Chemistry—A European Journal
Supporting Information

Poly-g-S-perillyl-l-glutamate and Poly-g-S-perillyl-d-glutamate:
Diastereomeric Alignment Media Used for the Investigation of the
Alignment Process

Marcel Alcaraz Janßen and Christina M. Thiele*[a]

License: CC BY-NC-ND 4.0 International - Creative Commons, Attribution - NonCommercial - NoDerivatives

http://orcid.org/0000-0001-7876-536X
http://orcid.org/0000-0001-7876-536X
http://orcid.org/0000-0001-7876-536X
https://creativecommons.org/licenses/by-nc-nd/4.0/


1. Gel permeation chromatography (GPC) 

GPC measurements were performed using a PSS SDV THF analytical linear XL column and 
a PSS SDV 5 µm precolumn. The detector used was a RI-2031 plus from JASCO. The 
following JASCO devices were used additionally PU-2086 Plus (pump), AS-2055 Plus 
(sampler) and CO-2060 Plus (oven). The chromatography was done at 25 °C oven 
temperature and a flow rate of 1 ml/min. Tetrahydrofuran with 0.1 % w/w 
tetrabutylammonium bromide (TBAB) was used as eluent. The polymer samples were 
prepared at a concentration of 1 mg/ml in the eluent with 0.1 % w/w toluene as internal 
standard. Calibration was done using polystyrene standards. All samples were filtered prior 
to injection, using 0.45 µm PTFE syringe filters. 

2. Circular dichroism spectroscopy (CD) 

Circular dichroism spectroscopy was performed on a JASCO J-1500 spectrometer. The 
polymers were dissolved in 1,1,2,2-tetrachloroethane at a concentration of 1 % w/w. A 
0.01 mm rectangular quartz glass cuvette in combination with a cell holder for cell type 106 
(Hellma Analytics) was used for the measurements in TCE. Additionally, the polymers were 
dissolved and measured in THF at a concentration of 1 mg/ml. The measurements with THF 
were performed using a 1 mm rectangular quartz glass cuvette (Hellma Analytics). Ten 
spectra were recorded for each sample. The resulting curves were averaged and the 
resulting standard deviation is displayed as error bar. The molar ellipticity ([θ]) was calculated 
from millidegrees (m°) using the expression [θ] = m°*M/(10*d*c), where M is the molecular 
weight of the repeating unit, c is the concentration and d is the path length. 

 

Figure 2.1: CD-spectra of poly-γ-S-perillyl-L-glutamate (black), poly-γ-S-perillyl-D-glutamate 
(blue) and a 1:1 mixture (red) of them in THF. 

  



3. NMR sample preparation and general NMR information 

The analytes (+)- and (-)-β-pinene and (+)- and (-)-IPC were purchased from Sigma Aldrich. 
(+)- and (-)-β-pinene and (-)-IPC were used as received. (+)-IPC was sublimated prior to use. 
CDCl3 was purchased form Sigma Aldrich and distilled over CaH2 before use.  

The anisotropic NMR samples were prepared by weighing the polymers and the appropriate 
analytes directly into 5 mm NMR tubes. Additionally, the desired amount of solvent was 
added. Acetone-d6 capillaries were added to each sample to provide an isotropic lock signal, 
which was also used for chemical shift referencing. The samples were centrifuged (800 rpm) 
and turned back and forth to ensure homogeneity. The homogeneity was additionally 
checked by 2H-imaging[1]. Quadrupolar splittings of the solvent signal were determined with 
2H-spectra. The compositions of the different samples used are given below. The β-pinene 
samples were used for measurements on different days and therefore refilled and 
homogenized to ensure the same concentration. 

All measurements within RDC analysis were performed at 300 K on a 700 MHz spectrometer 
(Bruker AVANCE III HD with a QCI cryo probe (1H/19F-31P/13C/15N/2H) with z-gradient and a 
BCU-II preconditioner). 

The scalar coupling constants (1JCH) as well as the total coupling constants (1TCH) were 
extracted from CLIP-HSQC-spectra[2]. These were recorded with 8192 data points in the 
direct dimension and 512 data points in the indirect dimension (NS=4, DS=32). The spectral 
width was set to 10.0 ppm (O2=2.0 ppm) in the direct dimension and 35.0 ppm 
(O1=32.5 ppm) in the indirect dimension. The INEPT delay was optimized for a coupling 
constant (1JCH) of 145 Hz. Zero filling was applied to 16384 data points in the direct 
dimension and to 1024 data points in the indirect dimension. Multiplication with a squared 
sine bell function (SSB=2) was done in both dimensions prior to Fourier transformation. 

The scalar coupling constants (nJHH) as well as the total coupling constants (nTHH) were 
extracted from non-pure shift 2D TSE-PSYCHEDELIC spectra[3,4]. These were recorded with 
8192 data points in the direct dimension and 128 or 256 data points (resulting in the same 
FID resolution of 0.78 Hz) in the indirect dimension (NS=16, DS=16). The spectral width was 
set to 8.5 ppm (O2=3 ppm) in the direct dimension and to 50 Hz or 100 Hz in the indirect 
dimension. Selective refocusing was done using RSnob[5] 180° pulses with a duration of 
58.3 ms (40Hz bandwidth). The selective offsets were set according to the desired protons 
(H1, H3a, H3s, H5, H7a and H10s). The bandwidth for the pulse shape used for selective 
refocusing was calculated with the Bruker Shape Tool of TopSpin 3.5 using the option 
“calculate bandwidth for refocusing –My”. Zero filling was applied to 16384 data points in the 
direct dimension and to 256 or 512 data points in the indirect dimension. Exponential 
(LB=0.3 Hz) and Gaussian (LB=-1.5 Hz, GB=0.5) window functions were applied for the 
direct and indirect dimension, respectively. If the same couplings were accessible in different 
spectra the corresponding mean is given. 

The signs of the scalar coupling constants (nJHH) and the signs of the total coupling constants 
(nTHH) were determined with COSY based spectra[4] and P.E.HSQMBC spectra[6]. The results 
from the P.E.HSQMBC spectra were used as starting point for the relative results from the 
the COSY based spectra. P.E.HSQMBC spectra were recorded with 4096 data points in the 
direct dimension and 256 data points in the indirect dimension (NS=16 (isotropic sample) or 
32 (anisotropic samples), DS=32). The spectral width was set to 6.0 ppm (O2=2 ppm) in the 
direct dimension and to 165 ppm (O2=80 ppm) in the indirect dimension. The INEPT delay 



was optimized for a long range coupling constant (nJCH) of 8 Hz. The delay in the G-BIRD 
element was optimized for a coupling constant (1JCH) of 145 Hz. A k-factor of 4 was used for 
1JCH-scaling. Selective refocusing during INEPT was done using RSnob[5] 180° pulses with a 
duration of 58.3 ms (40Hz bandwidth). The selective offsets were set according to the 
desired protons (H1, H3a, H3s, H5, H7a, H7s, H10a and H10s). The bandwidth for the pulse 
shape used for selective refocusing was calculated with the Bruker Shape Tool of TopSpin 
3.5 using the option “calculate bandwidth for refocusing –My”. Zero filling was applied to 
8192 data points in the direct dimension and to 512 data points in the indirect dimension. 
Multiplication with a squared sine bell function (SSB=2) was done in both dimensions prior to 
Fourier transformation. The COSY based spectra[4] were recorded with 4096 or 8192 data 
points (resulting both in a FID resolution of about 0.8 Hz) in the direct and 256 or 512 data 
points (resulting both in a FID resolution of about 13 Hz) in the indirect dimension (NS=8 or 
16, DS=32). The spectral width was set to 2.5 ppm (O2=0.8 ppm) or 4.6 ppm (O2=1.7 ppm) 
in the direct dimension and to 2.5 ppm (O2=0.8 ppm) or 4.6 ppm (O1=1.7 ppm) in the indirect 
dimension. A J scaling factor of 2 was applied. Selective refocusing was done using RSnob[5] 
180° pulses with a duration of 58.3 ms (40Hz bandwidth). The bandwidth for the pulse shape 
used for selective refocusing was calculated with the Bruker Shape Tool of TopSpin 3.5 
using the option “calculate bandwidth for refocusing –My”. The selective offsets were set 
according to the desired protons (H1, H3a, H5, H7a and H7s (anisotropic); H1, H3a and H7s 
(isotropic)). Zero filling was applied to 8192 or 16384 data points in the direct dimension and 
to 512 or 1024 data points in the indirect dimension. Gaussian (LB=-1.0Hz, GB0.35) and 
squared sine bell (SSB=2) window functions were applied to the direct and indirect 
dimension, respectively. 

In the case of the methyl groups, 1DCC RDCs were calculated from 1DCH RDCs according to 
the literature[7]. The descriptors a (antiperiplanar) and s (synperiplanar) describe the 
orientation of the diastereotopic protons relative to the dimethyl bridges. 

Calculations were done using the software RDC@hotFCHT[8,9]. The same structural models 
of the analytes as before were used[10]. The quality of the correlation of experimental and 
back-calculated RDCs is given by the RMSD (root-mean-square deviation), the Q-factor[11], 
the Q-Da[12] and the q-Baltzar[13]. Calculations for IPC as solute were done with error 
weighting of RDCs. Calculations for β-pinene as solute were done without error weighting of 
RDCs to avoid overestimation of HH RDCs. 

The signal assignment of the synthesized compounds was done using HSQC, HMBC and 
COSY experiments. 

   



4. IPC data 

Table 4.1: Data of the IPC samples. 

polymer m(polymer) 
[g] 

w(polymer) 
[%w/w] 

analyte m(analyte) 
[g] 

solvent 

PSPLG[a] 0.0593 10.5 (+)-IPC 0.0149 CDCl3 
PSPLG[a] 0.0597 10.6 (-)-IPC 0.0148 CDCl3 
PSPDG[a] 0.0580 10.6 (+)-IPC 0.0148 CDCl3 
PSPDG[a] 0.0579 10.5 (-)-IPC 0.0148 CDCl3 
PSPDG[b]/ 
PSPLG[b] (1:1) 

0.0295+0.0295 10.3 (+)-IPC 0.0143 CDCl3 

PSPDG[b]/ 
PSPLG[b] (1:1) 

0.0296+0.0296 10.3 (-)-IPC 0.0147 CDCl3 

[a] batch 1 [b] batch 2 

 

 

Table 4.2: Extracted isotropic coupling constants (1JCH) for (-)-IPC in CDCl3. 

coupling pair  1JCH [Hz] error [Hz] 

C10-H10 124.82 0.11 
C9-H9 123.67 0.10 
C8-H8 124.69 0.12 
C7-H7s 135.27 0.36 
C7-H7a 136.95 0.26 
C3-H3 142.02 0.18 
C4-H4s 126.73 0.40 
C4-H4a 126.94 0.30 
C5-H5 141.61 0.34 
C2-H2 126.64 0.40 
C1-H1 141.35 0.31 

 

  



 

Figure 4.1: CLIP-HSQC[2] spectra (700M Hz, 300 K) of (-)-IPC in an anisotropic phases of 
PSPLG/CDCl3 (green, 10.6 % w/w), PSPDG/CDCl3 (red, 10.5 % w/w), 
PSPLG/PSPDG(1:1)/CDCl3 (blue, 10.3 % w/w) and (-)-IPC in CDCl3 (black). The descriptors 
a (antiperiplanar) and s (synperiplanar) describe the orientation of the diastereotopic protons 
relative to the dimethyl bridge. Chemical shift referencing was done with respect to the 
isotropic measurement. The spectra from anisotropic measurements are shifted in order to 
obtain the stacked plot 

  



Table 4.3: Extracted coupling constants (1TCH) for (+)-IPC in PSPLG/CDCl3 (10.5% w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C10-H10 123.25 0.32 -0.79 0.22 
C9-H9 118.83 0.31 -2.42 0.21 
C8-H8 131.37 0.75 3.34 0.44 
C7-H7s 139.29 1.85 2.01 1.11 
C7-H7a 103.21 0.45 -16.87 0.35 
C3-H3 161.54 0.31 9.76 0.25 
C4-H4s 147.44 0.49 10.35 0.45 
C4-H4a 115.64 0.45 -5.65 0.37 
C5-H5 141.44 0.56 -0.09 0.45 
C2-H2 114.80 4.00 -5.92 2.20 
C1-H1 162.56 4.31 10.61 2.31 
C2-C10   0.22 0.06 
C6-C8   -0.91 0.12 
C6-C9   0.66 0.06 

 

Table 4.4: Extracted coupling constants (1TCH) for (-)-IPC in PSPLG/CDCl3 (10.6% w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C10-H10 123.00 0.20 -0.91 0.16 
C9-H9 119.73 0.26 -1.97 0.18 
C8-H8 125.87 0.74 0.59 0.43 
C7-H7s 163.33 1.36 14.03 0.86 
C7-H7a 100.90 0.47 -18.03 0.36 
C3-H3 159.55 0.28 8.77 0.23 
C4-H4s 132.04 0.56 2.66 0.48 
C4-H4a 110.29 0.34 -8.33 0.32 
C5-H5 138.21 0.62 -1.70 0.48 
C2-H2 101.70 0.79 -12.47 0.60 
C1-H1 156.53 4.00 7.59 2.16 
C2-C10   0.25 0.04 
C6-C8   -0.16 0.12 
C6-C9   0.54 0.05 

 

   



Table 4.5: Extracted coupling constants (1TCH) for (+)-IPC in PSPDG/CDCl3 (10.6% w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C10-H10 122.66 0.33 -1.08 0.22 
C9-H9 120.16 0.77 -1.75 0.44 
C8-H8 126.73 0.38 1.02 0.25 
C7-H7s 163.52 1.10 14.13 0.73 
C7-H7a 96.66 0.51 -20.14 0.38 
C3-H3 163.14 0.51 10.56 0.34 
C4-H4s 134.63 0.69 3.95 0.55 
C4-H4a 109.16 0.58 -8.89 0.44 
C5-H5 138.37 0.43 -1.62 0.38 
C2-H2 101.51 0.81 -12.56 0.61 
C1-H1 157.21 4.00 7.93 2.16 
C2-C10   0.30 0.06 
C6-C8   -0.28 0.07 
C6-C9   0.48 0.12 

 

Table 4.6: Extracted coupling constants (1TCH) for (-)-IPC in PSPDG/CDCl3 (10.5% w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C10-H10 123.69 0.17 -0.57 0.14 
C9-H9 119.43 1.16 -2.12 0.63 
C8-H8 132.02 0.53 3.66 0.33 
C7-H7s 138.62 1.30 1.67 0.83 
C7-H7a 102.50 0.67 -17.23 0.47 
C3-H3 161.99 0.44 9.99 0.31 
C4-H4s 149.85 0.43 11.56 0.41 
C4-H4a 115.51 0.38 -5.72 0.34 
C5-H5 141.91 0.40 0.15 0.37 
C2-H2 116.77 1.91 -4.94 1.16 
C1-H1 161.94 4.00 10.30 2.16 
C2-C10   0.16 0.04 
C6-C8   -1.00 0.09 
C6-C9   0.58 0.17 

 

   



Table 4.7: Extracted coupling constants (1TCH) for (+)-IPC in PSPLG/PSPDG(1:1)/CDCl3 
(10.3% w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C10-H10 123.11 0.51 -0.86 0.31 
C9-H9 119.69 0.54 -1.99 0.32 
C8-H8 127.23 0.38 1.27 0.25 
C7-H7s 151.10 1.32 7.91 0.84 
C7-H7a 107.45 0.47 -14.75 0.37 
C3-H3 157.12 0.53 7.55 0.36 
C4-H4s 137.07 0.80 5.17 0.60 
C4-H4a 114.79 0.44 -6.07 0.37 
C5-H5 139.18 1.00 -1.21 0.67 
C2-H2 110.18 1.31 -8.23 0.85 
C1-H1 157.02 1.19 7.83 0.75 
C2-C10   0.23 0.08 
C6-C8   -0.35 0.07 
C6-C9   0.55 0.09 

 

Table 4.8: Extracted coupling constants (1TCH) for (-)-IPC in PSPLG/PSPDG(1:1)/CDCl3 
(10.3% w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C10-H10 123.34 0.44 -0.7 0.3 
C9-H9 120.86 0.42 -1.4 0.3 
C8-H8 126.67 0.45 1.0 0.3 
C7-H7s 150.21 1.18 7.47 0.77 
C7-H7a 108.44 0.58 -14.26 0.42 
C3-H3 156.43 0.38 7.21 0.28 
C4-H4s 137.23 0.87 5.25 0.64 
C4-H4a 114.84 0.46 -6.05 0.38 
C5-H5 139.20 0.88 -1.20 0.61 
C2-H2 111.15 1.26 -7.74 0.83 
C1-H1 157.46 1.91 8.05 1.11 
C2-C10   0.20 0.08 
C6-C8   -0.27 0.08 
C6-C9   0.39 0.07 

 

   



Table 4.9: Orientational properties of IPC in PSPLG/CDCl3. 

 (+)-IPC (-)-IPC 

number of RDCs 11 11 
|∆vQ| [Hz] 134 139 
RMSD [Hz] 0.7097 0.4032 
Q-factor 0.0908 0.0448 
Q-Da 0.0282 0.0159 
q-Baltzar 0.0789 0.0802 
Euler α 69.97 48.63 
Euler β 84.52 70.76 
Euler γ 148.93 157.65 
Da [10-4] 4.087 4.054 
Dr [10-4] 1.481 2.364 
condition number 2.93 3.07 

 

Table 4.10: Orientational properties of IPC in PSPDG/CDCl3. 

 (+)-IPC (-)-IPC 

number of RDCs 11 11 
|∆vQ| [Hz] 194 184 
RMSD [Hz] 0.4821 0.7820 
Q-factor 0.0497 0.0982 
Q-Da 0.0171 0.0310 
q-Baltzar 0.0831 0.1047 
Euler α 48.14 71.66 
Euler β 73.70 86.51 
Euler γ 156.67 148.76 
Da [10-4] 4.52 4.08 
Dr [10-4] 2.36 1.70 
condition number 2.33 2.62 

 

Table 4.11: Orientational properties of IPC in PSPLG/PSPDG(1:1)/CDCl3. 

 (+)-IPC (-)-IPC 

number of RDCs 11 11 
|∆vQ| [Hz] 140 139 
RMSD [Hz] 0.3140 0.3685 
Q-factor 0.0452 0.0546 
Q-Da 0.0148 0.0182 
q-Baltzar 0.0475 0.0798 
Euler α 58.66 59.09 
Euler β 75.84 75.93 
Euler γ 153.40 154.10 
Da [10-4] 3.42 3.27 
Dr [10-4] 1.50 1.49 
condition number 2.18 2.67 

 



5. Pinene data 

Table 5.1: Data of the β-pinene samples. 

polymer m(polymer) 
[g] 

w(polymer) 
[%w/w] 

analyte m(analyte) 
[g] 

solvent 

PSPLG[b] 0.0595 10.4 (+)-β-pinene 0.0161 CDCl3 
PSPLG[b] 0.0588 10.5 (-)-β-pinene 0.0160 CDCl3 
PSPDG[b] 0.0592 10.3 (+)-β-pinene 0.0163 CDCl3 
PSPDG[b] 0.0603 10.8 (-)-β-pinene 0.0162 CDCl3 
PSPDG[b]/ 
PSPLG[b] (1:1) 

0.0300+0.0300 10.3 (+)-β-pinene 0.0163 CDCl3 

PSPDG[b]/ 
PSPLG[b] (1:1) 

0.0293+0.0293 10.4 (-)-β-pinene 0.0161 CDCl3 

[a] batch 1 [b] batch 2 

1
2 3

4

5

6
7

8

9

1
23

4

5

6
7

8

9

10

(+)- -pinene (-)- -pinene

10

 

 

Table 5.2 Extracted isotropic coupling constants (1JCH) for (-)-β-pinene in CDCl3. 

coupling pair  1JCH [Hz] error [Hz] 

C1-H1 142.99 0.27 
C9-H9 124.25 0.11 
C3-H3a 125.86 0.38 
C3-H3s 129.08 0.29 
C8-H8 124.79 0.17 
C7-H7a 137.61 0.26 
C10-H10a 153.76 0.15 
C10-H10s 155.71 0.17 
C5-H5 141.39 0.41 

 

   



Table 5.3: Extracted coupling constants (1TCH) for (+)-β-pinene in PSPLG/CDCl3 (10.4 % 
w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C1-H1 155.71 0.69 6.36 0.48 
C9-H9 125.03 0.31 0.39 0.21 
C3-H3a 120.25 0.41 -2.81 0.40 
C3-H3s 132.59 0.36 1.76 0.32 
C8-H8 123.32 0.40 -0.73 0.29 
C7-H7a 134.44 0.48 -1.58 0.37 
C10-H10a 159.49 0.53 2.87 0.34 
C10-H10s 171.74 0.46 8.01 0.31 
C5-H5 132.85 0.49 -4.27 0.45 
C6-C8   0.20 0.08 
C6-C9   -0.11 0.06 

 

Table 5.4: Extracted coupling constants (1TCH) for (-)-β-pinene in PSPLG/CDCl3 (10.5 % 
w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C1-H1 156.70 0.65 6.85 0.46 
C9-H9 124.00 0.27 -0.13 0.19 
C3-H3a 117.46 0.74 -4.20 0.56 
C3-H3s 135.62 0.36 3.27 0.32 
C8-H8 123.97 0.53 -0.41 0.35 
C7-H7a 129.99 0.59 -3.81 0.42 
C10-H10a 158.34 0.53 2.29 0.34 
C10-H10s 170.52 0.54 7.41 0.36 
C5-H5 132.67 0.62 -4.36 0.52 
C6-C8   0.11 0.10 
C6-C9   0.03 0.05 

 

   



Table 5.5: Extracted coupling constants (1TCH) for (+)-β-pinene in PSPDG/CDCl3 (10.3 % 
w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C1-H1 155.71 0.45 6.36 0.36 
C9-H9 123.27 0.34 -0.49 0.22 
C3-H3a 119.09 0.52 -3.39 0.45 
C3-H3s 135.78 0.42 3.35 0.35 
C8-H8 124.73 0.45 -0.03 0.31 
C7-H7a 129.58 0.54 -4.01 0.40 
C10-H10a 156.34 0.53 1.29 0.34 
C10-H10s 168.92 0.36 6.61 0.26 
C5-H5 132.53 0.65 -4.43 0.53 
C6-C8   0.01 0.08 
C6-C9   0.14 0.06 

 

Table 5.6: Extracted coupling constants (1TCH) for (-)-β-pinene in PSPDG/CDCl3 (10.8 % 
w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C1-H1 157.16 0.69 7.08 0.48 
C9-H9 124.34 0.45 0.05 0.28 
C3-H3a 120.63 0.47 -2.61 0.42 
C3-H3s 133.32 0.55 2.12 0.42 
C8-H8 123.51 0.40 -0.64 0.29 
C7-H7a 133.86 0.61 -1.88 0.44 
C10-H10a 158.10 0.56 2.17 0.35 
C10-H10s 172.62 0.45 8.46 0.31 
C5-H5 130.81 0.70 -5.29 0.55 
C6-C8   0.18 0.08 
C6-C9   -0.01 0.08 

 

   



Table 5.7 Extracted coupling constants (1TCH) for (+)-β-pinene in PSPLG/PSPDG(1:1)/CDCl3 
(10.3 % w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C1-H1 155.62 0.45 6.31 0.36 
C9-H9 124.32 0.34 0.04 0.22 
C3-H3a 120.03 0.50 -2.92 0.44 
C3-H3s 134.46 0.55 2.69 0.42 
C8-H8 124.23 0.31 -0.28 0.24 
C7-H7a 132.16 0.52 -2.73 0.39 
C10-H10a 157.67 0.32 1.95 0.24 
C10-H10s 170.01 0.54 7.15 0.35 
C5-H5 132.79 0.54 -4.30 0.48 
C6-C8   0.08 0.07 
C6-C9   -0.01 0.06 

 
Table 5.8: Extracted coupling constants (1TCH) for (-)-β-pinene in PSPLG/PSPDG(1:1)/CDCl3 
(10.4 % w/w). 

coupling pair  1TCH [Hz] error [Hz] 1DCH/1DCC [Hz] error [Hz] 

C1-H1 155.57 0.51 6.29 0.39 
C9-H9 124.11 0.18 -0.07 0.14 
C3-H3a 119.42 0.44 -3.22 0.41 
C3-H3s 134.12 0.35 2.52 0.32 
C8-H8 123.77 0.41 -0.51 0.29 
C7-H7a 132.26 0.36 -2.67 0.31 
C10-H10a 157.76 0.43 2.00 0.29 
C10-H10s 170.20 0.60 7.24 0.39 
C5-H5 132.47 0.50 -4.46 0.45 
C6-C8   0.14 0.08 
C6-C9   0.02 0.04 

 

   



Table 5.9 Extracted isotropic coupling constants (|nJHH|) for (-)-β-pinene in CDCl3. 

coupling pair  |nJHH| [Hz] error [Hz] 

H1-H10s n.o.[a]  
H1-H7s 5.57 0.06 
H1-H3s n.o.[a]  
H1-H5 5.32 0.08 
H1-H7a n.o.[a]  
H3s-H10a 1.25 0.04 
H3s-H10s 1.14 0.03 
H3a-H10a 2.51 0.06 
H3a-H10s 3.01 0.04 
H3a-H3s 17.45 0.11 
H3a-H5 n.o.[a]  
H3a-H7a n.o.[a]  
H5-H7s 6.07 0.05 
H5-H7a n.o.[a]  
H7a-H7s 9.89 0.07 
H10s-H10a 2.04 0.04 

[a] not observed, assumed to be 0 Hz 

 

Table 5.10 Extracted coupling constants (|nTHH|) for (+)-β-pinene in PSPLG/CDCl3 (10.4 % 
w/w). 

coupling pair  |nTHH| [Hz] error [Hz] nDHH [Hz] error [Hz] 

H1-H10s 1.65 0.06 -0.83 0.10 
H1-H7s 6.56 0.03 0.50 0.10 

H1-H3s 1.17 0.05 0.59 0.10 

H1-H5 5.23 0.06 -0.05 0.10 

H1-H7a 3.21 0.04 1.61 0.10 
H3a-H10a 1.25 0.02 0.63 0.10 
H3a-H10s 1.57 0.06 0.72 0.10 
H3a-H3s 21.37 0.17 -1.96 0.14 
H3a-H5 1.27 0.04 -0.64 0.10 
H3a-H7a 2.58 0.05 1.29 0.10 
H5-H7s 4.34 0.05 -0.87 0.10 
H5-H7a 3.70 0.05 -1.85 0.10 
H7a-H7s 5.50 0.06 2.20 0.10 

 

   



Table 5.11 Extracted coupling constants (|nTHH|) for (-)-β-pinene in PSPLG/CDCl3 (10.5 % 
w/w). 

coupling pair  |nTHH| [Hz] error [Hz] nDHH [Hz] error [Hz] 

H1-H10s 2.26 0.06 -1.13 0.10 
H1-H7s 5.02 0.05 -0.28 0.10 
H1-H3s 1.25 0.04 0.63 0.10 
H1-H5 5.35 0.08 0.02 0.10 

H1-H7a 1.35 0.03 0.68 0.10 

H3a-H10a 2.43 0.03 0.04 0.10 

H3a-H10s 2.19 0.05 0.41 0.10 
H3a-H3s 18.92 0.11 -0.74 0.11 
H3a-H5 1.30 0.04 -0.65 0.10 
H3a-H7a 3.12 0.05 1.56 0.10 
H5-H7s 7.42 0.07 0.68 0.10 
H5-H7a 2.51 0.07 -1.26 0.10 
H7a-H7s 9.43 0.11 0.23 0.10 

 

Table 5.12 Extracted coupling constants (|nTHH|) for (+)-β-pinene in PSPDG/CDCl3 (10.3 % 
w/w). 

coupling pair  |nTHH| [Hz] error [Hz] nDHH [Hz] error [Hz] 

H1-H10s 2.63 0.07 -1.32 0.10 
H1-H7s 4.96 0.12 -0.31 0.10 

H1-H3s 1.22 0.06 0.61 0.10 

H1-H5 5.35 0.06 0.02 0.10 

H1-H7a 1.20 0.02 0.60 0.10 
H3a-H10a 2.54 0.08 -0.02 0.10 
H3a-H10s 2.29 0.07 0.36 0.10 
H3a-H3s 16.67 0.09 0.39 0.10 
H3a-H5 1.44 0.08 -0.72 0.10 
H3a-H7a 2.54 0.04 1.27 0.10 
H5-H7s 7.81 0.14 0.87 0.10 
H5-H7a 2.04 0.04 -1.02 0.10 
H7a-H7s 11.59 0.13 -0.85 0.10 

 

   



Table 5.13 Extracted coupling constants (|nTHH|) for (-)-β-pinene in PSPDG/CDCl3 (10.8 % 
w/w). 

coupling pair  |nTHH| [Hz] error [Hz] nDHH [Hz] error [Hz] 

H1-H10s 2.47 0.09 -1.24 0.10 
H1-H7s 6.65 0.10 0.54 0.10 

H1-H3s 1.26 0.04 0.63 0.10 

H1-H5 5.26 0.09 -0.03 0.10 

H1-H7a 3.51 0.09 1.76 0.10 
H3a-H10a 1.21 0.03 0.65 0.10 
H3a-H10s 1.54 0.03 0.74 0.10 
H3a-H3s 19.23 0.10 -0.89 0.11 
H3a-H5 1.60 0.03 -0.80 0.10 
H3a-H7a 2.51 0.05 1.26 0.10 
H5-H7s 4.71 0.11 -0.68 0.10 
H5-H7a 4.10 0.09 -2.05 0.10 
H7a-H7s 7.17 0.12 1.36 0.10 

 

Table 5.14 Extracted coupling constants (|nTHH|) for (+)-β-pinene in 
PSPLG/PSPDG(1:1)/CDCl3 (10.3 % w/w). 

coupling pair  |nTHH| [Hz] error [Hz] nDHH [Hz] error [Hz] 

H1-H10s 2.12 0.05 -1.06 0.10 
H1-H7s 5.75 0.02 0.09 0.10 

H1-H3s 1.09 0.03 0.55 0.10 

H1-H5 5.31 0.02 -0.01 0.10 

H1-H7a 2.15 0.03 1.08 0.10 
H3a-H10a 1.91 0.05 0.30 0.10 
H3a-H10s 1.95 0.03 0.53 0.10 
H3a-H3s 18.97 0.06 -0.76 0.10 
H3a-H5 1.32 0.04 -0.66 0.10 
H3a-H7a 2.55 0.04 1.28 0.10 
H5-H7s 6.10 0.03 0.02 0.10 
H5-H7a 2.81 0.02 -1.41 0.10 
H7a-H7s 8.60 0.02 0.65 0.10 

 

   



Table 5.15 Extracted coupling constants (|nTHH|) for (-)-β-pinene in 
PSPLG/PSPDG(1:1)/CDCl3 (10.4 % w/w). 

coupling pair  |nTHH| [Hz] error [Hz] nDHH [Hz] error [Hz] 

H1-H10s 2.19 0.02 -1.10 0.10 
H1-H7s 5.76 0.02 0.10 0.10 

H1-H3s 1.15 0.06 0.58 0.10 

H1-H5 5.33 0.02 0.01 0.10 

H1-H7a 2.23 0.05 1.12 0.10 
H3a-H10a 1.95 0.01 0.28 0.10 
H3a-H10s 1.98 0.02 0.52 0.10 
H3a-H3s 19.01 0.10 -0.78 0.11 
H3a-H5 1.27 0.12 -0.64 0.10 
H3a-H7a 2.58 0.04 1.29 0.10 
H5-H7s 6.07 0.02 0.00 0.10 
H5-H7a 2.87 0.03 -1.44 0.10 
H7a-H7s 8.50 0.03 0.70 0.10 

 

 

Figure 5.1: Non-pure shift 2D TSE-PSYCHEDELIC[3,4] spectrum (700 MHz, 300 K) of (-)-β-
pinene in PSPDG/CDCl3 (10.8 % w/w) with excitation of H1. The descriptors a 
(antiperiplanar) and s (synperiplanar) describe the orientation of the diastereotopic protons 
relative to the dimethyl bridge. 

 



Table 5.16: Signs (m = minus, p = plus) of nJHH determined for (-)-β-pinene in CDCl3. 

coupling pair sign 

H1H5 p[a] 
H3s-H10a m[a] 
H3s-H10s m[a] 
H3aH10a m[a] 
H3aH10s m[a] 
H3aH3s m[b] 
H1H7s p[b] 
H5H7s p[a] 
H7sH7a m[b] 

[a] determined by P.E.HSQMBC [b] determined by a COSY based experiment 

 

Table 5.17: Signs (m = minus, p = plus) of nTHH determined for (-)-β-pinene (left) and (+)-β-
pinene (right) in PSPDG/CDCl3. 

coupling pair sign coupling pair sign 

H1H5 p[a] H1H5 p[a] 
H1H3s p[a] H1H3s p[a] 
H1H10s m[a] H1H10s m[a] 
H3aH10a m[a] H3aH10a m[a] 
H3aH10s m[a] H3aH10s m[a] 
H3aH3s m[a] H3aH3s m[a] 
H1H7s p[b] H1H7s p[b] 
H3aH7a p[b] H3aH7a p[b] 
H5H7a m[b] H5H7a m[b] 
H5H7s p[b] H5H7s p[b] 
H3aH5 m[b] H3aH5 m[b] 
H7sH7a m[b] H7sH7a m[b] 
H1H7a p[b] H1H7a p[b] 

[a] determined by P.E.HSQMBC [b] determined by a COSY based experiment 

   



As carried out above for isopinocampheol, results of the CH-RDC fits for the β-pinene 
enantiomers are given in the Tables 5.18 to 5.20. The observed condition number of 10.24 
indicates sub-optimal sampling of orientations and is strongly improved to a value of 3.80, 
when using the full CH and HH RDC dataset (see Tables 5.21 to 5.23) or the HH RDC 
dataset alone (4.61, see Tables 5.24 to 5.26).  
 
The tables also report the orientational properties derived from Eigen decomposition of the 
best-fit alignment tensor. Surprisingly, the sign of the tensor components Da and Dr are 
inconsistent over the entire dataset, as are the Euler angles. While this would at first glance 
suggest an enormous enantiodifferentiation, this is merely a result of numerical instability of 
the Eigen decomposition and subsequent sorting of eigenvalues according to their 
magnitude. For this particular system, two eigenvalues are fairly close in magnitude, and 
even slight changes in the tensor parameters may result in the conventional eigenvalue 
sorting to assign the value with larger magnitude to the 'zz' component - whether it is the 
positive value or the negative one. The eigenvectors are sorted accordingly and when used 
to calculate the Euler angles, again result in apparently different values.  
 
The full 3-by-3 Saupe order matrix (or the scaled equivalent full second rank alignment 
tensor) however show a much more consistent behavior. Here, the 'zz'-value is always 
positive while the 'yz'-value is very sensitive to the actual RDC dataset and is sometimes 
orders of magnitude smaller compared to other tensor components, indicating the high 
similarity in alignment along these directions. 
 
Comparisons based on the generalized scalar product (or the corresponding generalized 
angle β) are not affected, as the calculation of this parameter involves the full tensor(s), and 
does not employ Eigen decomposition. 
 
Thus, while the reported parameters are mathematically correct, they are inconvenient for 
quick cross-comparisons of orientational properties. Higher consistency of the reported 
values may be achieved by careful weighting of the individual RDCs. The most commonly 
suggested weighting scheme is weighting with the relative distances and gyromagnetic ratios 
(combined in the maximum dipolar coupling constant Dmax)[12]. This weighting scheme may 
be automatically applied by RDC@hotFCHT before the SVD fit.  
 
The results of the fits of the CH RDC set with automated Dmax scaling are reported 
exemplarily in Tables 5.27 to 5.29 and contrary to the corresponding values in Tables 5.18 to 
5.20 all show positive Da and Dr values. This shows exemplarily the sensitivity discussed 
above. 
 
The effects of Dmax weighting on the Saupe order matrix, the Eigen decomposition as well 
as the error estimation by Monte-Carlo bootstrapping[14] are summarized exemplarily for the 
CH RDC dataset of (+)-β-pinene in PSPLG/CDCl3 in Tables 5.30 and 5.31. 

   



Table 5.18: Orientational properties (using CH RDCs) of β-pinene in PSPLG/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 9 9 
|∆vQ| [Hz] 130 134 
RMSD [Hz] 0.2846 0.1476 
Q-factor 0.0710 0.0341 
Q-Da 0.0236 0.0129 
q-Baltzar 0.0970 0.0660 
Euler α 147.98 152.23 
Euler β 90.35 74.81 
Euler γ 77.83 75.67 
Da [10-4] -1.94 -1.84 
Dr [10-4] -0.98 -0.82 
condition number 10.24 10.24 

 

Table 5.19: Orientational properties (using CH RDCs) of β-pinene in PSPDG/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 9 9 
|∆vQ| [Hz] 170 190 
RMSD [Hz] 0.1854 0.2759 
Q-factor 0.0463 0.0636 
Q-Da 0.0178 0.0221 
q-Baltzar 0.0591 0.0805 
Euler α 158.26 157.19 
Euler β 70.33 86.82 
Euler γ 73.56 76.48 
Da [10-4] -1.67 -2.00 
Dr [10-4] -0.91 -0.99 
condition number 10.24 10.24 

 

Table 5.20: Orientational properties (using CH RDCs) of β-pinene in 
PSPLG/PSPDG(1:1)/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 9 9 
|∆vQ| [Hz] 149 149 
RMSD [Hz] 0.2574 0.1602 
Q-factor 0.0661 0.0406 
Q-Da 0.0244 0.0149 
q-Baltzar 0.0898 0.0868 
Euler α 155.50 154.95 
Euler β 81.03 81.41 
Euler γ 75.84 76.01 
Da [10-4] -1.69 -1.73 
Dr [10-4] -0.93 -0.91 
condition number 10.24 10.24 



Table 5.21: Orientational properties (using CH + HH RDCs) of β-pinene in PSPLG/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 22 22 
RMSD [Hz] 0.2371 0.1616 
Q-factor 0.0868 0.0570 
Q-Da 0.0181 0.0143 
q-Baltzar 0.1062 0.1300 
Euler α 8.23 153.06 
Euler β 122.30 75.27 
Euler γ 169.34 75.09 
Da [10-4] 2.09 -1.81 
Dr [10-4] 1.27 -0.97 
condition number 3.80 3.80 

 

Table 5.22: Orientational properties (using CH + HH RDCs) of β-pinene in PSPDG/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 22 22 
RMSD [Hz] 0.1707 0.2582 
Q-factor 0.0650 0.0890 
Q-Da 0.0164 0.0182 
q-Baltzar 0.1248 0.1204 
Euler α 158.45 7.63 
Euler β 70.38 116.88 
Euler γ 73.13 166.76 
Da [10-4] -1.66 2.27 
Dr [10-4] -1.00 1.26 
condition number 3.80 3.80 

 

Table 5.23: Orientational properties (using CH + HH RDCs) of β-pinene in 
PSPLG/PSPDG(1:1)/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 22 22 
RMSD [Hz] 0.2015 0.1642 
Q-factor 0.0786 0.0633 
Q-Da 0.0185 0.0149 
q-Baltzar 0.1296 0.1275 
Euler α 174.53 174.91 
Euler β 115.62 115.87 
Euler γ 162.41 162.58 
Da [10-4] 1.74 1.76 
Dr [10-4] 1.08 1.10 
condition number 3.80 3.80 

 

 



Table 5.24: Orientational properties (using HH RDCs only) of β-pinene in PSPLG/ CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 13 13 
|∆vQ| [Hz] 132 135 
RMSD [Hz] 0.1039 0.0967 
Q-factor 0.0845 0.1244 
Q-Da 0.0073 0.0077 
q-Baltzar 0.0889 0.1251 
Euler α 7.71 153.88 
Euler β 120.76 75.23 
Euler γ 168.43 74.23 
Da [10-4] 2.26 -2.02 
Dr [10-4] 1.34 -1.12 
condition number 4.61 4.61 

 

Table 5.25: Orientational properties (using HH RDCs only) of β-pinene in PSPDG/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 13 13 
|∆vQ| [Hz] 171 195 
RMSD [Hz] 0.1100 0.1010 
Q-factor 0.1449 0.0917 
Q-Da 0.0095 0.0064 
q-Baltzar 0.1449 0.0921 
Euler α 159.69 7.36 
Euler β 71.80 115.59 
Euler γ 72.13 166.15 
Da [10-4] -1.84 2.53 
Dr [10-4] -1.12 1.36 
condition number 4.61 4.61 

 

Table 5.26: Orientational properties (using HH RDCs only) of β-pinene in 
PSPLG/PSPDG(1:1)/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 13 13 
|∆vQ| [Hz] 150 151 
RMSD [Hz] 0.1031 0.1034 
Q-factor 0.1315 0.1290 
Q-Da 0.0086 0.0085 
q-Baltzar 0.1315 0.1299 
Euler α 174.82 175.11 
Euler β 114.90 114.73 
Euler γ 161.80 162.01 
Da [10-4] 1.91 1.94 
Dr [10-4] 1.18 1.20 
condition number 4.61 4.61 



Table 5.27: Orientational properties (using CH RDCs with Dmax scaling) of β-pinene in 
PSPLG/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 9 9 
|∆vQ| [Hz] 130 134 
RMSD [Hz] 0.4089 0.2775 
Q-factor 0.1020 0.0640 
Q-Da 0.0328 0.0249 
q-Baltzar 0.1052 0.0760 
Euler α 7.43 166.14 
Euler β 120.83 116.16 
Euler γ 167.58 157.85 
Da [10-4] 1.99 1.77 
Dr [10-4] 1.22 1.14 
condition number 9.67 9.67 

 

Table 5.28: Orientational properties (using CH RDCs with Dmax scaling) of β-pinene in 
PSPDG/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 9 9 
|∆vQ| [Hz] 170 190 
RMSD [Hz] 0.2727 0.3790 
Q-factor 0.0681 0.0874 
Q-Da 0.0253 0.0292 
q-Baltzar 0.0658 0.0870 
Euler α 161.25 2.99 
Euler β 111.21 114.41 
Euler γ 155.57 164.97 
Da [10-4] 1.72 2.07 
Dr [10-4] 0.95 1.25 
condition number 9.67 9.67 

 

   



Table 5.29: Orientational properties (using CH RDCs with Dmax scaling) of β-pinene in 
PSPLG/PSPDG(1:1)/CDCl3. 

 (+)-β-pinene (-)-β-pinene 

number of RDCs 9 9 
|∆vQ| [Hz] 149 149 
RMSD [Hz] 0.3525 0.2600 
Q-factor 0.0905 0.0660 
Q-Da 0.0333 0.0232 
q-Baltzar 0.1266 0.0835 
Euler α 173.57 175.51 
Euler β 114.21 115.31 
Euler γ 160.64 162.00 
Da [10-4] 1.68 1.79 
Dr [10-4] 1.03 1.03 
condition number 9.67 9.67 

 

Table 5.30: Tensor parameters (using CH RDCs ) of (+)-β-pinene in PSPLG/CDCl3. 

Averages and errors of saupe vector (Losonczi method) 
 zz xx-yy xy xz yz 
average 1.29·10-4 5.91·10-4 1.32·10-4 -1.33·10-4 -2.32·10-5 
error 2.36·10-5 3.69·10-5 1.43·10-5 7.93·10-5 4.04·10-5 
% error 18.25 6.25 10.80 59.79 173.83 

saupe order 2.30·10-4 1.32·10-4 -1.30·10-4   
matrix 1.32·10-4 -3.60·10-4 -2.47·10-5   
 -1.30·10-4 -2.47·10-5 1.30·10-4   

eigenvalues xx yy zz   
of saupe 4.71·10-5 3.41·10-4 -3.88·10-4   
matrix      

 

Table 5.31: Tensor parameters (using CH RDCs with Dmax scaling ) of (+)-β-pinene in 
PSPLG/CDCl3. 

Averages and errors of saupe vector (Losonczi method) 
 zz xx-yy xy xz yz 
average 8.87·10-5 5.83·10-4 1.61·10-4 -1.88·10-4 -1.06·10-6 
error 2.01·10-5 3.88·10-5 1.48·10-5 7.46·10-5 3.91·10-5 
% error 22.67 6.66 9.21 39.77 3702.80 

saupe order 2.46·10-4 1.61·10-4 -1.89·10-4   
matrix 1.61·10-4 -3.35·10-4 -2.34·10-7   
 -1.89·10-4 -2.34·10-7 8.85·10-5   

eigenvalues xx yy zz   
of saupe -1.54·10-5 -3.82·10-4 3.97·10-4   
matrix      

 

 



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