Illusory molecular expression of "penrose stairs" by an aromatic hydrocarbon

Article abstract of DOI:10.1002/anie.201102210

Ascending and Descending: A combination of two helical molecules and two twisting covalent axes in the form of a macrocycle conjures an illusory molecular object that has a seemingly impossible molecular structure, that is, an endlessly descending circle

Full text of DOI:10.1002/anie.201102210

Communications
DOI: 10.1002/anie.201102210
Penrose Stairs
Illusory Molecular Expression of “Penrose Stairs” by an Aromatic
Hydrocarbon**
Waka Nakanishi, Taisuke Matsuno, Junji Ichikawa, and Hiroyuki Isobe*
Conveying three-dimensional objects in the form of two-
dimensional line drawings is an important skill, especially in
scientific and technological fields.[1] Ever since the invention
of the symbolic and ingenious representation of benzene as a
hexagon, line drawings of chemical substances are among the
most indispensable means to depict molecules.[2] Line draw-
ings, however, can sometimes deceive and amuse the viewers
by representing impossible objects, as pointed out by Penrose
and Penrose.[1,3] The Penrose stairs, endlessly descending
stairs in a continuous circle, were expressed in art by M. C.
Escher in his famous lithograph, Ascending and Descending.[4]
We found that such an illusory structure emerged from a
molecule with unique caracole topology.[5] Notably, the
molecular Penrose stairs, cyclobis[4]helicene 1, deceive us in
a manner different from the original proposal of Penrose. The
dynamic behavior of 1 in solution has been observed to show a
possible combination of covalent and noncovalent chemistry
to explore unique molecular topologies in future.
Scheme 1. Synthesis of cyclobis[4]helicene 1. Reagents and conditions:
We started the synthesis of 1 by preparing the helicene
subunit by an intramolecular cyclization reaction of difluoro-
alkene 2.[6] As we reported previously,[7] difluoroalkene with
halogenated phenyl groups was prone to a skeletal rearrange-
ment, but the desired dihalo[4]helicene 3 was obtained under
milder cyclization conditions. Thus, 2 was subjected to a
Friedel–Crafts type cyclization with magic acid (FSO3H·SbF5)
at 08C and was further converted to 3 by dehydrogenation
with trityl tetrafluoroborate (Ph3CBF4) without isolation of
the cyclized intermediate (Scheme 1). NMR spectroscopical
analysis of 3 showed that the compound was obtained in 53%
yield from 2 after purification by silica gel column chroma-
a) FSO3H·SbF5 (2.5 equiv), HFIP/CH2Cl2, 08C; b) Ph3CBF4 (4.0 equiv),
ClCH2CH2Cl, reflux; c) [Ni(cod)2] (2.4 equiv), 1,5-cyclooctadiene
(2.4 equiv), 2,2’-bipyridine (2.4 equiv), toluene/DMF, 608C. The colors
of the hydrogen atoms indicate the assignment of proton resonances
shown in Figure 3.
tography; however, it was also contaminated with a trace
amount of byproducts including chrysene and uncyclized
compounds.
The convergent homocoupling of subunit 3 proceeded
smoothly by Ni-promoted biaryl coupling to afford cyclo-
bis[4]helicene 1.[8] Thus, 3 (ca. 60% purity, NMR analysis)
was mixed with [Ni(cod)2], 1,5-cyclooctadiene, and 2,2’-
bipyridine to give 1 in 26% yield (yield of isolated product
after 3 steps from 2) after purification by recrystallization and
GPC (Scheme 1). As a byproduct, a small amount of a cross-
coupling product between 3 and the uncyclized contaminant
was also isolated.[9] Although the coupling reaction also took
place with oxidative coupling of the corresponding cuprate,[10]
the yield of 1 was not improved despite the formidable
procedure that requires a stepwise conversion by metalation.
The molecular structure of 1 was established unequiv-
ocally by X-ray crystallographic analysis of a single crystal.[11]
Two helicene subunits with the same helical configuration are
coupled in one molecule, and the crystal is composed of a
mixture of two enantiomers (see below). Taking into account
the helical chirality of the subunits and the axial chirality at
the linkages,[12] we can assign the absolute configurations of
the enantiomers as (P,P,R,R) and (M,M,S,S), respectively
(P,P,R,R-form shown in Figure 1). In each helicene subunit,
the decrement distances of the middle helix measure 0.95 and
0.63 ꢀ, and the interplanar angles at the terminus are 238 and
[*] Dr. W. Nakanishi, T. Matsuno, Prof. Dr. H. Isobe
Department of Chemistry, Tohoku University
Aoba-ku, 980-8578 Sendai (Japan)
Fax: (+81)22-795-6589
E-mail: isobe@m.tohoku.ac.jp
Homepage: http://www.orgchem2.chem.tohoku.ac.jp/
Prof. Dr. J. Ichikawa
Department of Chemistry, University of Tsukuba
Tsukuba, 305-8571 Ibaraki (Japan)
[**] This study was in part supported by KAKENHI (21685005, 20108015
to H.I. and 22550094 to W.N.). We thank S. Hitosugi for preliminary
investigations on the helicene synthesis, Prof. T. Iwamoto (Tohoku
Univ.) for the use of X-ray instruments, Prof. M. Kotani (Tohoku
Univ.) for guidance on topology, and Prof. K. Sugihara (Meiji Univ.)
for comments on Penrose stairs. Support on the elemental analysis
by the Research and Analytical Center for Giant Molecules (Tohoku
Univ.), DART MS instruments by JEOL, and HFIP supply by Central
Glass Co. are also gratefully acknowledged.
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/anie.201102210.
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Angew. Chem. Int. Ed. 2011, 50, 6048 –6051

Figure 1. Molecular structure of cyclobis[4]helicene 1. a) ORTEP draw-
ing with thermal ellipsoids at 50% probability showing a representa-
tive structure of (P,P,R,R)-1. The structure was determined by X-ray
crystallographic analysis. b) Line drawing with the absolute configura-
tions of the helical chirality (P) and the axial chirality (R).
198 (Figure S1). The hydrogen atoms attached to the inner 14-
membered ring are packed in an overcrowded environ-
ment.[13] Four out of six interatomic distances among four
hydrogen atoms are less than the sum of the van der Waals
radii (< 2.4 ꢀ) and the other two are of the same order
(ca. 2.4 ꢀ; Figure S2).
Figure 2. Packing structure of cyclobis[4]helicene 1. Structures are
viewed along the longitudinal direction of 1, showing two neighboring
columns.
The peculiarity of the molecular topology of 1 became
apparent and perplexed us, when we depicted the structure in
line drawings especially with depth-cue effects and config-
uration assignments as shown in Figure 1b. According to the
definition,[12,14] (P)-helicene is the right-handed helix in
which, when viewed perpendicular to the central aromatic
rings, the viewer would track the aromatic stairs downward by
circling in a right-handed direction. Each of the helicene
subunits of 1 obeys this definition: the P-form stairs lead the
viewer downward in a right-handed manner (Figure 1b, with
the decrement distance of 0.95 and 0.63 ꢀ, see above).
However, when one tracks the overall circle of the molecule
that bears two P-form subunits in the right-handed manner,
one unexpectedly reaches the original position without
descending (Figure 1b). The situation is, conceptually, a
molecular expression of a well-known impossible object, the
Penrose stairs.[3,4] As is often the case with illusions in art,[1]
the deliberate examination of 1 from the side reveals a simple
trick; the axial twists of the single bond linkages enable the
tilted orientation of the central naphthalene moieties of the
subunits (see Figure 2 for the side view).[15] Interestingly, we
noticed that the trick can also be disclosed by applying
another, well-conceived chemical terminology for the config-
uration assignments.[12] When we apply P and M helical
notions to the axial chirality of the (P,P,R,R)-isomer, for
instance, the molecule shows left-handedness (M,M) for the
two pillaring axes that bridge two right-handed helicenes
(P,P). The alternative assignment, (P,P,M,M), indeed indi-
cates that the stairs are quadruply helical and both ascending
and descending in one travelling direction.[16]
the same configuration, each of the enantiomers segregates
into a separate column. As shown in Figure 2, the columns of
(P,P,R,R)-1 and (M,M,S,S)-1 appear alternately in the crystal.
Chiral segregation is most likely prompted to maximize the
intermolecular contact area by assembling molecules of
structural complementarity, that is, molecules of the same
configuration.
Theoretical calculations indicate that the unique topology
of 1 may be conjured away in the monomeric form in solution.
Thus, the epimerization, a conformational change from
(P,P,R,R) to (M,M,S,S) or vice versa, proceeds through a
transient intermediate of the meso form (7.5 kcalmolÀ1 higher
in energy than chiral forms) and requires an activation energy
of 10.1 kcalmolÀ1 (see Figure S4). The activation barrier is
lower than that required for the racemization of [5]heli-
cene,[17] which suggests that the time-averaged structure of 1
may be regarded as a flat plane without peculiar topology.[18]
Note also that such a dynamic structural change may be
inherent to the 14-membered sp2-carbon ring and may
normally take place at the defects of the nanocarbon
materials.[19,20]
However, the 1H NMR analysis shows that the large
aromatic hydrocarbon skeleton facilitates the self-aggrega-
tion of 1 in solution. We observed upfield shifts of proton
resonances by increasing the concentration of 1 in chloroform
(Figure 3 and Figure S5). We applied the isodesmic model of
indefinite self-aggregation to the concentration-dependent
shifts of the aromatic resonances[21] and obtained the associ-
We also noticed that 1 forms columns of a single
enantiomer in crystals. Stacking on top of a molecule with
Angew. Chem. Int. Ed. 2011, 50, 6048 –6051
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Communications
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Figure 3. Concentration- and temperature-dependent shifts of aromatic
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ation constant Kassoc of 64.9 Æ 5.1mÀ1 at 288 K (see Table S10).
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enthalpy-driven character of the aggregation with values of
[9] See Supporting Information for detail.
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DH = À3.82 kcalmolÀ1 and DS = À4.91 calmolÀ1
K
(Fig-
ure S6). The observation of aggregation suggests that the
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aggregation that is expected from the crystallographic anal-
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According to a theorem in line drawings,[1] Penrose stairs
such as in M. C. Escherꢁs lithograph can be categorized as the
anomalous images that are generically reconstructible and
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Received: March 30, 2011
Published online: May 23, 2011
Keywords: arenes · helical structures · line drawings ·
.
Penrose stairs · self-assembly
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