Statistical Approaches to Computed Chemical Shifts

Goodman suggests that in attempting to identify the structure of diastereomers, it is not the values of the chemical shifts that matter. Rather, the differences in the chemical shifts of pairs of diastereomers are critical in identifying which one is which. Since the difference in computed chemical shifts of diastereomers will likely mean a cancellation of systematic errors, these differences are likely to be more accurate than the chemical shifts themselves. 

Using Goodman s notation, suppose you have experimental NMR data on diastereomers A and B and the computed NMR shifts for structures a and b. The key is deciding whether A correlates with a or b and the same for B. Goodman proposed three variants on how to compare the chemical shift differences, and we will discuss here the simplest version, called CPI. The difference in the chemical shift of nucleus I between the two diastereomers is 

Goodman shows in a number of examples that CPI and its variants provide measures of when a computed structure s chemical shifts agree with the experimental values. Using Bayes theorem, a confidence level can also be assigned to these CP values. 

Smith and Goodman demonstrate that for a broad range of natural products, the DP4 method does an outstanding job in identifying the correct diastereomer, and an even better job of not misidentifying a wrong structure to the spectrum. Performance is markedly better than using the correlation coefficient or mean absolute error. 

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