Rotational spectroscopy

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into three states, J = K + 1, K, and K - 1, each J state of this so-called p-type triplet arising from a different orientation of the spin with respect to the rotational motion of the molecule. The energy difference between successive J terms in any of these triplets is about 2 cm (60 GHz), with the single exception of J = 1←0 difference which is about 4 cm. Selection rules for magnetic dipole transitions allow transitions between successive members of the triplet (ΔJ = ±1) so that for each value of the rotational angular momentum quantum number K there are two allowed transitions. The O nucleus has zero nuclear spin angular momentum, so that symmetry considerations demand that K have only odd values.

5906:

frequency in less than a microsecond and (ii) the use of a high speed (>40 GS/s) oscilloscope to digitise and Fourier transform the molecular free induction decay. The result is an instrument that allows the study of weakly bound molecules but which is able to exploit a measurement bandwidth (12 GHz) that is greatly enhanced compared with the Balle-Flygare FTMW spectrometer. Modified versions of the original CP-FTMW spectrometer have been constructed by a number of groups in the United States, Canada and Europe. The instrument offers a broadband capability that is highly complementary to the high sensitivity and resolution offered by the Balle-Flygare design.

2105:, between the vibrational motion of the nuclei in the rotating (non-inertial) frame. However, as long as the vibrational quantum number does not change (i.e., the molecule is in only one state of vibration), the effect of vibration on rotation is not important, because the time for vibration is much shorter than the time required for rotation. The Coriolis coupling is often negligible, too, if one is interested in low vibrational and rotational quantum numbers only. 3436: 7996: 5402: 20: 8008: 5863:. First, a short (typically 0-3 microsecond duration) microwave pulse is introduced on resonance with a rotational transition. Those molecules that absorb the energy from this pulse are induced to rotate coherently in phase with the incident radiation. De-activation of the polarisation pulse is followed by microwave emission that accompanies decoherence of the molecular ensemble. This 5782:, fundamental physical constraints exist on the operational bandwidth of instrument components. It is often impractical and costly to switch to measurements within an entirely different frequency region. The instruments and operating principals described below are generally appropriate to microwave spectroscopy experiments conducted at frequencies between 6 and 24 GHz. 1989: 2629:θ and φ which describe the direction of the molecular axis, and the quantum state is determined by two quantum numbers J and M. J defines the magnitude of the rotational angular momentum, and M its component about an axis fixed in space, such as an external electric or magnetic field. In the absence of external fields, the energy depends only on J. Under the 5091: 5102: 3286: 5888:

enhancement in the sensitivity and resolution of spectrometers along with a reduction in the complexity of observed spectra; (ii) it became possible to isolate and study molecules that are very weakly bound because there is insufficient energy available for them to undergo fragmentation or chemical reaction at such low temperatures.

4181: 2610: 1484:), which have both a zero dipole moment and isotropic polarizability, would not have a pure rotation spectrum but for the effect of centrifugal distortion; when the molecule rotates about a 3-fold symmetry axis a small dipole moment is created, allowing a weak rotation spectrum to be observed by microwave spectroscopy. 5450:

The water molecule is an important example of an asymmetric top. It has an intense pure rotation spectrum in the far infrared region, below about 200 cm. For this reason far infrared spectrometers have to be freed of atmospheric water vapour either by purging with a dry gas or by evacuation. The

6036:

Such transitions are called electric dipole-allowed transitions. Other transitions involving quadrupoles, octupoles, hexadecapoles etc. may also be allowed but the spectral intensity is very much smaller, so these transitions are difficult to observe. Magnetic-dipole-allowed transitions can occur in

5905:

at the University of Virginia designed a spectrometer which retains many advantages of the Balle-Flygare FT-MW spectrometer while innovating in (i) the use of a high speed (>4 GS/s) arbitrary waveform generator to generate a "chirped" microwave polarisation pulse that sweeps up to 12 GHz in

5892:

was a pioneer in using this instrument for the exploration of weakly bound interactions. While the Fabry-Perot cavity of a Balle-Flygare FTMW spectrometer can typically be tuned into resonance at any frequency between 6 and 18 GHz, the bandwidth of individual measurements is restricted to about

5745:

which includes all molecules except for spherical tops. This means that rotational transitions of molecules with no permanent dipole moment, which cannot be observed in absorption or emission, can be observed, by scattering, in Raman spectroscopy. Very high resolution Raman spectra can be obtained

2584:

Spherical top molecules have no net dipole moment. A pure rotational spectrum cannot be observed by absorption or emission spectroscopy because there is no permanent dipole moment whose rotation can be accelerated by the electric field of an incident photon. Also the polarizability is isotropic, so

481:

can be deduced. When this is not possible, as with most asymmetric tops, all that can be done is to fit the spectra to three moments of inertia calculated from an assumed molecular structure. By varying the molecular structure the fit can be improved, giving a qualitative estimate of the structure.

4472:

with two unpaired electrons so that there are magnetic-dipole allowed transitions which can be observed by microwave spectroscopy. The unit electron spin has three spatial orientations with respect to the given molecular rotational angular momentum vector, K, so that each rotational level is split

114:

For rotational spectroscopy, molecules are classified according to symmetry into spherical tops, linear molecules, and symmetric tops; analytical expressions can be derived for the rotational energy terms of these molecules. Analytical expressions can be derived for the fourth category, asymmetric

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The great majority of contemporary spectrometers use a mixture of commercially available and bespoke components which users integrate according to their particular needs. Instruments can be broadly categorised according to their general operating principles. Although rotational transitions can be

3455:

The probability of a transition taking place is the most important factor influencing the intensity of an observed rotational line. This probability is proportional to the population of the initial state involved in the transition. The population of a rotational state depends on two factors. The

173:

Rotational spectroscopy has primarily been used to investigate fundamental aspects of molecular physics. It is a uniquely precise tool for the determination of molecular structure in gas-phase molecules. It can be used to establish barriers to internal rotation such as that associated with the

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in the throat of an expanding gas jet. This was a revolutionary development because (i) cooling molecules to low temperatures concentrates the available population in the lowest rotational energy levels. Coupled with benefits conferred by the use of a Fabry-Perot cavity, this brought a great

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can serve as an absorption cell. An important variation of the technique in which an alternating current is applied across electrodes within the absorption cell results in a modulation of the frequencies of rotational transitions. This is referred to as Stark modulation and allows the use of

1555:

and anti-Stokes lines can be observed and they have similar intensities due to the fact that many rotational states are thermally populated. The selection rule for linear molecules is ΔJ = 0, ±2. The reason for the values ±2 is that the polarizability returns to the same value twice during a

6026:

For a symmetric top, the values of the 2 moments of inertia can be used to derive 2 molecular parameters. Values from each additional isotopologue provide the information for one more molecular parameter. For asymmetric tops a single isotopologue provides information for at most 3 molecular

1792: 4686: 5397:{\displaystyle {\tilde {\nu }}_{J^{\prime }\leftrightarrow J^{\prime \prime },K}=F\left(J^{\prime },K\right)-F\left(J^{\prime \prime },K\right)=2\left(B-2D_{JK}K^{2}\right)\left(J^{\prime \prime }+1\right)-4D_{J}\left(J^{\prime \prime }+1\right)^{3}\qquad J^{\prime \prime }=0,1,2,...} 4882: 3099: 320:. Rotation about each unique axis is associated with a set of quantized energy levels dependent on the moment of inertia about that axis and a quantum number. Thus, for linear molecules the energy levels are described by a single moment of inertia and a single quantum number, 5438:

refers to the total angular momentum, as before. Since there are three independent moments of inertia, there are two other independent quantum numbers to consider, but the term values for an asymmetric rotor cannot be derived in closed form. They are obtained by individual

2326: 5656:

components. The extent of splitting depends on the square of the electric field strength and the square of the dipole moment of the molecule. In principle this provides a means to determine the value of the molecular dipole moment with high precision. Examples include

4000: 4440:

is the harmonic vibration frequency, follows. If anharmonicity is to be taken into account, terms in higher powers of J should be added to the expressions for the energy levels and line positions. A striking example concerns the rotational spectrum of

731:(and, hence, of transitions in the rotational spectrum) for a molecule is determined by its symmetry. A convenient way to look at the molecules is to divide them into four different classes, based on the symmetry of their structure. These are 3966: 367:. Analysis of spectroscopic data with the expressions detailed below results in quantitative determination of the value(s) of the moment(s) of inertia. From these precise values of the molecular structure and dimensions may be obtained. 3609: 2072: 4509:

of the molecule. In the absence of an external electrical field, the rotational energy of a symmetric top is a function of only J and K and, in the rigid rotor approximation, the energy of each rotational state is given by

1984:{\displaystyle {\tilde {\nu }}/{\text{cm}}^{-1}={\frac {1}{\lambda /{\text{cm}}}}={\frac {\nu /{\text{s}}^{-1}}{c/\left({\text{cm}}\cdot \mathrm {s} ^{-1}\right)}}={\frac {\nu /{\text{s}}^{-1}}{2.99792458\times 10^{10}}}.} 6083:

This value of J corresponds to the maximum of the population considered as a continuous function of J. However, since only integer values of J are allowed, the maximum line intensity is observed for a neighboring integer

2431:

are the rotational quantum numbers of the upper and lower levels. In reality, this expression has to be modified for the effects of anharmonicity of the vibrations, for centrifugal distortion and for Coriolis coupling.

234:). When fine or hyperfine structure can be observed, the technique also provides information on the electronic structures of molecules. Much of current understanding of the nature of weak molecular interactions such as 3723: 2913: 5086:{\displaystyle {\tilde {\nu }}_{J^{\prime }\leftrightarrow J^{\prime \prime },K}=F\left(J^{\prime },K\right)-F\left(J^{\prime \prime },K\right)=2B\left(J^{\prime \prime }+1\right)\qquad J^{\prime \prime }=0,1,2,...} 4516: 398:

in the vibrational ground state, to which the rotational states refer, whereas the equilibrium bond length is at the minimum in the potential energy curve. The relation between the rotational constants is given by

2756:

is the rotational constant of the molecule and is related to the moment of inertia of the molecule. In a linear molecule the moment of inertia about an axis perpendicular to the molecular axis is unique, that is,

2731: 3281:{\displaystyle {\tilde {\nu }}_{J^{\prime }\leftrightarrow J^{\prime \prime }}=F\left(J^{\prime }\right)-F\left(J^{\prime \prime }\right)=2B\left(J^{\prime \prime }+1\right)\qquad J^{\prime \prime }=0,1,2,...} 6484:

Jennings, D.A.; Evenson, K.M; Zink, L.R.; Demuynck, C.; Destombes, J.L.; Lemoine, B; Johns, J.W.C. (April 1987). "High-resolution spectroscopy of HF from 40 to 1100 cm: Highly accurate rotational constants".

3091: 465: 3793: 4406: 3417: 1551:

that can be represented as an ellipsoid. The polarizability ellipsoid of spherical top molecules is in fact spherical so those molecules show no rotational Raman spectrum. For all other molecules both

5867:

occurs on a timescale of 1-100 microseconds depending on instrument settings. Following pioneering work by Dicke and co-workers in the 1950s, the first FTMW spectrometer was constructed by Ekkers and

4292: 2090:) decrease. Consequently, the rotation frequencies in each vibration state are different from each other. This can give rise to "satellite" lines in the rotational spectrum. An example is provided by 3003: 2625:

connected by rigid bonds. A linear molecule lies on a single axis and each atom moves on the surface of a sphere around the centre of mass. The two degrees of rotational freedom correspond to the

7160:

Grubbs, G.S.; Dewberry, C.T.; Etchison, K.C.; Kerr, K.E.; Cooke, S.A. (2007). "A search accelerated correct intensity Fourier transform microwave spectrometer with pulsed laser ablation source".

3830:, when it is calculated using the expression for the rigid rotor. To account for this a centrifugal distortion correction term is added to the rotational energy levels of the diatomic molecule. 343:

For nonlinear molecules which are symmetric rotors (or symmetric tops - see next section), there are two moments of inertia and the energy also depends on a second rotational quantum number,

5623: 4176:{\displaystyle {\tilde {\nu }}_{J^{\prime }\leftrightarrow J^{\prime \prime }}=2B\left(J^{\prime \prime }+1\right)-4D\left(J^{\prime \prime }+1\right)^{3}\qquad J^{\prime \prime }=0,1,2,...} 4867: 4805: 4747: 7125:

Brown, G.G.; Dian, B.C.; Douglass, K.O.; Geyer, S.M.; Pate, B.H. (2006). "The rotational spectrum of epifluorohydrin measured by chirped-pulse Fourier transform microwave spectroscopy".

1703: 6070:

In Raman spectroscopy the photon energies for Stokes and anti-Stokes scattering are respectively less than and greater than the incident photon energy. See the energy-level diagram at

2188: 678: 2525: 2479: 470:

where v is a vibrational quantum number and α is a vibration-rotation interaction constant which can be calculated if the B values for two different vibrational states can be found.

2086:, so low-frequency vibrational states are appreciably populated even at room temperatures. As the moment of inertia is higher when a vibration is excited, the rotational constants ( 1765: 5790:

A microwave spectrometer can be most simply constructed using a source of microwave radiation, an absorption cell into which sample gas can be introduced and a detector such as a

1251: 1191: 944: 2814: 4438: 3319: 791: 6015: 2571:

Rotational constants obtained from infrared measurements are in good accord with those obtained by microwave spectroscopy, while the latter usually offers greater precision.

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methods offering improved sensitivity. Absorption spectroscopy allows the study of samples that are thermodynamically stable at room temperature. The first study of the

3346: 1127: 1087: 5562:. Thus, observation of nuclear quadrupole splitting permits the magnitude of the nuclear quadrupole moment to be determined. This is an alternative method to the use of 2554: 5839:

was able to prepare a review of the results contained in approximately 100 research papers. Commercial versions of microwave absorption spectrometer were developed by

3372: 2127:, so the energy of rotation is added to the energy of vibration. For example, the rotational energy levels for linear molecules (in the rigid-rotor approximation) are 2429: 2379: 5769:. It shows the effect of nuclear spin, resulting in intensities variation of 3:1 in adjacent lines. A bond length of 109.9985 ± 0.0010 pm was deduced from the data. 3836: 971: 609: 582: 555: 1723: 3484: 7827: 5969: 5949: 5879:

Balle, Campbell, Keenan and Flygare demonstrated that the FTMW technique can be applied within a "free space cell" comprising an evacuated chamber containing a

4343: 4323: 4211: 3989: 3828: 2754: 718: 698: 528: 361: 338: 2000: 6203:"Quality assessment of ground-based microwave measurements of chlorine monoxide, ozone, and nitrogen dioxide from the NDSC radiometer at the Plateau de Bure" 2199: 5471:

moment. In that case, coupling of nuclear spin angular momentum with rotational angular momentum causes splitting of the rotational energy levels. If the

146:

from which very precise values of molecular bond lengths and angles can be derived in favorable cases. In the presence of an electrostatic field there is

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Balle, T.J.; Campbell, E.J.; Keenan, M.R.; Flygare, W.H. (1980). "A new method for observing the rotational spectra of weak molecular complexes: KrHCl".

4186:

In consequence, the spacing between lines is not constant, as in the rigid rotor approximation, but decreases with increasing rotational quantum number.

7500: 5922:

The spectrum was measured over a couple of hours with the aid of a chirped-pulse Fourier transform microwave spectrometer at the University of Bristol.

6799:

Burkhalter, James H.; Roy S. Anderson; William V. Smith; Walter Gordy (1950). "The Fine Structure of the Microwave Absorption Spectrum of Oxygen".

292:. Current projects in astrochemistry involve both laboratory microwave spectroscopy and observations made using modern radiotelescopes such as the 5096:

which is the same as in the case of a linear molecule. With a first order correction for centrifugal distortion the transition wavenumbers become

5794:. A spectrum can be obtained by sweeping the frequency of the source while detecting the intensity of transmitted radiation. A simple section of 4681:{\displaystyle F\left(J,K\right)=BJ\left(J+1\right)+\left(A-B\right)K^{2}\qquad J=0,1,2,\ldots \quad {\mbox{and}}\quad K=+J,\ldots ,0,\ldots ,-J} 6393:

Alexander, A. J.; Kroto, H. W.; Walton, D. R. M. (1967). "The microwave spectrum, substitution structure and dipole moment of cyanobutadiyne".

5893:

1 MHz. An animation illustrates the operation of this instrument which is currently the most widely used tool for microwave spectroscopy.

3653: 2822: 7718: 6119:

Nair, K.P.R.; Demaison, J.; Wlodarczak, G.; Merke, I. (236). "Millimeterwave rotational spectrum and internal rotation in o-chlorotoluene".

2123:, which was used before microwave spectroscopy had become practical. To a first approximation, the rotation and vibration can be treated as 7651: 7596: 7565: 2643: 2119:

Historically, the theory of rotational energy levels was developed to account for observations of vibration-rotation spectra of gases in

2585:

that pure rotational transitions cannot be observed by Raman spectroscopy either. Nevertheless, rotational constants can be obtained by

7560: 107:

where changes in rotational energy occur together with changes in vibrational energy, and also from ro-vibronic spectroscopy (or just

7933: 7751: 7613: 5668:. However, because the splitting depends on μ, the orientation of the dipole must be deduced from quantum mechanical considerations. 382:

this process is straightforward. For linear molecules with more than two atoms it is necessary to measure the spectra of two or more

95:

spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by

119:

need to be determined using numerical methods. The rotational energies are derived theoretically by considering the molecules to be

7882: 7701: 3035: 2593:

is a spherical top but the asymmetric C-H stretching band shows rotational fine structure in the infrared spectrum, illustrated in

2527:

so that a quantum of rotational energy is lost while a quantum of vibrational energy is gained. The purely vibrational transition,

405: 7822: 7624: 7545: 7525: 6724:

Simmons, James W.; Anderson, Wallace E.; Gordy, Walter (1950). "Microwave Spectrum and Molecular Constants of Hydrogen Cyanide".

5901:

Noting that digitisers and related electronics technology had significantly progressed since the inception of FTMW spectroscopy,

5747: 3734: 2124: 2114: 4350: 3377: 3374:=1 selection rule. The dashed lines show how these transitions map onto features that can be observed experimentally. Adjacent 7768: 7746: 7493: 4219: 1662:, written as cm, which is literally the number of waves in one centimeter, or the reciprocal of the wavelength in centimeters ( 1617:

series. Since Raman transitions involve two photons, it is possible for the molecular angular momentum to change by two units.

2924: 7834: 7756: 7406: 7378: 6869:

Cleeton, C.E.; Williams, N.H. (1934). "Electromagnetic waves of 1.1 cm wave-length and the absorption spectrum of ammonia".

7691: 7636: 7586: 84: 7203:

Wilcox, D.S.; Hotopp, K.M.; Dian, B.C. (2011). "Two-Dimensional Chirped-Pulse Fourier Transform Microwave Spectroscopy".

2594: 2586: 139: 104: 2621:

is a good starting point from which to construct a model of a rotating molecule. It is assumed that component atoms are

1448:. A consequence of this rule is that no microwave spectrum can be observed for centrosymmetric linear molecules such as 394:). A bond length obtained in this way is slightly different from the equilibrium bond length. This is because there is 7918: 7670: 7486: 7357: 7314: 7289: 5843:

in the 1970s and were once widely used for fundamental research. Most research laboratories now exploit either Balle-

5572: 794: 7923: 7741: 4814: 4752: 4694: 1504: 3810:

pulls the atoms apart. As a result, the moment of inertia of the molecule increases, thus decreasing the value of

8044: 7938: 7908: 7839: 7773: 1393:

The three moments of inertia have different values. Examples of small molecules that are asymmetric tops include

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axis. Since the unique moment of inertia is larger than the other two, the molecule is an oblate symmetric top.

7867: 7658: 7555: 7446: 7425: 7335: 7270: 5883:. This technique allows a sample to be probed only milliseconds after it undergoes rapid cooling to only a few 5426: 2133: 630: 371: 293: 316:

of the molecule. Free rotation is not possible for molecules in liquid or solid phases due to the presence of

8012: 7665: 7570: 6553: 5440: 495: 5517:) in HCN, all levels with J > 0 are split into 3. The energies of the sub-levels are proportional to the 7799: 7646: 7535: 5563: 1735: 45: 1424:

whose symmetry axis of highest order is a 2-fold rotation axis. Most large molecules are asymmetric tops.

1203: 1143: 896: 482:

Isotopic substitution is invaluable when using this approach to the determination of molecular structure.

7955: 7794: 7763: 7696: 2760: 1507:

implies that the molecular angular momentum can change by at most one unit. Moreover, the quantum number

157:

An important application of rotational spectroscopy is in exploration of the chemical composition of the

5819:) was performed by Cleeton & Williams in 1934. Subsequent experiments exploited powerful sources of 4414: 3294: 1625:

The units used for rotational constants depend on the type of measurement. With infrared spectra in the

1539:

photon is emitted. The general selection rule for such a transition to be allowed is that the molecular

1253:. The spectra look rather different, and are instantly recognizable. Examples of symmetric tops include 374:

and the moment of inertia of the molecule, and, knowing the atomic masses, can be used to determine the

55:

is concerned with the measurement of the energies of transitions between quantized rotational states of

7945: 7887: 7736: 7608: 3032:

dictate that during emission or absorption the rotational quantum number has to change by unity; i.e.,

743: 6373: 6371: 7971: 7950: 7591: 5974: 2589:. This occurs when a molecule is polar in the vibrationally excited state. For example, the molecule 1632: 1503:. Since these transitions are due to absorption (or emission) of a single photon with a spin of one, 7713: 3798:

The diagram at the right shows an intensity pattern roughly corresponding to the spectrum above it.

6368: 5791: 5779: 4485:

is associated with the total angular momentum of the molecule. For a given value of J, there is a 2

3636: 1133:. As a matter of convenience, spectroscopists divide molecules into two classes of symmetric tops, 7468: 5931:

This article uses the molecular spectroscopist's convention of expressing the rotational constant

7844: 7392: 5835:. The number of experiments in microwave spectroscopy surged immediately after the war. By 1948, 5447:

value. Formulae are available for molecules whose shape approximates to that of a symmetric top.

3324: 1487:

With symmetric tops, the selection rule for electric-dipole-allowed pure rotation transitions is

1092: 1052: 2530: 1130: 721: 7631: 7262: 6154:

Cheung, A.C.; Rank, D.M.; Townes, C.H.; Thornton, D.D. & Welch, W.J. (1968). "Detection of

5855:

The theoretical framework underpinning FTMW spectroscopy is analogous to that used to describe

5472: 5414:

has the effect of removing degeneracy present in the rigid rotor approximation, with different

4190: 3961:{\displaystyle F\left(J\right)=BJ\left(J+1\right)-DJ^{2}\left(J+1\right)^{2}\qquad J=0,1,2,...} 3475: 2083: 1445: 387: 151: 68: 3354: 2488: 2442: 8034: 8000: 7872: 7603: 7517: 6939: 2626: 2120: 874: 627:

of the system. The general convention, used in this article, is to define the axes such that

473:

For other molecules, if the spectra can be resolved and individual transitions assigned both

289: 108: 7254: 3604:{\displaystyle {\frac {N_{J}}{N_{0}}}=e^{-{\frac {E_{J}}{kT}}}=e^{-{\frac {BhcJ(J+1)}{kT}}}} 7212: 7169: 7134: 7070: 7035: 7000: 6965: 6913: 6878: 6808: 6733: 6696: 6665: 6581: 6536: 6494: 6402: 6214: 6175: 6128: 5864: 3628: 1547:, which means that it is not the same in all directions. Polarizability is a 3-dimensional 949: 810: 587: 560: 533: 317: 142:. Fitting the spectra to the theoretical expressions gives numerical values of the angular 72: 24: 5430:

Pure rotation spectrum of atmospheric water vapour measured at Mauna Kea (33 cm to 100 cm)

1708: 8: 7928: 7641: 7550: 7388: 5507: 5460: 2384: 2334: 1557: 1300: 858: 281: 255: 254:. Microwave transitions are measured in the laboratory and matched to emissions from the 251: 235: 158: 132: 80: 7216: 7173: 7138: 7074: 7039: 7004: 6977: 6969: 6917: 6882: 6812: 6737: 6700: 6669: 6656:

Hall, Richard T.; Dowling, Jerome M. (1967). "Pure Rotational Spectrum of Water Vapor".

6585: 6540: 6498: 6406: 6218: 6179: 6132: 2409: 2359: 2067:{\displaystyle {\tilde {\nu }}/{\text{cm}}^{-1}\approx {\frac {\nu /{\text{GHz}}}{30}}.} 7976: 7913: 7892: 7708: 7686: 7619: 7530: 7112:"Web page of B.H. Pate Research Group, Department of Chemistry, University of Virginia" 6071: 5954: 5934: 5735: 4506: 4328: 4308: 4196: 3974: 3813: 3620: 2739: 2560:

branch of the spectrum. Because of the thermal population of the rotational states the

2381:

are rotational constants for the upper and lower vibrational state respectively, while

1659: 1556:

rotation. The value ΔJ = 0 does not correspond to a molecular transition but rather to

1528: 703: 683: 513: 478: 364: 346: 323: 96: 2321:{\displaystyle {\tilde {\nu }}={\tilde {\nu }}_{\text{vib}}+B''J''(J''+1)-B'J'(J'+1),} 8039: 7877: 7804: 7778: 7442: 7421: 7402: 7374: 7353: 7331: 7310: 7285: 7266: 7255: 7228: 7185: 7026:

Ekkers, J.; Flygare, W.H. (1976). "Pulsed microwave Fourier transform spectrometer".

6798: 6506: 6414: 6242: 5889: 5868: 5844: 5800: 5518: 4442: 3807: 1783: 507: 499: 491: 395: 285: 143: 124: 76: 7097: 1444:

Transitions between rotational states can be observed in molecules with a permanent

111:) where rotational, vibrational and electronic energy changes occur simultaneously. 7220: 7177: 7142: 7078: 7043: 7008: 6973: 6921: 6886: 6816: 6741: 6704: 6673: 6589: 6544: 6502: 6410: 6222: 6183: 6136: 5856: 5708: 5688: 5658: 4189:

An assumption underlying these expressions is that the molecular vibration follows

3435: 2098: 2091: 1410: 1394: 1026: 1022: 1010: 700:

corresponding to the smallest moment of inertia. Some authors, however, define the

503: 370:

For a linear molecule, analysis of the rotational spectrum provides values for the

7436: 7396: 7368: 7325: 7304: 7300: 7253:; de Paula, J. (2006). "Molecular Spectroscopy: Section: Pure rotation spectra". 6856: 5860: 5840: 3423:

in the observed spectrum. Frequency or wavenumber units can also be used for the

3029: 2598: 2481:

so that there is simultaneous excitation of both vibration and rotation. For the

2102: 1434: 1337: 1256: 1135: 1006: 259: 250:, the technique has a key role in exploration of the chemical composition of the 247: 162: 6566: 6187: 7473: 6991:

Dicke, R.H.; Romer, R.H. (1955). "Pulse Techniques in Microwave Spectroscopy".

6227: 6202: 5880: 5742: 5704: 5634: 4302: 2622: 1540: 1014: 624: 313: 246:

bonds has been established through rotational spectroscopy. In connection with

136: 128: 7146: 6925: 6140: 2609: 363:, which defines the vector component of rotational angular momentum along the 44:, of the final and initial states, and is extensively split by the effects of 8028: 5676: 3093:. Thus, the locations of the lines in a rotational spectrum will be given by 2193:

In this approximation, the vibration-rotation wavenumbers of transitions are

1321: 239: 209: 7159: 7060: 6548: 2613:

Energy levels and line positions calculated in the rigid rotor approximation

1049:

A symmetric top is a molecule in which two moments of inertia are the same,

7509: 7250: 7232: 7189: 6890: 6820: 6777:, p. 102 gives the equations for diatomic molecules and symmetric tops 6166:

molecules in the interstellar medium by their microwave emission spectra".

6058: 6038: 5836: 5832: 5684: 5672: 5664: 5646: 4469: 728: 383: 243: 147: 116: 92: 6956:

Schwendemann, R.H. (1978). "Transient Effects in Microwave Spectroscopy".

6745: 6483: 6153: 1729:. The relationship between these two units is derived from the expression 7345: 7111: 6511: 5902: 5739: 5680: 3718:{\displaystyle {\text{population}}\propto (2J+1)e^{-{\frac {E_{J}}{kT}}}} 2908:{\displaystyle B={h \over {8\pi ^{2}cI_{B}}}={h \over {8\pi ^{2}cI_{C}}}} 2630: 2618: 1552: 1544: 530:, of the molecule. For any molecule, there are three moments of inertia: 474: 391: 375: 120: 7124: 6723: 5645:

degeneracy of each rotational state is partly removed, an instance of a

5468: 2597:. This spectrum is also interesting because it shows clear evidence of 1775: 1626: 1461: 309: 277: 7224: 7181: 7047: 7012: 6709: 6684: 6677: 6593: 6118: 7082: 6522: 6392: 5820: 5804: 5795: 5738:. Rotational transitions are Raman-allowed for any molecule with an 5566:

spectroscopy. The selection rule for rotational transitions becomes

1994:

As 1 GHz = 10 Hz, the numerical conversion can be expressed as

1771: 1726: 1030: 305: 88: 60: 2726:{\displaystyle F\left(J\right)=BJ\left(J+1\right)\qquad J=0,1,2,...} 1705:). On the other hand, for microwave spectra in the frequency scale ( 506:

can take only certain fixed values, which are related simply to the

6042: 5847:

or chirped-pulse Fourier transform microwave (FTMW) spectrometers.

5824: 5712: 5649:. For example, in linear molecules each energy level is split into 1129:. By definition a symmetric top must have a 3-fold or higher order 990: 379: 56: 5850: 340:, which defines the magnitude of the rotational angular momentum. 40:. Each rotational transition is labeled with the quantum numbers, 7474:

A list of microwave spectroscopy research groups around the world

2590: 1481: 1316: 1285: 1261: 1195: 826: 264: 19: 6314:, p. 104 shows part of the observed rotational spectrum of 3994:

Therefore, the line positions for the rotational mode change to

7478: 7463: 6315: 5884: 5859:. The behaviour of the evolving system is described by optical 1548: 1465: 1033:

and dihaloethynes. These molecules belong to the point groups C

974: 842: 5679:. Most species which can be observed in the gaseous state are 973:

can be taken to be zero. Examples of linear molecules include

6106:

Microwave Molecular Spectra in Technique of Organic Chemistry

5828: 3351:

The diagram illustrates rotational transitions that obey the

3086:{\displaystyle \Delta J=J^{\prime }-J^{\prime \prime }=\pm 1} 873:

and other hexahalides. The molecules all belong to the cubic

7202: 6621:, p. 102 shows the effect on the microwave spectrum of 6523:

Strandberg, M. W. P.; Meng, C. Y.; Ingersoll, J. G. (1949).

3456:

number of molecules in an excited state with quantum number

2108: 893:

For a linear molecule the moments of inertia are related by

460:{\displaystyle B_{v}=B-\alpha \left(v+{\frac {1}{2}}\right)} 6200: 5675:

molecule is placed in a magnetic field, an instance of the

3788:{\displaystyle J={\sqrt {\frac {kT}{2hcB}}}-{\frac {1}{2}}} 3460:, relative to the number of molecules in the ground state, 4401:{\displaystyle D={\frac {4B^{3}}{{\tilde {\omega }}^{2}}}} 3412:{\displaystyle J^{\prime \prime }{\leftarrow }J^{\prime }} 7418:

Rotational Structure in the Spectra of Diatomic Molecules

5734:

Molecular rotational transitions can also be observed by

4287:{\displaystyle D={\frac {h^{3}}{32\pi ^{4}I^{2}r^{2}kc}}} 4193:. In the harmonic approximation the centrifugal constant 2082:

The population of vibrationally excited states follows a

5785: 2998:{\displaystyle I={\frac {m_{1}m_{2}}{m_{1}+m_{2}}}d^{2}} 1560:

in which the incident photon merely changes direction.

1354:

As a detailed example, ammonia has a moment of inertia

6682: 6655: 5359: 5328: 5282: 5205: 5141: 5048: 5023: 4985: 4921: 4632: 4138: 4107: 4068: 4039: 3389: 3306: 3243: 3218: 3187: 3138: 3069: 1468:), which are non-polar. Tetrahedral molecules such as 1387: 740:

All three moments of inertia are equal to each other:

99:. Rotational spectroscopy is sometimes referred to as 6868: 5977: 5957: 5937: 5575: 5105: 4885: 4817: 4755: 4697: 4519: 4456:

The electric dipole moment of the dioxygen molecule,

4417: 4353: 4331: 4311: 4222: 4199: 4003: 3977: 3839: 3816: 3737: 3656: 3487: 3380: 3357: 3327: 3297: 3102: 3038: 2927: 2825: 2763: 2742: 2646: 2533: 2491: 2445: 2412: 2387: 2362: 2337: 2202: 2136: 2003: 1795: 1738: 1711: 1668: 1635: 1439: 1206: 1146: 1095: 1055: 952: 899: 746: 706: 686: 633: 590: 563: 536: 516: 485: 408: 349: 326: 3451:

is the quantum number of the lower rotational state.

3348:

denotes the upper level involved in the transition.

1043: 734: 312:

axes of fixed orientation in space, centered on the

16:

Spectroscopy of quantized rotational states of gases

7025: 7261:(8th ed.). Oxford University Press. pp. 6685:"Erratum: Pure Rotational Spectrum of Water Vapor" 6009: 5963: 5943: 5896: 5874: 5671:A similar removal of degeneracy will occur when a 5617: 5396: 5085: 4861: 4799: 4741: 4680: 4432: 4400: 4337: 4317: 4286: 4205: 4175: 3983: 3960: 3822: 3787: 3717: 3603: 3411: 3366: 3340: 3313: 3280: 3085: 2997: 2907: 2808: 2748: 2725: 2574: 2548: 2519: 2473: 2423: 2398: 2373: 2348: 2320: 2182: 2077: 2066: 1983: 1759: 1717: 1697: 1650: 1563:The selection rule for symmetric top molecules is 1245: 1185: 1121: 1081: 965: 938: 785: 712: 692: 672: 603: 576: 549: 522: 459: 355: 332: 1511:is limited to have values between and including + 115:top, for rotational levels up to J=3, but higher 8026: 6990: 5729: 5683:. Exceptions are odd-electron molecules such as 308:is free to rotate relative to a set of mutually 7298: 6574:Journal of Physical and Chemical Reference Data 5851:Fourier transform microwave (FTMW) spectroscopy 5618:{\displaystyle \Delta J=\pm 1,\Delta F=0,\pm 1} 103:rotational spectroscopy to distinguish it from 7387: 7249: 6456: 6362: 6326: 6287: 6262: 3430: 1531:the molecules undergo transitions in which an 7494: 7280:Banwell, Colin N.; McCash, Elaine M. (1994). 7279: 6683:Hall, Richard T.; Dowling, Jerome M. (1971). 6525:"The Microwave Absorption Spectrum of Oxygen" 6471: 6444: 6432: 6377: 6338: 6274: 4862:{\displaystyle A={h \over {8\pi ^{2}cI_{C}}}} 4800:{\displaystyle A={h \over {8\pi ^{2}cI_{A}}}} 4742:{\displaystyle B={h \over {8\pi ^{2}cI_{B}}}} 4489:+1- fold degeneracy with the quantum number, 123:and then applying extra terms to account for 7566:Vibrational spectroscopy of linear molecules 7306:Rotational spectroscopy of diatomic molecule 6955: 6904:Gordy, W. (1948). "Microwave spectroscopy". 6201:Ricaud, P.; Baron, P; de La Noë, J. (2004). 1364:about the 3-fold rotation axis, and moments 386:, such as OCS and OCS. This allows a set of 294:Atacama Large Millimeter/submillimeter Array 7469:Hyperphysics article on Rotational Spectrum 7098:"Balle-Flygare FTMW spectrometer animation" 6836:, p. 113, illustrates the spectrum of 5711:. The Zeeman effect has been observed with 5628: 3639:of the rotational state, which is equal to 7561:Nuclear resonance vibrational spectroscopy 7501: 7487: 7438:Rotational spectra and molecular structure 6855:obtained using 476.5 nm radiation from an 5772: 2637:(J), of the molecule can be expressed as, 1698:{\displaystyle {\tilde {\nu }}=1/\lambda } 7934:Inelastic electron tunneling spectroscopy 7614:Resonance-enhanced multiphoton ionization 7366: 6708: 6226: 5506:levels result. The effect is one type of 4876:This gives the transition wavenumbers as 3801: 3728:The maximum relative intensity occurs at 2601:in the asymmetric structure of the band. 2564:branch is slightly less intense than the 2183:{\displaystyle E_{\text{rot}}=hcBJ(J+1).} 2109:Effect of rotation on vibrational spectra 673:{\displaystyle I_{A}\leq I_{B}\leq I_{C}} 7702:Extended X-ray absorption fine structure 6564: 6467: 6465: 6104:Gordy, W. (1970). A. Weissberger (ed.). 5778:found across a very broad region of the 5425: 3991:is the centrifugal distortion constant. 3434: 2608: 18: 7434: 6862: 6108:. Vol. IX. New York: Interscience. 5748:Fourier Transform Infrared Spectrometer 5454: 1200:(rugby football, or cigar shaped) with 8027: 7415: 7323: 7282:Fundamentals of Molecular Spectroscopy 6833: 6786: 6774: 6643: 6618: 6606: 6420: 6350: 6311: 6299: 5478:of a rotational level is greater than 5451:spectrum has been analyzed in detail. 4505:is associated with rotation about the 4481:For symmetric rotors a quantum number 7482: 7344: 6903: 6758: 6462: 6103: 5786:Absorption cells and Stark modulation 5633:In the presence of a static external 3647:increases. Combining the two factors 2633:model, the rotational energy levels, 1760:{\displaystyle \nu \cdot \lambda =c,} 1381:about any axis perpendicular to the C 793:. Examples of spherical tops include 611:about three mutually orthogonal axes 8007: 6940:"June 1971, Hewlett-Packard Journal" 3635:increases. The second factor is the 1246:{\displaystyle I_{A}<I_{B}=I_{C}} 1186:{\displaystyle I_{A}=I_{B}<I_{C}} 939:{\displaystyle I_{A}\ll I_{B}=I_{C}} 6978:10.1146/annurev.pc.29.100178.002541 5827:, many of which were developed for 2809:{\displaystyle I_{B}=I_{C},I_{A}=0} 2604: 2115:Rotational–vibrational spectroscopy 1389:Asymmetric tops (asymmetric rotors) 887: 494:the free rotation of a molecule is 105:rotational-vibrational spectroscopy 23:Part of the rotational spectrum of 13: 6567:"The Spectrum of Molecular Oxygen" 5594: 5576: 5356: 5325: 5279: 5202: 5170: 5138: 5125: 5045: 5020: 4982: 4950: 4918: 4905: 4433:{\displaystyle {\tilde {\omega }}} 4135: 4104: 4065: 4036: 4023: 3439:Rotational level populations with 3404: 3386: 3358: 3333: 3314:{\displaystyle J^{\prime \prime }} 3303: 3240: 3215: 3184: 3160: 3135: 3122: 3066: 3053: 3039: 2534: 1907: 1440:Microwave and far-infrared spectra 1428: 486:Classification of molecular rotors 14: 8056: 7919:Deep-level transient spectroscopy 7671:Saturated absorption spectroscopy 7457: 7095: 6487:Journal of Molecular Spectroscopy 6121:Journal of Molecular Spectroscopy 5421: 1605:series, whereas transitions with 1045:Symmetric tops (symmetric rotors) 786:{\displaystyle I_{A}=I_{B}=I_{C}} 736:Spherical tops (spherical rotors) 280:molecule to be identified in the 8006: 7995: 7994: 7924:Dual-polarization interferometry 7508: 6761:Basic Principles of Spectroscopy 5750:. An example is the spectrum of 4476: 4445:which was fitted to terms up to 3022:are the masses of the atoms and 2579: 1522: 1505:conservation of angular momentum 390:to be set up and solved for the 7939:Scanning tunneling spectroscopy 7914:Circular dichroism spectroscopy 7909:Acoustic resonance spectroscopy 7350:Molecular Rotation Spectroscopy 7242: 7196: 7153: 7118: 7104: 7089: 7054: 7019: 6984: 6949: 6932: 6897: 6827: 6792: 6780: 6768: 6752: 6717: 6649: 6637: 6612: 6600: 6558: 6516: 6477: 6450: 6438: 6426: 6386: 6356: 6344: 6332: 6320: 6305: 6293: 6280: 6268: 6077: 6064: 6030: 6010:{\displaystyle {\bar {B}}=B/hc} 5971:in this article corresponds to 5897:Chirped-Pulse FTMW spectrometer 5875:Balle–Flygare FTMW spectrometer 5350: 5039: 4638: 4630: 4602: 4129: 3924: 3234: 2689: 2575:Structure of rotational spectra 2078:Effect of vibration on rotation 1651:{\displaystyle {\tilde {\nu }}} 1601:= +1 are said to belong to the 1535:photon is absorbed and another 168: 7868:Fourier-transform spectroscopy 7556:Vibrational circular dichroism 7464:infrared gas spectra simulator 7309:. Cambridge University Press. 6286:Moment of inertia values from 6256: 6235: 6194: 6147: 6112: 6097: 6020: 5984: 5925: 5916: 5130: 5113: 4910: 4893: 4424: 4384: 4028: 4011: 3680: 3665: 3585: 3573: 3419:transitions are separated by 2 3395: 3127: 3110: 3026:is the distance between them. 2312: 2295: 2273: 2256: 2225: 2209: 2174: 2162: 2010: 1802: 1675: 1642: 1: 7666:Cavity ring-down spectroscopy 7571:Thermal infrared spectroscopy 7367:McQuarrie, Donald A. (2008). 7284:(4th ed.). McGraw-Hill. 6382:Pure Rotational Raman Spectra 6091: 5730:Rotational Raman spectroscopy 4468:is zero, but the molecule is 3806:When a molecule rotates, the 1140:(saucer or disc shaped) with 79:molecules can be measured in 7800:Inelastic neutron scattering 7373:. University Science Books. 6507:10.1016/0022-2852(87)90021-X 6415:10.1016/0022-2852(76)90347-7 6243:"Astrochemistry in Virginia" 5564:nuclear quadrupole resonance 5490:levels are produced; but if 5467:, greater than 1/2 it has a 4501:. The third quantum number, 3321:denotes the lower level and 7: 7861:Data collection, processing 7737:Photoelectron/photoemission 6188:10.1103/PhysRevLett.21.1701 6017:in the Rigid rotor article. 4305:. The relationship between 3643:. This factor increases as 3631:. This factor decreases as 3431:Rotational line intensities 3341:{\displaystyle J^{\prime }} 2587:ro–vibrational spectroscopy 1725:), the unit is usually the 1658:), the unit is usually the 1122:{\displaystyle I_{B}=I_{C}} 1082:{\displaystyle I_{A}=I_{B}} 299: 46:nuclear quadrupole coupling 10: 8061: 7946:Photoacoustic spectroscopy 7888:Time-resolved spectroscopy 7435:Wollrab, James E. (1967). 6565:Krupenie, Paul H. (1972). 6457:Atkins & de Paula 2006 6363:Atkins & de Paula 2006 6327:Atkins & de Paula 2006 6288:Atkins & de Paula 2006 6263:Atkins & de Paula 2006 6228:10.5194/angeo-22-1903-2004 4811:symmetric top molecule or 2549:{\displaystyle \Delta J=0} 2112: 1432: 727:The particular pattern of 7990: 7972:Astronomical spectroscopy 7964: 7951:Photothermal spectroscopy 7901: 7860: 7853: 7815: 7787: 7729: 7679: 7579: 7516: 7147:10.1016/j.jms.2006.05.003 6926:10.1103/RevModPhys.20.668 6906:Reviews of Modern Physics 6472:Banwell & McCash 1994 6445:Banwell & McCash 1994 6433:Banwell & McCash 1994 6378:Banwell & McCash 1994 6339:Banwell & McCash 1994 6275:Banwell & McCash 1994 6141:10.1016/j.jms.2006.03.011 5801:phase-sensitive detection 5519:nuclear quadrupole moment 4451: 1031:acetylene (ethyne (HC≡CH) 5909: 5807:spectrum of a molecule ( 5792:superheterodyne receiver 5780:electromagnetic spectrum 5629:Stark and Zeeman effects 3367:{\displaystyle \Delta J} 2918:For a diatomic molecule 2520:{\displaystyle J'=J''-1} 2474:{\displaystyle J'=J''+1} 2439:branch of the spectrum, 1620: 825:and other tetrahalides, 7956:Pump–probe spectroscopy 7845:Ferromagnetic resonance 7637:Laser-induced breakdown 7416:Kovács, István (1969). 7330:(3rd ed.). Wiley. 6759:Chang, Raymond (1971). 6549:10.1103/PhysRev.75.1524 6380:, Section 4.2, p. 105, 6168:Physical Review Letters 5773:Instruments and methods 5510:. For example, with N ( 4507:principal rotation axis 623:with the origin at the 365:principal symmetry axis 152:electric dipole moments 150:which allows molecular 53:Rotational spectroscopy 8045:Rigid bodies mechanics 7652:Glow-discharge optical 7632:Raman optical activity 7546:Rotational–vibrational 7398:Microwave Spectroscopy 7324:Hollas, M. J. (1996). 7168:(9): 096106–096106–3. 6891:10.1103/PhysRev.45.234 6821:10.1103/PhysRev.79.651 6011: 5965: 5945: 5663:μ = 0.71521 ± 0.00020 5619: 5441:matrix diagonalization 5431: 5398: 5087: 4863: 4801: 4743: 4682: 4434: 4402: 4339: 4319: 4288: 4207: 4191:simple harmonic motion 4177: 3985: 3962: 3824: 3802:Centrifugal distortion 3789: 3719: 3605: 3476:Boltzmann distribution 3452: 3413: 3368: 3342: 3315: 3282: 3087: 2999: 2909: 2810: 2750: 2727: 2614: 2595:rovibrational coupling 2550: 2521: 2475: 2425: 2400: 2375: 2350: 2322: 2184: 2084:Boltzmann distribution 2068: 1985: 1761: 1719: 1699: 1652: 1446:electric dipole moment 1247: 1187: 1123: 1083: 1027:carbonyl sulfide (OCS) 1023:hydrogen cyanide (HCN) 967: 940: 811:carbon tetrachloride ( 787: 720:axis as the molecular 714: 694: 674: 605: 578: 551: 524: 461: 388:simultaneous equations 357: 334: 186:group relative to the 125:centrifugal distortion 69:power spectral density 49: 7873:Hyperspectral imaging 6958:Annu. Rev. Phys. Chem 6746:10.1103/PhysRev.77.77 6012: 5966: 5946: 5620: 5459:When a nucleus has a 5429: 5399: 5088: 4864: 4802: 4744: 4683: 4435: 4403: 4340: 4320: 4289: 4208: 4178: 3986: 3963: 3825: 3790: 3720: 3606: 3438: 3414: 3369: 3343: 3316: 3283: 3088: 3000: 2910: 2811: 2751: 2728: 2627:spherical coordinates 2612: 2551: 2522: 2476: 2426: 2401: 2376: 2351: 2323: 2185: 2121:infrared spectroscopy 2069: 1986: 1762: 1720: 1700: 1653: 1301:xenon tetrafluoride, 1248: 1188: 1124: 1084: 968: 966:{\displaystyle I_{A}} 946:. For most purposes, 941: 859:sulfur hexafluoride ( 795:phosphorus tetramer ( 788: 715: 695: 675: 606: 604:{\displaystyle I_{C}} 579: 577:{\displaystyle I_{B}} 552: 550:{\displaystyle I_{A}} 525: 462: 358: 335: 318:intermolecular forces 290:atmospheric chemistry 284:. The measurement of 276:was the first stable 109:vibronic spectroscopy 22: 7625:Coherent anti-Stokes 7580:UV–Vis–NIR "Optical" 5975: 5955: 5935: 5865:free induction decay 5573: 5455:Quadrupole splitting 5103: 4883: 4815: 4753: 4695: 4517: 4415: 4351: 4329: 4309: 4220: 4197: 4001: 3975: 3837: 3814: 3735: 3654: 3629:absolute temperature 3485: 3378: 3355: 3325: 3295: 3100: 3036: 2925: 2823: 2761: 2740: 2644: 2556:, gives rise to the 2531: 2489: 2443: 2410: 2385: 2360: 2335: 2200: 2134: 2097:Further, there is a 2001: 1793: 1736: 1718:{\displaystyle \nu } 1709: 1666: 1633: 1204: 1144: 1093: 1053: 1011:hydroxy radical (OH) 1007:carbon monoxide (CO) 950: 897: 744: 704: 684: 631: 588: 561: 534: 514: 406: 347: 324: 73:rotational frequency 25:trifluoroiodomethane 7929:Hadron spectroscopy 7719:Conversion electron 7680:X-ray and Gamma ray 7587:Ultraviolet–visible 7393:Schawlow, Arthur L. 7327:Modern Spectroscopy 7217:2011JPCA..115.8895W 7174:2007RScI...78i6106G 7139:2006JMoSp.238..200B 7075:1980JChPh..72..922B 7040:1976RScI...47..448E 7005:1955RScI...26..915D 6970:1978ARPC...29..537S 6918:1948RvMP...20..668G 6883:1934PhRv...45..234C 6813:1950PhRv...79..651B 6738:1950PhRv...77...77S 6701:1971JChPh..54.4968H 6670:1967JChPh..47.2454H 6586:1972JPCRD...1..423K 6541:1949PhRv...75.1524S 6499:1987JMoSp.122..477J 6407:1976JMoSp..62..175A 6219:2004AnGeo..22.1903R 6180:1968PhRvL..21.1701C 6133:2006JMoSp.237..137N 5857:FT-NMR spectroscopy 5508:hyperfine splitting 5461:spin quantum number 5434:The quantum number 4493:taking the values + 4301:is the vibrational 3427:axis of this plot. 2399:{\displaystyle J''} 2349:{\displaystyle B''} 1786:. It follows that 1558:Rayleigh scattering 372:rotational constant 282:interstellar medium 256:interstellar medium 252:interstellar medium 159:interstellar medium 133:hyperfine structure 91:spectroscopy or by 65:rotational spectrum 48:with the I nucleus. 7977:Force spectroscopy 7902:Measured phenomena 7893:Video spectroscopy 7597:Cold vapour atomic 7441:. Academic Press. 7389:Townes, Charles H. 7257:Physical Chemistry 6072:Raman spectroscopy 6041:molecules such as 6007: 5961: 5941: 5881:Fabry-Perot cavity 5736:Raman spectroscopy 5615: 5521:and a function of 5432: 5394: 5083: 4859: 4797: 4739: 4678: 4636: 4430: 4398: 4335: 4315: 4284: 4213:can be derived as 4203: 4173: 3981: 3958: 3820: 3785: 3715: 3621:Boltzmann constant 3601: 3453: 3409: 3364: 3338: 3311: 3278: 3083: 2995: 2905: 2806: 2746: 2723: 2615: 2546: 2517: 2471: 2435:For the so-called 2424:{\displaystyle J'} 2421: 2396: 2374:{\displaystyle B'} 2371: 2346: 2318: 2180: 2064: 1981: 1757: 1715: 1695: 1660:inverse centimeter 1648: 1597:Transitions with Δ 1411:nitrogen dioxide, 1379:= 2.8059 × 10 kg m 1362:= 4.4128 × 10 kg m 1243: 1183: 1119: 1079: 1015:carbon dioxide (CO 963: 936: 783: 724:of highest order. 710: 690: 670: 601: 574: 547: 520: 457: 380:diatomic molecules 353: 330: 304:A molecule in the 154:to be determined. 144:moments of inertia 97:Raman spectroscopy 50: 8022: 8021: 7986: 7985: 7878:Spectrophotometry 7805:Neutron spin echo 7779:Beta spectroscopy 7692:Energy-dispersive 7408:978-0-486-61798-5 7380:978-1-891389-50-4 7370:Quantum Chemistry 7225:10.1021/jp2043202 7211:(32): 8895–8905. 7182:10.1063/1.2786022 7162:Rev. Sci. Instrum 7127:J. Mol. Spectrosc 7048:10.1063/1.1134647 7028:Rev. Sci. Instrum 7013:10.1063/1.1715156 6993:Rev. Sci. Instrum 6710:10.1063/1.1674785 6678:10.1063/1.1703330 6594:10.1063/1.3253101 6395:J. Mol. Spectrosc 5987: 5964:{\displaystyle B} 5951:in cm. Therefore 5944:{\displaystyle B} 5890:William Klemperer 5116: 4896: 4857: 4795: 4737: 4635: 4443:hydrogen fluoride 4427: 4396: 4387: 4338:{\displaystyle D} 4318:{\displaystyle B} 4282: 4206:{\displaystyle D} 4014: 3984:{\displaystyle D} 3823:{\displaystyle B} 3808:centrifugal force 3783: 3770: 3769: 3711: 3660: 3597: 3543: 3510: 3113: 2983: 2903: 2865: 2749:{\displaystyle B} 2599:Coriolis coupling 2234: 2228: 2212: 2144: 2103:Coriolis coupling 2094:, H−C≡C−C≡C−C≡N. 2059: 2053: 2025: 2013: 1976: 1946: 1926: 1900: 1871: 1851: 1848: 1817: 1805: 1784:velocity of light 1678: 1645: 713:{\displaystyle A} 693:{\displaystyle A} 523:{\displaystyle I} 508:moment of inertia 500:rotational energy 492:quantum mechanics 450: 396:zero-point energy 356:{\displaystyle K} 333:{\displaystyle J} 288:is important for 286:chlorine monoxide 8052: 8010: 8009: 7998: 7997: 7858: 7857: 7769:phenomenological 7518:Vibrational (IR) 7503: 7496: 7489: 7480: 7479: 7452: 7431: 7412: 7384: 7363: 7341: 7320: 7301:Carrington, Alan 7299:Brown, John M.; 7295: 7276: 7260: 7237: 7236: 7205:J. Phys. Chem. A 7200: 7194: 7193: 7157: 7151: 7150: 7122: 7116: 7115: 7108: 7102: 7101: 7093: 7087: 7086: 7083:10.1063/1.439210 7058: 7052: 7051: 7023: 7017: 7016: 6988: 6982: 6981: 6953: 6947: 6946: 6944: 6936: 6930: 6929: 6901: 6895: 6894: 6866: 6860: 6854: 6853: 6852: 6844: 6843: 6831: 6825: 6824: 6796: 6790: 6784: 6778: 6772: 6766: 6764: 6756: 6750: 6749: 6721: 6715: 6714: 6712: 6681: 6653: 6647: 6641: 6635: 6633: 6631: 6630: 6616: 6610: 6604: 6598: 6597: 6571: 6562: 6556: 6552: 6520: 6514: 6510: 6481: 6475: 6469: 6460: 6454: 6448: 6442: 6436: 6430: 6424: 6418: 6390: 6384: 6375: 6366: 6365:, pp. 474–5 6360: 6354: 6348: 6342: 6336: 6330: 6324: 6318: 6309: 6303: 6297: 6291: 6284: 6278: 6272: 6266: 6260: 6254: 6253: 6251: 6249: 6239: 6233: 6232: 6230: 6198: 6192: 6191: 6165: 6164: 6163: 6151: 6145: 6144: 6116: 6110: 6109: 6101: 6085: 6081: 6075: 6068: 6062: 6056: 6055: 6054: 6034: 6028: 6024: 6018: 6016: 6014: 6013: 6008: 6000: 5989: 5988: 5980: 5970: 5968: 5967: 5962: 5950: 5948: 5947: 5942: 5929: 5923: 5920: 5833:Second World War 5818: 5817: 5816: 5768: 5767: 5766: 5758: 5757: 5726: 5725: 5724: 5709:hydroxyl radical 5702: 5701: 5700: 5689:nitrogen dioxide 5667: 5659:carbonyl sulfide 5655: 5644: 5624: 5622: 5621: 5616: 5561: 5542: 5516: 5505: 5489: 5403: 5401: 5400: 5395: 5363: 5362: 5349: 5348: 5343: 5339: 5332: 5331: 5313: 5312: 5297: 5293: 5286: 5285: 5268: 5264: 5263: 5262: 5253: 5252: 5220: 5216: 5209: 5208: 5185: 5181: 5174: 5173: 5153: 5152: 5145: 5144: 5129: 5128: 5118: 5117: 5109: 5092: 5090: 5089: 5084: 5052: 5051: 5038: 5034: 5027: 5026: 5000: 4996: 4989: 4988: 4965: 4961: 4954: 4953: 4933: 4932: 4925: 4924: 4909: 4908: 4898: 4897: 4889: 4868: 4866: 4865: 4860: 4858: 4856: 4855: 4854: 4842: 4841: 4825: 4806: 4804: 4803: 4798: 4796: 4794: 4793: 4792: 4780: 4779: 4763: 4748: 4746: 4745: 4740: 4738: 4736: 4735: 4734: 4722: 4721: 4705: 4687: 4685: 4684: 4679: 4637: 4633: 4601: 4600: 4591: 4587: 4569: 4565: 4541: 4537: 4467: 4466: 4465: 4439: 4437: 4436: 4431: 4429: 4428: 4420: 4407: 4405: 4404: 4399: 4397: 4395: 4394: 4389: 4388: 4380: 4376: 4375: 4374: 4361: 4344: 4342: 4341: 4336: 4324: 4322: 4321: 4316: 4293: 4291: 4290: 4285: 4283: 4281: 4274: 4273: 4264: 4263: 4254: 4253: 4240: 4239: 4230: 4212: 4210: 4209: 4204: 4182: 4180: 4179: 4174: 4142: 4141: 4128: 4127: 4122: 4118: 4111: 4110: 4083: 4079: 4072: 4071: 4045: 4044: 4043: 4042: 4027: 4026: 4016: 4015: 4007: 3990: 3988: 3987: 3982: 3967: 3965: 3964: 3959: 3923: 3922: 3917: 3913: 3897: 3896: 3881: 3877: 3853: 3829: 3827: 3826: 3821: 3794: 3792: 3791: 3786: 3784: 3776: 3771: 3768: 3754: 3746: 3745: 3724: 3722: 3721: 3716: 3714: 3713: 3712: 3710: 3702: 3701: 3692: 3661: 3658: 3642: 3610: 3608: 3607: 3602: 3600: 3599: 3598: 3596: 3588: 3559: 3546: 3545: 3544: 3542: 3534: 3533: 3524: 3511: 3509: 3508: 3499: 3498: 3489: 3474:is given by the 3418: 3416: 3415: 3410: 3408: 3407: 3398: 3393: 3392: 3373: 3371: 3370: 3365: 3347: 3345: 3344: 3339: 3337: 3336: 3320: 3318: 3317: 3312: 3310: 3309: 3287: 3285: 3284: 3279: 3247: 3246: 3233: 3229: 3222: 3221: 3195: 3191: 3190: 3168: 3164: 3163: 3144: 3143: 3142: 3141: 3126: 3125: 3115: 3114: 3106: 3092: 3090: 3089: 3084: 3073: 3072: 3057: 3056: 3004: 3002: 3001: 2996: 2994: 2993: 2984: 2982: 2981: 2980: 2968: 2967: 2957: 2956: 2955: 2946: 2945: 2935: 2914: 2912: 2911: 2906: 2904: 2902: 2901: 2900: 2888: 2887: 2871: 2866: 2864: 2863: 2862: 2850: 2849: 2833: 2815: 2813: 2812: 2807: 2799: 2798: 2786: 2785: 2773: 2772: 2755: 2753: 2752: 2747: 2732: 2730: 2729: 2724: 2688: 2684: 2660: 2605:Linear molecules 2555: 2553: 2552: 2547: 2526: 2524: 2523: 2518: 2510: 2499: 2480: 2478: 2477: 2472: 2464: 2453: 2430: 2428: 2427: 2422: 2420: 2405: 2403: 2402: 2397: 2395: 2380: 2378: 2377: 2372: 2370: 2355: 2353: 2352: 2347: 2345: 2327: 2325: 2324: 2319: 2305: 2294: 2286: 2266: 2255: 2247: 2236: 2235: 2232: 2230: 2229: 2221: 2214: 2213: 2205: 2189: 2187: 2186: 2181: 2146: 2145: 2142: 2099:fictitious force 2092:cyanodiacetylene 2073: 2071: 2070: 2065: 2060: 2055: 2054: 2051: 2049: 2040: 2035: 2034: 2026: 2023: 2020: 2015: 2014: 2006: 1990: 1988: 1987: 1982: 1977: 1975: 1974: 1973: 1957: 1956: 1955: 1947: 1944: 1941: 1932: 1927: 1925: 1924: 1920: 1919: 1918: 1910: 1901: 1898: 1891: 1882: 1881: 1880: 1872: 1869: 1866: 1857: 1852: 1850: 1849: 1846: 1844: 1832: 1827: 1826: 1818: 1815: 1812: 1807: 1806: 1798: 1766: 1764: 1763: 1758: 1724: 1722: 1721: 1716: 1704: 1702: 1701: 1696: 1691: 1680: 1679: 1671: 1657: 1655: 1654: 1649: 1647: 1646: 1638: 1612: 1502: 1494: 1479: 1478: 1477: 1459: 1458: 1457: 1422: 1421: 1420: 1407: 1405: 1404: 1380: 1363: 1350: 1348: 1347: 1334: 1332: 1331: 1312: 1311: 1310: 1297: 1296: 1295: 1282: 1281: 1280: 1272: 1271: 1252: 1250: 1249: 1244: 1242: 1241: 1229: 1228: 1216: 1215: 1192: 1190: 1189: 1184: 1182: 1181: 1169: 1168: 1156: 1155: 1128: 1126: 1125: 1120: 1118: 1117: 1105: 1104: 1088: 1086: 1085: 1080: 1078: 1077: 1065: 1064: 1002: 1001: 1000: 986: 985: 984: 972: 970: 969: 964: 962: 961: 945: 943: 942: 937: 935: 934: 922: 921: 909: 908: 889:Linear molecules 870: 869: 868: 854: 853: 852: 838: 837: 836: 822: 821: 820: 806: 805: 804: 792: 790: 789: 784: 782: 781: 769: 768: 756: 755: 719: 717: 716: 711: 699: 697: 696: 691: 679: 677: 676: 671: 669: 668: 656: 655: 643: 642: 610: 608: 607: 602: 600: 599: 583: 581: 580: 575: 573: 572: 556: 554: 553: 548: 546: 545: 529: 527: 526: 521: 504:angular momentum 466: 464: 463: 458: 456: 452: 451: 443: 418: 417: 362: 360: 359: 354: 339: 337: 336: 331: 275: 273: 272: 233: 231: 230: 222: 221: 207: 205: 204: 196: 195: 185: 184: 183: 174:rotation of the 163:radio telescopes 39: 37: 36: 8060: 8059: 8055: 8054: 8053: 8051: 8050: 8049: 8025: 8024: 8023: 8018: 7982: 7960: 7897: 7849: 7811: 7783: 7725: 7675: 7575: 7536:Resonance Raman 7512: 7507: 7460: 7455: 7449: 7428: 7420:. Adam Hilger. 7409: 7381: 7360: 7338: 7317: 7292: 7273: 7245: 7240: 7201: 7197: 7158: 7154: 7123: 7119: 7110: 7109: 7105: 7094: 7090: 7059: 7055: 7024: 7020: 6999:(10): 915–928. 6989: 6985: 6954: 6950: 6942: 6938: 6937: 6933: 6902: 6898: 6871:Physical Review 6867: 6863: 6857:argon ion laser 6851: 6848: 6847: 6846: 6842: 6840: 6839: 6838: 6837: 6832: 6828: 6797: 6793: 6785: 6781: 6773: 6769: 6757: 6753: 6722: 6718: 6654: 6650: 6642: 6638: 6629: 6626: 6625: 6624: 6622: 6617: 6613: 6605: 6601: 6569: 6563: 6559: 6521: 6517: 6482: 6478: 6470: 6463: 6455: 6451: 6443: 6439: 6431: 6427: 6419:Illustrated in 6391: 6387: 6376: 6369: 6361: 6357: 6349: 6345: 6337: 6333: 6325: 6321: 6310: 6306: 6298: 6294: 6285: 6281: 6273: 6269: 6261: 6257: 6247: 6245: 6241: 6240: 6236: 6199: 6195: 6162: 6159: 6158: 6157: 6155: 6152: 6148: 6117: 6113: 6102: 6098: 6094: 6089: 6088: 6082: 6078: 6069: 6065: 6053: 6050: 6049: 6048: 6046: 6035: 6031: 6025: 6021: 5996: 5979: 5978: 5976: 5973: 5972: 5956: 5953: 5952: 5936: 5933: 5932: 5930: 5926: 5921: 5917: 5912: 5899: 5877: 5861:Bloch equations 5853: 5841:Hewlett-Packard 5815: 5812: 5811: 5810: 5808: 5788: 5775: 5765: 5762: 5761: 5760: 5756: 5754: 5753: 5752: 5751: 5732: 5723: 5720: 5719: 5718: 5716: 5705:chlorine oxides 5699: 5696: 5695: 5694: 5692: 5662: 5650: 5638: 5631: 5574: 5571: 5570: 5544: 5530: 5511: 5499: 5483: 5473:quantum number 5457: 5424: 5412: 5355: 5351: 5344: 5324: 5320: 5319: 5315: 5314: 5308: 5304: 5278: 5274: 5273: 5269: 5258: 5254: 5245: 5241: 5231: 5227: 5201: 5197: 5196: 5192: 5169: 5165: 5164: 5160: 5137: 5133: 5124: 5120: 5119: 5108: 5107: 5106: 5104: 5101: 5100: 5044: 5040: 5019: 5015: 5014: 5010: 4981: 4977: 4976: 4972: 4949: 4945: 4944: 4940: 4917: 4913: 4904: 4900: 4899: 4888: 4887: 4886: 4884: 4881: 4880: 4850: 4846: 4837: 4833: 4829: 4824: 4816: 4813: 4812: 4788: 4784: 4775: 4771: 4767: 4762: 4754: 4751: 4750: 4730: 4726: 4717: 4713: 4709: 4704: 4696: 4693: 4692: 4631: 4596: 4592: 4577: 4573: 4555: 4551: 4527: 4523: 4518: 4515: 4514: 4479: 4464: 4461: 4460: 4459: 4457: 4454: 4419: 4418: 4416: 4413: 4412: 4390: 4379: 4378: 4377: 4370: 4366: 4362: 4360: 4352: 4349: 4348: 4330: 4327: 4326: 4310: 4307: 4306: 4269: 4265: 4259: 4255: 4249: 4245: 4241: 4235: 4231: 4229: 4221: 4218: 4217: 4198: 4195: 4194: 4134: 4130: 4123: 4103: 4099: 4098: 4094: 4093: 4064: 4060: 4059: 4055: 4035: 4031: 4022: 4018: 4017: 4006: 4005: 4004: 4002: 3999: 3998: 3976: 3973: 3972: 3918: 3903: 3899: 3898: 3892: 3888: 3867: 3863: 3843: 3838: 3835: 3834: 3815: 3812: 3811: 3804: 3775: 3755: 3747: 3744: 3736: 3733: 3732: 3703: 3697: 3693: 3691: 3687: 3683: 3657: 3655: 3652: 3651: 3640: 3589: 3560: 3558: 3554: 3550: 3535: 3529: 3525: 3523: 3519: 3515: 3504: 3500: 3494: 3490: 3488: 3486: 3483: 3482: 3473: 3465: 3433: 3403: 3399: 3394: 3385: 3381: 3379: 3376: 3375: 3356: 3353: 3352: 3332: 3328: 3326: 3323: 3322: 3302: 3298: 3296: 3293: 3292: 3239: 3235: 3214: 3210: 3209: 3205: 3183: 3179: 3175: 3159: 3155: 3151: 3134: 3130: 3121: 3117: 3116: 3105: 3104: 3103: 3101: 3098: 3097: 3065: 3061: 3052: 3048: 3037: 3034: 3033: 3030:Selection rules 3021: 3014: 2989: 2985: 2976: 2972: 2963: 2959: 2958: 2951: 2947: 2941: 2937: 2936: 2934: 2926: 2923: 2922: 2896: 2892: 2883: 2879: 2875: 2870: 2858: 2854: 2845: 2841: 2837: 2832: 2824: 2821: 2820: 2794: 2790: 2781: 2777: 2768: 2764: 2762: 2759: 2758: 2741: 2738: 2737: 2674: 2670: 2650: 2645: 2642: 2641: 2607: 2582: 2577: 2532: 2529: 2528: 2503: 2492: 2490: 2487: 2486: 2457: 2446: 2444: 2441: 2440: 2413: 2411: 2408: 2407: 2388: 2386: 2383: 2382: 2363: 2361: 2358: 2357: 2338: 2336: 2333: 2332: 2298: 2287: 2279: 2259: 2248: 2240: 2231: 2220: 2219: 2218: 2204: 2203: 2201: 2198: 2197: 2141: 2137: 2135: 2132: 2131: 2117: 2111: 2080: 2050: 2045: 2041: 2039: 2027: 2022: 2021: 2016: 2005: 2004: 2002: 1999: 1998: 1969: 1965: 1958: 1948: 1943: 1942: 1937: 1933: 1931: 1911: 1906: 1905: 1897: 1896: 1892: 1887: 1883: 1873: 1868: 1867: 1862: 1858: 1856: 1845: 1840: 1836: 1831: 1819: 1814: 1813: 1808: 1797: 1796: 1794: 1791: 1790: 1737: 1734: 1733: 1710: 1707: 1706: 1687: 1670: 1669: 1667: 1664: 1663: 1637: 1636: 1634: 1631: 1630: 1623: 1606: 1525: 1496: 1488: 1476: 1473: 1472: 1471: 1469: 1456: 1453: 1452: 1451: 1449: 1442: 1437: 1435:selection rules 1431: 1429:Selection rules 1419: 1416: 1415: 1414: 1412: 1403: 1400: 1399: 1398: 1396: 1390: 1384: 1378: 1371: 1365: 1361: 1355: 1346: 1343: 1342: 1341: 1339: 1330: 1327: 1326: 1325: 1323: 1322:Chloromethane, 1309: 1306: 1305: 1304: 1302: 1294: 1291: 1290: 1289: 1287: 1279: 1276: 1275: 1274: 1270: 1267: 1266: 1265: 1263: 1237: 1233: 1224: 1220: 1211: 1207: 1205: 1202: 1201: 1177: 1173: 1164: 1160: 1151: 1147: 1145: 1142: 1141: 1113: 1109: 1100: 1096: 1094: 1091: 1090: 1073: 1069: 1060: 1056: 1054: 1051: 1050: 1046: 1040: 1036: 1018: 999: 996: 995: 994: 992: 983: 980: 979: 978: 976: 957: 953: 951: 948: 947: 930: 926: 917: 913: 904: 900: 898: 895: 894: 890: 884: 880: 867: 864: 863: 862: 860: 851: 848: 847: 846: 844: 835: 832: 831: 830: 828: 819: 816: 815: 814: 812: 803: 800: 799: 798: 796: 777: 773: 764: 760: 751: 747: 745: 742: 741: 737: 705: 702: 701: 685: 682: 681: 664: 660: 651: 647: 638: 634: 632: 629: 628: 595: 591: 589: 586: 585: 568: 564: 562: 559: 558: 541: 537: 535: 532: 531: 515: 512: 511: 488: 442: 435: 431: 413: 409: 407: 404: 403: 348: 345: 344: 325: 322: 321: 302: 271: 268: 267: 266: 263: 260:radio telescope 248:radio astronomy 229: 226: 225: 224: 220: 217: 216: 215: 213: 203: 200: 199: 198: 194: 191: 190: 189: 187: 182: 179: 178: 177: 175: 171: 148:Stark splitting 35: 32: 31: 30: 28: 17: 12: 11: 5: 8058: 8048: 8047: 8042: 8037: 8020: 8019: 8017: 8016: 8004: 7991: 7988: 7987: 7984: 7983: 7981: 7980: 7974: 7968: 7966: 7962: 7961: 7959: 7958: 7953: 7948: 7943: 7942: 7941: 7931: 7926: 7921: 7916: 7911: 7905: 7903: 7899: 7898: 7896: 7895: 7890: 7885: 7880: 7875: 7870: 7864: 7862: 7855: 7851: 7850: 7848: 7847: 7842: 7837: 7832: 7831: 7830: 7819: 7817: 7813: 7812: 7810: 7809: 7808: 7807: 7797: 7791: 7789: 7785: 7784: 7782: 7781: 7776: 7771: 7766: 7761: 7760: 7759: 7754: 7752:Angle-resolved 7749: 7744: 7733: 7731: 7727: 7726: 7724: 7723: 7722: 7721: 7711: 7706: 7705: 7704: 7699: 7694: 7683: 7681: 7677: 7676: 7674: 7673: 7668: 7663: 7662: 7661: 7656: 7655: 7654: 7639: 7634: 7629: 7628: 7627: 7617: 7611: 7606: 7601: 7600: 7599: 7589: 7583: 7581: 7577: 7576: 7574: 7573: 7568: 7563: 7558: 7553: 7548: 7543: 7538: 7533: 7528: 7522: 7520: 7514: 7513: 7506: 7505: 7498: 7491: 7483: 7477: 7476: 7471: 7466: 7459: 7458:External links 7456: 7454: 7453: 7447: 7432: 7426: 7413: 7407: 7385: 7379: 7364: 7358: 7342: 7336: 7321: 7315: 7296: 7290: 7277: 7271: 7246: 7244: 7241: 7239: 7238: 7195: 7152: 7133:(2): 200–212. 7117: 7103: 7088: 7069:(2): 922–932. 7053: 7034:(4): 448–454. 7018: 6983: 6948: 6931: 6912:(4): 668–717. 6896: 6861: 6849: 6841: 6826: 6791: 6779: 6767: 6763:. McGraw-Hill. 6751: 6716: 6664:(7): 2454–61. 6648: 6636: 6627: 6611: 6599: 6580:(2): 423–534. 6557: 6535:(10): 1524–8. 6515: 6493:(2): 477–480. 6476: 6461: 6449: 6437: 6425: 6401:(2): 175–180. 6385: 6367: 6355: 6343: 6331: 6319: 6304: 6292: 6279: 6267: 6255: 6234: 6213:(6): 1903–15. 6193: 6174:(25): 1701–5. 6160: 6146: 6127:(2): 137–142. 6111: 6095: 6093: 6090: 6087: 6086: 6076: 6063: 6051: 6029: 6019: 6006: 6003: 5999: 5995: 5992: 5986: 5983: 5960: 5940: 5924: 5914: 5913: 5911: 5908: 5898: 5895: 5876: 5873: 5852: 5849: 5813: 5787: 5784: 5774: 5771: 5763: 5755: 5746:by adapting a 5743:polarizability 5731: 5728: 5721: 5697: 5635:electric field 5630: 5627: 5626: 5625: 5614: 5611: 5608: 5605: 5602: 5599: 5596: 5593: 5590: 5587: 5584: 5581: 5578: 5456: 5453: 5423: 5422:Asymmetric top 5420: 5410: 5405: 5404: 5393: 5390: 5387: 5384: 5381: 5378: 5375: 5372: 5369: 5366: 5361: 5358: 5354: 5347: 5342: 5338: 5335: 5330: 5327: 5323: 5318: 5311: 5307: 5303: 5300: 5296: 5292: 5289: 5284: 5281: 5277: 5272: 5267: 5261: 5257: 5251: 5248: 5244: 5240: 5237: 5234: 5230: 5226: 5223: 5219: 5215: 5212: 5207: 5204: 5200: 5195: 5191: 5188: 5184: 5180: 5177: 5172: 5168: 5163: 5159: 5156: 5151: 5148: 5143: 5140: 5136: 5132: 5127: 5123: 5115: 5112: 5094: 5093: 5082: 5079: 5076: 5073: 5070: 5067: 5064: 5061: 5058: 5055: 5050: 5047: 5043: 5037: 5033: 5030: 5025: 5022: 5018: 5013: 5009: 5006: 5003: 4999: 4995: 4992: 4987: 4984: 4980: 4975: 4971: 4968: 4964: 4960: 4957: 4952: 4948: 4943: 4939: 4936: 4931: 4928: 4923: 4920: 4916: 4912: 4907: 4903: 4895: 4892: 4853: 4849: 4845: 4840: 4836: 4832: 4828: 4823: 4820: 4791: 4787: 4783: 4778: 4774: 4770: 4766: 4761: 4758: 4733: 4729: 4725: 4720: 4716: 4712: 4708: 4703: 4700: 4689: 4688: 4677: 4674: 4671: 4668: 4665: 4662: 4659: 4656: 4653: 4650: 4647: 4644: 4641: 4629: 4626: 4623: 4620: 4617: 4614: 4611: 4608: 4605: 4599: 4595: 4590: 4586: 4583: 4580: 4576: 4572: 4568: 4564: 4561: 4558: 4554: 4550: 4547: 4544: 4540: 4536: 4533: 4530: 4526: 4522: 4478: 4475: 4462: 4453: 4450: 4426: 4423: 4409: 4408: 4393: 4386: 4383: 4373: 4369: 4365: 4359: 4356: 4334: 4314: 4303:force constant 4295: 4294: 4280: 4277: 4272: 4268: 4262: 4258: 4252: 4248: 4244: 4238: 4234: 4228: 4225: 4202: 4184: 4183: 4172: 4169: 4166: 4163: 4160: 4157: 4154: 4151: 4148: 4145: 4140: 4137: 4133: 4126: 4121: 4117: 4114: 4109: 4106: 4102: 4097: 4092: 4089: 4086: 4082: 4078: 4075: 4070: 4067: 4063: 4058: 4054: 4051: 4048: 4041: 4038: 4034: 4030: 4025: 4021: 4013: 4010: 3980: 3969: 3968: 3957: 3954: 3951: 3948: 3945: 3942: 3939: 3936: 3933: 3930: 3927: 3921: 3916: 3912: 3909: 3906: 3902: 3895: 3891: 3887: 3884: 3880: 3876: 3873: 3870: 3866: 3862: 3859: 3856: 3852: 3849: 3846: 3842: 3819: 3803: 3800: 3796: 3795: 3782: 3779: 3774: 3767: 3764: 3761: 3758: 3753: 3750: 3743: 3740: 3726: 3725: 3709: 3706: 3700: 3696: 3690: 3686: 3682: 3679: 3676: 3673: 3670: 3667: 3664: 3613: 3612: 3595: 3592: 3587: 3584: 3581: 3578: 3575: 3572: 3569: 3566: 3563: 3557: 3553: 3549: 3541: 3538: 3532: 3528: 3522: 3518: 3514: 3507: 3503: 3497: 3493: 3471: 3463: 3432: 3429: 3406: 3402: 3397: 3391: 3388: 3384: 3363: 3360: 3335: 3331: 3308: 3305: 3301: 3289: 3288: 3277: 3274: 3271: 3268: 3265: 3262: 3259: 3256: 3253: 3250: 3245: 3242: 3238: 3232: 3228: 3225: 3220: 3217: 3213: 3208: 3204: 3201: 3198: 3194: 3189: 3186: 3182: 3178: 3174: 3171: 3167: 3162: 3158: 3154: 3150: 3147: 3140: 3137: 3133: 3129: 3124: 3120: 3112: 3109: 3082: 3079: 3076: 3071: 3068: 3064: 3060: 3055: 3051: 3047: 3044: 3041: 3019: 3012: 3006: 3005: 2992: 2988: 2979: 2975: 2971: 2966: 2962: 2954: 2950: 2944: 2940: 2933: 2930: 2916: 2915: 2899: 2895: 2891: 2886: 2882: 2878: 2874: 2869: 2861: 2857: 2853: 2848: 2844: 2840: 2836: 2831: 2828: 2805: 2802: 2797: 2793: 2789: 2784: 2780: 2776: 2771: 2767: 2745: 2734: 2733: 2722: 2719: 2716: 2713: 2710: 2707: 2704: 2701: 2698: 2695: 2692: 2687: 2683: 2680: 2677: 2673: 2669: 2666: 2663: 2659: 2656: 2653: 2649: 2606: 2603: 2581: 2578: 2576: 2573: 2545: 2542: 2539: 2536: 2516: 2513: 2509: 2506: 2502: 2498: 2495: 2470: 2467: 2463: 2460: 2456: 2452: 2449: 2419: 2416: 2394: 2391: 2369: 2366: 2344: 2341: 2329: 2328: 2317: 2314: 2311: 2308: 2304: 2301: 2297: 2293: 2290: 2285: 2282: 2278: 2275: 2272: 2269: 2265: 2262: 2258: 2254: 2251: 2246: 2243: 2239: 2227: 2224: 2217: 2211: 2208: 2191: 2190: 2179: 2176: 2173: 2170: 2167: 2164: 2161: 2158: 2155: 2152: 2149: 2140: 2113:Main article: 2110: 2107: 2079: 2076: 2075: 2074: 2063: 2058: 2048: 2044: 2038: 2033: 2030: 2019: 2012: 2009: 1992: 1991: 1980: 1972: 1968: 1964: 1961: 1954: 1951: 1940: 1936: 1930: 1923: 1917: 1914: 1909: 1904: 1895: 1890: 1886: 1879: 1876: 1865: 1861: 1855: 1843: 1839: 1835: 1830: 1825: 1822: 1811: 1804: 1801: 1768: 1767: 1756: 1753: 1750: 1747: 1744: 1741: 1714: 1694: 1690: 1686: 1683: 1677: 1674: 1644: 1641: 1622: 1619: 1595: 1594: 1583: 1572: 1541:polarizability 1524: 1521: 1474: 1454: 1441: 1438: 1433:Main article: 1430: 1427: 1426: 1425: 1417: 1401: 1391: 1388: 1386: 1382: 1376: 1369: 1359: 1353: 1352: 1344: 1328: 1319: 1314: 1307: 1292: 1277: 1268: 1259: 1240: 1236: 1232: 1227: 1223: 1219: 1214: 1210: 1198:symmetric tops 1180: 1176: 1172: 1167: 1163: 1159: 1154: 1150: 1138:symmetric tops 1116: 1112: 1108: 1103: 1099: 1076: 1072: 1068: 1063: 1059: 1047: 1044: 1042: 1038: 1034: 1016: 997: 981: 960: 956: 933: 929: 925: 920: 916: 912: 907: 903: 891: 888: 886: 882: 878: 865: 849: 833: 817: 801: 780: 776: 772: 767: 763: 759: 754: 750: 738: 735: 709: 689: 667: 663: 659: 654: 650: 646: 641: 637: 625:center of mass 598: 594: 571: 567: 544: 540: 519: 498:, so that the 487: 484: 468: 467: 455: 449: 446: 441: 438: 434: 430: 427: 424: 421: 416: 412: 378:directly. For 352: 329: 314:center of mass 301: 298: 269: 227: 218: 201: 192: 180: 170: 167: 129:fine structure 33: 15: 9: 6: 4: 3: 2: 8057: 8046: 8043: 8041: 8038: 8036: 8033: 8032: 8030: 8015: 8014: 8005: 8003: 8002: 7993: 7992: 7989: 7978: 7975: 7973: 7970: 7969: 7967: 7963: 7957: 7954: 7952: 7949: 7947: 7944: 7940: 7937: 7936: 7935: 7932: 7930: 7927: 7925: 7922: 7920: 7917: 7915: 7912: 7910: 7907: 7906: 7904: 7900: 7894: 7891: 7889: 7886: 7884: 7881: 7879: 7876: 7874: 7871: 7869: 7866: 7865: 7863: 7859: 7856: 7852: 7846: 7843: 7841: 7838: 7836: 7833: 7829: 7826: 7825: 7824: 7821: 7820: 7818: 7814: 7806: 7803: 7802: 7801: 7798: 7796: 7793: 7792: 7790: 7786: 7780: 7777: 7775: 7772: 7770: 7767: 7765: 7762: 7758: 7755: 7753: 7750: 7748: 7745: 7743: 7740: 7739: 7738: 7735: 7734: 7732: 7728: 7720: 7717: 7716: 7715: 7712: 7710: 7707: 7703: 7700: 7698: 7695: 7693: 7690: 7689: 7688: 7685: 7684: 7682: 7678: 7672: 7669: 7667: 7664: 7660: 7657: 7653: 7650: 7649: 7648: 7645: 7644: 7643: 7640: 7638: 7635: 7633: 7630: 7626: 7623: 7622: 7621: 7618: 7615: 7612: 7610: 7609:Near-infrared 7607: 7605: 7602: 7598: 7595: 7594: 7593: 7590: 7588: 7585: 7584: 7582: 7578: 7572: 7569: 7567: 7564: 7562: 7559: 7557: 7554: 7552: 7549: 7547: 7544: 7542: 7539: 7537: 7534: 7532: 7529: 7527: 7524: 7523: 7521: 7519: 7515: 7511: 7504: 7499: 7497: 7492: 7490: 7485: 7484: 7481: 7475: 7472: 7470: 7467: 7465: 7462: 7461: 7450: 7444: 7440: 7439: 7433: 7429: 7423: 7419: 7414: 7410: 7404: 7400: 7399: 7394: 7390: 7386: 7382: 7376: 7372: 7371: 7365: 7361: 7359:0-486-49540-X 7355: 7351: 7347: 7343: 7339: 7333: 7329: 7328: 7322: 7318: 7316:0-521-53078-4 7312: 7308: 7307: 7302: 7297: 7293: 7291:0-07-707976-0 7287: 7283: 7278: 7274: 7268: 7264: 7259: 7258: 7252: 7251:Atkins, P. W. 7248: 7247: 7234: 7230: 7226: 7222: 7218: 7214: 7210: 7206: 7199: 7191: 7187: 7183: 7179: 7175: 7171: 7167: 7163: 7156: 7148: 7144: 7140: 7136: 7132: 7128: 7121: 7113: 7107: 7099: 7092: 7084: 7080: 7076: 7072: 7068: 7064: 7063:J. Chem. Phys 7057: 7049: 7045: 7041: 7037: 7033: 7029: 7022: 7014: 7010: 7006: 7002: 6998: 6994: 6987: 6979: 6975: 6971: 6967: 6963: 6959: 6952: 6941: 6935: 6927: 6923: 6919: 6915: 6911: 6907: 6900: 6892: 6888: 6884: 6880: 6876: 6872: 6865: 6858: 6835: 6830: 6822: 6818: 6814: 6810: 6806: 6802: 6795: 6789:, p. 102 6788: 6783: 6776: 6771: 6762: 6755: 6747: 6743: 6739: 6735: 6731: 6727: 6720: 6711: 6706: 6702: 6698: 6694: 6690: 6689:J. Chem. Phys 6686: 6679: 6675: 6671: 6667: 6663: 6659: 6658:J. Chem. Phys 6652: 6646:, p. 103 6645: 6640: 6620: 6615: 6609:, p. 101 6608: 6603: 6595: 6591: 6587: 6583: 6579: 6575: 6568: 6561: 6555: 6550: 6546: 6542: 6538: 6534: 6530: 6526: 6519: 6513: 6508: 6504: 6500: 6496: 6492: 6488: 6480: 6473: 6468: 6466: 6459:, p. 449 6458: 6453: 6446: 6441: 6435:, p. 63. 6434: 6429: 6422: 6416: 6412: 6408: 6404: 6400: 6396: 6389: 6383: 6379: 6374: 6372: 6364: 6359: 6353:, p. 111 6352: 6347: 6340: 6335: 6329:, p. 447 6328: 6323: 6317: 6313: 6308: 6301: 6296: 6290:, p. 445 6289: 6283: 6276: 6271: 6265:, p. 444 6264: 6259: 6244: 6238: 6229: 6224: 6220: 6216: 6212: 6208: 6204: 6197: 6189: 6185: 6181: 6177: 6173: 6169: 6150: 6142: 6138: 6134: 6130: 6126: 6122: 6115: 6107: 6100: 6096: 6080: 6073: 6067: 6060: 6044: 6040: 6033: 6023: 6004: 6001: 5997: 5993: 5990: 5981: 5958: 5938: 5928: 5919: 5915: 5907: 5904: 5894: 5891: 5886: 5882: 5872: 5870: 5866: 5862: 5858: 5848: 5846: 5842: 5838: 5834: 5830: 5826: 5822: 5806: 5802: 5797: 5793: 5783: 5781: 5770: 5749: 5744: 5741: 5737: 5727: 5714: 5710: 5706: 5690: 5686: 5682: 5678: 5677:Zeeman effect 5674: 5669: 5666: 5660: 5653: 5648: 5642: 5636: 5612: 5609: 5606: 5603: 5600: 5597: 5591: 5588: 5585: 5582: 5579: 5569: 5568: 5567: 5565: 5559: 5555: 5551: 5547: 5541: 5537: 5533: 5528: 5524: 5520: 5514: 5509: 5503: 5497: 5494:is less than 5493: 5487: 5481: 5477: 5476: 5470: 5466: 5462: 5452: 5448: 5446: 5442: 5437: 5428: 5419: 5417: 5413: 5391: 5388: 5385: 5382: 5379: 5376: 5373: 5370: 5367: 5364: 5352: 5345: 5340: 5336: 5333: 5321: 5316: 5309: 5305: 5301: 5298: 5294: 5290: 5287: 5275: 5270: 5265: 5259: 5255: 5249: 5246: 5242: 5238: 5235: 5232: 5228: 5224: 5221: 5217: 5213: 5210: 5198: 5193: 5189: 5186: 5182: 5178: 5175: 5166: 5161: 5157: 5154: 5149: 5146: 5134: 5121: 5110: 5099: 5098: 5097: 5080: 5077: 5074: 5071: 5068: 5065: 5062: 5059: 5056: 5053: 5041: 5035: 5031: 5028: 5016: 5011: 5007: 5004: 5001: 4997: 4993: 4990: 4978: 4973: 4969: 4966: 4962: 4958: 4955: 4946: 4941: 4937: 4934: 4929: 4926: 4914: 4901: 4890: 4879: 4878: 4877: 4874: 4872: 4851: 4847: 4843: 4838: 4834: 4830: 4826: 4821: 4818: 4810: 4789: 4785: 4781: 4776: 4772: 4768: 4764: 4759: 4756: 4731: 4727: 4723: 4718: 4714: 4710: 4706: 4701: 4698: 4675: 4672: 4669: 4666: 4663: 4660: 4657: 4654: 4651: 4648: 4645: 4642: 4639: 4627: 4624: 4621: 4618: 4615: 4612: 4609: 4606: 4603: 4597: 4593: 4588: 4584: 4581: 4578: 4574: 4570: 4566: 4562: 4559: 4556: 4552: 4548: 4545: 4542: 4538: 4534: 4531: 4528: 4524: 4520: 4513: 4512: 4511: 4508: 4504: 4500: 4496: 4492: 4488: 4484: 4477:Symmetric top 4474: 4471: 4449: 4447: 4444: 4421: 4391: 4381: 4371: 4367: 4363: 4357: 4354: 4347: 4346: 4345: 4332: 4312: 4304: 4300: 4278: 4275: 4270: 4266: 4260: 4256: 4250: 4246: 4242: 4236: 4232: 4226: 4223: 4216: 4215: 4214: 4200: 4192: 4187: 4170: 4167: 4164: 4161: 4158: 4155: 4152: 4149: 4146: 4143: 4131: 4124: 4119: 4115: 4112: 4100: 4095: 4090: 4087: 4084: 4080: 4076: 4073: 4061: 4056: 4052: 4049: 4046: 4032: 4019: 4008: 3997: 3996: 3995: 3992: 3978: 3955: 3952: 3949: 3946: 3943: 3940: 3937: 3934: 3931: 3928: 3925: 3919: 3914: 3910: 3907: 3904: 3900: 3893: 3889: 3885: 3882: 3878: 3874: 3871: 3868: 3864: 3860: 3857: 3854: 3850: 3847: 3844: 3840: 3833: 3832: 3831: 3817: 3809: 3799: 3780: 3777: 3772: 3765: 3762: 3759: 3756: 3751: 3748: 3741: 3738: 3731: 3730: 3729: 3707: 3704: 3698: 3694: 3688: 3684: 3677: 3674: 3671: 3668: 3662: 3650: 3649: 3648: 3646: 3638: 3634: 3630: 3626: 3622: 3618: 3593: 3590: 3582: 3579: 3576: 3570: 3567: 3564: 3561: 3555: 3551: 3547: 3539: 3536: 3530: 3526: 3520: 3516: 3512: 3505: 3501: 3495: 3491: 3481: 3480: 3479: 3477: 3470: 3466: 3459: 3450: 3446: 3442: 3437: 3428: 3426: 3422: 3400: 3382: 3361: 3349: 3329: 3299: 3275: 3272: 3269: 3266: 3263: 3260: 3257: 3254: 3251: 3248: 3236: 3230: 3226: 3223: 3211: 3206: 3202: 3199: 3196: 3192: 3180: 3176: 3172: 3169: 3165: 3156: 3152: 3148: 3145: 3131: 3118: 3107: 3096: 3095: 3094: 3080: 3077: 3074: 3062: 3058: 3049: 3045: 3042: 3031: 3027: 3025: 3018: 3011: 2990: 2986: 2977: 2973: 2969: 2964: 2960: 2952: 2948: 2942: 2938: 2931: 2928: 2921: 2920: 2919: 2897: 2893: 2889: 2884: 2880: 2876: 2872: 2867: 2859: 2855: 2851: 2846: 2842: 2838: 2834: 2829: 2826: 2819: 2818: 2817: 2803: 2800: 2795: 2791: 2787: 2782: 2778: 2774: 2769: 2765: 2743: 2720: 2717: 2714: 2711: 2708: 2705: 2702: 2699: 2696: 2693: 2690: 2685: 2681: 2678: 2675: 2671: 2667: 2664: 2661: 2657: 2654: 2651: 2647: 2640: 2639: 2638: 2636: 2632: 2628: 2624: 2620: 2611: 2602: 2600: 2596: 2592: 2588: 2580:Spherical top 2572: 2569: 2567: 2563: 2559: 2543: 2540: 2537: 2514: 2511: 2507: 2504: 2500: 2496: 2493: 2484: 2468: 2465: 2461: 2458: 2454: 2450: 2447: 2438: 2433: 2417: 2414: 2392: 2389: 2367: 2364: 2342: 2339: 2315: 2309: 2306: 2302: 2299: 2291: 2288: 2283: 2280: 2276: 2270: 2267: 2263: 2260: 2252: 2249: 2244: 2241: 2237: 2222: 2215: 2206: 2196: 2195: 2194: 2177: 2171: 2168: 2165: 2159: 2156: 2153: 2150: 2147: 2138: 2130: 2129: 2128: 2126: 2122: 2116: 2106: 2104: 2100: 2095: 2093: 2089: 2085: 2061: 2056: 2046: 2042: 2036: 2031: 2028: 2017: 2007: 1997: 1996: 1995: 1978: 1970: 1966: 1962: 1959: 1952: 1949: 1938: 1934: 1928: 1921: 1915: 1912: 1902: 1893: 1888: 1884: 1877: 1874: 1863: 1859: 1853: 1841: 1837: 1833: 1828: 1823: 1820: 1809: 1799: 1789: 1788: 1787: 1785: 1781: 1777: 1773: 1770:where ν is a 1754: 1751: 1748: 1745: 1742: 1739: 1732: 1731: 1730: 1728: 1712: 1692: 1688: 1684: 1681: 1672: 1661: 1639: 1628: 1618: 1616: 1613:belong to an 1610: 1604: 1600: 1592: 1588: 1584: 1581: 1577: 1573: 1570: 1566: 1565: 1564: 1561: 1559: 1554: 1550: 1546: 1542: 1538: 1534: 1530: 1529:Raman spectra 1523:Raman spectra 1520: 1518: 1514: 1510: 1506: 1500: 1492: 1485: 1483: 1467: 1463: 1447: 1436: 1423: 1408: 1392: 1375: 1368: 1358: 1351: 1335: 1320: 1318: 1315: 1313: 1298: 1283: 1260: 1258: 1255: 1254: 1238: 1234: 1230: 1225: 1221: 1217: 1212: 1208: 1199: 1197: 1178: 1174: 1170: 1165: 1161: 1157: 1152: 1148: 1139: 1137: 1132: 1131:rotation axis 1114: 1110: 1106: 1101: 1097: 1074: 1070: 1066: 1061: 1057: 1048: 1032: 1028: 1024: 1020: 1012: 1008: 1004: 988: 958: 954: 931: 927: 923: 918: 914: 910: 905: 901: 892: 876: 872: 856: 840: 824: 808: 778: 774: 770: 765: 761: 757: 752: 748: 739: 733: 732: 730: 729:energy levels 725: 723: 722:rotation axis 707: 687: 665: 661: 657: 652: 648: 644: 639: 635: 626: 622: 618: 614: 596: 592: 569: 565: 542: 538: 517: 509: 505: 501: 497: 493: 483: 480: 476: 471: 453: 447: 444: 439: 436: 432: 428: 425: 422: 419: 414: 410: 402: 401: 400: 397: 393: 389: 385: 384:isotopologues 381: 377: 373: 368: 366: 350: 341: 327: 319: 315: 311: 307: 297: 295: 291: 287: 283: 279: 274: 261: 257: 253: 249: 245: 241: 237: 236:van der Waals 211: 210:chlorotoluene 166: 164: 160: 155: 153: 149: 145: 141: 138: 134: 130: 126: 122: 118: 117:energy levels 112: 110: 106: 102: 98: 94: 90: 86: 82: 78: 74: 70: 66: 62: 58: 54: 47: 43: 26: 21: 8035:Spectroscopy 8011: 7999: 7979:(a misnomer) 7965:Applications 7883:Time-stretch 7774:paramagnetic 7592:Fluorescence 7540: 7510:Spectroscopy 7437: 7417: 7397: 7369: 7349: 7346:Kroto, H. W. 7326: 7305: 7281: 7256: 7243:Bibliography 7208: 7204: 7198: 7165: 7161: 7155: 7130: 7126: 7120: 7106: 7091: 7066: 7062: 7056: 7031: 7027: 7021: 6996: 6992: 6986: 6961: 6957: 6951: 6934: 6909: 6905: 6899: 6877:(4): 234–7. 6874: 6870: 6864: 6829: 6807:(4): 651–5. 6804: 6800: 6794: 6782: 6770: 6760: 6754: 6732:(1): 77–79. 6729: 6725: 6719: 6695:(11): 4968. 6692: 6688: 6661: 6657: 6651: 6639: 6614: 6602: 6577: 6573: 6560: 6532: 6528: 6518: 6490: 6486: 6479: 6474:, p. 45 6452: 6447:, p. 40 6440: 6428: 6423:, p. 97 6398: 6394: 6388: 6381: 6358: 6346: 6341:, p. 49 6334: 6322: 6307: 6302:, p. 95 6295: 6282: 6277:, p. 99 6270: 6258: 6246:. Retrieved 6237: 6210: 6207:Ann. Geophys 6206: 6196: 6171: 6167: 6149: 6124: 6120: 6114: 6105: 6099: 6079: 6066: 6059:nitric oxide 6039:paramagnetic 6032: 6022: 5927: 5918: 5900: 5878: 5854: 5837:Walter Gordy 5823:such as the 5789: 5776: 5733: 5685:nitric oxide 5673:paramagnetic 5670: 5661:, OCS, with 5651: 5647:Stark effect 5640: 5632: 5557: 5553: 5549: 5545: 5539: 5535: 5531: 5526: 5522: 5512: 5501: 5495: 5491: 5485: 5479: 5474: 5464: 5458: 5449: 5444: 5435: 5433: 5415: 5408: 5407:The term in 5406: 5095: 4875: 4870: 4808: 4690: 4502: 4498: 4494: 4490: 4486: 4482: 4480: 4470:paramagnetic 4455: 4446: 4410: 4298: 4296: 4188: 4185: 3993: 3970: 3805: 3797: 3727: 3644: 3632: 3624: 3616: 3614: 3468: 3461: 3457: 3454: 3448: 3444: 3440: 3424: 3420: 3350: 3290: 3028: 3023: 3016: 3009: 3007: 2917: 2735: 2634: 2623:point masses 2616: 2583: 2570: 2565: 2561: 2557: 2482: 2436: 2434: 2330: 2192: 2118: 2096: 2087: 2081: 1993: 1779: 1769: 1624: 1614: 1608: 1602: 1598: 1596: 1590: 1586: 1579: 1575: 1568: 1562: 1536: 1532: 1526: 1516: 1512: 1508: 1498: 1490: 1486: 1443: 1373: 1366: 1356: 1194: 1134: 991:dinitrogen ( 875:point groups 726: 680:, with axis 620: 616: 612: 489: 475:bond lengths 472: 469: 392:bond lengths 369: 342: 303: 172: 169:Applications 156: 121:rigid rotors 113: 100: 93:far infrared 64: 52: 51: 41: 7551:Vibrational 6964:: 537–558. 6834:Hollas 1996 6787:Hollas 1996 6775:Hollas 1996 6644:Hollas 1996 6619:Hollas 1996 6607:Hollas 1996 6421:Hollas 1996 6351:Hollas 1996 6312:Hollas 1996 6300:Hollas 1996 6027:parameters. 5831:during the 5740:anisotropic 5681:diamagnetic 2631:rigid rotor 2619:rigid rotor 1593:= 0, ±1, ±2 1589:≠ 0, then Δ 1578:= 0, then Δ 1545:anisotropic 1464:) or HCCH ( 479:bond angles 376:bond length 8029:Categories 7757:Two-photon 7659:absorption 7541:Rotational 7448:148319485X 7427:0852741421 7337:0471965227 7272:0198700725 7096:Jager, W. 6248:2 December 6092:References 5821:microwaves 5469:quadrupole 4873:molecule. 4497:...0 ... - 3659:population 3637:degeneracy 1960:2.99792458 1776:wavelength 1627:wavenumber 1462:dinitrogen 975:dioxygen ( 310:orthogonal 278:polyatomic 81:absorption 7835:Terahertz 7816:Radiowave 7714:Mössbauer 7401:. Dover. 7352:. Dover. 6801:Phys. Rev 6726:Phys. Rev 6529:Phys. Rev 5985:¯ 5903:B.H. Pate 5871:in 1975. 5805:microwave 5796:waveguide 5610:± 5595:Δ 5586:± 5577:Δ 5552:− 1, …, | 5443:for each 5360:′ 5357:′ 5329:′ 5326:′ 5299:− 5283:′ 5280:′ 5236:− 5206:′ 5203:′ 5187:− 5171:′ 5142:′ 5139:′ 5131:↔ 5126:′ 5114:~ 5111:ν 5049:′ 5046:′ 5024:′ 5021:′ 4986:′ 4983:′ 4967:− 4951:′ 4922:′ 4919:′ 4911:↔ 4906:′ 4894:~ 4891:ν 4835:π 4773:π 4715:π 4673:− 4667:… 4655:… 4628:… 4582:− 4425:~ 4422:ω 4385:~ 4382:ω 4247:π 4139:′ 4136:′ 4108:′ 4105:′ 4085:− 4069:′ 4066:′ 4040:′ 4037:′ 4029:↔ 4024:′ 4012:~ 4009:ν 3883:− 3773:− 3689:− 3663:∝ 3556:− 3521:− 3405:′ 3396:← 3390:′ 3387:′ 3359:Δ 3334:′ 3307:′ 3304:′ 3244:′ 3241:′ 3219:′ 3216:′ 3188:′ 3185:′ 3170:− 3161:′ 3139:′ 3136:′ 3128:↔ 3123:′ 3111:~ 3108:ν 3078:± 3070:′ 3067:′ 3059:− 3054:′ 3040:Δ 2881:π 2843:π 2535:Δ 2512:− 2277:− 2226:~ 2223:ν 2210:~ 2207:ν 2125:separable 2043:ν 2037:≈ 2029:− 2011:~ 2008:ν 1963:× 1950:− 1935:ν 1913:− 1903:⋅ 1875:− 1860:ν 1838:λ 1821:− 1803:~ 1800:ν 1774:, λ is a 1772:frequency 1746:λ 1743:⋅ 1740:ν 1727:gigahertz 1713:ν 1693:λ 1676:~ 1673:ν 1643:~ 1640:ν 1537:scattered 1338:propyne, 1286:ammonia, 1262:Benzene, 911:≪ 843:silane, ( 827:methane ( 658:≤ 645:≤ 496:quantized 429:α 426:− 306:gas phase 208:group in 89:microwave 61:gas phase 57:molecules 8040:Rotation 8001:Category 7730:Electron 7697:Emission 7647:emission 7604:Vibronic 7395:(1975). 7348:(2003). 7303:(2003). 7233:21728367 7190:17902981 6043:dioxygen 5825:klystron 5713:dioxygen 5707:and the 5529:. where 5418:values. 3447:= 0.05. 2568:branch. 2508:″ 2497:′ 2485:branch, 2462:″ 2451:′ 2418:′ 2393:″ 2368:′ 2343:″ 2303:′ 2292:′ 2284:′ 2264:″ 2253:″ 2245:″ 1543:must be 1533:incident 502:and the 300:Overview 296:(ALMA). 258:using a 240:hydrogen 140:coupling 137:Coriolis 85:emission 8013:Commons 7840:ESR/EPR 7788:Nucleon 7616:(REMPI) 7213:Bibcode 7170:Bibcode 7135:Bibcode 7071:Bibcode 7036:Bibcode 7001:Bibcode 6966:Bibcode 6914:Bibcode 6879:Bibcode 6809:Bibcode 6734:Bibcode 6697:Bibcode 6666:Bibcode 6582:Bibcode 6537:Bibcode 6495:Bibcode 6403:Bibcode 6215:Bibcode 6176:Bibcode 6129:Bibcode 5885:kelvins 5869:Flygare 5845:Flygare 5703:, some 4869:for an 4809:prolate 3619:is the 2591:methane 1782:is the 1629:scale ( 1482:methane 1395:water, 1317:Prolate 1196:Prolate 244:halogen 59:in the 7854:Others 7642:Atomic 7445: 7424: 7405: 7377: 7356: 7334: 7313: 7288: 7269: 7265:–469. 7231: 7188: 6316:silane 5687:, NO, 4871:oblate 4807:for a 4691:where 4452:Oxygen 4411:where 4297:where 3971:where 3641:2J + 1 3615:where 3291:where 3008:where 2816:, so 2736:where 2331:where 1553:Stokes 1549:tensor 1466:ethyne 1257:Oblate 1136:Oblate 619:, and 161:using 63:. The 7795:Alpha 7764:Auger 7742:X-ray 7709:Gamma 7687:X-ray 7620:Raman 7531:Raman 7526:FT-IR 6943:(PDF) 6632:SiNCS 6570:(PDF) 5910:Notes 5829:radar 5665:debye 2406:and 1621:Units 77:polar 75:) of 7443:ISBN 7422:ISBN 7403:ISBN 7375:ISBN 7354:ISBN 7332:ISBN 7311:ISBN 7286:ISBN 7267:ISBN 7229:PMID 7186:PMID 6765:p139 6250:2012 6061:, NO 6057:and 5637:the 5525:and 4749:and 4325:and 3627:the 3623:and 3015:and 2617:The 2356:and 1778:and 1611:= +2 1582:= ±2 1527:For 1515:to - 1501:= ±1 1409:and 1349:C≡CH 1218:< 1193:and 1171:< 1037:or D 881:or O 584:and 477:and 242:and 135:and 101:pure 71:vs. 7823:NMR 7263:431 7221:doi 7209:115 7178:doi 7143:doi 7131:238 7079:doi 7044:doi 7009:doi 6974:doi 6922:doi 6887:doi 6817:doi 6742:doi 6705:doi 6674:doi 6590:doi 6554:pdf 6545:doi 6512:pdf 6503:doi 6491:122 6411:doi 6223:doi 6184:doi 6137:doi 6125:237 5654:+ 1 5643:+ 1 5515:= 1 5504:+ 1 5488:+ 1 4634:and 3478:as 3441:Bhc 2233:vib 2143:rot 2052:GHz 1585:If 1574:If 1571:= 0 1493:= 0 1303:XeF 1089:or 845:SiH 813:CCl 490:In 87:by 83:or 8031:: 7828:2D 7747:UV 7391:; 7227:. 7219:. 7207:. 7184:. 7176:. 7166:78 7164:. 7141:. 7129:. 7077:. 7067:72 7065:. 7042:. 7032:47 7030:. 7007:. 6997:26 6995:. 6972:. 6962:29 6960:. 6920:. 6910:20 6908:. 6885:. 6875:45 6873:. 6815:. 6805:79 6803:. 6740:. 6730:77 6728:. 6703:. 6693:54 6691:. 6687:. 6672:. 6662:47 6660:. 6588:. 6576:. 6572:. 6543:. 6533:75 6531:. 6527:. 6501:. 6489:. 6464:^ 6409:. 6399:62 6397:. 6370:^ 6221:. 6211:22 6209:. 6205:. 6182:. 6172:21 6170:. 6156:NH 6135:. 6123:. 6084:J. 6045:, 5809:NH 5715:, 5693:NO 5691:, 5556:− 5548:+ 5543:, 5538:+ 5534:= 5498:, 5482:, 5463:, 5411:JK 4448:. 4243:32 3445:kT 2101:, 2057:30 2024:cm 1971:10 1967:10 1899:cm 1847:cm 1816:cm 1519:. 1495:, 1470:CH 1413:NO 1372:= 1340:CH 1336:, 1333:Cl 1324:CH 1299:; 1288:NH 1284:; 1041:. 1039:∞h 1035:∞v 1029:, 1025:, 1021:, 1013:, 1009:, 1005:, 989:, 885:. 861:SF 857:, 841:, 829:CH 809:, 615:, 557:, 510:, 265:NH 262:. 238:, 232:Cl 206:Cl 176:CH 165:. 131:, 127:, 29:CF 27:, 7502:e 7495:t 7488:v 7451:. 7430:. 7411:. 7383:. 7362:. 7340:. 7319:. 7294:. 7275:. 7235:. 7223:: 7215:: 7192:. 7180:: 7172:: 7149:. 7145:: 7137:: 7114:. 7100:. 7085:. 7081:: 7073:: 7050:. 7046:: 7038:: 7015:. 7011:: 7003:: 6980:. 6976:: 6968:: 6945:. 6928:. 6924:: 6916:: 6893:. 6889:: 6881:: 6859:. 6850:2 6845:N 6823:. 6819:: 6811:: 6748:. 6744:: 6736:: 6713:. 6707:: 6699:: 6680:. 6676:: 6668:: 6634:. 6628:3 6623:H 6596:. 6592:: 6584:: 6578:1 6551:. 6547:: 6539:: 6509:. 6505:: 6497:: 6417:. 6413:: 6405:: 6252:. 6231:. 6225:: 6217:: 6190:. 6186:: 6178:: 6161:3 6143:. 6139:: 6131:: 6074:. 6052:2 6047:O 6005:c 6002:h 5998:/ 5994:B 5991:= 5982:B 5959:B 5939:B 5814:3 5764:2 5759:N 5722:2 5717:O 5698:2 5652:J 5641:J 5639:2 5613:1 5607:, 5604:0 5601:= 5598:F 5592:, 5589:1 5583:= 5580:J 5560:| 5558:I 5554:J 5550:I 5546:J 5540:I 5536:J 5532:F 5527:J 5523:F 5513:I 5502:J 5500:2 5496:I 5492:J 5486:I 5484:2 5480:I 5475:J 5465:I 5445:J 5436:J 5416:K 5409:D 5392:. 5389:. 5386:. 5383:, 5380:2 5377:, 5374:1 5371:, 5368:0 5365:= 5353:J 5346:3 5341:) 5337:1 5334:+ 5322:J 5317:( 5310:J 5306:D 5302:4 5295:) 5291:1 5288:+ 5276:J 5271:( 5266:) 5260:2 5256:K 5250:K 5247:J 5243:D 5239:2 5233:B 5229:( 5225:2 5222:= 5218:) 5214:K 5211:, 5199:J 5194:( 5190:F 5183:) 5179:K 5176:, 5167:J 5162:( 5158:F 5155:= 5150:K 5147:, 5135:J 5122:J 5081:. 5078:. 5075:. 5072:, 5069:2 5066:, 5063:1 5060:, 5057:0 5054:= 5042:J 5036:) 5032:1 5029:+ 5017:J 5012:( 5008:B 5005:2 5002:= 4998:) 4994:K 4991:, 4979:J 4974:( 4970:F 4963:) 4959:K 4956:, 4947:J 4942:( 4938:F 4935:= 4930:K 4927:, 4915:J 4902:J 4852:C 4848:I 4844:c 4839:2 4831:8 4827:h 4822:= 4819:A 4790:A 4786:I 4782:c 4777:2 4769:8 4765:h 4760:= 4757:A 4732:B 4728:I 4724:c 4719:2 4711:8 4707:h 4702:= 4699:B 4676:J 4670:, 4664:, 4661:0 4658:, 4652:, 4649:J 4646:+ 4643:= 4640:K 4625:, 4622:2 4619:, 4616:1 4613:, 4610:0 4607:= 4604:J 4598:2 4594:K 4589:) 4585:B 4579:A 4575:( 4571:+ 4567:) 4563:1 4560:+ 4557:J 4553:( 4549:J 4546:B 4543:= 4539:) 4535:K 4532:, 4529:J 4525:( 4521:F 4503:K 4499:J 4495:J 4491:M 4487:J 4483:J 4463:2 4458:O 4392:2 4372:3 4368:B 4364:4 4358:= 4355:D 4333:D 4313:B 4299:k 4279:c 4276:k 4271:2 4267:r 4261:2 4257:I 4251:4 4237:3 4233:h 4227:= 4224:D 4201:D 4171:. 4168:. 4165:. 4162:, 4159:2 4156:, 4153:1 4150:, 4147:0 4144:= 4132:J 4125:3 4120:) 4116:1 4113:+ 4101:J 4096:( 4091:D 4088:4 4081:) 4077:1 4074:+ 4062:J 4057:( 4053:B 4050:2 4047:= 4033:J 4020:J 3979:D 3956:. 3953:. 3950:. 3947:, 3944:2 3941:, 3938:1 3935:, 3932:0 3929:= 3926:J 3920:2 3915:) 3911:1 3908:+ 3905:J 3901:( 3894:2 3890:J 3886:D 3879:) 3875:1 3872:+ 3869:J 3865:( 3861:J 3858:B 3855:= 3851:) 3848:J 3845:( 3841:F 3818:B 3781:2 3778:1 3766:B 3763:c 3760:h 3757:2 3752:T 3749:k 3742:= 3739:J 3708:T 3705:k 3699:J 3695:E 3685:e 3681:) 3678:1 3675:+ 3672:J 3669:2 3666:( 3645:J 3633:J 3625:T 3617:k 3611:, 3594:T 3591:k 3586:) 3583:1 3580:+ 3577:J 3574:( 3571:J 3568:c 3565:h 3562:B 3552:e 3548:= 3540:T 3537:k 3531:J 3527:E 3517:e 3513:= 3506:0 3502:N 3496:J 3492:N 3472:0 3469:N 3467:/ 3464:J 3462:N 3458:J 3449:J 3443:/ 3425:x 3421:B 3401:J 3383:J 3362:J 3330:J 3300:J 3276:. 3273:. 3270:. 3267:, 3264:2 3261:, 3258:1 3255:, 3252:0 3249:= 3237:J 3231:) 3227:1 3224:+ 3212:J 3207:( 3203:B 3200:2 3197:= 3193:) 3181:J 3177:( 3173:F 3166:) 3157:J 3153:( 3149:F 3146:= 3132:J 3119:J 3081:1 3075:= 3063:J 3050:J 3046:= 3043:J 3024:d 3020:2 3017:m 3013:1 3010:m 2991:2 2987:d 2978:2 2974:m 2970:+ 2965:1 2961:m 2953:2 2949:m 2943:1 2939:m 2932:= 2929:I 2898:C 2894:I 2890:c 2885:2 2877:8 2873:h 2868:= 2860:B 2856:I 2852:c 2847:2 2839:8 2835:h 2830:= 2827:B 2804:0 2801:= 2796:A 2792:I 2788:, 2783:C 2779:I 2775:= 2770:B 2766:I 2744:B 2721:. 2718:. 2715:. 2712:, 2709:2 2706:, 2703:1 2700:, 2697:0 2694:= 2691:J 2686:) 2682:1 2679:+ 2676:J 2672:( 2668:J 2665:B 2662:= 2658:) 2655:J 2652:( 2648:F 2635:F 2566:R 2562:P 2558:Q 2544:0 2541:= 2538:J 2515:1 2505:J 2501:= 2494:J 2483:P 2469:1 2466:+ 2459:J 2455:= 2448:J 2437:R 2415:J 2390:J 2365:B 2340:B 2316:, 2313:) 2310:1 2307:+ 2300:J 2296:( 2289:J 2281:B 2274:) 2271:1 2268:+ 2261:J 2257:( 2250:J 2242:B 2238:+ 2216:= 2178:. 2175:) 2172:1 2169:+ 2166:J 2163:( 2160:J 2157:B 2154:c 2151:h 2148:= 2139:E 2088:B 2062:. 2047:/ 2032:1 2018:/ 1979:. 1953:1 1945:s 1939:/ 1929:= 1922:) 1916:1 1908:s 1894:( 1889:/ 1885:c 1878:1 1870:s 1864:/ 1854:= 1842:/ 1834:1 1829:= 1824:1 1810:/ 1780:c 1755:, 1752:c 1749:= 1689:/ 1685:1 1682:= 1615:S 1609:J 1607:Δ 1603:R 1599:J 1591:J 1587:K 1580:J 1576:K 1569:K 1567:Δ 1517:J 1513:J 1509:K 1499:J 1497:Δ 1491:K 1489:Δ 1480:( 1475:4 1460:( 1455:2 1450:N 1418:2 1406:O 1402:2 1397:H 1383:3 1377:B 1374:I 1370:A 1367:I 1360:C 1357:I 1345:3 1329:3 1308:4 1293:3 1278:6 1273:H 1269:6 1264:C 1239:C 1235:I 1231:= 1226:B 1222:I 1213:A 1209:I 1179:C 1175:I 1166:B 1162:I 1158:= 1153:A 1149:I 1115:C 1111:I 1107:= 1102:B 1098:I 1075:B 1071:I 1067:= 1062:A 1058:I 1019:) 1017:2 1003:) 998:2 993:N 987:) 982:2 977:O 959:A 955:I 932:C 928:I 924:= 919:B 915:I 906:A 902:I 883:h 879:d 877:T 871:) 866:6 855:) 850:4 839:) 834:4 823:) 818:4 807:) 802:4 797:P 779:C 775:I 771:= 766:B 762:I 758:= 753:A 749:I 708:A 688:A 666:C 662:I 653:B 649:I 640:A 636:I 621:C 617:B 613:A 597:C 593:I 570:B 566:I 543:A 539:I 518:I 454:) 448:2 445:1 440:+ 437:v 433:( 423:B 420:= 415:v 411:B 351:K 328:J 270:3 228:7 223:H 219:7 214:C 212:( 202:4 197:H 193:6 188:C 181:3 67:( 42:J 38:I 34:3

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Knowledge

Rotational spectroscopy

Index