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.

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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

Cubic terms in potential energy      193 196
Cubic terms in potential energy, split degeneracy of overtone levels      199
Cyclic groups, $\mathcal{C}_{n}$       82ff.
Cyclic groups, correlation tables of      334 335
Cyclic groups, derivation of characters for      312
Dailey, B. P.      207
Darling, B. T.      194 197 199 273
Daure, P.      3
Dean, L. B.      202
Decius, J. C.      145 154 182 186 191 303
Deflation of matrix      228
Degeneracy, accidental      107
Degeneracy, degree of, for combination levels      151
Degeneracy, degree of, for overtone levels      37 151
Degeneracy, double      1 13 322
Degeneracy, necessary, for molecules with more than two-fold axes      107
Degeneracy, orientational      50
Degeneracy, produced by multiple potential minima      201
Degeneracy, produced by multiple potential minima, splitting of      201 207
Degeneracy, rotational      362
Degeneracy, splitting in unsynmictrically substituted isotopic molecules      186
Degeneracy, triple      113 322
Degenerate energy levels      37
Degenerate normal coordinates      see Normal coordinates
Degenerate species, characters of      94 352ff.
Degenerate species, correlation with species of subgroup      121 135 333ff.
Degenerate symmetry coordinates      119 123 135ff.
Degenerate vibrations      18
Degenerate vibrations, behavior with respect to symmetry operations      93
Degenerate vibrations, components of, have equal $\lambda$       107
Degenerate vibrations, Coriolis splitting of      367ff.
Degenerate vibrations, due to multiple potential minima      201
Degenerate vibrations, due to multiple potential minima, splitting for low barriers      201 207
Degenerate vibrations, higher vibrational levels of      152 331 352ff.
Degenerate vibrations, isotope effect on      186
Degenerate vibrations, kinetic energy of      106
Degenerate vibrations, normal coordinates for      19 93 107
Degenerate vibrations, potential energy of      106
Degenerate vibrations, species of overtones      332 352ff.
Degenerate vibrations, splitting, by anharmonicity      199
Degenerate vibrations, splitting, by isotopic substitution      186
Degenerate vibrations, transformation law      93
Degenerate vibrations, vibrational angular momentum      367
Degree of factor of secular determinant      116
Degrees of freedom, vibrational      see Secular equation number
Delta symbol, Kronecker      16
Dennison, D. M.      14 39 173 182 194 197—199 207 273 367 370
Depolarization of Raman lines, degree of      4
Depolarization ratio of scattered light, distinguishes totally symmetric Raman lines      52 161
Depolarization ratio of scattered light, for natural incident light      47 51 52
Depolarization ratio of scattered light, for polarized incident light      47 51 52
Depolarized Raman lines      52 161 366
Determinant, in expansion of secular equation      215
Determinant, minor of      68ff.
Determinant, of square matrix      295
Determinant, product of $\mathbf{F}$ and $\mathbf{G}$ determinants      68 267
Determinant, secular      see Secular equation
Diagonal form of energy matrix, transformation to      209
Diagonal matrix      294
Diagonal plane of symmetry, $\sigma_{d}$       84
Diagonalization of matrix      301
Difference frequencies      36
Dihedral groups, $\mathcal{D}_{n}$ , $\mathcal{D}_{nd}$ , $\mathcal{D}_{nh}$       82ff.
Dihedral groups, $\mathcal{D}_{n}$ , $\mathcal{D}_{nd}$ , $\mathcal{D}_{nh}$ , correlation tables      334—339
Dihedral groups, $\mathcal{D}_{n}$ , $\mathcal{D}_{nd}$ , $\mathcal{D}_{nh}$ , derivation of characters      316ff.
Dinsmore, II. L.      42 164 196
Dipole moment      see Electric moment
Dipole, magnetic, radiation due to      39
Dipole, oscillating, radiation due to      43
Dirac, P. A. M.      49
Direct product groups      320
Direct product, of matrices      294
Direct product, of representations      320 331
Direct product, of representations, in combination levels      150
Direction cosines      40
Direction cosines, averages over all orientations      292
Direction cosines, in terms of Eulerian angles      286
Distribution, Maxwellian, of rotational velocities      6
Double minima in potential energy      200
Doubly degenerate species,       113 322
Duchesne, J.      180 181 240
Duncan, W. J.      16 63 293
Dwyer, P. S.      218
Eckart, C.      274 370
Edgcll, W.      188
Edsall, J. T.      74
Effective moments of inertia      369
Eggers, D. P.      42 196
Eigenfunctions      see Wave functions
Eigenvalues      see Characteristic values
Eigenvectors      see Characteristic vectors
Einstein coefficients of emission and absorption      38 162
Electric circuit analogues of secular equations      232ff.
Electric moment (dipole moment)      5 39
Electric moment (dipole moment), derivative, determines infrared activity of vibrations      42
Electric moment (dipole moment), derivative, relation to bond moment      166
Electric moment (dipole moment), derivative, with respect to bond length      167
Electric moment (dipole moment), equilibrium value determines infrared activity of pure rotational transition      42
Electric moment (dipole moment), expansion in power series of normal coordinates      41
Electric moment (dipole moment), expansion in power series of normal coordinates, effect of higher terms      196
Electric moment (dipole moment), induced by electric field      43
Electric moment (dipole moment), integrals      38 156
Electric moment (dipole moment), of a bond      166
Electric moment (dipole moment), radiation, by oscillating      43
Electric moment (dipole moment), species of components ( $T_{x}$ , $T_{y}$ , $T_{z}$ )      323—330
Electric moment (dipole moment), symmetry of components      156
Electric moment (dipole moment), symmetry of components, same as translation components      157
Electric moment (dipole moment), transformation properties, L      57
Elements, of matrices      293
Elements, of symmetry      see Symmetry elements
Eliashevich, M.      55 61
Elimination method for characteristic values and vectors      222ff.
Ellipse, relation of principal axes to characteristic values      219
Ellipsoid, polarizability      193
Energy levels, rotational      361ff.
Energy levels, species of      147 155
Energy levels, torsional      206
Energy levels, vibrational      35
Energy levels, vibrational, combination      36
Energy levels, vibrational, degenerate      37
Energy levels, vibrational, energy of      35ff. 193
Energy levels, vibrational, expanded in power series of quantum numbers      193
Energy levels, vibrational, fundamental      36
Energy levels, vibrational, ground      36
Energy levels, vibrational, isotopic substitution, effect of      182
Energy levels, vibrational, overtone      36
Energy levels, vibrational, overtone, for degenerate fundamentals      37
Energy levels, vibrational, overtone, perturbation treatment of      188ff.
Energy levels, vibrational, resonance, effect of      197ff.
Energy matrix, characteristic equation of      214
Energy matrix, characteristic values and vectors of      209ff.
Energy matrix, characteristic values and vectors of, by matrix iteration      226ff.
Energy matrix, characteristic values and vectors of, by matrix iteration, for roots other than largest      228
Energy matrix, characteristic values and vectors of, by perturbation      229ff.
Energy matrix, characteristic values and vectors of, by relaxation      224
Energy matrix, characteristic values and vectors of, by successive elimination      222ff.
Energy matrix, characteristic values and vectors of, in transformation to diagonal form      209
Energy matrix, effect of subtracting constant matrix      210
Envelope of bands      367
Equations of motion, in Hamiltonian form      66
Equations of motion, in mass-weighted coordinates      15
Equations of motion, in normal coordinates      20
Equilibria, chemical, calculated from spectroscopic data      10
Equivalent atoms, sets of      85
Equivalent internal coordinates      109 117
Equivalent internal coordinates, form reducible representation      109
Equivalent representations      91
Eulerian angles      11 273 285ff.
Eulerian angles, definition of      286
Eulerian angles, transformation under symmetry operation      286

Ewald, P. P.      82
Exciting line for Raman spectrum      3
Exclusion, rule of mutual      246
Expansion, of potential energy      15 172 193
Expansion, of secular equation      68 214ff.
Expansion, of secular equation, for nonlinear XYZ molecule      69 71
External symmetry coordinates      125
Extreme value problem      218ff.
Eyring, H.      118
F matrix      see Potential energy)
Factoring of secular equation      see Secular equation
Ferigle, S. M.      59 303
Fermi resonance      198
Fermi, E.      49 198
Forbidden transitions      146
Force constants, agreement in isotopic molecules      171 182
Force constants, anharmonicity correction      194
Force constants, bond-bending and bond-stretching      174ff.
Force constants, bond-bending and bond-stretching, dimensions of      174
Force constants, bond-bending and bond-stretching, relative magnitude of      177
Force constants, for C ${}_{6}$ H ${}_{6}$       265ff.
Force constants, for central force coordinates      173
Force constants, for internal coordinates      64 170 174ff.
Force constants, for internal coordinates, for C ${}_{6}$ H ${}_{6}$       253ff.
Force constants, for symmetry coordinates      127ff.
Force constants, for symmetry coordinates, for C ${}_{6}$ H ${}_{6}$       260ff. 265ff.
Force constants, for valence force coordinates      174ff. (see also Potential energy)
Force constants, from fundamental frequencies      174ff. 265ff.
Force constants, from fundamental frequencies, anharmonicity correction      194
Force constants, from isotopic molecules      171 182
Force constants, in cartesian coordinates      25 169
Force constants, in normal coordinates, $\lambda$ , relation to vibrational frequencies      20ff.
Force constants, interaction      177ff.
Force constants, interaction, hybridization, effect of      180
Force constants, interaction, van der Waals forces      179 180
Force constants, intercomparison in different molecules      175
Force constants, number of independent      170
Force constants, perturbation treatment      188ff. 231
Force constants, product rule      183ff.
Force constants, redundancy, effect of      171
Force constants, sum rule      186ff.
Force constants, transfer of, to other molecules      175 182
Force functions more general than central or valence force approximations      177ff.
Forces, interatomic, from infrared and Raman studies      9
Fox, L.      225
Frank, N. H.      43
Frazer, R. A.      16 63 293
Free internal rotation      202ff.
Freedom, degrees of      17
Frequencies, vibrational      36
Frequencies, vibrational, characteristic      246
Frequencies, vibrational, combination      36 160 161 247
Frequencies, vibrational, difference      37
Frequencies, vibrational, from force constants      see Secular equation solution
Frequencies, vibrational, fundamental      see Fundamental frequencies
Frequencies, vibrational, isotopic substitution, effect of      182
Frequencies, vibrational, isotopic substitution, perturbation treatment of      188ff.
Frequencies, vibrational, mechanical      194
Frequencies, vibrational, overtone      9 36 246
Frequencies, vibrational, relation to force constants, $\lambda$ , in normal coordinates      20ff.
Frequencies, vibrational, resonance, effect of      197ff.
Frequencies, vibrational, separation of high and low      74 311
Frost, A. A.      232 233
Fundamental frequencies      9 36 246
Fundamental frequencies, anharmonicity effect      194
Fundamental frequencies, force constants from      174 265ff.
Fundamental frequencies, infrared selection rules      161
Fundamental frequencies, numbering of, in C ${}_{6}$ H ${}_{6}$       249
Fundamental frequencies, Raman selection rules      51 53 161 365
Fundamental levels      36
Fundamental levels, symmetry of      148
Gauss, K. F.      222 224
Generalized coordinates, form of secular equation in      26
Gerhard, S. L.      367
Glockler, G.      3
Gordy, W.      10 176
Ground level      36
Group, characters      see Characters
Group, classes of operations in      101
Group, definition and properties of      81 82
Group, operations      see Symmetry operations
Group, order of      85
Group, representation      312ff.
Group, representation, by linear transformations      91
Group, wave functions as basis for representation of      148 (see also Point groups)
Groups, isomorphic      91 320
Gwinn, W. IX      203
H ${}_{2}$ O molecule, energy level diagram      36
H ${}_{2}$ O molecule, factored secular equation      114
H ${}_{2}$ O molecule, normal vibrations      18
H ${}_{2}$ O molecule, symmetry elements of      78 79
Hainer, R. M.      362 363
Hamilton — Cayley theorem      217
Hamilton, W. R.      217
Hamiltonian, for nonrigid rotor      367
Hamiltonian, for rigid rotor      361
Hamiltonian, operator for polyatomic, molecules      279 281ff.
Hamilton’s equations of motion      66 308
harmonic oscillator      34ff.
Harmonic oscillator approximation      34 193
Harmonic oscillator, energy levels      35
Harmonic oscillator, potential and kinetic energy of      20 31
Harmonic oscillator, simple, electric circuit analogue of      237
Harmonic oscillator, wave functions      37
Harmonic oscillator, wave functions, degenerate, in polar coordinates      352 355
Harmonic oscillator, wave functions, integrals involving      289
Harrison, G.      11 2
Heath, D. F.      180 181
Heisenberg, W.      3 49
Heitler, W.      49 163
Hermite orthogonal functions      37
Hermite polynomial      38 152 289
Hermitian form      298
Hermitian matrix      296
Hermitian matrix, positive-definite      301
Hermitian matrix, real characteristic values of      300
Hibben, J. H.      3
Hicks, B. L.      218 362
High frequencies, separation from low frequencies      74 311
Hindered internal rotation      202 206
Hooke’s law      5
Horizontal plane of symmetry, $\sigma_{h}$       82
Horzborg, G.      39 173 176 182 365 366
Hotelling, H.      226
Howard, J. B.      115 170 181 203 273
Hughes, R. H.      232 238
Hybridization effect on force constants      180
Icosahedral groups, $\mathcal{I}$ , $\mathcal{I}_{h}$       85 330
Identity operation,       80
Improper axes of symmetry      79
Improper operation      105
Inactive frequencies in infrared and Raman spectra      see Selection rules
Independent internal coordinates      112
Independent normal modes      18
Independent symmetry coordinates      144
Induced dipole moment      43
Induced transition coefficient      38 162
Inertia, moment of      see Moment of inertia)
Infinite axis of symmetry in groups $\mathcal{C}_{\infty v}$ , $\mathcal{D}_{\infty v}$       330
Infinitesimal amplitudes      see Small vibration
Infrared absorption spectra of C ${}_{6}$ H ${}_{6}$       2
Infrared activity      see Selection rules
Infrared bands, rotational fine structure      361ff.
Infrared rotation-vibration spectra, band types      364
Infrared selection rules      see Selection rules
Infrared spectra, classical theory of      6
Infrared spectra, pure rotation      3 42 364
Ingold, C. K.      4 240
Intensity ratio of Stokes and anti — Stokes Raman lines      9 48 51
Intensity, absolute, of infrared fundamentals      162ff.

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