M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 81
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D., 465Dürer, A., 10, 16, 414, 416Dynamic properties, 212–213EEclipsed conformation, 101, 134Egyptian sculptures, 27Eiffel Tower, 41Einstein, A., 14Electrocyclic reactions, 350Electron diffraction, 11–12, 146, 158, 307, 490Electronic structurechanges during chemical reaction, 324–325conservation of orbital symmetry, 326–327frontier orbitals, 325–326maximum symmetry analysis, 327–328wave function description of, 241–249Electronic wave functionfundamental property, 240of hydrogen atom, 241–249many-electron atoms, 249–251one-electron atom, 241–249symmetry properties of, 240–241, 246Emerson, R.
W., 217Enantiomers, 71, 73, 100Enantiomorphs, 61, 68–69Energy calculations, for molecular crystals,470–473Environmental symmetry, influence of,290–294Equilibrium structure, 154–155Erni, H., 65, 66Escher, M. C., 119, 402, 404, 406, 415,459, 461Ethambutol, 74Ethane, 103, 104, 133, 362Ethylene cycloaddition, 343Ethylene dimerization, 328–340correlation diagram, 332–333, 335correspondence diagram, 337frontier orbital method, 328–329HOMO and LUMO of, 328–329MOs of ethylene–ethylene system, 332,335orthogonal approach, 338–340parallel approach, 328–332, 336–338state correlation, 332–336symmetry of reactants, transition structureand product in, 330Woodward–Hoffmann approach, 329Euclid, 484Euler, 78, 80IndexFFaraday, M., 19Fedorov, E.
S., 15, 46, 416, 437, 459Fejes Tóth, L., 81Ferrocene, 134–135Fibonacci series, 384–385Fischer, E., 62Flowers, 28–29, 34–35, 37–39, 43, 47Folk music, 31–33Free and crystalline molecules, structuredifferences in, 477–481Frontier orbitals, 325–326Fukui, K., 3, 313, 324, 325, 326, 328, 340Fuller, R. B., 4, 5, 6, 9, 446, 447, 473Fullerenes, 5–6, 8, 122–123GGal’pern, E. G., 6, 7Gardner, M., 65, 489Gas/solid structural differences, 478Gaudi, A., 200, 201Gay-Lussac, J.
L., 287Generalized crystallography, 424, 485, 491Generalized Woodward-Hoffmann rules, 350Genuine modes, 220Geodesic Dome, 6, 447Geometrical isomers, 100Geometrical model, of molecular crystals,457–465arrangements of molecular shapes,458–459dove-tail packing, 459–460head-to-head arrangement, 459–460head-to-tail arrangement, 459–460Geometrical symmetry, 37Gillespie, R. J., 151Glassy materials, definition of, 491Glide mirror, see Glide reflectionsGlide reflections, 372–374, 378Goniometers, 417–418Graphite, 6, 9, 122, 403Great dodecahedron, 85Great icosahedron, 85Great stellated dodecahedron, 85Grepioni, F., 472Gross, D. J., 12Groth, P., 59Group orbitals, 258Groups, 169–197, 204–215classes of, 174elements, 170–172irreducible representation of, 189multiplication tables for, 172, 173order of class and subgroup, 175Indexreducible representation of, 189representation of, 183–189similarity transformations in, 174–175subgroups, 174Group theory,120, 169–197, 204–215Grünbaum, B., 405, 489Guinier, A., 486, 487HHaeckel, E., 39, 80, 81Häckel, E., 6Haldane, J.
B. S., 70, 71Halevi, F. A., 313, 327, 328, 336Halevi’s method, 328Hamiltonian operator, 240Handedness, 3, 65, 70–72Hauptman, H., 448, 449Haüy, 418, 419, 420, 421Helical symmetry, 391Helices, translational symmetry of, 3Helium (He), MO construction in, 265Helix structure, 389Heptaprismane (C14 H14 ), 130Heraldic symmetry, 33See also bilateral symmetryHermann-Mauguin symmetry notations, 104Heterochiral, 61chairs, 66pairs of hands, 61segment, 74–75Heteronuclear diatomic molecules, 256Hexaprismane (C12 H12 ), 127, 130Highest occupied molecular orbital (HOMO),325–327of ethylene, 328–329H3 N · AlCl3 donor–acceptor complex,117–118Hodgkin, D., 440, 442Hoffmann, R., 3, 4, 313, 314, 324, 326, 327,328, 329, 331, 350, 351, 353, 354,355, 356, 360, 363HOMO, 325–329, 335, 340, 341, 343, 356Homochiral, 61chairs, 66pairs of hands, 61–62segment, 75Homomers, 100Homonuclear diatomic molecules, 256–257,263–266Houk, K. N., 318Hubcaps, 34–35Hückel–Möbius concept, 350–355Hückel ring, 351, 354Hückel system, 351, 353513Huffman, D., 9, 10Human bodybilateral symmetry of, 27symmetry of, 25–27, 30Human face, symmetry plane of, 30Humphreys, W.
J., 48, 50Hund, F., 251, 304, 326Hund’s rule, 304Hydrogen atom, 241–249Hydrogen (H2 ) molecule, 263–264Hydrogen-like orbitals, see Atomic orbitals(AOs)Hypersymmetry, in molecular crystals,474–476Hypostrophene, 156, 157IIceane hydrocarbon molecule, 131Ice crystal, 131Icosahedral packing, 446–449Icosahedral quasicrystal, 493Icosahedral structures, 9Icosahedron, 77, 79, 80, 83–85, 106, 125, 159Icosidodecahedron, 87–88Identity operation, 197Infinite lattices of crystal, 432–434Insulin, 440, 441, 442Intermolecular atomic radii, 457Internal coordinates, 213, 214, 224, 225, 229,230, 236International notations, see SymmetryIntramolecularcyclization, 343–450orbital correlation for, 343–346symmetry of reaction coordinate,346–350motion consequences, 153–161nonbonded interactions, 136–138geometrical consequences of, 1381,3 separations, 136–137van-der-Waals interactions, 137Inversion operation, 205, 246, 249Inversion symmetry, 53–55Iodine atom, total wave function of, 248Iodine heptafluoride (IF7 ), 158Ir4 (CO)12 , 160Iron dendrites formation, 31–32Irreducible representation, 189–191properties, 191–197symbols for, 194Isolobal analogy, 356–364Isomers, 98–100conformers, 100constitutional, 99514diastereomers, 99–100enantiomers, 100geometrical, 100hierarchy of, 100homomers, 100rotational, 99–100structural, 99–100JJahn–Teller active vibrations, 296Jahn–Teller distortion, 295–297, 300–305, 307Jahn–Teller effect, 294–308, 323Jahn–Teller phase transition, 301Jahn–Teller stabilization energy, 300Jones, D.
E. H., 5–6KKaolin, 453Kekulé, 19Kelvin, Lord/Thomson, W. H., 60, 458, 459Kepler, J., 10, 28, 42, 47, 80, 82, 161, 421,443, 486Keplerates, 81Kitaigordskii/Kitaigorodsky, A. I., 441, 467,468, 473Klug, A., 391, 447Knowles, W. S., 74Koestler, A., 1, 2, 80Kohn, W., 287, 288Kolbe, H., 97Koptsik, V. A., 75, 406, 438, 439, 440,445, 474Kotel’nikova, A., 135Krätschmer, W., 9, 10Kroto, H. W., 6, 7Kuhn, T., 492LLandau, L. D., 305, 306Law of rational indices, 417, 420Law of rational intercepts, 417,418, 420Laws of nature, and symmetry, 12–14Leaves, bilateral symmetry in, 28–29Le Bel, J.
A., 97Lee, T. D., 14, 15Left-and-right symmetry, 14Left-handed helices, 65Lehn, J.-M., 465Levine, D., 489, 491Levine, R. D., 289Lewis, G. N., 71, 151, 152, 357Lewis’ theory, 151–152Ligand field theory, 214, 290IndexLimiting groups, 104–105Limonene, 74Linear combination of atomic orbitals (LCAO),252Lipscomb, W. N., 159Lipscomb model, of rearrangement inpolyhedral boranes, 159L-nucleotides, 71Logos with rotational symmetry, 35–36Long-range pentagonal symmetry, 10Longuet-Higgins, H. C., 326, 334Lowest unoccupied molecular orbitals(LUMO), 325–329Lu, G.-D., 47Lucretius, 2, 457, 458Lunar Module, 30MMacGillavry, C., 402, 461Mackay, A.
L., 10, 11, 31, 70, 448, 483, 484,486, 487, 488, 490, 491, 492Mackay icosahedron, 448Mamedov, K., 404, 406Manganese trifluoride molecule, MnF3 ,Jahn–Teller distortion of, 302–303Mann, T., 25, 26, 44, 46Many-electron atomsorder of orbital energies in, 250–251wave function, 249–251Marginal stability, 42Matisse, H., 30, 153, 154, 155Matricescharacter of, 190column matrices, 177dimension, 176mathematical tool for symmetry operations,176–183square matrix, 176unit matrix, 176vectors and, 177–178Maximum symmetry analysis, 327–328Mazurs, E. G., 17Mendeleev, D. I., 17, 18, 30Mendeleev’s periodic system, 18Mermin, D., 492Metal halide molecules, 155Metal–carbonyl clusters, 160–161Metal–metal multiple bonds, 135Methane, 133consequences of substitution on symmetryof, 115–118molecular shape, 120–121, 143–1452-Methyl-1,4-butandiol, 75, 77Indexp-Methyl-N-(p-methylbenzylidine) aniline,482Mexican-hat type potential energy surface,303–304Meyer, V., 97Michelangelo, 253Miller indices, 420Minimum energy path, 320Mirror operation for movements, 213Mirror-rotation symmetry axis, 55Mirror symmetry, 175, 197–198Mislow, K., 16, 78Moiré patterns, 408–410Molecular crystalsarrangements of molecular shapes,458–459crystal field effects, 476–483densest molecular packing, 466–470energy calculations, 470–473geometrical model, 457–465hypersymmetry, 474–476structure predictions, 470–473Molecular orbitals (MOs), 252–261antibonding orbital, 254–255from atomic orbitals, 253–257bonding orbital, 254–255construction ofammonia, 268–269, 271–277benzene, 276–286helium molecule, 265homonuclear diatomics, 263–266hydrogen molecule, 263–264polyatomic molecules, 266–286water molecule, 266–270energy changes during formation of,256–257rule for construction of, 253–254symmetry of, 258Molecular packing, 466–470Molecular point groupsestablishing, 105–107symmetries, 104Molecular polarity, 57–60Molecular recognition, 289, 464, 465Molecular shapeselectronegative ligands and, 146–148with lone pair, 145–147, 149with multiple bonds, 145–146from points-on-the-sphere model, 141relative availability of space in valenceshell and, 147–148VSEPR model, 143–151Molecular vibrationsof carbon dioxide, 231, 233–236515in diimide, 229–233normal modes, 217–225selection rules, 227–229symmetry coordinate, 225–227Molecules, 252–287consequences of substitution on symmetryof, 115–118electronic states, 261–263homonuclear diatomics, 263–266helium, 265hydrogen, 263–264many-electron atom, 249–251molecular orbitals, 252–261, 264, 286–287one-electron wave function, 241–249polyatomic molecules, 266–286ammonia, 268–269, 271–277benzene, 276–286water, 266–268Movements, mirror operation for, 213Möbius ring, 352, 355Möbius systems, 351, 353–354Muetterties, E., 119, 123, 125, 126Mulliken, R.
S., 193, 195, 326Mulliken symbols, 193, 195Multiplicity, 55Music, 31–33NNakaya, U., 48, 49, 50, 51, 52, 53Nanoscience and nanotechnology, 4, 122Nanotubes and nanorods, 381–382Naproxen, 74Natta, G., 385, 388Needham, J., 47Newman, J., 169Noether, E., 313Nonbonded distances, regularities in, 136–139Noncrossing rule, 327, 335, 336Noncrystallographic symmetry, 10Non-enantiomorphous symmetry, 63Norgestrel, 74Normal coordinate analysis, 214, 226Normal modesbending mode, 224deformation modes, 224of molecular vibrations, 217–225number, 218–220stretching modes, 224symmertry, 220–224types, 224–225n-Prismanes (C2n H2n ), 130Noyori, R., 74Nyholm, R.
S., 151516OOClF3 , molecular configuration of, 140Octahedral AX6 molecules, consequences ofsubstitution, 115–117, 150Octahedron, 76, 79–81, 83notations, 450, 452–453One-dimensional space-groups, 376, 381, 385,387scheme for establishing symmetry class of,398–399One-electron atomwave functions, 241–249radial wave function, 241–242, 244–245symmetry properties, 246One-electron orbitals, shapes of, 246–247One-sided bands, symmetry classes, 375–378One-sided planar networks, symmetry classesof, 397ONF3 molecular geometry, 136OPF3 molecular configuration, 140, 149Optical activity, 61–63, 92Orbital correlation diagrams forbutadiene–cyclobutene interconversion,343–346Diels–Alder reaction, 340–343ethylene–butadiene cycloaddition, 342–343intramolecular cyclization, 343–346Orbitals, 242effect of inversion on, 246, 248–249sequence of energies in, 250–251, 266symmetry conservation, 3, 326–327d orbitalsenergies in octahedral and cubicenvironment, 292–293splittings in different ligand environments,292–294symmetry in octahedral and cubicenvironment, 291–292Orgel, L.
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