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

$\mathbf{G}$ matrix      61
$\mathbf{G}$ matrix, $\mathbf{s}$ vector method of calculating      55ff.
$\mathbf{G}$ matrix, and kinetic energy      62 307
$\mathbf{G}$ matrix, diagonalization of      211
$\mathbf{G}$ matrix, elements, schematic representation of      304
$\mathbf{G}$ matrix, elements, tabulation of      303ff.
$\mathbf{G}$ matrix, for C ${}_{6}$ H ${}_{6}$       255ff. 261ff.
$\mathbf{G}$ matrix, for nonlinear XYX molecule      63 69
$\mathbf{s}$ vectors      55
$\mathbf{s}$ vectors, for bending a bond out of a plane      58
$\mathbf{s}$ vectors, for bond stretching coordinate      56
$\mathbf{s}$ vectors, for calculation of $\mathbf{G}$ matrix      55ff.
$\mathbf{s}$ vectors, for torsion      60
$\mathbf{s}$ vectors, for valence angle bending      56
$\mathbf{s}$ vectors, total angular momentum, $\mathcal{M}$       277
$\mathcal{C}_{i}$       323
$\mathcal{C}_{nh}$       83 326 335
$\mathcal{C}_{nv}$       83 325 334 335
$\mathcal{C}_{n}$       82 323 334
$\mathcal{C}_{s}$       323
$\mathcal{C}_{\infty r}$       330
$\mathcal{D}_{nd}$       84 328 329 338 339
$\mathcal{D}_{nh}$       82 326 335—338
$\mathcal{D}_{n}$       82 318 324 334
$\mathcal{D}_{\infty n}$       330
$\mathcal{S}_{n}$       84 329 339
$\mathcal{T}$ , $\mathcal{T}_{d}$ , $\mathcal{T}_{h}$       85 330 339 340
$\mathcal{V}$       82 318 324
$\mathcal{V}_{d}$       84 328 329
$\mathcal{V}_{h}$       83 327 328
Absolute intensity of infrared absorption      162ff.
Absorption coefficient      162
Absorption intensity      see Intensity
Absorption spectrum, infrared, of C ${}_{6}$ H ${}_{6}$       2
Accidental degeneracy      107
Active frequencies in infrared and Raman spectra      see Selection rules
Adcock, W. A.      232 236
Addition, by circuit analogue      233
Addition, of matrices      293
Adel, A.      194 198
Aitken, A. C.      226 228 293
Alanneback, C.      49 115 180 240
Alternating axis of symmetry      79 80
Amplitudes of vibrations      16
Amplitudes of vibrations, normalization of      17
Analogue, electric, of secular equation      232ff.
Andrews, D. H.      232 240
Angle bending      see Bond bending
Angular momentum, component on axis      362
Angular momentum, coupling of rotational and vibrational      284 307
Angular momentum, rotational      277 284 361
Angular momentum, total      302
Angular momentum, vibrational      278 28 4 367
Angular velocity, $\omega$       273ff.
Angus, W. R.      4 183
Anhannonic terms      193 196
Anharinonieity constants. A      193
Anisotropy of polarizability      47 51
Anliarmonic vibrational levels, species of      146
Anti — Stokes lines      3 9 48 51
Antisymmetric vibrations giving depolarized Raman lines      101
Applications of results of infrared and Raman studies      9
Assignment of frequencies by use of isotope effect      182 188ff.
Asymmetric rotor      361
Asymmetric rotor, band types      361
Asymmetric rotor, degeneracy      362
Asymmetric rotor, energy      362
Asymmetric rotor, selection rules, infrared spectrum      364
Asymmetric rotor, selection rules, infrared spectrum, Raman spectrum      366
Asymmetry parameter      362
Axes, alternating      79 80
Axes, improper      79
Axes, of symmetry      78
Axes, principal, of inertia      284
Axes, principal, of polarizability      44
Axes, proper      78
Axes, rotary-refloction      79
Badger, R. M.      10 367
Band envelope      367
Band types for different rotor types, infrared      364
Band types for different rotor types, Raman      366
Barker, E. F.      198
Barriers      see Potential barriers hindering internal rotation
Bell, R. P.      174 240
Bending of bond out of plane      58
benzene      see C ${}_{6}$ H ${}_{6}$
Bernard, E.      240
Berry, C. E.      232
Berryman, L. H.      117
Bethe, H.      98
Bhagavantam, S.      3 77
Birkhoff, G.      16
Bjerrum, N.      14 173 174
Blade, E.      206
Bocher, M.      16
Bohr correspondence theorem      8
Bohr frequency rule      8
Bohr, N.      8
Bond bending coordinate      56 303
Bond bending force constants      174 176
Bond frequencies, characteristic      246
Bond moment      166
Bond moment, additivity approximation      168
Bond stretching force constants, numerical values      175ff. (see also Internal coordinates force
Bond-stretching vibrations      178 246 252
Born, M.      6 171 273
Bourgin, D. G.      162
Bradley, C. A.      179
Branch of rotation band,       367
Branch of rotation band,       361 305
Branch of rotation band,       30 1 365
Branch of rotation band,       364 365
Branch of rotation band,       307
Breit, G.      49
Brinkley, S. R.      182
Broekway, L. O.      240
Burnelle, L.      181
C ${}_{2}$ H ${}_{4}$ , bond stretching symmetry coordinates for      128
C ${}_{2}$ H ${}_{4}$ , changes of dipole moment in terms of bond moments of      167
C ${}_{2}$ H ${}_{6}$ , staggered model of      84
C ${}_{3}$ H ${}_{6}$ , symmetry coordinates of CCH bends      137ff.
C ${}_{6}$ D ${}_{2}$ H ${}_{4}$ (-dideuterobenzene)      249
C ${}_{6}$ D ${}_{6}$       see C ${}_{6}$ H ${}_{6}$
C ${}_{6}$ H ${}_{6}$ , analysis of vibrational spectra      0
C ${}_{6}$ H ${}_{6}$ , force constants      265ff.
C ${}_{6}$ H ${}_{6}$ , frequencies, calculated      265ff.
C ${}_{6}$ H ${}_{6}$ , frequencies, observed      2 4 251
C ${}_{6}$ H ${}_{6}$ , frequencies, observed, assignment of      253
C ${}_{6}$ H ${}_{6}$ , in-plane modes, internal coordinates for      243
C ${}_{6}$ H ${}_{6}$ , in-plane modes, kinetic energy in      254
C ${}_{6}$ H ${}_{6}$ , in-plane modes, potential energy in      254
C ${}_{6}$ H ${}_{6}$ , in-plane modes, species of      243
C ${}_{6}$ H ${}_{6}$ , in-plane modes, symmetry coordinates for      257
C ${}_{6}$ H ${}_{6}$ , in-plane modes, symmetry coordinates for, kinetic energy in      260ff.
C ${}_{6}$ H ${}_{6}$ , in-plane modes, symmetry coordinates for, orientation of      258
C ${}_{6}$ H ${}_{6}$ , in-plane modes, symmetry coordinates for, potential energy in      200ff.
C ${}_{6}$ H ${}_{6}$ , of and matrices      260ff.
C ${}_{6}$ H ${}_{6}$ , of normal coordinates      242
C ${}_{6}$ H ${}_{6}$ , of polarixability      245
C ${}_{6}$ H ${}_{6}$ , out-of-plane modes, interna] coordinates for      244
C ${}_{6}$ H ${}_{6}$ , out-of-plane modes, interna] coordinates for, kinetic energy in      256
C ${}_{6}$ H ${}_{6}$ , out-of-plane modes, interna] coordinates for, potential energy in      256
C ${}_{6}$ H ${}_{6}$ , out-of-plane modes, species of      243
C ${}_{6}$ H ${}_{6}$ , out-of-plane modes, symmetry coordinates for      259
C ${}_{6}$ H ${}_{6}$ , out-of-plane modes, symmetry coordinates for, kinetic energy in      2 50ff.
C ${}_{6}$ H ${}_{6}$ , out-of-plane modes, symmetry coordinates for, orientation of      259
C ${}_{6}$ H ${}_{6}$ , out-of-plane modes, symmetry coordinates for, potential energy in      260
C ${}_{6}$ H ${}_{6}$ , product rule for isotopes      218
C ${}_{6}$ H ${}_{6}$ , product rule for isotopes, for derivative of lower symmetry      249
C ${}_{6}$ H ${}_{6}$ , product rule for isotopes, rotation and translation in      248—250

C ${}_{6}$ H ${}_{6}$ , selection rules for      244ff.
C ${}_{6}$ H ${}_{6}$ , selection rules for, combinations      247
C ${}_{6}$ H ${}_{6}$ , selection rules for, fundamentals      245
C ${}_{6}$ H ${}_{6}$ , selection rules for, overtones      247
C ${}_{6}$ H ${}_{6}$ , species, of electric moment      244
C ${}_{6}$ H ${}_{6}$ , symmetry of      240
Cabannes, J.      49
Carter, G. K.      232 237 238
Cartesian coordinates, character of representation by      103ff.
Cartesian coordinates, kinetic energy in      25
Cartesian coordinates, mass-weighted      14
Cartesian coordinates, mass-weighted, potential energy in      15
Cartesian coordinates, potential energy in      25 169
Cartesian coordinates, solution of secular equation in      25
Cartesian coordinates, transformation to internal coordinates      55
Cayley, A.      217
Center of symmetry      79
Center of symmetry, mutual exclusion rule      240
Central force coordinates      173
Central force coordinates, approximation to potential energy in      174
Centrifugal distortion      370
CH ${}_{4}$ , construction of symmetry coordinates for      120
CH ${}_{4}$ , construction of symmetry coordinates for, factored potential energy matrix for      136
CH ${}_{4}$ , construction of symmetry coordinates for, redundant internal coordinates      112
CH ${}_{4}$ , construction of symmetry coordinates for, removal of redundancy      140
CH ${}_{4}$ , construction of symmetry coordinates for, species of normal coordinates      112
CH ${}_{4}$ , construction of symmetry coordinates for, symmetry operations of      80
Character operator formula      119 138
Character tables      323—330
Character tables, $\mathcal{C}_{i}$       323
Character tables, $\mathcal{C}_{nh}$       326
Character tables, $\mathcal{C}_{nv}$       325
Character tables, $\mathcal{C}_{n}$       323
Character tables, $\mathcal{C}_{s}$       323
Character tables, $\mathcal{C}_{\infty v}$       330
Character tables, $\mathcal{D}_{nf}$       328 329
Character tables, $\mathcal{D}_{nh}$       327 328
Character tables, $\mathcal{D}_{n}$       318 324
Character tables, $\mathcal{D}_{\infty h}$       330
Character tables, $\mathcal{J}$ , $\mathcal{J}_{h}$       330
Character tables, $\mathcal{O}$ , $\mathcal{O}_{h}$       330
Character tables, $\mathcal{S}_{n}$       329
Character tables, $\mathcal{T}$ , $\mathcal{T}_{d}$ , $\mathcal{T}_{h}$       330
Character tables, $\mathcal{V}$ , $\mathcal{V}_{d}$ , Character tables, $\mathcal{U}_{h}$       see $\mathcal{D}_{n}$
Characteristic bond frequencies      246
Characteristic equation of matrix      214
Characteristic values      209 222—229 299
Characteristic values, by iteration      226ff.
Characteristic values, by relaxation      224
Characteristic values, invariance of      264
Characteristic values, of Hermitian matrix      300
Characteristic values, of secular equation      209ff.
Characteristic vectors of matrix      209ff. 222—229 300
Characteristic vectors of matrix, by iteration      226ff.
Characteristic vectors of matrix, by relaxation      224
Characters, derivation of, cyclic groups      312
Characters, derivation of, dihedral groups      316ff.
Characters, derivation of, direct product groups      320ff.
Characters, equivalent representations have same      92
Characters, of cartesian displacement coordinates      103ff.
Characters, of combination levels      149ff.
Characters, of degenerate species      94 352ff.
Characters, of dipole moment      157
Characters, of general vibrational level      155
Characters, of internal coordinates      106 109ff.
Characters, of irreducible representations      97 98
Characters, of normal coordinates      91
Characters, of overtone levels      151ff.
Characters, of polarizability      158
Characters, of reducible representation expressed in terms of characters of irreducible representations      99
Characters, of regular representation      113
Characters, of rotations      323—330
Characters, of three-dimensional representation      356 357
Characters, of transformation      92
Characters, of transformation, of wave function      148
Characters, of translations      323—330
Characters, of two-dimensional representation      319 354
Characters, of vibrational coordinates      106
Characters, of wave functions      149
Characters, operations in same class have same      101
Characters, orthogonality relations of      313ff.
Characters, per unshifted atom      105
Checking of transformations to symmetry coordinates      264
Circular motion in degenerate normal vibrations      19
Class of symmetry operations      99
Classes of a group      101
Classes of a group, product of      314
Classical kinetic energy      273ff. 277
Classical treatment of infrared and Raman spectra      6
Cleveland, F. P.      61 182
CO ${}_{3}$       see XY ${}_{3}$ molecule planar
Coblentz, W. W.      2
Collar, A. R.      16 63 293
Column matrix      297
Combination frequencies      36 247
Combination frequencies, infrared selection rules      160
Combination frequencies, Raman selection rules      161
Combination levels      36
Combination levels, degeneracy, degree of      151
Combination levels, species of      148ff. 247 331
Commutation of matrices      294 295 302 315
Complete sets      117
Complex conjugate of matrices      295
Components of matrices      297
Conformability of matrices      298
Conjugate transpose matrices      296
Constant matrix      294
Coolidge, A. S.      39 222
Cooper, J. L. B.      225
Coordinate transformation      see Transformation of coordinates
Coordinates, bending      56 303
Coordinates, central force      173
Coordinates, framework      203
Coordinates, group      203
Coordinates, internal      see Internal coordinates
Coordinates, mass-weighted cartesian      14
Coordinates, molecule-fixed      285
Coordinates, nonrotating      285
Coordinates, normal      see Normal coordinates
Coordinates, rotating with molecule      12 274 285
Coordinates, rotating with molecule, conditions defining      12 13
Coordinates, space-fixed      285
Coordinates, symmetry      see Symmetry coordinates
Coordinates, valence force      174
Coriolis coupling      275 367ff.
Coriolis coupling, select ion rules for      369
Coriolis splitting of degenerate vibrational levels      367ff.
Correlation tables      334ff.
Correlation tables, $\mathcal{C}_{nh}$       335
Correlation tables, $\mathcal{C}_{nv}$       334 335
Correlation tables, $\mathcal{C}_{n}$       334
Correlation tables, $\mathcal{D}_{nd}$       338 339
Correlation tables, $\mathcal{D}_{nh}$       335—338
Correlation tables, $\mathcal{D}_{n}$       334
Correlation tables, $\mathcal{O}$ , $\mathcal{O}_{h}$       340
Correlation tables, $\mathcal{S}_{n}$       339
Correlation tables, $\mathcal{T}$       339
Correlation tables, $\mathcal{T}_{d}$ , $\mathcal{T}_{d}$       340
Correlation theorem      121
Correlation, of species of group with species of subgroup      121 135 333ff.
Correlation, of vibrations of isotopic molecules of different symmetries      185 249
Correspondence theorem, Bohr      8
cosets      87 123 350
Coulson, C. A.      180
Coupling between rotation and vibration      275 284 367
Crawford, B. L., Jr      42 67 74 117 140 164 182 191 193 196 203 240 265 267—269
Cross terms, in formula for vibrational energy levels      193
Cross terms, in kinetic or potential energy      see Interaction constants
Cross, P. C.      169 362 363
Cubic groups, $\mathcal{T}$ , $\mathcal{T}_{d}$ , $\mathcal{T}_{h}$ , $\mathcal{O}$ , $\mathcal{O}_{h}$ , $\mathcal{J}$ , $\mathcal{J}_{h}$       85 330

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