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Identifying absolute configurations of PCB atropisomers by comparison of their experimental specific rotations
with their DFT calculated values
Journal: Canadian Journal of Chemistry
Manuscript ID cjc-2018-0458.R1
Manuscript Type: Article
Date Submitted by the Author: 14-Dec-2018
Complete List of Authors: Daramola, Oluwadamilola; University of Manitoba, ChemistryCullen, John; University of Manitoba, Chemistry
Is the invited manuscript for consideration in a Special
Issue?:Not applicable (regular submission)
Keyword: PCB atropisomers, optical rotation, absolute configuration, DFT
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Identifying absolute configurations of PCB atropisomers
by comparison of their experimental specific rotations
with their DFT calculated values
Oluwadamilola Daramola
Department of Chemistry, University of Manitoba,
144 Dysart Road, Winnipeg MB R3T-2N2, Canada
and John Cullen
Department of Chemistry, University of Manitoba,
144 Dysart Road, Winnipeg MB R3T-2N2, Canada
Corresponding author: John Cullen (phone: 1-204-474-6441, fax: 1-204-474-7608,email: [email protected])
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Abstract
Nineteen enantiomer pairs of polychlorinated biphenyls (PCBs) with three or four chloro
substituents about the central carbon-carbon bond form a stable subclass of compounds whose
biological effects vary with their chirality. Optical rotations for this group of PCBs were determined
from density functional calculations employing extended atomic orbital gauge invariant basis sets. A
comparison of these results with the experimental ones found from the literature for nine of the pairs
enabled the identification of their absolute configurations as analytes in gas chromatography studies.
Keywords: PCB atropisomers, optical rotation, absolute configuration, DFT
Introduction
Polychlorinated biphenyls (PCB) are a class of well documented environmental pollutants1.
Because of their carcinogenic, neurotoxic and endocrine disruption properties their persistence and
bioaccumulation pose a serious threat to both aquatic and terrestrial environments. Of the 209 possible
PCB congeners, 78 are chiral due to the asymmetric distribution of the chlorines on the two phenyl
rings. However, only 19 of these have their chirality locked in under ambient conditions2. With phenyl
rings perpendicular to each other, free energy rotation barriers3 ranging from 177 kJ/mol to 246 kJ/mol,
prevent racemization, even at the relatively high temperatures used for gas chromatographic
separations. These axial enantiomers, called atropisomers, constitute 6 percent by weight of the total
PCBs released into the environment and have been found to undergo considerable atropisomeric
enrichment in wildlife, laboratory animals and humans4. Animal and epidemiological studies have
shown that the environmental effects of this subclass of PCBs is implicated in a range of developmental
neurological disorders such as learning deficits and impaired motor coordination5.
The chirality of these compounds brings about new challenges in their analytical identifications
and environmental effects. Manufactured in a batch chlorination process, PCB atropisomers enter the
environment as racemic mixtures. Having identical physicochemical properties, mixtures of PCB
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atropisomer pairs will undergo physical and transport processes undifferentiated. In contrast, biological
processes are predominantly chiral in nature. For example, a racemic mixture of PCB 846 is found to be
significantly more toxic than either purified atropisomer7. In order to experimentally ascertain and gain
an understanding of the myriad biochemical reactions occurring at the molecular level the separation
and identification of the absolute configuration of each occurring PCB congener is a prerequisite. To
date this has only been accomplished for a few atropisomers, by use of high pressure liquid
chromatography (HPLC) with an enantioselective stationary phase to separate out the pairs followed by
either crystallization/x-ray diffraction on the analytes8 or the application of experimental circular
dichroism (CD) combined with ab initio calculations9. At higher coarse grain levels, the gas
chromatography (GC) elution order of fourteen of the PCB enantiomer pairs has been standardized on
six commonly used enantioselective columns10, while in separate studies the specific rotation of each
analyte for nine enantiomer pairs has been correlated with both their HPLC11 and GC elution order13.
Specific rotation, is an intensive property defined as the change in orientation of [𝛼]𝜈,
monochromatic plane-polarized light, at a given frequency or equivalent wavelength, per unit
distance–concentration product, as the light passes through a sample of a compound in solution.
Quantum mechanically can be calculated from the trace of a frequency-dependent tensor, , [𝛼]𝜈 𝛽𝑥𝑦
which is composed of a sum of products of electric and magnetic transition dipoles between ground and
excited states.14 can be reexpressed within the framework of time-dependent linear-response 𝛽𝑥𝑦
theory15 and in the case of DFT, the tensor is found through a set of time-dependent coupled-perturbed
Kohn-Sham equations.16 Once a PCB atropisomer is identified by its chromatographic eluting order
one may identify its chirality and corresponding absolute configuration by measuring its specific
rotation, and matching the result with the quantum chemical computed values for the two possible [𝛼]𝜈
absolute configurations of the enantiomer. In this paper using density functional calculations we
present the results for all 19 PCB atropisomer pairs and determine the chirality for those PCB
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atropisomers whose specific rotations been previously reported11,12. These results also provide
benchmarks that with future experimental measurements will enable the resolution of the absolute
configurations of the remaining pairs.
Computational Method
All calculations were performed using the Gaussian 16 package17. The geometry for each PCB pair
was fully optimized in vacuum using density functional theory (DFT) with the combination of Becke’s
three-parameter (B3) hybrid exchange functional18 and the Lee–Yang–Parr (LYP) correlation
functional19 in conjunction with a 6-31G(d) basis set. Traditionally, the DFT B3LYP/6-31G(d) is used
due to its low trade off of speed, and accuracy20. The specific optical rotations for wavelengths 436,
546 and 578 nm were then computed for all nineteen atropisomeric PCB pairs using time-dependent
DFT B3LYP. To capture polarizability effects an extended aug-cc-pVDZ basis set is employed in a
gauge invariant atomic orbital (GIAO) form to insure final computed values are independent of the
choice of the origin of the coordinate system used in the calculation16. This method produces similar
results as state of the art but much more computationally demanding coupled cluster calculations21 with
average deviations from experimental values of approximately 20 degrees [dm(g/cm3)]-1.
To compare with experimental optical rotation data measured in ethanol11,12, calculations were
repeated for ten of the enantiomer PCB pairs. Solvent effects were incorporated22 using the integral
equation formalism version of the polarizable continuum dynamic/nonequilibrium model (PCM). To
better take into account polarization effects of the continuum, PCB geometries were optimized with an
aug-cc-pVDZ basis set. Finally, we used these results to identify the absolute configurations of the
analytes whose elution sequences were mapped over 6 commonly used gas chromatography
enantioselective columns by Kania-Korwel and Lehmler10 .
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Results and Discussion
The 19 possible PCB atropisomer structures are shown in Figure 1. The stereochemistry
classification23 starts by arbitrarily selecting one phenyl ring to have precedence over the other. The
priorities of the first two groups or substituents on this ring bordering the axial carbon are then
determined. The third priority needed to complete the R or S designation is resolved by choosing the
highest priority group or substituent found bordering the axial carbon on the opposite perpendicular
ring. For an unsubstituted biphenyl with rings perfectly perpendicular to each other no optical rotation
would be observed. This can be derived from Rosenfeld’s perturbation treatment24,14 of the optical
rotatory strength for an electronic excitation from the ground state, , to the excited state, 𝑅𝑘 𝜓0 𝜓𝑘
where
[1]𝑅𝑘 = 𝐼𝑚{⟨𝜓0│𝜇𝑒│𝜓𝑘⟩ ∙ ⟨𝜓𝑘│𝜇𝑚│𝜓0⟩}
Here is the imaginary component of a dot product of transition matrix elements of and , the 𝑅𝑘 𝜇𝑒 𝜇𝑚
electric and magnetic dipole vectors respectively. With respect to any given symmetry element the
unsubstituted biphenyl states can be classified as even or odd. In turn and will have selection 𝜇𝑒 𝜇𝑚
rules25 opposite to each other for the transition resulting in either or ⟨𝜓0│𝜇𝑒│𝜓𝑘⟩ ⟨𝜓𝑘│𝜇𝑚│𝜓0⟩
equalling zero. will only become nonzero when chlorination of the biphenyl results in the loss of 𝑅𝑘
total symmetry. This is the case when each PCB has either a 2,3,6 or 2,3,4,6 chlorinated primary ring
and a chlorination pattern on the secondary phenyl ring. PCBs sharing a common 2,3,6 chlorinated ring
or 2,3,4,6 chlorinated ring are denoted here as belonging to the 236 PCB set or 2346 PCB set
respectively. In Table 1 members within each set are listed and classified according to the chlorination
pattern found on their secondary phenyl ring. PCB 176 (2,2´,3,3´,4,6,6´ heptachlorobiphenyl),
depending on choice taken for the primary phenyl ring, is a member of both sets. The computed [𝛼]𝜈
results at 436 nm for the PCB R-enantiomers are graphically shown in Figure 2. Specific rotations for
236 PCB set are seen to lie lower and are roughly parallel to those found in the 2346 PCB set.
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Complete results at wavelengths 436, 546 and 578 nm for all enantiomers in the two sets are
presented in Table 2. In principle, should be computed from the thermodynamic average of all [𝛼]𝜈
possible conformer geometries, in practice because of the high rotational barriers3 between the rings
only the most stable equilibrium geometry is used here. The variance of in Table 2 between R and [𝛼]𝜈
S enantiomers of each PCB which theoretically should not exist can be traced to numerical errors in the
convergence of the initial geometry optimization performed for each enantiomer. For example, in the
case of PCB 144, the difference in the nuclear repulsion energy between the two optimized enantiomer
structures is 1.218 millihartrees when in theory it should be exactly zero. The corresponding increase in
magnitude of with shortening wavelengths observed in Table 2 can be empirically fitted to [𝛼]𝜈
[2][𝛼]𝜈 = ∑𝑗
𝐴𝑗
𝜆2 ― 𝜆2𝑗
This is known as the Drude equation26, where the and are constants, and is valid in spectral 𝐴𝑗𝑠 𝜆𝑗𝑠
regions far from absorption bands. Experimental absorption spectra27 of all 209 PCB congeners show
that lowest excited states lie in the 245-265 nm region confirming the validity of equation [2] for the
visible region. This also confirms the validity of the methodology used in the calculations, based on the
Rosenfeld’s perturbation treatment24, which becomes inadequate in absorption regions where Cotton
effects28 occur.
Results in Table 2 for the PCBs 171, 132 and 183 correctly predict the absolute configurations
deduced previously9. Here the corresponding experimental optical rotations at 589 nm reported in
hexane for the S enantiomers9 were 44 ± 6, 39 ± 15 and -15 ± 3 degrees [dm(g/cm3)]-1. This compares
with our 43.17, 56.19 and -8.72 values computed at 578 nm. In general, sources of computational errors
arise from using B3LYP, an approximate DFT functional, a finite basis set, an incomplete PCM solvent
model, ignoring vibrational effects29, geometry optimization and lack of thermal averaging over other
less probable geometries. Stephens and coworkers30 examined the reliability of predicting absolute
configurations by calculating for a set of 65 rigid molecules their specific rotations in the gas phase and
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comparing these results to their experimental values determined in a variety of solvents. For the subset
of the several molecules with one chiral centre there is 100% agreement, for molecules having two or
more chiral centres there was a 12-13% failure rate. However, the methodology employed in this paper
selected rigid molecules based on a gas phase lowest energy conformation which is 2 kcal/mol below
or lower than other stable conformers present. This can be experimentally incorrect due to errors in the
B3LYP method as well as lack of consideration of solvation effects. Optical rotations of different
conformers can differ greatly in sign and magnitude, and the conformer whose computed optical
rotation matches experiment may not be the lowest energy one found in the gas phase31. This source of
error does not arise in our study where there is only one possible stable conformation with one chiral
centre for each PCB.
Table 3 presents a comparison of our calculated results in ethanol and the experimental work [𝛼]𝜈
on the optical rotation11,12 and gas chromatographic retention times13 of 10 PCBs. There is close
agreement between predicted and experimentally measured specific rotations, with the exception of
PCB 84. Despite the large deviations found here, when signs of experimental and computed optical
rotations are matched, the corresponding absolute configurations are in complete agreement with the
recent X-ray study from Lehmler’s group8. The experimental points for the R enantiomers at 436 nm
are also plotted in Figure 2. From Table 1, PCBs having matching chlorination patterns on their
secondary rings are PCBs 84, 131 at carbons 2,3; PCBs 136, 176 at carbons 2,3,6; PCBs 176, 197 at
carbons 2,3,4,6; PCBs 135, 175 at carbons 2,3,5 and PCBs 174, 196 at carbons 2,3,4,5. The specific
rotations found in each of the last 4 pairs lie close in value and follow the parallel trend of the
computed gas phase results of the 236 and 2346 PCB sets seen in Figure 2. In contrast, the
experimental point for PCB 84 at 110 degrees [dm(g/cm3)]-1 below that of PCB 131 lies outside the
range of the graph suggesting possibly an experimental error here.
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The retention time, r, the amount of time a compound spends in the chromatographic column after
it has been injected is a measure of the compound’s relative binding strength to the stationary phase.
Here the stationary phase, Chirasil-Dex, schematically depicted in Figure 3 is composed of 2,3,6-tri-O-
methyl--cyclodextrins linked via a octamethylene spacer to polydimethylsiloxane. Seven glucosidic
units link together to form a truncated cone architecture with a hydrophobic cavity and a bottom
hydrophilic rim. Methylation of the larger top rim distorts the structure32 improving
enantioseparations33. NMR experiments show these cyclodextrins are dynamically very flexible
enabling the selective formation of guest-host inclusion complexes for a wide range of molecules34.
The small Gibbs free binding energy differences between enantiomers which can be as little as 0.1
kJ/mol results in a pairing pattern of retention times seen in Table 3 which facilitates atropisomer
identification. Here the R enantiomer elutes first before the S enantiomer except for PCB 135 and PCB
174. The very small binding energy differences and complexity of the dynamics of the host system
preclude modelling the interplay of intermolecular forces, hydrophobic interactions and cyclodextrin
strain energy driving complex formation with any degree of certainty.
Because no single type of enantioselective gas chromatography column can resolve the
atropisomers of all chiral PCBs, Kania-Korwel and Lehmler10 have conducted a study to standardize
the relative elution orders of twelve of the PCB atropisomers over six commonly used gas
chromatography columns taken as a group. Table 3 from their paper lists the relative elution orders for
seven atropisomers whose optical rotations are experimentally known. In our Table 4, we have repeated
this table replacing optical rotation signs with the corresponding absolute configuration designations
deduced from our calculations.
Conclusion
Due to small binding energy differences to the stationary phase between enantiomer pairs, mixtures
of chiral PCBs produce a pairing pattern in their retention times both in gas or high pressure liquid
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chromatography. This allows one to isolate each enantiomer pair and experimentally determine the
optical rotation and order of elution. By comparing literature results10-12 with our theoretical
calculations the absolute configuration of each PCB enantiomer was ascertained.
Acknowledgements
We thank the University of Manitoba and WestGrid for computing support and the Canada Summer
Jobs program for financial support. O.D. would also like to thanks Dr. James Xidos for his helpful
discussions.
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References
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(17) Gaussian 16, Revision B.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2016.
(18) Becke, A. D. J. Chem. Phys. 1993, 98, 1372.
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(20) Frisch, M. J.; Trucks, G. W.; Cheeseman, J. R. in Recent Developments and Applications of Modern Density Functional Theory: Seminario, J. M.; Ed.; Theoretical and Computational Chemistry; Elsevier Science: Amsterdam, 1996, 4, 679-707.
(21) Ruud, K.; Stephens, P. J.; Devlin, F. J; Taylor, P.R.; Cheeseman, J. R.; Frisch, M. J. Chem. Phys. Lett. 2003, 373, 606-614
(22) Mennucci, B.; Tomasi, J.; Cammi, R.; Cheeseman, J. R.; Frisch, M. J.; Devlin, F. J.; Gabriel, S.; Stephens, P. J. J. Phys. Chem. A. 2002, 106, 6102-6113
(23) Wolf, C. Principles of Chirality and Dynamic Stereochemistry 2008, Chapter 2, 9-11, Royal Society of Chemistry eBook Collection 2007
(24) Rosenfeld, von L. Z. f r Physik 1928, 52, 161-174𝑢
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(26) Drude, P. The Theory of Optics 1902, Longmans, London; reprinted 1959, Dover, New York
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(28) Cotton, A. Compt. Rend. 1895, 120, 989 and 1044
(29) Bishop, D. M. Rev. Mod. Phys. 1990, 62, 251-374
(30) Stephens, P. J.; McCann, D.M.; P.R.; Cheeseman, J. R.; Frisch, M. J. Chirality 2005, 17, S52-S64
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(32) Schonbeck, C.; Westh, P.; Holm, R. J. Phys. Chem. B 2014, 10120-10129
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(33) Juvancz, Z.; Alexander, G.; Szeitli, J. J. High Resol. Chromatogr. 1987, 10, 105–107; Dai,Y.; Hai, J.; Tang, W.; Ng, S-C. in Modified Cyclodextrins for Chiral Separations, Ed. Tang, W.; Ng, S-C.; Sun, D., Springer Heidelberg New York Dordrecht London, 2013
(34) Dodziuk, H., Ed. in Cyclodextrins and Their Complexes 2006, 1-26, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Table and Figure Captions
Table 1. A classification of the PCB members belonging the 236 and 2346 PBC sets according to the chlorination pattern on their secondary rings
Table 2. Calculated specific rotations in degrees [dm(g/cm3)]-1and predicted R or S chirality for the 19 atropisomers
Table 3. GC retention times, r, specific rotations, , calculated and experimental (in blue) for 10 [𝛼]𝜈PCB atropsiomers
Table 4. Elution order, i.e. 1st/2nd , for the absolute configurations of 7 PCB atropisomers over 6 common used gas chromatograph columns
Figure 1a. PCB atropisomers which have R chiralities for [𝛼]𝜈 > 0
Figure 1b. PCB atropisomers which have S chiralities for [𝛼]𝜈 > 0
Figure 2. Specific Rotations of PCB R Atropisomers at 436 nm
Figure 3. Schematic depiction of Chirasil-Dex
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Table 1. A classification of the PCB members belonging the 236 and 2346 PBC sets according to the chlorination pattern on their secondary rings
Cl positions on Secondary Ring
2,3 2,3,4 2 2,3,6 2,4 2,3,4,6 2,3,5 2,3,4,5 2,5 2,4,5
236 PBC set PCB 84
PCB 132
PCB 45
PCB 136
PCB 91
PCB 176
PCB 135
PCB 174
PCB 95
PCB 149
2346 PBC set PCB 131
PCB 171
PCB 88
PCB 176
PCB 139
PCB 197
PCB 175
PCB 196
PCB 144
PCB 183
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Table 2. Calculated specific rotations in degrees [dm(g/cm3)]-1and predicted R or S chirality for the 19 atropisomers
436 nm 546 nm 578 nm
Compound R S R S R S
PCB 84 -145.41 +146.27 -81.05 +81.53 -70.58 +71.00
PCB 132 -115.38 +115.12 -64.62 +64.47 -56.31 +56.19
PCB 45 -74.06 +72.80 -41.29 +40.57 -35.95 +35.33
PCB 136 -67.55 +68.06 -37.84 +38.11 -32.97 +33.21
PCB 91 -63.82 +63.34 -35.39 +35.42 -31.12 +30.86
PCB 176 -54.87 +55.67 -30.75 +31.19 -26.80 +27.17
PCB 135 -41.61 +41.76 -23.21 +23.30 -20.22 +16.41
PCB 174 -29.50 +29.53 -16.53 +16.54 -14.40 +14.41
PCB 95 +36.96 -37.83 +20.66 -21.14 +18.00 -18.42
PCB 149 +25.86 -25.49 +14.39 -14.18 +12.52 -12.34
PCB 131 -122.07 +122.03 -68.76 +68.74 -59.98 +59.96
PCB 171 -87.63 +87.60 -49.51 +49.48 -43.20 +43.17
PCB 88 -58.72 +60.83 -33.20 +34.42 -28.97 +30.04
PCB 176 -54.87 +55.67 -30.75 +31.19 -26.80 +27.17
PCB 139 -48.89 +50.73 -27.74 +28.86 -24.22 +25.21
PCB 197 -38.12 +39.28 -21.56 +22.21 -18.81 +19.38
PCB 175 -30.10 +30.18 -17.09 +17.13 -14.91 +14.96
PCB 196 -21.84 +21.79 -12.58 +12.54 -11.00 +10.97
PCB 144 +25.72 -23.83 +14.01 -12.94 +12.16 -11.22
PCB 183 +18.72 -18.56 +10.15 -10.06 +8.80 -8.72
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Table 3. GC retention times, r, specific rotations, , calculated and experimental (in blue) for [𝛼]𝜈10 PCB atropsiomers
Compound R-Enantiomer S-Enantiomer
r (min) 436 nm 546 nm 578 nm r (min) 436 nm 546 nm 578 nm
61.13 -153.43 -85.14 -74.07 61.32 +153.45 +85.13 +74.08
PCB 84
-242 -135 -115 +241 +138 +125
-120.52 -67.49 -58.80 +120.34 +67.38 +58.70
PCB 131
-110 -63 -52 +111 +63 +60
77.29 -114.98 -64.19 -55.91 78.02 +115.00 +64.20 +55.91
PCB 132
-111 -62 -51 +110 +61 +54
65.41 -73.25 -40.71 -35.42 65.66 +73.27 +40.71 +35.42
PCB 136
-70 -41 -35 +73 +43 +37
76.80 -43.49 -24.19 -21.03 77.13 +45.46 +25.27 +21.97
PCB 176
-66 -39 -33 +63 +35 +31
68.47 -52.64 -29.46 -25.68 68.22 +52.60 +29.44 +25.66
PCB 135
-42 -22 -21 +31 +18 +17
-43.89 -24.82 -21.65 +43.18 +24.42 +21.31
PCB 197
-32 -18 -16 +32 +18 +16
-35.91 -20.36 -17.78 +35.92 +20.37 +17.78
PCB 175
-34 -20 -17 +34 +20 +16
92.13 -32.37 -18.18 -15.85 91.63 +32.33 +18.15 +15.83
PCB 174
-30 -21 -15 +31 +20 +16
-31.74 -18.28 -16.00 +31.63 +18.22 +15.95
PCB 196
-29 -24 -22 +30 +26 +21
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Table 4. Elution order, i.e. 1st/2nd , for the absolute configurations of 7 PCB atropisomers over 6 common used gas chromatograph columns
Compound 20B BDM BGB BPM CB CD
PCB 84 R/S S/R R/S
PCB 132 R/S R/S R/S R/S
PCB 136 R/S R/S R/S
PCB 176 R/S R/S R/S
PCB 174 R/S S/R R/S S/R
PCB 183 R/S
PCB 149 S/R S/R S/R 20B: 20% -cyclodextrin (in 35%-phenyl)-methylpolysiloxane CB: 30% hepatkis (2,3-di-O-methyl-6-O-tert-butyldimethyl-silyl)--cyclodextrin CD: Chirasil-Dex (2,3,6-tri-O-methyl--cyclodextrin) BGB: 20% tertbutyldimethyl-silyl--cyclodextrin BDM: ChiralDex B-DM (2,3-di-O-methyl-6-tert-butyl-silyl--cyclodextrin) BPM: ChiralDex B-PM (2,3,6-tri-O-methyl-silyl--cyclodextrin)
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Figure 1a. PCB atropisomers which have R chiralities for [𝛼]𝜈 > 0
PCB 95 PCB 144 PCB 149 PCB 183
Figure 1b. PCB atropisomers which have S chiralities for [𝛼]𝜈 > 0
PCB 84 PCB 131 PCB 132 PCB 171
PCB 45 PCB 88 PCB 136 PCB 176
PCB 91 PCB 139 PCB 135 PCB 175
PCB 174 PCB 196 PCB 197
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Figure 2. Specific Rotations of PCB R Atropisomers at 436 nm
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Figure 3. Schematic depiction of Chirasil-Dex
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