Giving substance to the Losanitsch series

Article abstract of DOI:10.1039/c2cc17734j

A series of oligoparaxylene model compounds with two to six paraxylene units was synthesised and the resulting mixtures of atropisomers with one to five axes of chirality were analysed by dynamic ¹H NMR spectroscopy. The number of atropisomers was found to constitute part of the Losanitsch series. The Royal Society of Chemistry 2012.

Full text of DOI:10.1039/c2cc17734j

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Cite this: Chem. Commun., 2012, 48, 3158–3160
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COMMUNICATION
Giving substance to the Losanitsch serieswz
Sergio Grundera and J. Fraser Stoddart*ab
Received 9th December 2011, Accepted 17th January 2012
DOI: 10.1039/c2cc17734j
A series of oligoparaxylene model compounds with two to six
paraxylene units was synthesised and the resulting mixtures of
atropisomers with one to five axes of chirality were analysed by
dynamic 1H NMR spectroscopy. The number of atropisomers
was found to constitute part of the Losanitsch series.
Losanitsch investigated this problem as early as in the end of the
19th century while he was analysing isomers of paraffins6 and
establishing the Losanitsch series (2, 3, 6, 10, 20, 36, 72, 136, 272...).
The series can be described using the following formula1b with
A being the number of isomers, n being the number of chiral
elements, and [ꢀ] being the Gauss brackety where [(n + 1)/2] is
the largest integer not greater than (n + 1)/2:
A molecule containing more than one chiral element leads to the
existence of a number of possible isomers which is not always
trivial to deduce. When the chiral elements are associated with
a constitutionally unsymmetrical compound, the number of
isomers A as a function of chiral elements n is
A = 2nꢁ1 + 2[(n + 1)/2]ꢁ1
(2)
In order to give expression to the Losanitsch series, we
have designed and synthesised a series of model compounds
containing one to five chiral elements. Several design criteria
were taken into account to provide a system which exists as an
equilibrating mixture of isomers and which is synthetically
accessible. For the chiral elements we decided to choose
axes of chirality,7 since the formation of one compound
leads after equilibration to a mixture of all possible isomers.
Oligoparaxylenes (OPXs)8 are ideally suited for this task. The
steric hindrance between the ortho-methyl groups on each
biphenyl subunit renders the planar conformation of the
molecule a high energy state and results in a twist between
the planes of adjacent phenylene units. As a consequence,
nonplanar isomers are generated with chiral axes whose helical
sense is maintained as a result of hindered rotation about the
single aryl–aryl bonds. The linear arrangement of modules with
chiral axes leads to the formation of atropisomers with barriers to
rotation9 of about 18 kcal molꢁ1 which are ideal DGa values for
the targeted experiments because they are low enough to permit
isomerisation and equilibration, yet high enough to be probed on
the 1H NMR time-scale. Furthermore the methyl groups in the
OPXs are ideal 1H NMR probes of the stereochemistry.
Compounds 2-mer–6-mer (Fig. 1) were synthesised employing
transition metal catalysed Suzuki–Miyaura10 cross-coupling
reactions (see the ESI for detailsz).
A = 2n.
(1)
When the chiral elements are located in a symmetrical linear
manner in the molecule, however, the number of isomers is
not so simple to deduce because of the possibility of meso
compounds, that is, achiral isomers which are superimposable on
their mirror images. This problem in the mathematical sciences is
often referred to1 as ‘‘beads on a string’’ and is described as the
number of possibilities associated with arranging black or white
beads on a string. There are, for example, three possibilities
arranging two black or white beads on a string, black-black,
white-white, and black-white, which is the same as white-black.
This same problem is transferred to many areas of stereochemistry2
such as in carbohydrates,3 mechanically interlocked molecules,4
and atropisomers,5 to name but a few, where the presence of
multiple chiral centres, axes, and planes leads to a complex
mixture of isomers, complicating the characterisation of such
compounds. Identifying a formula describing the number of
isomers as a function of the chiral elements is central to
overcoming the challenging characterisation and analysis. It
is not trivial, however, because one has to differentiate whether
there are odd or even numbers of chiral elements. In the case
of compounds containing chiral axes, only an even number of
axes of chirality leads to the existence of meso compounds.
a Department of Chemistry, Northwestern University,
2145 Sheridan Road, Evanston, IL 60208, USA.
E-mail: stoddart@northwestern.edu
b NanoCentury KAIST Institute and Graduate School of EEWS
(WCU), Korea Advanced Institute of Science and Technology
(KAIST), 373-1 Guseong Dong, Yuseong Gu, Daejeon 305-701,
Republic of Korea
w This article is part of the ChemComm ‘Chirality’ web themed issue.
z Electronic supplementary information (ESI) available: experimental
details, variable temperature 1H NMR spectra of the mixtures and
structural details of the 10 individual isomers of the 5-mers and the
20 isomers of the 6-mers. See DOI: 10.1039/c2cc17734j
Fig. 1 Model compounds 2-mer–6-mer containing one to five
chiral axes.
c
3158 Chem. Commun., 2012, 48, 3158–3160
This journal is The Royal Society of Chemistry 2012

Fig. 2 (a) (R)-2-Mer and its mirror image (S)-2-mer. (b) (RR)-3-Mer, its enantiomer (SS)-3-mer and the meso compound (RS)-3-mer.
(c) The 4-mer with its three axes of chirality leads to three pairs of enantiomers, namely (RRR)-4-mer/(SSS)-4-mer, (RSR)-4-mer/(SRS)-4-mer,
and (RRS)-4-mer/(SSR)-4-mer. VT NMR experiments of 3-mer (d) and 4-mer (e) in deuterated toluene (C7D8) revealing four anisochronous
methyl peaks in the case of the 3-mer and 12 in the case of the 4-mer at low temperatures.
In order to investigate the different isomers generated by
multiple axes of chirality (Table 1), variable temperature (VT)
NMR spectroscopyz was performed over a range of temperatures
from 360 K down to 240 K. Deuterated toluene (C7D8) as the
solvent was found to afford the best resolution between signals
for the probe methyl group protons in the different isomers. All
1H NMR spectra were recorded – after the samples had been
allowed to stand in the NMR probe to equilibrate at selected
temperatures for 15 min – in C7D8 at 10 degree intervals.
As the simplest member in the series of model compounds,
the 2-mer consists (Fig. 2a) of two paraxylene units and one
chiral axis, leading to two enantiomers, namely (R)-2-mer and
(S)-2-mer. As a consequence of the C2 symmetry present in
both the (R)- and (S)-isomers, both methyl groups are homotopic
by internal comparison and equivalent by external comparison,
resulting in only one (isochronous) methyl resonance being
observed in the 1H NMR spectrum of the racemic modification.
Adding a second axis of chirality as in the 3-mer leads to the
existence of three isomers (Fig. 2b), namely (RR)-, (SS)- and
(RS)-3-mer. The two enantiomers (RR)- and (SS)-3-mer have
C2 symmetry and are chiral. The meso-isomer (RS)-3-mer has
reflection symmetry (Ci) and is achiral. While the enantiomers
(RR)/(SS)-3-mer behave as one compound in the 1H NMR
spectrum, they are diastereoisomeric with the meso-isomer
(RS)-3-mer. Overall, in the case of the 3-mer, two compounds
can be identified in a mixture (and equilibrating) in C7D8 during
VT 1H NMR spectroscopy (Fig. 2d) at lower temperatures.
Following coalescence at higher (B340 K) temperatures, two
broad resonances for the constitutionally heterotopic methyl
group protons are observed at 352 K, both of which subsequently
separate out, giving a total of four equal intensity anisochronous
signals for the two homotopic pairs in the enantiomers and the
two enantiotopic pairs in the meso-isomer.
Composed of four torsionally hindered paraxylene units,
the 4-mer has three axes of chirality, leading to the existence of
six isomers – namely, three pairs of enantiomers, (RRR)-
4-mer/(SSS)-4-mer, (RRS)-4-mer/(SSR)-4-mer, and (RSR)-4-mer
and (SRS)-4-mer. The four conformational symmetrical (C2)
isomers, namely, the (RRR)-, (SSS)-, (RSR)- and (SRS)-isomers
all contain three enantiotopic pairs of constitutionally hetero-
topic methyl groups giving rise to three anisochronous signals in
1
the low temperature H NMR spectrum for each enantiomeric
pair, i.e., six resonances overall for the (RRR)-, (SSS)-, (RSR)-
and (SRS)-isomers. In the case of the conformationally
unsymmetrical (C1) enantiomers, (RRS)-4-mer/(SSR)-4-mer, all
six methyl groups are heterotopic when atropisomerism is slow on
the 1H NMR time-scale and so they give rise to six anisochronous
resonances in total in the low temperature 1H NMR spectrum.
At high temperatures, three broad resonances are observed in
keeping with the constitution of the 4-mer. On cooling down
c
This journal is The Royal Society of Chemistry 2012
Chem. Commun., 2012, 48, 3158–3160 3159

1
identified in the H NMR spectra at low temperatures agrees
Table 1 Conformational analysis of the isomers
with the number of isomers calculated using the Losanitsch
formula, and hence we have shown experimentally that such
multiple chiral element systems obey the Losanitsch series.
These findings may be helpful in the characterisation of
molecules with complex arrangements of chiral elements.
This work was, in part, supported by the Non-Equilibrium
Energy Research Center which is an Energy Frontier Research
Center funded by the US. Department of Energy, Offices of
Basic Energy Sciences under Award Number DE-SC0000989.
S.G. thanks the Swiss National Science Foundation for financial
support, while J.F.S. acknowledges support from the WCU
Program (R31-2008-000-10055) at KAIST in Korea.
Heterotopic Me
Compound Isomer
Point group
Individuala Totalb
2-mer
3-mer
3-mer
4-mer
4-mer
4-mer
5-mer
5-mer
5-mer
5-mer
5-mer
5-mer
6-mer
6-mer
6-mer
6-mer
6-mer
6-mer
6-mer
6-mer
6-mer
6-mer
R/S
RR/SS
RS
C2
C2
Ci
1
2
1
4
2
RRR/SSS
RSR/SRS
RRS/SSR
RRRR/SSSS
RSSR/SRRS
RRRS/SSSR
RRSR/SSRS
RRSS
C2
C2
C1
C2
C2
C1
C1
Ci
3
3
6
4
12
32
4
8
8
4
RSRS
Ci
4
RRRRR/SSSSS C2
RRSRR/SSRSS C2
RSSSR/SRRRS C2
RSRSR/SRSRS C2
RRRRS/SSSSR C1
RRRSR/SSSRS C1
RRRSS/SSSRR C1
RRSSR/SSRRS C1
RRSRS/SSRSR C1
RSRRS/SRSSR C1
5
80
Notes and references
5
5
5
10
10
10
10
10
10
y The Gauss bracket is defined by the floor function. Floor(x) = [x] is
the largest integer not greater than x. The floor function maps a real
number to the largest previous integer (The number in the Gauss
bracket is rounded down, i.e., [2] = 2, [2.5] = 2). For n = 1, the
Losanitsch formula gives A = 20 + 20 = 2. For n = 2, A = 21 + 20 = 3.
For n = 3, A = 22 + 21 = 6. For n = 4, A = 23 + 21 = 10. For n = 5,
A = 24 + 22 = 20. For n = 6, A = 25 + 22 = 36, and so on.
z VT NMR spectra were recorded on a Bruker Avance 600 MHz
spectrometer, which was temperature-calibrated using neat ethylene
glycol or MeOH. The chemical shifts (d) for 1H spectra, given in ppm,
are referenced to the residual proton signal of the deuterated solvent.
All 1H NMR spectra were recorded after the samples had been left in
the NMR probe to equilibrate at every temperature for 15 min.
Number of heterotopic Me groups in 1H NMR spectroscopy for
a
b
every individual isomer. Number of total heterotopic Me groups in
1H NMR spectroscopy for a mixture of all isomers of a certain length.
1 (a) N. Hoffman, Math. J., 1978, 9, 267–272; (b) N. J. A. Sloane,
Notices Amer. Math. Soc., 2003, 50, 912–915.
2 M. Farina and C. Morandi, Tetrahedron, 1974, 30, 1819–1831.
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1934, 56, 2109–2111; (b) G. Bringmann, A. J. Price Mortimer, P. A.
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the solution (Fig. 2e), these three resonances first of all
separate into six and then finally into 12 peaks of similar
intensities. These 12 peaks constitute the sum of three peaks
for the (RRR) and (SSS) enantiomers, three peaks for the
(RSR) and (SRS) enantiomers and six peaks for the (RRS) and
(SSR) enantiomers.
Applying the Losanitsch formula to n = 4, 10 isomers are
expected for the 5-mer: two pairs of C2 enantiomers RRRR/
SSSS and RSSR/SRRS, two pairs of C1 enantiomers RRRS/
SSSR and RRSR/SSRS and two Ci meso-isomers RRSS and
RSRS, leading to a total number of 32 heterotopic methyl
groups. For the 6-mer (n = 5), 20 isomers are expected existing
as: four pairs of C2 enantiomers RRRRR/SSSSS, RRSRR/
SSRSS, RSSSR/SRRRS, RSRSR/SRSRS, and six pairs of
C1 enantiomers RRRRS/SSSSR, RRRSR/SSSRS, RRRSS/
SSSRR, RRSSR/SSRRS, RRSRS/SSRSR, RSRRS/SRSSR
leading to a total number of 80 heterotopic methyl groups.
It was not possible, however, to resolve all these peaks in the
VT NMR spectra (see Fig. S1 and S2 in the ESI) recorded
at 600 MHz.
6 S. M. Losanitsch, Ber. Dtsch. Chem. Ges., 1897, 30, 1917–1926.
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¨
¨
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In conclusion, we have prepared a series of model com-
pounds consisting of one up to five axes of chirality arranged
symmetrically in a linear oligoparaxylene system. These multiple
chiral elements produce a number of atropisomers which were
probed by VT NMR spectroscopy. The number of isomers
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c
3160 Chem. Commun., 2012, 48, 3158–3160
This journal is The Royal Society of Chemistry 2012