Design and synthesis of the first triply twisted Moebius annulene

Article abstract of DOI:10.1038/nchem.1955

As long as 50 years ago theoretical calculations predicted that Moebius annulenes with only one π surface and one edge would exhibit peculiar electronic properties and violate the Hueckel rules. Numerous synthetic attempts notwithstanding, the first singly twisted Moebius annulene was not prepared until 2003. Here we present a general, rational strategy to synthesize triply or even more highly twisted cyclic π systems. We apply this strategy to the preparation of a triply twisted [24]dehydroannulene, the structure of which was confirmed by X-ray analysis. Our strategy is based on the topological transformation of 'twist' into 'writhe'. The advantage is twofold: the product exhibits a lower degree of strain and precursors can be designed that inherently include the writhe, which, after cyclization, ends up in the Moebius product. With our strategy, triply twisted systems are easier to prepare than their singly twisted counterparts.

Full text of DOI:10.1038/nchem.1955

ARTICLES
PUBLISHED ONLINE: 25 MAY 2014 | DOI: 10.1038/NCHEM.1955
Design and synthesis of the first triply twisted
¨
Mobius annulene
1
2
2
3
4
1
´
Gaston R. Schaller , Filip Topic , Kari Rissanen , Yoshio Okamoto , Jun Shen and Rainer Herges
*
*
¨
As long as 50 years ago theoretical calculations predicted that Mobius annulenes with only one p surface and one edge
would exhibit peculiar electronic properties and violate the Huckel rules. Numerous synthetic attempts notwithstanding,
¨
¨
the first singly twisted Mobius annulene was not prepared until 2003. Here we present a general, rational strategy to
synthesize triply or even more highly twisted cyclic p systems. We apply this strategy to the preparation of a triply
twisted [24]dehydroannulene, the structure of which was confirmed by X-ray analysis. Our strategy is based on the
topological transformation of ‘twist’ into ‘writhe’. The advantage is twofold: the product exhibits a lower degree of strain
¨
and precursors can be designed that inherently include the writhe, which, after cyclization, ends up in the Mobius product.
With our strategy, triply twisted systems are easier to prepare than their singly twisted counterparts.
ost objects in our everyday lives exhibit two sides: in and molecular framework15–17. Meanwhile, a number of Mo¨bius-extended
out, or front and back. Mo¨bius bands are exceptions. porphyrins have been synthesized that have a stability similarly
M
Any band with an odd number of twists has one side enhanced by steric constraints18–21
.
and one edge. Ribbons with an even number of twists (including
zero) exhibit two sides. Unfortunately, sidedness is not an intrinsic
topological parameter because its definition requires the object to be
Results and discussion
Topological design. Given the tremendous problems in
embedded in a surrounding space. Orientability is an intrinsic prop- synthesizing singly twisted Mo¨bius systems, triply twisted
erty, and therefore is used frequently to describe the topology of annulenes seem to be rather out of reach. On realistic inspection,
objects1–3. An object is said to be non-orientable if a chiral shape
drawn onto the surface can be transformed into its mirror image
simply by moving it over the surface. This seems trivial, but, for
strain and reduced p overlap loom. Moreover, a simple synthetic
analysis adds further implications to the heap of obstacles. From a
naive point of view one could propose a cyclotrimerization of
instance, the Fisher formula of D-lactic acid drawn onto a Mo¨bius three singly twisted precursors or, alternatively, the cyclization of
band is transformed into the structure of L-lactic acid by shifting a triply twisted starting structure (Fig. 1a). However, as soon as
it once around the ribbon. If our universe were non-orientable it
would be possible to convert D-lactic into L-lactic acid by simply
moving a sample around in space (see Supplementary Fig. 1).
one leaves this rather low level of abstraction, and dares to
translate the rather simple-minded picture into real chemistry,
one gradually realizes that the situation is fairly hopeless. How to
Other examples of non-orientable objects are the Klein bottle, Boy’s stabilize a 1808, or even a 5408, twist in a linear p system—by
surface, the Roman surface and the Crosscap (see Supplementary substitution or a molecular rack? Even if one could do so, a
Fig. 2). The peculiar properties of non-orientable surfaces have
attracted and inspired mathematicians, as well as artists, musi-
simple cardboard model reveals that a twisted band would never
bend. Hence, the ends of the bands would not find each other for
cians and authors. Interest in chemistry started in 1964 when cyclization. Anyhow, putting aside all the above concerns, if the
Edgar Heilbronner predicted that Mo¨bius annulenes, being aro- target structure (against all odds) could form, it would be
matic with 4n electrons, would violate the Hu¨ckel rules4. The
1808 twist induces strain in the p system and reduces p overlap.
Heilbronner concluded that therefore only [n]annulenes with a
tremendously strained.
In this quandary, hope comes from topology. It is an everyday-
life experience (telephone cord, garden hose) that twisted bands
ring size larger than n ¼ 20 would be stable. This forethought wind around themselves to release strain. Topologists call this
was confirmed recently by theoretical calculations5–10. Using a sys- phenomenon the projection of ‘twist’ into ‘writhe’ (Fig. 1b).
tematic generation procedure, and by subsequent energy calcu-
lations of several hundred thousand [n]annulene isomers of ring
sizes n ¼ 8–24, we can prove that there are numerous Mo¨bius
Whereas a twist (Tw) is straightforward to define (it is just the
sum of the dihedral angles of the vectors normal to the p
plane)22,23, the topological parameter ‘writhe’ (Wr) is less obvious,
annulenes (about 50% of all structures); however, there is no at least in its precise mathematical definition. Writhe is defined as
Mo¨bius global minimum among the uncharged [n]annulenes11–14
.
the double Gaussian integral over a closed curve C in three-dimen-
sional (3D) Euclidean space R3 (ref. 24):
Obviously, the energy gain through Mo¨bius aromaticity is overcom-
pensated by the strain imposed by the twist. Unfortunately, the
numerous higher-energy local-minimum structures are kinetically
unstable. They would immediately ‘untwist’ and release strain
energy, even at low temperatures, to form the more stable Hu¨ckel
structures. The first Mo¨bius annulene synthesis, therefore, used a
strategy to stabilize the strained part of the Mo¨bius ring by a suitable
ꢁ
ꢂ
ꢀ ꢀ
dr2 × dr1 · r12
1
Wr =
ꢃ
ꢃ
ꢃ
ꢃ
3
4p
r12
C
r1, r2: points passing along C. r12 ¼ r2 2 r1.
1Institute for Organic Chemistry, University of Kiel, Otto-Hahn Platz 4, 24098 Kiel, Germany, 2Department of Chemistry, Nanoscience Center, University of
Jyva¨skyla¨, PO Box 35, 40014 Jyva¨skyla¨, Finland, 3Nagoya University, 1E Miyahigashi-cho, Showa-ku, Nagoya 466-0804, Japan, 4College of Materials Science
and Chemical Engineering, Harbin Engineering University, 145 Nantong Street, Harbin 150001, China. e-mail: rherges@oc.uni-kiel.de; kari.t.rissanen@jyu.fi
*
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NATURE CHEMISTRY DOI: 10.1038/NCHEM.1955
ARTICLES
observed in 2D projections if the object is viewed from all vantage
a
points (over the sphere of all projection directions)22,23,25–27
.
Tw and Wr are real numbers that can be either positive or
negative. Both topological parameters are connected by the
Cyclo-
28
˘
˘
Calugareanu theorem :
trimerization
Lk = Tw + Wr
The linking number Lk is always an integer. If the linking number Lk
is even (0,+2,+4, . . .) the band is orientable and two-sided, if Lk is
odd (+1, +3, +5, . . .) the ribbon is non-orientable and one-sided.
Whereas Tw and Wr of a band are interconvertible by topological
transformation (just by stretching, compressing or bending), the
linking number Lk can only be changed by cutting the band, twisting
and rejoining both ends. Probably the most important implication
of twist and writhe interconversion in chemistry or biology is
‘DNA supercoiling’. There are enzymes (topoisomerases) that cut
the double strand and give it a twist, which results in winding of
the DNA around itself (increasing writhe at the expense of twist)
to form a more compact superstructure29. Using the definition of
the linking number, a topological extension of the Hu¨ckel rules
can be derived30–33. Annulenes with Lk ¼ 0, +2, +4 (even) exhibit
a two-sided (orientable) p system. They are aromatic with 4n þ 2
p electrons. Annulenes with Lk ¼+1, +3, +5 (odd) exhibit a
one-sided (non-orientable) p system. They are aromatic with 4n
Cyclization
b
Local
crossing
Cyclization
electrons delocalized in the cyclic p system34–36
.
We and others proposed that, similar to ‘DNA supercoiling’, the
strain induced by the twist in annulenes can also be reduced by pro-
jection into writhe37,38. In fact, doubly twisted annulenes and por-
phyrins have been known for a long time37. However, they have
not been identified as such, probably because they form figure-
eight structures in which the twist is almost completely projected
into writhe. Based on quantum chemical calculations, Rzepa and
co-workers proposed a number of writhe structures with linking
numbers Lk . 1 that are aromatic with 4n electrons delocalized in
Lk = 6
T
w = 6
Wr = 0
Self-crossing
Mo¨bius topological p systems39–41
.
Lk = 6
w = 0
Wr = 6
We now set out to develop a general construction principle to
design multiply twisted or writhed annulenes. To prove our strategy
we synthesized a Mo¨bius dehydroannulene with Lk ¼ 3. As stated
above, a twist is difficult to stabilize in a linear precursor molecule.
Therefore, our strategy is based on building blocks that include a
‘hidden’ writhe (writhe units) instead of a twist. Helicene-type mol-
ecules are suitable writhe units. Unlike twisted building blocks,
which tend to untwist, helicene-type writhe units are stable
because their overlapping ends stabilize the (hidden) writhe. Thus,
on the combination of three writhe units, a Mo¨bius annulene with
LK ¼ 3 could, in principle, be synthesized. Unfortunately, the situ-
ation is more complicated. Writhe units are chiral, and they can
be combined in an ‘additive’ and a ‘subtractive’ manner. Three
different situations have to be distinguished (Fig. 2a–c).
The combination of two writhe units with opposite chiralities
leads to products with no writhe (the positive and the negative
writhe cancel each other). Two writhe units of the same chirality
linked together in an additive manner form helical systems in
which cyclization is difficult, because the two ends are far from
each other. In a subtractive combination the two ends are close.
However, ring closure at this stage would be premature as a
figure-eight structure with Lk ¼ 2 and Hu¨ckel topology would
be formed. Fortunately, p systems in chemistry have a finite
thickness, and the ends are thus bent away from each other.
Now a third writhe unit of the same chirality exactly fits and can
complement the ring (Fig. 2d). The product has Lk ¼ 23.
Nevertheless, it is only weakly strained, because most of the twist
is projected into writhe.
T
Positive
crossing
Negative
crossing
Figure 1 | Strategies to introduce multiple twists in a cycle. a, Naive
strategies may include the cyclotrimerization of three components each
containing a single twist, or cyclization of a band with three twists. Both
strategies are hampered because linear p systems cannot be twisted easily,
and if constrained to do so would probably not cyclize easily. b, The
transformation of twist (Tw) into writhe (Wr) in a closed band by winding
around itself can release strain and suggests an alternative strategy. Tw is a
measure of how often the upper edge of the band crosses the lower edge in
2D projections (local crossings, top), and Wr is a measure of the number of
crossings of the ribbon axis with itself. The middle illustration shows three
local self-crossings in the 2D projection of the view along the z axis
(orthogonal to the paper plane). To calculate the writhe either the average of
self-crossings in all projections from all vantage points has to be calculated
or the double Gaussian integral has to be solved. Local crossings and self-
crossings can be either positive or negative. To assign a sign to a crossing
the band has to be given a direction and the crossings are analysed as
shown in the bottom illustration (right handed, þ; left handed, 2). Tw and
Wr can take any positive or negative real number, Lk is always an integer.
In the case of a polygon (for example, annulenes) the double integral
can be replaced by a double sum. Fortunately, there is also a descrip- Synthesis. To translate our general strategy into the synthetically
tive interpretation: Wr is the average number of self-crossings accessible chemical compound 1, we chose 2,2′-diethynyl-1,1′-
2
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NATURE CHEMISTRY DOI: 10.1038/NCHEM.1955
ARTICLES
dimethylformamide (DMF). The Bestmann–Ohira reagent was
used to convert 3 into 5 in 74% yield. As a major side-product,
23% of the rac-2-formyl-2′-ethynyl-1,1′-binaphthyl (4) was
formed. Even with a fourfold excess of the Bestmann–Ohira
reagent a complete conversion could not be obtained. To avoid
the excessive formation of polymers a stepwise synthesis of the
ring was pursued. At first a linear trimer was prepared from rac-
2,2′-bis(bromoethynyl)-1,1′-binaphthyl (7) and the dimethylthexyl-
silyl (DMTS)-monoprotected writhe unit 8. A final ring-closure
reaction should furnish the target Mo¨bius dehydroannulene
(Fig. 3). Monoprotection of 5 with dimethylthexylsilyl chloride
(DMTS-Cl) is not selective. A mixture of the starting material 5,
monoprotected 8 and diprotected 6 in 25%, 65% and 10% yield
was obtained. As compared to the expected statistical 25:50:25
ratio, the product ratio is shifted towards monoprotection because
of the large size of the DMTS group, which hinders the introduction
of a second protecting group. Separation of the three products by
column chromatography and deprotection of 6 is no problem.
Therefore, an almost complete conversion of 5 into 8 could be
achieved after several iterations. A Cadiot–Chodkiewicz coupling
reaction of 7 with two equivalents of 8 gave the linear trimer 9 in
32% yield. The main side-products were oligomers. Whereas
higher oligomers can be separated easily by chromatography, the
dimer and tetramer that result from an incomplete reaction (reactive
ethynyl bromide and ethynyl end groups) exhibit similar retention
times as those of the trimer target product 9. It is therefore impor-
tant to drive the reaction to completion at higher temperatures and
long reaction times. A separation of the diastereomers 9a/b, 9c/d
and 9e/f by analytical HPLC was possible, but not worthwhile on
a preparative scale. Notwithstanding that only the enantiomeric
pair 9a/b can form the Mo¨bius dehydroannulene, ring closure of
either pure 9a/b or the mixture of diastereomers 9a/b, 9c/d and
9e/f after deprotection with TBAF (tetra-n-butylammonium fluor-
ide) would give the same mixture of oligomers as side-
products. Hence, a final separation of the Mo¨bius compound
from oligomeric products is inevitable. The synthesis was therefore
continued with a statistical mixture of 25% 9a/b, 50% 9c/d and 25%
9e/f. Deprotection with TBAF gave 10 in quantitative yields. As
expected, the mixture of diastereomers of 10 exhibits four
signals between d ¼ 2.69 and 2.74 with equal intensity. The
matrix-assisted laser desorption/ionization spectrum finally
proved the formation of 10.
a
Cancellation
+
of writhe
Wr = –1
Wr = +1
Wr = 0
b
Additive
Δh
Δh
Δh
+
Wr = –1, Δh = 1
Wr = –1, Δh = 1
Wr = –2, Δh = 2
c
Δs
Subtractive
+
Wr = –1, Δh = 1
Wr = –2, Δs ≥ 0, Δh = 0
Wr = –1, Δh = 1
d
Wr = –1
Δs = Δh
Lk = –3
(Tw = 0; Wr = –3)
e
f
Lk = –3
T
w = 3
Wr = –6
1
Figure 2 | Combining building blocks with writhe to produce a triply
twisted system and identification of a target structure. a–d, Different
combinations of writhe units (a–c) and formation of a Mo¨bius ring with
Lk ¼ 23 (d). Structures with Lk ¼ 3, Tw ¼ 0 and Wr ¼ 3 are difficult to draw.
e,f, To derive clearly recognizable chemical structures that can be drawn in
2D, we use the homeomorphic Lk ¼ 3, Tw ¼ 23 and Wr ¼ 6 projection (e).
The bridging units that connect the loops are not twisted in the 3D structure
(d). The twists arise from the topological transformation from d to e and
projection into 2D. Target structure 1 is presented in this projection (f).
However, for the discussion of the topology, and particularly of twist and
writhe, or properties that rely on the 3D geometry (such as orbital overlap),
please refer to the 3D structure as represented in d.
The final intramolecular cyclization of the mixture of diastereo-
mers 10 was performed under Eglinton conditions at high dilution.
Besides 11% of the target Mo¨bius ring 1, hexamers, nonamers and
dodecamers were formed. A ring with Lk ¼ 1 (1c/d), which could be
formed from the diastereomers 10c–f, was not observed. DFT calcu-
lations predict that this singly twisted Mo¨bius ring is highly strained,
and 16.4 kJ mol21 less stable than the triply twisted Mo¨bius dehy-
droannulene 1a/b (see Supplementary Fig. 6 and Supplementary
Table 1). If one considers that only 25% of 10 (10a/b) can cyclize
to give the Mo¨bius product, the yield for ring closure from 10a/b
is 44%. To favour the formation of ring systems, the reaction was
performed for a period of three weeks at room temperature, and
binaphthalene (5, Fig. 3) as the writhe units, and Glaser or Cadiot– then the temperature was increased by 10 8C per day to 70 8C.
Chodkiewicz coupling reactions to connect them to a ring. Structure Under these reaction conditions the linear trimer 10 was consumed
1 includes a system of 24 p electrons. Density functional theory completely (see Supplementary Fig. 7a–c) and thus the number of
(DFT) calculations (B3LYP/6-31G*) predict rather large dihedral side-products was reduced. Whereas the Mo¨bius ring 1a/b remained
angles (a ¼ 78.88) and the interruption of conjugation between unreacted, the linear oligomeric products with two reactive ends
the naphthyl rings in 1. Nevertheless, the p system of the 24- formed longer polymer chains as the reaction proceeded
electron periphery exhibits a triply twisted Mo¨bius topology. This (see Supplementary Fig. 7d,e). The polymers can be separated
is clearly visible in the frontier orbitals (see Supplementary Figs 3 easily from the Mo¨bius compound 1a/b by chromatography.
and 4).
More difficult was the separation of the hexamers, which was
The writhe unit 5 was prepared in two steps (Fig. 3). Starting performed by recycling gel permeation chromatography and
from rac-2,2′-dibromo-1,1′-binaphthyl (2), rac-2,2′-diformyl-1,1′- HPLC (see Supplementary Fig. 8; for experimental details see
binaphthyl (3) was prepared in 63% yield using n-BuLi and Supplementary Chapter 3).
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ARTICLES
a
(ii)
(iii)
96%
+
R
R
O
4
23%
5 74%
2 R = Br
(i) 63%
3 R = CHO
Br
Br
DMTS
32%
7
(v) 98%
+
(iv)
8
8
DMTS
10%
65%
(vi)
DMTS
DMTS
6
(viii)
11%
R
R
1
9
R = DMTS
(vii) 100%
10R = H
b
7a:(S )-7
a
7b: (R)-7
Ratio
1
Ratio
1a: (S,S,S)-1a
1b: (R,R,R)-1
(viii)
(viii)
9a: (S,S,S)-9a
9b:(R,R,R)-9
10a: (
10b: (
S,S,S)-10a
R,R,R)-10
|Lk| = 3
|Lk| = 1
1
2
1
(vii)
(vi)
1c: (S,S,R)-1
1d: (R,R,S)-1
9c: (S,S,R)-9
9d: (R,R,S)-9
10c: (S,S,R)-10
10d: (R,R,S)-10
2
1
9e: (S,R,S)-9
9f: (R,S,R)-9
10e: (S,R,S)-10
10f: (R,S,R)-10
Hexamers, nonamers,
8a: (S)-8a
dodecamers, etc.
2
0
(viii)
8b:(R)-8
¨
Figure 3 | Synthesis of the Mobius dehydroannulene. a, Reagents: (i) (1) n-BuLi, THF, (2) DMF, yield of 3 ¼ 63%; (ii) Bestmann–Ohira reagent, K2CO3,
MeOH, yields of 5 ¼ 74% and 4 ¼ 23%; (iii) NBS, AgNO3, acetone, yield of 7 ¼ 96%; (iv) (1) LiN(TMS)2, THF, (2) DMTS-Cl, yields of 8 ¼ 65%, 5 ¼ 25%
and 6 ¼ 10%; (v) TBAF, THF, yield of 8 ¼ 98%; (vi) Pd2(dba)3, LiI, CuI, PMP, DMSO, yield of 9 ¼ 32%; (vii) TBAF, THF, yield of 10 ¼ 100%; (viii) Cu(OAc)2,
pyridine, MeOH, yield of 1 ¼ 11%. All references for the synthesis are given in the Supplementary Chapter 3. b, Owing to the axial chirality of the writhe units
and the three possible ways to combine them, three diastereomers (enantiomeric pairs) are formed on the reaction of 7 with 8. In principle, the final ring
closure of 10a–f can furnish two cyclic trimers with Mo¨bius topology, besides oligomers and polymers. The Mo¨bius structure 1c/d with Lk ¼ 1 is not formed
because ring closure is energetically unfavourable. The red stereo descriptors indicate those stereoisomers that have the correct stereochemistry to form the
target (triply twisted) Mo¨bius product (1a/b). The compounds that are not highlighted with red stereo descriptors form either oligomers or a Mo¨bius
product with Lk ¼ 1. TMS, trimethylsilyl; dba, dibenzylideneacetone; DMTS, dimethyl-(1,1,2-trimethylpropyl)silyl; TBAF, tetra-n-butylammonium fluoride; NBS,
N-bromosuccinimide; PMP, 1,2,2,6,6-pentamethylpiperidine; DMSO, dimethyl sulfoxide.
1H and 13C NMR spectra proved the correct stereochemistry of was provided by X-ray crystallography (Fig. 4; see Supplementary
the Mo¨bius ring 1a/b. The enantiomers 1a and 1b exhibit D3 sym- Chapter 2). The experimentally determined geometry in the solid
metry. Therefore six signals are observed in the 1H NMR spectrum, state is in good agreement with our previous DFT (B3LYP/6-31G*)
and 12 signals appear in the 13C NMR spectrum (see Supplementary calculation (see Supplementary Table 2). The racemate 1a/b crystallized
Fig. 9). The final proof of the structure and Mo¨bius topology (Lk ¼ 3) in the centric space group P21/n with one Mo¨bius molecule and one
4
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ARTICLES
a
α
Molecular
Normal vectors
structure (X-ray)
on π plane
b
Lk = 3
Sign
T
w = 1.42, Wr = 1.58
inversion
α = 73.6°, 79.2°, 85.3°
Tips of normal vectors
connected
Band cut along the middle
→ trefoil knot
Figure 5 | Topological procedure to determine the linking number Lk of the
p system of 1. A band orthogonal to the p system is constructed and cut
down the middle. The fact that a trefoil knot is obtained confirms the linking
number, Lk ¼ 3, of the original band (see also Supplementary Fig. 5).
c
2.0
1.0
rings; Lk ¼ 1, one ring (double the diameter); Lk ¼ 2, two rings cate-
nated; and Lk ¼ 3, a trefoil knot (see also Supplementary Fig. 5).
That a trefoil knot is obtained confirms the linking number Lk ¼
3 of the p system of Mo¨bius annulene 1.
0.0
–1.0
–2.0
Conclusions
Based on fundamental topological principles, we developed a general
strategy to construct multiply twisted Mo¨bius compounds. The key to
our strategy is well-defined helical ‘writhe precursors’. On cyclization,
these writhe units give rise to a high linking number in the final ring
product without imposing considerable strain. The successful syn-
thesis of a triply twisted Mo¨bius dehydroannulene (Lk ¼ 3) presented
in this paper proves the practicality of our general design strategy.
Mo¨bius compounds are escaping from their cloistered existence.
They are no more exotic than catenanes, rotaxanes or other topological
structures in chemistry. Triply or more highly twisted Mo¨bius struc-
tures are probably easier to synthesize than singly twisted ones.
These chiral one-sided compounds exhibit a high potential for a
250 275 300 325 350 375 400 425
Wavelength (nm)
¨
Figure 4 | Structure of the Mobius dehydroannulene 1a/b with Lk 5 3 as
determined by X-ray crystallography. a,b, Ball and stick model (a) and
space-filling model (b). a, dihedral angle formed by two adjacent naphthyl
units. Chloroform molecules are omitted for clarity. c, CD spectra of both
enantiomers (1a/b, red and blue lines, respectively) of the Mo¨bius
dehydroannulene after separation on a chiral column.
chloroform solvate in the asymmetric unit. Separation of the two number of applications in molecular and optoelectronics43–49
.
enantiomers was achieved by chromatography on a chiral column
(Chiralcel OD; for details see Supplementary Chapter 1.12). The
Cotton effect of the circular dichroism (CD) spectra shows clear
mirror images of both enantiomers (Fig. 4c). The CD intensity
seems rather strong compared with those of other binaphthyl
derivatives42, although the Mo¨bius molecule contains three
binaphthyl units. This strong CD may partly be associated with
the Mo¨bius structure. Topological analysis using the program
ANEWWRITHM (F. Ko¨hler, University of Kiel)24 confirms the
linking number Lk ¼+3 (enantiomers have linking numbers of
opposite sign). The values for twist and writhe, Tw ¼ 1.42 and
Wr ¼ 1.58, reveal that more than half of the twist is projected into
writhe. This explains the high yield of macrocyclization, and the
low strain of the molecule despite its high linking number, Lk ¼ 3.
Methods
All the synthetic methods are described in the Supplementary Information.
Received 14 January 2014; accepted 11 April 2014;
published online 25 May 2014
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the
rigorous
mathematical
proof
(program
ANEWWRITHM), the linking number can be determined by a
simple topological procedure (Fig. 5). Consider the p system as a
band or construct a band orthogonal to the p system (as in
Fig. 5) and cut it down the middle. Depending on the linking
number the following objects are obtained: Lk ¼ 0, two separate
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NATURE CHEMISTRY DOI: 10.1038/NCHEM.1955
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Acknowledgements
We acknowledge The Academy of Finland (K.R., project no. 263256 and 265328) and the
National Doctoral Program in Nanoscience, Finland (F.T., PhD Fellowship) for financial
support. K.R. and F.T. thank G. Schaller and L. Kaufmann (Freie Universita¨t Berlin,
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Author contributions
G.R.S. worked out the topological construction strategy, developed the syntheses, carried
out the experiments and characterized the compounds. R.H. developed the topological
strategy and directed the study. F.T. prepared the single crystals, collected the data and
solved and refined the structure together with K.R. K.R. supervised the X-ray diffraction
part of the work. Y.O. and J.S. performed the separation and CD measurement of the
enantiomers. G.R.S., R.H., F.T. and K.R. wrote the manuscript.
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Additional information
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excited-state reactions. J. Am. Chem. Soc. 88, 1564–1565 (1966).
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Supplementary information and chemical compound information are available in the
online version of the paper. Reprints and permissions information is available online at
www.nature.com/reprints. Correspondence and requests for materials should be addressed to
K.R. and R.H.
35. Higashino, T. et al. Mo¨bius antiaromatic bisphosphorus complexes of
[30]hexaphyrins. Angew. Chem. Int. Ed. 49, 4950–4954 (2010).
Competing financial interests
The authors declare no competing financial interests.
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