DiCE: Diastereomeric in Silico Chiral Elucidation, Expanded DP4

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DiCE: Diastereomeric in-silico Chiral Elucidation, Expanded DP4 Probability Theory Method for Diastereomer and Structural Assignment Dongyue Xin, Paul-James Jones, and Nina C. Gonnella J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.8b00338 • Publication Date (Web): 06 Apr 2018 Downloaded from http://pubs.acs.org on April 8, 2018

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The Journal of Organic Chemistry

1

Title: DiCE: Diastereomeric in-silico Chiral Elucidation, Expanded DP4 Probability Theory Method for Diastereomer and Structural Assignment

Authors: Dongyue Xin1, Paul James Jones2, and Nina C. Gonnella1

1. Material and Analytical Sciences, Boehringer Ingelheim Pharmaceuticals, Inc., Ridgefield, Connecticut, USA. 2. Information Technology, Boehringer Ingelheim Pharmaceuticals, Inc., Ridgefield, Connecticut, USA.

E-mail: [email protected]

ACS Paragon Plus Environment

The Journal of Organic Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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2

Graphical Abstract:


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3 Abstract:

NMR chemical shift prediction at the B3LYP/cc-pVDZ level of theory was used to

develop a highly accurate probability theory algorithm for determination of stereochemistry of diastereomers as well as regiochemistry. DFT-GIAO calculations were performed for each conformer using geometry optimization and a CPCM solvent model. Boltzmann averaged shielding constants were converted to chemical shifts for 1H and

13

C using generalized linear

scaling terms determined in four different solvents for 1H and 13C and extended to 15N in DMSO. The probability theory algorithm DiCE, was based on the DP4 method and developed for 1H, 13

C and

15

N using individual and combined probability data. Chemical shift calculation errors

were fitted to a Student’s t-distribution for 1H and

13

C and normal distribution for

15

application yielded high accuracy for structural assignment with low computational cost.


N. The


Page 4 of 31

4

Introduction:

Stereochemistry is a critical structural element with profound consequences in a compound’s physical and biological properties. There are numerous pharmaceutical examples where stereochemistry significantly affected a molecule’s activity. Compounds such as Zoloft, an antidepressant for major depressive disorders, obsessive-compulsive disorder, panic disorder, and social anxiety disorder has two chiral centers yet only the S,S diastereomer, which has significant activity, is marketed.1 Likewise the antibiotic penicillin has three stereocenters yielding eight possible stereoisomers, yet only the 2S,5R,6R diastereomer has significant antibacterial activity and chloramphenicol, an antibiotic for the treatment for meningitis, cholera, and typhoid fever, shows only the R,R diastereomer is active (Figure 1).2 In addition to compound activity, determining the correct structure, including correct stereochemistry, is essential in protecting intellectual property and avoiding costly patent disputes.3,4 NH (S) (S)

HOOC 2

N (R)

S Cl

OH OH

O

(S)

5

(R)

(R)

6

H R

NH

O2N

O

(R)

HN

O

Cl

Cl

Cl Zoloft

Penicillin

Chloramphenicol

Figure 1. Chemical structures of Zoloft, Penicillin and Chloramphenicol with the active stereochemistry shown. Two powerful technologies for determining stereochemistry of diastereomers include single crystal X-ray and NMR spectroscopy. While X-ray crystallography can unequivocally establish stereochemistry of diastereomers, the technology requires sufficient quantity, purity and solubility of the material as well as the time and resources to grow a diffraction quality crystal.


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5 Nuclear magnetic resonance (NMR) spectroscopy has an advantage over X-ray in that generating a diffraction quality crystal is not needed. This advantage further extends to the ability of NMR technology to analyze compound mixtures where only microgram quantities of material are available. NMR spectroscopy has been applied to solve stereochemistry of diastereomers of rigid systems with well-defined conformational orientation but faces severe challenges in chiral elucidation with compounds having flexible, rotatable bonds. Chemical synthesis in combination with NMR spectroscopy offers an alternate approach to solving diastereomeric structures however a significant amount of time and resources need to be employed in synthesizing multiple stereoisomers. This approach is not practical for structures having multiple stereo centers and many possibilities. The nuclear Overhauser effect (NOE), which is dependent on the through space distance (< 4 Å for small molecules) separating the cross-relaxing nuclei, has been used in determination of relative and in some cases absolute stereochemistry for rigid diastereotopic chemical scaffolds but this approach is not definitive for flexible systems. Conversion of highly flexible molecules to a rigid/cyclic structure has been used with NOE studies to provide chiral elucidation of diastereomers, however such chemical modifications require synthetic resources and thus are dependent on their availability.5 For flexible molecules, NMR methods have been applied to measure long-range heteronuclear coupling constants that can be used to assign relative stereochemistry however in such cases additional comparisons with NOE data, degradation products and synthetic controls have been required.6 Overall significant challenges are associated with use of NMR spectroscopy in elucidation of stereochemistry of diastereomers and readers are referred to the text of Neuhaus and Williamson for a full understanding of the application of NOE data in structural and conformational analysis.7 DP4 is a method that invokes the use of probabilities from differences between DFT-GIAO NMR calculations and experimental NMR data.8 This method is reported to provide successful probabilities for determining stereochemistry of diastereomers for


13

C and 1H when only one


Page 6 of 31

6 experimental data set is available. To augment this process we developed a probability theory process called DiCE (Diastereomeric in-silico Chiral Elucidation) to be compatible with our previously reported chemical shift prediction approach9 performed at the B3LYP/cc-pVDZ level of theory. Calculations used a CPCM solvent model and geometry optimization of each conformer. Generalized linear scaling terms were obtained for four different solvents which contributed to the improved accuracy in chemical shift prediction for 1H and was also extended to

13

C. This process

15

N in DMSO.10 Statistical distribution was evaluated for individual

solvents and generalized for combined solvents when appropriate. The probability theory algorithm was developed for individual solvents as well as combined solvent data. A combined total of 1,745

13

C, 1,133 1H and 182

15

N chemical shift differences were used in the statistical

distribution calculations. This approach was also found to be powerful in identifying regiochemistry for cases where chemical shift prediction yields ambiguous or inconclusive results. Overall, the methods described herein were developed for 1H,

13

C, and

15

N nuclei in

order to strengthen NMR-based structure elucidation of stereochemistry and regiochemistry for organic, bio-organic and pharmaceutically relevant small molecules.

Results and Discussions

In development of DiCE, conformers of each structural candidate were generated with LowModeMD using the Molecular Operating Environment (MOE 2014.09)11 software. Geometry optimization was carried out for the low energy conformers at B3LYP/cc-pVDZ level of theory using a CPCM solvent model as previously described.9,10 DFT-GIAO calculations were performed for geometry-optimized conformers at the same level of theory. Shielding constants were obtained by Boltzmann averaging and then converted to chemical shifts by generalized


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7 linear scaling. This procedure was shown to provide accurate calculated chemical shifts with low computational cost.9 Generalized linear scaling terms could be determined using sets of structurally diverse organic molecules. Shielding constants for selected molecules are calculated, plotted against experimental chemical shifts and analyzed by linear regression. Assuming a large enough data set was used, the resulting linear scaling terms could be generally applicable to other molecules. We have previously reported general linear scaling terms for

13

C in various solvents and for

15

N

in DMSO.9,10 In this study, generalized linear scaling analyses were expanded to 1H chemical shift prediction in four common NMR solvents (Table 1). In most cases, the correlation coefficients R2 are higher than 0.995 and the absolute value of slopes are close to 1, indicating low random error and high reliability of the calculation method.12 13

Table 1. Summary of all general linear scaling terms. Number of Nucleus

Solvent

Slope

Intercept

R2

chemical shifts

13

C9

1

H

15

N10

DMSOa

-0.9770

189.14

0.9986

617

a

-0.9758

188.78

0.9982

422

MeOH

-0.9766

190.59

0.9977

352

MeCN

-0.9705

189.66

0.9988

354

DMSO

-0.9726

31.31

0.9963

351

CHCl3

-1.0089

31.50

0.9948

331

MeOH

-0.9923

31.41

0.9962

218

MeCN

-0.9872

31.36

0.9967

233

DMSO

-0.9776

-126.77

0.9971

182

CHCl3

a. The slight differences from what was previously published are due to the inclusion of more molecules in this study.



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8

DiCE applied a probability theory approach similar to DP48,14, which is based on statistical analysis of calculation errors. Specifically, errors between experimental chemical shifts δexp and calculated chemicals shifts δcalc for a significant number of known molecules are fitted to a probability density function such as normal distribution or Student’s t-distribution and the resulting fitting parameters could be used to calculate the probability of getting specific calculation errors for each candidate structure. A percentage probability PN%(i) of each candidate i being the correct structure based on NMR chemical shift prediction of nucleus N could be further calculated with equation 1.8 In equation 1, F is the cumulative distribution function of either a normal distribution with mean µ and standard deviation σ or a Student’s tdistribution with an additional degrees of freedom parameter ν. These similarities also are found in DP4+8, an alternate approach based on DP4.

% | , , … , =

∏ $1 −

∑( )$[∏$1 −

− , − ! , # "

− , − ! , # ] "

× 100 % (1)

Two unique features distinguish DiCE probability analysis from DP4 and DP4+. The first feature employs the use of generalized linear scaling terms in converting shielding constants to calculated chemical shifts according to δcalc = (intercept – δexp) / slope. Unlike linear scaling within each molecule, as described in DP4 and DP4+, this conversion is not affected by the number of atoms in the molecule. This is especially important when dealing with nuclei which may be underrepresented in the organic molecules of interest. The second feature involves the use of

15

N probabilities in the DiCE calculations. Because nuclei such as 15N are typically not as

prevalent in small organic molecules, linear scaling within the molecule would typically be based on only a few data points which can compromise the chemical shift prediction outcome.


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9 Therefore, generalized linear scaling becomes important for improved accuracy of

15

N chemical

shift prediction and associated calculated probabilities. Our previously reported systematic study of

15

N NMR chemical shift prediction7 provides both an extensive evaluation of relevant nitrogen

types and a generalized linear scaling term for the 15N nucleus. This work set the foundation for the expansion of DiCE to include singular and combined

15

N probabilities. For the combined

probability calculations, introduction of a third nucleus offers an added dimension of accuracy in predicting challenging stereochemistry problems. Overall the aforementioned differences in DiCE calculations have shown an improvement in accuracy over DP4. A simplified equation was developed to calculate the combined probability PDiCE%(i) from all available percentage probabilities of individual nuclei PN%(i) (equation 2; see the Supporting Information for a derivation).

,-.% =

∏ % × 100 % ∑[∏ % ] (2)

To generate the statistical terms, shielding constants were converted to calculated chemical shifts δcalc with generalized linear scaling terms (Table 1) and errors (δexp - δcalc) in each solvent were individually fitted to Student’s t-distribution. Because deviations of the statistical terms for both

13

C and 1H were found to be only marginal in different solvents (Table S1 in Supporting

Information), the calculation errors from all solvents were combined for each nucleus producing universal statistical parameters compatible with all solvents. A total of 1745

13

C and 1133 1H

chemical shifts were fitted to t distributions with Stats module of Scipy15 to obtain mean µ = 0 ppm (as a result of generalized linear scaling process), standard deviations σ = 2.038 ppm (13C) and σ = 0.113 (1H) ppm and degrees of freedom ν = 36.46 (13C) and ν = 3.523 (1H). These statistical parameters, together with the previously published parameters for

15

N10, form the

basis of DiCE probability calculations (Table 2). Compared with DP4 error distributions (dashed



Page 10 of 31

10 curves in Figure 2), the DiCE distributions (solid curves in Figure 2) are narrower, indicating chemical shift calculation method is more accurate in DiCE. Table 2. A summary of DiCE statistical parameters. Number of

Standard

Degrees of

Type of

deviation (σ)

freedom (ν)

distribution

13

C

2.038

36.46

Student’s t

1745

1

H

0.113

3.523

Student’s t

1133

N10

4.78

-

normal

182

Nucleus

15


chemical shifts

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11

Figure 2. Statistical fitting of calculation errors to t distributions for a, 13C (µ = 0 ppm, σ = 2.038 ppm, ν = 36.46) and b, 1H (µ = 0 ppm, σ = 0.113 ppm, ν = 3.523). Fitting curves simulated from DP4 statistical parameters were shown in dashed line for comparison. The performance of DiCE on stereochemistry assignment was evaluated using a set of structurally complex natural products or synthetic intermediates 1 – 15 (Figure 3). These examples were selected due to their unsatisfactory DP4 results and most were also highlighted in the DP4+ study.8,16,17 For each structure, all diastereomer candidates could be obtained by varying the stereochemistry at asterisk-labeled chiral centers. 1H and were calculated for diastereomers with available 1H and

13

13

C DiCE probabilities

C experimental data and then further

combined to generate a single DiCE probability according to equation 2.



Page 12 of 31

12 O

OH O *

Ph

OH HOOC *

*

Ph

O

OH

1a-b8

2a-b8

* 3a-d8 OH

HO O

*

*

* Ph * O 6a-d8

5a-h8

4a-b8 *

O

* * OH

O BzO * OPMB

OH OH OH *

*

O 8a-h8

8

7a-d O

OBn

* * * OH OH

9a-b8

O

O * O

OH O

OH OH *

10a-b16 O

* * Ph

*

11a-d16

*

O O *

13a-b16

O 14a-b16

Ph O

12a-d16 H

O

O *

O

* H 15a-b17

Figure 3. Structures of challenging compounds studied with DP4, DP4+ and DiCE. Stereochemistry was varied at each carbon labeled with an asterisk. Table 3 summarizes

13

C, 1H and combined DiCE performance for 46 diastereomer examples.

The corresponding DP4 and DP4+ values were also included for comparison. Similar to DP4 and DP4+, the DiCE percentage probability values reflect the confidence in the prediction. The prediction results were classified into three arbitrary probability categories as previously reported16. If the probability for the correct diastereomer was higher than 95 %, stereochemistry could be correctly assigned with high confidence and the prediction is considered successful (labeled with +). In cases where the correct diastereomer shows a probability between 50 %


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13 and 95 %, although the correct diastereomer ranks higher than the others, the prediction confidence is marked as successful but moderate to low confidence (?). Otherwise, the prediction is regarded as unsuccessful (-). (see SI for numerical probabilities) Table 3. Comparison of DiCE with DP4 and DP4+a, b. DP4

DP4+c

1a

+

+

1b

-

2a

13

C DiCEc

H DiCE

DiCEd

+

?

+

+

+

?

+

+

+

+

+

+

2b

-

+

+

-

?

3a

-

?

?

-

?

3b

-

+

+

?

+

3c

?

+

+

+

+

3d

?

+

-

-

-

4b

+

+

+

?

+

5a

+

+

?

?

+

5b

-

?

?

-

?

5c

?

+

?

?

5d

+

+

+

?

5e

-

+

?

-

+

5f

+

+

?

?

+

5h

-

?

+

-

+

6a

?

+

-

+

+

6b

-

+

?

-

?

6c

-

+

-

+

+

6d

+

+

+

+

+

7a

-

?

?

-

+

7b

-

+

?

?

+

8a

-

-

?

+

+

8b

?

-

?

-

?

8c

-

-

-

-

-


1

+


Page 14 of 31

14

8d

-

?

-

?

+

8e

-

?

-

-

-

8f

?

?

?

-

+

8g

-

-

-

-

-

8h

-

-

-

-

-

9a

-

+

-

?

?

9b

?

+

+

-

+

10a

-

+

?

?

+

11a

-

+

+

-

+

11b

-

+

-

-

-

11c

-

-

?

?

+

11d

+

+

?

-

?

12a

+

?

-

+

?

12b

?

+

?

?

+

12c

+

+

-

+

+

12d

-

+

-

+

+

13a

+

+

+

+

+

13b

-

+

+

?

+

14a

-

+

+

?

+

15a

+

+

+

?

+

15b

-

?

+

+

+

# of +

12

31

17

11

31

# of ?

8

9

16

16

9

# of -

26

6

13

19

6

a. DP4 and DP4+ data obtained from the original papers Probability for the correct isomer:

+,

8,16,17

or calculated as originally described.

P ≥ 95 %; ?, 95 % > P ≥ 50 % and -, P < 50 %. b. Relevant

experimental data are not available for compounds 4a, 5g, 7c, 7d, 10b, 14b. c. systematic errors

9

were excluded from

13

13

C atoms with known

C DiCE calculation. Details can be found in Supporting 1

Information. d. Combined probabilities using H and

13

C data.


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15 A summary of five different methods was presented at the end of Table 3 and the percentages of entries in each category were shown in Figure 4. Both

13

C DiCE and 1H DiCE appear to

perform better than DP4 in terms of the success rate while

13

effective than 1H DiCE when used alone. Moreover, combining

13

C DiCE seems to be more C and 1H DiCE into a single

DiCE measurement significantly improves the accuracy of the prediction (Figure 4), consistent with the observations in the DP4+ study.16 Of all 46 examples, the combined DiCE calculations could successfully assign the correct stereochemistry for 40 diastereomers, of which 31 were assigned with high confidence (> 95 %) and 9 were assigned with > 75 % probability. This corresponds to a success rate of 87 % for the examples shown in Table 3 while the rate for DP4 is only 43 %. In practice, the success rate could be even better since the examples in this study were already proven to be challenging by DP4.

Figure 4. Percentage of entries within each category for five methods. Catagories: green, successful, P ≥ 95 %; yellow, successful but questionable confidence, 95 % > P ≥ 50 %; red, unsuccessful, P < 50 %.



Page 16 of 31

16 Both DiCE and DP4+ have shown improved performance over DP4, for 1H and

13

C nuclei, in

solving difficult stereochemistry problems.16,17 For this study, both DiCE and DP4+ show overall comparable performance. Specifically, DiCE and DP4+ are largely in agreement but DiCE performs better in cases 5h, 7a, 8a, 8d, 8f, 11c and 15b while DP4+ is superior for entries 2b, 3c, 5c, 6b, 9a, 11b and 11d. Relative to DP4 and DP4+, DiCE has the advantage of using a generalized linear scaling reference which improves accuracy especially for compounds having few atoms. DiCE does not require use of unscaled data and the method used in chemical shift prediction enables high accuracy at low computational cost.9

Case Study 1 Compound 2b was selected to illustrate the difference between generalized linear scaling and linear scaling within each molecule. Experimental data of isomer 2b was compared with the calculated chemical shifts of 2a and 2b converted from shielding constants via two linear scaling methods. Figure 5 shows the calculation errors e = δexp – δcalc of generalized linear scaling conversion (Figure 5a, 5c) and linear scaling within each molecule (Figure 5b, 5d) for 2a and 2b respectively. In each graph, the atoms are ordered according to the chemical shifts with the more downfield atom on the right side of the bar graph (Figure 5a). Mean absolute error (MAE) was calculated in each case to quantify the deviation from experimental data. With generalized linear scaling, the calculated chemical shifts favor the correct diasteromer 2b (Figure 5c, MAE = 1.75 ppm) over 2a (Figure 5a, MAE = 2.17 ppm), which is consistent with a 96 % probability for the correct isomer 2b in

13

C DiCE calculation. However, although the same sets of shielding

constants were analyzed, in the case of linear scaling within the molecule, the incorrect diastereomer 2a (Figure 5b, MAE = 1.15 ppm) shows a better match with the experimental data than 2b (Figure 5d, MAE = 1.92 ppm) yielding a false high probability for incorrect structure 2a.


Page 17 of 31

17 A comparison of Figures 5a and 5c show that application of generalized linear scaling accurately identify 2b as the correct stereoisomer over 2a. Figures 5b and 5d however illustrate how linear scaling within the molecule significantly reduced the MAE for structure 2a while slightly increasing the MAE for 2b, as slopes and intercepts are different for the two structures, leading to an incorrect prediction of 2a. Therefore, real errors caused by incorrectness of the structure might be suppressed or even completely concealed by linear scaling within the molecule. This may consequently skew the probability calculations and lead to high probabilities for incorrect structures in DP4 calculations.

O

OH

7 8

O 6

1

OH 2

2a

10

2a MAE= 2.17 ppm (gls)

15

Downfield

2a MAE= 1.15 ppm (ls)

10

∆δ δ (ppm)

15

4

2b

b 20

a 20

3 5

9

∆δ δ (ppm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5 0 -5

5 0 -5

-10

-10

-15

-15

-20

-20 5 4 2 3 8 7 9 6 1

5 4 2 3 8 7 9 6 1

Position

Position



18

c 20 15

2b MAE= 1.75 ppm (gls)

d 20 15

2b MAE= 1.92 ppm (ls)

10

∆δ δ (ppm)

10

∆δ δ (ppm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 31

5 0 -5

5 0 -5

-10

-10

-15

-15

-20

-20 5 4 2 3 8 7 9 6 1

5 4 2 3 8 7 9 6 1

Position

Position

Figure 5. Deviation of calculated chemical shifts from experimental chemical shifts of 2b. Calculated chemical shifts from: a) 2a with generalized linear scaling (gls), mean absolute error (MAE) = 2.17 ppm; b) 2a with linear scaling within the molecule (ls), MAE = 1.15 ppm; c) 2b with generalized linear scaling (gls), MAE = 1.75 ppm; d) 2b with linear scaling within the molecule (ls), MAE = 1.92 ppm. Given that error distribution varies between structures, the performance of linear scaling within the molecule is likely to be highly dependent on the target molecule. Unlike linear scaling within the molecule, generalized linear scaling has the advantage of not being biased by specific molecules, especially when the number of atoms for the specific nucleus is limited. In addition, in the process of generating the generalized linear scaling terms, systematic errors for certain functional groups could be readily identified, such as heavy halogens Cl and Br in cases of

13

C

calculations9,18 and NH2 groups in 15N calculations10. Since those systematic errors do not follow the same statistical distribution as the other atoms, they have been excluded from probability calculations. Case Study 2


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19 In general DiCE probabilities have yielded impressive results. An example is compound 16 (Figure 6) where four of the five stereo-centers are varied. Experimental data was available for 16a and 16b.19,20 For 16a 1H DiCE (> 99.9 %) performs better than 13C DiCE (84.42 %) however the combined analysis is > 99.9 %. The results for 16b have both

13

C DiCE (99.78 %) and 1H

(99.18 %) predicting the correct stereochemistry with high confidence. This example illustrates the power of DiCE in predicting the correct stereochemistry from a field of 16 complex disastereomers with multiple chiral centers. (Table 4)

O

O * *

O

* *

O

HO

O

O O

HO

OH

O

O

HO

OH

16

OH

16a

16b

Figure 6. Chemical structure of compound 16 (Tricholomalide B) with chiral centers where the stereochemistry was varied marked with an asterisk.

Table 4. 1H and 13C DiCE calculations for compound 16.

16a Isomer

13

C

1

H

16b 13

C + 1H

13

C

1

H

13

C + 1H

16a

84.42

> 99.99

> 99.99

0.00

0.00

0.00

16b

0.00

0.00

0.00

99.78

99.18

> 99.99

16c

0.00

0.00

0.00

0.00

0.00

0.00

16d

0.00

0.00

0.00

0.00

0.00

0.00

16e

0.00

0.00

0.00

0.00

0.00

0.00

16f

0.00

0.00

0.00

0.00

0.00

0.00



Page 20 of 31

20

a.

16g

0.00

0.00

0.00

0.00

0.00

0.00

16h

0.00

0.00

0.00

0.00

0.00

0.00

16i

0.00

0.00

0.00

0.00

0.00

0.00

16j

15.58

0.00

0.00

0.00

0.00

0.00

16k

0.00

0.00

0.00

0.00

0.00

0.00

16l

0.00

0.00

0.00

0.00

0.00

0.00

16m

0.00

0.00

0.00

0.00

0.00

0.00

16n

0.00

0.00

0.00

0.00

0.03

0.00

16o

0.00

0.00

0.00

0.04

0.00

0.00

16p

0.00

0.00

0.00

0.19

0.78

0.00

13

9

C atoms with known systematic errors were excluded from

13

C DiCE calculation. Details can be

found in Supporting Information.

Case Study 3

DiCE could be readily expanded to nuclei other than 1H and combined 1H and

13

C. Based on the fact that

13

C DiCE probabilities are improved over those of a single nucleus, we

explored the inclusion of other nuclei besides 1H and

13

C to further improve the accuracy of the

DiCE probability calculation. In previous work, we systematically investigated

15

N NMR

chemical shift prediction as a useful tool in the structure elucidation of nitrogen-rich molecules such as pharmaceutically relevant compounds and natural products.10 These statistical parameters from the previous study can be readily applied in

15

N DiCE calculations for

combined analysis. As a proof-of-concept study, palau’amine21 17 (Figure 7), a nitrogen-rich polycyclic dimeric pyrrole-imidazole alkaloid natural product, was investigated with multi-nucleus DiCE calculations. Historically, the structure of palau’amine has been revised several times and particularly the relative configurations of the eight stereogenic centers have puzzled the scientific community for almost 15 years.21 The stereochemistry at C12, C17 and C20 appeared


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21 to be especially ambiguous and had the most disagreements in the literature until the final structural revision22 and total synthesis of this natural product23. To test the performance of

DiCE, 1H, 13C and 15N DiCE calculations were performed for eight possible isomers generated by varying the stereochemistry at positions 12, 17 and 20 in dibromopalau’amine 18 (Figure 7) as experimental 15N data is available in the literature for this palau’amine derivative.22

Br

Br H H N N

H H N N

H2N

H2N HO N H HN

N

N

H

Cl H2N 17 Palau'amine

H2N HO N HH HN 20

O

N 12

H2N

N H Cl

O

H

17

H2N 18 Dibromopalau'amine

Figure 7. Structures of Palau’amine 17 and Dibromopalau’amine 18. Of the eight diastereomers, none of the single nucleus DiCE calculations could reliably assign the relative stereochemistry for dibromopalau’amine. In fact, only probability for the correct isomer while 1H and second highest probability structure. Combining

13

C DiCE yielded the highest

15

N DiCE ranked the correct isomer as the

13

C and 1H DiCE could lead to higher tendency

for the correct isomer 18a (12R, 17R, 20R), but even so the probability value is only 76 %, indicating ambiguity in the prediction. However, after the inclusion of

15

N DiCE, the probability

for the correct diastereomer was > 98 % (Table 5). This improved performance may be attributed to the independence of DiCE probabilities for different nuclei. The probabilities for the correct and incorrect diastereomers are comparable to signal and noise. Ideally, noise, if



Page 22 of 31

22 completely random, could be canceled out by averaging more independent measurements while signal would become more prominent in this process. Therefore, the incorporation of the

15

N

DiCE calculation can be highly beneficial for structure elucidation of nitrogen containing compounds.

Table 5. Summary of DiCE probabillities for dibromopalau’amine. Isomer

Stereochemistry

13 13

Ca

(12, 17, 20)

1

15

Na

H

1

H + 13C

C + 1H + 15

N

18a

(R, R, R)

66.17

30.20

16.24

76.87

98.74

18b

(S, R, R)

6.86

5.97

0.02

1.58

0.00

18c

(R, S, R)

8.65

36.09

1.27

12.01

1.21

18d

(S, S, R)

0.01

1.63

82.06

0.00

0.00

18e

(R, R, S)

9.50

26.11

0.07

9.54

0.05

18f

(S, R, S)

0.00

0.00

0.00

0.00

0.00

18g

(R, S, S)

8.81

0.00

0.33

0.00

0.00

18h

(S, S, S)

0.00

0.00

0.00

0.00

0.00

a. Atoms with known systematic errors

9,10

were excluded from DiCE calculation. Details can be found in

Supporting Information.

Case Study 4 Use of

15

N chemical shift DiCE probabilities has also been effective in defining and

corroborating regiochemistry. This has been notably illustrated with oxazoles (Figure 8, 19a, 19b), isoxazoles (Figure 8, 20a, 20b) and oxadiazoles (Figure 8, 21a, 21b). As previously reported10,

15

N chemical shift prediction can be a powerful tool in structure determination.

However such results may be augmented with the application of probabilities especially when the chemical shift differences are within accepted statistical distribution range. Examples given


Page 23 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


23 in Table 6 show that even with molecules having only one nitrogen atom, probabilities may be accurately predicted using DiCE. Notably, compounds 19a and 21b show chemical shift 15

N. The DiCE analysis

differences that fall within an accepted statistical distribution range for

of 19a and 21b supports the correct isomer with ≥ 95% confidence in the structure.

11

NH O

R2

N

R1

R

O

R1

N

R2

O

COOEt

N

Et

N

O

8

R 3

oxazole

R1

2N

N O

2

R

Br

1

R

2N

O

R

20b

F3C

Br N

N 2

O

NH2

20a

R2 N

6

O

isoxazole

R1

7

19b

R

N

N

Ph

R

N

3

19a

R2

O

N

O

2N 1

R

N O

4 2

Ph

N

N

4

O Br

oxadiazole

21a

21b

Figure 8. Numbered chemical structures showing regiochemistry of oxazoles, isoxazoles and oxadiazoles.

Table 6. 15N DiCE probabilities for compounds 19-21. δ Entry

Atom Number

exp

-δ

Correct

calc

(ppm)

10

Incorrect


15

N DiCE Probability (%)

Correct

Incorrect


Page 24 of 31

24 a

19a

19b

20a 20b 21a 21b a. Calculated

15

b

a

b

isomer

isomer

isomer

isomer

3

1.4

9.8

95.0

5.0

3

7.0

17.5

7

1.5

0.7

8

2.2

-19.3

> 99.9

< 0.1

11

-8.4

-7.1

2

1.7

17.1

c

6

-0.4

11.2

> 99.9

< 0.1

2

1.7

12.2

98.5

1.5

2

4.4

-14.8

97.4

4

7.2

2.3

2.6

2

-3.1

-0.9

95.3

4

-0.7

-10.6

4.7

N chemical shifts for the correct isomer. 1

2

b. Calculated values for the regioisomer with swapped R - and R -substituents 10

c. Systematic error correction of -16.5 ppm was applied . This atom was excluded from DiCE calculation.

Comparision of DiCE, DP4 and DP4+. Although the basic protocols for DiCE, DP4 and DP4+ all involve DFT calculations and probability theory calculations, the implementation details and therefore the performance vary significantly. Table 7 lists the differences between DiCE, DP4 and DP4+. In terms of shielding constant calculation, both DP4+ and DiCE applied a solvent model and geometry optimization at the DFT level, which lead to improved accuracy in shielding constant calculations relative to DP4. Another critical step in the process is the conversion of shielding constants to calculated chemical shifts. DiCE applied generalized linear scaling which could readily identify systematic errors for certain functional groups and reduce bias in specific molecules compared with linear scaling within the molecule, a method employed both by DP4 and DP4+. As noted previously, generalized linear scaling has an advantage in improved accuracy over linear scaling within the


Page 25 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25 molecule since it may be applied to molecules where nuclei of interest are sparse. This was notably demonstrated in the ability to expand DiCE to include probability calculations with

15

N

data, yielding significant benefit for structure elucidation of nitrogen-containing compounds. In addition, the generalized linear scaling terms enable widespread application for 1H and four different solvents and for

13

C in

15

N in DMSO. Hence because the process is generalized and the

reference term is not linked to a specific molecule, the procedure may be broadly applied to different compounds. This facilitates the process and allows an element of automation to be incorporated in the method. The general performance of DiCE appears to be better than DP4 and similar to DP4+ for 1H and 13C based on the molecules studied in Table 3. In addition, DiCE was specifically developed for the B3LYP/cc-pVDZ method which we previously reported afforded us accurate predictions at low computational cost.9 Because we use the same method for geometry optimization and shielding constant calculation, this economy in computer time is naturally extended to the DiCE calculations.

Table 7. Comparison of DiCE, DP4 and DP4+.

Solvent model

DP4

DP4+

DiCE

None

PCM

CPCM

None

B3LYP/6-31G*

B3LYP/cc-pVDZ

Geometry optimization at DFT level Shielding constant calculation (GIAO) Use unscaled shift Linear scaling within molecule Generalized linear scaling

B3LYP/6-31G**

mPW1PW91/631+G**

B3LYP/cc-pVDZ

No

Yes

No

Yes

Yes

No

No

No

Yes



Page 26 of 31

26 Systematic error identified and

No

No

Yes

excluded Nuclei Performance for molecules studied

1

H, 13C Fair

1

H, 13C

1

H, 13C, 15N

Good

Good

Conclusions

We developed a probability theory algorithm for 1H,

13

C and

15

N NMR data that

improved the accuracy in prediction of stereochemistry and regiochemistry in cases where only one set of experimental data is available. The algorithm was generated using NMR chemical shift calculations at the B3LYP cc-pVDZ level of theory using geometry optimization and CPCM solvent model. Generalized linear scaling terms calculated for four different solvents had a major impact on predicted accuracy. Improved chemical shift predictions enabled higher level of precision in calculating statistical distribution, standard deviation and degrees of freedom. DiCE was found to be highly successful at making accurate predictions in very challenging diastereomer and regioisomer cases where chemical shift prediction comparisons were ambiguous or inconclusive.

Experimental:

Sample Preparation:

All compounds shown were purchased from Sigma Aldrich,

Matrix Scientific, Enamine, SynChem Inc., Maybridge Inc., or Combi-blocks Inc. NMR


Page 27 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


27

samples were dissolved in approximately 600 µL deuterated solvent and used without further manipulation unless otherwise indicated.

NMR Spectroscopy: NMR spectra were acquired using a Bruker Avance III 600 MHz NMR spectrometer (Bruker-Biospin) operating 600.04 MHz for 1H, 150.88 MHz for

13

C

and 60.8 MHz for 15N and using a 5 mm TXI Z gradient probe. Spectra were acquired at 300 K. One dimensional spectra were obtained using a sweep width of 12 kHz, a relaxation delay of 2.0 sec, an acquisition time of 1.32 s and 32 K data points for 1H NMR spectra; a sweep width of 36 kHz, a relaxation delay of 0.5 sec, an acquisition time of 0.904 s and 65 K data points for

13

C NMR spectra.

1

H and

13

C chemical shift

assignments were referenced to residual solvent peak: chloroform (7.24 ppm, 77.0 ppm), DMSO (2.50 ppm, 39.5 ppm), methanol (3.30 ppm, 49.0 ppm), acetonitrile (1.93 ppm, 1.3 ppm). Chemical shift assignments were made using two dimensional gradient selected Correlated Spectroscopy (1H,1H-gCOSY), rotating frame nuclear Overhauser effect correlation spectroscopy (1H,1H-ROESY),

gradient selected Heteronuclear

Single-Quantum Correlation (1H,13C-gHSQC) and gradient selected Heteronuclear Multiple Bond Correlation (1H,13C-gHMBC) spectra.24-27 ROESY data were collected with a 300-500 ms mixing time. Computational Methods: The procedure used to compute NMR chemical shifts begins with a minimized chemical structure. A conformational search is conducted in the gas phase using the LowModeMD algorithm,28 in the Molecular Operating Environment (MOE 2014.09) software.11 An upper energy limit of 7.0 kcal/mol and an upper



Page 28 of 31

28

conformation limit of 30 produced a computationally tractable number of conformers and an accurate solution. Input files for optimization with quantum mechanical methods were generated and geometry optimizations, calculation of analytical frequencies, and calculation of NMR isotropic shielding constants were performed at the density functional theory level in Gaussian 09, revision D.01.29 The effects of solvation were achieved using the conductor-like polarizable continuum model (CPCM)30 with four different solvents. Isotropic shielding constants were computed for all optimized conformers within 7 kcal/mol of the lowest energy conformer and with no imaginary frequencies. Boltzmannweighting factors for each conformer were determined using the relative free energies obtained from the frequency calculation. The gauge-independent atomic orbital approach31,32 was used for the prediction of NMR isotropic shielding constants, which were converted to chemical shifts by generalized linear scaling after Boltzmann averaging. The functional used in geometry optimizations and GIAO calculations was B3LYP,33,34 with the correlation consistent cc-pVDZ basis set of Dunning.35 DiCE probabilities were calculated with in-house developed program. ASSOCIATED CONTENT: Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Generalized linear scaling plots, statistical parameters in various solvents, derivation of equation 2, DiCE probabilities for compounds 1-15, experimental and calculated chemical shifts for compounds 1-16 and 18.


Page 29 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


29

NOTES: The authors declare no competing financial interests. ACKNOWLEDGMENT: We gratefully acknowledge Mr. David Craska for support in set-up and management of our High Performance Computing resources and Mr. Scot Campbell for assistance with NMR data collection.



Page 30 of 31

30

References:

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DiCE: Diastereomeric in Silico Chiral Elucidation, Expanded DP4

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