Axial coordination changes the morphology of porphyrin assemblies in an organogel system

Article abstract of DOI:10.1039/b602025a

The gelation properties of a zinc porphyrin bearing peripheral urea groups (1·Zn) were evaluated in the absence and the presence of several diamines. In aromatic solvents such as benzene, toluene and p-xylene, 1·Zn only provided the precipitate. In contra

Full text of DOI:10.1039/b602025a

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www.rsc.org/obc | Organic & Biomolecular Chemistry
Axial coordination changes the morphology of porphyrin assemblies in an
organogel system†
Takanori Kishida,a Norifumi Fujita,a Osamu Hirataa and Seiji Shinkai*a,b
Received 10th February 2006, Accepted 16th March 2006
First published as an Advance Article on the web 13th April 2006
DOI: 10.1039/b602025a
The gelation properties of a zinc porphyrin bearing peripheral urea groups (1·Zn) were evaluated in the
absence and the presence of several diamines. In aromatic solvents such as benzene, toluene and
p-xylene, 1·Zn only provided the precipitate. In contrast, 1·Zn with 0.5 and 1.0 equiv. of piperazine
formed gels, and the gel with 0.5 equiv. of piperazine showed a unique physical property called
‘thixotropy’. On the other hand, upon addition of similar diamines such as DABCO, ethylenediamine
and N,Nꢀ-dimethylethylenediamine, 1·Zn did not gelate these solvents. When the critical gelation
concentration was plotted against the ratio of piperazine versus 1·Zn, it afforded a minimum
breakpoint at 0.5 equiv. and the critical concentration increased with further increase in the fraction of
piperazine, indicating that the stable gel is formed from the 1·Zn + piperazine 2 : 1 complex and the
subsequent transformation to the 1 : 1 complex rather destabilizes the gel. Very interestingly, it was
clearly shown by SEM and TEM observations that such structural changes of the unit complex induced
by the ratio of piperazine versus 1·Zn can lead to gradual morphological transitions: that is, spherical
structure at 0 equiv., 1-D fibrous structure at 0.5 equiv. and 2-D sheet-like structure at 1.0 equiv. In
addition, UV-VIS spectra revealed that 1·Zn itself adopts a J-aggregation mode, whereas 1·Zn +
piperazine 2 : 1 and 1 : 1 complexes adopt an H-like aggregation mode. On the other hand, upon
addition of 0.5 equiv. of other diamines, 1·Zn + diamine complexes result in different morphologies
other than the 1-D fibrous structure. To explore a reasonable rationale for these results, we conducted
computational studies. As a result, we found that the complex symmetry of the unit complex plays an
important role in determining the final ordered structure.
porphyrin ring can tune the aggregation mode of porphyrin rings
in organogel systems; for example, J-aggregated 1 and 2 create 2-D
sheet-like structures, whereas H-aggregated 1·Cu and 3 create 1-
Introduction
Organogels are thermo-reversible soft materials composed of
D fibrous structures.6,7 Furthermore, if one can reversibly change
the unit structure of gelator molecules, their gelation properties
and morphologies would become reversibly controllable. As far
as we are aware, there are few successful examples.2–5 Especially,
examples in which the gelation properties are drastically affected
by additives have scarcely been reported.5 We thus approached a
new strategy for controlling metalloporphyrin-based superstruc-
tures by addition of diamine ligands which can act as axial
ligands. It is well-known that metalloporphyrins self-assemble
with coordinative molecules to create geometrical complexes and
their shapes largely depend on the kind and the amount of
coordinal molecules added.8–12 It occurred to us that the skilful
use of such axial ligands in organogel systems would allow us to
control gelation properties and gel morphology by a change in the
aggregation mode of porphyrin–diamine complexes. With this idea
in mind, we used Zn(II) complexes of 1 (1·Zn) and several diamine
molecules and evaluated whether diamine molecules can play an
important role in controlling the porphyrin-based superstructures.
three-dimensional (3-D) networks created by the spontaneous
assembly of low molecular mass molecules. In the field of
supramolecular chemistry, they can be recognized as specific
systems in which nano- and micro-scale geometrical superstruc-
tures such as one-dimensional (1-D) fibrous, two-dimensional
(2-D) sheet-like and 3-D ribbon-like and helical structures are
created according to their specific self-assembling manners.1–5 The
fact implies that the superstructure of molecular assemblies thus
created strongly reflects the shape of each molecular unit, because
they basically are constructed by assembling molecular units via
various non-covalent interactions. Therefore, to clarify a correla-
tion relationship between the molecular shape and the aggregation
mode would enable us to explore new potential applications of
nano- and micro-scale objects in chemistry and material sciences.
Recently, we found that introduction of hydrogen-bond-forming
groups into peripheral meso-phenyl groups or a metal ion into a
aDepartment of Chemistry and Biochemistry, Graduate School of Engineer-
ing, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, Fukuoka, 819-
0395, Japan
Results and discussion
bCenter of Future Chemistry, Kyushu University, 744 Motooka, Nishi-ku,
Fukuoka, Fukuoka, 819-0395, Japan. E-mail: seijitcm@mbox.nc.kyushu-
u.ac.jp; Fax: +81 92 802 2820
Gelation properties
† Electronic supplementary information (ESI) available: UV-VIS absorp-
tion spectral change of the benzene solution of 4·Zn by piperazine. See
DOI: 10.1039/b602025a
The gelation abilities of 1·Zn in the absence and the presence of
several diamines were tested for three aromatic solvents by the
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Table 1 Gelation properties of 1·Zn in the absence and the presence of
The precipitate of 1·Zn gives a spherical structure with 0.1–5 lm
diameter (Fig. 2a and 2d). When 1·Zn and piperazine form the
2 : 1 complex, the resultant benzene gel creates a 1-D fibrous
structure which develops into a highly 3-D network (Fig. 2b
and 2e). Furthermore, the structure of 1 : 1 complex + benzene
gel is transformed into a 2-D sheet-like structure (Fig. 2c and
2f). The more-magnified visual image (Fig. 2f) obtained from
TEM observation shows the presence of a fine striped structure,
indicating that a highly-ordered molecular array is constructed
in this sheet-like structure. The fact supports the view that the
physical properties of these gels are controllable by the amount of
piperazine added.
diaminesa
Diamine (the stoichiometry
for 1·Zn)
Benzene
Toluene
p-Xylene
None
P
P
P
Piperazine (0.5 equiv.)
Piperazine (1.0 equiv.)
DABCO (0.5 or 1.0 equiv.)
Other diaminesb (0.5 or
1.0 equiv.)
G (3.0)
G (30)
PG
G (3.0)
G (20)
PG
G (2.0)
G (10)
PG
P
P
P
a G, PG and P denote gelation, partial gelation and precipitate, respectively.
The critical gelation concentration (g dm−3) is shown in parenthesis.
P and PG are at [gelator] = 30 g dm−3
.
b Ethylenediamine and N,Nꢀ-
We took SEM images of the aggregates of 1·Zn + other diamine
complexes in benzene. While all dried samples prepared from
1·Zn + diamine 1 : 1 complexes commonly form the morphology
based on the 2-D sheet-like structure (Fig. 2c and 3d–e), some dried
samples prepared form 2 : 1 complexes afford new morphologies
different from that of 1·Zn + piperazine 2 : 1 complex which gives
the 1-D fibrous structure: that is, the 2-D sheet-like structure for
DABCO and the amorphous structure for ethylenediamine and
N,Nꢀ-dimethylethylenediamine (Fig. 2b and 3a–c). In addition,
FT-IR spectral data consistently support the morphological dif-
ference of 2 : 1 complexes dependent on the sort of diamine (Fig. 4b
and 4d–f). In general, when hydrogen-bonding interactions among
urea groups become stronger, IR absorption bands assignable to
amide I and amide II appear at lower and higher wave number
region, respectively. Amide I and amide II of each 1·Zn + diamine
2 : 1 complex were observed at expected wave numbers; (pipera-
zine) 1627 and 1580, (DABCO) 1628 and 1575, (ethylenedi-
amine) 1630 and 1571, (N,Nꢀ-dimethylethylenediamine) 1631 and
1571 cm−1. These data mean that the hydrogen-bonding interac-
tions among urea groups in 1·Zn + piperazine and DABCO 2 : 1
complexes are stronger than those in 1·Zn + ethylenediamine and
N,Nꢀ-dimethylethylenediamine 2 : 1 complexes, suggesting that
former two complexes fabricate more ordered superstructures than
latter two complexes. These results indicate that the morphological
difference dependent on the sort of diamine reflects the gel
properties of 1·Zn.
dimethylethylenediamine.
‘stable-to-inversion of a test tube’ method (Table 1). 1·Zn did not
gelate all solvents tested herein with 30 g dm−3. Interestingly, when
each amine was added to 1·Zn, 1·Zn with 0.5 and 1.0 equiv. of
piperazine acted as a good gelator for benzene, toluene and p-
xylene, whereas 1·Zn with other amines formed a partial gel (1,4-
diazabicyclo[2.2.2]octane (DABCO)) or precipitates (ethylene-
diamine and N,Nꢀ-dimethylethylenediamine). Furthermore, we
found that 1·Zn + 0.5 equiv. of piperazine gel used herein
shows a unique physical behaviour called ‘thixotropy’ in aromatic
solvents.13 Generally, a low molecular-weight gel cannot regenerate
its original gel state once it is converted from the gel state to
the sol state by physical stimuli such as vibration. As shown in
Fig. 1, on the other hand, 1·Zn with 0.5 equiv. of piperazine
gel again formed its original gel state when it was left at room
temperature for a few seconds after its gel state had been collapsed
by vibration. In contrast, 1·Zn with 1.0 equiv. of piperazine gel did
not show such behaviour, resulting in the precipitate after several
minutes. This difference of physical properties is dependent on the
added amount of piperazine and seems to determine the shape and
morphology of these gels. Through these findings, we tried to seek
a reasonable rationale as to why the gelation properties of 1·Zn are
drastically affected by added piperazine. We thus investigated the
properties of 1·Zn + diamine from the both sides of morphological
observation and spectral analyses.
Stoichiometry of complexes
SEM and TEM observations
Secondly, we investigated the correlation between the unit struc-
ture and the aggregation mode of 1·Zn + piperazine complex in the
gel phase in detail. To estimate the stochiometry of 1·Zn + piper-
azine complexes in benzene gels, we evaluated whether the critical
gelation concentrations (CGC) of 1·Zn + piperazine complex in
benzene gels are influenced by the concentration of piperazine
First of all, to have an insight into the morphology of the
architectures formed by 1·Zn and 1·Zn + piperazine gels in
benzene, we conducted SEM and TEM observations. Surprisingly,
as seen from Fig. 2, the superstructures are remarkably changed
depending upon the stoichiometry between piperazine and 1·Zn.
Fig. 1 Photographs showing the thixotropic behaviour of 1·Zn + piperazine 2 : 1 complex + benzene gel; (a) the benzene gel, [1·Zn] = 10 g dm−3
(5.2 mM), [piperazine] = 0.5 equiv. for 1·Zn, (b) shaking the gel with a vibrator, (c) leaving the gel for several seconds, (d) the regenerated gel state.
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Fig. 2 SEM (a–c) and TEM (d–f) images of xerogels prepared from (a and d) the aggregate of 1·Zn and 1·Zn + piperazine (b and e) 2 : 1 and (c and f)
1 : 1 complexes gels in benzene; [1·Zn] = 10 g dm−3 (5.2 mM), [piperazine] = 0.5 or 1.0 equiv. for 1·Zn. Inset shows cross-section analysis in the image of
(f). White line in the image represents the place scanned.
Fig. 3 SEM images of dried samples prepared from the aggregates of 1·Zn + diamine (a–c) 2 : 1 and (d–f) 1 : 1 complexes in benzene; (a and d) DABCO,
(b and e) ethylenediamine and (c and f) N,Nꢀ-dimethylethylenediamine, [1·Zn] = 10 g dm−3 (5.2 mM), [diamine] = 0.5 and 1.0 equiv. for 1·Zn.
with respect to 1·Zn. When less than 0.2 equiv. of piperazine is
added, the mixture gives the precipitate, whereas when more than
0.2 equiv. of piperazine is added, 1·Zn + piperazine complex is able
to gelate benzene. A plot of CGC versus [piperazine]/[1·Zn] gives a
minimum at [piperazine]/[1·Zn] = 0.5 and the CGC increases with
the increase in [piperazine]/[1·Zn] (Fig. 5). This change indicates
that the benzene gel is most stabilized when 1·Zn and piperazine
form the 2 : 1 complex originating from axial coordination to
Zn(II), whereas it is gradually destabilized by transformation to
the 1 : 1 complex with the increase in the added amount of
piperazine.
Further evidence for the stoichiometry of these complexes
1
was obtained from H NMR spectra using 4·Zn as a reference
compound, because no useful information was obtained from
1·Zn itself because of the serious peak broadening. The chemical
shift of the b-proton in 1H NMR titration of a benzene solution of
4·Zn by piperazine showed that 4·Zn and piperazine initially form
a 2 : 1 4·Zn–piperazine complex, which is then transformed to a
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Fig. 6 1H NMR titration of piperazine into the benzene solution of 4·Zn.
Dd is the change in chemical shift of the b-proton.
the fact that the added diamine does not directly affect the
hydrogen-bonding network among the urea groups in the gel phase
of 1·Zn, we assume that 4·Zn without urea groups can be used
as a model compound of 1·Zn in order to gain information about
the formation of the complex in a solution phase.
UV-VIS absorption spectroscopic analyses
Fig. 4 FT-IR spectra of (a) the aggregate of 1·Zn only, 1·Zn + piperazine
(b) 2 : 1 and (c) 1 : 1 complexes gels and the aggregates of 1·Zn + (d)
DABCO, (e) ethylenediamine and (f) N,Nꢀ-dimethylethylenediamine 2 : 1
complexes in benzene; [1·Zn] = 10 g dm−3 (5.2 mM), [piperazine] = 0.5
and 1.0 equiv. and [other diamine] = 0.5 equiv. for 1·Zn.
UV-VIS absorption measurements of 1·Zn in the absence and
the presence of piperazine were carried out to obtain an insight
into the aggregation mode. The UV-VIS absorption spectrum
of a homogeneous solution of reference compound 4·Zn gave
a Soret band at 425.5 nm in benzene. In the aggregate of 1·Zn
in benzene, it shifted to longer wavelength (441.0 nm), indicating
that it assembles into a J-aggregate (Fig. 7a and 8a). Upon the
addition of piperazine to the benzene solution of 4·Zn, the Soret
Fig. 5 A plot of CGC versus [piperazine]/[1·Zn] in benzene; G and P
denote gelation and precipitate, respectively.
1 : 1 complex with the increase in the ratio of [piperazine]/[4·Zn]
with the same concentration of [1·Zn] (5.2 mM) as observed for
other spectral and microscopic analyses (Fig. 6). This view was
judged from 1H NMR titration datum of porphyrin derivative +
diamine complex reported by Andersonet al.11 In addition, the FT-
IR spectra showed that the addition of piperazine does not give any
damage on the hydrogen-bonding network among intramolecular
urea-to-urea groups in 1·Zn [amide I and amide II: (0 equiv.)
1632 and 1571, (0.5 equiv.) 1628 and 1580, (1.0 equiv.) 1628
and 1580 cm−1] (Fig. 4a–c). These spectral results consistently
support the view that 1·Zn and piperazine form 2 : 1 and 1 : 1
complexes owing to axial coordination in the gel phase. Judging
from both results of these data and SEM observations, the
gradual transformation of the unit component induced by axial
coordination can successfully result in the dimensional control of
porphyrin-based superstructures. In addition, considering from
Fig. 7 UV-VIS absorption spectra of (a) the aggregate (i, 5.2 mM) of
1·Zn and the solution (ii, 1.5 × 1−6 M) of 4·Zn and (b) 1·Zn + piperazine
2 : 1 (i, 5.2 mM) and 1 : 1 (ii, 5.2 mM) complex gels and the solution
of 4·Zn + piperazine 1 : 1 complex (iii, 1.5 × 1−6 M) in benzene at
25 ◦C. The saturated spectrum obtained from the titration of piperazine
into the benzene solution of 4·Zn was adopted as the spectrum of 4·Zn +
piperazine 1 : 1 complex (refer to the ESI).
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Fig. 8 Schematic representations of aggregation modes of (a) 1·Zn only, 1·Zn + piperazine (b) 2 : 1 and (c) 1 : 1 complexes in the aggregates.
band of 4·Zn + piperazine 1 : 1 complex was observed at 432.0 nm
(Fig. 7b). In the 1·Zn + piperazine 1 : 1 complex + benzene gel, on
the other hand, the new Soret band was observed at 411.0 nm with
the Soret band attributable to the complex monomer (432.0 nm).
These results imply that porphyrin rings in 1 : 1 complexes adopt
an H-like aggregation mode in the gel phase, as shown in Fig. 8c.14
On the other hand, the Soret band for 1·Zn + piperazine 2 : 1
complex + benzene gel also appeared at the shorter wavelength
(409.5 nm). Critically speaking, this peak should be compared to
the Soret band of homogeneous solution of 4·Zn + piperazine 2 : 1
complex. However, its spectral data could not be obtained because
of its absence in the concentration region of UV-VIS absorption
measurements. Therefore, we compared our data with the UV-
VIS absorption spectral data of porphyrin derivative + diamine
complex reported by Hunter et al. When they formed a sandwich-
shaped complex, the Soret band of the complex appeared at a
longer wavelength than that of the porphyrin derivative itself.15
Judging from these data, one may regard that the Soret band
obtained herein (409.5 nm) stems from the formation of an H-like
aggregated stacking created by 2 : 1 complexes, but not from the
formation of 2 : 1 complex (Fig. 8b).
the complex symmetry. This finding is complementary with SEM
observation, suggesting that these results imply that complex
symmetry is one of indispensable prerequisites to construct
ordered superstructures.
Furthermore, we also found the difference between two sym-
metrical complexes composed of piperazine or DABCO which
create 1-D fibrous or 2-D sheet-like structure, respectively. In the
former, piperazine coordinates to zinc porphyrin with adopting
a chair conformation. Accordingly, one can recognize from the
side view of the complex that two porphyrin rings in the complex
shift to some extent in the parallel direction: in other words, two
porphyrin rings are not overlapped precisely (Fig. 9a). In contrast,
those in the complex containing DABCO are precisely overlapped
because of the symmetrical structure (Fig. 9b). One may regard,
therefore, that this slight structural difference would lead to the
large difference in the hydrogen-bond pattern determining their
structural dimension, as shown in possible aggregation modes
illustrated in Fig. 10.
The schematic representation of hydrogen-bonding pattern
formed in the H-like aggregated porphyrin column is mentioned
in Fig. 10. Generally, the hydrogen-bond-forming urea-to-urea
distance is 0.43–0.46 nm.17 However, in an energy-minimized
structure, the nearest urea-to-urea distance in the complex is
longer than the distance suitable to formation of hydrogen-bonds.
Therefore, we assume an aggregation mode depicted in Fig. 10:
that is, 1·Zn + piperazine or DABCO 2 : 1 complex creates H-like
aggregated columns driven by p–p stacking and hydrogen-bonding
interactions. Then, it is reasonable to propose the interdigitated
hydrogen-bonding network among these columns, adjusting the
urea-to-urea distance by rotation of porphyrin rings in the
complex. Herein, we again assume that there is some difference
in the growth mechanism of the hydrogen-bonding networks
constructed from two complexes: that is, as shown in Fig. 10(i), in
the case of the H-like aggregated porphyrin column created from
the piperazine complex, the column has some distortion in the
axial direction because the complex features the lower symmetrical
Computational studies on the influence of diamines
As mentioned above, it is now apparent from SEM observations
and FT-IR spectra that the aggregates of 1·Zn + diamine 2 : 1
complexes provide different morphologies depending on the sort
of diamine. To explore a reasonable rationale for this result, we
conducted computational studies for 2 : 1 complexes of reference
compound 5,10,15,20-tetrakis-(4-methoxyphenyl)porphine zinc
and diamine.16 These energy-minimized structures are shown
in Fig. 9. It is seen from Fig. 9 that two porphyrin rings in
complexes with piperazine or DABCO are nearly in parallel,
whereas those in complexes with ethylenediamine or N,Nꢀ-
dimethylethylenediamine are largely tilted, so that their structures
lose symmetry: that is, the diamine structure remarkably influences
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Fig. 9 Side views of the energy-minimized structures of 5,10,15,20-tetrakis-(4-methoxyphenyl)porphine zinc + diamine 2 : 1 comlexes with Discover
3/Insight II 98; (a) piperazine, (b) DABCO, (c) ethylenediamine and (d) N,Nꢀ-dimethylethylenediamine.
structure in the porphyrin rings. The columnar distortion should
arise from the subtle disorder of urea groups arrangement along
the column, which hampers the columns from assembling into
the 2-D direction. On the other hand, as shown in Fig. 10(ii),
the higher symmetrical structure in the DABCO complex creates
the better ordered porphyrin column. Then, the peripheral urea
groups can be appropriately pre-organized along the column to
form the more energetically stable hydrogen-bonding network.
As a result, the complex can effectively assemble into the 2-D
direction.
using a Shimadzu FT-IR 8700 spectrometer. Mass spectral data
were obtained using a Perseptive Voyager RP MALDI TOF mass
spectrometer. UV-VIS absorption spectra were measured on a
Shimadzu UV-2500PC spectrophotometer.
SEM measurements
The gel prepared in a sample tube was frozen by liquid. The
sample was evaporated by a vacuum pump under reduced pressure
for 1 d at room temperature. The obtained sample was shielded
with platin. The accelerating voltage of the transmission electron
microscope was 25 kV and the beam current was 10 lA.
Conclusion
TEM measurements
In conclusion, we demonstrated that novel architectures of
porphyrin assemblies can be designed utilizing metal–ligand
interaction with diamines acting as axial ligands, and the su-
perstructure fabricated from the complex creates an organogel
showing a thixotropic behaviour. In this study, it has become
clear that the unit components, which are affected by the sort
and the stoichiometry of added diamine, remarkably influence
the gelation properties, physical properties and morphologies.
Especially, addition of piperazine induces remarkable changes in
the formation and transformation of the complex. We believe,
therefore, that this kind of molecular recognition in the gel
system will be applicable to drug delivery systems, collection of
waste materials and pollutants, recovery of precious bio-active
compounds, etc.
A piece of the gel was placed in a carbon-coated copper grid.
The sample was dried by a vacuum pump under reduced pressure
for 1 d at room temperature. The accelerating voltage of the
transmission electron microscope was 120 kV and the beam
current was 65 A.
Materials
5,10,15,20-tetrakis-[4-[3-(3-N-Dodecylureido)propoxy]phenyl]-
porphine zinc (1·Zn) and 5,10,15,20-tetrakis-[4-[2-ethylhexoxy]-
phenyl]porphyrin were prepared according to the literature
reported previously and identified by FT-IR and 1H NMR spectral
evidence and elemental analysis.7,18
Synthesis of 5,10,15,20-tetrakis-[4-[2-ethylhexoxy]phenyl]porphine
zinc (4·Zn)
Experimental
To a solution of 5,10,15,20-tetrakis-[4-[2-ethylhexoxy]phenyl]-
porphyrin (100 mg, 0.147 mmol) in 20 mL of chloroform–
methanol = 3 : 1 (v/v) was added zinc acetate dihydrate (321 mg,
1.47 mmol) and the mixture was warmed at room temperature for
Equipment
1H NMR spectra were measured on a Bruker DMX 600 spec-
trometer. J values are given in Hz. IR spectra were obtained
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Fig. 10 Proposed mechanisms for different aggregation modes between 1·Zn + piperazine (i) and DABCO (ii) 2 : 1 complexes. The middle figures
represent the interdigitated hydrogen-bonding pattern forming among H-like aggregated complex columns. The right figures represent an axial distortion
of an H-like aggregated complex column.
2 h. The solution was evaporated under reduced pressure. The solid
residue was purified through chromatography [silica gel, CHCl3] to
Acknowledgements
give 4·Zn in 90% (93 mg); mp 180–182 ◦C; dH( 600 MHz; CDCl3;
Me4Si) 0.72–1.39 (m, 2-ethylhexyl, 56 H), 1.52–1.55 (m, CH, 4 H),
3.64 (d, OCH, J = 5.5, 8H), 6.96 (d, Ph–H, J = 8.6, 8 H), 7.95 (d,
Ph–H, J = 8.5, 8 H), 8.86 (s, b-pyrrole, 8H); IR mmax/cm−1 1243
(OC), 2858 (CH), 2923 (CH); MS [dithranol] m/z: 1091.4 [M +
H]+; Anal. calcd for C76H92N4O4Zn: C, 76.65; H, 7.79; N, 4.70.
Found: C, 76.52; H, 7.76; N, 4.82%.
This work was partially supported by The Mitsubishi Foundation
and Grant-in-Aid for Young Scientists (B) (No. 16750122), Scien-
tific Research on Priority Area (No. 17036051), Scientific Research
(S) (15105004), the 21st Century COE Program “Functional
Innovation of Molecular Informatics” from the MEXT of Japan.
We would like to thank K. Yoshizawa of Kyushu University for
valuable discussions on computational studies.
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