Potassium oxalurate monohydrate

Zhang, L.-F.

doi:10.1107/S1600536809005637

metal-organic compounds

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ISSN: 2056-9890

Volume 65| Part 3| March 2009| Pages m308-m309

doi:10.1107/S1600536809005637

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Potassium oxalurate monohydrate

Lian-Feng Zhang ^a ^*

^aCollege of Chemistry and Pharmacy Engineering, Nanyang Normal University, Nanyang 473061, People's Republic of China
^*Correspondence e-mail: zhanglf2009@126.com

(Received 7 February 2009; accepted 17 February 2009; online 21 February 2009)

The title salt, poly[aqua-μ₃-oxalurato-potassium(I)], [K(C₃H₃N₂O₄)(H₂O)]_n, which was obtained from a water solution of oxaluric acid and KOH at room temperature, crystallizes as potassium and oxalurate ions along with a water molecule. The K⁺ cation lies on a crystallographic twofold rotation axis (site symmetry 2, Wyckoff position f), and the water and oxalurate molecules are located within different mirror planes (site symmetry m, Wyckoff position g). The K⁺ cation is eight-coordinated by six O atoms of six oxalurate ligands and two O atoms from two water molecules in a distorted square-antiprismatic geometry. All of the eight coordinated O atoms are in a monodentate bridging mode, with alternate bridged K⋯K distances of 3.5575 (12) and 3.3738 (12) Å. The oxalurate ligand shows a μ₃-bridging coordination mode, which links the K⁺ cation into a three-dimensional network. The oxalurate ligands and the water molecules are involved in inter- and intramolecular N—H⋯O, and O—H⋯O hydrogen bonds, which stabilize the network.

Related literature

For oxalurate metal complexes, see: Falvello et al. (2002 ). For elongated K—O bonds, see: Karapetyan (2008 ); Kunz et al. (2009 ).

Experimental

Crystal data

[K(C₃H₃N₂O₄)(H₂O)]
M_r = 188.19
Orthorhombic, P n n m
a = 7.7313 (17) Å
b = 12.799 (3) Å
c = 6.9313 (16) Å
V = 685.9 (3) Å³
Z = 4
Mo Kα radiation
μ = 0.75 mm⁻¹
T = 296 K
0.41 × 0.39 × 0.28 mm

Data collection

Bruker SMART CCD area-detector diffractometer
Absorption correction: multi-scan (SADABS; Bruker, 1997 ) T_min = 0.748, T_max = 0.816
3320 measured reflections
699 independent reflections
633 reflections with I > 2σ(I)
R_int = 0.013

Refinement

R[F² > 2σ(F²)] = 0.026
wR(F²) = 0.077
S = 1.09
699 reflections
66 parameters
H-atom parameters constrained
Δρ_max = 0.17 e Å⁻³
Δρ_min = −0.34 e Å⁻³

Table 1
Selected bond lengths (Å)

K1—O1	2.7291 (11)
K1—O3ⁱ	2.7812 (11)
K1—O5	2.8458 (13)
K1—O4ⁱⁱ	2.9775 (13)
Symmetry codes: (i) $[-x+{\script{3\over 2}}, y+{\script{1\over 2}}, -z+{\script{1\over 2}}]$ ; (ii) x+1, y, z.

Table 2
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N1—H1⋯O4ⁱⁱⁱ	0.86	2.10	2.936 (2)	164
N2—H2A⋯O1^iv	0.86	2.17	2.997 (2)	163
N2—H2A⋯O2^iv	0.86	2.37	3.069 (2)	139
N2—H2B⋯O3	0.86	2.01	2.667 (2)	133
N2—H2B⋯O5^v	0.86	2.38	3.076 (3)	138
O5—H1W⋯O2ⁱ	0.83	1.97	2.791 (2)	172
O5—H1W⋯O3ⁱ	0.83	2.59	3.068 (2)	118
O5—H2W⋯O2^vi	0.83	2.14	2.973 (2)	178
Symmetry codes: (i) $[-x+{\script{3\over 2}}, y+{\script{1\over 2}}, -z+{\script{1\over 2}}]$ ; (iii) -x+1, -y+1, -z; (iv) x-1, y, z; (v) $[x-{\script{1\over 2}}, -y+{\script{1\over 2}}, z-{\script{1\over 2}}]$ ; (vi) $[x-{\script{1\over 2}}, -y+{\script{1\over 2}}, z+{\script{1\over 2}}]$ .

Data collection: SMART (Bruker, 1997); cell refinement: SAINT (Bruker, 1997); data reduction: SAINT; 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.

Supporting information

Crystal structure: contains datablocks I, global. DOI: 10.1107/S1600536809005637/si2155sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536809005637/si2155Isup2.hkl

checkCIF report

Comment top

Oxaluric acid is the condensation product of oxalic acid and urea. Deprotonated oxalurate possesses four oxygen atoms and two amine N atoms, which can serve as hydrogen-bond acceptors and hydrogen-bond donors, respectively. In addition, one or more of six different atoms can bind to metal centers in any of at least three distinct coordination modes, namely, chelating, terminal, or bridging coordination (Falvello, 2002).

As shown in Fig. 1, the asymmetric structure unit consists of one K⁺ cation, one C₃H₃N₂O₄^- anion, and one water molecule. The K⁺ cation is surrounded by six oxalurate ligands and two water molecules, making close contacts with eight O atoms at 2.7291 (11)–2.9775 (13) A ° in a distorted square antiprismatic geometry of the central atom (Karapetyan, 2008; Kunz, 2009) (Table 1). All the eight coordinated O atoms are in the monodentate bridging mode, with the bridged K···K distance of 3.558 (1) and 3.374 (1) Å alternately. The oxalurate ligand, which is planar, shows a µ₃-bridging coordination mode and links the K⁺ cation into a three-dimensional network (Fig. 2). The oxalurate ligands and water molecules are involved in inter- and intramolecular N—H···O, and O—H···O hydrogen bonds, which stabilize the network (Table 2).

Related literature top

For oxalurate metal complexes, see: Falvello et al. (2002). For elongated K—O bonds, see: Karapetyan (2008); Kunz et al. (2009).

Experimental top

A 10 ml sample of a KOH solution (0.5 mol/L) was added to a water suspension of oxaluric acid, HOOCCONHCONH₂ (0.5 mmol/10 ml). The KOH addition produced a partial solubilization of the acid and then the precipitation of a white solid. After 20 min of stirring, the solid was filtered off, washed with i-PrOH. The single crystals suitable for X-ray analysis were obtained by slow diffusion of Et₂O into the water solution of the solid.

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

	Fig. 1. A perspective view of the asymmetric unit, showing the atomic numbering and displacement ellipsoids drawn at the 30% probability level.
	Fig. 2. A view of the compound packing down the a axis.

poly[aqua-µ₃-oxalurato-potassium(I)] top

Crystal data top

[K(C₃H₃N₂O₄)(H₂O)]	F(000) = 384
M_r = 188.19	D_x = 1.823 Mg m⁻³
Orthorhombic, Pnnm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2 2n	Cell parameters from 1939 reflections
a = 7.7313 (17) Å	θ = 2.9–28.2°
b = 12.799 (3) Å	µ = 0.75 mm⁻¹
c = 6.9313 (16) Å	T = 296 K
V = 685.9 (3) Å³	Block, pink
Z = 4	0.41 × 0.39 × 0.28 mm

Data collection top

Bruker SMART CCD area-detector diffractometer	699 independent reflections
Radiation source: fine-focus sealed tube	633 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.013
ϕ and ω scans	θ_max = 25.5°, θ_min = 3.1°
Absorption correction: multi-scan (SADABS; Bruker, 1997)	h = −9→9
T_min = 0.748, T_max = 0.816	k = −15→15
3320 measured reflections	l = −8→6

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)] = 0.026	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.077	H-atom parameters constrained
S = 1.09	w = 1/[σ²(F_o²) + (0.0457P)² + 0.2142P] where P = (F_o² + 2F_c²)/3
699 reflections	(Δ/σ)_max < 0.001
66 parameters	Δρ_max = 0.17 e Å⁻³
0 restraints	Δρ_min = −0.34 e Å⁻³

Crystal data top

[K(C₃H₃N₂O₄)(H₂O)]	V = 685.9 (3) Å³
M_r = 188.19	Z = 4
Orthorhombic, Pnnm	Mo Kα radiation
a = 7.7313 (17) Å	µ = 0.75 mm⁻¹
b = 12.799 (3) Å	T = 296 K
c = 6.9313 (16) Å	0.41 × 0.39 × 0.28 mm

Data collection top

Bruker SMART CCD area-detector diffractometer	699 independent reflections
Absorption correction: multi-scan (SADABS; Bruker, 1997)	633 reflections with I > 2σ(I)
T_min = 0.748, T_max = 0.816	R_int = 0.013
3320 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.026	0 restraints
wR(F²) = 0.077	H-atom parameters constrained
S = 1.09	Δρ_max = 0.17 e Å⁻³
699 reflections	Δρ_min = −0.34 e Å⁻³
66 parameters

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

	x	y	z	U_iso*/U_eq
K1	1.0000	0.5000	0.24337 (6)	0.0336 (2)
O1	0.89541 (18)	0.34475 (10)	0.0000	0.0329 (4)
O2	0.90620 (19)	0.17010 (11)	0.0000	0.0478 (5)
O3	0.55768 (18)	0.16337 (10)	0.0000	0.0349 (4)
O4	0.30509 (18)	0.44721 (10)	0.0000	0.0396 (4)
N1	0.5439 (2)	0.34235 (12)	0.0000	0.0278 (4)
H1	0.6069	0.3977	0.0000	0.033*
N2	0.2646 (2)	0.27328 (14)	0.0000	0.0414 (5)
H2A	0.1538	0.2794	0.0000	0.050*
H2B	0.3111	0.2122	0.0000	0.050*
C1	0.8300 (3)	0.25554 (15)	0.0000	0.0266 (5)
C2	0.6290 (2)	0.24914 (14)	0.0000	0.0239 (4)
C3	0.3632 (2)	0.35754 (14)	0.0000	0.0281 (5)
O5	0.7184 (2)	0.46547 (13)	0.5000	0.0490 (5)
H1W	0.6919	0.5284	0.5000	0.073*
H2W	0.6298	0.4287	0.5000	0.073*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
K1	0.0406 (3)	0.0241 (3)	0.0362 (4)	−0.00314 (16)	0.000	0.000
O1	0.0213 (7)	0.0206 (7)	0.0567 (10)	−0.0038 (5)	0.000	0.000
O2	0.0210 (7)	0.0224 (7)	0.0999 (15)	0.0037 (6)	0.000	0.000
O3	0.0226 (7)	0.0171 (7)	0.0650 (11)	−0.0027 (6)	0.000	0.000
O4	0.0227 (7)	0.0203 (7)	0.0758 (12)	0.0033 (6)	0.000	0.000
N1	0.0175 (8)	0.0165 (8)	0.0493 (11)	−0.0020 (6)	0.000	0.000
N2	0.0172 (8)	0.0219 (8)	0.0852 (16)	0.0006 (7)	0.000	0.000
C1	0.0194 (10)	0.0224 (9)	0.0379 (11)	−0.0015 (7)	0.000	0.000
C2	0.0197 (10)	0.0190 (9)	0.0330 (11)	−0.0007 (7)	0.000	0.000
C3	0.0184 (9)	0.0221 (9)	0.0438 (13)	0.0014 (7)	0.000	0.000
O5	0.0247 (8)	0.0271 (8)	0.0952 (14)	0.0024 (7)	0.000	0.000

Geometric parameters (Å, º) top

K1—O1	2.7291 (11)	O3—K1^vii	2.7812 (11)
K1—O1ⁱ	2.7291 (11)	O3—K1^viii	2.7812 (11)
K1—O3ⁱⁱ	2.7812 (11)	O4—C3	1.232 (2)
K1—O3ⁱⁱⁱ	2.7812 (11)	O4—K1^v	2.9775 (13)
K1—O5^iv	2.8458 (13)	O4—K1^ix	2.9775 (13)
K1—O5	2.8458 (13)	N1—C2	1.362 (2)
K1—O4^v	2.9775 (13)	N1—C3	1.410 (2)
K1—O4^vi	2.9775 (13)	N1—H1	0.8600
K1—K1ⁱ	3.3738 (12)	N2—C3	1.321 (3)
K1—K1^iv	3.5575 (12)	N2—H2A	0.8600
K1—H1W	2.9950	N2—H2B	0.8600
O1—C1	1.249 (2)	C1—C2	1.556 (3)
O1—K1ⁱ	2.7291 (11)	O5—K1^iv	2.8458 (13)
O2—C1	1.242 (2)	O5—H1W	0.8312
O3—C2	1.228 (2)	O5—H2W	0.8317

O1—K1—O1ⁱ	103.64 (4)	O3ⁱⁱ—K1—K1^iv	50.24 (2)
O1—K1—O3ⁱⁱ	153.54 (4)	O3ⁱⁱⁱ—K1—K1^iv	50.24 (2)
O1ⁱ—K1—O3ⁱⁱ	84.00 (3)	O5^iv—K1—K1^iv	51.32 (2)
O1—K1—O3ⁱⁱⁱ	84.00 (3)	O5—K1—K1^iv	51.32 (2)
O1ⁱ—K1—O3ⁱⁱⁱ	153.54 (4)	O4^v—K1—K1^iv	124.509 (19)
O3ⁱⁱ—K1—O3ⁱⁱⁱ	100.48 (4)	O4^vi—K1—K1^iv	124.509 (19)
O1—K1—O5^iv	136.56 (4)	K1ⁱ—K1—K1^iv	180.0
O1ⁱ—K1—O5^iv	92.67 (4)	C1—O1—K1	141.79 (2)
O3ⁱⁱ—K1—O5^iv	66.81 (4)	C1—O1—K1ⁱ	141.79 (2)
O3ⁱⁱⁱ—K1—O5^iv	66.07 (4)	K1—O1—K1ⁱ	76.36 (4)
O1—K1—O5	92.67 (4)	C2—O3—K1^vii	138.06 (4)
O1ⁱ—K1—O5	136.56 (4)	C2—O3—K1^viii	138.06 (4)
O3ⁱⁱ—K1—O5	66.07 (4)	K1^vii—O3—K1^viii	79.52 (4)
O3ⁱⁱⁱ—K1—O5	66.81 (4)	C3—O4—K1^v	120.01 (9)
O5^iv—K1—O5	102.63 (4)	C3—O4—K1^ix	120.01 (9)
O1—K1—O4^v	65.19 (4)	K1^v—O4—K1^ix	69.02 (4)
O1ⁱ—K1—O4^v	73.70 (4)	C2—N1—C3	126.81 (16)
O3ⁱⁱ—K1—O4^v	93.71 (3)	C2—N1—H1	116.6
O3ⁱⁱⁱ—K1—O4^v	131.30 (4)	C3—N1—H1	116.6
O5^iv—K1—O4^v	157.65 (5)	C3—N2—H2A	120.0
O5—K1—O4^v	77.49 (3)	C3—N2—H2B	120.0
O1—K1—O4^vi	73.70 (4)	H2A—N2—H2B	120.0
O1ⁱ—K1—O4^vi	65.19 (4)	O2—C1—O1	127.80 (18)
O3ⁱⁱ—K1—O4^vi	131.30 (4)	O2—C1—C2	115.29 (17)
O3ⁱⁱⁱ—K1—O4^vi	93.71 (3)	O1—C1—C2	116.91 (17)
O5^iv—K1—O4^vi	77.49 (3)	O3—C2—N1	124.44 (17)
O5—K1—O4^vi	157.65 (5)	O3—C2—C1	119.70 (17)
O4^v—K1—O4^vi	110.98 (4)	N1—C2—C1	115.87 (16)
O1—K1—K1ⁱ	51.82 (2)	O4—C3—N2	123.36 (18)
O1ⁱ—K1—K1ⁱ	51.82 (2)	O4—C3—N1	119.31 (17)
O3ⁱⁱ—K1—K1ⁱ	129.76 (2)	N2—C3—N1	117.34 (17)
O3ⁱⁱⁱ—K1—K1ⁱ	129.76 (2)	K1^iv—O5—K1	77.37 (4)
O5^iv—K1—K1ⁱ	128.68 (2)	K1^iv—O5—H1W	92.2
O5—K1—K1ⁱ	128.68 (2)	K1—O5—H1W	92.2
O4^v—K1—K1ⁱ	55.491 (19)	K1^iv—O5—H2W	135.9
O4^vi—K1—K1ⁱ	55.491 (19)	K1—O5—H2W	135.9
O1—K1—K1^iv	128.18 (2)	H1W—O5—H2W	110.2
O1ⁱ—K1—K1^iv	128.18 (2)

O1ⁱ—K1—O1—C1	−177.2 (2)	K1^vii—O3—C2—C1	−73.10 (14)
O3ⁱⁱ—K1—O1—C1	−72.9 (2)	K1^viii—O3—C2—C1	73.10 (14)
O3ⁱⁱⁱ—K1—O1—C1	28.56 (19)	C3—N1—C2—O3	0.0
O5^iv—K1—O1—C1	73.8 (2)	C3—N1—C2—C1	180.0
O5—K1—O1—C1	−37.78 (19)	O2—C1—C2—O3	0.0
O4^v—K1—O1—C1	−112.67 (19)	O1—C1—C2—O3	180.0
O4^vi—K1—O1—C1	124.22 (19)	O2—C1—C2—N1	180.0
K1ⁱ—K1—O1—C1	−177.2 (2)	O1—C1—C2—N1	0.0
K1^iv—K1—O1—C1	2.8 (2)	K1^v—O4—C3—N2	−40.86 (6)
O1ⁱ—K1—O1—K1ⁱ	0.0	K1^ix—O4—C3—N2	40.86 (6)
O3ⁱⁱ—K1—O1—K1ⁱ	104.25 (5)	K1^v—O4—C3—N1	139.14 (6)
O3ⁱⁱⁱ—K1—O1—K1ⁱ	−154.26 (4)	K1^ix—O4—C3—N1	−139.14 (6)
O5^iv—K1—O1—K1ⁱ	−109.03 (4)	C2—N1—C3—O4	180.0
O5—K1—O1—K1ⁱ	139.40 (3)	C2—N1—C3—N2	0.0
O4^v—K1—O1—K1ⁱ	64.50 (3)	O1—K1—O5—K1^iv	139.06 (3)
O4^vi—K1—O1—K1ⁱ	−58.60 (3)	O1ⁱ—K1—O5—K1^iv	−107.82 (4)
K1^iv—K1—O1—K1ⁱ	180.0	O3ⁱⁱ—K1—O5—K1^iv	−57.25 (3)
K1—O1—C1—O2	−92.22 (16)	O3ⁱⁱⁱ—K1—O5—K1^iv	56.75 (3)
K1ⁱ—O1—C1—O2	92.22 (16)	O5^iv—K1—O5—K1^iv	0.0
K1—O1—C1—C2	87.78 (16)	O4^v—K1—O5—K1^iv	−157.09 (5)
K1ⁱ—O1—C1—C2	−87.78 (16)	O4^vi—K1—O5—K1^iv	87.77 (8)
K1^vii—O3—C2—N1	106.90 (14)	K1ⁱ—K1—O5—K1^iv	180.0
K1^viii—O3—C2—N1	−106.90 (14)

Symmetry codes: (i) −x+2, −y+1, −z; (ii) −x+3/2, y+1/2, −z+1/2; (iii) x+1/2, −y+1/2, z+1/2; (iv) −x+2, −y+1, −z+1; (v) −x+1, −y+1, −z; (vi) x+1, y, z; (vii) x−1/2, −y+1/2, z−1/2; (viii) −x+3/2, y−1/2, −z+1/2; (ix) x−1, y, z.

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1···O4^v	0.86	2.10	2.936 (2)	164
N2—H2A···O1^ix	0.86	2.17	2.997 (2)	163
N2—H2A···O2^ix	0.86	2.37	3.069 (2)	139
N2—H2B···O3	0.86	2.01	2.667 (2)	133
N2—H2B···O5^vii	0.86	2.38	3.076 (3)	138
O5—H1W···O2ⁱⁱ	0.83	1.97	2.791 (2)	172
O5—H1W···O3ⁱⁱ	0.83	2.59	3.068 (2)	118
O5—H2W···O2^x	0.83	2.14	2.973 (2)	178

Symmetry codes: (ii) −x+3/2, y+1/2, −z+1/2; (v) −x+1, −y+1, −z; (vii) x−1/2, −y+1/2, z−1/2; (ix) x−1, y, z; (x) x−1/2, −y+1/2, z+1/2.

Experimental details

Crystal data
Chemical formula	[K(C₃H₃N₂O₄)(H₂O)]
M_r	188.19
Crystal system, space group	Orthorhombic, Pnnm
Temperature (K)	296
a, b, c (Å)	7.7313 (17), 12.799 (3), 6.9313 (16)
V (Å³)	685.9 (3)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	0.75
Crystal size (mm)	0.41 × 0.39 × 0.28

Data collection
Diffractometer	Bruker SMART CCD area-detector diffractometer
Absorption correction	Multi-scan (SADABS; Bruker, 1997)
T_min, T_max	0.748, 0.816
No. of measured, independent and observed [I > 2σ(I)] reflections	3320, 699, 633
R_int	0.013
(sin θ/λ)_max (Å⁻¹)	0.606

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.026, 0.077, 1.09
No. of reflections	699
No. of parameters	66
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.17, −0.34

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

Selected bond lengths (Å) top

K1—O1	2.7291 (11)	K1—O5	2.8458 (13)
K1—O3ⁱ	2.7812 (11)	K1—O4ⁱⁱ	2.9775 (13)

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

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1···O4ⁱⁱⁱ	0.86	2.10	2.936 (2)	164.4
N2—H2A···O1^iv	0.86	2.17	2.997 (2)	162.6
N2—H2A···O2^iv	0.86	2.37	3.069 (2)	138.6
N2—H2B···O3	0.86	2.01	2.667 (2)	132.9
N2—H2B···O5^v	0.86	2.38	3.076 (3)	137.8
O5—H1W···O2ⁱ	0.83	1.97	2.791 (2)	171.6
O5—H1W···O3ⁱ	0.83	2.59	3.068 (2)	117.5
O5—H2W···O2^vi	0.83	2.14	2.973 (2)	178.3

Symmetry codes: (i) −x+3/2, y+1/2, −z+1/2; (iii) −x+1, −y+1, −z; (iv) x−1, y, z; (v) x−1/2, −y+1/2, z−1/2; (vi) x−1/2, −y+1/2, z+1/2.

Acknowledgements

The authors thank Nan Yang Normal University for supporting this work.

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