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

Journal logoCRYSTALLOGRAPHIC
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ISSN: 2056-9890
Volume 65| Part 8| August 2009| Pages o1999-o2000

An ortho­rhom­bic polymorph of 6-de­­oxy-6-iodo-1,2:3,4-di-O-iso­propyl­­idene-α-D-galacto­pyran­oside

aX-ray Crystallography Unit, School of Physics, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia, bSyngene International Ltd, Biocon Park, Plot Nos. 2 & 3, Bommasandra 4th Phase, Jigani Link Rd, Bangalore 560 100, India, cDepartment of Printing, Manipal Institute of Technology, Manipal 576 104, India, and dDepartment of Chemistry, National Institute of Technology-Karnataka, Surathkal, Mangalore 575 025, India
*Correspondence e-mail: hkfun@usm.my

(Received 20 July 2009; accepted 22 July 2009; online 25 July 2009)

The title compound, C12H19IO5, is the ortho­rhom­bic polymorph of a previously reported monoclinic form [Krajewski et al. (1987[Krajewski, J. W., Gluzinski, P., Jarosz, S., Bleidelis, J., Mishnyov, A. & Kemme, A. (1987). Bull. Pol. Acad. Sci. Chem. 35, 91-102.]). Bull. Pol. Acad. Sci. Chem. 35, 91–102]. The dihedral angles between the six-membered ring and the two five-membered rings are 67.66 (14) and 71.79 (13)°, whereas the dihedral angle between the five-membered rings is 74.41 (12)°, indicating that all three rings are twisted from each other. The six-membered ring has a twist-boat conformation while both of the five-membered rings have envelope conformations. The crystal structure is stabilized by a network of C—H⋯O contacts linking the mol­ecules into a two-dimensional array parallel to the ab plane.

Related literature

For the monoclinic polymorph of the title compound, see: Krajewski et al. (1987[Krajewski, J. W., Gluzinski, P., Jarosz, S., Bleidelis, J., Mishnyov, A. & Kemme, A. (1987). Bull. Pol. Acad. Sci. Chem. 35, 91-102.]). For the synthesis and biological evaluation of 6-substituted purines, see: Gambogi Braga et al. (2007[Gambogi Braga, F., Soares Coimbra, E., De Oliveira Matos, M., Lino Carmo, A. M., Damato Cancio, M. & Da Silva, A. D. (2007). Eur. J. Med. Chem. 42, 530-537.]). For halogenation reagent systems, see: Classon et al. (1988[Classon, B., Liu, Z. & Samuelsson, B. (1988). J. Org. Chem. 53, 6126-6130.]). For the synthesis of perosamine derivatives, see: Stevens et al. (1970[Stevens, C. L., Glinski, P. R., Taylor, K. G., Blumberg, P. & Gupta, S. K. (1970). J. Am. Chem. Soc. 92, 3160-3168.]). For the synthesis of labilose, see: Westwood et al. (1967[Westwood, J. H., Chalk, R. C., Ball, D. H. & Long, L. (1967). J. Org. Chem. 32, 1643-1644.]). For ring conformations and ring puckering analysis, see: Boeyens (1978[Boeyens, J. C. A. (1978). J. Cryst. Mol. Struct. 8, 317-320.]); Cremer & Pople (1975[Cremer, D. & Pople, J. A. (1975). J. Am. Chem. Soc. 97, 1354-1358.]). For the stability of the temperature controller used in the data collection, see: Cosier & Glazer (1986[Cosier, J. & Glazer, A. M. (1986). J. Appl. Cryst. 19, 105-107.]).

[Scheme 1]

Experimental

Crystal data
  • C12H19IO5

  • Mr = 370.17

  • Orthorhombic, P 21 21 21

  • a = 7.3595 (1) Å

  • b = 11.5145 (2) Å

  • c = 16.9945 (2) Å

  • V = 1440.13 (4) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 2.23 mm−1

  • T = 100 K

  • 0.17 × 0.11 × 0.11 mm

Data collection
  • Bruker SMART APEXII CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Bruker, 2005[Bruker (2005). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]) Tmin = 0.703, Tmax = 0.785

  • 27359 measured reflections

  • 7509 independent reflections

  • 6211 reflections with I > 2σ(I)

  • Rint = 0.046

Refinement
  • R[F2 > 2σ(F2)] = 0.035

  • wR(F2) = 0.096

  • S = 1.07

  • 7509 reflections

  • 167 parameters

  • H-atom parameters constrained

  • Δρmax = 0.87 e Å−3

  • Δρmin = −1.24 e Å−3

  • Absolute structure: Flack (1983[Flack, H. D. (1983). Acta Cryst. A39, 876-881.]), 3286 Friedel pairs

  • Flack parameter: −0.020 (19)

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
C8—H8B⋯O2i 0.97 2.42 3.377 (3) 169
C12—H12C⋯O2ii 0.96 2.60 3.477 (4) 152
Symmetry codes: (i) [-x+1, y-{\script{1\over 2}}, -z+{\script{3\over 2}}]; (ii) [-x, y-{\script{1\over 2}}, -z+{\script{3\over 2}}].

Data collection: APEX2 (Bruker, 2005[Bruker (2005). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 2005[Bruker (2005). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; program(s) used to solve structure: SHELXTL (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL and PLATON (Spek, 2009).

Supporting information


Comment top

Libilomycin, an antibiotic which inhibits the growth of Gram-positive bacteria (Westwood et al., 1967) and which is effective against certain tumor cells, is produced by the microorganism, streptomyces albosporeas (Stevens et al., 1970), and contains 6-iodo,6-deoxy-1,2,3,4-di-O-isopropylidine-α-D-galactopyranoside as a part of its structure (Classon et al., 1988). These intermediates are used for the synthesis of 6-substituted purines which show high activity against Leishmania amazonensis (Gambogi Braga et al., 2007). These results prompted us to synthesize the title compound, (I).

Compound (I), Fig. 1, crystallized in the orthorhombic space group P212121 but has been reported previously (Krajewski et al., 1987) in the monoclinic space group P21, with a = 11.157 (2) Å, b = 20.047 (4) Å, c = 14.188 (2) Å and β = 107.67 (1)°. The dihedral angles between the six-membered ring systems, ring A (C1/C3/C4/C6/C7/O5), and the five-membered ring systems [rings B (C1—C3/O1—O2) and C (C4—C6/O3—O4)] are 67.66 (14)° and 71.79 (13)°, repectively. Moreover, the dihedral angle between rings B and C is 74.41 (12)° indicating that all the three rings are twisted from each other. Ring A adopts the twist-boat conformation (Boeyens, 1978; Cremer & Pople, 1975) with puckering amplitude Q = 0.629 (2) Å, ϕ = 75.3 (3)° and θ = 325.6 (2)°. On the other hand, each of rings B and C adopt an envelope conformation with flap atoms O2 and C5, respectively, but having different puckering parameters. For ring B, the puckering amplitude Q = 0.285 (2) Å and ϕ = 294.9 (5)° whereas for ring C, the puckering amplitude Q = 0.323 (3) Å and ϕ = 150.8 (4)°.

The crystal packing (Fig. 2 & Fig. 3) is consolidated by C8—H8B···O2 and C12—H12C···O2 contacts (Table 1) that link the molecules into a 2-D array parallel to the ab plane.

Related literature top

For the monoclinic polymorph of the title compound, see: Krajewski et al. (1987). For the synthesis and biological evaluation of 6-substituted purines, see: Gambogi Braga et al. (2007). For halogenation reagent systems, see: Classon et al. (1988). For the synthesis of perosamine derivatives, see: Stevens et al. (1970). For the synthesis of labilose, see: Westwood et al. (1967). For ring conformations and ring puckering analysis, see: Boeyens (1978); Cremer & Pople (1975). For the stability of the temperature controller used in the data collection, see: Cosier & Glazer (1986).

Experimental top

Triphenylphosphine (0.53 g, 1.9 mmol) and imidazole (0.4 g, 5.7 mmol) was added to the mixture of 1,2,3,4-di-O-isopropylidine-α-D-galactopyranoside (0.5 g, 1.9 mmol) in toluene: acetonitrile (2: 1, 10 ml). The mixture was heated to 70 °C. Iodine (0.6 g, 3.8 mmol) was then added portion-wise for a period of 30 min and mixture was further stirred for 2 hours. The completion of the reaction was confirmed by TLC (30% EtOAc/hexane, Rf - 0.6). The brown reaction mixture was concentrated under vacuum and the residue was purified by column chromatography using 25% ethylacetate in petroleum ether to get desired compound as white crystals. (Yield 600 mg, 83%, m.p. 334–336 K).

Refinement top

C-bound H atoms were positioned geometrically [C—H = 0.96–0.98 Å] and refined using a riding model, with Uiso(H) = 1.2Ueq(C) and 1.5Ueq(methyl-C). A rotating group model was used for the methyl groups.

The maximum and minimum residual electron density peaks of 0.87 and -1.24 eÅ-3, respectively, were located 0.85 Å and 0.52 Å from the H8A and I1 atoms, respectively.

Computing details top

Data collection: APEX2 (Bruker, 2005); cell refinement: SAINT (Bruker, 2005); data reduction: SAINT (Bruker, 2005); program(s) used to solve structure: SHELXTL (Sheldrick, 2008); program(s) used to refine structure: SHELXTL (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2009).

Figures top
[Figure 1] Fig. 1. The molecular structure of (I), showing 50% probability displacement ellipsoids and the atom numbering scheme.
[Figure 2] Fig. 2. Crystal packing viewed along the a axis. The C-H···O contacts are shown as dashed lines.
[Figure 3] Fig. 3. Crystal packing viewed along the c axis. The C-H···O contacts are shown as dashed lines.
6-deoxy-6-iodo-1,2:3,4-di-O-isopropylidene-α-D-galactopyranoside top
Crystal data top
C12H19IO5F(000) = 736
Mr = 370.17Dx = 1.707 Mg m3
Orthorhombic, P212121Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2abCell parameters from 6517 reflections
a = 7.3595 (1) Åθ = 3.0–30.1°
b = 11.5145 (2) ŵ = 2.23 mm1
c = 16.9945 (2) ÅT = 100 K
V = 1440.13 (4) Å3Block, colourless
Z = 40.17 × 0.11 × 0.11 mm
Data collection top
Bruker SMART APEXII CCD area-detector
diffractometer
7509 independent reflections
Radiation source: fine-focus sealed tube6211 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.046
ϕ and ω scansθmax = 37.5°, θmin = 2.1°
Absorption correction: multi-scan
(SADABS; Bruker, 2005)
h = 1212
Tmin = 0.703, Tmax = 0.785k = 1917
27359 measured reflectionsl = 2829
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)] = 0.035H-atom parameters constrained
wR(F2) = 0.096 w = 1/[σ2(Fo2) + (0.0418P)2 + 0.1348P]
where P = (Fo2 + 2Fc2)/3
S = 1.07(Δ/σ)max = 0.003
7509 reflectionsΔρmax = 0.87 e Å3
167 parametersΔρmin = 1.24 e Å3
0 restraintsAbsolute structure: Flack (1983), 3286 Friedel pairs
Primary atom site location: structure-invariant direct methodsAbsolute structure parameter: 0.020 (19)
Crystal data top
C12H19IO5V = 1440.13 (4) Å3
Mr = 370.17Z = 4
Orthorhombic, P212121Mo Kα radiation
a = 7.3595 (1) ŵ = 2.23 mm1
b = 11.5145 (2) ÅT = 100 K
c = 16.9945 (2) Å0.17 × 0.11 × 0.11 mm
Data collection top
Bruker SMART APEXII CCD area-detector
diffractometer
7509 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2005)
6211 reflections with I > 2σ(I)
Tmin = 0.703, Tmax = 0.785Rint = 0.046
27359 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.035H-atom parameters constrained
wR(F2) = 0.096Δρmax = 0.87 e Å3
S = 1.07Δρmin = 1.24 e Å3
7509 reflectionsAbsolute structure: Flack (1983), 3286 Friedel pairs
167 parametersAbsolute structure parameter: 0.020 (19)
0 restraints
Special details top

Experimental. The crystal was placed in the cold stream of an Oxford Cyrosystems Cobra open-flow nitrogen cryostat (Cosier & Glazer, 1986) operating at 100.0 (1) K.

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
I10.48767 (2)0.062287 (16)0.585388 (10)0.02322 (5)
O10.3941 (3)0.30650 (19)0.54871 (11)0.0202 (4)
O20.4126 (2)0.41053 (17)0.66190 (11)0.0174 (4)
O30.0095 (3)0.31453 (16)0.74636 (10)0.0169 (3)
O40.0869 (3)0.13209 (18)0.77122 (12)0.0181 (4)
O50.2158 (2)0.16776 (16)0.61095 (11)0.0162 (3)
C10.2269 (3)0.2856 (2)0.58845 (16)0.0166 (4)
H1A0.12560.30410.55320.020*
C20.4873 (3)0.4031 (2)0.58404 (14)0.0167 (4)
C30.2281 (3)0.3722 (2)0.65788 (15)0.0166 (4)
H3A0.14760.43790.64660.020*
C40.1835 (3)0.3209 (3)0.73797 (15)0.0167 (4)
H4A0.23350.37100.77930.020*
C50.0464 (3)0.2160 (2)0.79401 (15)0.0165 (4)
C60.2485 (3)0.1941 (2)0.75132 (13)0.0152 (5)
H6A0.33590.19070.79480.018*
C70.3309 (3)0.1412 (2)0.67660 (15)0.0165 (5)
H7A0.45220.17370.66770.020*
C80.3433 (4)0.0106 (3)0.68407 (16)0.0194 (5)
H8A0.22200.02210.68640.023*
H8B0.40590.00920.73250.023*
C90.4481 (4)0.5139 (3)0.53734 (17)0.0235 (6)
H9A0.31930.52670.53530.035*
H9B0.49450.50570.48480.035*
H9C0.50580.57870.56260.035*
C100.6874 (4)0.3785 (3)0.59115 (18)0.0220 (5)
H10A0.70490.30320.61420.033*
H10B0.74300.43640.62400.033*
H10C0.74210.38040.53990.033*
C110.0254 (4)0.2444 (3)0.88146 (15)0.0241 (5)
H11A0.09460.27390.89100.036*
H11B0.04400.17530.91200.036*
H11C0.11360.30180.89630.036*
C120.2321 (4)0.1723 (3)0.77260 (18)0.0205 (5)
H12A0.23070.14350.71960.031*
H12B0.31830.23460.77660.031*
H12C0.26620.11090.80780.031*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
I10.02406 (8)0.02602 (9)0.01959 (7)0.00713 (7)0.00446 (7)0.00100 (6)
O10.0212 (9)0.0223 (10)0.0170 (8)0.0053 (8)0.0033 (7)0.0029 (8)
O20.0136 (7)0.0220 (10)0.0167 (8)0.0033 (6)0.0016 (6)0.0022 (7)
O30.0124 (7)0.0161 (7)0.0222 (7)0.0003 (6)0.0014 (6)0.0023 (6)
O40.0133 (8)0.0188 (9)0.0223 (9)0.0002 (6)0.0036 (7)0.0023 (7)
O50.0169 (8)0.0149 (9)0.0166 (7)0.0011 (6)0.0038 (6)0.0004 (7)
C10.0177 (9)0.0178 (12)0.0143 (9)0.0010 (8)0.0028 (9)0.0001 (9)
C20.0173 (9)0.0193 (10)0.0134 (8)0.0026 (8)0.0025 (11)0.0023 (8)
C30.0145 (10)0.0180 (12)0.0172 (10)0.0018 (8)0.0006 (8)0.0008 (9)
C40.0127 (9)0.0207 (13)0.0167 (10)0.0020 (8)0.0012 (8)0.0009 (9)
C50.0150 (10)0.0179 (12)0.0166 (10)0.0003 (8)0.0014 (8)0.0017 (8)
C60.0125 (9)0.0197 (13)0.0135 (10)0.0002 (8)0.0011 (7)0.0007 (9)
C70.0127 (10)0.0218 (13)0.0149 (10)0.0004 (8)0.0003 (8)0.0005 (9)
C80.0186 (11)0.0227 (14)0.0170 (11)0.0044 (9)0.0011 (9)0.0041 (10)
C90.0251 (13)0.0236 (14)0.0218 (12)0.0012 (10)0.0004 (10)0.0054 (11)
C100.0175 (10)0.0292 (15)0.0193 (11)0.0012 (9)0.0031 (10)0.0007 (11)
C110.0227 (13)0.0313 (15)0.0182 (10)0.0003 (11)0.0021 (10)0.0010 (10)
C120.0170 (11)0.0200 (14)0.0245 (13)0.0021 (9)0.0014 (9)0.0036 (11)
Geometric parameters (Å, º) top
I1—C82.155 (3)C5—C111.530 (4)
O1—C11.424 (3)C6—C71.533 (4)
O1—C21.438 (3)C6—H6A0.9800
O2—C31.430 (3)C7—C81.512 (4)
O2—C21.435 (3)C7—H7A0.9800
O3—C51.420 (3)C8—H8A0.9700
O3—C41.429 (3)C8—H8B0.9700
O4—C61.428 (3)C9—H9A0.9600
O4—C51.431 (3)C9—H9B0.9600
O5—C11.412 (3)C9—H9C0.9600
O5—C71.434 (3)C10—H10A0.9600
C1—C31.545 (4)C10—H10B0.9600
C1—H1A0.9800C10—H10C0.9600
C2—C101.505 (4)C11—H11A0.9600
C2—C91.530 (4)C11—H11B0.9600
C3—C41.519 (4)C11—H11C0.9600
C3—H3A0.9800C12—H12A0.9600
C4—C61.554 (4)C12—H12B0.9600
C4—H4A0.9800C12—H12C0.9600
C5—C121.501 (4)
C1—O1—C2110.17 (19)C7—C6—H6A110.4
C3—O2—C2107.52 (19)C4—C6—H6A110.4
C5—O3—C4106.8 (2)O5—C7—C8108.2 (2)
C6—O4—C5107.3 (2)O5—C7—C6109.1 (2)
C1—O5—C7112.42 (19)C8—C7—C6110.4 (2)
O5—C1—O1109.9 (2)O5—C7—H7A109.7
O5—C1—C3114.4 (2)C8—C7—H7A109.7
O1—C1—C3104.4 (2)C6—C7—H7A109.7
O5—C1—H1A109.3C7—C8—I1110.61 (18)
O1—C1—H1A109.3C7—C8—H8A109.5
C3—C1—H1A109.3I1—C8—H8A109.5
O2—C2—O1104.41 (18)C7—C8—H8B109.5
O2—C2—C10108.2 (2)I1—C8—H8B109.5
O1—C2—C10110.8 (2)H8A—C8—H8B108.1
O2—C2—C9110.8 (2)C2—C9—H9A109.5
O1—C2—C9109.8 (2)C2—C9—H9B109.5
C10—C2—C9112.5 (2)H9A—C9—H9B109.5
O2—C3—C4106.4 (2)C2—C9—H9C109.5
O2—C3—C1104.0 (2)H9A—C9—H9C109.5
C4—C3—C1115.6 (2)H9B—C9—H9C109.5
O2—C3—H3A110.2C2—C10—H10A109.5
C4—C3—H3A110.2C2—C10—H10B109.5
C1—C3—H3A110.2H10A—C10—H10B109.5
O3—C4—C3108.9 (2)C2—C10—H10C109.5
O3—C4—C6104.1 (2)H10A—C10—H10C109.5
C3—C4—C6115.4 (2)H10B—C10—H10C109.5
O3—C4—H4A109.4C5—C11—H11A109.5
C3—C4—H4A109.4C5—C11—H11B109.5
C6—C4—H4A109.4H11A—C11—H11B109.5
O3—C5—O4104.70 (19)C5—C11—H11C109.5
O3—C5—C12107.7 (2)H11A—C11—H11C109.5
O4—C5—C12109.4 (2)H11B—C11—H11C109.5
O3—C5—C11111.4 (2)C5—C12—H12A109.5
O4—C5—C11109.8 (2)C5—C12—H12B109.5
C12—C5—C11113.5 (2)H12A—C12—H12B109.5
O4—C6—C7109.1 (2)C5—C12—H12C109.5
O4—C6—C4104.4 (2)H12A—C12—H12C109.5
C7—C6—C4112.0 (2)H12B—C12—H12C109.5
O4—C6—H6A110.4
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C8—H8B···O2i0.972.423.377 (3)169
C12—H12C···O2ii0.962.603.477 (4)152
Symmetry codes: (i) x+1, y1/2, z+3/2; (ii) x, y1/2, z+3/2.

Experimental details

Crystal data
Chemical formulaC12H19IO5
Mr370.17
Crystal system, space groupOrthorhombic, P212121
Temperature (K)100
a, b, c (Å)7.3595 (1), 11.5145 (2), 16.9945 (2)
V3)1440.13 (4)
Z4
Radiation typeMo Kα
µ (mm1)2.23
Crystal size (mm)0.17 × 0.11 × 0.11
Data collection
DiffractometerBruker SMART APEXII CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Bruker, 2005)
Tmin, Tmax0.703, 0.785
No. of measured, independent and
observed [I > 2σ(I)] reflections
27359, 7509, 6211
Rint0.046
(sin θ/λ)max1)0.857
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.035, 0.096, 1.07
No. of reflections7509
No. of parameters167
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.87, 1.24
Absolute structureFlack (1983), 3286 Friedel pairs
Absolute structure parameter0.020 (19)

Computer programs: APEX2 (Bruker, 2005), SAINT (Bruker, 2005), SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2009).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C8—H8B···O2i0.972.423.377 (3)169
C12—H12C···O2ii0.962.603.477 (4)152
Symmetry codes: (i) x+1, y1/2, z+3/2; (ii) x, y1/2, z+3/2.
 

Footnotes

Thomson Reuters Researcher ID: A-3561-2009.

Acknowledgements

HKF and WCL thank Universiti Sains Malaysia (USM) for a Research University Golden Goose Grant (No. 1001/PFIZIK/811012). WCL thanks USM for a student assistantship. AMI is grateful to the Director, NITK, Surathkal, India, for providing research facilities

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Volume 65| Part 8| August 2009| Pages o1999-o2000
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