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organic compounds\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890
Volume 65| Part 10| October 2009| Page o2389
doi:10.1107/S160053680903548X

trans-4,5-Dihydr­­oxy-1,3-di­phenyl­imidazolidine-2-thione

Zhenfeng Zhang,a* Meilin Wei,a Jiange Wangb and Guisheng Zhanga

aCollege of Chemistry and Environmental Science, Henan Normal University, Xinxiang 453007, People's Republic of China, and bCollege of Chemistry, Luoyang Normal University, Xinxiang 453007, People's Republic of China
*Correspondence e-mail: zzf5188@sohu.com

(Received 21 August 2009; accepted 2 September 2009; online 9 September 2009)

In the title compound, C15H14N2O2S, the five-membered ring adopts an envelope conformation and the two hydr­oxy groups lie on opposite sides of the ring. The six-membered rings are oriented at a dihedral angle of 22.63 (3)°. In the crystal structure, inter­molecular O—H⋯S and O—H⋯O hydrogen bonds link the mol­ecules into a two-dimensional network.

Related literature

For the biological activity of imidazolidine-2-one derivatives, see: Lam et al. (1994[Lam, P. Y. S., Jadhav, P. K., Eyermann, C. J., Hodge, C. N., Ru, Y., Bacheler, L. T., Meek, J. L., Otto, M. J., Rayner, M. M., Wong, Y. N., Chang, C.-H., Weber, P. C., Jackson, D. A., Sharpe, T. R. & Erickson-Viitanen, S. (1994). Science, 263, 380-384.]); Lenzen & Ahmad (2001[Lenzen, S. & Ahmad, R. (2001). Ger. Offen. DE10012401.]); Perronnet & Teche (1973[Perronnet, J. & Teche, A. (1973). US Patent 3 905 996.]). For related structures, see: Enders et al. (1979[Enders, E., Ebbighausen, V., Gau, W., Wunsche, C. & Stendel, W. (1979). US Patent 4 173 645.]); Zhang et al. (2007[Zhang, Z.-F., Zhang, J.-M., Guo, J.-P. & Qu, G.-R. (2007). Acta Cryst. E63, o2821-o2823.]).

[Scheme 1]

Experimental

Crystal data

  • C15H14N2O2S

  • Mr = 286.34

  • Orthorhombic, P c a 21

  • a = 20.5119 (4) Å

  • b = 7.1020 (4) Å

  • c = 9.6659 (3) Å

  • V = 1408.09 (9) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.23 mm−1

  • T = 294 K

  • 0.35 × 0.22 × 0.20 mm
Data collection

  • Bruker SMART CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Sheldrick, 2003[Sheldrick, G. M. (2003). SADABS. University of Göttingen, Germany.]) Tmin = 0.923, Tmax = 0.944

  • 7542 measured reflections

  • 2521 independent reflections

  • 2273 reflections with I > 2σ(I)

  • Rint = 0.045
Refinement

  • R[F2 > 2σ(F2)] = 0.037

  • wR(F2) = 0.119

  • S = 1.09

  • 2521 reflections

  • 183 parameters

  • H-atom parameters constrained

  • Δρmax = 0.26 e Å−3

  • Δρmin = −0.40 e Å−3

  • Absolute structure: Flack (1983[Flack, H. D. (1983). Acta Cryst. A39, 876-881.]), 1123 Friedel pairs

  • Flack parameter: 0.16 (10)

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A D⋯A D—H⋯A
O1—H1⋯S1i 0.91 2.41 3.261 (2) 156
O2—H2⋯O1ii 0.82 2.13 2.930 (3) 167
Symmetry codes: (i) x, y+1, z; (ii) [-x+1, -y+1, z+{\script{1\over 2}}].

Data collection: SMART (Bruker, 1997[Bruker (1997). SMART and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 1997[Bruker (1997). SMART and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); molecular graphics: SHELXTL (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); software used to prepare material for publication: SHELXTL.

Supporting information

Crystal structure: contains datablocks I, global. DOI: 10.1107/S160053680903548X/hk2762sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S160053680903548X/hk2762Isup2.hkl

checkCIF report


Comment top

Imidazolidine-2-one derivates often exhibit powerful bioactivities, such as good herbicidal activity (Perronnet & Teche,1973), antidiabetic properties (Lenzen & Ahmad, 2001) and anti-HIV activity (Lam et al., 1994). Enders et al. (1979) have earlier reported the synthesis and use of 4,5-dihydroxyimidazolidine-2-thiones. However, to the best of our knowledge, there are few N,N'-diaryl substituted 4,5-dihydroxyimidazolidine-2 -thiones reported so far. As a typical example of such compounds, we report herein the crystal structure of the title compound.

In the molecule of the title compound, (I), (Fig. 1) the five-membered ring A (N1/N2/C1-C3) adopts an envelope conformation with atom C3 displaced by -0.369 (3) Å from the plane of the other ring atoms. The two hydroxyl groups lie on opposite sides of the ring. The C1-N1 [1.357 (3) Å] and C1-N2 [1.373 (3) Å] bonds are longer than the corresponding bonds in trans-4,5-dihydroxyimidazolidine-2-thione, (II), [1.335 (2) and 1.336 (2) Å; Zhang et al., 2007]. Conversely, the C1═S1 [1.669 (3) Å] and C2-C3 [1.526 (4) Å] bonds in (I) are shorter than the corresponding bonds in (II) [1.684 (2) and 1.537 (2) Å, respectively]. Rings B (C4-C9) and C (C10-C15) are, of course, planar and they are oriented at a dihedral angle of B/C = 22.63 (3)°.

In the crystal structure, intermolecular O-H···S A and O-H···O hydrogen bonds (Table 1) link the molecules into a two-dimensional network (Fig. 2), in which they may be effective in the stabilization of the structure.

Related literature top

For the biological activity of imidazolidine-2-one derivatives, see: Lam et al. (1994); Lenzen & Ahmad (2001); Perronnet & Teche (1973). For related structures, see: Enders et al. (1979); Zhang et al. (2007).

Experimental top

For the preparation of the title compound, 1,3-diphenylthiourea (0.1 mol), glyoxal (40%, 18 g) and ethanol (95%, 30 ml) were added into a three-necked round-bottomed flask equipped with a stirrer. The mixture was then refluxed with stirring for ca 30 min and thereafter the solvent was removed. The residue was washed with cold ethanol, and the resulting solid product was recrystallized from hot ethanol to give the crystals of the title compound. 1H NMR(DMSO, 400 MHz) of (I): δ 7.52–7.28 (m, 10H), δ 7.10 (d, J = 8.0 Hz, 2H), δ 5.19 (d, J = 8.4 Hz, 2H).

Refinement top

Atom H1 (for OH) is located in a difference Fourier map and only its temperature factor is refined. The remaining H atoms were positioned geometrically with O-H = 0.82 Å (for OH) and C-H = 0.93 and 0.98 Å for aromatic and methine H atoms, respectively, and constrained to ride on their parent atoms, with Uiso(H) = xUeq(C,O), where x = 1.5 for OH H and x = 1.2 for all other H atoms.

Computing details top

Data collection: SMART (Bruker, 1997); cell refinement: SAINT (Bruker, 1997); data reduction: SAINT (Bruker, 1997); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. The molecular structure of the title molecule, with the atom-numbering scheme. Displacement ellipsoids are drawn at the 30% probability level.
[Figure 2] Fig. 2. A partial packing diagram of the title compound. For the sake of clarity, H atoms not involved in hydrogen bonding have been omitted. Hydrogen bonds are shown as dashed lines. Selected atoms are labelled. [Symmetry codes: (i) x, y + 1, z; (ii) -x + 1, -y + 1, z + 1/2; (iii) -x + 1, -y + 1, z - 1/2; (iv) x, y - 1, z].
trans-4,5-Dihydroxy-1,3-diphenylimidazolidine-2-thione top
Crystal data top
C15H14N2O2SF(000) = 600
Mr = 286.34Dx = 1.351 Mg m−3
Orthorhombic, Pca21Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2c -2acCell parameters from 871 reflections
a = 20.5119 (4) Åθ = 2.9–27.9°
b = 7.1020 (4) ŵ = 0.23 mm−1
c = 9.6659 (3) ÅT = 294 K
V = 1408.09 (9) Å3Block, colorless
Z = 40.35 × 0.22 × 0.20 mm
Data collection top
Bruker SMART CCD area-detector
diffractometer		2521 independent reflections
Radiation source: fine-focus sealed tube2273 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.045
ϕ and ω scansθmax = 25.5°, θmin = 2.9°
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)		h = −24→24
Tmin = 0.923, Tmax = 0.944k = −8→8
7542 measured reflectionsl = −11→11
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.037H-atom parameters constrained
wR(F2) = 0.119 w = 1/[σ2(Fo2) + (0.0758P)2 + 0.1052P]
where P = (Fo2 + 2Fc2)/3
S = 1.09(Δ/σ)max = 0.001
2521 reflectionsΔρmax = 0.26 e Å−3
183 parametersΔρmin = −0.40 e Å−3
0 restraintsAbsolute structure: Flack (1983), 1123 Friedel pairs
Primary atom site location: structure-invariant direct methodsAbsolute structure parameter: 0.16 (10)
Crystal data top
C15H14N2O2SV = 1408.09 (9) Å3
Mr = 286.34Z = 4
Orthorhombic, Pca21Mo Kα radiation
a = 20.5119 (4) ŵ = 0.23 mm−1
b = 7.1020 (4) ÅT = 294 K
c = 9.6659 (3) Å0.35 × 0.22 × 0.20 mm
Data collection top
Bruker SMART CCD area-detector
diffractometer		2521 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)		2273 reflections with I > 2σ(I)
Tmin = 0.923, Tmax = 0.944Rint = 0.045
7542 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.037H-atom parameters constrained
wR(F2) = 0.119Δρmax = 0.26 e Å−3
S = 1.09Δρmin = −0.40 e Å−3
2521 reflectionsAbsolute structure: Flack (1983), 1123 Friedel pairs
183 parametersAbsolute structure parameter: 0.16 (10)
0 restraints
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
xyzUiso*/Ueq
S10.57085 (3)0.08292 (10)0.82543 (8)0.0490 (2)
O10.50025 (9)0.6924 (3)0.73031 (18)0.0461 (5)
H10.51110.79820.77860.16 (3)*
O20.41663 (9)0.4806 (3)1.01911 (19)0.0496 (5)
H20.44490.43761.07000.074*
N10.55261 (10)0.4549 (3)0.8636 (2)0.0377 (5)
N20.46089 (9)0.2969 (3)0.8350 (2)0.0390 (5)
C10.52752 (11)0.2806 (4)0.8419 (2)0.0377 (5)
C20.50147 (11)0.5976 (4)0.8604 (2)0.0369 (6)
H2A0.50710.68780.93630.044*
C30.43958 (12)0.4818 (4)0.8810 (2)0.0380 (6)
H30.40530.52860.81940.046*
C40.61952 (11)0.4991 (4)0.8966 (2)0.0365 (5)
C50.64923 (14)0.4175 (4)1.0118 (3)0.0488 (7)
H50.62680.32931.06470.059*
C60.71267 (15)0.4689 (5)1.0472 (4)0.0610 (8)
H60.73270.41251.12290.073*
C70.74579 (15)0.6012 (5)0.9721 (4)0.0626 (9)
H70.78800.63580.99660.075*
C80.71551 (16)0.6831 (6)0.8587 (3)0.0703 (10)
H80.73760.77370.80750.084*
C90.65245 (13)0.6318 (4)0.8203 (3)0.0551 (7)
H90.63280.68700.74370.066*
C100.41476 (10)0.1456 (4)0.8282 (3)0.0381 (5)
C110.40282 (15)0.0370 (5)0.9455 (3)0.0505 (7)
H110.42760.05421.02510.061*
C120.35357 (17)−0.0971 (4)0.9426 (4)0.0585 (8)
H120.3456−0.17151.02000.070*
C130.31627 (13)−0.1201 (4)0.8242 (4)0.0612 (8)
H130.2824−0.20710.82370.073*
C140.32898 (15)−0.0150 (5)0.7067 (3)0.0563 (8)
H140.3046−0.03370.62680.068*
C150.37826 (14)0.1181 (4)0.7087 (3)0.0450 (6)
H150.38700.18920.63010.054*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.0455 (3)0.0357 (4)0.0658 (4)0.0026 (3)0.0023 (3)−0.0088 (3)
O10.0571 (12)0.0356 (12)0.0456 (9)−0.0020 (8)0.0007 (7)0.0041 (8)
O20.0486 (10)0.0555 (14)0.0447 (9)0.0059 (10)0.0092 (8)0.0014 (9)
N10.0353 (10)0.0304 (12)0.0473 (11)−0.0039 (9)−0.0010 (8)−0.0025 (8)
N20.0370 (10)0.0310 (12)0.0489 (9)−0.0026 (8)−0.0008 (9)−0.0005 (10)
C10.0369 (11)0.0410 (15)0.0353 (10)−0.0014 (10)0.0006 (9)−0.0012 (11)
C20.0401 (13)0.0327 (16)0.0379 (12)0.0032 (10)−0.0019 (8)−0.0044 (10)
C30.0399 (12)0.0335 (16)0.0407 (11)0.0028 (11)−0.0016 (10)−0.0030 (10)
C40.0378 (12)0.0293 (14)0.0423 (11)−0.0014 (11)0.0020 (9)−0.0078 (10)
C50.0449 (14)0.0473 (18)0.0542 (13)−0.0027 (12)−0.0048 (11)0.0048 (12)
C60.0506 (17)0.062 (2)0.0708 (19)0.0008 (15)−0.0181 (15)0.0007 (16)
C70.0369 (14)0.072 (2)0.0792 (19)−0.0100 (15)−0.0032 (13)−0.0167 (17)
C80.0579 (17)0.082 (3)0.071 (2)−0.0333 (17)0.0108 (15)0.0005 (18)
C90.0545 (14)0.062 (2)0.0488 (13)−0.0183 (14)0.0016 (13)0.0044 (16)
C100.0354 (10)0.0335 (14)0.0453 (11)−0.0013 (9)0.0018 (10)−0.0037 (12)
C110.0591 (16)0.0430 (18)0.0494 (13)−0.0023 (14)−0.0004 (13)0.0042 (13)
C120.069 (2)0.0369 (18)0.0694 (17)−0.0075 (14)0.0181 (15)0.0062 (15)
C130.0464 (14)0.0455 (19)0.092 (2)−0.0086 (12)0.0099 (16)−0.0186 (19)
C140.0497 (16)0.054 (2)0.0654 (18)−0.0037 (15)−0.0079 (12)−0.0150 (15)
C150.0498 (15)0.0362 (16)0.0490 (13)−0.0011 (12)−0.0005 (11)−0.0015 (12)
Geometric parameters (Å, º) top
S1—C11.669 (3)C6—C71.368 (5)
O1—C21.427 (3)C6—H60.9300
O1—H10.9123C7—C81.387 (5)
O2—C31.416 (3)C7—H70.9300
O2—H20.8200C8—C91.394 (4)
N1—C11.357 (3)C8—H80.9300
N1—C41.444 (3)C9—H90.9300
N1—C21.459 (3)C10—C151.390 (4)
N2—C11.373 (3)C10—C111.393 (4)
N2—C101.433 (3)C11—C121.389 (4)
N2—C31.454 (3)C11—H110.9300
C2—C31.526 (4)C12—C131.386 (6)
C2—H2A0.9800C12—H120.9300
C3—H30.9800C13—C141.384 (6)
C4—C91.374 (4)C13—H130.9300
C4—C51.396 (4)C14—C151.384 (4)
C5—C61.394 (4)C14—H140.9300
C5—H50.9300C15—H150.9300
C2—O1—H186.1C7—C6—H6119.6
C3—O2—H2109.5C5—C6—H6119.6
C1—N1—C4126.4 (2)C6—C7—C8119.0 (3)
C1—N1—C2110.97 (19)C6—C7—H7120.5
C4—N1—C2122.5 (2)C8—C7—H7120.5
C1—N2—C10126.6 (2)C7—C8—C9121.1 (3)
C1—N2—C3111.1 (2)C7—C8—H8119.5
C10—N2—C3119.53 (19)C9—C8—H8119.5
N1—C1—N2108.0 (2)C4—C9—C8119.5 (3)
N1—C1—S1125.46 (17)C4—C9—H9120.3
N2—C1—S1126.6 (2)C8—C9—H9120.3
O1—C2—N1111.04 (18)C15—C10—C11120.3 (2)
O1—C2—C3110.76 (19)C15—C10—N2120.0 (2)
N1—C2—C3102.8 (2)C11—C10—N2119.6 (2)
O1—C2—H2A110.7C12—C11—C10119.4 (3)
N1—C2—H2A110.7C12—C11—H11120.3
C3—C2—H2A110.7C10—C11—H11120.3
O2—C3—N2112.5 (2)C13—C12—C11119.9 (3)
O2—C3—C2113.8 (2)C13—C12—H12120.0
N2—C3—C2101.37 (19)C11—C12—H12120.0
O2—C3—H3109.6C14—C13—C12120.7 (3)
N2—C3—H3109.6C14—C13—H13119.7
C2—C3—H3109.6C12—C13—H13119.7
C9—C4—C5119.9 (2)C15—C14—C13119.6 (3)
C9—C4—N1119.9 (2)C15—C14—H14120.2
C5—C4—N1120.1 (2)C13—C14—H14120.2
C6—C5—C4119.6 (3)C14—C15—C10120.1 (3)
C6—C5—H5120.2C14—C15—H15120.0
C4—C5—H5120.2C10—C15—H15120.0
C7—C6—C5120.9 (3)
C4—N1—C1—N2170.7 (2)C1—N1—C4—C5−56.2 (3)
C2—N1—C1—N2−4.7 (3)C2—N1—C4—C5118.7 (3)
C4—N1—C1—S1−9.7 (3)C9—C4—C5—C6−1.2 (4)
C2—N1—C1—S1174.86 (17)N1—C4—C5—C6−176.5 (3)
C10—N2—C1—N1−172.8 (2)C4—C5—C6—C71.3 (5)
C3—N2—C1—N1−11.8 (3)C5—C6—C7—C8−0.6 (5)
C10—N2—C1—S17.7 (3)C6—C7—C8—C9−0.4 (5)
C3—N2—C1—S1168.61 (19)C5—C4—C9—C80.2 (4)
C1—N1—C2—O1−100.5 (2)N1—C4—C9—C8175.6 (3)
C4—N1—C2—O183.9 (2)C7—C8—C9—C40.5 (5)
C1—N1—C2—C318.0 (2)C1—N2—C10—C15−112.5 (3)
C4—N1—C2—C3−157.6 (2)C3—N2—C10—C1587.9 (3)
C1—N2—C3—O2−99.8 (2)C1—N2—C10—C1172.9 (3)
C10—N2—C3—O262.7 (3)C3—N2—C10—C11−86.6 (3)
C1—N2—C3—C222.0 (2)C15—C10—C11—C12−0.8 (4)
C10—N2—C3—C2−175.5 (2)N2—C10—C11—C12173.7 (3)
O1—C2—C3—O2−143.2 (2)C10—C11—C12—C13−0.9 (5)
N1—C2—C3—O298.1 (2)C11—C12—C13—C142.2 (5)
O1—C2—C3—N295.8 (2)C12—C13—C14—C15−1.8 (5)
N1—C2—C3—N2−22.9 (2)C13—C14—C15—C100.1 (4)
C1—N1—C4—C9128.4 (3)C11—C10—C15—C141.2 (4)
C2—N1—C4—C9−56.7 (3)N2—C10—C15—C14−173.3 (2)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1···S1i0.912.413.261 (2)156
O2—H2···O1ii0.822.132.930 (3)167
Symmetry codes: (i) x, y+1, z; (ii) −x+1, −y+1, z+1/2.

Experimental details

Crystal data
Chemical formulaC15H14N2O2S
Mr286.34
Crystal system, space groupOrthorhombic, Pca21
Temperature (K)294
a, b, c (Å)20.5119 (4), 7.1020 (4), 9.6659 (3)
V (Å3)1408.09 (9)
Z4
Radiation typeMo Kα
µ (mm−1)0.23
Crystal size (mm)0.35 × 0.22 × 0.20
Data collection
DiffractometerBruker SMART CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 2003)
Tmin, Tmax0.923, 0.944
No. of measured, independent and
observed [I > 2σ(I)] reflections		7542, 2521, 2273
Rint0.045
(sin θ/λ)max (Å−1)0.606
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.037, 0.119, 1.09
No. of reflections2521
No. of parameters183
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å−3)0.26, −0.40
Absolute structureFlack (1983), 1123 Friedel pairs
Absolute structure parameter0.16 (10)

Computer programs: SMART (Bruker, 1997), SAINT (Bruker, 1997), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), SHELXTL (Sheldrick, 2008).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1···S1i0.912.413.261 (2)155.8
O2—H2···O1ii0.822.132.930 (3)166.9
Symmetry codes: (i) x, y+1, z; (ii) −x+1, −y+1, z+1/2.
 

Acknowledgements

Financial support from Henan Normal University and the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (grant No. 2008IRTSTHN002) is gratefully acknowledged. The authors also thank the Physiochemical Analysis Measurement Laboratory, College of Chemistry, Luoyang Normal University, for performing the X-ray analysis.

References

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ISSN: 2056-9890
Volume 65| Part 10| October 2009| Page o2389
doi:10.1107/S160053680903548X
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