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Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890
Volume 64| Part 3| March 2008| Pages o578-o579

4-Hydr­­oxy-5-(4-meth­oxy­phen­yl)pyrrolidin-2-one

aInstitute of Science, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia, bX-ray Crystallography Unit, School of Physics, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia, and cDepartment of Chemistry, Faculty of Science, Prince of Songkla University, Hat-Yai, Songkhla 90112, Thailand
*Correspondence e-mail: hkfun@usm.my

(Received 4 February 2008; accepted 6 February 2008; online 13 February 2008)

In the title compound, C11H13NO3, the pyrrolidin-2-one ring is in an envelope conformation with the hydroxyl and 4-methoxy­phenyl substituents mutually cis. The methoxy group is slighty twisted away from the mean plane of the attached benzene ring. The mol­ecules are arranged into screw chains along the c axis. These chains are inter­connected via inter­molecular O—H⋯O and N—H⋯O hydrogen bonds into sheets parallel to the ac plane. The crystal structure is further stabilized by weak inter­molecular C—H⋯O and C—H⋯π inter­actions.

Related literature

For details of ring conformations, see: Cremer & Pople (1975[Cremer, D. & Pople, J. A. (1975). J. Am. Chem. Soc. 97, 1354-1358.]). For the biological properties of pyrrolidine alkaloids, see for example: Iida et al. (1986[Iida, H., Yamazaki, N. & Kibayashi, C. (1986). Tetrahedron Lett. 27, 5393-5396.]); Royles (1996[Royles, B. J. L. (1996). Chem. Rev. 95, 1961-2001.]). For the syntheses of compounds containing the tetra­mic acid ring, see for example: Chandrasekhar et al. (2006[Chandrasekhar, S., Saritha, B., Jagadeshwar, V. & Prakash, S. J. (2006). Tetrahedron Asymmetry, 17, 1380-1386.]); Gurjar et al. (2006[Gurjar, M. K., Borhade, R. G., Puranik, V. G. & Ramana, C. V. (2006). Tetrahedron Lett., 47, 6979-6981.]); Yoda et al. (1996[Yoda, H., Nakajima, T. & Takabe, K. (1996). Tetrahedron Lett. 31, 5531-5534.]). For bond-length data, see: Allen et al. (1987[Allen, F. H., Kennard, O., Watson, D. G., Brammer, L., Orpen, A. G. & Taylor, R. (1987). J. Chem. Soc. Perkin Trans. 2, pp. S1-S19.]).

[Scheme 1]

Experimental

Crystal data
  • C11H13NO3

  • Mr = 207.22

  • Orthorhombic, P c a 21

  • a = 11.9862 (6) Å

  • b = 11.6251 (6) Å

  • c = 7.1539 (4) Å

  • V = 996.83 (9) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 0.10 mm−1

  • T = 100.0 (1) K

  • 0.43 × 0.20 × 0.17 mm

Data collection
  • Bruker SMART APEX2 CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Bruker, 2005[Bruker (2005). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]) Tmin = 0.958, Tmax = 0.983

  • 8681 measured reflections

  • 1562 independent reflections

  • 1218 reflections with I > 2σ(I)

  • Rint = 0.066

Refinement
  • R[F2 > 2σ(F2)] = 0.047

  • wR(F2) = 0.109

  • S = 1.09

  • 1562 reflections

  • 145 parameters

  • 1 restraint

  • H atoms treated by a mixture of independent and constrained refinement

  • Δρmax = 0.22 e Å−3

  • Δρmin = −0.24 e Å−3

Table 1
Hydrogen-bond geometry (Å, °)

Cg1 is the centroid of the C5–C10 ring.

D—H⋯A D—H H⋯A DA D—H⋯A
N1—H1N1⋯O2i 0.88 (4) 2.05 (4) 2.917 (3) 167 (4)
O2—H1O2⋯O3ii 0.90 (4) 1.98 (4) 2.800 (2) 152 (3)
C3—H3A⋯O1iii 0.98 2.33 3.193 (3) 146
C11—H11A⋯O1iv 0.96 2.49 3.395 (3) 158
C6—H6ACg1v 0.93 2.81 3.514 (3) 133
C9—H9ACg1vi 0.93 2.68 3.554 (3) 157
Symmetry codes: (i) [-x+{\script{3\over 2}}, y, z-{\script{1\over 2}}]; (ii) [-x+2, -y+1, z+{\script{1\over 2}}]; (iii) [x+{\script{1\over 2}}, -y+2, z]; (iv) [-x+{\script{3\over 2}}, y-1, z-{\script{1\over 2}}]; (v) [x+{\script{3\over 2}}, -y, z]; (vi) [-x+2, -y+1, z-{\script{1\over 2}}].

Data collection: APEX2 (Bruker, 2005[Bruker (2005). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: APEX2; data reduction: SAINT (Bruker, 2005[Bruker (2005). APEX2, SAINT and SADABS. Bruker AXS Inc., Madison, Wisconsin, USA.]); 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, 2003[Spek, A. L. (2003). J. Appl. Cryst. 36, 7-13.]).

Supporting information


Comment top

Many naturally occurring compounds containing a tetramic acid ring system such as radicamine, fuligorobin and codonopsinine possess potent antibiotic, antiviral, antifungal, cytotoxic (Royles, 1996) as well as hypotensive activities (Iida et al., 1986). The title compound, C11H13NO3, can act as an essential intermediate in the synthesis of such tetramic acid derivatives (Chandrasekhar et al., 2006; Gurjar et al., 2006; Yoda et al., 1996), which eventually can be used as a template in multi-step syntheses of biologically active natural products. We have synthesized the title compound (I) and its structure is reported here, Fig. 1.

In (I), the pyrrolidine-2-one ring adopts an envelope conformation with atom C3 displaced from the C1/C2/C3/N1 plane by 0.219 (3) Å, and with puckering parameters (Cremer & Pople, 1975) Q = 0.357 (3) Å and ϕ = 117.9 (4)°. The bond angles around C1 atom are indicative of sp2 hybridization. The hydroxyl and 4-methoxyphenyl substituents are attached to the pyrrolidin-2-one ring at atom C3 and C4, respectively and is in cis-configuration (Fig. 1). The methoxy group is slightly twisted away from the mean plane of the phenyl ring as shown by the torsion angle C11–O3–C8–C7 = -5.2 (4)° All bond lengths and angles show normal values (Allen et al., 1987)

In the crystal packing of the title compound (Fig. 2), the molecules are arranged into screw chains along the c direction. These chains are interconnected via intermolecular O—H···O and N—H···O hydrogen bonds (Table 1) into sheets parallel to the ac plane. The crystal is further stabilized by weak intermolecular C—H···O and C—H···π interactions; C6—H6A···Cg1 (symmetry code: 3/2 - x, y, 1/2 + z) and C9—H9A··· Cg1 (symmetry code: 2 - x, 1 - y, -1/2 + z), Cg1 is the centroid of C5–C10 phenyl ring.

Related literature top

For details of ring conformations, see: Cremer & Pople (1975). For the biological properties of pyrrolidine alkaloids, see for example Iida et al. (1986); Royles (1996). For the syntheses of compounds containing the tetramic acid ring, see for example Chandrasekhar et al. (2006); Gurjar et al. (2006); Yoda et al. (1996). Forbond-length data, see: Allen et al. (1987).

Experimental top

The synthetic approach to the title compound began with the esterification of p-hydroxyphenylglycine (10.00 g, 60.10 mmol) and thionyl chloride in methanol to give the ester product (10.30 g, 95%). Amine protection (10.00 g, 54.9 mmol) was then carried out using tert-butoxycarbonyl (Boc2O) and triethylamine (Et3N) in tetrahydrofuran (THF) to give the N-Boc protected product in 85% yield (13.12 g). The hydroxyl functional group (13.01 g, 46.66 mmol) was protected by converting it to the methyl ether using potassium carbonate and methyl iodide (12.72 g, 93%). Condensation between the N-Boc methyl ester (8.30 g, 28.30 mmol) and methyl malonyl chloride in equimolar amounts furnished an intermediate diester (10.60 g, 95%). Dieckmann cyclization of this intermediate diester (5.50 g, 13.99 mmol) with potassium tert-butoxide (t-BuOK) in toluene gave the carbon skeleton β,β diketoester in 45% yield (1.65 g). Demethoxycarbonylation of the β,β diketoester (0.30 g, 1.1 mmol) was successfully carried out by refluxing in 50 ml acetonitrile to give the basic pyrrolidinone ring skeleton (0.23 g, 99%). Reduction of this diketone (0.16 g, 0.77 mmol) was then carried out in sodium borohydride/methanol at 273 K to give the title compound (0.04 g, 24%). Single crystals suitable for X-ray structure determination were obtained by slow evaporation of an ethyl acetate-petroleum ether (2:1 v/v) solution after several days.

Refinement top

H atoms attached to O and N atoms were located in a difference Fourier map and were refined isotropically. H atoms bound to C were placed in calculated positions with d(C—H) = 0.93 Å, Uiso=1.2Ueq (C) for aromatic 0.98 Å, Uiso = 1.2Ueq (C) for CH, 0.97 Å, Uiso = 1.2Ueq (C) for CH2, 0.96 Å, Uiso = 1.5Ueq (C) for CH3 atoms. A rotating group model was used for the methyl groups. A total of 1121 Friedel pairs were merged before final refinement as there is no large anomalous dispersion for the determination of the absolute configuration.

Computing details top

Data collection: APEX2 (Bruker, 2005); cell refinement: APEX2 (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, 2003).

Figures top
[Figure 1] Fig. 1. The molecular structure of (I), showing 40% probability displacement ellipsoids and the atomic numbering.
[Figure 2] Fig. 2. The crystal packing of (I), viewed along the b axis. Hydrogen bonds were drawn as dashed lines.
4-hydroxy-5-(4-methoxyphenyl)pyrrolidin-2-one top
Crystal data top
C11H13NO3F(000) = 440
Mr = 207.22Dx = 1.381 Mg m3
Orthorhombic, Pca21Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2c -2acCell parameters from 1562 reflections
a = 11.9862 (6) Åθ = 1.8–30.0°
b = 11.6251 (6) ŵ = 0.10 mm1
c = 7.1539 (4) ÅT = 100 K
V = 996.83 (9) Å3Block, colorless
Z = 40.43 × 0.20 × 0.17 mm
Data collection top
Bruker SMART APEX2 CCD area-detector
diffractometer
1562 independent reflections
Radiation source: fine-focus sealed tube1218 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.066
Detector resolution: 8.33 pixels mm-1θmax = 30.0°, θmin = 1.8°
ω scansh = 1613
Absorption correction: multi-scan
(SADABS; Bruker, 2005)
k = 1616
Tmin = 0.958, Tmax = 0.983l = 109
8681 measured reflections
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.047Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.109H atoms treated by a mixture of independent and constrained refinement
S = 1.09 w = 1/[σ2(Fo2) + (0.0466P)2 + 0.0367P]
where P = (Fo2 + 2Fc2)/3
1562 reflections(Δ/σ)max < 0.001
145 parametersΔρmax = 0.22 e Å3
1 restraintΔρmin = 0.24 e Å3
Crystal data top
C11H13NO3V = 996.83 (9) Å3
Mr = 207.22Z = 4
Orthorhombic, Pca21Mo Kα radiation
a = 11.9862 (6) ŵ = 0.10 mm1
b = 11.6251 (6) ÅT = 100 K
c = 7.1539 (4) Å0.43 × 0.20 × 0.17 mm
Data collection top
Bruker SMART APEX2 CCD area-detector
diffractometer
1562 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2005)
1218 reflections with I > 2σ(I)
Tmin = 0.958, Tmax = 0.983Rint = 0.066
8681 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0471 restraint
wR(F2) = 0.109H atoms treated by a mixture of independent and constrained refinement
S = 1.09Δρmax = 0.22 e Å3
1562 reflectionsΔρmin = 0.24 e Å3
145 parameters
Special details top

Experimental. The data was collected with the Oxford Cyrosystem Cobra low-temperature attachment.

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
O10.69354 (13)1.02873 (16)1.1878 (3)0.0282 (5)
O20.93282 (14)0.80442 (16)1.3464 (3)0.0238 (4)
H1O20.977 (3)0.742 (3)1.345 (6)0.045 (10)*
O30.87847 (13)0.33500 (15)0.8900 (3)0.0239 (4)
N10.76602 (18)0.86418 (18)1.0604 (3)0.0228 (5)
H1N10.704 (3)0.838 (3)1.009 (6)0.043 (10)*
C10.7727 (2)0.9651 (2)1.1524 (4)0.0223 (6)
C20.89395 (19)0.9844 (2)1.2029 (5)0.0243 (6)
H2A0.90121.01051.33110.029*
H2B0.92791.04081.12060.029*
C30.94736 (19)0.8665 (2)1.1771 (4)0.0222 (6)
H3A1.02620.87251.14230.027*
C40.8761 (2)0.8158 (2)1.0169 (4)0.0207 (6)
H4A0.90180.84950.89890.025*
C50.8762 (2)0.6876 (2)0.9962 (4)0.0199 (6)
C60.79693 (19)0.6171 (2)1.0788 (4)0.0221 (6)
H6A0.74350.64971.15680.027*
C70.79523 (19)0.4993 (2)1.0483 (4)0.0229 (6)
H7A0.74030.45381.10300.028*
C80.8756 (2)0.4503 (2)0.9363 (4)0.0214 (6)
C90.95804 (18)0.5175 (2)0.8550 (4)0.0226 (6)
H9A1.01300.48390.78120.027*
C100.95734 (19)0.6345 (2)0.8850 (4)0.0220 (6)
H10A1.01240.67960.82980.026*
C110.7980 (2)0.2604 (2)0.9764 (5)0.0287 (7)
H11A0.80570.18410.92660.043*
H11B0.72420.28850.95120.043*
H11C0.81030.25881.10890.043*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0208 (9)0.0270 (10)0.0367 (12)0.0068 (8)0.0016 (9)0.0014 (9)
O20.0184 (8)0.0253 (10)0.0276 (11)0.0048 (8)0.0014 (8)0.0003 (9)
O30.0211 (8)0.0217 (9)0.0288 (11)0.0006 (7)0.0017 (8)0.0027 (8)
N10.0133 (10)0.0230 (11)0.0321 (14)0.0000 (9)0.0023 (10)0.0027 (10)
C10.0202 (12)0.0228 (12)0.0238 (16)0.0016 (10)0.0008 (10)0.0026 (12)
C20.0194 (12)0.0219 (13)0.0317 (16)0.0007 (10)0.0029 (11)0.0019 (12)
C30.0137 (11)0.0240 (13)0.0289 (14)0.0009 (10)0.0009 (11)0.0020 (12)
C40.0179 (12)0.0200 (13)0.0242 (14)0.0006 (10)0.0001 (10)0.0017 (11)
C50.0137 (11)0.0218 (13)0.0243 (15)0.0006 (10)0.0000 (10)0.0009 (11)
C60.0170 (11)0.0255 (13)0.0239 (14)0.0016 (9)0.0024 (11)0.0013 (12)
C70.0167 (12)0.0243 (13)0.0278 (15)0.0008 (10)0.0027 (11)0.0001 (12)
C80.0178 (12)0.0212 (13)0.0251 (15)0.0021 (10)0.0030 (10)0.0015 (11)
C90.0173 (12)0.0254 (13)0.0252 (14)0.0029 (9)0.0040 (11)0.0021 (12)
C100.0170 (12)0.0239 (13)0.0251 (14)0.0011 (9)0.0024 (11)0.0013 (13)
C110.0250 (13)0.0263 (15)0.0346 (18)0.0003 (11)0.0035 (12)0.0030 (14)
Geometric parameters (Å, º) top
O1—C11.229 (3)C4—H4A0.9800
O2—C31.420 (3)C5—C61.387 (4)
O2—H1O20.90 (3)C5—C101.399 (4)
O3—C81.381 (3)C6—C71.387 (4)
O3—C111.437 (3)C6—H6A0.9300
N1—C11.347 (3)C7—C81.376 (4)
N1—C41.468 (3)C7—H7A0.9300
N1—H1N10.88 (4)C8—C91.387 (3)
C1—C21.515 (3)C9—C101.378 (4)
C2—C31.524 (4)C9—H9A0.9300
C2—H2A0.9700C10—H10A0.9300
C2—H2B0.9700C11—H11A0.9600
C3—C41.547 (4)C11—H11B0.9600
C3—H3A0.9800C11—H11C0.9600
C4—C51.498 (3)
C3—O2—H1O2109 (3)C3—C4—H4A108.2
C8—O3—C11117.8 (2)C6—C5—C10117.2 (2)
C1—N1—C4112.6 (2)C6—C5—C4123.0 (2)
C1—N1—H1N1123 (2)C10—C5—C4119.7 (2)
C4—N1—H1N1123 (2)C7—C6—C5121.8 (2)
O1—C1—N1125.4 (2)C7—C6—H6A119.1
O1—C1—C2127.0 (2)C5—C6—H6A119.1
N1—C1—C2107.6 (2)C8—C7—C6119.3 (2)
C1—C2—C3103.9 (2)C8—C7—H7A120.3
C1—C2—H2A111.0C6—C7—H7A120.3
C3—C2—H2A111.0C7—C8—O3124.0 (2)
C1—C2—H2B111.0C7—C8—C9120.7 (2)
C3—C2—H2B111.0O3—C8—C9115.3 (2)
H2A—C2—H2B109.0C10—C9—C8119.1 (2)
O2—C3—C2107.6 (2)C10—C9—H9A120.5
O2—C3—C4111.8 (2)C8—C9—H9A120.5
C2—C3—C4101.6 (2)C9—C10—C5121.9 (2)
O2—C3—H3A111.8C9—C10—H10A119.1
C2—C3—H3A111.8C5—C10—H10A119.1
C4—C3—H3A111.8O3—C11—H11A109.5
N1—C4—C5113.8 (2)O3—C11—H11B109.5
N1—C4—C3101.1 (2)H11A—C11—H11B109.5
C5—C4—C3116.9 (2)O3—C11—H11C109.5
N1—C4—H4A108.2H11A—C11—H11C109.5
C5—C4—H4A108.2H11B—C11—H11C109.5
C4—N1—C1—O1172.0 (3)N1—C4—C5—C10154.0 (2)
C4—N1—C1—C28.0 (3)C3—C4—C5—C1088.6 (3)
O1—C1—C2—C3164.1 (3)C10—C5—C6—C72.1 (4)
N1—C1—C2—C315.8 (3)C4—C5—C6—C7176.1 (3)
C1—C2—C3—O286.1 (3)C5—C6—C7—C81.4 (4)
C1—C2—C3—C431.4 (3)C6—C7—C8—O3176.9 (2)
C1—N1—C4—C5154.0 (2)C6—C7—C8—C90.3 (4)
C1—N1—C4—C327.9 (3)C11—O3—C8—C75.2 (4)
O2—C3—C4—N179.4 (2)C11—O3—C8—C9177.4 (2)
C2—C3—C4—N135.1 (2)C7—C8—C9—C101.2 (4)
O2—C3—C4—C544.7 (3)O3—C8—C9—C10176.3 (2)
C2—C3—C4—C5159.2 (2)C8—C9—C10—C50.4 (4)
N1—C4—C5—C624.2 (4)C6—C5—C10—C91.2 (4)
C3—C4—C5—C693.2 (3)C4—C5—C10—C9177.1 (2)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1N1···O2i0.88 (4)2.05 (4)2.917 (3)167 (4)
O2—H1O2···O3ii0.90 (4)1.98 (4)2.800 (2)152 (3)
C3—H3A···O1iii0.982.333.193 (3)146
C11—H11A···O1iv0.962.493.395 (3)158
C6—H6A···Cg1v0.932.813.514 (3)133
C9—H9A···Cg1vi0.932.683.554 (3)157
Symmetry codes: (i) x+3/2, y, z1/2; (ii) x+2, y+1, z+1/2; (iii) x+1/2, y+2, z; (iv) x+3/2, y1, z1/2; (v) x+3/2, y, z; (vi) x+2, y+1, z1/2.

Experimental details

Crystal data
Chemical formulaC11H13NO3
Mr207.22
Crystal system, space groupOrthorhombic, Pca21
Temperature (K)100
a, b, c (Å)11.9862 (6), 11.6251 (6), 7.1539 (4)
V3)996.83 (9)
Z4
Radiation typeMo Kα
µ (mm1)0.10
Crystal size (mm)0.43 × 0.20 × 0.17
Data collection
DiffractometerBruker SMART APEX2 CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Bruker, 2005)
Tmin, Tmax0.958, 0.983
No. of measured, independent and
observed [I > 2σ(I)] reflections
8681, 1562, 1218
Rint0.066
(sin θ/λ)max1)0.703
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.047, 0.109, 1.09
No. of reflections1562
No. of parameters145
No. of restraints1
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.22, 0.24

Computer programs: APEX2 (Bruker, 2005), SAINT (Bruker, 2005), SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2003).

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1N1···O2i0.88 (4)2.05 (4)2.917 (3)167 (4)
O2—H1O2···O3ii0.90 (4)1.98 (4)2.800 (2)152 (3)
C3—H3A···O1iii0.982.33403.193 (3)146
C11—H11A···O1iv0.962.48613.395 (3)158
C6—H6A···Cg1v0.932.80913.514 (3)133
C9—H9A···Cg1vi0.932.67913.554 (3)157
Symmetry codes: (i) x+3/2, y, z1/2; (ii) x+2, y+1, z+1/2; (iii) x+1/2, y+2, z; (iv) x+3/2, y1, z1/2; (v) x+3/2, y, z; (vi) x+2, y+1, z1/2.
 

Footnotes

Additional correspondence author, email: suchada.c@psu.ac.th.

Acknowledgements

The authors acknowledge the generous support of both the Universiti Teknologi MARA and Universiti Sains Malaysia as well as the financial support of the Ministry of Science, Technology and Innovation (E-Science grant No. SF0050–02-01–01). HKF and SC thank the Malaysian Government and Universiti Sains Malaysia for the Scientific Advancement Grant Allocation (SAGA) grant No. 304/PFIZIK/653003/A118.

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Volume 64| Part 3| March 2008| Pages o578-o579
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