# How is bond angle of a molecule measured?

Simply, how are (average?) bond angles for simple (or complex) molecules such as methane or ethene measured (determined)?

I'm guessing that X Ray crystallography can be used to determine bond angles for, well, materials that have a regular crystalline form. However, is there some other technique for determining bond angles in non crystalline molecules?

I have researched on Chemistry SE and on the wider web and I can't find this question addressed - which I find strange as it seems to me an elementary question. Apologies if this question has already been addressed in Chem SE - I just wasn't able to find it using my search terms. I can find many resources about predicting bond angle and none on measuring them.

• One method is rotational spectroscopy: en.wikipedia.org/wiki/Rotational_spectroscopy – Buck Thorn Jul 28 '20 at 19:36
• – Karsten Theis Jul 28 '20 at 19:43
• Also related: chemistry.stackexchange.com/questions/57784/… (I search "X-ray bond angle" on this site). – Karsten Theis Jul 28 '20 at 19:46
• Thanks to both for such quick, relevant and helpful links. @buck if you can post as an answer I will accept. karsten, as you have shown, most of the trick in getting the right answer is asking the right question. In other SEs (ahem , maths, ahem, CS) you get your knees cut off for asking anything other than a perfect question. – Clive Long Jul 28 '20 at 22:17
• Of course for methane, there is no need to measure anything ... ;-) – Karl Jul 28 '20 at 22:28

The most obvious method is single crystal xray crystallography, of course, and for simple molecules, IR and microwave spectroscopy in the gas phase can be used.

For many complex (e.g. bioorganic) molecules, this fails, but there are two (afaik) last hopes to help solve/prove structures if they don´t crystallise and the usual NMR spectroscopy with added computational chemistry is not enough.

1. Single molecule xray diffraction, a very new approach that can only just be done on the one most brilliant xray "laser" source in the world, the XFEL in Hamburg. It cost 1.2 billion euros to build, and this is the "killer" application it is supposed to prove feasible.

2. RDC (residual dipolar coupling) measurements with NMR, a very fancy method where the interesting compound is trapped in an oriented (sort of "stretched") gel. If the molecules of the compound have a preferred orientation in that gel (they usually do, because very few biomolecules are spherical), you observe dipolar splittings in the spectra, which would normally be averaged out due to the free tumbling of the molecules. These couplings can be used to calculate relations between distances and angles between the magnetic field and the direct connecting line between the atoms involved.

No 2 of course relies heavily on additional input from conventional (spectroscopic) methods and computer simulations.

• I tried finding data on 1H-13C NOEs for methane but had a hard time. That should be a pretty good way to obtain bond distances I would think. For simple molecules simulation (I am thinking of RDCs) should not always be necessary, depending on the amount of data. Motional averaging is always an issue, but presumably also for rotational spectroscopy. – Buck Thorn Jul 30 '20 at 21:43
• @BuckThorn interesting thought - AFAIK, heteronuclear NOEs are not all that popular and have mostly focused on abundant nuclei like 1H/19F. Even then, going from a NOE intensity to an actual distance is not trivial; for homonuclear NOEs you need a “reference” peak for which you already know the distance (eg a geminal CH2 which can be accurately calculated computationally). In methane this would not be possible as there is only one 1H/13C NOE. Not sure if anybody’s actually tried doing it on a labelled protein, though. (see eg Craig Butts’ work for the small molecule stuff I mentioned earlier.) – orthocresol Jul 31 '20 at 4:50
• @orthocresol Heteronuclear NOEs are often measured for specific applications in protein NMR and since 13C/15N labelling is commonly performed their measurement has become fairly routine. For something like methane you probably have to go back a half century to find studies in the literature on the determination of its bond length from NMR. The catch is that you have two unknowns, the bond length and the rotational correlation time, but I'm sure it's been done (or rather I'd be extremely surprised if it hasn't). – Buck Thorn Jul 31 '20 at 8:50
• @BuckThorn good to know, thanks. :-) Yes the two unknowns issue is why reference peak is needed in that procedure. Going very offtopic here, but do you happen to know how one might otherwise determine $\tau_c$? – orthocresol Jul 31 '20 at 9:25
• @orthocresol For protons in methane this does not appear to be simple because there are a number of different relaxation mechanisms. A seminal ref is J. Chem. Phys. 39, 552 (1963). It might be complicated even for 13C but I'm still trying to find the relevant ref. – Buck Thorn Jul 31 '20 at 9:51