1957:. These transitions are perfectly possible; they merely occur at a lower rate. If the rate for an E1 transition is non-zero, the transition is said to be permitted; if it is zero, then M1, E2, etc. transitions can still produce radiation, albeit with much lower transitions rates. The transition rate decreases by a factor of about 1000 from one multipole to the next one, so the lowest multipole transitions are most likely to occur.
2549:
1232:
2372:
2378:
4484:
of the molecule and the image charges perpendicular to the surface reinforce each other. In contrast, the dipole moments of the molecule and the image charges parallel to the surface cancel out. Therefore, only molecular vibrational peaks giving rise to a dynamic dipole moment perpendicular to the
1098:
In Raman and infrared spectroscopy, the selection rules predict certain vibrational modes to have zero intensities in the Raman and/or the IR. Displacements from the ideal structure can result in relaxation of the selection rules and appearance of these unexpected phonon modes in the spectra.
1285:
involves a kind of vibronic coupling. It results in much-increased intensity of fundamental and overtone transitions as the vibrations "steal" intensity from an allowed electronic transition. In spite of appearances, the selection rules are the same as in Raman spectroscopy.
3682:
711:
transitions that are spin-forbidden are much weaker than spin-allowed transitions. Both can be observed, in spite of the
Laporte rule, because the actual transitions are coupled to vibrations that are anti-symmetric and have the same symmetry as the dipole moment operator.
2544:{\displaystyle {\begin{matrix}\Delta J=0,\pm 1,\pm 2,\pm 3\\(0\not \leftrightarrow 0,1,2;\ {\begin{matrix}{1 \over 2}\end{matrix}}\not \leftrightarrow {\begin{matrix}{1 \over 2}\end{matrix}},{\begin{matrix}{3 \over 2}\end{matrix}};\ 1\not \leftrightarrow 1)\end{matrix}}}
2246:
1247:
spectra. The excited-state wave function is the product of two wave functions such as vibrational and rotational. The general principle is that the symmetry of the excited state is obtained as the direct product of the symmetries of the component wave functions. In
4150:
1320:, or E3 for octupole. In transitions where the change in angular momentum between the initial and final states makes several multipole radiations possible, usually the lowest-order multipoles are overwhelmingly more likely, and dominate the transition.
3901:
1935:
1686:
1836:
4269:
3534:
1397:
1464:
4007:
3354:
2240:
173:
1960:
Semi-forbidden transitions (resulting in so-called intercombination lines) are electric dipole (E1) transitions for which the selection rule that the spin does not change is violated. This is a result of the failure of
2628:
3571:
2928:
2833:
2974:
2879:
2367:{\displaystyle {\begin{matrix}\Delta J=0,\pm 1,\pm 2\\(J=0\not \leftrightarrow 0,1;\ {\begin{matrix}{1 \over 2}\end{matrix}}\not \leftrightarrow {\begin{matrix}{1 \over 2}\end{matrix}})\end{matrix}}}
750:
of the molecule. It follows that, for a vibrational transition to be allowed, the symmetry of the excited state wave function must be the same as the symmetry of the transition moment operator.
318:
1746:
392:
2779:
1581:
1544:
1507:
4674:
Fateley, W. G., Neil T. McDevitt, and
Freeman F. Bentley. "Infrared and Raman selection rules for lattice vibrations: the correlation method." Applied Spectroscopy 25.2 (1971): 155-173.
2715:
3773:
2135:
4047:
3204:
1259:
gas shows rotational fine structure superimposed on the vibrational spectrum. This is typical of the infrared spectra of heteronuclear diatomic molecules. It shows the so-called
3246:
3123:
4184:
4041:
3935:
3813:
3807:
3724:
3159:
3018:
1847:
1601:
452:
3416:
2660:
3565:
3447:
3385:
3282:
3081:
3051:
1757:
230:
203:
4454:
4319:
4190:
3453:
4413:
2101:
2008:
1346:
746:= 1). The symmetry of the ground-state wave function is the same as that of the molecule. It is, therefore, a basis for the totally symmetric representation in the
4375:
4345:
2064:
2034:
1405:
1218:
3941:
3288:
2174:
4695:
Zhao, Yanyuan, et al. "Phonons in Bi 2 S 3 nanostructures: Raman scattering and first-principles studies." Physical Review B 84.20 (2011): 205330. || DOI:
96:
1168:
4971:
55:, and so on. The selection rules may differ according to the technique used to observe the transition. The selection rule also plays a role in
4875:
2104:
1328:
2560:
1244:
1150:
4996:
4949:
4929:
4853:
4826:
4799:
4760:
4717:
4658:
4550:
695:. It follows that transitions in which the spin "direction" changes are forbidden. In formal terms, only states with the same total
3677:{\displaystyle {\begin{matrix}\Delta L=0,\pm 1,\pm 2,\pm 3\\(L=0\not \leftrightarrow 0,1,2;\ 1\not \leftrightarrow 1)\end{matrix}}}
259:
In practice, to determine a selection rule the integral itself does not need to be calculated: It is sufficient to determine the
2885:
2790:
2934:
2839:
4966:
1943:
These considerations generate different sets of transitions rules depending on the multipole order and type. The expression
4683:
Arenas, D. J., et al. "Raman study of phonon modes in bismuth pyrochlores." Physical Review B 82.21 (2010): 214302. || DOI:
1282:
1204:
269:
1697:
1211:
346:
2721:
1084:
4986:
4542:
1549:
1512:
618:
1469:
1295:
1183:
2666:
1300:
In general, electric (charge) radiation or magnetic (current, magnetic moment) radiation can be classified into
4499:
4465:
4145:{\displaystyle {\begin{matrix}\Delta L=0,\pm 1,\\\pm 2,\pm 3,\pm 4\\(L=0\not \leftrightarrow 0,1)\end{matrix}}}
2037:
1117:
for rotational transitions, derived from the symmetries of the rotational wave functions in a rigid rotor, is Δ
638:
455:
241:
60:
3730:
1940:
Thus, parity does not change for E-even or M-odd multipoles, while it changes for E-odd or M-even multipoles.
2114:
4791:
1272:
4585:
symmetry, the positive and negative parts will be equal to each other, so the integral has a value of zero.
248:(and thus the probability) of the transition between states 1 and 2; if the value of this integral is
3168:
459:
1583:
are, respectively, the initial and final angular momenta of the atom. The corresponding quantum numbers
4991:
754:
721:
3896:{\displaystyle {\begin{matrix}\Delta L=0,\pm 1,\\\pm 2,\pm 3\\(L=0\not \leftrightarrow 0)\end{matrix}}}
1099:
Therefore, the appearance of new modes in the spectra can be a useful indicator of symmetry breakdown.
320:
If the transition moment function is symmetric over all of the totally symmetric representation of the
3213:
3090:
1930:{\displaystyle \pi (\mathrm {M} \lambda )=\pi _{\mathrm {i} }\pi _{\mathrm {f} }=(-1)^{\lambda +1}\,.}
1681:{\displaystyle |J_{\mathrm {i} }-J_{\mathrm {f} }|\leq \lambda \leq J_{\mathrm {i} }+J_{\mathrm {f} }}
462:
of its three components. The symmetry characteristics of each component can be obtained from standard
4900:
1945:
700:
4891:
Stanton, L. (1973). "Selection rules for pure rotation and vibration-rotation hyper-Raman spectra".
4581:) signifies symmetric with respect to the centre of symmetry. If the transition moment function has
4157:
4014:
3908:
3780:
3697:
3132:
2991:
1076:. Examination of the character table shows that all four vibrations are Raman-active, but only the T
466:. Rules for obtaining the symmetries of a direct product can be found in texts on character tables.
4494:
4277:
2067:
1831:{\displaystyle \pi (\mathrm {E} \lambda )=\pi _{\mathrm {i} }\pi _{\mathrm {f} }=(-1)^{\lambda }\,}
1249:
1178:
731:
696:
401:
68:
3391:
4264:{\displaystyle {\begin{matrix}\Delta L=0,\pm 1,\\\pm 2\\(L=0\not \leftrightarrow 0)\end{matrix}}}
3529:{\displaystyle {\begin{matrix}\Delta L=0,\pm 1,\pm 2\\(L=0\not \leftrightarrow 0,1)\end{matrix}}}
2633:
2108:
1136:
770:
725:
3541:
3423:
3361:
3258:
3057:
3027:
1392:{\displaystyle \mathbf {J} _{\mathrm {i} }=\mathbf {J} _{\mathrm {f} }+{\boldsymbol {\lambda }}}
1057:, may be used as an example to illustrate the application of these principles. The molecule is
687:
The wave function of a single electron is the product of a space-dependent wave function and a
208:
181:
4945:
4925:
4871:
4849:
4822:
4795:
4756:
4713:
4654:
4546:
4418:
4283:
1334:
1301:
1256:
1173:
83:
56:
4380:
2073:
1975:
4908:
1459:{\textstyle \Vert {\boldsymbol {\lambda }}\Vert ={\sqrt {\lambda (\lambda +1)\,}}\;\hbar ~,}
1159:
774:
692:
463:
773:, the operator transforms as one of the second-order terms in the right-most column of the
769:. The excited state wave function must also transform as at least one of these vectors. In
16:
Formal constraint on the possible transitions of a system from one quantum state to another
4504:
1231:
582:
578:
40:
4354:
4324:
4002:{\displaystyle {\begin{matrix}\Delta L=0,\pm 1\\(L=0\not \leftrightarrow 0)\end{matrix}}}
3349:{\displaystyle {\begin{matrix}\Delta L=0,\pm 1\\(L=0\not \leftrightarrow 0)\end{matrix}}}
2235:{\displaystyle {\begin{matrix}\Delta J=0,\pm 1\\(J=0\not \leftrightarrow 0)\end{matrix}}}
2043:
2013:
1340:
Since the total angular momentum has to be conserved during the transition, we have that
4904:
4816:
4348:
1327:, which for the photon must be at least 1, since it is a vector particle (i.e., it has
688:
52:
236:
of the two states, "state 1" and "state 2", involved in the transition, and
4980:
1092:
1088:
395:
233:
36:
4753:
The Raman Effect: A Unified
Treatment of the Theory of Raman Scattering by Molecules
1188:
735:
574:
4480:
on a substrate, the molecule induces opposite image charges in the substrate. The
4864:
324:
to which the atom or molecule belongs, then the integral's value is (in general)
168:{\displaystyle m_{1,2}=\int \psi _{1}^{*}\,\mu \,\psi _{2}\,\mathrm {d} \tau \,,}
1962:
1114:
1108:
1058:
747:
321:
4477:
1317:
1192:
245:
4696:
4684:
4621:
Cotton, Section 10.6 Selection rules for fundamental vibrational transitions
637:
symmetry, so the symmetry of the transition moment function is given by the
24:
4912:
74:
In the following, mainly atomic and molecular transitions are considered.
4473:
4472:
is applied to identify the peaks observed in vibrational spectra. When a
1333:= 1). Thus, there is no radiation from E0 (electric monopoles) or M0 (
260:
44:
1323:
The emitted particle carries away angular momentum, with quantum number
730:
In vibrational spectroscopy, transitions are observed between different
64:
20:
4481:
1313:
63:, that is, reactions where the spin state changes at least once from
4573:) symmetry is antisymmetric with respect to the centre of symmetry.
2623:{\displaystyle \Delta M_{J}=0,\pm 1\ (M_{J}=0\not \leftrightarrow 0}
35:, formally constrains the possible transitions of a system from one
1243:
There are many types of coupled transition such as are observed in
1230:
86:
the basis for a spectroscopic selection rule is the value of the
1091:
are forbidden in both infrared and Raman spectra. However, when
48:
734:. In a fundamental vibration, the molecule is excited from its
691:
wave function. Spin is directional and can be said to have odd
1751:
Parity is also preserved. For electric multipole transitions
1279:
branch. This follows from the application of selection rules.
1252:
transitions, the excited states involve three wave functions.
1236:
1068:
symmetry. The vibrations of methane span the representations A
1949:
is often used, but this does not mean that these transitions
656:
symmetry. The transitions are therefore forbidden. Likewise,
617:
transitions are forbidden. The
Laporte rule (law) applies to
454:
holds. The symmetry of the transition moment function is the
4456:
it obeys a selection rule table similar to the table above.
1095:
is taken into account, the transitions are weakly allowed.
2923:{\displaystyle \pi _{\mathrm {f} }=-\pi _{\mathrm {i} }\,}
2828:{\displaystyle \pi _{\mathrm {f} }=-\pi _{\mathrm {i} }\,}
2969:{\displaystyle \pi _{\mathrm {f} }=\pi _{\mathrm {i} }\,}
2874:{\displaystyle \pi _{\mathrm {f} }=\pi _{\mathrm {i} }\,}
4377:
is the total angular momentum of the electron(s). Since
4956:
Chapter 4: The interaction of radiation with a crystal.
1271:
branch, located at the vibration frequency, is absent.
470:
Symmetry characteristics of transition moment operator
4485:
surface will be observed in the vibrational spectrum.
4195:
4052:
3946:
3818:
3576:
3458:
3293:
2502:
2481:
2460:
2383:
2340:
2319:
2251:
2179:
1727:
1712:
1408:
779:
757:, the transition moment operator transforms as either
4612:
Cotton
Section 9.6, Selection rules and polarizations
4421:
4383:
4357:
4327:
4286:
4193:
4160:
4050:
4017:
3944:
3911:
3816:
3783:
3733:
3700:
3574:
3544:
3456:
3426:
3394:
3364:
3291:
3261:
3216:
3171:
3135:
3093:
3060:
3030:
2994:
2937:
2888:
2842:
2793:
2724:
2669:
2636:
2563:
2381:
2249:
2177:
2117:
2076:
2046:
2016:
1978:
1850:
1760:
1700:
1604:
1552:
1515:
1472:
1349:
577:
is a selection rule formally stated as follows: In a
404:
349:
272:
211:
184:
99:
468:
4936:Section 4.1.5: Selection rules for Raman activity.
4863:
4448:
4407:
4369:
4339:
4313:
4263:
4178:
4144:
4035:
4001:
3929:
3895:
3801:
3767:
3718:
3676:
3559:
3528:
3441:
3410:
3379:
3348:
3276:
3240:
3198:
3153:
3117:
3075:
3045:
3012:
2968:
2922:
2873:
2827:
2773:
2709:
2654:
2622:
2543:
2366:
2234:
2129:
2095:
2058:
2028:
2002:
1929:
1830:
1740:
1680:
1575:
1538:
1501:
1458:
1391:
446:
386:
313:{\displaystyle \,\psi _{1}^{*}\;\mu \;\psi _{2}~.}
312:
224:
197:
167:
39:to another. Selection rules have been derived for
4767:Chapter 7, Vibrational Resonance Raman Scattering
1741:{\displaystyle \mu =M_{\mbox{i}}-M_{\mbox{f}}\,.}
1080:vibrations can be seen in the infrared spectrum.
387:{\displaystyle \psi _{1}^{*}\;\mu \;\psi _{2}\,,}
2774:{\displaystyle \Delta M_{J}=0,\pm 1,\pm 2,\pm 3}
2107:. Which transitions are allowed is based on the
2105:secondary total angular momentum quantum number
4972:Lecture notes from The University of Sheffield
4967:National Institute of Standards and Technology
339:The transition moment integral is zero if the
4539:Point Group Character Tables and Related Data
1576:{\displaystyle ~\mathbf {J} _{\mathrm {f} }~}
1539:{\displaystyle ~\mathbf {J} _{\mathrm {i} }~}
1312:(magnetic) of order 2, e.g., E1 for electric
1212:
8:
4280:, the total angular momentum of the atom is
2137:is used to indicate a forbidden transition.
1417:
1409:
1502:{\displaystyle \lambda _{z}=\mu \,\hbar ~;}
333:
253:
4697:https://doi.org/10.1103/PhysRevB.84.205330
4685:https://doi.org/10.1103/PhysRevB.82.214302
2710:{\displaystyle \Delta M_{J}=0,\pm 1,\pm 2}
1446:
1219:
1205:
1132:
684:symmetry and the transition is forbidden.
369:
365:
293:
289:
4420:
4382:
4356:
4326:
4285:
4194:
4192:
4159:
4051:
4049:
4016:
3945:
3943:
3910:
3817:
3815:
3782:
3764:
3732:
3699:
3575:
3573:
3543:
3457:
3455:
3425:
3407:
3393:
3363:
3292:
3290:
3260:
3215:
3170:
3134:
3092:
3059:
3029:
2993:
2965:
2958:
2957:
2943:
2942:
2936:
2919:
2912:
2911:
2894:
2893:
2887:
2870:
2863:
2862:
2848:
2847:
2841:
2824:
2817:
2816:
2799:
2798:
2792:
2732:
2723:
2677:
2668:
2635:
2602:
2571:
2562:
2505:
2501:
2484:
2480:
2463:
2459:
2382:
2380:
2343:
2339:
2322:
2318:
2250:
2248:
2178:
2176:
2116:
2084:
2075:
2045:
2015:
1977:
1923:
1911:
1888:
1887:
1876:
1875:
1857:
1849:
1827:
1821:
1798:
1797:
1786:
1785:
1767:
1759:
1734:
1726:
1711:
1699:
1671:
1670:
1656:
1655:
1637:
1630:
1629:
1615:
1614:
1605:
1603:
1563:
1562:
1557:
1551:
1526:
1525:
1520:
1514:
1489:
1477:
1471:
1443:
1423:
1412:
1407:
1384:
1374:
1373:
1368:
1357:
1356:
1351:
1348:
403:
380:
374:
359:
354:
348:
298:
283:
278:
273:
271:
216:
210:
189:
183:
161:
153:
152:
146:
141:
137:
131:
126:
104:
98:
4922:The vibrational spectroscopy of polymers
3768:{\displaystyle \Delta L=0,\pm 1,\pm 2\,}
2139:
4844:Harris, D.C.; Bertolucci, M.D. (1978).
4630:Cotton, Chapter 10 Molecular Vibrations
4515:
2130:{\displaystyle ~\not \leftrightarrow ~}
1490:
1447:
1413:
1385:
1158:
1142:
1135:
332:allowed. Otherwise, the transition is "
581:environment, transitions between like
4866:Chemical Applications of Group Theory
4815:Condon, E.V.; Shortley, G.H. (1953).
1595:-axis angular momentum) must satisfy
7:
4537:Salthouse, J.A.; Ware, M.J. (1972).
4532:
4530:
4528:
3199:{\displaystyle \Delta L=\pm 1,\pm 3}
4415:has a similar mathematical form as
4942:Vibrational Spectroscopy of Solids
4920:Bower, D.I; Maddams, W.F. (1989).
4198:
4161:
4055:
4018:
3949:
3912:
3821:
3784:
3734:
3701:
3579:
3545:
3461:
3427:
3395:
3365:
3296:
3262:
3217:
3172:
3136:
3094:
3061:
3031:
2995:
2959:
2944:
2913:
2895:
2864:
2849:
2818:
2800:
2725:
2670:
2637:
2564:
2386:
2254:
2182:
1889:
1877:
1858:
1799:
1787:
1768:
1672:
1657:
1631:
1616:
1564:
1527:
1375:
1358:
154:
14:
1466:and its z-projection is given by
742:= 0) to the first excited state (
4466:surface vibrational spectroscopy
3241:{\displaystyle \Delta L=0,\pm 2}
3118:{\displaystyle \Delta L=0,\pm 2}
2010:is the total angular momentum,
1558:
1521:
1369:
1352:
1125:is a rotational quantum number.
4522:Harris & Bertolucci, p. 130
1337:, which do not seem to exist).
1151:Rotational–vibrational coupling
668:, even), so the triple product
244:. This integral represents the
4944:. Cambridge University Press.
4924:. Cambridge University Press.
4821:. Cambridge University Press.
4776:Harris & Berolucci, p. 198
4741:Harris & Berolucci, p. 123
4732:Harris & Berolucci, p. 339
4603:Harris & Berolucci, p. 336
4594:Harris & Berolucci, p. 330
4254:
4236:
4179:{\displaystyle \Delta S=\pm 1}
4135:
4111:
4036:{\displaystyle \Delta S=\pm 1}
3992:
3974:
3930:{\displaystyle \Delta S=\pm 1}
3886:
3868:
3802:{\displaystyle \Delta S=\pm 1}
3719:{\displaystyle \Delta S=\pm 1}
3667:
3622:
3519:
3495:
3339:
3321:
3154:{\displaystyle \Delta L=\pm 1}
3013:{\displaystyle \Delta L=\pm 1}
2649:
2595:
2534:
2429:
2357:
2288:
2225:
2207:
1908:
1898:
1865:
1854:
1841:while for magnetic multipoles
1818:
1808:
1775:
1764:
1638:
1606:
1440:
1428:
438:
429:
417:
411:
1:
4893:Journal of Raman Spectroscopy
4349:nuclear spin angular momentum
447:{\displaystyle ~y(x)=-y(-x)~}
4818:The Theory of Atomic Spectra
3411:{\displaystyle \Delta L=0\,}
1283:Resonance Raman spectroscopy
4848:. Oxford University Press.
2655:{\displaystyle \Delta J=0)}
1169:Ro–vibrational spectroscopy
619:electric dipole transitions
5013:
4997:Nuclear magnetic resonance
4710:Molecular Rotation Spectra
4543:Cambridge University Press
3560:{\displaystyle \Delta S=0}
3442:{\displaystyle \Delta S=0}
3380:{\displaystyle \Delta S=0}
3277:{\displaystyle \Delta S=0}
3076:{\displaystyle \Delta n=0}
3046:{\displaystyle \Delta L=0}
1953:occur, only that they are
1293:
1106:
719:
341:transition moment function
265:transition moment function
242:transition moment operator
88:transition moment integral
59:, where some are formally
4940:Sherwood, P.M.A. (1972).
4846:Symmetry and Spectroscopy
3693:
3537:
3419:
3085:None or one electron jump
2979:
2882:
2836:
2718:
2663:
2557:
2375:
2243:
2171:
2165:
2155:Magnetic quadrupole (M2)
2152:Electric quadrupole (E2)
2142:
1955:electric-dipole-forbidden
1296:angular momentum coupling
1255:The infrared spectrum of
1235:The infrared spectrum of
1184:Angular momentum coupling
225:{\displaystyle \psi _{2}}
198:{\displaystyle \psi _{1}}
4665:Chapter 9, Anharmonicity
4500:Spin-forbidden reactions
4449:{\displaystyle ~J=L+S~,}
4314:{\displaystyle ~F=I+J~,}
2038:azimuthal quantum number
1053:The molecule methane, CH
781:Character table for the
519:Electric polarizability
328:zero and the transition
252:then the transition is "
61:spin-forbidden reactions
4870:(3rd ed.). Wiley.
4792:Oxford University Press
4408:{\displaystyle ~F=I+J~}
2161:Magnetic octupole (M3)
2158:Electric octupole (E3)
2096:{\displaystyle ~M_{J}~}
2003:{\displaystyle ~J=L+S~}
1087:, it can be shown that
699:are "spin-allowed". In
557:Optical spectra (weak)
4913:10.1002/jrs.1250010105
4786:Softley, T.P. (1994).
4470:surface selection rule
4450:
4409:
4371:
4341:
4315:
4265:
4180:
4146:
4037:
4003:
3931:
3897:
3803:
3769:
3720:
3688:Intermediate coupling
3678:
3561:
3530:
3443:
3412:
3381:
3350:
3278:
3242:
3200:
3155:
3119:
3077:
3047:
3014:
2970:
2924:
2875:
2829:
2775:
2711:
2656:
2624:
2545:
2368:
2236:
2131:
2097:
2060:
2030:
2004:
1931:
1832:
1742:
1682:
1577:
1540:
1503:
1460:
1393:
1275:molecules display the
1240:
1085:harmonic approximation
621:, so the operator has
448:
388:
314:
226:
199:
169:
4862:Cotton, F.A. (1990).
4649:Califano, S. (1976).
4451:
4410:
4372:
4342:
4316:
4266:
4181:
4147:
4038:
4004:
3932:
3898:
3804:
3770:
3721:
3679:
3562:
3531:
3444:
3413:
3382:
3351:
3279:
3243:
3201:
3156:
3120:
3078:
3048:
3015:
2971:
2925:
2876:
2830:
2776:
2712:
2657:
2625:
2546:
2369:
2237:
2149:Magnetic dipole (M1)
2146:Electric dipole (E1)
2132:
2098:
2061:
2031:
2005:
1946:forbidden transitions
1932:
1833:
1743:
1683:
1578:
1541:
1504:
1461:
1394:
1234:
755:infrared spectroscopy
722:infrared spectroscopy
449:
394:is anti-symmetric or
389:
315:
227:
200:
170:
4708:Kroto, H.W. (1992).
4419:
4381:
4355:
4325:
4284:
4191:
4158:
4048:
4015:
3942:
3909:
3814:
3781:
3731:
3698:
3572:
3542:
3454:
3424:
3392:
3362:
3289:
3259:
3214:
3169:
3133:
3091:
3058:
3028:
2992:
2935:
2886:
2840:
2791:
2722:
2667:
2634:
2561:
2379:
2247:
2175:
2143:Allowed transitions
2115:
2074:
2044:
2014:
1976:
1848:
1758:
1698:
1602:
1550:
1513:
1470:
1406:
1347:
701:crystal field theory
502:Electric quadrupole
402:
347:
270:
209:
182:
97:
4905:1973JRSp....1...53S
4751:Long, D.A. (2001).
4712:. new York: Dover.
4495:Superselection rule
4370:{\displaystyle ~J~}
4340:{\displaystyle ~I~}
4278:hyperfine structure
2068:spin quantum number
2059:{\displaystyle ~S~}
2029:{\displaystyle ~L~}
1179:Rovibronic coupling
1137:Coupling in science
1129:Coupled transitions
789:
716:Vibrational spectra
697:spin quantum number
633:orbitals also have
523:x, y, z, xy, xz, yz
506:x, y, z, xy, xz, yz
471:
364:
288:
136:
4651:Vibrational states
4446:
4405:
4367:
4337:
4311:
4261:
4259:
4176:
4142:
4140:
4033:
3999:
3997:
3927:
3893:
3891:
3799:
3765:
3716:
3674:
3672:
3557:
3526:
3524:
3439:
3408:
3377:
3346:
3344:
3274:
3238:
3196:
3151:
3115:
3073:
3043:
3010:
2966:
2920:
2871:
2825:
2771:
2707:
2652:
2620:
2541:
2539:
2517:
2496:
2475:
2364:
2362:
2355:
2334:
2232:
2230:
2127:
2109:hydrogen-like atom
2093:
2056:
2026:
2000:
1927:
1828:
1738:
1731:
1716:
1678:
1573:
1536:
1499:
1456:
1389:
1335:magnetic monopoles
1245:vibration–rotation
1241:
1143:Classical coupling
1103:Rotational spectra
780:
771:Raman spectroscopy
732:vibrational states
726:Raman spectroscopy
664:symmetry (meaning
625:symmetry (meaning
569:Electronic spectra
469:
444:
384:
350:
310:
274:
222:
195:
165:
122:
57:chemical reactions
4987:Quantum mechanics
4877:978-0-471-51094-9
4442:
4424:
4404:
4386:
4366:
4360:
4336:
4330:
4307:
4289:
4274:
4273:
3657:
3208:One electron jump
3163:One electron jump
3127:One electron jump
2986:One electron jump
2594:
2524:
2513:
2492:
2471:
2458:
2351:
2330:
2317:
2126:
2120:
2092:
2079:
2055:
2049:
2025:
2019:
1999:
1981:
1730:
1715:
1572:
1555:
1535:
1518:
1495:
1452:
1444:
1257:hydrogen chloride
1229:
1228:
1174:Vibronic coupling
1051:
1050:
561:
560:
443:
407:
306:
84:quantum mechanics
5004:
4955:
4935:
4916:
4881:
4869:
4859:
4833:
4832:
4812:
4806:
4805:
4783:
4777:
4774:
4768:
4766:
4748:
4742:
4739:
4733:
4730:
4724:
4723:
4705:
4699:
4693:
4687:
4681:
4675:
4672:
4666:
4664:
4646:
4640:
4637:
4631:
4628:
4622:
4619:
4613:
4610:
4604:
4601:
4595:
4592:
4586:
4563:
4557:
4556:
4534:
4523:
4520:
4455:
4453:
4452:
4447:
4440:
4422:
4414:
4412:
4411:
4406:
4402:
4384:
4376:
4374:
4373:
4368:
4364:
4358:
4346:
4344:
4343:
4338:
4334:
4328:
4320:
4318:
4317:
4312:
4305:
4287:
4270:
4268:
4267:
4262:
4260:
4185:
4183:
4182:
4177:
4151:
4149:
4148:
4143:
4141:
4042:
4040:
4039:
4034:
4008:
4006:
4005:
4000:
3998:
3936:
3934:
3933:
3928:
3902:
3900:
3899:
3894:
3892:
3808:
3806:
3805:
3800:
3774:
3772:
3771:
3766:
3725:
3723:
3722:
3717:
3683:
3681:
3680:
3675:
3673:
3655:
3566:
3564:
3563:
3558:
3535:
3533:
3532:
3527:
3525:
3448:
3446:
3445:
3440:
3417:
3415:
3414:
3409:
3386:
3384:
3383:
3378:
3355:
3353:
3352:
3347:
3345:
3283:
3281:
3280:
3275:
3247:
3245:
3244:
3239:
3205:
3203:
3202:
3197:
3160:
3158:
3157:
3152:
3124:
3122:
3121:
3116:
3082:
3080:
3079:
3074:
3052:
3050:
3049:
3044:
3022:No electron jump
3019:
3017:
3016:
3011:
2975:
2973:
2972:
2967:
2964:
2963:
2962:
2949:
2948:
2947:
2929:
2927:
2926:
2921:
2918:
2917:
2916:
2900:
2899:
2898:
2880:
2878:
2877:
2872:
2869:
2868:
2867:
2854:
2853:
2852:
2834:
2832:
2831:
2826:
2823:
2822:
2821:
2805:
2804:
2803:
2780:
2778:
2777:
2772:
2737:
2736:
2716:
2714:
2713:
2708:
2682:
2681:
2661:
2659:
2658:
2653:
2629:
2627:
2626:
2621:
2607:
2606:
2592:
2576:
2575:
2550:
2548:
2547:
2542:
2540:
2522:
2518:
2514:
2506:
2497:
2493:
2485:
2476:
2472:
2464:
2456:
2373:
2371:
2370:
2365:
2363:
2356:
2352:
2344:
2335:
2331:
2323:
2315:
2241:
2239:
2238:
2233:
2231:
2140:
2136:
2134:
2133:
2128:
2124:
2118:
2102:
2100:
2099:
2094:
2090:
2089:
2088:
2077:
2065:
2063:
2062:
2057:
2053:
2047:
2035:
2033:
2032:
2027:
2023:
2017:
2009:
2007:
2006:
2001:
1997:
1979:
1936:
1934:
1933:
1928:
1922:
1921:
1894:
1893:
1892:
1882:
1881:
1880:
1861:
1837:
1835:
1834:
1829:
1826:
1825:
1804:
1803:
1802:
1792:
1791:
1790:
1771:
1747:
1745:
1744:
1739:
1733:
1732:
1728:
1718:
1717:
1713:
1687:
1685:
1684:
1679:
1677:
1676:
1675:
1662:
1661:
1660:
1641:
1636:
1635:
1634:
1621:
1620:
1619:
1609:
1594:
1590:
1586:
1582:
1580:
1579:
1574:
1570:
1569:
1568:
1567:
1561:
1553:
1545:
1543:
1542:
1537:
1533:
1532:
1531:
1530:
1524:
1516:
1508:
1506:
1505:
1500:
1493:
1482:
1481:
1465:
1463:
1462:
1457:
1450:
1445:
1424:
1416:
1398:
1396:
1395:
1390:
1388:
1380:
1379:
1378:
1372:
1363:
1362:
1361:
1355:
1331:
1326:
1311:
1307:
1290:Angular momentum
1221:
1214:
1207:
1160:Quantum coupling
1133:
790:
551:
544:
537:
532:Magnetic dipole
524:
513:
507:
497:Optical spectra
494:
489:Electric dipole
480:
472:
464:character tables
453:
451:
450:
445:
441:
405:
393:
391:
390:
385:
379:
378:
363:
358:
319:
317:
316:
311:
304:
303:
302:
287:
282:
239:
231:
229:
228:
223:
221:
220:
204:
202:
201:
196:
194:
193:
174:
172:
171:
166:
157:
151:
150:
135:
130:
115:
114:
5012:
5011:
5007:
5006:
5005:
5003:
5002:
5001:
4977:
4976:
4963:
4952:
4939:
4932:
4919:
4890:
4887:
4885:Further reading
4878:
4861:
4860:
4856:
4843:
4841:
4836:
4829:
4814:
4813:
4809:
4802:
4785:
4784:
4780:
4775:
4771:
4763:
4750:
4749:
4745:
4740:
4736:
4731:
4727:
4720:
4707:
4706:
4702:
4694:
4690:
4682:
4678:
4673:
4669:
4661:
4648:
4647:
4643:
4638:
4634:
4629:
4625:
4620:
4616:
4611:
4607:
4602:
4598:
4593:
4589:
4564:
4560:
4553:
4536:
4535:
4526:
4521:
4517:
4513:
4505:Singlet fission
4491:
4462:
4417:
4416:
4379:
4378:
4353:
4352:
4323:
4322:
4282:
4281:
4258:
4257:
4233:
4232:
4223:
4222:
4189:
4188:
4187:
4186:
4156:
4155:
4139:
4138:
4108:
4107:
4080:
4079:
4046:
4045:
4044:
4043:
4013:
4012:
3996:
3995:
3971:
3970:
3940:
3939:
3938:
3937:
3907:
3906:
3890:
3889:
3865:
3864:
3846:
3845:
3812:
3811:
3810:
3809:
3779:
3778:
3729:
3728:
3727:
3726:
3696:
3695:
3671:
3670:
3619:
3618:
3570:
3569:
3568:
3567:
3540:
3539:
3523:
3522:
3492:
3491:
3452:
3451:
3450:
3449:
3422:
3421:
3390:
3389:
3388:
3387:
3360:
3359:
3343:
3342:
3318:
3317:
3287:
3286:
3285:
3284:
3257:
3256:
3212:
3211:
3210:
3209:
3167:
3166:
3165:
3164:
3131:
3130:
3129:
3128:
3089:
3088:
3087:
3086:
3056:
3055:
3054:
3026:
3025:
3024:
3023:
2990:
2989:
2988:
2987:
2953:
2938:
2933:
2932:
2907:
2889:
2884:
2883:
2858:
2843:
2838:
2837:
2812:
2794:
2789:
2788:
2728:
2720:
2719:
2673:
2665:
2664:
2632:
2631:
2598:
2567:
2559:
2558:
2538:
2537:
2516:
2515:
2495:
2494:
2474:
2473:
2426:
2425:
2377:
2376:
2361:
2360:
2354:
2353:
2333:
2332:
2285:
2284:
2245:
2244:
2229:
2228:
2204:
2203:
2173:
2172:
2166:Rigorous rules
2113:
2112:
2080:
2072:
2071:
2042:
2041:
2012:
2011:
1974:
1973:
1971:
1907:
1883:
1871:
1846:
1845:
1817:
1793:
1781:
1756:
1755:
1722:
1707:
1696:
1695:
1666:
1651:
1625:
1610:
1600:
1599:
1592:
1588:
1584:
1556:
1548:
1547:
1519:
1511:
1510:
1473:
1468:
1467:
1404:
1403:
1367:
1350:
1345:
1344:
1329:
1324:
1309:
1308:(electric) or M
1305:
1298:
1292:
1225:
1131:
1111:
1105:
1079:
1075:
1071:
1066:
1056:
1002:
990:
983:
976:
953:
881:
843:
830:
822:
813:
804:
786:
728:
720:Main articles:
718:
583:atomic orbitals
579:centrosymmetric
571:
566:
554:
549:
547:
542:
540:
535:
522:
511:
505:
492:
478:
475:Transition type
400:
399:
370:
345:
344:
294:
268:
267:
237:
212:
207:
206:
185:
180:
179:
142:
100:
95:
94:
80:
43:transitions in
41:electromagnetic
33:transition rule
17:
12:
11:
5:
5010:
5008:
5000:
4999:
4994:
4989:
4979:
4978:
4975:
4974:
4969:
4962:
4961:External links
4959:
4958:
4957:
4950:
4937:
4930:
4917:
4886:
4883:
4876:
4854:
4840:
4837:
4835:
4834:
4827:
4807:
4800:
4790:. Oxford, UK:
4788:Atomic Spectra
4778:
4769:
4761:
4743:
4734:
4725:
4718:
4700:
4688:
4676:
4667:
4659:
4641:
4632:
4623:
4614:
4605:
4596:
4587:
4565:Anything with
4558:
4551:
4524:
4514:
4512:
4509:
4508:
4507:
4502:
4497:
4490:
4487:
4461:
4458:
4445:
4439:
4436:
4433:
4430:
4427:
4401:
4398:
4395:
4392:
4389:
4363:
4333:
4310:
4304:
4301:
4298:
4295:
4292:
4272:
4271:
4256:
4253:
4250:
4247:
4244:
4241:
4238:
4235:
4234:
4231:
4228:
4225:
4224:
4221:
4218:
4215:
4212:
4209:
4206:
4203:
4200:
4197:
4196:
4175:
4172:
4169:
4166:
4163:
4152:
4137:
4134:
4131:
4128:
4125:
4122:
4119:
4116:
4113:
4110:
4109:
4106:
4103:
4100:
4097:
4094:
4091:
4088:
4085:
4082:
4081:
4078:
4075:
4072:
4069:
4066:
4063:
4060:
4057:
4054:
4053:
4032:
4029:
4026:
4023:
4020:
4009:
3994:
3991:
3988:
3985:
3982:
3979:
3976:
3973:
3972:
3969:
3966:
3963:
3960:
3957:
3954:
3951:
3948:
3947:
3926:
3923:
3920:
3917:
3914:
3903:
3888:
3885:
3882:
3879:
3876:
3873:
3870:
3867:
3866:
3863:
3860:
3857:
3854:
3851:
3848:
3847:
3844:
3841:
3838:
3835:
3832:
3829:
3826:
3823:
3820:
3819:
3798:
3795:
3792:
3789:
3786:
3775:
3763:
3760:
3757:
3754:
3751:
3748:
3745:
3742:
3739:
3736:
3715:
3712:
3709:
3706:
3703:
3692:
3689:
3685:
3684:
3669:
3666:
3663:
3660:
3654:
3651:
3648:
3645:
3642:
3639:
3636:
3633:
3630:
3627:
3624:
3621:
3620:
3617:
3614:
3611:
3608:
3605:
3602:
3599:
3596:
3593:
3590:
3587:
3584:
3581:
3578:
3577:
3556:
3553:
3550:
3547:
3536:
3521:
3518:
3515:
3512:
3509:
3506:
3503:
3500:
3497:
3494:
3493:
3490:
3487:
3484:
3481:
3478:
3475:
3472:
3469:
3466:
3463:
3460:
3459:
3438:
3435:
3432:
3429:
3418:
3406:
3403:
3400:
3397:
3376:
3373:
3370:
3367:
3356:
3341:
3338:
3335:
3332:
3329:
3326:
3323:
3320:
3319:
3316:
3313:
3310:
3307:
3304:
3301:
3298:
3295:
3294:
3273:
3270:
3267:
3264:
3253:
3249:
3248:
3237:
3234:
3231:
3228:
3225:
3222:
3219:
3206:
3195:
3192:
3189:
3186:
3183:
3180:
3177:
3174:
3161:
3150:
3147:
3144:
3141:
3138:
3125:
3114:
3111:
3108:
3105:
3102:
3099:
3096:
3083:
3072:
3069:
3066:
3063:
3042:
3039:
3036:
3033:
3020:
3009:
3006:
3003:
3000:
2997:
2984:
2981:
2977:
2976:
2961:
2956:
2952:
2946:
2941:
2930:
2915:
2910:
2906:
2903:
2897:
2892:
2881:
2866:
2861:
2857:
2851:
2846:
2835:
2820:
2815:
2811:
2808:
2802:
2797:
2786:
2782:
2781:
2770:
2767:
2764:
2761:
2758:
2755:
2752:
2749:
2746:
2743:
2740:
2735:
2731:
2727:
2717:
2706:
2703:
2700:
2697:
2694:
2691:
2688:
2685:
2680:
2676:
2672:
2662:
2651:
2648:
2645:
2642:
2639:
2619:
2616:
2613:
2610:
2605:
2601:
2597:
2591:
2588:
2585:
2582:
2579:
2574:
2570:
2566:
2556:
2552:
2551:
2536:
2533:
2530:
2527:
2521:
2512:
2509:
2504:
2503:
2500:
2491:
2488:
2483:
2482:
2479:
2470:
2467:
2462:
2461:
2455:
2452:
2449:
2446:
2443:
2440:
2437:
2434:
2431:
2428:
2427:
2424:
2421:
2418:
2415:
2412:
2409:
2406:
2403:
2400:
2397:
2394:
2391:
2388:
2385:
2384:
2374:
2359:
2350:
2347:
2342:
2341:
2338:
2329:
2326:
2321:
2320:
2314:
2311:
2308:
2305:
2302:
2299:
2296:
2293:
2290:
2287:
2286:
2283:
2280:
2277:
2274:
2271:
2268:
2265:
2262:
2259:
2256:
2253:
2252:
2242:
2227:
2224:
2221:
2218:
2215:
2212:
2209:
2206:
2205:
2202:
2199:
2196:
2193:
2190:
2187:
2184:
2181:
2180:
2170:
2167:
2163:
2162:
2159:
2156:
2153:
2150:
2147:
2144:
2123:
2087:
2083:
2052:
2022:
1996:
1993:
1990:
1987:
1984:
1970:
1967:
1938:
1937:
1926:
1920:
1917:
1914:
1910:
1906:
1903:
1900:
1897:
1891:
1886:
1879:
1874:
1870:
1867:
1864:
1860:
1856:
1853:
1839:
1838:
1824:
1820:
1816:
1813:
1810:
1807:
1801:
1796:
1789:
1784:
1780:
1777:
1774:
1770:
1766:
1763:
1749:
1748:
1737:
1725:
1721:
1710:
1706:
1703:
1689:
1688:
1674:
1669:
1665:
1659:
1654:
1650:
1647:
1644:
1640:
1633:
1628:
1624:
1618:
1613:
1608:
1566:
1560:
1529:
1523:
1498:
1492:
1488:
1485:
1480:
1476:
1455:
1449:
1442:
1439:
1436:
1433:
1430:
1427:
1422:
1419:
1415:
1411:
1400:
1399:
1387:
1383:
1377:
1371:
1366:
1360:
1354:
1291:
1288:
1267:branches. The
1227:
1226:
1224:
1223:
1216:
1209:
1201:
1198:
1197:
1196:
1195:
1186:
1181:
1176:
1171:
1163:
1162:
1156:
1155:
1154:
1153:
1145:
1144:
1140:
1139:
1130:
1127:
1115:selection rule
1107:Main article:
1104:
1101:
1077:
1073:
1069:
1064:
1054:
1049:
1048:
1033:
1018:
1015:
1012:
1009:
1006:
1003:
1000:
996:
995:
993:
988:
981:
974:
969:
966:
963:
960:
957:
954:
951:
947:
946:
923:
921:
918:
915:
912:
909:
906:
902:
901:
899:
897:
894:
891:
888:
885:
882:
879:
875:
874:
861:
859:
856:
853:
850:
847:
844:
841:
837:
836:
834:
832:
828:
823:
820:
814:
811:
805:
802:
796:
793:
784:
777:table, below.
717:
714:
660:orbitals have
639:triple product
570:
567:
565:
562:
559:
558:
555:
552:
545:
538:
533:
529:
528:
527:Raman spectra
525:
520:
516:
515:
508:
503:
499:
498:
495:
490:
486:
485:
482:
476:
456:direct product
440:
437:
434:
431:
428:
425:
422:
419:
416:
413:
410:
383:
377:
373:
368:
362:
357:
353:
309:
301:
297:
292:
286:
281:
277:
234:wave functions
219:
215:
192:
188:
176:
175:
164:
160:
156:
149:
145:
140:
134:
129:
125:
121:
118:
113:
110:
107:
103:
79:
76:
29:selection rule
15:
13:
10:
9:
6:
4:
3:
2:
5009:
4998:
4995:
4993:
4990:
4988:
4985:
4984:
4982:
4973:
4970:
4968:
4965:
4964:
4960:
4953:
4951:0-521-08482-2
4947:
4943:
4938:
4933:
4931:0-521-24633-4
4927:
4923:
4918:
4914:
4910:
4906:
4902:
4898:
4894:
4889:
4888:
4884:
4882:
4879:
4873:
4868:
4867:
4857:
4855:0-19-855152-5
4851:
4847:
4838:
4830:
4828:0-521-09209-4
4824:
4820:
4819:
4811:
4808:
4803:
4801:0-19-855688-8
4797:
4793:
4789:
4782:
4779:
4773:
4770:
4764:
4762:0-471-49028-8
4758:
4754:
4747:
4744:
4738:
4735:
4729:
4726:
4721:
4719:0-486-49540-X
4715:
4711:
4704:
4701:
4698:
4692:
4689:
4686:
4680:
4677:
4671:
4668:
4662:
4660:0-471-12996-8
4656:
4652:
4645:
4642:
4639:Cotton p. 327
4636:
4633:
4627:
4624:
4618:
4615:
4609:
4606:
4600:
4597:
4591:
4588:
4584:
4580:
4576:
4572:
4568:
4562:
4559:
4554:
4552:0-521-08139-4
4548:
4544:
4540:
4533:
4531:
4529:
4525:
4519:
4516:
4510:
4506:
4503:
4501:
4498:
4496:
4493:
4492:
4488:
4486:
4483:
4482:dipole moment
4479:
4475:
4471:
4467:
4459:
4457:
4443:
4437:
4434:
4431:
4428:
4425:
4399:
4396:
4393:
4390:
4387:
4361:
4350:
4331:
4308:
4302:
4299:
4296:
4293:
4290:
4279:
4251:
4248:
4245:
4242:
4239:
4229:
4226:
4219:
4216:
4213:
4210:
4207:
4204:
4201:
4173:
4170:
4167:
4164:
4153:
4132:
4129:
4126:
4123:
4120:
4117:
4114:
4104:
4101:
4098:
4095:
4092:
4089:
4086:
4083:
4076:
4073:
4070:
4067:
4064:
4061:
4058:
4030:
4027:
4024:
4021:
4010:
3989:
3986:
3983:
3980:
3977:
3967:
3964:
3961:
3958:
3955:
3952:
3924:
3921:
3918:
3915:
3904:
3883:
3880:
3877:
3874:
3871:
3861:
3858:
3855:
3852:
3849:
3842:
3839:
3836:
3833:
3830:
3827:
3824:
3796:
3793:
3790:
3787:
3776:
3761:
3758:
3755:
3752:
3749:
3746:
3743:
3740:
3737:
3713:
3710:
3707:
3704:
3690:
3687:
3686:
3664:
3661:
3658:
3652:
3649:
3646:
3643:
3640:
3637:
3634:
3631:
3628:
3625:
3615:
3612:
3609:
3606:
3603:
3600:
3597:
3594:
3591:
3588:
3585:
3582:
3554:
3551:
3548:
3516:
3513:
3510:
3507:
3504:
3501:
3498:
3488:
3485:
3482:
3479:
3476:
3473:
3470:
3467:
3464:
3436:
3433:
3430:
3404:
3401:
3398:
3374:
3371:
3368:
3357:
3336:
3333:
3330:
3327:
3324:
3314:
3311:
3308:
3305:
3302:
3299:
3271:
3268:
3265:
3254:
3251:
3250:
3235:
3232:
3229:
3226:
3223:
3220:
3207:
3193:
3190:
3187:
3184:
3181:
3178:
3175:
3162:
3148:
3145:
3142:
3139:
3126:
3112:
3109:
3106:
3103:
3100:
3097:
3084:
3070:
3067:
3064:
3040:
3037:
3034:
3021:
3007:
3004:
3001:
2998:
2985:
2982:
2978:
2954:
2950:
2939:
2931:
2908:
2904:
2901:
2890:
2859:
2855:
2844:
2813:
2809:
2806:
2795:
2787:
2784:
2783:
2768:
2765:
2762:
2759:
2756:
2753:
2750:
2747:
2744:
2741:
2738:
2733:
2729:
2704:
2701:
2698:
2695:
2692:
2689:
2686:
2683:
2678:
2674:
2646:
2643:
2640:
2617:
2614:
2611:
2608:
2603:
2599:
2589:
2586:
2583:
2580:
2577:
2572:
2568:
2554:
2553:
2531:
2528:
2525:
2519:
2510:
2507:
2498:
2489:
2486:
2477:
2468:
2465:
2453:
2450:
2447:
2444:
2441:
2438:
2435:
2432:
2422:
2419:
2416:
2413:
2410:
2407:
2404:
2401:
2398:
2395:
2392:
2389:
2348:
2345:
2336:
2327:
2324:
2312:
2309:
2306:
2303:
2300:
2297:
2294:
2291:
2281:
2278:
2275:
2272:
2269:
2266:
2263:
2260:
2257:
2222:
2219:
2216:
2213:
2210:
2200:
2197:
2194:
2191:
2188:
2185:
2168:
2164:
2160:
2157:
2154:
2151:
2148:
2145:
2141:
2138:
2121:
2111:. The symbol
2110:
2106:
2085:
2081:
2069:
2050:
2039:
2020:
1994:
1991:
1988:
1985:
1982:
1969:Summary table
1968:
1966:
1964:
1958:
1956:
1952:
1948:
1947:
1941:
1924:
1918:
1915:
1912:
1904:
1901:
1895:
1884:
1872:
1868:
1862:
1851:
1844:
1843:
1842:
1822:
1814:
1811:
1805:
1794:
1782:
1778:
1772:
1761:
1754:
1753:
1752:
1735:
1723:
1719:
1708:
1704:
1701:
1694:
1693:
1692:
1667:
1663:
1652:
1648:
1645:
1642:
1626:
1622:
1611:
1598:
1597:
1596:
1496:
1486:
1483:
1478:
1474:
1453:
1437:
1434:
1431:
1425:
1420:
1381:
1364:
1343:
1342:
1341:
1338:
1336:
1332:
1321:
1319:
1315:
1303:
1297:
1289:
1287:
1284:
1280:
1278:
1274:
1273:Symmetric top
1270:
1266:
1262:
1258:
1253:
1251:
1246:
1238:
1233:
1222:
1217:
1215:
1210:
1208:
1203:
1202:
1200:
1199:
1194:
1190:
1187:
1185:
1182:
1180:
1177:
1175:
1172:
1170:
1167:
1166:
1165:
1164:
1161:
1157:
1152:
1149:
1148:
1147:
1146:
1141:
1138:
1134:
1128:
1126:
1124:
1120:
1116:
1110:
1102:
1100:
1096:
1094:
1093:anharmonicity
1090:
1086:
1081:
1067:
1060:
1046:
1042:
1038:
1034:
1031:
1027:
1023:
1019:
1016:
1013:
1010:
1007:
1004:
998:
997:
994:
991:
984:
977:
970:
967:
964:
961:
958:
955:
949:
948:
944:
940:
936:
932:
928:
924:
922:
919:
916:
913:
910:
907:
904:
903:
900:
898:
895:
892:
889:
886:
883:
877:
876:
873:
869:
865:
862:
860:
857:
854:
851:
848:
845:
839:
838:
835:
833:
831:
824:
819:
815:
810:
806:
801:
797:
794:
792:
791:
787:
778:
776:
772:
768:
764:
760:
756:
751:
749:
745:
741:
737:
733:
727:
723:
715:
713:
710:
706:
702:
698:
694:
690:
685:
683:
679:
675:
671:
667:
663:
659:
655:
651:
647:
643:
640:
636:
632:
628:
624:
620:
616:
612:
608:
604:
600:
596:
592:
588:
584:
580:
576:
568:
563:
556:
534:
531:
530:
526:
521:
518:
517:
509:
504:
501:
500:
496:
491:
488:
487:
483:
481:transforms as
477:
474:
473:
467:
465:
461:
457:
435:
432:
426:
423:
420:
414:
408:
397:
381:
375:
371:
366:
360:
355:
351:
342:
337:
335:
331:
327:
323:
307:
299:
295:
290:
284:
279:
275:
266:
262:
257:
255:
251:
247:
243:
235:
217:
213:
190:
186:
162:
158:
147:
143:
138:
132:
127:
123:
119:
116:
111:
108:
105:
101:
93:
92:
91:
89:
85:
77:
75:
72:
70:
66:
62:
58:
54:
53:atomic nuclei
50:
46:
42:
38:
37:quantum state
34:
30:
26:
22:
4992:Spectroscopy
4941:
4921:
4899:(1): 53–70.
4896:
4892:
4865:
4845:
4842:
4817:
4810:
4787:
4781:
4772:
4752:
4746:
4737:
4728:
4709:
4703:
4691:
4679:
4670:
4650:
4644:
4635:
4626:
4617:
4608:
4599:
4590:
4582:
4578:
4574:
4570:
4566:
4561:
4538:
4518:
4469:
4463:
4275:
2980:LS coupling
1972:
1959:
1954:
1950:
1944:
1942:
1939:
1840:
1750:
1690:
1401:
1339:
1322:
1299:
1281:
1276:
1268:
1264:
1260:
1254:
1242:
1189:NMR coupling
1122:
1121:= ±1, where
1118:
1112:
1097:
1082:
1062:
1052:
1044:
1040:
1036:
1029:
1025:
1021:
986:
979:
972:
942:
938:
934:
930:
926:
871:
867:
863:
826:
817:
808:
799:
788:point group
782:
766:
762:
758:
752:
743:
739:
736:ground state
729:
708:
704:
686:
681:
677:
673:
669:
665:
661:
657:
653:
652:, which has
649:
645:
641:
634:
630:
626:
622:
614:
610:
606:
602:
598:
594:
590:
586:
575:Laporte rule
572:
340:
338:
329:
325:
264:
258:
249:
177:
87:
81:
73:
32:
28:
18:
1963:LS coupling
1109:Rigid rotor
1059:tetrahedral
748:point group
510:Constraint
322:point group
4981:Categories
4839:References
1509:and where
1318:quadrupole
1302:multipoles
1294:See also:
1250:rovibronic
1193:J-coupling
246:propagator
4755:. Wiley.
4653:. Wiley.
4227:±
4214:±
4199:Δ
4171:±
4162:Δ
4102:±
4093:±
4084:±
4071:±
4056:Δ
4028:±
4019:Δ
3965:±
3950:Δ
3922:±
3913:Δ
3859:±
3850:±
3837:±
3822:Δ
3794:±
3785:Δ
3759:±
3750:±
3735:Δ
3711:±
3702:Δ
3613:±
3604:±
3595:±
3580:Δ
3546:Δ
3486:±
3477:±
3462:Δ
3428:Δ
3396:Δ
3366:Δ
3312:±
3297:Δ
3263:Δ
3233:±
3218:Δ
3191:±
3182:±
3173:Δ
3146:±
3137:Δ
3110:±
3095:Δ
3062:Δ
3032:Δ
3005:±
2996:Δ
2955:π
2940:π
2909:π
2905:−
2891:π
2860:π
2845:π
2814:π
2810:−
2796:π
2766:±
2757:±
2748:±
2726:Δ
2702:±
2693:±
2671:Δ
2638:Δ
2587:±
2565:Δ
2420:±
2411:±
2402:±
2387:Δ
2279:±
2270:±
2255:Δ
2198:±
2183:Δ
1913:λ
1902:−
1885:π
1873:π
1863:λ
1852:π
1823:λ
1812:−
1795:π
1783:π
1773:λ
1762:π
1720:−
1702:μ
1649:≤
1646:λ
1643:≤
1623:−
1491:ℏ
1487:μ
1475:λ
1448:ℏ
1432:λ
1426:λ
1418:‖
1414:λ
1410:‖
1386:λ
1316:, E2 for
1089:overtones
1072:+ E + 2T
775:character
680:also has
512:x + y + z
433:−
424:−
372:ψ
367:μ
361:∗
352:ψ
334:forbidden
296:ψ
291:μ
285:∗
276:ψ
254:forbidden
214:ψ
187:ψ
159:τ
144:ψ
139:μ
133:∗
124:ψ
120:∫
65:reactants
45:molecules
25:chemistry
4577:(German
4571:ungerade
4569:(German
4489:See also
4478:adsorbed
4474:molecule
4249:↮
4124:↮
3987:↮
3881:↮
3662:↮
3635:↮
3508:↮
3334:↮
2615:↮
2529:↮
2478:↮
2436:↮
2337:↮
2301:↮
2220:↮
2122:↮
1061:and has
629:, odd).
627:ungerade
585:such as
564:Examples
484:Context
460:parities
261:symmetry
232:are the
78:Overview
69:products
4901:Bibcode
4460:Surface
4347:is the
2103:is the
2066:is the
2036:is the
1083:In the
765:and/or
761:and/or
493:x, y, z
458:of the
398:, i.e.
263:of the
240:is the
90:
21:physics
4948:
4928:
4874:
4852:
4825:
4798:
4759:
4716:
4657:
4579:gerade
4549:
4468:, the
4441:
4423:
4403:
4385:
4365:
4359:
4335:
4329:
4321:where
4306:
4288:
3656:
2593:
2523:
2457:
2316:
2125:
2119:
2091:
2078:
2070:, and
2054:
2048:
2024:
2018:
1998:
1980:
1951:cannot
1571:
1554:
1534:
1517:
1494:
1451:
1402:where
1314:dipole
693:parity
676:×
672:×
666:gerade
648:×
644:×
442:
406:
305:
178:where
4511:Notes
609:, or
51:, in
49:atoms
47:, in
31:, or
4946:ISBN
4926:ISBN
4872:ISBN
4850:ISBN
4823:ISBN
4796:ISBN
4757:ISBN
4714:ISBN
4655:ISBN
4547:ISBN
4351:and
3691:(6)
3252:(5)
2983:(4)
2785:(3)
2555:(2)
2169:(1)
1691:and
1587:and
1546:and
1263:and
1113:The
724:and
689:spin
573:The
514:= 0
250:zero
205:and
27:, a
23:and
4909:doi
4476:is
4464:In
4276:In
4154:If
4011:If
3905:If
3777:If
3694:If
3538:If
3420:If
3358:If
3255:If
2630:if
2040:,
1239:gas
1237:HCl
1191:or
968:-1
925:(2
753:In
396:odd
336:".
326:not
256:".
82:In
67:to
19:In
4983::
4907:.
4895:.
4794:.
4545:.
4541:.
4527:^
1965:.
1047:)
1045:yz
1043:,
1041:xz
1039:,
1037:xy
1028:,
1024:,
1017:1
1014:-1
1011:-1
985:,
978:,
962:-1
945:)
941:-
933:-
929:-
911:-1
905:E
896:-1
893:-1
870:+
866:+
825:6
816:6
807:3
798:8
703:,
615:f,
601:,
593:,
548:,
541:,
343:,
330:is
71:.
4954:.
4934:.
4915:.
4911::
4903::
4897:1
4880:.
4858:.
4831:.
4804:.
4765:.
4722:.
4663:.
4583:u
4575:g
4567:u
4555:.
4444:,
4438:S
4435:+
4432:L
4429:=
4426:J
4400:J
4397:+
4394:I
4391:=
4388:F
4362:J
4332:I
4309:,
4303:J
4300:+
4297:I
4294:=
4291:F
4255:)
4252:0
4246:0
4243:=
4240:L
4237:(
4230:2
4220:,
4217:1
4211:,
4208:0
4205:=
4202:L
4174:1
4168:=
4165:S
4136:)
4133:1
4130:,
4127:0
4121:0
4118:=
4115:L
4112:(
4105:4
4099:,
4096:3
4090:,
4087:2
4077:,
4074:1
4068:,
4065:0
4062:=
4059:L
4031:1
4025:=
4022:S
3993:)
3990:0
3984:0
3981:=
3978:L
3975:(
3968:1
3962:,
3959:0
3956:=
3953:L
3925:1
3919:=
3916:S
3887:)
3884:0
3878:0
3875:=
3872:L
3869:(
3862:3
3856:,
3853:2
3843:,
3840:1
3834:,
3831:0
3828:=
3825:L
3797:1
3791:=
3788:S
3762:2
3756:,
3753:1
3747:,
3744:0
3741:=
3738:L
3714:1
3708:=
3705:S
3668:)
3665:1
3659:1
3653:;
3650:2
3647:,
3644:1
3641:,
3638:0
3632:0
3629:=
3626:L
3623:(
3616:3
3610:,
3607:2
3601:,
3598:1
3592:,
3589:0
3586:=
3583:L
3555:0
3552:=
3549:S
3520:)
3517:1
3514:,
3511:0
3505:0
3502:=
3499:L
3496:(
3489:2
3483:,
3480:1
3474:,
3471:0
3468:=
3465:L
3437:0
3434:=
3431:S
3405:0
3402:=
3399:L
3375:0
3372:=
3369:S
3340:)
3337:0
3331:0
3328:=
3325:L
3322:(
3315:1
3309:,
3306:0
3303:=
3300:L
3272:0
3269:=
3266:S
3236:2
3230:,
3227:0
3224:=
3221:L
3194:3
3188:,
3185:1
3179:=
3176:L
3149:1
3143:=
3140:L
3113:2
3107:,
3104:0
3101:=
3098:L
3071:0
3068:=
3065:n
3053:,
3041:0
3038:=
3035:L
3008:1
3002:=
2999:L
2960:i
2951:=
2945:f
2914:i
2902:=
2896:f
2865:i
2856:=
2850:f
2819:i
2807:=
2801:f
2769:3
2763:,
2760:2
2754:,
2751:1
2745:,
2742:0
2739:=
2734:J
2730:M
2705:2
2699:,
2696:1
2690:,
2687:0
2684:=
2679:J
2675:M
2650:)
2647:0
2644:=
2641:J
2618:0
2612:0
2609:=
2604:J
2600:M
2596:(
2590:1
2584:,
2581:0
2578:=
2573:J
2569:M
2535:)
2532:1
2526:1
2520:;
2511:2
2508:3
2499:,
2490:2
2487:1
2469:2
2466:1
2454:;
2451:2
2448:,
2445:1
2442:,
2439:0
2433:0
2430:(
2423:3
2417:,
2414:2
2408:,
2405:1
2399:,
2396:0
2393:=
2390:J
2358:)
2349:2
2346:1
2328:2
2325:1
2313:;
2310:1
2307:,
2304:0
2298:0
2295:=
2292:J
2289:(
2282:2
2276:,
2273:1
2267:,
2264:0
2261:=
2258:J
2226:)
2223:0
2217:0
2214:=
2211:J
2208:(
2201:1
2195:,
2192:0
2189:=
2186:J
2086:J
2082:M
2051:S
2021:L
1995:S
1992:+
1989:L
1986:=
1983:J
1925:.
1919:1
1916:+
1909:)
1905:1
1899:(
1896:=
1890:f
1878:i
1869:=
1866:)
1859:M
1855:(
1819:)
1815:1
1809:(
1806:=
1800:f
1788:i
1779:=
1776:)
1769:E
1765:(
1736:.
1729:f
1724:M
1714:i
1709:M
1705:=
1673:f
1668:J
1664:+
1658:i
1653:J
1639:|
1632:f
1627:J
1617:i
1612:J
1607:|
1593:z
1591:(
1589:μ
1585:λ
1565:f
1559:J
1528:i
1522:J
1497:;
1484:=
1479:z
1454:,
1441:)
1438:1
1435:+
1429:(
1421:=
1382:+
1376:f
1370:J
1365:=
1359:i
1353:J
1330:J
1325:λ
1310:λ
1306:λ
1304:E
1277:Q
1269:Q
1265:R
1261:P
1220:e
1213:t
1206:v
1123:J
1119:J
1078:2
1074:2
1070:1
1065:d
1063:T
1055:4
1035:(
1032:)
1030:z
1026:y
1022:x
1020:(
1008:0
1005:3
1001:2
999:T
992:)
989:z
987:R
982:y
980:R
975:x
973:R
971:(
965:1
959:0
956:3
952:1
950:T
943:y
939:x
937:,
935:y
931:x
927:z
920:0
917:0
914:2
908:2
890:1
887:1
884:1
880:2
878:A
872:z
868:y
864:x
858:1
855:1
852:1
849:1
846:1
842:1
840:A
829:d
827:σ
821:4
818:S
812:2
809:C
803:3
800:C
795:E
785:d
783:T
767:z
763:y
759:x
744:v
740:v
738:(
709:d
707:-
705:d
682:u
678:g
674:u
670:g
662:g
658:d
654:u
650:u
646:u
642:u
635:u
631:p
623:u
613:-
611:f
607:d
605:-
603:d
599:p
597:-
595:p
591:s
589:-
587:s
553:z
550:R
546:y
543:R
539:x
536:R
479:μ
439:)
436:x
430:(
427:y
421:=
418:)
415:x
412:(
409:y
382:,
376:2
356:1
308:.
300:2
280:1
238:μ
218:2
191:1
163:,
155:d
148:2
128:1
117:=
112:2
109:,
106:1
102:m
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.