2,2-Bis(1H-indol-3-yl)indolin-3-one

Li, Z.-H.; Xu, J.; Wu, W.-L.; Su, W.-P.

doi:10.1107/S1600536809017553

organic compounds

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ISSN: 2056-9890

Volume 65| Part 6| June 2009| Page o1353

doi:10.1107/S1600536809017553

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2,2-Bis(1H-indol-3-yl)indolin-3-one

Zhao-Hao Li,^a,^b Jing Xu,^a,^b Wen-Liang Wu ^a,^b and Wei-Ping Su ^b ^*

^aGraduate School, The Chinese Academy of Sciences, Beijing 100039, People's Republic of China, and ^bThe State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, The Chinese Academy of Sciences, Fuzhou, Fujian 350002, People's Republic of China
^*Correspondence e-mail: xujing@fjirsm.ac.cn

(Received 22 April 2009; accepted 11 May 2009; online 20 May 2009)

In the title molecule, C₂₄H₁₇N₃O, the mean plane of the indolone ring forms dihedral angles of 112.0 (1) and 103.1 (1)° with the planes of the two indole rings. The dihedral angle between the mean planes of the two indole rings is 63.5 (1)°. In the crystal structure, molecules are linked via intermolecular N—H⋯O hydrogen bonds, forming a two-dimensional network parallel to the ab plane.

Related literature

For the applications of indole derivatives, see: Ramesh et al. (2009 ). For the isolation of the title compound as a natural product, see: Ganachaud et al. (2008 ); Stull et al. (1995 ).

Experimental

Crystal data

C₂₄H₁₇N₃O
M_r = 363.41
Monoclinic, P 2₁ /n
a = 10.559 (4) Å
b = 8.931 (3) Å
c = 19.899 (7) Å
β = 98.480 (6)°
V = 1856.1 (11) Å³
Z = 4
Mo Kα radiation
μ = 0.08 mm⁻¹
T = 293 K
0.40 × 0.35 × 0.15 mm

Data collection

Rigaku Mercury CCD diffractometer
Absorption correction: multi-scan (CrystalClear; Rigaku/MSC, 2005 ) T_min = 0.968, T_max = 0.988
14004 measured reflections
4245 independent reflections
3606 reflections with I > 2σ(I)
R_int = 0.024

Refinement

R[F² > 2σ(F²)] = 0.048
wR(F²) = 0.118
S = 1.06
4245 reflections
253 parameters
H-atom parameters constrained
Δρ_max = 0.21 e Å⁻³
Δρ_min = −0.19 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N2—H2B⋯O1ⁱ	0.86	2.12	2.9412 (17)	159
N3—H3B⋯O1ⁱⁱ	0.86	2.18	2.9830 (16)	156
Symmetry codes: (i) $[-x+{\script{3\over 2}}, y-{\script{1\over 2}}, -z+{\script{1\over 2}}]$ ; (ii) $[-x+{\script{5\over 2}}, y-{\script{1\over 2}}, -z+{\script{1\over 2}}]$ .

Data collection: CrystalClear (Rigaku/MSC, 2005); cell refinement: CrystalClear; data reduction: CrystalClear; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 ); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1999 ); software used to prepare material for publication: SHELXL97.

Supporting information

Crystal structure: contains datablocks I, global. DOI: 10.1107/S1600536809017553/lh2811sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536809017553/lh2811Isup2.hkl

checkCIF report

Comment top

Indole derivatives are used as bioactive drugs and they exibit anti-allergic, central nervous system depressant and muscle relaxant properties (Ramesh et al., 2009). The title compound is a natural product that has been isolated from bacterial sources (Stull et al.., 1995; Ganachaud et al.., 2008). Recently, we found different indole derivatives could be formed by oxidation solely on the basis of the reaction solvent and temperature. As part of our studies, we report herein the synthesis and crystal structure of the title compound (I) (Fig. 1).

The title compound is a trimeric condensation product of indole through the formation of a quaternary carbon (C8) centre. The indolone ring forms dihedral angle of 112.0 (1)° and 103.1 (1)°, respectively, with the two indole rings (C9/C10/C11/C12/C13/C14/C15/C16/N2) and (C17/C18/C19/C20/C21/C22/C23/C24/N3). The mean planes of the two indole form a dihedral angle of 63.5 (1)°. In the crystal structure, the carbonyl atom O1 acts as a bifurcated acceptor for the N-H groups of atoms N2 and N3 to form a two-dimensional network parallel to the ab plane (Table 1, Fig. 2).

Related literature top

For the applications of indole derivatives, see: Ramesh et al. (2009). For the isolation of the title compound as a natural product, see: Ganachaud et al. (2008); Stull et al. (1995).

Experimental top

The title compound was obtained from a mixture of 1H-indole (78 mg) with ^tBuCOOH (0.18 ml) and H₃PMo₁₂O₁₄ (9 mg) in toluene (1 ml) and CH₃COOH (1 ml) under a nitrogen atmosphere at room temperature for 24 h. The crude product was isolated and purified by silica gel columnchromatography. Yellow prism-shaped crystals of (I) suitable for X-ray diffraction were grown by slow evaporation of a dichloromethane solution at room temperature.

Computing details top

Data collection: CrystalClear (Rigaku/MSC, 2005); cell refinement: CrystalClear (Rigaku/MSC, 2005); data reduction: CrystalClear (Rigaku/MSC, 2005); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top

	Fig. 1. The molecular structure of (I), showing 30% probability displacement ellopsoids. H atoms are shown as small spheres.
	Fig. 2. Part of the crystal structure of (I) showing the hydrogen bonded layers parallel to the ab plane. Intermolecular hydrogen bonds are shown as dashed lines and H atoms not involved in H-bonding have been omitted.

2,2-Bis(1H-indol-3-yl)indolin-3-one top

Crystal data top

C₂₄H₁₇N₃O	F(000) = 760
M_r = 363.41	D_x = 1.300 Mg m⁻³
Monoclinic, P2₁/n	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yn	Cell parameters from 4234 reflections
a = 10.559 (4) Å	θ = 3.0–27.5°
b = 8.931 (3) Å	µ = 0.08 mm⁻¹
c = 19.899 (7) Å	T = 293 K
β = 98.480 (6)°	Prism, yellow
V = 1856.1 (11) Å³	0.40 × 0.35 × 0.15 mm
Z = 4

Data collection top

Rigaku Mercury CCD diffractometer	4245 independent reflections
Radiation source: fine-focus sealed tube	3606 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.024
Detector resolution: 14.6306 pixels mm^-1	θ_max = 27.5°, θ_min = 2.1°
CCD_Profile_fitting scans	h = −11→13
Absorption correction: multi-scan (CrystalClear; Rigaku/MSC, 2005)	k = −11→11
T_min = 0.968, T_max = 0.988	l = −22→25
14004 measured reflections

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.048	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.118	H-atom parameters constrained
S = 1.06	w = 1/[σ²(F_o²) + (0.0513P)² + 0.4603P] where P = (F_o² + 2F_c²)/3
4245 reflections	(Δ/σ)_max < 0.001
253 parameters	Δρ_max = 0.21 e Å⁻³
0 restraints	Δρ_min = −0.19 e Å⁻³

Crystal data top

C₂₄H₁₇N₃O	V = 1856.1 (11) Å³
M_r = 363.41	Z = 4
Monoclinic, P2₁/n	Mo Kα radiation
a = 10.559 (4) Å	µ = 0.08 mm⁻¹
b = 8.931 (3) Å	T = 293 K
c = 19.899 (7) Å	0.40 × 0.35 × 0.15 mm
β = 98.480 (6)°

Data collection top

Rigaku Mercury CCD diffractometer	4245 independent reflections
Absorption correction: multi-scan (CrystalClear; Rigaku/MSC, 2005)	3606 reflections with I > 2σ(I)
T_min = 0.968, T_max = 0.988	R_int = 0.024
14004 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.048	0 restraints
wR(F²) = 0.118	H-atom parameters constrained
S = 1.06	Δρ_max = 0.21 e Å⁻³
4245 reflections	Δρ_min = −0.19 e Å⁻³
253 parameters

Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
O1	0.96565 (9)	0.43252 (10)	0.15911 (5)	0.0369 (2)
N1	0.95403 (12)	0.04726 (13)	0.11858 (6)	0.0406 (3)
H1A	0.9668	−0.0474	0.1239	0.049*
N2	0.75509 (12)	0.05077 (15)	0.28328 (7)	0.0490 (3)
H2B	0.6914	−0.0017	0.2923	0.059*
N3	1.31856 (12)	0.10180 (15)	0.26178 (6)	0.0471 (3)
H3B	1.3724	0.0659	0.2945	0.056*
C1	0.89773 (13)	0.11138 (16)	0.05986 (7)	0.0374 (3)
C2	0.85094 (14)	0.0420 (2)	−0.00189 (8)	0.0483 (4)
H2A	0.8532	−0.0615	−0.0065	0.058*
C3	0.80181 (17)	0.1314 (2)	−0.05518 (8)	0.0635 (5)
H3A	0.7706	0.0868	−0.0966	0.076*
C4	0.7967 (2)	0.2867 (3)	−0.04991 (9)	0.0746 (6)
H4A	0.7630	0.3437	−0.0874	0.090*
C5	0.84151 (19)	0.3558 (2)	0.01064 (8)	0.0604 (5)
H5A	0.8383	0.4595	0.0147	0.072*
C6	0.89185 (13)	0.26719 (17)	0.06585 (7)	0.0392 (3)
C7	0.94976 (12)	0.30732 (14)	0.13383 (6)	0.0315 (3)
C8	0.99057 (13)	0.15946 (14)	0.17220 (6)	0.0321 (3)
C9	0.81798 (14)	0.15783 (17)	0.32497 (7)	0.0417 (3)
C10	0.79721 (18)	0.2065 (2)	0.38885 (8)	0.0557 (4)
H10A	0.7324	0.1655	0.4100	0.067*
C11	0.8753 (2)	0.3166 (2)	0.41938 (8)	0.0616 (5)
H11A	0.8635	0.3509	0.4621	0.074*
C12	0.97253 (17)	0.3786 (2)	0.38756 (8)	0.0550 (4)
H12A	1.0236	0.4541	0.4093	0.066*
C13	0.99417 (15)	0.32982 (17)	0.32449 (7)	0.0424 (3)
H13A	1.0597	0.3712	0.3040	0.051*
C14	0.91605 (13)	0.21709 (15)	0.29179 (7)	0.0351 (3)
C15	0.90865 (13)	0.13904 (15)	0.22798 (7)	0.0342 (3)
C16	0.80919 (14)	0.04053 (17)	0.22537 (8)	0.0432 (3)
H16A	0.7823	−0.0240	0.1894	0.052*
C17	1.34968 (13)	0.18478 (15)	0.20847 (7)	0.0380 (3)
C18	1.46884 (15)	0.23042 (18)	0.19416 (9)	0.0491 (4)
H18A	1.5436	0.2065	0.2230	0.059*
C19	1.47219 (15)	0.31203 (18)	0.13592 (9)	0.0511 (4)
H19A	1.5507	0.3436	0.1251	0.061*
C20	1.36003 (15)	0.34840 (18)	0.09265 (8)	0.0461 (4)
H20A	1.3651	0.4030	0.0533	0.055*
C21	1.24194 (14)	0.30469 (15)	0.10722 (7)	0.0380 (3)
H21A	1.1679	0.3304	0.0782	0.046*
C22	1.23417 (12)	0.22113 (14)	0.16619 (6)	0.0322 (3)
C23	1.13200 (12)	0.15690 (14)	0.19763 (6)	0.0326 (3)
C24	1.18882 (14)	0.08515 (16)	0.25473 (7)	0.0412 (3)
H24A	1.1454	0.0325	0.2846	0.049*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O1	0.0351 (5)	0.0344 (5)	0.0407 (5)	0.0007 (4)	0.0040 (4)	−0.0052 (4)
N1	0.0497 (7)	0.0320 (6)	0.0391 (6)	−0.0014 (5)	0.0029 (5)	−0.0058 (5)
N2	0.0361 (7)	0.0527 (8)	0.0603 (8)	−0.0086 (6)	0.0138 (6)	0.0105 (6)
N3	0.0361 (7)	0.0560 (8)	0.0472 (7)	0.0108 (6)	−0.0002 (5)	0.0156 (6)
C1	0.0288 (7)	0.0464 (8)	0.0367 (7)	−0.0010 (6)	0.0041 (5)	−0.0075 (6)
C2	0.0377 (8)	0.0583 (9)	0.0474 (8)	−0.0003 (7)	0.0016 (6)	−0.0203 (7)
C3	0.0549 (11)	0.0890 (14)	0.0415 (9)	0.0140 (10)	−0.0100 (8)	−0.0235 (9)
C4	0.0916 (16)	0.0844 (14)	0.0395 (9)	0.0287 (12)	−0.0181 (9)	−0.0053 (9)
C5	0.0750 (12)	0.0580 (10)	0.0423 (8)	0.0195 (9)	−0.0110 (8)	−0.0010 (7)
C6	0.0353 (7)	0.0455 (8)	0.0347 (7)	0.0055 (6)	−0.0015 (6)	−0.0053 (6)
C7	0.0252 (6)	0.0364 (7)	0.0330 (6)	0.0018 (5)	0.0048 (5)	−0.0025 (5)
C8	0.0327 (7)	0.0322 (6)	0.0311 (6)	−0.0015 (5)	0.0034 (5)	−0.0032 (5)
C9	0.0367 (8)	0.0463 (8)	0.0437 (8)	0.0066 (6)	0.0114 (6)	0.0125 (6)
C10	0.0577 (10)	0.0660 (11)	0.0486 (9)	0.0120 (9)	0.0249 (8)	0.0170 (8)
C11	0.0735 (13)	0.0775 (13)	0.0365 (8)	0.0178 (10)	0.0174 (8)	0.0021 (8)
C12	0.0601 (11)	0.0623 (10)	0.0419 (8)	0.0047 (8)	0.0051 (7)	−0.0090 (7)
C13	0.0425 (8)	0.0485 (8)	0.0366 (7)	−0.0009 (6)	0.0067 (6)	−0.0014 (6)
C14	0.0327 (7)	0.0391 (7)	0.0338 (6)	0.0038 (5)	0.0058 (5)	0.0054 (5)
C15	0.0309 (7)	0.0353 (7)	0.0359 (7)	−0.0004 (5)	0.0039 (5)	0.0026 (5)
C16	0.0367 (8)	0.0436 (8)	0.0486 (8)	−0.0051 (6)	0.0044 (6)	0.0023 (6)
C17	0.0338 (7)	0.0366 (7)	0.0430 (7)	0.0063 (5)	0.0037 (6)	0.0013 (6)
C18	0.0297 (7)	0.0524 (9)	0.0640 (10)	0.0058 (6)	0.0030 (7)	0.0001 (8)
C19	0.0359 (8)	0.0515 (9)	0.0686 (11)	−0.0027 (7)	0.0172 (7)	−0.0014 (8)
C20	0.0472 (9)	0.0473 (8)	0.0463 (8)	−0.0034 (7)	0.0154 (7)	0.0031 (7)
C21	0.0371 (7)	0.0407 (7)	0.0359 (7)	0.0006 (6)	0.0049 (6)	0.0006 (6)
C22	0.0313 (7)	0.0308 (6)	0.0346 (6)	0.0036 (5)	0.0051 (5)	−0.0022 (5)
C23	0.0319 (7)	0.0327 (6)	0.0334 (6)	0.0029 (5)	0.0056 (5)	0.0001 (5)
C24	0.0376 (8)	0.0436 (8)	0.0428 (8)	0.0054 (6)	0.0070 (6)	0.0096 (6)

Geometric parameters (Å, º) top

O1—C7	1.2274 (16)	C9—C14	1.411 (2)
N1—C1	1.3571 (18)	C10—C11	1.367 (3)
N1—C8	1.4731 (16)	C10—H10A	0.9300
N1—H1A	0.8600	C11—C12	1.398 (3)
N2—C16	1.363 (2)	C11—H11A	0.9300
N2—C9	1.371 (2)	C12—C13	1.379 (2)
N2—H2B	0.8600	C12—H12A	0.9300
N3—C24	1.3645 (19)	C13—C14	1.400 (2)
N3—C17	1.3731 (19)	C13—H13A	0.9300
N3—H3B	0.8600	C14—C15	1.4405 (19)
C1—C6	1.399 (2)	C15—C16	1.3652 (19)
C1—C2	1.3997 (19)	C16—H16A	0.9300
C2—C3	1.367 (3)	C17—C18	1.391 (2)
C2—H2A	0.9300	C17—C22	1.4136 (19)
C3—C4	1.392 (3)	C18—C19	1.374 (2)
C3—H3A	0.9300	C18—H18A	0.9300
C4—C5	1.374 (2)	C19—C20	1.396 (2)
C4—H4A	0.9300	C19—H19A	0.9300
C5—C6	1.394 (2)	C20—C21	1.378 (2)
C5—H5A	0.9300	C20—H20A	0.9300
C6—C7	1.4451 (18)	C21—C22	1.4031 (19)
C7—C8	1.5542 (18)	C21—H21A	0.9300
C8—C23	1.5046 (19)	C22—C23	1.4434 (18)
C8—C15	1.5155 (19)	C23—C24	1.3640 (19)
C9—C10	1.391 (2)	C24—H24A	0.9300

C1—N1—C8	111.79 (11)	C10—C11—C12	121.26 (16)
C1—N1—H1A	124.1	C10—C11—H11A	119.4
C8—N1—H1A	124.1	C12—C11—H11A	119.4
C16—N2—C9	109.42 (12)	C13—C12—C11	121.24 (17)
C16—N2—H2B	125.3	C13—C12—H12A	119.4
C9—N2—H2B	125.3	C11—C12—H12A	119.4
C24—N3—C17	109.29 (12)	C12—C13—C14	119.00 (15)
C24—N3—H3B	125.4	C12—C13—H13A	120.5
C17—N3—H3B	125.4	C14—C13—H13A	120.5
N1—C1—C6	111.45 (12)	C13—C14—C9	118.37 (13)
N1—C1—C2	128.48 (14)	C13—C14—C15	135.19 (13)
C6—C1—C2	120.06 (14)	C9—C14—C15	106.43 (13)
C3—C2—C1	117.83 (16)	C16—C15—C14	106.67 (12)
C3—C2—H2A	121.1	C16—C15—C8	124.66 (13)
C1—C2—H2A	121.1	C14—C15—C8	128.66 (12)
C2—C3—C4	122.53 (15)	N2—C16—C15	109.91 (14)
C2—C3—H3A	118.7	N2—C16—H16A	125.0
C4—C3—H3A	118.7	C15—C16—H16A	125.0
C5—C4—C3	120.11 (17)	N3—C17—C18	130.01 (13)
C5—C4—H4A	119.9	N3—C17—C22	107.46 (12)
C3—C4—H4A	119.9	C18—C17—C22	122.53 (14)
C4—C5—C6	118.52 (17)	C19—C18—C17	117.69 (14)
C4—C5—H5A	120.7	C19—C18—H18A	121.2
C6—C5—H5A	120.7	C17—C18—H18A	121.2
C5—C6—C1	120.95 (14)	C18—C19—C20	121.24 (14)
C5—C6—C7	131.01 (14)	C18—C19—H19A	119.4
C1—C6—C7	107.97 (12)	C20—C19—H19A	119.4
O1—C7—C6	128.53 (13)	C21—C20—C19	121.07 (14)
O1—C7—C8	124.16 (12)	C21—C20—H20A	119.5
C6—C7—C8	107.31 (11)	C19—C20—H20A	119.5
N1—C8—C23	111.98 (11)	C20—C21—C22	119.54 (13)
N1—C8—C15	109.37 (11)	C20—C21—H21A	120.2
C23—C8—C15	113.41 (11)	C22—C21—H21A	120.2
N1—C8—C7	101.43 (10)	C21—C22—C17	117.92 (12)
C23—C8—C7	111.57 (10)	C21—C22—C23	135.52 (12)
C15—C8—C7	108.37 (11)	C17—C22—C23	106.56 (12)
N2—C9—C10	130.02 (15)	C24—C23—C22	106.43 (12)
N2—C9—C14	107.57 (13)	C24—C23—C8	125.45 (12)
C10—C9—C14	122.41 (15)	C22—C23—C8	128.05 (11)
C11—C10—C9	117.71 (15)	C23—C24—N3	110.25 (13)
C11—C10—H10A	121.1	C23—C24—H24A	124.9
C9—C10—H10A	121.1	N3—C24—H24A	124.9

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N2—H2B···O1ⁱ	0.86	2.12	2.9412 (17)	159
N3—H3B···O1ⁱⁱ	0.86	2.18	2.9830 (16)	156

Symmetry codes: (i) −x+3/2, y−1/2, −z+1/2; (ii) −x+5/2, y−1/2, −z+1/2.

Experimental details

Crystal data
Chemical formula	C₂₄H₁₇N₃O
M_r	363.41
Crystal system, space group	Monoclinic, P2₁/n
Temperature (K)	293
a, b, c (Å)	10.559 (4), 8.931 (3), 19.899 (7)
β (°)	98.480 (6)
V (Å³)	1856.1 (11)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	0.08
Crystal size (mm)	0.40 × 0.35 × 0.15

Data collection
Diffractometer	Rigaku Mercury CCD diffractometer
Absorption correction	Multi-scan (CrystalClear; Rigaku/MSC, 2005)
T_min, T_max	0.968, 0.988
No. of measured, independent and observed [I > 2σ(I)] reflections	14004, 4245, 3606
R_int	0.024
(sin θ/λ)_max (Å⁻¹)	0.650

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.048, 0.118, 1.06
No. of reflections	4245
No. of parameters	253
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.21, −0.19

Computer programs: CrystalClear (Rigaku/MSC, 2005), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), DIAMOND (Brandenburg, 1999).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N2—H2B···O1ⁱ	0.86	2.12	2.9412 (17)	159.0
N3—H3B···O1ⁱⁱ	0.86	2.18	2.9830 (16)	156.3

Symmetry codes: (i) −x+3/2, y−1/2, −z+1/2; (ii) −x+5/2, y−1/2, −z+1/2.

Acknowledgements

This work was supported by the Natural Science Foundation of Fujian province (grant No. 2006 J0273) and the `One Hundred Talent' Projects from the Chinese Academy of Sciences.

References

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