How might one distinguish between two acyclic diastereomers other than by X-ray diffraction?

I have a mixture of two racemic diastereomers (R,R and R,S - and their enantiomers), and while I can fairly easily tell with 2D spectra which NMR signals correspond to one molecule and which signals correspond to the other, I can't find any way to tell which molecule is which (the system is acyclic and so rotation is unrestricted). The ratio is not quite 1:1 (I have several samples with slightly different ratios), so if another technique could determine that, say, the R,S compound is the major compound, that would allow me to assign the NMR spectrum.


I'm wrapping up my current project so it probably doesn't matter practically to me, but nevertheless I'm curious: is there any way to tell which is which, by NMR or another method? (Even if I could purify it fully, it's an oil, so XRD isn't on the cards).
I realise the answer is probably just "Obtain enantiopure starting materials and see what compound you get".




It is possible... to a certain extent. Broadly speaking, the strategy is as such:


* calculate the chemical shifts of both diastereomers using DFT
* match them against the experimentally determined chemical shifts for each peak
* use some kind of statistical measure to determine how "confident" you are in the assignment


The calculated shifts of course don't match up 'perfectly' with the experimental shifts; but all things being equal, it is *more likely* that they match up than not, so the statistical measures essentially take into account the error (i.e. experimental shift minus calculated shift) in order to determine which NMR spectrum is likely to be which compound. This technique has been used quite successfully for structure (re-)assignment. In your case, where you have the spectra of both diastereomers and want to match them against only two possibilities, then the statistical measure to use would be 'CP3', see:


* Smith, S. G.; Goodman, J. M. Assigning the Stereochemistry of Pairs of Diastereoisomers Using GIAO NMR Shift Calculation. *J. Org. Chem.* **2009,** *74* (12), 4597–4607. DOI: [10.1021/jo900408d](https://doi.org/10.1021/jo900408d).


The alternative case would be where you have one spectrum only and you don't know which diastereomer it is, in which case you should use 'DP4' (or its derivatives):


* Smith, S. G.; Goodman, J. M. Assigning Stereochemistry to Single Diastereoisomers by GIAO NMR Calculation: The DP4 Probability. *J. Am. Chem. Soc.* **2010,** *132* (37), 12946–12959. DOI: [10.1021/ja105035r](https://doi.org/10.1021/ja105035r).
* (there are many more followup papers on DP4 so please do a literature search if you're interested)


Now, the issue with this is that most of the compounds shown there (and virtually all of the compounds assigned with these methods) is that they are polycyclic or otherwise structurally rigid. The reason for this is fairly obvious: you don't need to worry about (too much) conformational flexibility & hence averaging. So, I'd be wary of naively applying CP3/DP4 to your molecule.




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Generally speaking, I'd say that accurate prediction of NMR shifts for flexible molecules is still an open research question. Essentially, you need to generate an ensemble of conformers, rank them in terms of energy, and then calculate the NMR shifts as an average, weighted by the Boltzmann population $p \propto \exp(-E/k\_\mathrm{B}T)$. I did some research on this in my PhD, and in my experience the main issue here is that getting *sufficiently accurate* energies is very difficult — if you have many conformers which are very close in energy, then you have to get the energies *extremely* accurate, otherwise the relative populations are way off, and you get inaccurate results.


However, there has been progress on this made in recent years. In particular, `crest` (along with `xtb`) is a really good programme for generating conformer ensembles. The energies should not be trusted too much as it uses a relatively low level of theory, but once you have the geometries you can recalculate the energies with something more expensive. <https://github.com/grimme-lab/crest> Here are some more references:


* Wu, J.; Lorenzo, P.; Zhong, S.; Ali, M.; Butts, C. P.; Myers, E. L.; Aggarwal, V. K. Synergy of synthesis, computation and NMR reveals correct baulamycin structures. *Nature* **2017,** *547* (7664), 436–440. DOI: [10.1038/nature23265](https://doi.org/10.1038/nature23265).
* Grimme, S.; Bannwarth, C.; Dohm, S.; Hansen, A.; Pisarek, J.; Pracht, P.; Seibert, J.; Neese, F. Fully Automated Quantum-Chemistry-Based Computation of Spin-Spin-Coupled Nuclear Magnetic Resonance Spectra. *Angew. Chem., Int. Ed.* **2017,** *56* (46), 14763–14769. DOI: [10.1002/anie.201708266](https://doi.org/10.1002/anie.201708266).
* Grimme, S. Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations. *J. Chem. Theory Comput.* **2019,** *15* (5), 2847–2862. DOI: [10.1021/acs.jctc.9b00143](https://doi.org/10.1021/acs.jctc.9b00143).
* Bohle, F.; Grimme, S. Hydrocarbon Macrocycle Conformer Ensembles and
13C-NMR Spectra. *Angew. Chem., Int. Ed.* **2022,** *61* (14) . DOI: [10.1002/anie.202113905](https://doi.org/10.1002/anie.202113905).


I expect that some of these methods are already, or will soon be, implemented in the ORCA suite of programmes. (However, I'm not super up to date; it's been a couple of years since I really looked at computational NMR...)


So, the tools are all there, but I don't think it's a thoroughly proven / tried-and-tested method. If you actually manage to use these to assign your molecule (and get some hard proof using some other analytical method to supplement it), I expect it would be publishable!




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Finally, if your compound has a particularly common structure (for example, if it's a polyketide), it may be possible to use empirical correlations between J-couplings and local stereochemistry to "map out" the stereochemistry along a chain. This is a slightly older, and IMO more crude, method — but it does exist. Some terms to look for are J-based configurational analysis, and Kishi's "universal NMR database".


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If the computational approaches don't give a definite result, the historical approach is to react the mixture with a reagent that is selective for one structure. Without knowing the structures of your compounds, I cannot suggest anything specific, but there are many options. Chiral reagents (particularly enzymes) can even be used to distinguish between enantiomers. In your case, even altering one enantiomer of one of the diastereomers should be sufficient for you to tell which NMR peaks have been affected.


If you are willing to share the structures of the compounds of interest, you may be able to get specific recommendations of reagents to use.


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