What procedure should one employ when trying to determine a chemical structure from an NMR spectrum? I have discussed a number of such examples in the past, most recently the procedure by Goodman for dealing with the situation where one has the experimental spectra of 2 diastereomers and you are trying to identify the structures of this pair.^{1} Now, Goodman provides an extension for the situation where you have a single experimental NMR spectrum and you are trying to determine which of a number of diasteromeric structures best accounts for this spectrum.^{2} Not only does this prescription provide a means for identifying the best structure, it also provides a confidence level.

The method, called DP4, works as follows. First, perform an MM conformational search of every diastereomer. Select the conformations within 10 kJ of the global minimum and compute the ^{13}C and ^{1}H NMR chemical shifts at B3LYP/6->31G(d,p) – note no reoptimizations! Then compute the Boltzmann weighted average chemical shift. Scale these shifts against the experimental values. You’re now ready to apply the DP4 method. Compute the error in each chemical shift. Determine the probability of this error using the Student’s *t* test (with mean, standard deviation, and degrees of freedom as found using their database of over 1700 ^{13}C and over 1700 ^{1}H chemical shifts). Lastly, the DP4 probability is computed as the product of these probabilities divided by the sum of the product of the probabilities over all possible diastereomers. This process is not particularly difficult and Goodman provides a Java applet to perform the DP4 computation for you!

In the paper Smith and Goodman demonstrate that in identifying structures for a broad range of natural products, the DP4 method does an outstanding job at identifying the correct diastereomer, and an even better job of not misidentifying a wrong structure to the spectrum. Performance is markedly better than the typical procedures used, like using the correlation coefficient or mean absolute error. I would strongly encourage those people utilizing computed NMR spectra for identifying chemical structures to considering employing the DP4 method – the computational method is not particularly computer-intensive and the quality of the results is truly impressive.

Afternote: David Bradley has a nice post on this paper, including some comments from Goodman.

### References

(1) Smith, S. G.; Goodman, J. M., "Assigning the Stereochemistry of Pairs of Diastereoisomers Using GIAO NMR Shift Calculation," *J. Org. Chem.*, **2009**, *74*, 4597-4607, DOI: 10.1021/jo900408d

(2) Smith, S. G.; Goodman, J. M., "Assigning Stereochemistry to Single Diastereoisomers by GIAO NMR Calculation: The DP4 Probability," *J. Am. Chem. Soc.*, **2010**, *132*, 12946-12959, DOI: 10.1021/ja105035r

Computational Organic Chemistry » cyclopenta[b]benzofuran – stereochemistry and mechanism of formation responded on 23 Aug 2011 at 3:11 pm

#[...] error is found for 4d. Better still, is that these authors utilized the DP4 method of Goodman3 (see this post), which finds that 4d agrees with the experiment with 100% [...]

Computational Organic Chemistry » Computed NMR spectra predicts the structure of Nobilisitine A responded on 01 Dec 2011 at 8:49 am

#[...] where you have an experimental spectrum and a number of potential diastereomeric structures. (See this post for a discussion of the DP4 method.)The DP4 analysis suggests that 2 is the correct structure with a probability of [...]

Computational Organic Chemistry » Welwitindolinones structure responded on 03 Mar 2012 at 2:42 pm

#[...] of 2 is 0.08 ppm but 0.36ppm for the R epimer. As a check of these results, DP4 analysis3 (see this post) of 2 indicated a 100% probability for the S epimer using only the proton chemical shifts or with [...]

Alan Shusterman responded on 02 Apr 2012 at 3:54 pm

#The DP4 method has to be taken with a grain of salt at this point in time.

First, I was unable to reproduce the list of (13C) “scaled shifts” for compd 15A, Nankakurine A in Smith and Goodman 2010, Table 2, *using the formula supplied by Smith and Goodman*. I communicated these results to Prof. Goodman in early February 2012, but the issue remains unresolved. Until my error, if it exists, is identified, I have to assume that the error lies in the published procedure and the procedure is *currently* unusable as published.

Second, DP4 method relies on several questionable assumptions about the distributions of errors, the parameters associated with this distribution, and the calculation of “probabilities” from this distribution. Therefore, one use caution in how one refers to the numerical values that DP4 assigns to probabilities. When DP4 assigns “100% probability” to a structure assignment, this does not necessarily guarantee certainty. It just means that the DP4 probability (and not even necessarily the true probability) for this structure assignment is higher than one with a lower DP4 probability value.