Talk:Molecular symmetry

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Some work

I have been making some stylistic rewrites of this article for readability/tone and consistency, and will probably continue to do so. Leave a note if something I do looks or reads silly. Baccyak4H (Yak!) 16:09, 18 October 2007 (UTC)

Overall the article is much improved after your edits. I have made a few (4) more revisions. Dirac66 01:55, 19 October 2007 (UTC)

Thanks for the feedback and the continued improvement. "Matrixes"...  :-) Baccyak4H (Yak!) 02:19, 19 October 2007 (UTC)

• mmmm matrices... even in my native language it is matrices that way so no excuses there. V8rik 21:17, 19 October 2007 (UTC)

Thionyl chloride

In the symmetry groups section I think Thionyl chloride is not planar, please edit — Preceding unsigned comment added by 94.7.221.165 (talk) 12:15, 29 September 2011 (UTC)

Thank you for pointing this out. The word "planar" in the description is misleading as it incorrectly suggests that the molecule is planar. The correct geometry is shown at the article Thionyl chloride. The symmetry group is in fact C_s as the article says, but the mirror plane is the plane which bisects the Cl-S-Cl angle, with one Cl on each side of the plane. I will change the verbal description to read "Mirror plane, no other symmetry". Dirac66 (talk) 12:55, 29 September 2011 (UTC)

Diagrams - further explanation needed

@Project Osprey: The diagrams you have added are well drawn and seem helpful. I expanded the description of the first diagram, and added a link to chirality for the second. What I think is also needed on the second diagram is an explanation of the subscripts R and S on the X and Y groups, please. Are they somehow related to R- and S- enantiomers?? Dirac66 (talk) 03:45, 10 February 2016 (UTC)

I'll be honest and say that I adapted the second diagram from one on the Japanese Wikipedia. My interpretation was that the R- and S- tags do refer to the chirality of those X and Y groups; so that the top middle and right compounds are meso compounds. Would you agree with that? --Project Osprey (talk) 09:31, 10 February 2016 (UTC)

The top middle molecule is meso, but I am not certain about the top right since it has no mirror plane. However in this article, the Symmetry elements section deals with much simpler molecules – the examples given are H₂O, NH₃, XeF₄, SiF₄ and C₂H₆. So I think that examples with chiral substituents may be mystifying to many readers who can follow the discussion on the simpler molecules.

Instead I suggest that we move this diagram down to a new section near the end of the article, perhaps entitled Symmetry and chirality or Symmetry with chiral substituents. This section could include brief definitions and links for terms such as chiral(ity), enantiomer and meso.

I also glanced at the Japanese article with these diagrams which you mention. Although I can read no Japanese, the figures in that article suggest it is about stereochemistry of organic molecules, and not about molecular symmetry as such. Dirac66 (talk) 16:54, 10 February 2016 (UTC)

That seems reasonable, advanced definitions of chirality are based around molecular symmetry, so it could probably do with its own section. I'm pretty sure that inversion centers count, surely mesotartaric acid can have either a mirror plane or an inversion center depending on its conformation. --Project Osprey (talk) 21:44, 10 February 2016 (UTC)

Mistake in the Point Group Chart

Hello, It should be Cn, not C2, in the Point Group Chart at "Two or more C2, n>2?". Also the indices seem inconsistent. Greetings, --Hexapol (talk) 19:41, 4 April 2018 (UTC)

1. Yes, I agree that it should be "Two or more C_n, n>2?", since the groups T_d, I_h and O_h all have several axes which are C₃ or C₄ or C₅.

2. Could you be more specific about why the indices are inconsistent? Drawing a new image is a much bigger job than modifying text, so it would be best to specify all the errors before someone tries to draw a new image.

3. For now I will try to enlarge the image so that it is legible without clicking on it. Dirac66 (talk) 21:06, 4 April 2018 (UTC)

For example it should be "D_∞h" instead of D∞h. The same applies to the point groups C_∞v, O_h, T_d, C_nh, C_nv and S_2n. D_vd should to be changed to D_nd. The point group D_n is missing as it is a copy-paste-error. Different colors or shapes for the point groups and questions could help to make the chart more clear. --Hexapol (talk) 15:17, 7 April 2018 (UTC)

Yes, I agree with your list of specific corrections: the symbols after the first letter of the group names should be subscripts, D_vd should be D_nd, and the group D_n should be added. As for different colors or shapes, we would have to see a specific version to decide if it is an improvement.

So if you have the appropriate drawing software, I encourage you to create a new image. If not, perhaps someone else will see this list of suggestions and draw the image. I unfortunately do not have the required software, so I can only make verbal corrections. Dirac66 (talk) 22:43, 7 April 2018 (UTC)

Two more specific corrections: (1) Every circle with a yes and no coming from it is a question and should have a question mark. (2) There is a question which now leads to D_vd for Yes and n_σv for No. The answers should be D_nd for Yes (as already noted), and D_n for No. So the missing circle for D_n is actually mislabelled as n_σv. Dirac66 (talk) 02:19, 8 April 2018 (UTC)

ChemDraw

For the big table: in my view, ChemDraw images are superior to the images produced by molecular modeling programs. ChemDraw images are just easier to visualize. I sympathize with our wish to impress readers with beautifully colored images; they impress me too. But maybe we should consider one prosaic ChemDraw image per pt group. --Smokefoot (talk) 02:12, 30 March 2021 (UTC)

I agree it is cluttered at present. If by ChemDraw images you mean skeletal formulae, I think they would be a good addition to the table. However I don't think they should replace all the 3D images. The benefit of 3D over skeletal for both novices and experienced chemists is 3D is less abstract. It doesn't require as much mental processing or prior knowledge for a reader to understand what three-dimensional shape is being described, and that is clearly important in this article. --Ben (talk) 18:04, 30 March 2021 (UTC)

New example does not have S₄ symmetry

The latest molecule added may be a nice example of a ChemDraw image, but it is not an example of S₄ symmetry because there are only two equivalent fluorine atoms and not four. For S₄ symmetry we need another F on each benzene ring in the para position relative to the first fluorine.

Also I don't know if either the difluoro or the tetrafluoro version actually exists. The other molecules in the table have links to their Wikipedia articles where the reader can find evidence that the molecules exist. Dirac66 (talk) 15:30, 30 March 2021 (UTC)

(C6H3FO2)2B-Symmetry question

|thumb|S4 symmetry study]]

The tetrafluoride would be T_d, of course.

--Smokefoot (talk) 19:37, 30 March 2021 (UTC)

The diagram of the difluoro molecule is clearer, but I still don't think the molecule has S₄ symmetry. In your new diagram the location of the C₄ axis is clear but the location of the σ plane is not. It should be σ_h for a horizontal plane, meaning perpendicular to the C₄ axis. So you have placed the red F in the correct final position, but the black F should finish below the left-hand benzene ring, i.e. para to where you have actually placed it. But in this location there was no F there initially, so S₄ is not a symmetry operation.

As for my mention of a tetrafluoro molecule, I was referring not to the tetrafluoride CF₄ which is T_d, but rather to the (C6H2F2O2)2B isomer obtained from your difluoro by replacing the two H para to the two F's with two more F's. That would have S4 symmetry, although I have no idea whether the molecule actually exists.

In any case if the correct symmetry of a molecule is not obvious, Wikipedia policy requires that a source be provided. I think the problem is that this molecule is too obscure and complicated, so should not really be in the article with no source for the symmetry. Dirac66 (talk) 20:54, 30 March 2021 (UTC)

Agreed, S₄ pt group is a tricky one, i.e., difficult to see (that's the reason I was editing on it: we encountered an example recently). S₄ is not as bad as T_h or T (no molecular examples given), but tricky.

Now about the location of the plane: All symmetry elements (planes, axes, inv centers) must contain unique atoms. So one knows that the plane goes through boron. Next, we know that S₄ pt group is defined by the S₄ operation (aside from trivial identity operation), and the S₄ operation is defined by C₄ and a orrthoganal plane of symmetry (usually called σ_h). So the σ_h is orthogonal to the C4.

(C₆H₂F₂O₂)₂B^- would be D_2d, I think. Three orthogonal C₂'s--Smokefoot (talk) 21:49, 30 March 2021 (UTC)

An S₄ axis implies that all off-axis atoms are in sets of 4, not 2, so the difluoro molecule cannot have an S₄ axis. Yes, an S₄ operation brings fluorine 1 to the position of fluorine 2, but repeating the operation brings fluorine 2 to a nonexistent fluorine 3 so it is not a true symmetry operation. Therefore the difluoro molecule does not have symmetry S₄ and I will mark it as Citation needed.

For my tetrafluoro suggestion I agree that the symmetry would be D_2d. It does have an S₄ axis but its complete group is D_2d as you say. Therefore I withdraw the suggestion that it be used as an example for the S₄ group.

As for tetraphenylborate, I find it difficult to visualize the drawing in 3 dimensions and I suspect it may be D_2d also. I think it needs a citation too. Dirac66 (talk) 16:18, 31 March 2021 (UTC)

@Benjah-bmm27: Ben can you please look at the species that we are debating. S4 pt group or no. And can you please comment on this assertion "An S₄ axis implies that all off-axis atoms are in sets of 4, not 2..."

Hello, interesting question. My understanding is that an S₄ improper rotation requires a C₄ rotation and a reflection in the plane perpendicular to the C₄ axis. I made a model of your example, Smokefoot, and got a different outcome from the final σ operation, with the non-red fluorine pointing down (not up as in the diagram). I think the molecular after the reflection is non-superimposable on the starting structure (and the molecule is chiral).

Housecroft example

Greenwood & Earnshaw give cyclo-Cl₄B₄N₄R₄ as a molecule in the S₄ point group. Housecroft gives a tetrafluorospiropentane as an example. I found a few more from a quick search using Google Scholar, including tetracyclopropylmethane (QEMJIB from Kozhushkov et al., Angew. Chem. Int. Ed. (2001) 40, 180-183). There's also an S₄ water octamer, coordination nanotubes, ThCp₄ and UCp₄, an In₄L₄ complex and a spirobis(silastannaindacene). --Ben (talk) 19:38, 31 March 2021 (UTC)

OK, basically what Dirac was saying. More pondering tonight! Thanks to you both. --Smokefoot (talk) 19:46, 31 March 2021 (UTC)

Thinking about it, looks like your borate example is C₂, like 1,3-dichloroallene. --Ben (talk) 20:53, 31 March 2021 (UTC)

Thank you both. I think the above diagram of the tetrafluorospiropentane labelled "Housecroft example" is very clear and certainly S₄, so I suggest we use that as the best example of the S₄ group. It would be good to add the complete bibliographic information; I can't find it in my 2nd edition (2005) of Housecroft and Sharpe so perhaps it is in a later edition.

And I'm still uncertain if the tetraphenylborate is C₂ or C_2v because from the diagram I can't make out the exact orientation of the two phenyl on the right side of the diagram. Dirac66 (talk) 00:38, 1 April 2021 (UTC)

Agreed that Housecroft is very clear and better than wrong (always a good idea). It also illustrates that molecular modeling can produce useful images for visualization. The ones that I object to are the spacefilling blobs. I dont like BPh4-. Diff to visualize and its a particular rotamer. --Smokefoot (talk) 02:05, 1 April 2021 (UTC)

The tetrafluorospiropentane example is from Housecroft, C. E.; Sharpe, A. G. (2008). Inorganic Chemistry (3rd ed.). Prentice Hall. pp. 111–112. ISBN 978-0-13-175553-6. --Ben (talk) 09:05, 1 April 2021 (UTC)

Conformation

Isn't it true that point groups are said to be applicable to molecules even if the molecule is not necessarily always in a conformation that has that symmetry, from a strict geometrical point of view? For example, in the article we say that meso-tartaric acid has inversion symmetry. But that's only strictly true if it's in a particular conformation. If it gets twisted this way or that, then it no longer has inversion symmetry, but we can still apply the term to the molecule. I believe the symmetry "up to" conformation is useful in calculating the entropy. Can someone confirm what I'm saying? Can we put something in the article about this? Eric Kvaalen (talk) 19:14, 23 October 2021 (UTC)

The usual point group assignment assumes that the molecule is at its equilibrium geometry corresponding to a potential energy minimum. Asymmetric vibrations lower the symmetry, not only for meso-tartaric acid but even for molecules as simple as water which has an asymmetric stretch, and CO₂ which has a bending vibration as well as an asymmetric stretch. The only molecules with no asymmetric vibrations are diatomic molecules. The article considers the question in the final section on Molecular nonrigidity. Dirac66 (talk) 21:06, 23 October 2021 (UTC)

@Dirac66: Yes, I know all that, and I did see that final section, but I found it a bit arcane. My question is, shouldn't we say near the beginning that we often or usually assign point groups to molecules based on the way moieties are attached to them, not on whether they are geometrically exactly in a conformation that has the symmetry in question. For instance we say that meso-tartaric acid has inversion symmetry, even if it doesn't always, from a geometrical point of view. Here's another example: Let's say there's a compound tetra(chloro-fluoro-methyl)methane. If the chloro-fluoro-methyl groups all have the same chirality, then I think we would say that the molecule has (chiral) tetrahedral symmetry (denoted "T"), even if the side groups at any point in time may not be rotated exactly the same way, and consequently the symmetry elements of T are not in force. (I realize that quantum mechanically we can't really say that the molecule has a particular conformation at a given point in time -- there's a multidimensional wave function obeying the Heisenberg uncertainty principle.) Eric Kvaalen (talk) 05:04, 24 October 2021 (UTC)

Double group?

The last section on Molecular rotation and molecular nonrigidity refers to a "double group". I cannot find the term "double group" defined anywhere on Wikipedia. Searching Wikipedia for an article "double group" leads to a redirect to "space group", but that article does not contain the words "double group". Also it refers to crystal symmetry including translation in space, rather than molecular symmetry about a point. Could someone add (here or elsewhere with a link from here) an explanation of what is meant by a "double group"? Could it be related to a direct product of groups? Dirac66 (talk) 17:57, 5 March 2022 (UTC)

There is a citation (Ref 25) to an article in the Journal of Chemical Physics in that section; the abstract mentioned that a "double group theory" due to Hougen is used to separate "torsional and a-rotational motions." I agree that it does bear some explanation if it's to be mentioned here, currently it's unclear. I can't access the original article to read further. KeeYou Flib (talk) 20:02, 5 March 2022 (UTC)

Actually I just found this; might shed some light. https://www.google.com/books/edition/Chemical_Group_Theory/f8b7ck4NQ8YC?hl=en&gbpv=1&dq=Hougen%27s+double+group+theory&pg=PA158&printsec=frontcover KeeYou Flib (talk) 20:03, 5 March 2022 (UTC)

I see the "double group" also in the context of molecules having half-odd-integer electron spin (usually ions or radicals) such that that rotation by 2π results in negating the wavefunction. The group is twice as big and the character table is extended and has a new operator R for rotation by 2π. I don't understand it well and this book may help: section 7.6 of http://www.matfys.lth.se/education/FYS256/aryasetiawan.pdf. Also I see that Point group#List_of_point_groups speaks of doubling but has little explanation or references; I've want to understand that, and would like to know how these "double groups" are related. –MadeOfAtoms (talk) 01:19, 6 March 2022 (UTC)