M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 82
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E., 71, 72Osawa, E., 6, 7Oscillating reactions, 392PPacioli, L., 7, 8, 82Paddlanes, 135–136Paracrystal lattice, 486–487Parity violation, 70Pasteur, L., 61, 62, 64, 67, 68, 70, 71, 490Pasteur’s models, 61, 64Paul, I. C., 59, 60Pauli exclusion principle, 151, 251Pauling, L., 17, 137, 387, 388, 389, 390, 455,459, 461, 462, 492p-chloroacetanilide crystal, 57, 59IndexPearson, R. G., 313, 320, 327, 347, 348, 349Penicillamine, 74Penrose, R., 10, 11, 489, 490Penrose tilings, 11, 489Pentagonal dodecahedron, 79, 80, 82, 84, 493Pentagonal prism, 40–41Pentagonal symmetry, 10, 79, 489Pentaprismane (C10 H10 ), 127, 130, 156Periodic tables, 17–19Permutational isomerism, 156–157PF3 Cl2 , 149PF2 Cl3 , 149PF5 -type molecules, 158Phosphine, 147Photosynthetic reaction center, 107–109Piezoelectricity, 60Pinecone scales, 384Planetary model, 80, 82Plantago media, 384–385Plato, 76Platonic solids, 76–81, 88, 126, 128See also regular convex polyhedraPoint groupdimensionality and periodicity insymmetry, 56–58establishing, 105–107symmetry, 55–56, 104–105Point groups, 105–115C2h , 105, 191, 195, 230Cnh , 105, 107Cnv , 105, 107Cs , 105, 109, 178, 179, 349C1 , 105, 189C2 , 105, 108, 170, 173, 184C3 , 105, 108, 173, 193, 272, 273C4 , 105, 108, 115C5 , 105, 108, 115C6 , 108, 115C2v , 105, 111, 193–194, 209, 221C3v , 105, 111, 209, 268, 271, 273C4v , 105, 111, 258–260, 360C∞v , 105, 111D2d, 105, 112D3d, 105, 112D4d, 125, 112D∞h , 105, 114, 231, 263, 264, 265D2h , 105, 113, 328, 330D3h , 105, 113D4h , 105, 113D5h , 105, 113D6h , 105, 113, 277–278Dnd , 106–107Dnh , 106D2 , 105, 111, 328, 330IndexD3 , 105, 111D4 , 105, 111D5 , 105, 111Ih , 115Oh , 115, 261, 291S4 , 105, 110S6 , 105, 110T, 105Td , 105, 125Th , 105Points-on-the-sphere model, 141Polanyi, M., 17, 318Polar axis, 57Polarity and symmetry, 57, 59–60Polar line, 57Polycyclic hydrocarbons, 125–132Polyethylene chain molecule, 385–386Polyhedral boranes, 159Polyhedral molecular geometries, 119–161boron hydride cages, 123–125intramolecular motion consequences,153–161non-bonded distances regularities, 136–139polycyclic hydrocarbons, 125–132structures with central atom, 133–136VSEPR model, 139–153analogies, 142–143historical perpectives, 151–153molecular shapes, 143–151Polyhedrane molecules, 119, 128Polyhedra, 76–90Polymorphism, 481–483Polypeptide chain, helical structures, 387–388P4 O6 , 132(PO)4 O6 molecule structure, 132Pople, J., 287, 288Potassium tetrafluoroaluminate (KAlF4 ),133–134Potential energy surface, 315–324reaction coordinate, 319–320saddle point, 316, 318transition state and transition structure,316–319Powell, H.
M., 151Pólya, G., 405, 407Prelog, V., 2, 65, 66, 69, 70Primitive organisms, pentagonal symmetry of,79–80Principal quantum numbers, 241–242Prismane molecules, 119, 130Prismatic cyclopentadienyl, 134Prisms, 89–90, 125, 130symmetry, 40–41Projection formulae, 101517Projection operator, 211–212Propoxyphene, 74Pseudo-Jahn–Teller effect, 294, 307, 323Pseudorotation, 153, 154, 158, 159Pseudosymmetry, 314Pyroelectricity, 60QQuantum chemical calculations, 151, 154, 258,287–290, 304, 319, 338, 340, 343,350, 353, 483Quantum numbers, 241–242, 250Quartz crystals, 63, 68, 417Quasicrystals, 4, 9, 11, 424, 489–494Quasi-regular polyhedra, 89RRadial symmetry, 29, 31Radiolarians, 80, 81Rational indices, law of, 417, 420Rational intercepts, law of, 417–418, 420Reaction coordinate, 319–320symmetry rules for, 320–324Reducible representation, 189–191Regular convex polyhedra, 76–80, 83–85,89–90characteristic symmetry elements, 77,79–80Regular dodecahedron, 79, 84, 119Regular icosahedron, 79, 123Regular pentagonal dodecahedron, 80, 82Regular polygons, 77, 78, 84, 90Regular star polyhedra, 85Regular tetrahedron, 117, 121, 133Renner, R., 294, 305, 306, 307Renner–Teller effect, 294, 306–307Representationcharacter of, 191–197of groups, 183–189irreducible, 189–191reducible, 189–191reduction, 206–208shortcut to determine, 204–205Reston, J., 54Reverse coupe du roi, 76Rh4 (CO)12 , 159Rhombicosidodecahedron, 87Rhombicuboctahedron, 87Rock salt crystal structure, 438–440Rotational isomerism, 100–104projectional representation, 102, 104Rotational isomers, 99–100Rotational symmetry, 33–36elemental angle, 34518in flowers, 34in hubcaps, 34–35logos with, 35–36in machinery rotating parts, 34–35in Norwegian tulip, 37–38order of, 33–34in sculptures of interweaving fish anddolphins, 36in Taiwanese stamp with two fish, 33–34in Vinca minor, 37–38in yin yang contour, 33–34Rotation axis with intersecting symmetryplanes, 37–39Ru3 (CO)12 , 472–473Ruskin, J., 494SSaddle-shaped sculpture, 317Salem, L., 314, 326Scattered leaf arrangements , 384, 392Schoenflies notation, 104–105Schrödinger, E., 240, 241, 252Schrödinger equation, 240–241, 252Scoresby, W., 48, 49Screw-axis symmetry, 382–384Screws, 64–65Scriven, M., 16Selection rules, in molecular vibrations,227–229Semiregular (Archimedean) polyhedra,87–90Shared electron pair, 151–152Sharpless, K.
B., 74Shechtman, D., 11, 12, 490–491Shephard, G. C., 405, 489Shubnikov, A. V., 10, 15, 67, 68, 75, 198, 199,406, 438, 439, 440, 445SiBr2 , bending potential energy functions, 156Sidgwick, N. V., 151Similarity transformation, 174Simulated diffraction pattern, 11Single bond, rotational isomerism relative to,103–104Singular point symmetry, 55–57Small stellated dodecahedron, 85Smalley, R.
E., 6, 7Sn[Fe2 (CO)8 ]2 , molecular geometry of, 363Snow crystals, 40, 42, 43, 46, 47, 48, 49, 53Snowflakesclassification, 50–53formation, 44, 49–50hexagonal symmetry, 42, 47–50malformed crystals, 50morphology of, 40, 42–44Indexphotomicrographs, 48, 50symmetries, 39–53, 55Snub cube, 87, 90Snub dodecahedron, 87SO2 Cl2 , 171, 182Sodalite unit, 89Sodium chloride, 416–417, 454–455, 477Space-groups symmetries, 56band symmetries, 375–381in crystal symmetries, 432–440dimensionality, 372expanding to infinity, 371–375glide-reflection, 373–374, 380identity period in, 373, 385one-sided bands, 375–380planar decoration with, 372–373rods, 381–395similarity symmetry, 381–395spirals, 381–395translation presence in, 373, 378–379, 385two-dimensional, 395–410two-sided bands, 378–381Sphere, 85–86Sphere packing, 442–446Spin quantum number, 250Spiral staircase, 71screw-axis symmetry in, 382–383Spiral symmetry, 391–393Square matrix, 176Square prismatic [Re2 Cl8 ]2− ion structure,134–135SrBr2 , bending potential energy functions,155–156Staggered conformation, 101, 104Stalactites and stalagmites, 31Standing wave theory, 43–44Starfish, 38–40Steno, 417Steinhardt, P., 489, 491Structural isomerism and isomers, 99–100Sulfones, 138Sulfur dichloride, 146Sulfur difluoride, 145–146Sulfur hexafluoride (SF6 ), consequences ofsubstitution, 115–116Sulphuric acid, 138Symmetrybands symmetry, 375–381bilateral, 25–33broken, 14–15center, 53–55chemical, 2–3, 14, 16chirality, 60–76classes of one-sidedIndexbands, 375–380planar networks, 395–401combined, 37–53concept of, 1–3, 16consequences of substitution on,115–119coordinate in molecular vibrations,225–227definitions, 15–16and degeneracy of energy levels, 243–244,260–261element and consequences, 37environmental, 290–294forbidden chemical reactions, 314, 331and group theory, 169–170and harmony, 18of human body, 25–27importance of, 14, 19inversion, 53–55and Jahn–Teller effect, 294–308laws of nature and, 12–14left-and-right, 14notations, 104–105of crystallographic groups, 105of limiting groups, 104–105planes, rotation axis with in, 37–39polarity, 57–60polyhedra, 76–90rods, 381–395rotational, 33–36rotation axis, 37–39rulesfor chemical reactions, 313–315, 320,340, 343for reaction coordinate, 320–324similarity symmetry, 381–395singular point, 55–58snowflakes, 39–53, 55species, 189spirals symmetry, 381–395translational, 55–57Symmetry-adapted linear combinations(SALCs), 258, 266–267, 271–274,277, 279–281, 283, 285–287Synergy, importance for chemistry, 5T‘t Hooft, G., 14Teller, E., 294–297, 299, 300–302, 305–308,322, 323Tetraarsene (As4 ), 120–121Tetragonal bipyramidal systems, 148Tetrahedral AX4 molecule, consequences ofsubstitution, 115–116519Tetrahedral sulphur configurations, 138Tetrahedrane (CH)4, 126–127, 129, 363, 364Tetrahedron notations, 450–451, 453Tetralithiotetrahedrane (CLi)4 , 134Tetra-tert-butyltetrahedrane, 126–127Thalidomide, 72–73Thompson, D.
W., 6, 97, 391Thompson, W. H./Lord Kelvin, 60, 458,459, 499Three-dimensional space-groups, 375, 437,469, 474–475, 485unit cell, 433, 438, 439, 444Tobacco mosaic virus (TMV), 391Transition-state geometries, of chemicalreactions, 316–319Translational antisymmetry, 200–201Translational symmetry, 55–57Trees, conical and radial symmetries of, 29Triacontrahedral quasicrystal, 493Triamantane molecule structure, 132–1331,3,5-Triphenylbenzene molecules, packing incrystal structure, 457–458Triprismane (CH)6 , 127, 130Tronev, V. G., 135Truncated cube, 87–88Truncated cuboctahedrane (CH)48, 129Truncated cuboctahedron, 87Truncated dodecahedrane (CH)60, 129Truncated dodecahedron, 87–88Truncated icosahedral geometry, 6, 9Truncated icosahedrane (CH)60, 129Truncated icosahedron, 7–8, 88–89Truncated icosidodecahedrane (CH)120, 129Truncated icosidodecahedron, 87Truncated octahedron, 87–89Truncated tetrahedron, 87–88T symmetry, 114Twinned cuboctahedron, 449Two-dimensional space-groups, 375, 395–410lattice point, 398–399Moirés, 408–410planar decorations with, 372–373plane lattices, 398, 400–402primitive cell, 398scheme for establishing symmetry class of,398–399side-effects of decorations, 406–408simple networks, 401–406symmetry classes, 395–401unit cell, 398, 402, 405UUnit matrix, 176Index520VValence Shell Electron Pair Repulsion(VSEPR) model, 139–153analogies, 142–143historical perceptives, 151–153molecular shapes, 143–151quantum-mechanical foundations for, 151three-dimensional consequences of,142–143van der Waals radii, 137van ‘t Hoff, J.
H., 97Vatsayana, 422Vectorsand matrix, 177–178reflection by horizontal mirror plane, 179representation in three-dimensional space,177rotation by an angle α in xy plane, 180Vibrational transitions, 228Vinca minor, rotational symmetry in, 37–38Vinyl polymers, 385–387WWald, G., 62Walnut clusters, 143Water and ice, structural difference between,440–441Water (H2 O) moleculecartesian displacement vectors, 222MO construction in, 266–270molecular shapes, 143–145normal modes of vibration for, 220symmetry coordinates of, 225–227Watson, J. D., 3, 4, 388, 390, 462Wave function, see Electronic wave functionWeinberg, S., 13Wells, A. F., 442, 443, 444, 450Weyl, H., 16, 33, 79Whyte, L.
L., 42, 63Wickham, A., 485Wigner, E. P., 12, 13, 14, 17, 240, 313Wigner’s theorem, 240Wigner–Witmer rules, 313Witmer, E. E., 313Williams, I. H., 317Woodward, R. B., 313, 314, 324, 326, 327,328, 329, 331, 350, 351, 353, 354,355Woodward–Hoffmann diagrams, 327Woodward–Hoffmann rules, 350–351,353–354W6 S8 (Pet3 )6 crystal structure, 81, 83YYang, C. N., 14, 15, 47, 197Young, L.
B., 371ZZachariasen, W. H., 485, 486Zhabotinsky, A. M., 392, 393Zeolites structure, 89Ziegler, K., 385Zimmerman, H. E., 351, 353Zirconium borohydride [Zr(BH4 )4 ], 121ZnCl2 , bending potential energy functions,155–156.
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