A permutation approach to the assignment of the configuration to diastereomeric tetrads by comparison of experimental and ab initio calculated differences in NMR data

Scoring permutations of experimental chemical shift deviations and DFT/GIAO calculated deviations of isotropic shieldings for sets of four diastereomers can help to assign their relative configurations. This method was exercised on a set of diastereomeric Cinchona alkaloid derivatives, where 13C NMR data always identified the proper configuration. The presented approach is also an attempt to quantify the assignment by exclusion.


S2. Manual workflow example
Here the approach is exemplified by conducting the entire process manually and stepwise on the example of three signals assigned to three atoms (C-6, C-7, and C-8) for diastereomeric tetrad 1. For automatic processing, a simple computer program can be implemented, for example see Section S6.

Part A. Initial data
Interpretation of 13 C NMR data for four diastereomers 1a-1d. Assignment of chemical shifts to particular atoms. 24 differently ordered non-repeating assignments of four configurations to four compounds, corresponding to permutations of experimental and DFT data №1 And corresponding data are set together for all atoms and all isomers Selected comparison measure (cf. Table 1 in main text) is calculated to rank all the 24 permutations. In the example below: aggregate overlap Overlap score: 20.0 Overlap score: 9.6 Overlap score: 0.0 Finally the permutations are sorted according to their scores, the highest ranking permutation reflects the assignment predicted by computation 1. IF signs of Δ exp and Δ DFT match add lower value from |Δ exp| and |Δ DFT| 2. Repeat for next item S5

S3. Peripheral discussion
Alternative number of stereocenters (N) and diastereomers N =1: For one varying stereocenter there are can be two diastereomers. The number of permutations (P 2 = 2! = 2) reduces the approach to the method by Goodman and Smith of comparing two isomers (CP3), and offers no advantage. N = 3: For three varying stereocenters and eight possible diastereomers the number of permutations increases significantly (P 8 = 8! = 40320). The method could easily be applied by using the algorithm run by a computer, however both experimental and DFT computed data have to be obtained with very high precision and accuracy which is often unattainable for some compounds. N = 4: For four varying centers and sixteen diastereomers the number of permutation becomes very large (P 16 = 16! = 2 × 10 13 ) to the point of unfeasibility.
Alternative definition of midpoint.
Referencing the data instead of averages of chemical shifts and isotropic shieldings can be done using alternatively the corresponding median values. This approach was considered, because the midpoint is unaffected by the extreme values. However, for the studied compounds 1-7 no advantage of using the median was noted, the correct permutations received slightly worse scores, and separation between two highest rating permutations did not improve. In case of assignments of four possible configurations to three compounds the application of the median had a noticeably lower success ratio. Tables   Table S1. Percentage of correctly identified configuration by highest ranking permutation for sets of three diastereomers of compounds 1-7. This is an expanded version of Table 4 (correl), permutation corresponding to correct assignment is highlighted in green, scores corresponding to best match of the data (highest CP1, CP2, CP3, aggregate overlap, correlation; and lowest RMS deviation and MAE) are highlighted in blue.

S7. Computer program (python) for quick calculation of permutations and their scores
Prerequisites: python 2.7, open source libraries: openpyxl, numpy. Excel file (Book1.xlsx) arranged as in the example below.