Allen H.C., Cross P.C. — Molecular Vib-Rotors: the Theory and Interpretation of High Resolution Infrared Spectra :: Электронная библиотека попечительского совета мехмата МГУ

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Allen H.C., Cross P.C. — Molecular Vib-Rotors: the Theory and Interpretation of High Resolution Infrared Spectra

Allen H.C., Cross P.C. — Molecular Vib-Rotors: the Theory and Interpretation of High Resolution Infrared Spectra

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Название: Molecular Vib-Rotors: the Theory and Interpretation of High Resolution Infrared Spectra

Авторы: Allen H.C., Cross P.C.

Аннотация:

Since 1945 there has been a vigorous development in infrared instrumentation.
Commercial spectrometers are now available that can resolve the rotational structure of vibrational bands of.lighter molecules, and many research instruments are available that can resolve the rotational structure in the spectra. of moderately heavy molecules. Much of the basic theory for the interpretation of these spectra was developed during the early years of quantum mechanics. The.available knowledge up to 1945 is well covered in the excellent book by Herzberg. - In the past fifteen years fIluch of this theory has been correlated and extended. Unfortunately, most of this work was scattered throughout the literature. It is our purpose to present this material in an orderly manneF, to relate the diverse notations, and to summarize some of the accumulated experience in applying the theory to the analysis of observed spectra. The treatment in the first five. chapters is intended to give a consistent development of the basic theory. The aim has been to present the theory with sufficient completeness to enable the reader to understand its derivation and to be prepared to extend and adapt the methods involved to new problems. No attempt has been made to include all the esoteric extensions of he theory that have been made in the past few years, since these treatments are so detailed that the notation becomes ponderous and confusing to the beginner.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1963

Количество страниц: 324

Добавлена в каталог: 19.09.2009

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Предметный указатель

reduced energy of asymmetric rotor      20
reduced energy of asymmetric rotor, coefficients of matrix elements      21
reduced energy of asymmetric rotor, explicit solutions      30
reduced energy of asymmetric rotor, factors of      25
reduced energy of asymmetric rotor, matrix elements      19
reduced energy of asymmetric rotor, transformations to diagonalize      31ff
matrix element of reduced energy, definition      19
matrix element of reduced energy, table of values of      232
$\delta$ asymmetry parameter      27 264
$\delta$ asymmetry parameter, coefficients of in perturbation expansion of $E(\delta)$       264 267
$\tau$ energy level index      16 18 28
$\triangle {F}_{2}$ values, A-type bands of asymmetric rotor      189
$\triangle {F}_{2}$ values, A-type bands of asymmetric rotor, dependence on inertial constants      190 192 193
$\triangle {F}_{2}$ values, B-type bands of asymmetric rotor      217
$\triangle {F}_{2}$ values, B-type bands of asymmetric rotor, dependence on inertial constants      217ff
$\triangle {F}_{2}$ values, C-type bands of asymmetric rotor      205
$\triangle {F}_{2}$ values, C-type bands of asymmetric rotor, dependence on inertial constants      205 206 207
$\triangle {F}_{2}$ values, definition      116
$\triangle {F}_{2}$ values, linear rotors      116
$\triangle {F}_{2}$ values, of HCN      119 121
$\triangle {F}_{2}$ values, symmetric rotors, parallel bands      134
$\triangle {F}_{2}$ values, symmetric rotors, perpendicular bands      149 151
$\xi$ -vibrational-rotational interaction constant, calculation of      283ff
$\xi$ -vibrational-rotational interaction constant, definition      48 283
$\xi$ -vibrational-rotational interaction constant, matrix of      284
$\xi$ -vibrational-rotational interaction constant, relation to potential constants      287ff
$\xi$ -vibrational-rotational interaction constant, sum rule      55ff 60
${({I}_{g})}_{v}$ -effective moment of inertia      39
${A}_{v}$ , vib-rotor effective rotational constant      38
${b}^{*}$ asymmetry parameter, definition      21
${B}_{v}$ , vib-rotor effective rotational constant      38
${CDH}_{3}$ methane- ${d}_{1},$ parallel band of      134ff
${CDH}_{3}$ methane- ${d}_{1},$ perpendicular band of      159ff
${CDH}_{3}$ methane- ${d}_{1},$ rotational constants of      138 163
${CD}_{2}{H}_{2}$ methane- ${d}_{2}$ C-type band of      205 208 210
${CD}_{3}H$ methane- ${d}_{3}, \triangle {F}_{2}''$ values      146
${CD}_{3}H$ methane- ${d}_{3}, \triangle {F}_{2}''$ values, hybrid band of      164ff
${CD}_{3}H$ methane- ${d}_{3}, \triangle {F}_{2}''$ values, parallel band of      139ff
${CD}_{3}H$ methane- ${d}_{3}, \triangle {F}_{2}''$ values, rotational constants      141 146 170
${CFH}_{3}$ methyl fluoride, perpendicular band of      154ff
${CFH}_{3}$ methyl fluoride, perpendicular band of, rotational constants of      159
${CH}_{3}CN$ methyl cyanide      57
${CO}_{2}$ carbon dioxide      87
${CO}_{2}$ carbon dioxide, Fermi resonance in      71
${CS}_{2}$ carbon disulfide      87
${C}_{2}DH$ acetylene- ${d}_{1}$       121 122
${C}_{2}DH$ acetylene- ${d}_{1}, \Sigma - \Sigma$ band of      122
${C}_{2}{D}_{2}$ acetylene- ${d}_{2}$       87 120
${C}_{2}{D}_{2}$ acetylene- ${d}_{2}, \Sigma - \Sigma$ band of      120
${C}_{2}{H}_{2}$ acetylene      87 120 121
${C}_{2}{H}_{2}$ acetylene, $\Sigma - \Sigma$ band of      120
${C}_{3v}$ point group, character table      89
${C}_{3}$ point group, character table      90
${C}_{3}{H}_{4}$ methyl acetylene, perpendicular band of      153 154
${C}_{3}{O}_{2}$ carbon suboxide      87
${C}_{4}{H}_{4}$ ethylene, A-type band of      195ff
${C}_{4}{H}_{4}$ ethylene, C-type band of      206 209
${C}_{4}{H}_{4}$ ethylene, molecular model of      197
${C}_{4}{H}_{4}$ ethylene, nuclear spin statistics of      195
${C}_{4}{H}_{4}$ ethylene, sub-bands of A-type band      199
${C}_{4}{H}_{6}$ dimethyl acetylene, free internal rotation in      175
${C}_{v},$ vib-rotor effective rotational constant      38
${C}_{\infty v}$ point group for nonsymmetrical linear molecules      86
${D}_{3}$ point group, character table      90
${D}_{\infty h}$ point group for symmetrical linear molecules      86
${D}_{\infty}(Z)$ two-dimensional rotation group      22
${D}_{\infty}(Z)$ two-dimensional rotation group, classification of symmetric rotor wave functions under      22
${E}^{+}$ factor of asymmetric rotor energy matrix      25
${E}^{-}$ factor of asymmetric rotor energy matrix      25
${H}_{2}S$ hydrogen sulfide, A-type band of      202 203
${H}_{2}S$ hydrogen sulfide, effect of inertial constants on band appearance      186
${K}_{-1},$ K double suffix notation, definition      26
${K}_{-1},$ K double suffix notation, symmetry classification by parity of      27
${NH}_{3}$ ammonia      170ff
${NH}_{3}$ ammonia, inversion in      170ff
${NH}_{3}$ ammonia, vibrational levels of      171
${NH}_{3}$ ammonia, vibrational selection rules for      171
${NH}_{3}$ ammonia, vibrational-rotational band of      172 173 174
${O}^{+}$ factor of asymmetric rotor energy matrix      25
${O}^{-}$ factor of asymmetric rotor energy matrix      25
${\rho}_{\alpha}$ -molecular displacement vector      3
${\tau}_{gg'jj'}$ centrifugal distortion constants, definition      40 269
${\tau}_{gg'jj'}$ centrifugal distortion constants, dependence on internal coordinates      273ff
${\tau}_{gg'jj'}$ centrifugal distortion constants, methods of evaluation      269ff
${\tau}_{gg'jj'}$ centrifugal distortion constants, symmetry properties of      278ff
A axis, of least moment of inertia      15
A rotational constant, definition      15
A-type band of an asymmetric rotor      178ff
A-type band of an asymmetric rotor $\triangle{F}_{2}$ values of      189 192 193
A-type band of an asymmetric rotor ${D}_{2}O$       229
A-type band of an asymmetric rotor ${H}_{2}S$       202 203
A-type band of an asymmetric rotor, ${C}_{2}{H}_{4}$       195ff
A-type band of an asymmetric rotor, definition      107 178
A-type band of an asymmetric rotorHDO      198 200 201
A-type band of an asymmetric rotornearly symmetric rotors      192
A-type band of an asymmetric rotorselection rules      107 178
A-type band of an asymmetric rotorstructure of      178
A-type band of an asymmetric rotortransition dependence on inertial constants      185 188
Allen, H.C, Jr.      111 208 209 262
Angular momentum, classical      5
Angular momentum, classical, internal      6 48
Angular momentum, classical, operators      9ff
Angular momentum, classical, operators, commutation rules      10 14
Angular momentum, classical, operators, matrix elements of      10ff
Angular velocity      3
Angular velocity, components of      6
Anharmonicity      1 47 50
Asymmetric rotor, analysis of bands      177ff
Asymmetric rotor, band envelope method of analysis      227
Asymmetric rotor, band types      see “A-type” “B-type” “C-type”
Asymmetric rotor, correlation of species, notation for classification of energy levels      25ff
Asymmetric rotor, definition      18
Asymmetric rotor, dependence of energy levels on inertial constants      188
Asymmetric rotor, determination of band constants      220ff
Asymmetric rotor, energies      28ff
Asymmetric rotor, energies, approximate methods for      263ff
Asymmetric rotor, energies, approximate methods for, correspondence principle      266
Asymmetric rotor, energies, approximate methods for, perturbation about $\delta = 0$       264ff
Asymmetric rotor, energies, approximate methods for, perturbation about b = 0      263ff
Asymmetric rotor, energies, higher approximations to      33ff
Asymmetric rotor, energies, line strengths, definition      95
Asymmetric rotor, energies, line strengths, tables of      290
Asymmetric rotor, energies, reduced, E(b)      20
Asymmetric rotor, energies, reduced, E(k)      18ff
Asymmetric rotor, energies, reduced, E(k), matrix elements of      19 20
Asymmetric rotor, energies, reduced, E(k), relation to E(—k)      19
Asymmetric rotor, energies, reduced, E(k), tables of      235ff
Asymmetric rotor, energies, reduced, E(k), transformations to diagonalize      31ff
Asymmetric rotor, energies, wave functions      21ff
Asymmetric rotor, energies, wave functions, correlation of notations      28
Asymmetric rotor, wave functions, correlation to symmetric rotor      24
Asymmetric rotor, wave functions, correlation to symmetric rotor, species classification      27
Asymmetric rotor, wave functions, correlation to symmetric rotor, symmetry properties      21ff
Asymmetric rotor, wave functions, correlation to symmetric rotor, V group representations      24
Axes, principal moments of inertia      7
Axes, principal moments of inertia, identification with x, y, z      16
b, asymmetry parameter, coefficients in perturbation expansion of E(b)      263 265
b, asymmetry parameter, coefficients in perturbation expansion of E(b), definition      21
b-axis, intermediate moment of inertia of      15
B-type band of an asymmetric rotor      206ff
B-type band of an asymmetric rotor, $\triangle {F}_{2}$ values of      217
B-type band of an asymmetric rotor, definition      107 206
B-type band of an asymmetric rotor, of ${D}_{2}O$       228
B-type band of an asymmetric rotor, of ${H}_{2}O$       220 221 222
B-type band of an asymmetric rotor, selection rules      107 207
B-type band of an asymmetric rotor, structure of      206ff
B-type band of an asymmetric rotor, sub-bands of      211 212 214 215 216
B-type band of an asymmetric rotor, transition dependence on inertial constants      213
Barker, E.F.      76
Benedict, W.S.      170 175 200 227

Boltzmann factor      110 179
Bose — Einstein statistics      87 88 126
Boyd, D.R.J.      53 55
Branches of spectral bands      107ff
Branches of spectral bands, line strengths      290ft
C rotational constant, definition      15
C rotational constant, oblate symmetric rotors      17
c-axis, greatest moment of inertia of      15
C-type band of an asymmetric rotor      204ff
C-type band of an asymmetric rotor, $\triangle {F}_{2}$ values of      205 206 207
C-type band of an asymmetric rotor, definition      107 204
C-type band of an asymmetric rotor, of ${CD}_{2}{H}_{2}$       205 208 210
C-type band of an asymmetric rotor, of ${C}_{2}{H}_{4}$       206 209
C-type band of an asymmetric rotor, selection rules      107 204
C-type band of an asymmetric rotor, structure of      204
C-type band of an asymmetric rotor, sub-bands of      204
C-type band of an asymmetric rotor, transition dependence on inertial constants      204 205
Center of mass      2 3
Centrifugal distortion      39ff 269ff
Centrifugal distortion, approximate treatment      39ff
Centrifugal distortion, asymmetric rotor      39ff
Centrifugal distortion, constants, definition of      43
Centrifugal distortion, constants, definition of, general theory of      269ff
Centrifugal distortion, effect on intensities      111
Centrifugal distortion, linear rotor      46
Centrifugal distortion, spherical rotor      46
Centrifugal distortion, sum rules including      262
Centrifugal distortion, symmetric rotor      46
Commutation rules, angular momenta      9ff
Commutation rules, angular momenta, molecule-fixed axes      10
Commutation rules, angular momenta, space-fixed axes      14
Commutation rules, direction cosines      96
Condon, E.U.      10
Continued fraction, evaluation of $<{P}_{2}^{4}>$       43
Continued fraction, solution of secular determinant      30
Coordinate system, vib-rotor molecule      2
Coordinates, displacement      3
Coordinates, Eulerian angles      2 8 78
Coordinates, mass-weighted cartesian      4 48
Coordinates, normal      3 4 48 54ff
Coordinates, rotating      2 3
Coordinates, rotating, conditions on      3 4
Coordinates, space-fixed      2
Coordinates, symmetry      55 57
Coriolis force      48ff
Coriolis interaction      39 48ff
Coriolis interaction, asymmetric rotor      67ff
Coriolis interaction, contribution to ${\alpha}_{i}$       39 50
Coriolis interaction, definition      48
Coriolis interaction, Jahn's rule      50
Coriolis interaction, linear rotors      48ff
Coriolis interaction, spherical rotors      67
Coriolis interaction, symmetric rotors      53ff
Coriolis interaction, symmetric rotors, higher order effects      64ff
Coriolis interaction, symmetric rotors, overtone and combination bands      61ff
Costain, C.C.      75 129
Cross, P.C.      2 6 7 10 13 15 21 46 55 227 266 287
Dalby, F.W.      221 222
Darling and Dennison resonance      72 see
Darling, B.T.      71 72
Decius, J.C.      2 6 7 21 55 287
Degeneracy of rotational levels      17 22 86 88
Degeneracy of rotational levels, asymmetric rotor lines      22
Degeneracy of rotational levels, linear rotors      17 86
Degeneracy of rotational levels, spherical rotors      17
Degeneracy of rotational levels, symmetric rotors      17 88
Dennison, D.M.      28 71 72 76 77
Direction cosines      94
Direction cosines, commutation rules      96
Direction cosines, matrix elements of      99ff 102
Displacement vector      3
e parity of changes in ${K}_{-1}$ or K      26 107ff
E(k) reduced energy of asymmetric rotor      18ff
E(k) reduced energy of asymmetric rotor, coefficients of matrix elements      20
E(k) reduced energy of asymmetric rotor, explicit solutions      30
E(k) reduced energy of asymmetric rotor, factors of      25
E(k) reduced energy of asymmetric rotor, matrix elements      19
E(k) reduced energy of asymmetric rotor, tables of      235ff
E(k) reduced energy of asymmetric rotor, transformations to diagonalize      31ff
Eckart, C.      3
Effective moments of inertia      37 38 39
Eggers, D.F.      111
Electric moment      94ff
Electric moment, expansion of      94
Electric moment, in rotating axis system      94
Electric moment, in space-fixed axes system      94
Emmerson, M.      111
Energy calculations, asymmetric rotor      28ff
Energy matrix, diagonalization of      31
Energy matrix, factors of      24
Energy matrix, general matrix elements of      15
Energy matrix, reduced, matrix elements of      19
Eulerian angles      2 8 78
Factors of asymmetric rotor energy matrix      24ff
Factors of asymmetric rotor energy matrix, in $S(J,K,M,\gamma)$ representation      24
Factors of asymmetric rotor energy matrix, symmetry classification      25ff
Fermi resonance      39 70ff
Fermi resonance, in ${CO}_{2}$       71
Fermi resonance, in ${C}_{2}{D}_{2}$       71
Fermi resonance, in ${C}_{2}{H}_{2}$       71
Fermi resonance, in ${H}_{2}O$       71
Fermi resonance, in ${H}_{2}S$       71
Fermi resonance, in HCN      71
Fermi — Dirac statistics      87 88 126
Fermi, E.      71
Four group      see “V”
Gailar, N.      200 227
Giguere, P.      227
Gordy, W.      2
Guenther, A.H.      127
Hainer, R.M.      10 13 15 266
Hamiltonian, classical      5ff
Hamiltonian, Coriolis interaction      47
Hamiltonian, internal rotation      79
Hamiltonian, rigid rotor      7 9
Hamiltonian, rigid rotor, matrix elements      15
Hamiltonian, semirigid rotor      2ff
Hamiltonian, semirigid rotor, including centrifugal distortion      37
Hamiltonian, semirigid rotor, quantum mechanical      2 6 7 33
Hamiltonian, semirigid rotor, second-order perturbation      34
harmonic oscillator      8
HCN hydrogen cyanide      116ff
HCN hydrogen cyanide, $\Pi - \Pi$ -nbandof      117 118
HCN hydrogen cyanide, $\Pi - \Sigma$ band of      124
HCN hydrogen cyanide, $\Sigma - \Sigma$ band of      116 117 118
HCN hydrogen cyanide, $\triangle {F}_{2}$ values of      119 121
HCN hydrogen cyanide, rotational constants of      119
HDO water- ${d}_{1}$ , A-type band of      198 200 201
Hecht, K.T.      67
Herzberg, G.      2 16 49 78 133 150 152 160 164 185
Hooke's law potential      8 39
Howard, J.C.      2 84
Hybrid band, symmetric rotor of      61ff 164ff
Hybrid band, symmetric rotor of, example ${CD}_{3}H$       164ff
Inertial constants, effect on appearance of, A-type band      186 188 189
Innes, K.K.      227 261
Integral values of K, proof of      231
Intensity perturbations in asymmetric rotors      111
Internal angular momentum, definition      6
Internal rotation      77ff
Internal rotation, ${CH}_{3}{BF}_{2}$ -type molecules      78ff
Internal rotation, ${X}_{2}{Y}_{4}-,{X}_{2}{Y}_{6}$ -type molecules      77
Internal rotation, barrier to      77
Internal rotation, energy matrix      81ff
Internal rotation, energy matrix, free rotation      82
Internal rotation, energy matrix, high barriers      83
Internal rotation, energy matrix, low barriers      82
Internal rotation, kinetic energy      78
Internal rotation, symmetry of rotational levels      80
Inversion of molecules      72ff

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