M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 25
Текст из файла (страница 25)
The relatively high barrier at e = 0◦ for SiBr2 indicates anunambiguously bent configuration. Further enlarging the scale revealsa small barrier at e = 0◦ for SrBr2 , so small that it lies below the levelof the ground vibrational state. Such structures are called quasilinear.Rapid interconversion of the nuclei takes place in the bullvalenemolecule under very mild conditions in fluid media.
This processinvolves making and breaking bonds, but this is accompanied by onlyvery small shifts in the nuclear positions. The molecular formula is(CH)10 and the carbon skeleton is shown at the top of Figure 3-49.There are only four different kinds of carbon positions (and hydrogen1563 Molecular Shape and GeometryFigure 3-48. Bending motion and a sampler of potential energy functions. Top:bending vibration of a linear triatomic molecule, where r is the instantaneousdistance between the end atoms and re is the equilibrium distance of the linearconfiguration (r<re ); Bottom: Comparison of bending potential functions for linearand bent models of symmetric triatomic molecules [111].positions, accordingly) and all four positions are being interconvertedsimultaneously [112].Hypostrophene is another (CH)10 hydrocarbon whose trivial namewas chosen to reflect its behavior, the Greek hypostrophe meaningturning about [115].
The molecule is ceaselessly undergoing theintramolecular rearrangements indicated at the bottom of Figure 3-49.The atoms have a complete time-averaged equivalence yet hypostrophene could not be converted into pentaprismane.Permutational isomerism among inorganic substances was discovered by R. S. Berry for trigonal bipyramidal structures [116].3.7. Polyhedral Molecular Geometries157Figure 3-49. The interconversion of bullvalene [113] (top) and hypostrophene[114].Although the trigonal bipyramid and the square pyramid havedifferent symmetries, D3h versus C4v , they easily interconvert bymeans of bending vibrations as is illustrated in Figure 3-50.
Thechange in the potential energy during this structural reorganizationis also shown. The permutational isomerism of an AX5 molecule,e.g., PF5 , is easy to visualize as the two axial ligands replace two ofthe three equatorial ones, while the third equatorial ligand becomesthe axial ligand in the transitional square pyramidal structure. Therearrangements quickly follow one another without any position beingconstant for any significant time period. The C4v form originates froma D3h structure and yields then again to another D3h form. A somewhat similar pathway was established for the (CH3 )2 NPF4 moleculein which the dimethylamine group is permanently locked in an equatorial position whereas the fluorines exchange in pairs all the time [117].The structure of the (CH3 )2 NPF4 molecule and its investigation byNMR spectroscopy is also a good example to demonstrate the importance of the relationship between the lifetime of a configuration andthe time-scale of the investigating technique.
The 31 P NMR spectraof (CH3 )2 NPF4 at low temperatures provide evidence of two differentkinds of P–F bond in this molecule, viz., axial and equatorial. At lowtemperatures the interconversion is slow and the lifetimes of the fluorines in the axial and equatorial positions are much greater than the1583 Molecular Shape and GeometryFigure 3-50. Berry-pseudorotation of PF5 -type molecules with a potential energyfunction and R.
Stephen Berry (photograph by the authors).interaction time for producing the spectrum. So the two kinds of P–Fbond give separate resonances in the spectrum. At higher temperatures the intramolecular exchange of the fluorine positions accelerates and the lifetimes of the fluorines in the axial and equatorialpositions decrease. As the interaction time needed to produce thespectrum remains the same, the spectrum becomes simpler and thenonequivalent fluorines are no longer distinguished. Since the timescale of NMR spectroscopy is commensurable with the lifetimes ofseparate configurations in intramolecular motion, different molecular shapes may be observed at different temperatures. Other techniques utilize interactions at different time-scales.
Thus, for example,the time-scale of electron diffraction is several orders of magnitudesmaller and, accordingly, the two different fluorine positions willalways be distinguished in an electron diffraction analysis.Iodine heptafluoride, IF7 , has a pentagonal bipyramidal structureof at least approximately D5h symmetry [118]. Its dynamic behaviorhas been desribed by pseudorotation.
The rearrangement that characterizes the PF5 molecule also describes well the permutation of3.7. Polyhedral Molecular Geometries159the atomic nuclei in five-atom polyhedral boron skeletons in boranemolecules [119].W. N. Lipscomb elaborated a general concept for the rearrangements of polyhedral boranes according to which two commontriangulated faces are stretched to a square face in the borane polyhedra [120]. There is an intermediate polyhedral structure with squarefaces. In the final step of the rearrangement, the intermediate configuration may revert to the original polyhedron with no net change,but it may as well turn into a different arrangement.
The arrangement has rectangular faces with an orthogonal linkage with respectto the bonding situation in the original polyhedron (Figure 3-51). Ofthe many possible examples, the rearrangements of dicarba-closododecaboranes are illustrated in Figure 3-52. There are three isomersof this beautiful carborane molecule:1,2-dicarba-closo-dodecaborane, or o-C2 B10 H12 ,1,7-dicarba-closo-dodecaborane, or m-C2 B10 H12 , and1,12-dicarba-closo-dodecaborane, or p-C2 B10 H12 .Whereas the ortho isomer easily transforms into the meta isomerin agreement with the above mentioned model, the para isomer isobtained only under more drastic conditions and only in a smallamount [121].A similar model has been proposed for the so-called carbonylscrambling mechanism in molecules like Co4 (CO)12 , Rh4 (CO)12 ,Figure 3-51.
Lipscomb model of the rearrangement in polyhedral boranes(top) with the polyhedral rearrangement of icosahedron/cuboctahedron/icosahedron[122].1603 Molecular Shape and GeometryFigure 3-52. Structures of ortho-, meta-, and para-dicarba-closo-dodecaborane[123].and Ir4 (CO)12 [124]. The carbonyl ligands can have several modesof coordination, viz., terminal and a variety of bridging possibilities.
Rapid interconversion between the different coordination modesis possible, even in the solid state [125]. These metal-carbonylmolecules belong to a large class of compounds whose generalformula is Mm (CO)n , where M is a transition metal. The usually smallFigure 3-53. The structure of [Co6 (CO)14 ]4– in two representations after [127]: Left:the octahedron of the cobalt cluster possesses six terminal and eight triply bridgingcarbonyl groups; Right: an omnicapped cube of the carbonyl oxygen envelopes thecobalt octahedron.References161m-atomic metal clustser polyhedron is enveloped by another polyhedron whose vertices are occupied by the carbonyl oxygens [126]. Anattractive example is the structure of [Co6 (CO)14 ]4– in which the octahedral metal cluster has six terminal and eight triply bridging carbonylgroups, as shown in Figure 3-53.
This structure may also be represented by an omnicapped cube enveloping an octahedron, which isalso depicted in Figure 3-53. These models are reminiscent of anothermodel in which, also, polyhedra were enveloping other polyhedra.That model was Kepler’s planetary system in his Mysterium cosmographicum published in 1595 and mentioned in the previous Chapter.References1. D. W. Thompson, On Growth and Form, Cambridge University Press, 1917.2. A comprehensive account of the origins and early history of stereochemistryis given in O.
B. Ramsay, Stereochemistry. Heyden, London, 1981.3. Kolbe in Ramsay, Stereochemistry, p. 93.4. L. Pauling, The Nature of the Chemical Bond and the Structure of Moleculesand Crystals: An Introduction to Modern Structural Chemistry, Third Edition,Cornell University Press, Ithaca, New York, 1960.5. I. Hargittai, “Degas Dancers – An Illustration for Rotational Isomers.”J. Chem. Educ. 1983, 60, 94. Full color reproductions of the original areavailable in editions of Degas’ work. The original of the drawing with theoutstretched hands of ther dancer is in the Louvre, Musée de l’Impressionismein Paris, and of the other in The Hermitage in St. Petersburg.6.
Hargittai, J. Chem. Educ. 94.7. N. F. M. Henry, K. Lonsdale, eds., International Tables for X-ray Crystallography, Vol. I., Symmetry Groups, Kynoch Press, Birmingham, 1969.8. J. H. Conway, D. H. Huson, “The Orbifold Notation for Two-DimensionalGroups.” Struct. Chem. 2002, 13, 247–257.9. F. A. Cotton, Chemical Applications of Group Theory, Third Edition, WileyInterscience, New York, 1990; M.
Orchin, H. H. Jaffe, “Symmetry. PointGroups, and Character Tables; I, Symmetry Operations and Their Importancefor Chemical Problems.” J. Chem. Educ. 1970, 47, 372–377.10. Ibid.11. M. F. Perutz, Proteins and Nucleic Acids: Structure and Function. Elsevier,Amsterdam, 1962, pp. 64 and 66.12. See, e.g., I. Hargittai, The DNA Doctor: Candid Conversations with JamesD. Watson.
World Scientific, Singapore, 2007, p. 10.13. I. Hargittai, Candid Science III: More Conversations with Famous Chemists.Ed. M. Hargittai. Imperial College Press, London, 2003, “Johann Deisenhofer”, pp. 342–353.1623 Molecular Shape and Geometry14. Hargittai, Candid Science III, pp. 349–350.15. Hargittai, Candid Science III, p. 345.16. See, e.g., J.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
