Talk:Rotational spectroscopy

This article contains the following sentence:

For convenience molecules are divided into four classes: (1) Linear molecules (2) Symmetric Tops. (3) Asymmetric Tops. dealing with each in turn:

Clearly, only three classes are named (and only these three are discussed). However, a fourth class must also be considered, namely (4) Spherical Tops. A section on spherical tops should be added here.

page needs dramatic rewrite

For some reason, this page seems really lame. It really needs to be updated to offer a more structured description of the topic. Suprisingly bad.

I found some misinformation concerning the P branch and R branch (it has been corrected). I haven't had time to look through the rest of the article, though I think that the validity of the information should be checked-- consider the mixup that I found and other possible mixups in the article.

figures required

Need to add some figures, explaining the spectrum. Also a section for experimental determination and applications.

I've added a figure for a linear molecule, but some explanation of the Q-branch transitions that are sometimes observed is needed, and I'm not really qualified to do so. I have a scan of a spectrum recorded in my university labs on a FTIR machine of an HCl / DCl mixture. Does anyone know if there would be any problem with me putting this up? David-i98 (talk) 10:52, 29 January 2008 (UTC)

I've noticed that the rotational energy levels in the figure (Image:Vibrationrotationenergy.svg) become progressively closer with increasing J. It is my understanding, however, that the energy level gap between successive levels grows as J increases.--GregRM (talk) 23:54, 15 February 2008 (UTC)

Whoops, that was a bit stupid. I've fixed it now. David-i98 (talk) 15:07, 11 March 2008 (UTC)

work in progress!

I am a research-active academic who specialises in microwave spectroscopy. I agree with the general comments which say this page needs some work and wish to develop the page, acting on some of the criticisms. I will be providing some new figures in the coming days/weeks and suggesting other amendments also. I have started by tweaking the opening paragraphs. There were some factual inaccuracies (rotational and microwave spectroscopy are not exactly synonymous, for example). I have tried to retain the spirit of the previous draft.

I will be trying to engage the lively global community of researchers who use rotational spectroscopy so that we can get an excellent page in the coming weeks. — Preceding unsigned comment added by Nnrw (talk • contribs) 16:01, 21 May 2012 (UTC)

The statement that "rotational and microwave spectroscopy are not exactly synonymous" would be more helpful to the reader if we indicate the differences. For example 1) rotational transitions are not always at frequencies observed with microwave apparatus, 2) some microwave transitions involve other molecular changes such as inversion, and 3) (most important I think) even typical rotational transitions can be observed by microwave OR Raman spectroscopy, and some molecules can only be studied in Raman. Dirac66 (talk) 17:38, 21 May 2012 (UTC)

I've removed the figure showing the ro-vibrational spectrum of CO and replaced it with a pure rotational spectrum of CF3I which I took at the University of Bristol. I've also removed the ro-vibrational spectrum of CH4 that was somewhat further down. I want to draw a distinction here between ro-vibrational spectroscopy (described elsewhere on wikipedia, linked to in the opening paragraph) and pure rotational spectroscopy which is somewhat different. — Preceding unsigned comment added by Nnrw (talk • contribs) 14:40, 22 May 2012 (UTC)

Re: comment by Dirac. I agree with the need to change that sentence and have made a few changes. With regard to Dirac66 point 3, I think Raman is used most often for measurements of ro-vibrational or ro-vibronic transitions rather than rotational so have left that out. I'm not a Raman specialist though, my background is in pure-rotational spectroscopy. Further comments and edits welcomed. — Preceding unsigned comment added by Nnrw (talk • contribs) 14:47, 22 May 2012 (UTC)

Raman has some application to pure rotational spectroscopy as well, and is of especial interest for non-dipolar molecules which have no microwave spectrum. However mentioning Raman to the article intro might well be confusing. Instead I will start a new section at the end to mention Raman, and mention only pure rotational transitions. Dirac66 (talk) 00:15, 23 May 2012 (UTC)

Diagrams

I've replaced the illustration that showed transitions in ro-vibrational specta with another that shows transitions in pure rotational spectra. All of the theory alongside the figure relates to pure rotational spectra so I think it's better this way. The same diagam also shows how these map onto the rotational transitions that can be observed experimentally. It is important to distinguish between the energies associated with rotational levels, and those associated with transitions and I try to do that with this plot.Nnrw (talk) 16:12, 24 May 2012 (UTC)

I agree that the new diagram is better for this article because it shows pure rotational transitions. However I do have a few more comments.

1. Why show the transitions as emissions? I have never done microwave spectroscopy but I always assumed that absorption spectra (ΔJ = +1) are measured. Isn't that why a microwave source (or chirped-pulse laser) is required? Atkins and de Paula (Physical Chemistry 8th ed, p.448, Fig.13.19) refer to a "typical pure rotation absorption spectrum".

I'm delighted someone's watching what I'm doing and thanks for the feedback. Please keep it coming. A few responses; In 2012, it's not true that absorption spectra are always measured. It's true that this was the usual way of doing things before 1975. Around that time, Fourier transform (FT) techniques were first applied in microwave spectroscopy and everything changed in a big way. A FT experiment involves (i) first cooling molecules through gas jet expansion (ii) irradiating molecules with a polarisation pulse (the molecules absorb) before finally (iii) detecting the molecular emission that accompanies the subsequent decoherence. FTMW is the electric dipole analogue of NMR and is governed by the Bloch equations in the same way. To cut a long story short, I can do no better on how FTMW works than the animation here: <http://www.chem.ualberta.ca/~jaeger/research/ftmw/ftmw.htm> which I will eventually link from the article, after having a chance to work on the experiment section. The great majority of research worldwide now uses FTMW spectrometers, absorption cells are very rarely used.Nnrw (talk) 14:08, 25 May 2012 (UTC)

2. The CF₃I spectrum now at the top of the article is more complex and should be moved down to the Symmetric top section, and better explain the observed splitting. (Is it really due to nuclear quadrupole coupling of ¹²⁷I as the caption says? I would have guessed that it is due to centrifugal distortion.)

The splitting in each J-J transition is definitely nuclear quadrupole coupling. This has been studied a few times, I'm not sure if you have the fortunate privilege of a university library. If so, you might find a few papers by searching for "pure rotational CF3I trifluoroiodomethane" or something like that using a search engine. The nuclear quadrupole coupling constant of iodine in CF3I was last measured in 2010. Centrifugal distortion induces a small shift in the position of each J-J transition. In the frequency range covered by the diagram, this is a very, very small effect (so small it's invisible on the figure). Centrifugal distortion is a much bigger shift at mm wavelengths. The connections and distinctions between millimetre and microwave spectroscopies might usefully be covered in a future version of this page. I would like to overhaul the sections that go beyond the rigid rotor. The section on centrifugal distortion is currently a little misleading. It actually shouldn't really be referred to as the "non-rigid rotor", the phrase "semi-rigid rotor" is conventionally used because higher order distortion terms (ie there's others in addition to D) are neglected by the model presented on the page.Nnrw (talk) 14:08, 25 May 2012 (UTC)

On the suggestion of moving the diagram down to the symmetric top section, I would really like to leave it where it is. I think the introductory preamble should be aimed at microwave spectroscopy very generally, not necessarily just for linear molecules. The spectrum of CF3I is a nice prototype because you can see the regular 2B spacing in the spectrum between the J-J transitions and the spectrum also illustrates hyperfine coupling very nicely (can be referred to in a future version of the page).Nnrw (talk) 14:32, 25 May 2012 (UTC)

3. Finally, the old diagram with P,Q,R branches can be recycled to the article on Rovibrational coupling (which should be renamed Rotational-Vibrational Spectroscopy, now its main section title) and added to the diagram which is already in that article. A future project after this one. Dirac66 (talk) 12:47, 25 May 2012 (UTC)

I agree this would be a good idea, if there's nothing like it already there. I need to concentrate on just one page at a time.

Further re absorption vs. emission - I looked for the University of Virginia information and found this website] about astrochemistry which does involve emission spectra. But are chirped-pulse spectra in a laboratory context absorption or emission?

chirped-pulse FTMW involves exactly the same sequence of events ((i) cooling (ii) polarisation (absorption) (iii) detecting the emission) as does the older variant of FTMW. A single experiment (done in a fraction of a second) involves the molecules first absorbing the radiation and detecting the emission as they relax.Nnrw (talk) 14:08, 25 May 2012 (UTC)

Perhaps the diagrams are all right (at least for astrophysics)but the Experimental section should explain when absorption is observed and when emission is observed.

I think the diagram is OK but welcome further opinions. I agree regarding the second point and we will get there but there is a huge amount more work needed before this can be easily summarised, given what I say above about how FTMW and CP-FTMW work. What is needed is (i) an explanation of how FTMW works, then (ii) why FTMW superceded absorption cells in research and the technological changes that made this possible then (iii) how a CP-FTMW works and (iv) the technology that now allows construction of a chirped-pulse FTMW spectrometer. Boiling this down to a reasonably basic level will require some good choices of words. Answering a different query, chirped-pulse FTMW spectrometers don't use chirped pulse lasers, they exploit high speed electronics (arbitrary waveform generators and oscilloscopes). Given that the page can be accessed by anyone at any time, I won't induce confusion by trying to explain all of this at once. I will get there in the end, I hope.Nnrw (talk) 14:08, 25 May 2012 (UTC)

Also the mention of the Virginia work needs a hyperlink - have I found the most appropriate page? Dirac66 (talk) 13:09, 25 May 2012 (UTC)

The link to chirped pulse amplification wasn't appropriate in this context. I've added a link to a page maintained by the research group that developed by CP-FTMW. This may be too complex for this audience. On the other hand, when a simple and more accessible description of CP-FTMW has been provided, it will be a useful complement to what we have on the main page.Nnrw (talk) 14:39, 25 May 2012 (UTC)

OK, thanks for all your answers. As you can see, I know enough about this topic to ask a few questions but not to answer them very well. I have taught a brief intro as part of a molecular spectroscopy course, but have never actually worked in the field. So in general I accept your answers and I have learned from the discussion. As other readers may share my questions, the answers should eventually be incorporated into the article, but I understand that this will take time, perhaps several months.

As for the the energy level diagram for P,Q and R branches, I have added it to the article on Rovibrational coupling (i.e. spectroscopy) so that it is retained in Wikipedia. Dirac66 (talk) 18:49, 25 May 2012 (UTC)

Missing quantum number M

OK, another concern today. In the section Structure of rotational spectra, subsection Linear molecules, the article now says "These molecules have two degenerate modes of rotation ... Since we cannot distinguish between the two modes, we need only one rotational quantum number (J) to describe the rotational motion of the molecule." I would say that the rotation is described by two degrees of freedom (not degenerate modes) which are the angles θ and φ. The Schrodinger equation is the one for a particle on the surface of a sphere, with spherical harmonics as eigenfunctions. The two quantum numbers are J and M. Of course the energy depends only on J in the absence of an external field, so only J is observable in ordinary microwave spectroscopy. But M does become observable in Stark-effect or Zeeman-effect experiments.

Similarly the section Structure of rotational spectra, subsection Symmetric top refers only to two quantum numbers J and K. Actually there are 3 degrees of rotational freedom = the two for a linear molecule plus a third rotation about the symmetry axis. This leads to 3 quantum numbers J, K and M. Again E is independent of M, unless there is an external field. Dirac66 (talk) 17:45, 26 May 2012 (UTC)

Rotational Raman spectroscopy

This is a major omission and leads to several misleading statements which apply to infrared spectroscopy but not to Raman spectroscopy. I will attend to this eventually, but I can't give a time-scale at the moment. Anyone else interested? Petergans (talk) 12:42, 30 October 2012 (UTC)

I presume you would use as a starting point the existing Section 6 on Rotational Raman spectroscopy which I added on 22 May. Of course one could add much more, and also revise statements elsewhere in the article to specify what applies to microwave and what to Raman. Dirac66 (talk) 15:00, 30 October 2012 (UTC)

Missed that! I was hit by the statement in the lead "Rotational spectra can be observed for molecules that have a permanent electric dipole moment" and did not look too closely at the rest. I'm working on Electromagnetic absorption by water at the moment, which is, in parts, truly awful. If you would like to clean this one up, that would be great. BTW, I would not restrict dipole-allowed transitions to microwave spectroscopy, they can also be observed in the far infrared.Petergans (talk) 19:00, 31 October 2012 (UTC)

I have now fixed up the intro and added a mention of far IR and a paragraph on Raman. But I will leave the H2O article to you as I don't know very much about it.

Electromagnetic absorption by water is now done. Please look it over, especially for typos! Petergans (talk) 20:40, 2 November 2012 (UTC)

I found a few small ones in the VUV section only. Perhaps you were more distracted when you wrote that section. Dirac66 (talk) 23:18, 2 November 2012 (UTC)

Does C60 belong in this article?

The Historical Achievements section contains a paragraph about buckminsterfullerene (C₆₀) which could be interpreted to mean (although it does not actually say) that C₆₀ was discovered by observation of its microwave spectrum. However, this is impossible because C₆₀ has zero dipole moment by symmetry, and therefore has no microwave spectrum. It is true that microwave observations of astrophysical molecules such as HC₅N and HC₇N led to the research that resulted in the discovery of C₆₀, the actual observation of C₆₀ was made by other means - initially mass spectroscopy and later IR (vibrational) and NMR.

I therefore question whether C₆₀ should even be mentioned in this article. If it is mentioned, then it should be made clear that although rotational spectra of other molecules stimulated the research, C₆₀ itself does not have a rotational spectrum. Dirac66 (talk) 03:14, 1 November 2012 (UTC)

This article needs to be revised

For the following reasons

1. The lead is too long and too detailed
2. Duplication of categories linear, spherical top etc.
3. Selection rules (both IR and Raman) should be a separate section
4. Early on there needs to be a clear statement of the rigid rotor and how it is modified by the effects of centrifugal distortion, Coriolic coupling, hyperfine splitting etc.
5. There does not appear to be any mention of intensities (Boltzmann distribution)
6. I would like to see some spectra, even vibration-rotation spectra would be preferable to none. I've see the vib-rot spectra of CO and CH₄ in the version 13 March. they are not good because the resolution insufficient to show separate lines. HCl might be better as the speparation between lines is greater, making it easier to observe. Incidentally, the ir spectrum of the C-H stretching vibration of methane shows the effect of Coriolis coupling even though the resolution is poor.

How to proceed? Petergans (talk) 12:22, 8 November 2012 (UTC)

Comments on points above

I put a lot of work into editing this back in August but have run out of time and don't expect to be able to do much soon. I welcome other contributors.

1. On the query about the inclusion of C60- I am inclined to agree, it's not entirely appropriate here. I'd be OK with seeing that changed.
2. I agree the page needs a lot of work. A lot of work could be done with the quantum mechanical background, but I'm actually not sure it's useful being here on this page at all. There is anoter separate wikipedia page devoted entirely to the "rigid rotor" and that may be a way to go. I mean, move all the background quantum mechanics, all of it, to a separate page. The existing wikipedia "rigid rotor" page could be useful in this respect. The problem is that it's really impossible to put it all on this rotaitonal spectroscopy page without either cutting corners and writing stuff that's formally incorrect or burdening the page with so much mathematical derivation that it becomes impenetrable and dull to the non-specialist. As an example of cutting corners- strictly speaking there are many centrifugal distortion terms, not just DJ, which is just one term in an expansion. What's here is formally incorrect. The opportunity that would be presented by shifting the theory is that it would be possible to add things about topics that aren't covered here at all. How about something about instruments and/or experimental principles (barely mentioned)? You would currently draw the impression that a researcher doing pure rotational spectroscopy does nothing but maths. Nothing could be further from the truth. Researchers do very difficult experiments, computers usually do the maths. This all begins to look like a big job.
3. There is already one spectrum- Figure 1. I agree it might benefit from more, but please, no ro-vibrational or ro-vibronic spectra. It is worth drawing a distinction between ro-vibrational and pure rotational spectroscopy. There is another wikipedia page on ro-vibrational spectroscopy and the instrumental methods involved are different. I would like to see this page refer only to pure rotational transitions and spectra. It is important not to create confusion by conflating ro-vibrational and pure rotational spectroscopy. As it is currently written, the opening paragraph makes explicitly clear the distinction between pure rotational and ro-vibrational spectra and contains a link to the ro-vibrational spectra page. I can provide more spectra if useful- I have 60 GB worth of these taken in my lab. I just didn't want to clutter the page with more spectra than are strictly needed. Do people want another 1,2,3 or more?
4. Some information about level populations and line intensities (hence Boltzmann populations) is certainly needed here. Ths will be useful in connecting to experimental methods if anything about instruments is eventually added. The great majority of contemporary research involves probing expanding gas samples such that the effective temperature of the sample probed is 1 K (hence maximising the population of low J levels, enhancing sensitivity). It will be difficult to talk about these methods until something is added about populations as a function of T. Much needed.
5. I would be interested in hearing whether people want additional and more accurate information here about experimental methods or are happy with just the broad overview of the field and the underpinning quantum mechanics that is curently presented.

Nnrw (talk) 10:42, 9 November 2012 (UTC)

1. OK, I have now deleted C60. Thanks for the encouragement.
2. Re moving the quantum mechanics (however defined) to another page. OK provided we first ensure that the content deleted from here is actually on another page, with links from here so interested readers can find it. I would oppose deleting first with an intent to put it elsewhere eventually - we are all busy and that might take some time. Dirac66 (talk) 19:06, 9 November 2012 (UTC)

I can suggest that the results of quantum mechanical theory be in this article but the proof or derivation of the expressions be elsewhere, much as it is at present. I'd like to make just 2 further comments on the above. i) Limiting centrifugal distortion to one term is not incorrect, rather, it is a first approximation. ii) the diagram File:Rotational spectrum example.png is inadequate; it seems to show something of an intensity pattern, but without explanation. Petergans (talk) 20:36, 9 November 2012 (UTC)

Yes, most of the "quantum mechanics" in this article consists of results such as simple energy level formulas and selection rules which should be retained as a guide to understanding spectra. The exception (which I would favour removing from this article) is the (second) section on the Asymmetric top which is at a much higher level, based on the "scaled rotational Hamiltonian" and so on. I think all mention of Hamiltonian operators should be removed to another article more closely related to quantum mechanics. Dirac66 (talk) 01:21, 10 November 2012 (UTC)

I agree none of the underpinning theory should be deleted from this page unless there is something authoritative elsewhere. It would indeed be a big job to make it all available and understandable, not one I'm really ready for now. I understand that the centrifugal distortion expression is a first approximation but I think I still feel it is misleading, for the following reason; the relationship is reported as though it were an exact equality. If the accompanying text instead said something along the lines of...."after inclusion of a first-order correction to account for centrifugal distortion....", then I would be much happier. If an expression which is formally an approximation is not labelled as such, then it is incorrect, in my opinion.Nnrw (talk) With the "Rotational Spectrum Example" file, I was aiming to make explicit the connection from transitions between rotational energy levels to the frequencies of transitions that are observed in laboratory spectra. I find that undergraduates don't always immediately understand that transition frequencies are observed in spectra (and not levels directly) and I wanted to help with that. I appreciate the intensities aren't explained. I could add a note to say that transition intensities are a function of temperature (this would be easy, can do if needed) but have the impression that this wasn't the only source of your dissatisfaction. Is there anything else wrong with the figure that you'd like fixed, or which would be a reason to delete it completely? Alternatively, do you think we should put anything else in it's place to make the connection between levels, transitions, and the rotational constant? I'll leave unchanged for now.Nnrw (talk) 18:06, 16 November 2012 (UTC)

Carbon dioxide

I note User:Nnrw's aversion to the inclusion of anything to do with ro-vibrational spectra. What about the case of CO₂? This molecule is centrosymmetric so no pure rotation spectrum can be observed by microwave spectroscopy. However, the ro-vibrational spectrum of the asymmetric stretching vibration is easy to observe at about 2350 cm^-1 in the infrared and can be used to determine rotational constants, gas temperature (e.g. in the atmosphere) etc. Worth inclusion? Methane?Petergans (talk) 14:51, 10 November 2012 (UTC)

I think Nnrw's point is that we have another article on ro-vib spectra, which is called Rovibrational coupling although a better title (I think) would be Rotational-vibrational spectroscopy. That article does need much improvement, but in principle all the ro-vib material could be included there. There is some merit in dividing the two subjects into two articles, since ro-vib uses IR which is a different experimental technique. It also gives slightly different information, such as the rotational constants of the vibrationally excited state. Good point. I've amended the bit on spherical tops accordingly. Petergans (talk) 13:32, 11 November 2012 (UTC) This article is linked to the other one, and we can add more links where appropriate. For methane for example which is a spherical top with no pure rotational spectrum in microwave or IR, we can point out in this article that information is available from ro-vib spectra, but put any further details in the ro-vib article. Dirac66 (talk) 23:36, 10 November 2012 (UTC)

I'm away all next week so I may not be working on this article during that time. Now I have to pack my bag and go to the airport. Petergans (talk) 13:32, 11 November 2012 (UTC)

Dirac66 reports my thoughts about linking to the "ro-vibrational coupling" page exactly. I also agree with the proposal to re-name the "ro-vibrational coupling" page as "ro-vibrational spectroscopy" and will add my own comment to that page to that effect. The other page is even quieter than this one so I guess that change will probably happen.Nnrw (talk) 18:06, 16 November 2012 (UTC)

centrifugal distortion

Please check the formula for line spacing. I think it should be 2B + f(D), but I don't have access to reference books here in Italy. Petergans (talk) 09:04, 15 November 2012 (UTC)

Do you mean v(J'-J") = 2B(J"+1)-4D(J"+1)³? This does follow from the previous equation F(J) = 2B(J"+1) - DJ"²(J"+1)², since ΔJ²(J+1)² = (J"+1)²(J"+2)² - J"²(J"+1)² = (J"+1)²[(J"+2)²-J"²] = (J"+1)²(4J"+4) = 4(J"+1)³. Also Atkins and de Paula agree - 8th edn, p.448. Dirac66 (talk) 20:27, 15 November 2012 (UTC)

Intuitively I see the effect of centrifugal distortion as a deviation from the rigid rotor, that is, the spacing between adjacent lines J and J+1 equal to 2B minus a correction. I'll check my reference books tomorrow after I return home. Petergans (talk) 10:07, 18 November 2012 (UTC)

OK, I have now relabelled this formula which was incorrectly referred to as line spacing. Actually it is the correct formula for line position or line location, or at least the first-order approximation to same as Nnrw has pointed out above in the section Comments on above points. In the Linear molecule section of the article, only the line positions are given in the text, although the equal line spacings (without centrifugal distortion) are mentioned in the Figure caption. Dirac66 (talk) 12:45, 18 November 2012 (UTC)

Dipole selection rule - removal of apparent inconsistency

There is now an apparent inconsistency in the article as to why no spectrum is observed in molecules with no dipole. The intro says that a permanent (non-zero) electric dipole moment is required to have a spectrum, but the spherical top section says that spherical tops have no spectrum because there is no change in dipole moment with rotational quantum number. A reader may wonder why change in dipole is not mentioned in the intro.

I understand that this inconsistency is only apparent, because the statement in the intro refers to a molecular frame of reference in which a dipole is constant (at least in each quantum state), whereas the statement about spherical tops describes the rotation of the dipole vector with the molecule as a change in the lab frame of reference. But this is not mentioned in the article, and I think it would be unnecessarily complicated to explain properly. Instead I will change the language in the spherical top section to conform to the intro. Dirac66 (talk) 23:56, 16 November 2012 (UTC)

Now the new section on Selection rules contains the statement that a change in dipole is required. This is a useful viewpoint in vibrational spectroscopy (IR), but is confusing for rotational spectroscopy since in the molecular frame the dipole is constant. I think it will be simpler to follow Hollas (3rd ed, p.95) and just say that to have a rotational spectrum the molecule must have a permanent dipole.

Similarly for Raman this section now says that the polarizability must change. Hollas (p.111) says that the polarizability must be anisotropic (and therefore in the lab frame, the ellipsoid changes upon rotation). I will make these changes and cite Hollas. Dirac66 (talk) 03:05, 18 December 2012 (UTC)

Asymmetric top section

The section on asymmetric tops seems the most confusing in the article. Some suggestions:

• The notation should conform to the rest of the article. Are $A$ and $B$ the rotational constants defined elsewhere as ${\tilde {A}}$ and ${\tilde {B}}$? And since there is no ${\tilde {C}}$ elsewhere in the article, we should specify that $C$ is defined analogously for the third axis.

• Also the quantum number k should be K. Elsewhere in the article, k is the Boltzmann constant.

• Define what is meant by scaled rotational Hamiltonian and scaled rotational energy levels.

• The banded Hamiltonian is well described, but would still benefit from a diagram.

• Finally, the most difficult sentence (and a half): The Hamiltonian can be formulated in six different settings, dependent on the mapping of the principal axes to lab axes and handedness. For the most asymmetric, right-handed representation, ... This is my preferred candidate for removal, as I have no idea what it means and I suspect it requires long explanations. Dirac66 (talk) 23:09, 18 November 2012 (UTC)

I agree. Hollas states briefly that an eigenvalue problem has to be solved for each J value. As far as I can see, the formulae shown refer to specific cases where the molecular structure is approximately that of a symmetric top. I would delete most of this, but give good citations for the theory, maybe in the microwave books? For illustration the rotational spectrum of water vapour (far infrared) has been studied in detail[ http://dx.doi.org/10.1063/1.1703330 http://dx.doi.org/10.1063/1.1703330]. Petergans (talk) 12:00, 2 December 2012 (UTC)

I'm also in agreement, it doesn't belong here. I would not be in favour of deleting the section entirely- but of moving it to a sub-page and linking to it from the main page. I hope that someone in the future would give some attention to making sure everything on that sub-page is correct. Personally, I would also want to do that with the information for symmetric tops. As the page evolves, I would imagine this would mean we have the best of both worlds. Full mathematical derivations on the sub-pages but an interesting/engaging main page relatively free of maths.Nnrw (talk) 17:18, 2 December 2012 (UTC)

I've reduced the content to an absolute minimum, with a citation that gives the approximate formulae. BTW, if anyone has themselves obtained spectra, it is OK to upload them to WP as "own work" and then display them in the article. Petergans (talk) 12:01, 3 December 2012 (UTC)

Much better now. It is at the same level as the rest, so readers who understand the article can understand this section. Dirac66 (talk) 19:41, 3 December 2012 (UTC)

Comments on own work noted- I would be happy to cite the results I have from a ro-vib. spectrum, and to cite an IR spectrum I have as own work while providing full details, but not to display that same spectrum in the article because of introducing confusion with ro-vib. spectroscopy. WIll do this with the CO spectum when I have a moment.Nnrw (talk) 18:41, 4 December 2012 (UTC)

Incorrect page reference

And one other loose end. In the section Rotational line intensities, the page in Banwell and McCash is given as p. 4P0 (sic). I don't have this book to check so could someone please correct this? (Perhaps try p.400 because the closest digit to P on a keyboard is 0.) Dirac66 (talk) 23:09, 18 November 2012 (UTC)

Corrected. Petergans (talk) 12:01, 20 November 2012 (UTC)

Spherical top

Hollas, "Modern Spectrocopy",3rd. edition, p 103, section 5.2.5, describes how rotation about any 3-fold axis in SiH₄ gives rise to centrifugal distortion and hence a small dipole moment is generated. In fact part of the far ir spectrum (that is, pure rotation spectrum) of SiH₄ is illustrated, Fig. 5.10, from Rosenberg & Ozier, Can. J. Phys., 1974, 52, 575. Maybe this should go in the symmetric rotor section? I must also assume that a similar spectrum has been obseved with methane.

See also Arieh Rosenberg and Irving Ozier J. Chem. Phys. 65, 418 (1976); http://dx.doi.org/10.1063/1.432784 (7 pages)"Collision‐induced absorption of gaseous silane in the far infrared".

More goodies at http://dx.doi.org/10.1139/p75-250 (pdf at http://fermi.uchicago.edu/publications/PDF/oka061.pdf)

Petergans (talk) 16:55, 20 November 2012 (UTC)

Hyperfine interaction

I've removed this section as there is nothing relevant to rotational spectra. Any objections? N.b. I've added nuclear spin statistics to the intensities section. Petergans (talk) 16:25, 27 November 2012 (UTC)

I didn't really like that section, certainly no objection to its removal. On the other hand, we should put something in about hyperfine interactions in the future. Hyperfine interactions are relevant to rotational spectra- each J-J transition in the microwave spectrum of CF3I (see figure at the top of the page) is split by the effects of nuclear quadrupole coupling, for example (the nuclear electric quadrupole moment of a quadrupolar nucleus couples to the overall rotation of the nuclear framework). If we do, I suggest it should just be an explanation of the observed splittings rather than a full derivation. That would be consistent with the other formulae available above for energy levels and transition frequencies. Fine interactions (ie involving electron spin-rotation) are also important but molecules that have these have always been very hard to study so there's less in the literature. Doing so involves correcting for coupling of the unpaired electron spin with the magnetic field of the earth using Helmholtz coils. The described coupling otherwise leads to compicated splitting patterns and hence, very messy observations. Rotational spectroscopy of such radicals is a current research frontier because many radicals are important in the chemistry of the atmosphere. See, for example, Suma et al's paper in Science Vol. 311, pp. 1278 (2006).Nnrw (talk) 11:46, 28 November 2012 (UTC)128.240.229.68 (talk) 11:44, 28 November 2012 (UTC)

Neither Banwell nor Hollas has anything on quadrupole splitting. I found a page on it in Chang, Basic principles of Spectroscopy. He quotes HCN as an example Simmons, James W. (1950). "Microwave Spectrum and Molecular Constants of Hydrogen Cyanide". Phys. Rev. 77: 77–79. doi:10.1103/PhysRev.77.77. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help) for which the quadrupole moment was determined. Petergans (talk) 17:02, 28 November 2012 (UTC)

No problem. I have the book widely regarded as the "bible" of microwave spectroscopy on my desk- "Microwave Molecular Spectra" by Walter L. Gordy and Robert L. Cook. This book has been out of print for a long time, unfortunately. It has a chapter (about 60 pages!) on nuclear hyperfine structure in rotational spectra which I hope, at some point, I can draw upon to put some basic information here. A note on the nuclear spin statistics section fo this page- it currently uses ethyne to illustrate nuclear spin statistics but the problem is, this molecule doesn't have a pure rotational spectrum (as stated further up the page). The description of the spin statistical weights is good as is but can we change this example? Some good alternatives suggested in Gordy and Cook would be NH3, CH3Cl, CH3CCH which are C3v so C3 rotation about the a axis interchanges hydrogens and transition intensities also reflect statistical weight distributions.Nnrw (talk) —Preceding undated comment added 11:20, 29 November 2012 (UTC)

I've put in something on quadrupole splitting, based on Chang. I don't think it's worth putting in much more detail on this topic. I had a vague memory about the intensity alternation in an acetylene spectrum. Now that you mention the absence of a pure rotatio spectrum I realize it must have been in connection with, dare I say it, the ro-vibrational spectrum. Petergans (talk) 12:39, 29 November 2012 (UTC)

If the intensity alternation is observed in ro-vib spectra it should be in that article. But if it is observed in pure rotational Raman spectra it can be mentioned here in the Raman section. We have to check where it is actually observed.

Also we should mention that 3:1 statistical weights are analogous to those of the spin isomers of hydrogen, although that article does not now mention spectroscopy. Dirac66 (talk) 12:57, 29 November 2012 (UTC)

I found "Callomon, J.H. (1957). "HIGH RESOLUTION RAMAN SPECTROSCOPY OF GASES: VIII. ROTATIONAL SPECTRA OF ACETYLENE, DIACETYLENE, DIACETYLENE-d2, AND DIMETHYLACETYLENE". Canadian Journal of Physics. 35 (4): 373–382. doi:10.1139/p57-043. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)". No details in the abstract. I can't see the contents unless I go in to Uni. Petergans (talk) 15:21, 29 November 2012 (UTC)

This title certainly seems promising and I would expect they must have observed the intensity alternation. Boris P. Stoicheff was a top Raman researcher. But my on-line access doesn't seem to work for CJP either, so I would have to talk to a librarian to see the article, not this week I'm afraid. For now we could use one of Nnrw's examples in the microwave section and acetylene in the Raman section, pointing out the similarity of course. Dirac66 (talk) 21:58, 29 November 2012 (UTC)

I've tried to get at that Canadian Journal of Physics paper but I'm not allowed access to it through my university subscription either.Nnrw (talk)

Sorry to bring this up, but Hollas, p157, illustrates a ro-vib. band of acetylene with very clear 1,3 intensity alternation. Please give some more thought to the question of rigorous exclusion of ro-vib spectra. This article is no longer about just microwave spectroscopy. It already has far infrared and Raman bits. Petergans (talk) 22:02, 12 December 2012 (UTC)

I have finally borrowed Hollas, and I agree that this spectrum should be given as an example of intensity alternation. However since it is a ro-vib spectrum, I would place it in that article instead of this one. For this article, we should remove the claim that the [nonexistent] pure microwave spectrum of acetylene shows intensity alternation. And if one of us ever sees the source paper of Callomon and Stoicheff, we can mention the intensity alternation in the Raman spectrum, and add that the ro-vib spectrum shows an analogous phenomenon (and vice versa in that article). Dirac66 (talk) 21:56, 16 December 2012 (UTC)

I propose next to turn my attention to the article Rotational-vibrational spectroscopy which is woefully inadequate. 3 questions. 1) who would like to join in with this idea? 2) I can foresee a more than 5-times expansion. How can this be done such that it will qualify for did you know? 3) can anyone provide good-quality spectra for illustrations? Petergans (talk) 22:02, 12 December 2012 (UTC)

I am interested in that article as well, and will try to help from time to time. But I think the subject is too specialized for the Did you know? feature, which is intended more for general readers. Dirac66 (talk) 21:56, 16 December 2012 (UTC)

Callomon-Stoicheff Raman paper now accessible

I tried again to access the 1957 paper by Callomon and Stoicheff on the Raman spectra of acetylenes which none of us could access in December, and this time I was able to download it. Perhaps the publisher had a technical problem which has been resolved, so that others with university subscriptions can now access this article also.

Anyway I have now read the paper. There is a plate after the second page with the spectra, and the intensity alternation is visible for acetylene and diacetylene, but not really for diacetylene-d₂ and dimethylacetylene. However the text is concerned mostly with determination of bond lengths and does not mention the intensity alternation. Except for a sentence in the final paragraph which says that the resolution of 0.3 cm^-1 corresponds to a certain moment of inertia for molecules having nuclei with spin ≠ 0 and twice this value for nuclei with zero spin. This rather cryptic mention suggests to me that by 1957 the effect of nuclear spin was well known and no longer required detailed explanation. However as a Wikipedia reference for the existence of intensity alternation, I think we need instead a reference which says explicitly that there is intensity alternation in some molecule, and at least briefly relates the alternation to nuclear spin statistics. Dirac66 (talk) 00:31, 8 February 2013 (UTC)

There is an illustration at Rotational-vibrational spectroscopy#Polyatomic linear molecules which shows the intensity variation in C₂H₂ clearly. The separation between adjacent rotational lines is a little less than 1 cm^-1, so the fine structure will not be fully resolved at the resolution quoted by Stoicheff. Certainly I think the effect was old hat by 1957. It's probably all in the old Gerhard Herzberg books, which used to be the standard reference source for this kind of stuff. Petergans (talk) 10:25, 8 February 2013 (UTC)

Bibliography

We currently have both "references" and a "bibliography" at the bottom of this page. The references are pretty comprehensive, I think we can safely delete the entire bibliography for neatness. What do you think???Nnrw (talk) —Preceding undated comment added 16:29, 29 November 2012 (UTC)

I created the bibliography principally for the Banwell and Hollas books as the text contains various references to different pages in these books. The other books are perhaps for "further reading". In that regard, it may be seen that I have removed references to Atkins and de Paula. The problem is that page and section citations are useless because they change with every edition. I have the 8th. edition and the coverage of rotational spectra is excellent. This is a quandary: on the one hand the book is widely available, so it is suitable for further study. On the other hand, specific page citations will only be accurate for specific editions. Petergans (talk) 16:59, 29 November 2012 (UTC)

Please remember that not every reader has access to every book. I agree that the bibliography is useful and should be retained, both the books in the references and the further reading. My library (and perhaps other libraries) does not have Banwell and McCash, whereas Atkins and de Paula is on my personal desk, so it would be useful (for me and perhaps for others) to restore the references to Atkins and de Paula as another possible source of information. My library does have Hollas in 1987 and 1996 editions, but the article's references to the 1976 edition Typo! are still useful to me (even if the page numbers are wrong) because they tell me that the information is in the book, and then I can usually locate it in a few minutes with the help of the book's index. For the same reason I think that references to Atkins and de Paula would be useful even to readers who happen to own an edition different from the one cited. Dirac66 (talk) 19:53, 29 November 2012 (UTC)

I make the distiction between citations used for verification, as per WP policy on verification, and references for further reading and/or understanding. I used Banwell and Hollas for verification (these were the books reccomended on our undergraduate spectroscopy course). I've added Atkins and de Paula to the bibliography, in a way that I hope overcomes the edition problem. Petergans (talk) 09:06, 30 November 2012 (UTC)

OK- fine with me.Nnrw (talk)

Biographies

I am surprised at how few biographical articles there are related to this field. Only Townes if I'm reading correctly. Any suggestions for key researchers who might deserve biographical articles? I would consider doing the necessary research to get articles started. ronningt (talk) 00:02, 30 November 2012 (UTC)

We do also have a good article on C.V. Raman, probably because he did win a Nobel prize. And we have an article on Willis H. Flygare but it is too short and more is needed. Two names that come to mind with no Wikipedia articles now are W.(Walter?) Gordy, mentioned once in the history section and cited twice in the references. Also Takeshi Oka, a Japanese-Canadian in Herzberg's group in Ottawa. I believe both did quite a lot of microwave spectroscopy. And as mentioned above, Boris P. Stoicheff in Raman spectroscopy, but he has an article now. Dirac66 (talk) 01:30, 30 November 2012 (UTC)

The suggestion of Walter Gordy is a good one. The article on Flygare definitely needs expansion. There is a brief wikipedia article on E. Bright Wilson who was certainly a microwave pioneer and must be a leading candidate for a bio. The first measurements of microwave molecular spectra were reported by Brebis Bleaney in 1934. His results were obtained at lower resolution that that which followed and he didn't do as much thereafter as people like Gordy and Townes who were his contemporaries. With respect to microwave spectroscopy, William Klemperer has to be an important person to include from the last 30 years or so. He was amongst the first researchers to show that microwave spectroscopy could be used to study individual van der Waals and hydrogen bonds in isolation. I have now discovered he actually already has a good bio on wikipedia. We should link to it, when we have the right material to connect from. I don't know anything about rotational Raman spectroscopy and will stick to what I know!Nnrw (talk)

Thanks for the suggestions. I agree that Gordy would be a valuable addition, and so I'll work on tracking down some information for his.ronningt (talk) 12:39, 1 December 2012 (UTC)

Sorry- My memory failed with my comment above- Brebis Bleaney didn't do the first study in 1934, that was Cleeton and Williams. The first high resolution stuff using klystron/magnetron sources, right after the Second World War was done simultaneously by Townes and Bleaney (according to Townes in his memoirs, though Bleaney published first as I remember).Nnrw (talk) 17:27, 2 December 2012 (UTC)

Vibration-rotation spectra

I've added this section as a brief mention is essential. I think the present placings of this and the section on effect of vibration on rotation are wrong, so I'll probably include them with quadrupole splitting and Stark effect when I can think of a suitable sub-section title for the 4 topics. Petergans (talk) 10:09, 1 December 2012 (UTC)

OK. I've added the following sentence; "Rotational constants can be reported either as wavenumber in units of cm^-1 or frequency in units of MHz. The former is more appropriate when reporting data for small, light molecules and the latter is most often used by microwave spectroscopists working on larger species but there is no agreed standard." I don't know if this is the most appropriate place for it but some statement on units seems needed. The discussion on instruments is all in MHz/GHz now and that's what I use when reporting data. Most microwave spectroscopists operate between 6 and 18 GHz for practical reasons. If we worked in cm-1, all our rotational constants would be expressed as multiplied by 10^-7 or some similar factor and it's just nicer to work with round numbers. What do you think?Nnrw (talk) I've also added a note to the sentence comparing the rotational constants obtained from IR and microwave to point out that rotational constants obtained from microwave spectroscopy are generally obtained to higher precision.Nnrw (talk)

I've now identified a few problems with the sentence; "For example, carbon monoxide, 12CO, has a vibration frequency of 2143 cm-1 and a rotational constant B of 1.925 cm-1, which compares well with the value of 1.92118 cm-1 obtained by microwave spectroscopy." It is properly and helpfully cited as Banwell and McCash so I looked up the source. The rotational constant is given in Banwell as "B" rather than B_e (the equlibrium constant), or either of the vibrational state-specific B₀ or B₁. These labels are important because this section of the wiki page starts by explaining how rotational constants are affected by vibration and explicitly defines these three parameters. We therefore should use the labels within the article. The data from the microwave experiment isn't the most accurate available figure, it's from a Gordy paper in 1950 (instruments were not as accurate as they are now). A better current figure for a microwave spectroscopy B_e is available through the NIST microwave spectral database (primary source from 1990 is cited from this link within the database); <http://physics.nist.gov/PhysRefData/MolSpec/Diatomic/Html/Tables/CO.html> and is 1.93160(2) cm^-1. The number in brackets is one standard deviation in units of the last sig. fig. (ie a measure of the experimental precision) Banwell's citation to its own source for the IR data is "Miss J. Cook at York University" and not to a publication. Banwell does say though, that the rotational constant is obtained by simply dividing the interval between adjacent lines by 2. That's very crude, and it's neither B₀, B₁ or B_e. The purpose of the sentence on the wiki page is to compare the results of data obtained through infrared spectroscopy with microwave and the problem is that it's giving a very false impression- you can do much better than implied by Banwell. It's possible to extract the ground state B₀, an excited state B₁, calculate B_e and measure a centrifugal distortion constant from an easily-obtained IR spectrum, I regularly mark this exercise for our teaching lab and I have some data to work with. I get a B_e of 1.9316(4) cm^-1 from a typical data set after a more rigorous spectral assignment. This is much closer to the microwave result. The precision of modern spectroscopy is certainly much better than implied by the comparison in Banwell and McCash. Can we either delete the sentence highlighted above or do a comparison from less shaky foundations?Nnrw (talk) —Preceding undated comment added 22:35, 1 December 2012 (UTC)

Do as you think fit, my expertise is in ir and Raman spectroscopy. I kept this bit short so as not to stray too far into the ro-vib territory. The fact that the spectrum is displayed in a book is sufficient for a citation. Petergans (talk) 11:50, 2 December 2012 (UTC)

OK, thanks. I've removed the sentence. I don't think it would be right to cite my own unpublished IR spectrum of CO. I had hoped to find some authoritative and downloadable source of a modern IR spectrum of CO so that I could just update the numbers but the one available from the NIST webbook <http://webbook.nist.gov/cgi/cbook.cgi?ID=C630080&Mask=80#IR-Spec> is similarly old and only has 4 cm-1 resolution so the rotational structure is entirely smoothed out! I'll pick this up again sometime in the hope of restoring the comparison but with some modern data.Nnrw (talk)

Instruments and Methods

I've added a section on "Instruments and Methods" in place of the original "Experimental Determination of the Spectrum". All the information in the original section is subsumed into the new one. I'm not sure exactly what the right title is for the section. I know this will not be a comprehensive list of all experimental methods covered by this page. For example, I don't know the details of how a rotational Raman experiment is conducted. I also havn't said anything specific about mm-wave spectroscopy (components and instruments are somewhat different above 24 GHz in frequency) or about teraherz spectroscopy. I've selected a format that should make it easy for people to add new sections on particular methods as appropriate.Nnrw (talk) Nnrw (talk)

Rotational levels vs Rotational lines

Something occurred to me whilst writing about the instruments. The section labelled "rotational line intensities" was really a discussion of rotational level populations. Temperature is a very important factor behind experimentally-observed spectral line intensities but there are also others. For example, in a FTMW experiment, it's important to ensure the pulse length and power level are optimised for the dipole of the molecule that you wish to observe. In a Balle-Flygare instrument there's also a major effect that comes from the response/performance of the cavity which changes as a function of frequency. In principal, the instrumental response function in CP-FTMW instruments is linear with frequency but it's not always achieved in practice. I have therefore relabelled the section on "rotational line intensities" as "rotational level populations" and made the same alteration in the text a few lines down, and also changing the first sentence in that section. I'm still thinking about whether the reference to line intensities before the part on nuclear spin statistics is correct (can't remember whether the spin statistics affect the level populations or the transition dipole moment and thus line intensities, need to check books).Nnrw (talk)

Your comments about intensities are interesting. A similar thing is observed with Carbon-13 NMR where the pulse length is often shorter than the relaxation time, affecting intensities. I see this as an experimental effect which causes intensities to differ from the "theoretical" values. The relative line intensities shown in the figure are the theoretical intensities, as usually observed in infrared spectra. Petergans (talk) 11:41, 2 December 2012 (UTC)

I think focusing on the theoretical intensities alone is common in this sort of discussion and also appropriate here. It might be worth a note that each experimental technique requires calibration or reference measurements to establish the intensity, but even this might not be needed. I prefer the "rotational line intensities" label since it makes it clear why this section relates to rotational spectroscopy. The line intensities are strongly dependent on the population levels, so the content of the discussion feels appropriate to me. What seems to be missing is a comment linking the intensities to the transition dipole.ronningt (talk) 12:58, 2 December 2012 (UTC)

Historical Overview Section Removed

I felt the first 3 sections of the page needed some rationalising. The "historical overview" section had outlived its purpose- I relocated and reworded almost all the historical material into either "Applications" or the "Absorption Spectroscopy and Stark Modulation" section. Very little material has actually been removed- just the comment about Charles Townes's recollections of RADAR attenuation by water vapour in his memoirs "How the Laser Happened". I'll hope to reinstate the reference at some point because that's a great book. Nnrw (talk)

Re-written lead

This is now more of a summary of the article contents. Anything significant that I may have removed should now go into the appropriate place in the body of the article. Petergans (talk) 15:19, 4 December 2012 (UTC)

That's mostly fine. I've changed the following (1) restored the sentence about molecular rotational motions being quenched in solids or liquids. This is essential because users may be interested to know why there's an FTIR in every teaching lab and an FT-NMR spectrometer in every university but not an FT-MW instrument. Good point, but does not belong in the lead. I've expanded and moved it into overview Petergans (talk) 09:17, 5 December 2012 (UTC)(ii) changed "energy of transition" to "energies of transitions" just because there's usually more than one transition in a spectrum.(iii) changed "centrifugal distortion, quadrupole splitting and Coriolis coupling" to "centrifugal distortion, fine, hyperfine and Coriolis coupling" because this is more correct. Quadrupole splitting is just one example of hyperfine coupling- there's also nuclear spin-rotation. Getting into fine coupling interactions, we have electron spin-rotation, Fermi contact and dipole-dipole interactions, at least. There may be others I don't remember. No need to summarise all of these but we should get the basic elements right (ie fine and hyperfine coupling interactions both important). Coriolis coupling is very rarely observed, hyperfine and fine interactions are often seen and we have to cater for them when analysing spectra. It follows from the above that the current "Quadrupole splitting" section will need to be changed to something else in time that better reflects the full range of hyperfine coupling interactions.Nnrw (talk) 18:24, 4 December 2012 (UTC)

Another point- when saying that microwave spectra "can be measured in absorption or emission", I'm not sure it's wrong, but I'm not sure the statement is exactly right either, it might be slightly misleading (I wouldn't get away with it when writing a paper). Absorption is certainly correct. The problem is the emission I talked about in the instrumental section (which I will rephrase to remove jargon when I have a chance) is spontaneous coherent emission of the entire molecular ensemble, it's a decoherence phenomenon rather than a molecular emission of the sort Einstein describes. Someone who knows about NMR will know what I mean- it's the same principle there. You really can't do a straightforward "traditional emission" experiment in the lab-the reason is that the radiative lifetime of a rotationally-excited state is way too long, so the gas pulse involved in a Balle-Flygare FTMW experiment expires before your molecules emit. Fortunately the timescales involved in the decoherence that can be measured are only microseconds so you can do that experiment. As well, of course, what's picked up by radiotelescopes will be emission in the more traditional sense (ie the opposite of absorption). So like I say, it's not exactly wrong- but I'm not sure "absorption" and "emission" should be counterpoised in that sentence the way they are currently. I admit, unerstanding the whole "spontaneous coherent emission" idea is difficult- I still struggle with it, and the Bloch equations. Nnrw (talk) 18:50, 4 December 2012 (UTC)

I had radioastronomy in mind when I put in emission. Petergans (talk) 19:05, 4 December 2012 (UTC)

Zeeman Effect

There's nothing here about the Zeeman effect yet. This is the effect of a magnetic field on transition frequencies and would be worth including because it's the reason that molecules with unpaired electrons are hard to study by microwave spectroscopy in the lab. Somewhat analogous to the Stark effect. There's already a more detailed page on wikipedia about the Zeeman effect to link to. I imagine we'll get around to this at some point in the future.Nnrw (talk) 18:35, 4 December 2012 (UTC)

212.159.115.44 (talk) 08:51, 13 February 2014 (UTC)== Oxygen?? ==

The atmospheric attenuation of microwaves in dry air with a precipitable water vapor level of 0.001 mm. The downward spikes in the graph correspond to frequencies at which microwaves are absorbed more strongly, such as by oxygen molecules

I found this spectrum in microwave transmission; I've added O₂ to the section on linear molecues. However, this does not explain the spectrum shown here completely since O₂ has magnetic-dipole allowed doublets between ca,. 54 and 66 Ghz and 120 Ghz. Where do the other spikes come from? Petergans (talk) 10:38, 6 December 2012 (UTC)

Perhaps you could ask User:Westeros91 who is listed as the author of this image. Dirac66 (talk) 22:20, 16 December 2012 (UTC)

The explanation of the spectrum as it appears on the page, "Pure rotation spectrum of atmospheric water vapour measured at Mauna Kea (33 cm-1 to 100 cm-1)", differs from that shown to the right. I know nothing about this subject area but the explanation on the page suggests that the spectrum is for water, rather than a spectrum of the mixture of gases present in air which is what I assume it is.

Raman selection rules

The section Selection rules now gives the Raman rule for symmetric tops as

ΔK = 0, ΔJ = 0, ±1, ±2

ΔK ≠ 0, ΔJ = ±2

The reference given is Banwell and McCash, which I do not have. However both Hollas (p.116) and Atkins and de Paula (8th ed, p.449) give only the case ΔK = 0, so I ask that someone recheck Banwell and McCash concerning ΔK ≠ 0. It is my understanding that a ΔK ≠ 0 Raman transition for a symmetric top is forbidden because rotation around the symmetry axis does not change the polarizability. Dirac66 (talk) 22:20, 16 December 2012 (UTC)

You are right. I mis-copied from Banwell&McCash. I hope the corrected text is OK. Petergans (talk) 10:31, 18 December 2012 (UTC)

15N2 Raman spectrum

For linear molecules the Selection rules section correctly gives the Raman rule as ΔJ = 0, ±2. However the Rotational Raman spectroscopy claims that the ¹⁵N₂ spectrum is resolved into P, Q, R, and S branches, referenced to Hollas p.113. But in Hollas the mention of O, P, Q, R and S branches at equation (5.51) refers to a general molecule, not to a linear molecule. For 1he ¹⁵N₂ spectrum in Figure 5.17, all labelled lines are S: S(0), S(10) and S(20) for both Stokes and anti-Stokes series, implying that the intermediate lines are also S - S(1), S(2), S(3), etc. The Q branch for pure rotational spectra is just the Rayleigh line, and there is no mention of P or R branches which would violate the selection rule. So I propose to delete the P and R branches from the discussion of ¹⁵N₂, and just mention the (Stokes and anti-Stokes) S-branches and the Rayleigh line.

Corrected. Petergans (talk) 11:35, 18 December 2012 (UTC)

As for the intensity alternation, we could point out here that an analogous phenomenon is observed in the vib-rot spectrum of acetylene, with a link to the vib-rot article after the point has been included in that article. Dirac66 (talk) 22:59, 16 December 2012 (UTC)

I'm some way along the re-write of the vib-rot article (User:Petergans/sandbox). It's difficult to decide how much to include from pure rotation as there is obviously extensive overlap. It would help if someone could provide original spectra, either pure rotation or vib-rot; the pictures would be much easier to follow than the verbal descriptions that we have to use when there are no pictures.

"is resolved into P, Q, R, and S branches" - this is a typical typo that happens to me these days - the fingers don't do what the brain asks for and the eye does not see the errors. Thank you for your help in spotting the ones that I miss. Petergans (talk) 10:52, 18 December 2012 (UTC)

This article is terrible. Selection rule delta J +-2? LOL

Details are fine, but put in the basic info too. I looked this up to show someone some spectroscopy and laughed very hard. 70.162.46.129 (talk) 06:00, 2 May 2014 (UTC)

Be bold and fix it yourself, this is all produced by volunteers. If you need help with the details of working on Wikipedia, let me know and I can help. SchreiberBike talk 06:49, 2 May 2014 (UTC)

The selection rule ΔJ = ±2 applies to Raman spectroscopy which is a two-photon process, not to absorption of a single microwave photon. This is specified in the article but could perhaps be made clearer.

As for "basic info", could you specify here what you think is missing. If you point out specific gaps in the article, someone else may be willing to fill them. Dirac66 (talk) 13:25, 2 May 2014 (UTC)

I have now divided the Selection rules section into two subsections for microwave (one-photon) and Raman (two-photon) subsections. Dirac66 (talk) 18:27, 4 May 2014 (UTC)

Notational inconsistency for rotational constant

@Petergans: (and other editors)

The notation for rotational constants is inconsistent in this article. There are two obvious ways to harmonize the notation so I will consult before choosing one.

In the sections Overview, Effect of rotation on vibrational spectra, and Rotational line intensities B is the rotational constant in cm^-1, as in the books by Banwell and McCash and by Atkins and de Paula.

However in the sections Linear molecules, Centrifugal distortion and Symmetric top, the rotational constant in cm^-1 is B/hc or ${\bar {B}}$, as in the Article Rigid rotor.

Clearly one article should have one notation for this quantity. My preference would be to follow the spectroscopy books and use B, with a note when we link the Rigid rotor article to say why we have divided by hc. But I will wait a week for other opinions before proceeding.

And after this article is made consistent, we can look at related articles such as Rotational-vibrational spectroscopy and Rotational temperature. Dirac66 (talk) 22:03, 5 April 2015 (UTC)

OK, no response after 8 days so I have changed to B throughout. Dirac66 (talk) 23:54, 13 April 2015 (UTC)

Effect of rotation on vibrational spectra

I do not know who wrote that section and what exactly they tried to convey, but it is mostly wrong. The energy of rotation is not "added to, or subtracted from" the energy of vibration, but is always added. Moreover, two different vibrational states have different rotational constants ($B''$ and $B'$), so their energies are

$T''=G(v'')+B''J''(J''+1),$

$T'=G(v')+B'J'(J'+1),$

and hence the vibration-rotation wavenumbers of transitions are

${\tilde {\nu }}=T'-T''={\tilde {\nu }}_{\text{vib}}+B''J''(J''+1)-B'J'(J'+1)$

with $J'=J''+1$ for the R branch and $J'=J''-1$ for the P branch. The Q branch has $J'=J''$, but since $B'\neq B''$, the rotational energy is still changed, and thus this does not correspond to a "pure vibration". — Mikhail Ryazanov (talk) 05:35, 24 June 2016 (UTC)

This section does need some rewriting. Yes, the energy of rotation is always added to the energy of vibration, but I think the intended meaning is that the rotational energy change can be either positive or negative.

The expression with a single rotational constant is valid for a harmonic oscillator as specified, since the bond length has the same value for all vibrational levels if the oscillator is strictly harmonic, and it is briefly mentioned that the equation is modified in reality for the effects of anharmonicity. However it would probably be more helpful to specify that these effects include the two rotational constants.

Also for a harmonic oscillator (only), the Q-branch does correspond to a purely vibrational transition (though not a pure vibration as stated).

I will rewrite this section to clarify these points. Dirac66 (talk) 19:32, 24 June 2016 (UTC)

OK, I have rewritten the section to correct these errors. There was also confusion between equations for energy levels and for transition energies or wavenumbers, which you implied with your italics although I did not mention the point yesterday. Anyway I think the article has this section correct now - please check. Dirac66 (talk) 01:58, 26 June 2016 (UTC)

Thank you! It looks much better now. Although I think that talking about "rigid rotors" in a section related to vibrations might be confusing. :–) Maybe something like "To a first approximation, the rotation and vibration can be treated as separable, 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 ..." would be clearer?

Regarding energies/wavenumbers, the italics were actually supposed to stress the difference between the energies of the states and the (photon energies)/wavenumbers/frequencies of the transitions. I was using term values, which have the same units as transition wavenumbers (as in the Rydberg–Ritz principle). Spectroscopists often use energies/wavenumbers/frequencies interchangeably (and this article seems to do so), but it might be indeed better to write more strictly. — Mikhail Ryazanov (talk) 10:05, 28 June 2016 (UTC)

Yes, your wording re separability is better so I have now inserted it into the article. As for italics to distinguish energies and wavenumbers, I think it is clearer to just use the words energies and wavenumbers where appropriate. Dirac66 (talk) 17:38, 28 June 2016 (UTC)