 1,3-distancesmay be accompanied by considerable changes in the bond lengthsFigure 3-31. The molecular geometry of ONF3 with: Left: bond lengths and bondangles; and Right: nonbonded distances [82].3.7. Polyhedral Molecular Geometries137and bond angles within the three-atom group.
The intramolecular 1,3interactions have also been called intramolecular van der Waals interactions, and L. S. Bartell postulated a set of intramolecular nonbonded1,3 radii [83]. These 1,3 nonbonded radii are intermediate in valuebetween the corresponding covalent radii and “traditional” van derWaals radii, all compiled for some elements in Table 3-5.Figure 3-32 shows some structural peculiarities which originallyprompted Bartell to recognize the importance of the intramolecularnonbonded interactions [84].
It was an interesting observation that thethree outer carbon atoms in H2 C=C(CH3 )2 were arranged as if theywere at the corners of an approximately equilateral triangle, as shownin Figure 3-32. The central carbon atom in this arrangement is obviously not in the center of the triangle, consequently, the bond anglebetween the bulky methyl groups is smaller than the ideal 120◦ . In theTable 3-5. Covalent, 1,3 Intramolecular Nonbonded and van der Waals Radii ofSome Elements1,3 IntramolecularVan der WaalsElementCovalentnonbonded radiusb (Å)radiusa (Å)radiusa (Å)BCNOF0.8170.7720.700.660.641.331.251.141.131.081.501.401.35AlSiPSCl1.2021.171.101.040.991.661.551.451.451.441.901.851.80Ga1.261.72Ge1.221.58As1.211.612.00Se1.171.582.00Br1.141.591.95aAfter L.
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