Wilson E.B. — Molecular Vibrations. The Theory of Infrared and Raman Vibrational Spectra :: Электронная библиотека попечительского совета мехмата МГУ

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Wilson E.B. — Molecular Vibrations. The Theory of Infrared and Raman Vibrational Spectra

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Название: Molecular Vibrations. The Theory of Infrared and Raman Vibrational Spectra

Автор: Wilson E.B.

Аннотация:

A pedagogical classic and an essential reference for anyone engaged in research in molecular spectroscopy, focusing on the mathematics involved in detailed vibrational analyses of polyatomic molecules. Leads the reader gradually from application of wave mechanics to potential functions and methods of solving the secular determinant. 16 appendices.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 4-th

Год издания: 1980

Количество страниц: 388

Добавлена в каталог: 30.10.2006

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Предметный указатель

Selection rules for rotation-vibration spectra symmetric rotor molecules      364 366
Selection rules for rotation-vibration spectra, asymmetric rotor molecules      364 366ff.
Selection rules for rotation-vibration spectra, linear molecules      363—366ff.
Selection rules for rotation-vibration spectra, spherical rotor molecules      364 366ff.
Selection rules infrared vibration spectrum      159
Selection rules infrared vibration spectrum for C ${}_{6}$ H ${}_{6}$       244ff.
Selection rules infrared vibration spectrum for vibrational quantum numbers      42
Selection rules infrared vibration spectrum in electric moment integrals      41
Selection rules, for rotational infrared spectrum      42 363ff.
Selection rules, for rotational Raman spectrum      53 365
Selection rules, for translational quantum number      40
Selection rules, for vibrational Raman spectrum      51 53 161 365
Selection rules, for vibrational Raman spectrum by polarizability integrals      50 161
Selection rules, for vibrational Raman spectrum for C ${}_{6}$ H ${}_{6}$       244ff.
Selection rules, for vibrational Raman spectrum polarizability derivatives in      48
Selection rules, violation in liquid state      146
Semidefinite matrix      298
Separation, of electronic from rotational and vibrational wave equations      6
Separation, of high and low frequencies      74 311
Separation, of rotation and vibration      11 34 243ff.
Separation, of rotation and vibration, approximate      283
Sets, equivalent internal coordinates      109
Sets, of equivalent atoms      85ff.
Sharpness of totally symmetric: Raman lines for spherical rotor      367
Shutts, L. W.      232
Simanouti, T.      180
Similarity transformation      301
Simultaneous equations solution      222ff.
Simultaneous equations solution by analogue computers      232ff.
Simultaneous equations solution by relaxation      224
Simultaneous equations solution by successive elimination      222ff.
Singular matrix      295
Slater, J. C.      43
Small vibrations in classical mechanics      14ff
Solid state      3
Sommorfield, A.      8
Southwell, R. V.      224 225
Space-fixed coordinates      285
Spciscr, A      77 121
Species, correlation with those of subgroup      121 135 333
Species, degenerate, characters of      94 352ff.
Species, degenerate, correlation with those of subgroup      121 135 333ff.
Species, degenerate, doubly      113 322
Species, degenerate, triply      113 322
Species, in reduction of reducible representation      99 100 113
Species, multiplication of      331
Species, notation      322
Species, number of normal vibrations of a given      99 107
Species, occur $n^{(\lambda)}$ times in reducible representation      99 100 113
Species, of anharmonic vibrational levels      146
Species, of combinations (binary), of degenerate levels      149ff.
Species, of combinations (binary), of degenerate levels, and nondegenerate levels      149
Species, of combinations (binary), of nondegenerate levels      148
Species, of components, of electric dipole moment ( $T_{x}$ , $T_{y}$ , $T_{z}$ )      323—330
Species, of components, of polarizability      161 323—330
Species, of fundamentals      148
Species, of general vibrational levels      155
Species, of normal coordinates      92
Species, of polarizability, rotation, translation (character tables)      323 330
Species, of wave functions      147 (see also Irreducible representation)
Species, overtones, of degenerate levels      152ff. 247 332 352ff.
Species, overtones, of nondegenerate levels      151
Spherical part of polarizability      47 51 360
Spherical rotor      361
Spherical rotor, band types      364
Spherical rotor, degeneracy      362
Spherical rotor, energy, nonrigid      369
Spherical rotor, energy, rigid      362
Spherical rotor, selection rules, infrared spectrum      364
Spherical rotor, selection rules, Raman spectrum      366
Splitting      see Degenerate vibrations
Spontaneous transition coefficient      38
Square matrix      299
Sruekal, A.      3 49
Staggered model of ethane      84
Stepanov, B.      182
Stokes Raman lines      3 9 48 51
Stretching force constants, numerical values      175 (see also Internal coordinates force
Stretching vibrations      178 216 252
Structure, molecular, from infrared and Raman, studies      10
Structure, of representations      108
Structure, of representations, determination of the $n^{(\lambda)}$       99 100 113
Subgroup      85
Subgroup, order of, is a divisor of order of group      86
Subgroup, reduction of representation in      121 135 333ff. 350
Subgroup, sends a single atom into itself      85
Submatrices      298 311
Successive elimination solution of secular equation      222ff.
Sum rule, for isotopic frequencies      180ff.
Sum rule, for isotopic intensities      192
Sun, C. E.      140
Superposition of normal modes      18 19
Sutherland, G, B. B. M.      2
Svordlov, L. M.      186
Symmetric matrix      290 301
Symmetric rotor      301
Symmetric rotor, band types      304
Symmetric rotor, degeneracy      302
Symmetric rotor, energy, nonrigid      368
Symmetric rotor, energy, rigid      302
Symmetric rotor, intensity, absolute, parallel band      101
Symmetric rotor, selection rides, infrared spectrum      304
Symmetric rotor, selection rides, Raman spectrum      306
Symmetrically complete sets      117
Symmetrically equivalent atoms, sets of      85
Symmetrization of secular equation      21 1ff.
Symmetry axes      see Axes of symmetry
Symmetry coordinates      115ff.
Symmetry coordinates, construction of, degenerate      119 123
Symmetry coordinates, construction of, degenerate, when $n^{(\gamma)}> 1$       135ff.
Symmetry coordinates, construction of, external      125
Symmetry coordinates, construction of, internal      117ff.
Symmetry coordinates, construction of, internal, internal, for C ${}_{6}$ H ${}_{6}$       257ff.
Symmetry coordinates, construction of, internal, internal, for CH ${}_{4}$       120
Symmetry coordinates, construction of, nondegenerate      118
Symmetry coordinates, factoring of secular equation by      115 347ff.
Symmetry coordinates, orientation of degenerate      116 119ff. 124
Symmetry coordinates, orientation of degenerate, for C ${}_{6}$ H ${}_{6}$       258
Symmetry coordinates, potential and kinetic energy in terms of      127ff. 347
Symmetry coordinates, potential and kinetic energy in terms of, for C ${}_{6}$ H ${}_{6}$       260ff.
Symmetry coordinates, potential and kinetic energy in terms of, numerical checking      264
Symmetry coordinates, species of, for C ${}_{6}$ H ${}_{6}$       243
Symmetry coordinates, transformation from internal coordinates      117ff.
Symmetry elements      78
Symmetry elements, axes of symmetry      78—80
Symmetry elements, center of symmetry      79
Symmetry elements, plane of symmetry      78
Symmetry elements, plane of symmetry, diagonal      84
Symmetry elements, plane of symmetry, horizontal      82
Symmetry elements, plane of symmetry, vertical      80
Symmetry operations      78
Symmetry operations, character per mishitted atom      105
Symmetry operations, class of      99
Symmetry operations, effect on representative point      84
Symmetry operations, group of      81
Symmetry operations, identity      80
Symmetry operations, improper      105
Symmetry operations, invariance of potential and kinetic energies under      88ff. 318
Symmetry operations, inverse of      81

Symmetry operations, inversion through a center      79 103
Symmetry operations, order of, in product      81
Symmetry operations, proper      105
Symmetry operations, reflection through a plane      78—84
Symmetry operations, rotation about an axis, alternating      79
Symmetry operations, rotation about an axis, proper      78 (see also Symmetry elements)
Symmetry species      see Species
Symmetry types      see Species
Tamres, M.      232 233
Taylor, A. M.      2
Taylor, W. J.      65
Teller, E.      49 182 183 188 193 365 367 370
Teller-Redlich product, rule      see Product rule
Tensor properties of polarizability      43
Tetrahedral groups, $\mathcal{T}$ , $\mathcal{T}_{d}$ , $\mathcal{T}_{h}$       85 330 339 340
Thompson, H. W.      177 178
Thorndike, A. M.      162 168
Tisza, L.      98 151 154 198 199 370
Tompa, H.      67 115
Top      see Asymmetric rotor; Spherical rotor; Symmetric rotor
Torsion angle, $\tau$       60
Torsional energy levels      206
Torsional force constant for C ${}_{6}$ H ${}_{6}$       256
Total angular momentum      362
Total angular momentum vector, $\mathcal{M}$       277
Totally symmetric Raman lines, polarization of      366
Totally symmetric Raman lines, sharpness of      367
Transformation of coordinates      20
Transformation of coordinates, between cartesian and internal coordinates      55
Transformation of coordinates, from internal to normal coordinates      74
Transformation of coordinates, from internal to symmetry coordinates      117ff.
Transformation of coordinates, from internal to symmetry coordinates, character operator formula for      119 138
Transformation of coordinates, from internal to symmetry coordinates, for C ${}_{6}$ H ${}_{6}$       257ff.
Transformation of coordinates, from internal to symmetry coordinates, numerical checking of      264
Transformation of coordinates, from internal to symmetry coordinates, of kinetic energy      127ff.
Transformation of coordinates, from internal to symmetry coordinates, of potential energy      127ff.
Transformation of coordinates, from normal to internal coordinates      72 73
Transformation of coordinates, group of linear      90
Transformation of coordinates, inverse      20
Transformation of coordinates, linear      20 91
Transformation of coordinates, linear, in matrix notation      297
Transformation of coordinates, orthogonal      21
Transformation properties, of electric dipole moment components      157
Transformation properties, of Eulerian angles      280
Transformation properties, of polarizability components      157 359
Transformation properties, of wave functions      148 (see also Characters)
Transition probability      38 162
Translation, as mode of zero frequency      22ff.
Translation, effect on isotope, product rule      184 248—250
Translation, potential energy, independent of      24
Translation, species of (character tables)      323—330
Transpose, of matrix      295
Transpose, of product of matrices      296
Triply degenerate species,       113 322
Tunnel effect      201 207
Turner, T. E.      362
Types, of infrared bands      364
Types, of Raman bands      366
Unit matrix      294
Unitary matrix      296 301
Unitary matrix, characteristic values of absolute value unity      300
Urey — Bradley potential function      179
Urey, H. C.      6 179
Valence angle bending      56 303
Valence force coordinates, potential energy in      174
Valence forces, approximation to potential energy      174
Van der Waals forces      179 180
Van Vleck, J. II.      8 49 163 169 232 284 370
Variational method solution of secular equation      218ff.
Variational method solution of secular equation, for unsyinmetric energy matrix      220
Vector, as column or row matrix      297; see $\mathbf{s}$ vectors
Venkatarayudu, T.      77 117
Verleysen, A.      240
Vertical plane of symmetry, $\sigma_{v}$       80
Vibration-rotation interaction      275 284 367ff.
Vibration-rotation interaction, perturbation operator for      368
Vibrational angular momentum      278 284 367
Vibrational angular momentum, coupling with rotational      284 367
Vibrational assignments by isotope relations      182 188ff.
Vibrational coordinates, characters of      106
Vibrational degrees of freedom      17
Vibrational energy levels      see Energy levels
Vibrational frequencies      see Frequencies
Vibrational isotope effect      see Isotope effect
Vibrational partition function      165
Vibrational quantum number      35ff.
Vibrational quantum number, selection rides for      42
Vibrational Raman spectrum      3 305
Vibrational selection rules      see Selection rules
Vibrational wave function      37 (see also Harmonic oscillator wave
Vibrations, anharmonicity and interactions of      see Potential energy)
Vibrations, bond-bending and bond-stretelling      178 246 252
Vibrations, degenerate      see Degenerate vibrations
Vibrations, interaction with rotation      275 284 367ff.
Vibrations, modes, determination of      17 71ff.
Vibrations, normal      see Normal vibrations
Vibrations, number of, of a given species      99 107
Vibrations, partition function for      1 55
Vibrations, small, in classical mechanics      11ff.
Vibrations, study by mechanical and electrical models      232ff.
Vibrations, symmetry properties and species of      147ff.
Violation of selection rules in liquid state      146
Walter, J.      118
Washburn, H. W      232
Water molecule      see H ${}_{2}$ O molecule
Wave equation      9 34 279
Wave equation, vibrational      34
Wave equation, vibrational, in normal coordinates      147
Wave equation, vibrational, symmetry of      147ff.
Wave functions, factoring into electronic, vibrational, rotational, and translational parts      39
Wave functions, form basis of group representation      148
Wave functions, form basis of group representation, character for transformations of      149
Wave functions, harmonic oscillator      37 289
Wave functions, mixing of      198
Wave functions, of triply degenerate fundamentals      356
Wave functions, orthogonality      40 42 52
Wave functions, species of      147
Wayland, H.      215
Weiskopf, V.      163
Wells, A. J.      162 168
Weyl, II.      77
Wheatley, P. J.      181
Whittaker, E. T.      14 75 215
Wigner, E.      77 79 98 106 117 118
Wilcox, E. E.      232
Williams, V. Z.      2
Wilson, E. B., Jr      9 35 38 55 61 65 67 68 74 88 115 140 162 168 170 181 182 186 188 197 198 203 232 238 240 249 273 287 352 370
Wu, T. Y.      176
X ${}_{3}$ molecule, equilateral, normal vibrations of      18
XY ${}_{3}$ molecule, planar equilateral      81 89 100
XY ${}_{3}$ molecule, planar equilateral, normal vibrations of      93
XY ${}_{3}$ molecule, planar equilateral, symmetry of normal coordinates      92—97
XYZ nonlinear molecule, $\mathbf{G}$ matrix      63 69ff.
XYZ nonlinear molecule, $\mathbf{G}$ matrix, expanded secular equation      71
Zerner, F.      6
Zero frequency vibrations, rotation and translation      22ff.
Zero matrix      294
Zero-order frequencies      see Mechanical frequencies of vibration
Zero-point energy      36
Zumwalt, L. R.      367

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