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

Perturbation method, for isotopic mass effect      188ff. 231
Perturbation operator for vibrational-rotational interaction      368
Perturbation theory      189 197
Perturbations due to anharmonic terms in potential energy      193ff. (see also Resonance)
Pitzer, K. S.      9 65 203 206
Placzek, G.      49 98 198 365
Planar molecules      33
Plane of symmetry      78 80 82 84
Point groups      82
Point groups, $\mathcal{C}_{i}$       84 323
Point groups, $\mathcal{C}_{nh}$       83 326
Point groups, $\mathcal{C}_{nv}$       83 325
Point groups, $\mathcal{C}_{n}$       82 323
Point groups, $\mathcal{C}_{s}$       83 323
Point groups, $\mathcal{C}_{\infty v}$       330
Point groups, $\mathcal{D}_{nd}$       84 328—329
Point groups, $\mathcal{D}_{nh}$       82 327—328
Point groups, $\mathcal{D}_{n}$       82 324
Point groups, $\mathcal{D}_{\infty h}$       330
Point groups, $\mathcal{I}$ , $\mathcal{I}_{h}$       85 330
Point groups, $\mathcal{O}$ , $\mathcal{O}_{h}$       85 330
Point groups, $\mathcal{S}_{n}$       84 329
Point groups, $\mathcal{T}$ , $\mathcal{T}_{d}$ , $\mathcal{D}_{h}$       85 330
Point groups, $\mathcal{V}$       82 324
Point groups, $\mathcal{V}_{d}$       84 328
Point groups, $\mathcal{V}_{h}$       83 327
Polar normal coordinates      352
Polarizability      5
Polarizability, and intensity of scattered light      45
Polarizability, anistropy of      47 51
Polarizability, averaged over all molecular orientations      46
Polarizability, characters of      158
Polarizability, derivatives, in Raman intensities      48
Polarizability, ellipsoid      193
Polarizability, equilibrium value in Rayleigh scattering      48
Polarizability, integrals      50 161
Polarizability, invariance of spherical part      52 360
Polarizability, principal values of      44 51
Polarizability, principal values of, expansion in normal coordinates      48
Polarizability, species of (character tables)      323—330
Polarizability, species of (character tables), components determine Raman activity      161
Polarizability, spherical and anisotropic part of      47 51 360
Polarizability, tensor properties of      43
Polarizability, transformat ion of components      157 359
Polarization of scattered radiation      4 43ff. 161 366
Polarization ratio      see Depolarization ratio
Polarized Raman lines      52 161 366
Polynomial form of secular equation      214
Polynomial form of secular equation, coefficients of      215
Polynomial form of secular equation, coefficients of, evaluation of, by Hamilton — Cayley Polynomial form of secular equation, coefficients of, evaluation of, theorem      217
Polynomial form of secular equation, coefficients of, evaluation of, by trace method      216
Positive definite matrix      298 301
Potential barriers hindering internal rotation      202
Potential barriers hindering internal rotation, degeneracy due to multiple minima      201
Potential barriers hindering internal rotation, degeneracy due to multiple minima, splitting of energy levels      201 207
Potential barriers hindering internal rotation, determination of height      206
Potential constants      see Force constants
Potential energy, anharmonic terms in      193—196
Potential energy, anharmonic terms in, restriction by symmetry      196
Potential energy, cubic, quartic, and higher terms      193ff.
Potential energy, cubic, quartic, and higher terms, overtone levels, splitting by      199
Potential energy, cubic, quartic, and higher terms, symmetry and number of      196
Potential energy, expansion in power series of      15 193
Potential energy, expansion in power series of, effect of redundancy      172
Potential energy, factoring in symmetry coordinates      115
Potential energy, factoring in symmetry coordinates, for CH ${}_{4}$       136
Potential energy, for C ${}_{6}$ H ${}_{6}$       255ff.
Potential energy, for molecules with inversion doubling      201
Potential energy, functions having several minima      200ff.
Potential energy, in cartesian displacement coordinates      25 169
Potential energy, in central force coordinates      174
Potential energy, in dependent coordinate systems      287
Potential energy, in internal coordinates      64 170
Potential energy, in internal coordinates, for C ${}_{6}$ H ${}_{6}$       254ff.
Potential energy, in mass-weighted cartesian coordinates.      15
Potential energy, in normal coordinates      20 193
Potential energy, in orbital valence force field      181
Potential energy, in symmetry coordinates      127ff. 347
Potential energy, in symmetry coordinates, for C ${}_{6}$ H ${}_{6}$       260ff.
Potential energy, in symmetry coordinates, numerical checking      204
Potential energy, in valence force coordinates      174
Potential energy, independent of translation and rotation      24—
Potential energy, interaction constants      169 177
Potential energy, invariance, under isotopic substitution      171 182 192
Potential energy, invariance, under isotopic substitution, to symmetry operations      88 89 318
Potential energy, minimum of      15 288
Potential energy, most general quadratic form of      169ff.
Potential energy, number of constants in      170
Potential energy, of degenerate vibrations      106
Potential energy, of degenerate vibrations, components have equal $\lambda$       107
Potential energy, of simple harmonic oscillator      20 34
Potential energy, symmetry      87
Potential energy, terms of involving displacement of non-bonded atoms      179
Potential energy, terms of involving displacement of non-bonded atoms, relation to van der Waals forces      179 180
Potential energy, transformation from internal to symmetry coordinates      127ff.
Potential energy, transformation from internal to symmetry coordinates, rules for shortcut      130 131
Potential energy, transformation from internal to symmetry coordinates, rules for shortcut, proof of      132ff.
Potential energy, transformation from internal to symmetry coordinates, when $n^{(\gamma)} > 1$       138ff.
Potential energy, Urey — Bradley form      179
Potential function      see Potential energy
Potential minima, molecules with several      200ff.
Principal axes, of inertia      284
Principal axes, of polarizability ellipsoid      44
Principal moments of inertia      284
Principal values, of moments of inertia      284
Principal values, of polarizability      44 51
Product ratio of isotopic frequencies independent of potential constants      183
Product rule of Teller and Redlich for isotopic frequencies      183
Product rule of Teller and Redlich for isotopic frequencies, effect of translation and rotation      184 248—250
Product rule of Teller and Redlich for isotopic frequencies, for C ${}_{6}$ H ${}_{6}$       248ff.
Product rule of Teller and Redlich for isotopic frequencies, when symmetries differ      185 249
Products, of inertia, vanish in principal axes      284
Products, of irreducible representations      331
Products, of matrices      294
Products, of matrices, direct      294
Products, of symmetry operations, order of      81
Proper axes of symmetry      78
Proper operation      105
Q branch      364 365
Quadratic form, in matrix notation      297
Quadratic form, most general, of potential energy      169
Quadrupole, electric, radiation due to      39
Quantum numbers, rotational, , total angular momentum      362
Quantum numbers, rotational, , component of angular momentum along axis      362
Quantum numbers, rotational, , component of angular momentum along Z axis of nonrotating coordinate system      50 363
Quantum numbers, selection rules for      42 (see also Selection rules)
Quantum numbers, translational, selection rule for      40
Quantum numbers, vibrational      35ff.
Quartic terms in potential energy      193 196
R branch      364 365
Radiation, by accelerated charge      6
Radiation, by electric quadrupole      39
Radiation, by magnetic dipole      39
Radiation, by oscillating dipole      43
Raman activity      see Selection rules
Raman band types      366
Raman lines      see Raman spectrum
Raman rotation-vibration spectra      365
Raman scattering      48 49
Raman selection rules      see Selection rules
Raman spectrum      3
Raman spectrum, anti — Stokes line in      3 9 48 51
Raman spectrum, band types      366
Raman spectrum, classical theory of      7
Raman spectrum, classical theory of, averaging over orientations      46
Raman spectrum, classical theory of, intensities      43—48
Raman spectrum, depolarization ratios      47 51 52
Raman spectrum, intensity ratio of Stokes and anti — Stokes lines in      9 48 51
Raman spectrum, isotope effect      192
Raman spectrum, of C ${}_{6}$ H ${}_{6}$       4 251 253

Raman spectrum, polarizability derivatives determine activity of      48
Raman spectrum, polarization of lines in      4 47 51 52 161 366
Raman spectrum, quantum theory of      9 48ff.
Raman spectrum, quantum theory of, conditions on      50
Raman spectrum, quantum theory of, intensities in      48—53
Raman spectrum, quantum theory of, orientational degeneracy in      50
Raman spectrum, rotation      4 365
Raman spectrum, selection rules      51 53 161 365
Raman spectrum, sharpness of, totally symmetric lines      367
Raman spectrum, Stokes line in      3 9 48 51
Raman spectrum, vibration      3 365
Raman, C. V.      3
Rank of $\mathbf{G}$ matrix, test for completeness of coordinate set      145
Rasetti, F.      49
Rawlins, F. I. G.      2
Rayleigh scattering intensity      48 49
Rayleigh scattering intensity, equilibrium polarizability in      48
Rayleigh, Lord      218 227 230
Rayleigh’s principle      218ff. 227
Real matrix      296
Reciprocal matrix      295
Recursion formula for Hermite polynomials      38
Redlich, O.      67 115 183 197
Reduced representations      96
Reducible representations      98 341
Reducible representations, formed by equivalent internal coordinate sets      109
Reduction of representation, in subgroup      121 185 333ff. 350
Reduction of representation, into group species      99 100 113
Redundancy      111ff.
Redundancy, condition      112 171
Redundancy, condition, to second order      172 179
Redundancy, effect of, on force constant determination      171
Redundancy, effect of, on potential energy expansion      172
Redundancy, removal of      140ff.
Redundancy, removal of, for CH ${}_{4}$       140
Reflection through a plane      78—84
Regular representation      113 3 2
Reitwiesner, G.      362
Relaxation method for characteristic values and vectors      224
Representations, by equivalent sets of internal coordinates      109
Representations, completely reduced      96
Representations, direct products of      320 331
Representations, equivalent      91
Representations, irreducible      see Irreducible representation
Representations, of groups      312ff.
Representations, of groups, by linear transformations      91
Representations, reducible      98 109 341
Representations, reduction      see Reduction of representation
Representations, regular      113 312
Representations, structure of      108
Representations, structure of, determination of the $n^{(\gamma)}$       99 100 113
Resolution      see Reduction of representation
Resonance, quantum mechanical      197ff.
Resonance, quantum mechanical, first order (Fermi)      198
Resonance, quantum mechanical, second order (Darling and Dennison)      199
Richardson, W. S.      182
Richtmyer, F. K.      6
Rigid rotor      361
Rigid rotor, approximation      284
Rigid rotor, degeneracies      362
Rigid rotor, energy levels      362
Rigid rotor, Hamiltonian      361
Robinson, G.      215
Rocard, Y.      49
Rock, S. M.      232
Rojansky, V.      189
Rollcfson, R.      162
Rollefson, A. II.      162
Rosenthal, J. E.      77 82 98 115 188
Rosser, S. E.      182
Rotating coordinates      12 274 285
Rotation spectra, infrared      3 42 364
Rotation spectra, Raman      4 365
Rotation, about an axis, alternating      79
Rotation, about an axis, proper      78
Rotation, internal      202ff.
Rotation, internal, as mode of zero frequency      22ff.
Rotation, internal, effect on isotope product rule      184 248—250
Rotation, internal, potential energy independent of      24
Rotation, species of (character tables)      323—330
Rotation-reflection axis      79 80
Rotation-vibration interaction      275 284 367ff.
Rotation-vibration interaction, perturbation operator for      868
Rotation-vibration spectra      363ff.
Rotational angular momentum      277 284 361
Rotational angular momentum, coupling with vibrational      284 367
Rotational energy      361ff.
Rotational energy, selection rules      42 53 363ff.
Rotor types      361
Rotor types, band types for      364 366
Rotor types, energies of      362
Rotor types, selection rules for      364ff.
Rotor, rigid      see Rigid rotor
Row matrix      297
Ruark, A. E.      6
S branch      367
Salant, E. O.      188
Scalar product      297
Scattering of light      48 49
Schaefer, C.      2
Schiff, L. I.      9
Schmidt orthogonalizatiou process      212
Schmidt, E.      212
Schoenfiies, A. M.      82
Schr $\ddot{o}$ dinger equation      9 34 279
Schr $\ddot{o}$ dinger, E.      35
Schur, I.      77
Secular determinant      see Secular equation
Secular equation solution, $\lambda$ diagonal      234 238
Secular equation solution, $\lambda$ not restricted to diagonal      233
Secular equation solution, as extreme value problem      218ff.
Secular equation solution, as variational problem      218ff.
Secular equation solution, as variational problem, for unsymmetric energy matrix      220
Secular equation solution, by analogue computers      232ff.
Secular equation solution, by matrix iteration      226ff.
Secular equation solution, by matrix iteration, examples      270ff.
Secular equation solution, by matrix iteration, for roots other than largest      228
Secular equation solution, by mechanical models      232
Secular equation solution, by numerical approximation      218
Secular equation solution, by perturbation methods      229ff.
Secular equation solution, by relaxation      224
Secular equation solution, by successive elimination      222ff.
Secular equation solution, general, methods for      208ff.
Secular equation solution, in polynomial form      214ff.
Secular equation solution, with automatic convergence      236
Secular equation, characteristic values of      209ff.
Secular equation, degree of factor of      116
Secular equation, expansion of      68 214ff.
Secular equation, expansion of, for nonlinear XYZ molecule      69 71
Secular equation, factoring of      113ff. 347ff.
Secular equation, factoring of, effect of internal rotation      205
Secular equation, factoring of, for linear molecules      32
Secular equation, factoring of, for planar molecules      33
Secular equation, in $|\mathbf{F} - \lambda\mathbf{G}^{-1}|$ form      64
Secular equation, in $|\mathbf{F}\mathbf{G} - \lambda\mathbf{E}|$ form      65
Secular equation, in $|\mathbf{G} - \lambda\mathbf{F}^{-1}|$ form      65
Secular equation, in $|\mathbf{G}\mathbf{F} -\lambda\mathbf{E}|$ form      64
Secular equation, in cartesian coordinates      26
Secular equation, in form convenient for machine solution      65
Secular equation, in generalized coordinates      26
Secular equation, in internal coordinates      64
Secular equation, in mass-weighted cartesian coordinates      16
Secular equation, minors of      68ff.
Secular equation, number of nonzero roots      17
Secular equation, polynomial form of      214
Secular equation, symmetrization of      211ff.
Seidel      224
Selection rules      8 39
Selection rules for Coriolis interaction      369
Selection rules for rotation-vibration spectra      363ff.

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