supplementary materials


gk2161 scheme

Acta Cryst. (2008). E64, m1166-m1167    [ doi:10.1107/S1600536808025701 ]

(2,4-Dioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylato-[kappa]2O4,O5)(4-oxido-2-oxo-1,2-dihydropyrimidine-5-carboxylato-[kappa]2O4,O5)bis(1,10-phenanthroline-[kappa]2N,N')yttrium(III) dihydrate

W. Xiong, H. Xing, Y. Su and Z. Chen

Abstract top

In the title compound, [Y(C5H2N2O4)(C5H3N2O4)(C12H8N2)2]·2H2O, the YIII ion lies on a twofold rotation axis and exhibits a distorted square-antiprismatic coordination geometry. It is chelated by two 1,10-phenanthroline ligands, a 2,4-dioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylate monoanion and a 4-oxido-2-oxo-1,2-dihydropyrimidine-5-carboxylate dianion. The H atom involved in an N-H...N hydrogen bond between the 1,2-dihydropyrimidine units has half occupancy and is disordered around a twofold rotation axis.

Comment top

2,4-Dioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylic acid has attracted much attention because of its potential biological activity and pharmaceutical properties, such as anticancer, antibacterial and antihypertensive properties (Tobiki et al., 1980; Castan et al., 1990). Here we report the crystal structure of YIII complex with 2,4-dioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylic acid and 1,10-phenenthroline as ligands. The title complex turned out to be isostructural with the analogues Eu, Tb, Yb (Sun & Jin, 2004) and Er (Xing et al., 2008) complexes; see Sun & Jin (2004) for their detailed description.

Related literature top

For the crystal structures of the isostructural Er, Eu, Tb and Yb complexes, see: Sun & Jin (2004); Xing et al. (2008). For other related literature, see: Tobiki et al. (1980); Castan et al. (1990).

Experimental top

A mixture of 2,4-dihydroxypyrimidine-5-carboxylic acid (0.0312 g, 0.2 mmol), YCl3.6H2O (0.0607 g, 0.2 mmol), phenanthroline dihydrate (0.0396 g, 0.2 mmol), NaOH (0.0160 g, 0.4 mmol) and water (15 ml) was sealed in a 25 ml, Teflon-lined stainless-steel reactor and heated to 383 K for 120 h. It was then cooled over 48 h to give colourless crystals in 70% yield. Elemental analysis calculated for C34H25N8O10Y: C 51.40, H 3.17, N 14.10%; found: C 51.77, H 3.29, N 14.49%.

Refinement top

H atoms of the water molecule were located in a difference Fourier map and allowed to ride on their parent atom [Uiso(H) = 1.5Ueq(O)]. Other H atoms were placed at calculated positions (C—H = 0.93 Å and N—H = 0.86 Å) and were included in the refinement in the riding model approximation, with Uiso(H) = 1.2Ueq(C, N). The pyrimidine hydrogen atom H4 is shared by two N—H groups and thus has an occupancy factor of 0.5.

Computing details top

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT (Bruker, 2004); 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 compound with the atom-numbering scheme and 30% displacement ellipsoids.
(2,4-Dioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylato- κ2O4,O5)(4-oxido-2-oxo-1,2-dihydropyrimidine-5- carboxylato-κ2O4,O5)bis(1,10-phenanthroline- κ2N,N')yttrium(III) dihydrate top
Crystal data top
[Y(C5H2N2O4)(C5H3N2O4)(C12H8N2)2]·2H2OF000 = 1616
Mr = 794.53Dx = 1.637 Mg m3
Monoclinic, C2/cMo Kα radiation
λ = 0.71073 Å
Hall symbol: -C 2ycCell parameters from 7855 reflections
a = 17.1740 (13) Åθ = 2.3–27.9º
b = 14.4385 (11) ŵ = 1.89 mm1
c = 13.2365 (10) ÅT = 295 (2) K
β = 100.8810 (10)ºPrism, colourless
V = 3223.2 (4) Å30.24 × 0.08 × 0.06 mm
Z = 4
Data collection top
Bruker APEXII
diffractometer
3152 independent reflections
Radiation source: fine-focus sealed tube2986 reflections with I > 2σ(I)
Monochromator: graphiteRint = 0.035
T = 295(2) Kθmax = 26.0º
φ and ω scansθmin = 1.9º
Absorption correction: multi-scan
(SADABS; Bruker, 1998)
h = 21→21
Tmin = 0.660, Tmax = 0.895k = 17→17
12035 measured reflectionsl = 16→16
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)] = 0.046H-atom parameters constrained
wR(F2) = 0.096  w = 1/[σ2(Fo2) + (0.0141P)2 + 9.88P]
where P = (Fo2 + 2Fc2)/3
S = 1.21(Δ/σ)max < 0.001
3152 reflectionsΔρmax = 0.41 e Å3
240 parametersΔρmin = 0.51 e Å3
Primary atom site location: structure-invariant direct methodsExtinction correction: none
Crystal data top
[Y(C5H2N2O4)(C5H3N2O4)(C12H8N2)2]·2H2OV = 3223.2 (4) Å3
Mr = 794.53Z = 4
Monoclinic, C2/cMo Kα
a = 17.1740 (13) ŵ = 1.89 mm1
b = 14.4385 (11) ÅT = 295 (2) K
c = 13.2365 (10) Å0.24 × 0.08 × 0.06 mm
β = 100.8810 (10)º
Data collection top
Bruker APEXII
diffractometer
3152 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 1998)
2986 reflections with I > 2σ(I)
Tmin = 0.660, Tmax = 0.895Rint = 0.035
12035 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.046240 parameters
wR(F2) = 0.096H-atom parameters constrained
S = 1.21Δρmax = 0.41 e Å3
3152 reflectionsΔρmin = 0.51 e Å3
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds 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 > 2sigma(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*/UeqOcc. (<1)
Y11.00000.88802 (3)0.25000.02339 (12)
N10.90591 (16)0.75076 (19)0.2117 (2)0.0324 (6)
N20.96510 (16)0.80446 (19)0.4073 (2)0.0304 (6)
N30.83326 (16)1.02589 (19)0.0065 (2)0.0297 (6)
H30.83790.98420.05140.036*
N40.78240 (19)1.1684 (2)0.0310 (2)0.0387 (7)
H40.75851.21990.01310.046*0.50
O10.90470 (14)0.93356 (15)0.11247 (17)0.0329 (6)
O20.93006 (14)0.99886 (16)0.31195 (17)0.0337 (6)
O30.84729 (15)1.10907 (17)0.34049 (17)0.0371 (6)
O40.76917 (16)1.11986 (18)0.13684 (19)0.0451 (7)
C10.8770 (2)1.0594 (2)0.2805 (2)0.0272 (7)
C20.84980 (19)1.0723 (2)0.1678 (2)0.0269 (7)
C30.86584 (18)1.0066 (2)0.0941 (2)0.0248 (7)
C40.7937 (2)1.1063 (2)0.0423 (3)0.0324 (7)
C50.8085 (2)1.1498 (2)0.1311 (3)0.0358 (8)
H50.79761.19280.17880.043*
C60.9900 (2)0.8317 (3)0.5036 (3)0.0386 (8)
H61.00890.89200.51480.046*
C70.9896 (3)0.7758 (3)0.5890 (3)0.0512 (11)
H71.00740.79820.65520.061*
C80.9624 (3)0.6872 (3)0.5735 (3)0.0599 (12)
H80.96260.64830.62960.072*
C90.9342 (2)0.6545 (3)0.4735 (3)0.0463 (10)
C100.9355 (2)0.7169 (2)0.3922 (3)0.0327 (8)
C110.9042 (2)0.6886 (2)0.2883 (3)0.0325 (8)
C120.8716 (2)0.5993 (2)0.2699 (3)0.0419 (9)
C130.8735 (3)0.5372 (3)0.3546 (4)0.0607 (13)
H130.85340.47760.34230.073*
C140.9036 (3)0.5634 (3)0.4513 (4)0.0618 (13)
H140.90450.52150.50480.074*
C150.8370 (2)0.5768 (3)0.1686 (4)0.0510 (11)
H150.81480.51850.15330.061*
C160.8357 (2)0.6401 (3)0.0926 (3)0.0490 (10)
H160.81190.62620.02520.059*
C170.8707 (2)0.7264 (3)0.1173 (3)0.0397 (9)
H170.86930.76930.06470.048*
O50.6925 (3)0.1887 (2)0.6600 (3)0.0956 (14)
H510.67930.24540.66440.143*
H520.70820.16810.72080.143*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Y10.0287 (2)0.0187 (2)0.0207 (2)0.0000.00062 (16)0.000
N10.0322 (16)0.0288 (15)0.0352 (16)0.0037 (12)0.0040 (12)0.0035 (12)
N20.0318 (15)0.0294 (15)0.0297 (15)0.0002 (12)0.0051 (12)0.0008 (12)
N30.0389 (16)0.0276 (15)0.0204 (13)0.0051 (12)0.0001 (12)0.0021 (11)
N40.057 (2)0.0273 (15)0.0278 (15)0.0107 (14)0.0016 (14)0.0018 (12)
O10.0421 (14)0.0265 (12)0.0255 (12)0.0100 (10)0.0052 (10)0.0034 (9)
O20.0441 (14)0.0324 (13)0.0226 (12)0.0133 (11)0.0011 (10)0.0006 (10)
O30.0510 (15)0.0374 (14)0.0227 (12)0.0125 (12)0.0064 (11)0.0021 (10)
O40.0562 (17)0.0369 (15)0.0358 (14)0.0044 (13)0.0074 (12)0.0002 (12)
C10.0345 (18)0.0240 (16)0.0224 (16)0.0025 (14)0.0032 (13)0.0017 (13)
C20.0328 (17)0.0263 (16)0.0207 (16)0.0053 (14)0.0031 (13)0.0002 (13)
C30.0284 (16)0.0237 (16)0.0209 (15)0.0008 (13)0.0014 (13)0.0007 (12)
C40.0373 (19)0.0291 (18)0.0280 (17)0.0006 (15)0.0012 (14)0.0021 (14)
C50.050 (2)0.0292 (18)0.0263 (18)0.0094 (16)0.0031 (16)0.0026 (14)
C60.039 (2)0.042 (2)0.0339 (19)0.0026 (17)0.0042 (16)0.0029 (16)
C70.056 (3)0.070 (3)0.028 (2)0.010 (2)0.0082 (18)0.0061 (19)
C80.066 (3)0.069 (3)0.044 (2)0.008 (2)0.009 (2)0.024 (2)
C90.048 (2)0.043 (2)0.048 (2)0.0034 (19)0.0101 (19)0.0158 (19)
C100.0306 (18)0.0296 (18)0.0384 (19)0.0007 (14)0.0078 (15)0.0034 (15)
C110.0311 (18)0.0269 (17)0.0399 (19)0.0005 (14)0.0072 (15)0.0017 (15)
C120.042 (2)0.0279 (19)0.058 (2)0.0074 (16)0.0137 (19)0.0027 (17)
C130.074 (3)0.030 (2)0.080 (3)0.018 (2)0.017 (3)0.004 (2)
C140.076 (3)0.042 (3)0.068 (3)0.017 (2)0.016 (3)0.021 (2)
C150.051 (2)0.035 (2)0.069 (3)0.0161 (19)0.016 (2)0.018 (2)
C160.047 (2)0.050 (2)0.049 (2)0.0137 (19)0.0063 (19)0.022 (2)
C170.039 (2)0.039 (2)0.040 (2)0.0064 (17)0.0052 (16)0.0062 (16)
O50.145 (4)0.059 (2)0.067 (2)0.004 (2)0.017 (2)0.0089 (19)
Geometric parameters (Å, °) top
Y1—O2i2.247 (2)C2—C31.423 (4)
Y1—O22.247 (2)C5—H50.9300
Y1—O1i2.302 (2)C6—C71.391 (5)
Y1—O12.302 (2)C6—H60.9300
Y1—N12.547 (3)C7—C81.362 (6)
Y1—N1i2.547 (3)C7—H70.9300
Y1—N2i2.573 (3)C8—C91.403 (6)
Y1—N22.573 (3)C8—H80.9300
N1—C171.329 (4)C9—C101.407 (5)
N1—C111.358 (4)C9—C141.426 (6)
N2—C61.326 (4)C10—C111.439 (5)
N2—C101.363 (4)C11—C121.408 (5)
N3—C31.373 (4)C12—C151.399 (6)
N3—C41.383 (4)C12—C131.431 (6)
N3—H30.8600C13—C141.342 (6)
N4—C51.343 (4)C13—H130.9300
N4—C41.362 (4)C14—H140.9300
N4—H40.8600C15—C161.355 (6)
O1—C31.247 (4)C15—H150.9300
O2—C11.275 (4)C16—C171.395 (5)
O3—C11.248 (4)C16—H160.9300
O4—C41.258 (4)C17—H170.9300
C1—C21.489 (4)O5—H510.8533
C2—C51.364 (4)O5—H520.8518
O2i—Y1—O289.15 (13)C3—C2—C1122.6 (3)
O2i—Y1—O1i74.69 (8)O1—C3—N3117.7 (3)
O2—Y1—O1i81.79 (9)O1—C3—C2126.6 (3)
O2i—Y1—O181.79 (8)N3—C3—C2115.7 (3)
O2—Y1—O174.69 (8)O4—C4—N4122.7 (3)
O1i—Y1—O1146.81 (11)O4—C4—N3121.5 (3)
O2i—Y1—N1147.62 (8)N4—C4—N3115.8 (3)
O2—Y1—N1105.31 (9)N4—C5—C2124.8 (3)
O1i—Y1—N1135.17 (8)N4—C5—H5117.6
O1—Y1—N174.65 (9)C2—C5—H5117.6
O2i—Y1—N1i105.31 (9)N2—C6—C7124.0 (4)
O2—Y1—N1i147.62 (8)N2—C6—H6118.0
O1i—Y1—N1i74.65 (9)C7—C6—H6118.0
O1—Y1—N1i135.17 (8)C8—C7—C6118.5 (4)
N1—Y1—N1i77.82 (13)C8—C7—H7120.7
O2i—Y1—N2i79.43 (8)C6—C7—H7120.7
O2—Y1—N2i148.38 (8)C7—C8—C9120.4 (4)
O1i—Y1—N2i122.30 (9)C7—C8—H8119.8
O1—Y1—N2i74.55 (8)C9—C8—H8119.8
N1—Y1—N2i73.15 (9)C8—C9—C10117.0 (4)
N1i—Y1—N2i63.90 (9)C8—C9—C14123.6 (4)
O2i—Y1—N2148.38 (8)C10—C9—C14119.4 (4)
O2—Y1—N279.43 (9)N2—C10—C9122.8 (3)
O1i—Y1—N274.55 (8)N2—C10—C11117.7 (3)
O1—Y1—N2122.30 (9)C9—C10—C11119.5 (3)
N1—Y1—N263.90 (9)N1—C11—C12122.7 (3)
N1i—Y1—N273.15 (9)N1—C11—C10118.0 (3)
N2i—Y1—N2124.07 (12)C12—C11—C10119.3 (3)
C17—N1—C11117.1 (3)C15—C12—C11117.5 (4)
C17—N1—Y1123.5 (2)C15—C12—C13123.2 (4)
C11—N1—Y1117.9 (2)C11—C12—C13119.3 (4)
C6—N2—C10117.4 (3)C14—C13—C12121.2 (4)
C6—N2—Y1123.8 (2)C14—C13—H13119.4
C10—N2—Y1117.0 (2)C12—C13—H13119.4
C3—N3—C4125.9 (3)C13—C14—C9121.2 (4)
C3—N3—H3117.0C13—C14—H14119.4
C4—N3—H3117.0C9—C14—H14119.4
C5—N4—C4120.3 (3)C16—C15—C12119.9 (4)
C5—N4—H4119.9C16—C15—H15120.0
C4—N4—H4119.9C12—C15—H15120.0
C3—O1—Y1132.1 (2)C15—C16—C17118.8 (4)
C1—O2—Y1140.2 (2)C15—C16—H16120.6
O3—C1—O2122.6 (3)C17—C16—H16120.6
O3—C1—C2118.5 (3)N1—C17—C16123.9 (4)
O2—C1—C2118.8 (3)N1—C17—H17118.1
C5—C2—C3117.2 (3)C16—C17—H17118.1
C5—C2—C1120.2 (3)H51—O5—H52108.2
O2i—Y1—N1—C178.9 (4)C4—N3—C3—O1174.8 (3)
O2—Y1—N1—C17104.9 (3)C4—N3—C3—C26.6 (5)
O1i—Y1—N1—C17161.4 (3)C5—C2—C3—O1177.5 (3)
O1—Y1—N1—C1735.9 (3)C1—C2—C3—O11.8 (5)
N1i—Y1—N1—C17108.3 (3)C5—C2—C3—N34.0 (5)
N2i—Y1—N1—C1742.2 (3)C1—C2—C3—N3176.7 (3)
N2—Y1—N1—C17174.6 (3)C5—N4—C4—O4178.8 (4)
O2i—Y1—N1—C11157.1 (2)C5—N4—C4—N30.5 (5)
O2—Y1—N1—C1189.1 (2)C3—N3—C4—O4176.4 (3)
O1i—Y1—N1—C114.6 (3)C3—N3—C4—N44.3 (5)
O1—Y1—N1—C11158.1 (3)C4—N4—C5—C22.7 (6)
N1i—Y1—N1—C1157.7 (2)C3—C2—C5—N40.3 (6)
N2i—Y1—N1—C11123.8 (3)C1—C2—C5—N4179.0 (3)
N2—Y1—N1—C1119.3 (2)C10—N2—C6—C71.8 (5)
O2i—Y1—N2—C67.0 (4)Y1—N2—C6—C7162.4 (3)
O2—Y1—N2—C663.6 (3)N2—C6—C7—C80.4 (6)
O1i—Y1—N2—C620.7 (3)C6—C7—C8—C91.3 (7)
O1—Y1—N2—C6127.8 (3)C7—C8—C9—C100.0 (7)
N1—Y1—N2—C6176.6 (3)C7—C8—C9—C14178.8 (5)
N1i—Y1—N2—C699.0 (3)C6—N2—C10—C93.2 (5)
N2i—Y1—N2—C6139.5 (3)Y1—N2—C10—C9162.2 (3)
O2i—Y1—N2—C10157.3 (2)C6—N2—C10—C11176.5 (3)
O2—Y1—N2—C10132.1 (2)Y1—N2—C10—C1118.1 (4)
O1i—Y1—N2—C10143.6 (2)C8—C9—C10—N22.3 (6)
O1—Y1—N2—C1067.9 (2)C14—C9—C10—N2178.8 (4)
N1—Y1—N2—C1019.1 (2)C8—C9—C10—C11177.4 (4)
N1i—Y1—N2—C1065.3 (2)C14—C9—C10—C111.5 (6)
N2i—Y1—N2—C1024.8 (2)C17—N1—C11—C124.1 (5)
O2i—Y1—O1—C368.1 (3)Y1—N1—C11—C12162.8 (3)
O2—Y1—O1—C323.3 (3)C17—N1—C11—C10174.4 (3)
O1i—Y1—O1—C323.2 (3)Y1—N1—C11—C1018.7 (4)
N1—Y1—O1—C3134.3 (3)N2—C10—C11—N10.2 (5)
N1i—Y1—O1—C3171.6 (3)C9—C10—C11—N1179.6 (3)
N2i—Y1—O1—C3149.3 (3)N2—C10—C11—C12178.7 (3)
N2—Y1—O1—C389.8 (3)C9—C10—C11—C121.1 (5)
O2i—Y1—O2—C172.0 (3)N1—C11—C12—C152.7 (6)
O1i—Y1—O2—C1146.7 (4)C10—C11—C12—C15175.7 (3)
O1—Y1—O2—C19.7 (3)N1—C11—C12—C13178.8 (4)
N1—Y1—O2—C178.6 (3)C10—C11—C12—C132.8 (6)
N1i—Y1—O2—C1170.0 (3)C15—C12—C13—C14176.4 (5)
N2i—Y1—O2—C14.0 (4)C11—C12—C13—C142.0 (7)
N2—Y1—O2—C1137.6 (4)C12—C13—C14—C90.6 (8)
Y1—O2—C1—O3176.0 (2)C8—C9—C14—C13176.5 (5)
Y1—O2—C1—C24.6 (5)C10—C9—C14—C132.3 (7)
O3—C1—C2—C515.4 (5)C11—C12—C15—C160.1 (6)
O2—C1—C2—C5164.0 (3)C13—C12—C15—C16178.4 (4)
O3—C1—C2—C3165.3 (3)C12—C15—C16—C171.3 (6)
O2—C1—C2—C315.2 (5)C11—N1—C17—C162.8 (5)
Y1—O1—C3—N3158.7 (2)Y1—N1—C17—C16163.3 (3)
Y1—O1—C3—C222.8 (5)C15—C16—C17—N10.2 (6)
Symmetry codes: (i) −x+2, y, −z+1/2.
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
N3—H3···O3ii0.861.992.853 (4)178
N3—H3···O2ii0.862.633.189 (4)124
N4—H4···N4iii0.861.812.667 (6)174
O5—H51···O3iv0.852.152.998 (4)173
O5—H52···O4v0.852.102.935 (4)169
Symmetry codes: (ii) x, −y+2, z−1/2; (iii) −x+3/2, −y+5/2, −z; (iv) −x+3/2, −y+3/2, −z+1; (v) x, y−1, z+1.
Table 1
Selected geometric parameters (Å, °)
top
Y1—O22.247 (2)Y1—N12.547 (3)
Y1—O12.302 (2)Y1—N22.573 (3)
O2i—Y1—O289.15 (13)N1—Y1—N1i77.82 (13)
O2—Y1—O1i81.79 (9)O2—Y1—N2i148.38 (8)
O2—Y1—O174.69 (8)O1—Y1—N2i74.55 (8)
O1i—Y1—O1146.81 (11)N1—Y1—N2i73.15 (9)
O2i—Y1—N1147.62 (8)O2—Y1—N279.43 (9)
O2—Y1—N1105.31 (9)O1—Y1—N2122.30 (9)
O1i—Y1—N1135.17 (8)N1—Y1—N263.90 (9)
O1—Y1—N174.65 (9)N2i—Y1—N2124.07 (12)
Symmetry codes: (i) −x+2, y, −z+1/2.
Table 2
Hydrogen-bond geometry (Å, °)
top
D—H···AD—HH···AD···AD—H···A
N3—H3···O3ii0.861.992.853 (4)178
N3—H3···O2ii0.862.633.189 (4)124
N4—H4···N4iii0.861.812.667 (6)174
O5—H51···O3iv0.852.152.998 (4)173
O5—H52···O4v0.852.102.935 (4)169
Symmetry codes: (ii) x, −y+2, z−1/2; (iii) −x+3/2, −y+5/2, −z; (iv) −x+3/2, −y+3/2, −z+1; (v) x, y−1, z+1.
Acknowledgements top

The authors thank the Science Foundation of Guangxi Province, China (Gui ke qing 0542021) and the Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry, for financial support.

references
References top

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