A dual-catalysis approach to enantioselective [2 + 2] photocycloadditions using visible light

Article abstract of DOI:10.1126/science.1251511

In contrast to the wealth of catalytic systems that are available to control the stereochemistry of thermally promoted cycloadditions, few similarly effective methods exist for the stereocontrol of photochemical cycloadditions. A major unsolved challenge in the design of enantioselective catalytic photocycloaddition reactions has been the difficulty of controlling racemic background reactions that occur by direct photoexcitation of substrates while unbound to catalyst. Here, we describe a strategy for eliminating the racemic background reaction in asymmetric [2 + 2] photocycloadditions of a,b-unsaturated ketones to the corresponding cyclobutanes by using a dual-catalyst system consisting of a visible light-absorbing transition-metal photocatalyst and a stereocontrolling Lewis acid cocatalyst. The independence of these two catalysts enables broader scope, greater stereochemical flexibility, and better efficiency than previously reported methods for enantioselective photochemical cycloadditions.

Full text of DOI:10.1126/science.1251511

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contract FA8750-12-2-0303, and a National Security Science
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Supplementary Materials
www.sciencemag.org/content/344/6182/386/suppl/DC1
Materials and Methods
Figs. S1 to S6
Movies S1 to S58
References and Notes
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9715–9720 (2008).
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31 December 2013; accepted 17 March 2014
Published online 27 March 2014;
10.1126/science.1250298
REPORTS
certain structural motifs that are otherwise dif-
ficult to construct (3, 4). For example, the most
straightforward methods for the construction of
cyclobutanes and other strained four-membered
rings are photochemical [2 + 2] cycloaddition
reactions. The stereochemical control of photo-
cycloadditions, however, remains much more
challenging than the stereocontrol of analo-
gous non-photochemical reactions (5, 6) despite
A Dual-Catalysis Approach to
Enantioselective [2 + 2]
Photocycloadditions Using Visible Light
Juana Du,* Kazimer L. Skubi,* Danielle M. Schultz,* Tehshik P. Yoon†
In contrast to the wealth of catalytic systems that are available to control the stereochemistry of thermally the chemistry community’s sustained interest
promoted cycloadditions, few similarly effective methods exist for the stereocontrol of photochemical in photochemical stereoinduction over the last
cycloadditions. A major unsolved challenge in the design of enantioselective catalytic photocycloaddition century (7, 8).
reactions has been the difficulty of controlling racemic background reactions that occur by direct
photoexcitation of substrates while unbound to catalyst. Here, we describe a strategy for eliminating
Although many strategies using covalent chiral
auxiliaries (9, 10) or noncovalent chiral controllers
the racemic background reaction in asymmetric [2 + 2] photocycloadditions of a,b-unsaturated ketones to (11, 12) have been used to dictate absolute stereo-
the corresponding cyclobutanes by using a dual-catalyst system consisting of a visible light–absorbing
transition-metal photocatalyst and a stereocontrolling Lewis acid cocatalyst. The independence of these
two catalysts enables broader scope, greater stereochemical flexibility, and better efficiency than
previously reported methods for enantioselective photochemical cycloadditions.
chemistry in photochemical cycloaddition reac-
tions, the development of methods that utilize
substoichiometric stereodifferentiating chiral cat-
alysts has proven a more formidable challenge.
odern stereoselective synthesis enables is important in a variety of fields ranging from
the construction of a vast array of or- drug discovery to materials engineering. Photo-
Department of Chemistry, University of Wisconsin–Madison,
1101 University Avenue, Madison, WI 53706, USA.
M
ganic molecules with precise control chemical reactions could have a substantial im-
over their three-dimensional structure (1, 2), which pact on these fields by affording direct access to †Corresponding author. E-mail: tyoon@chem.wisc.edu
*These authors contributed equally to this work.
392
25 APRIL 2014 VOL 344 SCIENCE www.sciencemag.org

REPORTS
This is largely due to the difficulty of controlling unbound achiral substrate, free from the influence the catalyzed reaction might be (Fig. 1A, path ii),
uncatalyzed background photochemical processes of a chiral catalyst, necessarily results in racemic the net enantiomeric excess (ee) of the product
(Fig. 1A, path i). The direct photoexcitation of an products; thus, regardless of how enantioselective will be low unless the rate of the uncatalyzed
A
B
racemic pathway
O
O
MLn
Ph
O
O
O
R'
R'
h
1+
i-Pr2NEt
Ru(bpy)3
R
* *
R
MLn
Ph
Me
path i
+
i-Pr2NEt
Me
O
Me
2+
+[cat]*
O
–[cat]*
–[cat]*
[cat]*
+[cat]*
R'
Ru*(bpy)3
h
MLn
Ph
O
O
O
[cat]*
2+
[2+2]
O
MLCT
Ru(bpy)3
+
Ph
Me
Me
R'
h
R
* *
R
MLn, – e–
Me
Me
path ii
enantioselective pathway
C
O
O
5 mol% Ru(bpy)3Cl2
20 mol% Lewis acid
30 mol% ligand
O
O
O
O
Me
Ph
Ph
Me
Ph
Me
Entry
Ligand Yield (%)*
ee (%)
Lewis acid
Gd(OTf)3
Gd(OTf)3
Gd(OTf)3
Gd(OTf)3
Gd(OTf)3
Gd(OTf)3
Eu(OTf)3
2:3
3:1
--
+
i-Pr2NEt, MeCN
visible light, rt, 4 h
Me
--
4
5
6
7
8
8
--
--
1
2
3
4
5
6
32
0
Me
Me
2.5 equiv.
1
2
3
27
32
56
43
41
74
3:1
2.5:1
6:1
0
Ph
Ph
Ph
O
O
OH
OH
Me
Me
O
O
–6
21
56
78
85
OH
OH
N
N
N
Ph
>10:1
3.5:1
7:1
Me
Me
Me
Me
Me
4
6
5
7
Me
CO2t-Bu
8†
Eu(OTf)3
Eu(OTf)3
8
8
O
H
N
N
9†, ‡
71
7:1
92
N
N
NHn-Bu
NHn-Bu
O
Me
O
O
OH
OH
7
8
Me
Fig. 1. Design plan for enantioselective catalytic [2 + 2] cycloaddi- trifluoromethanesulfonate. rt, room temperature. *Yields determined by
tion reactions. (A) Competing enantioselective and racemic pathways in 1H–nuclear magnetic resonance (NMR) analysis using an internal standard.
asymmetric photocycloadditions. (B) Ru(bpy)32+-catalyzed [2 + 2] cyclo- †Optimized conditions: 5 equivalents of methyl vinyl ketone, 5 mol % Ru
addition reaction using visible light. bpy, 2,2ʹ-bipyridine; MLCT, metal-to- (bpy)3Cl2, 10 mol % Lewis acid, 20 mol % ligand, 0.2 M MeCN, 2 hours.
ligand charge transfer. (C) Survey of chiral Lewis acid cocatalysts. OTf, ‡Reaction conducted at –20°C for 15 hours.
standard conditions
A
B
O
O
O
O
5 mol% Ru(bpy)3Cl2
x mol% Lewis acid (1:2 Eu(OTf)3:8)
5 mol% Ru(bpy)3Cl2
10 mol% Eu(OTf)3
20 mol% 8
2 equiv. i-Pr2NEt
0.2 M MeCN
O
O
O
O
Ph
Ph
Me
Me
Ph
Ph
Me
Me
2 equiv. i-Pr2NEt
0.2 M MeCN
visible light, –20 °C, 15 h
Me
Me
5 equiv.
Me
1
2
Me
5 equiv.
visible light, 20 °C, 15 h
1
2
Entry
Yield (%)
Variation from standard conditions
none
1
2
3
4
5
71
0
no light
no Ru(bpy)3Cl2
no Eu(OTf)3
no i-Pr2NEt
0
0
0
Fig. 2. Control experiments for the asymmetric visible light–photocatalyzed [2 + 2] cycloaddition. (A) Omission of any reaction component results in
no [2 + 2] cycloaddition. (B) Enantioselectivity of the photocatalyzed [2 + 2] cycloaddition is not affected by the concentration of chiral Lewis acid catalyst.
www.sciencemag.org SCIENCE VOL 344 25 APRIL 2014
393

REPORTS
O
5 mol% Ru(bpy)3Cl2
10 mol% Eu(OTf)3
20 mol% 8
2 equiv. i-Pr2NEt
0.2 M MeCN
Fig. 3. Substrate scope of the enantioselec-
O
O
O
tive [2 + 2] cycloaddition reaction. Diastereo-
mer ratios (dr) measured by 1H-NMR analysis of the
unpurified reaction mixtures. Reported yields rep-
resent total isolated yields of the 1,2-cis and 1,2-
trans isomers. For each entry, yields represent the
average of two reproducible experiments. *Reac-
tion conducted for 24 hours.
R1
R3
R1
R3
R2
R2
5 equiv.
O
1
2
visible light, 20 °C, 15 h
O
O
O
O
O
O
O
Me
Me
Me
Me
Cl
Me
Me
Br
Me
MeO
Me
2a
2b:
2c:
2d:
: 71% yield
7:1 dr
92% ee
65% yield
7:1 dr
69% yield
5.5:1 dr
54% yield*
6:1 dr
86% ee
90% ee
90% ee
O
O
O
O
O
O
F
O
O
MeO
O
Me
Me
Me
Me
Me
Me
Me
Me
2e:
2.5:1 dr
2f:
2g:
2h:
66% yield
70% yield
7:1 dr
62% yield
3:1 dr
72% yield
8:1 dr
91% ee
93% ee
89% ee
93% ee
O
O
O
O
O
O
O
O
Me
Et
Me
Me
Me
i-Pr
Et
OBn
2i:
2j:
2k:
2l:
68% yield*
4:1 dr
34% yield*
3:1 dr
52% yield
4:1 dr
62% yield*
9:1 dr
91% ee
88% ee
90% ee
90% ee
racemic background cycloaddition can be dimin- electron reduction of a Lewis acid–activated aryl Hoveyda for Cu-catalyzed asymmetric allylic
ished. Bach, whose laboratory has reported the enone by a Ru(I) complex generated by visible- alkylation (25), provided [2 + 2] cycloadduct 2
only highly enantioselective catalytic photocyclo- light irradiation of Ru(bpy)32+ in the presence of with promising ee (entry 5). To our knowledge,
additions to date, has approached this problem by an amine donor. There are two distinct features of this class of ligand has not previously been used
designing elegant reactions in which the catalyst- this process that together prevent uncatalyzed in lanthanide-catalyzed asymmetric reactions; how-
2+
substrate complex absorbs light at longer wave- background reactions. First, Ru(bpy)3 is acti- ever, its modular structure (26) facilitated the rapid
lengths than the free substrate. This has been vated by visible light (lmax = 450 nm) at wave- synthesis and evaluation of a small library of lig-
accomplished either by using a chiral hydrogen- lengths where the enone substrates do not absorb ands composed of various salicylaldehyde and
bonding xanthone-based photosensitizer (13–15) (21); direct photoexcitation of the enone does not amino acid units. A Lewis acid cocatalyst com-
or by using a chiral Lewis acid catalyst capable of occur with the household white light sources ap- posed of the optimal ligand (8) and Gd(OTf)3
inducing a bathochromic shift in the bound sub- plied in our studies. Second, a Lewis acid (LiBF4) afforded cyclobutane 2 in 56% ee (entry 6). Fur-
strate (16, 17). In both cases, Bach has achieved im- is an essential additive for cycloaddition to pro- ther optimization studies revealed that by replac-
pressive enantioselectivities with substoichiometric ceed; the Li+ cation presumably activates the enone ing the Gd salt with Eu(OTf)3 and by performing
chiral controllers. However, effective stereocon- substrate toward one-electron reduction and sta- the reaction at lower temperatures, the ee of 2
trol requires careful irradiation with a monochromatic bilizes the resulting radical anion species (22). We could be increased to 92% (entries 7 to 9).
light source that selectively excites the catalyst- hypothesized, therefore, that a dual-catalyst sys-
The optimized conditions require 5 mol %
substrate complex at a wavelength where absorption tem consisting of Ru(bpy)32+ and an appropriate Ru(bpy)3Cl2 as a visible-light photocatalyst and
by the free substrate is minimized. The contribution chiral Lewis acid cocatalyst would promote high- 10 mol % of a Lewis acid complex composed of
of background reaction, though lessened in these ly enantioselective [2 + 2] cycloadditions without a 1:2 ratio of Eu(OTf)3 and chiral ligand 8. A series
systems, nevertheless remains appreciable and re- the complications arising from uncatalyzed back- of control experiments verify the necessity of each
sults in a dependence of the ee on catalyst con- ground photoreactions.
reaction component (Fig. 2A). In the absence of
centration; optimal selectivities are obtained only In our initial screen of Lewis acids, we found light, photocatalyst, or Lewis acid catalyst, either
at high catalyst loadings (typically ~50 mol %) at that trivalent lanthanide salts such as Gd(OTf)3 singularly or in combination, no product is formed
which the catalyzed process can outcompete the were particularly effective cocatalysts for the pro- and enone substrate 1 can be recovered in good
racemic background cycloaddition. Thus, the lack duction of [2 + 2] cycloadducts 2 and 3 (Fig. 1C, yield. Yet, although the rate of cycloaddition is
of a general strategy for completely eliminating entry 1). This observation is consistent with the dependent on the concentration of Lewis acid
uncatalyzed background photochemistry continues high kinetic lability of lanthanides (23), which catalyst, there is no noticeable impact on the ee of
to be a fundamental impediment to the discovery may aid catalyst turnover by facilitating displace- the product. Catalyst loadings varying from 2.5
of efficient enantioselective catalytic photocyclo- ment of the bidentate product by a monodentate to 20 mol % produced cycloadduct 2 with the
additions.
enone substrate. Next, we evaluated a series of Gd same ee in each case (Fig. 2B). These experi-
Given these considerations, we speculated complexes bearing chiral ligands that we hoped ments indicate that all of the [2 + 2] cycloadduct
that the visible light–induced (18) photocatalytic would influence the stereochemistry of the [2 + 2] is being formed via a pathway involving the chiral
[2 + 2] cycloaddition (19, 20) recently reported in cycloaddition. Unfortunately, several ligand classes Lewis acid and that there is no contribution from
our laboratory (Fig. 1B) might be an ideal plat- (e.g., 4–6) that have been effective in previously a competitive racemic background process, con-
form for the development of a highly enantiose- reported Lewis acid–catalyzed enantioselective sistent with our design plan.
lective catalytic photocycloaddition that is free of transformations (24) provided negligible ee’s in
Previous approaches toward asymmetric cat-
racemic background reaction. The crucial activa- this reaction (entries 2 to 4). By contrast, Schiff alytic photocycloaddition reactions have exhib-
tion step in this cycloaddition involves the one- base dipeptide ligand 7, originally reported by ited rather limited scope. Minor modifications
394
25 APRIL 2014 VOL 344 SCIENCE www.sciencemag.org

REPORTS
Me
N
Me
Fig. 4. Diastereocontrol through independent
modification of chiral Lewis acid structure. (A)
Stereoselective access to 1,2-cis cycloadducts 3
through reduction of chiral Schiff base ligand 8 to
amine 9. (B) Substrate scope of 1,2-cis cyclobutanes
via enantioselective [2 + 2] photocycloaddition. Dias-
tereomer ratios measured by 1H-NMR analysis of the
unpurified reaction mixtures. Reported yields repre-
sent total isolated yields of the 1,2-cis and 1,2-trans
isomers. For each entry, yields represent the aver-
age of two reproducible experiments. *Reaction
conducted for 14 hours. †Reaction conducted for
36 hours. ‡Reaction conducted at 37°C. §Isolated
yield of only cis isomer.
O
O
A
N
Ph
Me
O
NHn-Bu
OH
O
Me
8
2
O
5 mol% Ru(bpy)3Cl2
10 mol% Eu(OTf)3
30 mol% 8 or 9
O
74% yield
7:1 dr (2:3)
85% ee
Me
Ph
+
NaBH4
i-Pr2NEt, MeCN
visible light, rt, 14 h
Me
1
5 equiv.
O
O
Me
Me
N
Ph
Me
N
H
OH
O
NHn-Bu
O
Me
3
9
78% yield
4.5:1 dr (3:2)
95% ee
O
O
B
O
O
O
O
O
O
Me
Me
Me
Me
Me
Me
MeO
Cl
Br
Me
Me
Me
Me
†
3a
3b
3c
3d
: 78% yield
4.5:1 dr
95% ee
: 79% yield
3.5:1 dr
95% ee
: 65% yield
3.5:1 dr
95% ee
: 74% yield
2.5:1 dr
90% ee
O
O
O
O
O
O
O
O
MeO
O
Me
Me
Me
i-Pr
Me
Me
Me
†
3g: 64% yield
3:1 dr
84% ee
3e: 80% yield*
2:1 dr
3h: 70% yield *
2:1 dr
3j: 67% yield
3.5:1 dr
94% ee
90% ee
86% ee
O
O
O
O
O
O
O
O
Me
Et
i-Pr
F
Me
Me
Me
OBn
: 80% yield*
2.5:1 dr
, ‡
†
†, §
*
3k
3l
3m
3n
: 72% yield
1.5:1 dr
: 49% yield
2:1 dr
: 80% yield
3.5:1 dr
97% ee
90% ee
84% ee
94% ee
to the substrate can result in substantial spectral cycloadditions has involved intramolecular reac- structurally diverse chiral Lewis acid catalysts.
changes that affect the ability to selectively photo- tions of cyclic enone substrates and thus furnished The factors governing the success of chiral Lewis
excite the catalyst-bound substrate (15). In con- bicyclic products. Our intermolecular cycloaddi- acids in asymmetric catalysis have been studied
trast, the results summarized in Fig. 3 demonstrate tion of acyclic enones can produce a diverse range for decades and are now well-understood (32).
that our dual-catalytic system tolerates wide-ranging of simple monocyclic cyclobutane products in The ability to combine the power and versatility
structural variation (27). Successful substrates in- good ee.
of chiral Lewis acids with the unique reactivity of
clude aryl enones bearing electron-donating and One important advantage of this dual-catalytic photocatalytically generated intermediates has the
-withdrawing substituents, heteroaryl enones, and system is the functional independence of the potential to be a valuable platform for the devel-
g-substituted enones. The enantioselectivity re- photocatalyst and the chiral Lewis acid catalyst opment of a wide range of broadly useful stereo-
mains high for all of these cycloadducts regard- (29). Extensive variations can be made to the controlled reactions.
less of the ultraviolet (UV) absorptivity of the structure of the chiral Lewis acid without any
substrates (28). For example, the phenyl and deleterious effect on the photochemical proper-
naphthyl enones leading to cyclobutanes 2a and ties of the Ru(bpy)32+ chromophore. This feature
2g both provide high ee even though the UV facilitates both the optimization of the enantiose-
absorption of the latter extends to considerably lectivity and the discovery of complementary re-
longer wavelengths (fig. S1). Consistent with our activity. For example, reduction of Schiff base
studies of racemic crossed enone cycloadditions ligand 8 with NaBH4 afforded secondary amine
(20), we observe the formation of readily separa- ligand 9, the Eu(OTf)3 complex of which was
ble by-products arising from competitive reduc- also a highly enantioselective Lewis acid cocata-
tive coupling and aryl enone homodimerization lyst for [2 + 2] cycloaddition. These conditions,
processes. The use of a fivefold excess of the however, favored the formation of 1,2-cis diastereo-
aliphatic enone increases the overall rate of for- mer 3 in good ee (Fig. 4A) (30). The scope of the
mation of [2 + 2] cycloadducts and minimizes the cycloaddition using 9 exhibits the same general
formation of homocoupling products. Overall, breadth as reactions conducted with ligand 8
these results represent a substantial improvement (Fig. 4B), but with complementary diastereose-
in the structural variety of enantioenriched [2 + 2] lectivity (31).
References and Notes
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Asymmetric Catalysis (Springer, Berlin, New York, 1999).
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Materials and Methods
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29 January 2014; accepted 10 March 2014
10.1126/science.1251511
lensing, whereby the light emanating from the
supernova is bent to form an Einstein-Chwolson
ring, or several discrete magnified images (typically
two or four) if the alignment is not axisymmetric.
Pan-STARRS1 has surveyed sufficient volume
to expect such a chance alignment (15, 16), and
it is possible that the angular extent of the lensed
images was simply too small to be resolved by
the observations available. However, for this hy-
pothesis to be confirmed, we must explain why
the existing observations give such conclusive
Detection of the Gravitational Lens
Magnifying a Type Ia Supernova
Robert M. Quimby,1* Masamune Oguri,1,2 Anupreeta More,1 Surhud More,1 Takashi J. Moriya,3,4
Marcus C. Werner,1,5 Masayuki Tanaka,6 Gaston Folatelli,1 Melina C. Bersten,1
Keiichi Maeda,7 Ken’ichi Nomoto1
Objects of known brightness, like type Ia supernovae (SNIa), can be used to measure distances.
If a massive object warps spacetime to form multiple images of a background SNIa, a direct
test of cosmic expansion is also possible. However, these lensing events must first be distinguished photometric and spectroscopic evidence for the
from other rare phenomena. Recently, a supernova was found to shine much brighter than presence of the supernova’s host galaxy, but the
normal for its distance, which resulted in a debate: Was it a new type of superluminous supernova same observations fail to obviously indicate
or a normal SNIa magnified by a hidden gravitational lens? Here, we report that a spectrum
obtained after the supernova faded away shows the presence of a foreground galaxy—the
first found to strongly magnify a SNIa. We discuss how more lensed SNIa can be found than
previously predicted.
the presence of a foreground lens.
We used the Keck-I telescope with the Low-
Resolution Imaging Spectrograph (LRIS) (17)
with the upgraded red channel (18) to observe
the host galaxy and any foreground objects at the
peculiar supernova, PS1-10afx, was collapse supernova. A rare class of superluminous sky position of PS1-10afx on 7 September 2013
discovered by the Panoramic Survey supernovae (SLSN) (2) have shown similarly high (see fig. S1) (16). As illustrated in Fig. 1, there
Telescope & Rapid Response System bolometric outputs, but PS1-10afx distinguishes are two narrow emission features that persist at
A
1 (Pan-STARRS1) on 31 August 2010 (universal itself from all other SLSN on two important the location of PS1-10afx now that the super-
time) (1). The unusually red color of the object counts: PS1-10afx is much redder (cooler) and nova itself has faded away. The [O II] emission
spurred the Pan-STARRS1 team to conduct an evolved much faster than any SLSN. A generic doublet (ll = 3726.1, 3728.8 Å in the rest
array of follow-up observations, including optical feature of SLSN models (3–9) is that they em- frame) from the host galaxy previously identi-
and near-infrared spectroscopy, which yielded a ploy high temperatures (T) and/or large photo- fied (1) is clearly recovered (fig. S2), but we
redshift of z = 1.39. Combined with relatively spheric radii (R) to generate high luminosities additionally detected a second emission line at
bright photometric detections, this redshift would (L) (recalling that L º T 4R2). The observations ~7890 Å. Because there are no strong emission
imply a peak luminosity of 4 × 1044 erg s−1
which is 400 times brighter than the typical core- suggesting that if it is a SLSN, it is in a class of (~3300 Å in the host frame), this detection sug-
,
of PS1-10afx do not fit with these models, lines expected from the host at this wavelength
its own.
gests the presence of a second object coincident
The most probable identification for the 7890 Å
1Kavli Institute for the Physics and Mathematics of the Universe
An alternate hypothesis (10) is that PS1-10afx with PS1-10afx.
(WPI), Todai Institutes for Advanced Study, The University of is actually a regular type Ia supernova (SNIa)
Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8583,
with a normal luminosity, but its apparent bright- feature is [O II] at z = 1.1168 T 0.0001. At this
ness has been magnified by a gravitational lens. redshift, other strong emission lines such as H-b
Spectra of PS1-10afx are well fit by normal SNIa or [O III] would lie outside of our wavelength
templates, as are the colors and light curve shapes. coverage. However, as depicted in Fig. 1, we
However, normal SNIa exhibit a tight relation detected a Mg II absorption doublet (ll = 2795.5,
between the widths of their light curves and their 2802.7 Å in the rest frame) at z = 1.1165 T 0.0001.
peak luminosities (11–14), and PS1-10afx appears Blueshifted absorption outflows are typical of
30 times brighter than expected, according to this star-forming galaxies (19), so this estimate is
relation. Such a large magnification of brightness compatible with that derived from the emission
can only occur naturally from strong gravitational lines. We also identify possible Mg I (l = 2853.0)
Japan. 2Department of Physics, The University of Tokyo, Tokyo
113-0033, Japan. 3Argelander Institute for Astronomy, Uni-
versity of Bonn Auf dem Hügel 71, D-53121 Bonn, Germany.
4Research Center for the Early Universe, Graduate School of
Science University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-
0033, Japan. 5Department of Mathematics, Duke University,
Durham, NC 27708, USA. 6National Astronomical Observatory
of Japan 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan.
7Department of Astronomy, Kyoto University, Kitashirakawa-
Oiwake-cho Sakyo-ku, Kyoto 606-8502, Japan.
*Corresponding author. E-mail: robert.quimby@ipmu.jp
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