Bis(μ-4-amino-N-oxidobenzamide)­bis­[(4-amino-N-oxidobenzamide)­aqua­cobalt] dihydrate

Ding, X.; Li, L.

doi:10.1107/S2414314616016400

metal-organic compounds

IUCrDATA

ISSN: 2414-3146

Volume 1| Part 10| October 2016| x161640

https://doi.org/10.1107/S2414314616016400

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Bis(μ-4-amino-N-oxidobenzamide)bis[(4-amino-N-oxidobenzamide)aquacobalt] dihydrate

Xulong Ding ^a and Li Li ^a ^*

^aHubei Key Laboratory for Processing and Application of Catalytic Materials, College of Chemical Engineering, Huanggang Normal University, Huanggang, 438000, People's Republic of China
^*Correspondence e-mail: 1379489633@qq.com

Edited by J. Simpson, University of Otago, New Zealand (Received 10 October 2016; accepted 14 October 2016; online 21 October 2016)

The structure of the title compound, [Co₂(C₇H₇N₂O₂)₄(H₂O)₂]·2H₂O, consists of a centrosymmetric binuclear [Co₂(4-Apha)₄(H₂O)₂] complex molecule (4-AphaH = 4-aminophenylhydroxamic acid), and two solvent water molecules. Each Co^II cation is six coordinate, binding five oxygen atoms from three 4-Apha⁻ ligands and a water molecule in a slightly distorted octahedral geometry. Two of the 4-Apha⁻ ligands bridge two neighbouring Co^II ions to form the binuclear complex. A three-dimensional network structure is generated by O—H⋯O, N—H⋯O, and N—H⋯N hydrogen bonds.

Keywords: crystal structure; binuclear structure; cobalt complex.

CCDC reference: 1508944

Structure description

The asymmetric unit of the title compound consists of a Co^II cation bound to two bidentate Apha⁻ ligands and a water molecule. The Co1—O4A and Co1A—O4 bonds, [symmetry code: (A) −x, −y, −z], generate the centrosymmetric binuclear [Co₂(4-Apha)₄(H₂O)₂] complex, Fig. 1. The structure also has two solvent water molecules. Two of the 4-Apha⁻ ligands bridge the adjacent Co^II nuclei in a μ² fashion while the two others are bidentate, each coordinating to a single Co^II atom. A water molecule also binds to the Co nucleus, completing the slightly distorted octahedral coordination geometry. The Co—O distances range from 2.0741 (15) to 2.1655 (15) Å, which agrees well with the values observed in related structures (Chen et al., 2014 , 2015 ). The Co1⋯Co1A distance is 3.1727 (5) Å with a Co1—O4—Co1A angle of 97.44 (6)°.

Figure 1
The structure of title complex with displacement ellipsoids drawn at the 30% probability level. [Symmetry code: (A) −x, −y, −z.]

In the crystal, N—H⋯O hydrogen bonds form between the NH₂ groups of 4-Apha⁻ ligands as donors and the O atoms of coordinated or solvate water molecules as acceptors, Table 1. N—H⋯N hydrogen bonds form between the NH groups of the 4-Apha⁻ ligands and the NH₂ groups of adjacent ligands. The coordinated and solvent water molecules act as both hydrogen-bond donors and acceptors, Table 1, and this multitude of classical hydrogen bonds combines to generate a three-dimensional supramolecular network structure, Fig. 2.

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
O5—H5A⋯O2ⁱ	0.85	1.85	2.681 (2)	164
N1—H1B⋯O6ⁱⁱ	0.81	2.41	3.106 (3)	144
N1—H1A⋯O4ⁱⁱⁱ	0.86	2.20	3.060 (3)	174
O5—H5B⋯O3ⁱ	0.85	2.05	2.817 (2)	150
N3—H3A⋯O6^iv	0.87	2.20	3.047 (3)	163
N3—H3B⋯O5^v	0.86	2.24	3.103 (2)	178
O6—H6A⋯O2	0.85	1.99	2.822 (3)	164
O6—H6A⋯N2	0.85	2.58	3.392 (3)	160
N4—H4⋯N3^vi	0.86	2.28	3.063 (3)	152
Symmetry codes: (i) -x, -y+1, -z; (ii) $[x-{\script{1\over 2}}, -y+{\script{1\over 2}}, z+{\script{1\over 2}}]$ ; (iii) $[-x+{\script{1\over 2}}, y+{\script{1\over 2}}, -z+{\script{1\over 2}}]$ ; (iv) $[x-{\script{1\over 2}}, -y+{\script{1\over 2}}, z-{\script{1\over 2}}]$ ; (v) $[x+{\script{1\over 2}}, -y+{\script{1\over 2}}, z-{\script{1\over 2}}]$ ; (vi) $[-x+{\script{1\over 2}}, y-{\script{1\over 2}}, -z-{\script{1\over 2}}]$ .

Figure 2
Crystal packing of title complex viewed along the b axis with hydrogen bonds drawn as dashed lines.

Synthesis and crystallization

A mixture of 4-AphaH (0.0150 g, 0.1 mmol), Co(CH₃COO)₂·4H₂O (0.0249 g, 0.1 mmol) and H₂O/ethanol (v/v = 1:1, 1 ml) was sealed in a 6 ml Pyrex tube. The tube was heated at 60°C for 3 d under autogenous pressure. Slow cooling of the resulting solution to room temperature gave brown prism-like crystals. The yield was 0.0128 g (64%, based on 4-AphaH).

Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2.

Table 2
Experimental details

Crystal data
Chemical formula	[Co₂(C₇H₇N₂O₂)₄(H₂O)₂]·2H₂O
M_r	794.51
Crystal system, space group	Monoclinic, P2₁/n
Temperature (K)	296
a, b, c (Å)	10.6382 (7), 7.6075 (5), 19.8693 (13)
β (°)	93.219 (1)
V (Å³)	1605.49 (18)
Z	2
Radiation type	Mo Kα
μ (mm⁻¹)	1.11
Crystal size (mm)	0.28 × 0.25 × 0.23

Data collection
Diffractometer	Bruker APEXII CCD
Absorption correction	Multi-scan (SADABS; Bruker, 2005 )
T_min, T_max	0.746, 0.784
No. of measured, independent and observed [I > 2σ(I)] reflections	10770, 3984, 3123
R_int	0.033
(sin θ/λ)_max (Å⁻¹)	0.669

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.033, 0.086, 0.95
No. of reflections	3984
No. of parameters	226
No. of restraints	2
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.59, −0.48
Computer programs: APEX2 and SAINT (Bruker, 2005), SHELXS97 and SHELXTL (Sheldrick, 2008 ), SHELXL2014/7 (Sheldrick, 2015 ), and DIAMOND (Brandenburg, 1999 ).

Structural data

CCDC reference: 1508944

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2414314616016400/sj4066sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314616016400/sj4066Isup2.hkl

checkCIF report

Computing details top

Data collection: APEX2 (Bruker, 2005); cell refinement: APEX2 and SAINT (Bruker, 2005); data reduction: SAINT (Bruker, 2005); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2015); molecular graphics: SHELXTL (Sheldrick, 2008) and DIAMOND (Brandenburg, 1999); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Bis(µ-4-amino-N-oxidobenzamide)bis[(4-amino-N-oxidobenzamide)aquacobalt] dihydrate top

Crystal data top

[Co₂(C₇H₇N₂O₂)₄(H₂O)₂]·2H₂O	F(000) = 820
M_r = 794.51	D_x = 1.643 Mg m⁻³
Monoclinic, P2₁/n	Mo Kα radiation, λ = 0.71073 Å
a = 10.6382 (7) Å	Cell parameters from 2780 reflections
b = 7.6075 (5) Å	θ = 2.9–27.8°
c = 19.8693 (13) Å	µ = 1.11 mm⁻¹
β = 93.219 (1)°	T = 296 K
V = 1605.49 (18) Å³	Prism, brown
Z = 2	0.28 × 0.25 × 0.23 mm

Data collection top

Bruker APEXII CCD diffractometer	3123 reflections with I > 2σ(I)
φ and ω scans	R_int = 0.033
Absorption correction: multi-scan (SADABS; Bruker, 2005)	θ_max = 28.4°, θ_min = 2.1°
T_min = 0.746, T_max = 0.784	h = −13→14
10770 measured reflections	k = −10→9
3984 independent reflections	l = −26→20

Refinement top

Refinement on F²	2 restraints
Least-squares matrix: full	Hydrogen site location: mixed
R[F² > 2σ(F²)] = 0.033	H-atom parameters constrained
wR(F²) = 0.086	w = 1/[σ²(F_o²) + (0.0398P)² + 1.2061P] where P = (F_o² + 2F_c²)/3
S = 0.95	(Δ/σ)_max < 0.001
3984 reflections	Δρ_max = 0.59 e Å⁻³
226 parameters	Δρ_min = −0.48 e Å⁻³

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.

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

	x	y	z	U_iso*/U_eq
Co1	0.02073 (3)	0.19515 (4)	0.02648 (2)	0.01957 (9)
O1	0.03470 (15)	0.1624 (2)	0.13027 (7)	0.0276 (3)
O3	0.02485 (14)	0.26232 (19)	−0.07576 (7)	0.0243 (3)
O2	0.17079 (15)	0.3594 (2)	0.05349 (7)	0.0271 (3)
N2	0.17829 (18)	0.3738 (3)	0.12290 (9)	0.0280 (4)
H2	0.2269	0.4511	0.1423	0.034*
C8	0.12639 (19)	0.2018 (3)	−0.17786 (10)	0.0203 (4)
O5	−0.11627 (15)	0.39954 (19)	0.04215 (7)	0.0263 (3)
H5A	−0.1234	0.4649	0.0074	0.039*
H5B	−0.0824	0.4815	0.0659	0.032*
C14	0.10440 (19)	0.1713 (3)	−0.10601 (10)	0.0194 (4)
C7	0.1105 (2)	0.2684 (3)	0.15950 (10)	0.0218 (4)
C4	0.1405 (2)	0.2830 (3)	0.37565 (11)	0.0301 (5)
C12	0.0396 (2)	0.2982 (3)	−0.28674 (10)	0.0267 (5)
H12	−0.0247	0.3530	−0.3125	0.032*
C11	0.1431 (2)	0.2297 (3)	−0.31795 (10)	0.0239 (4)
C1	0.12380 (19)	0.2772 (3)	0.23381 (10)	0.0210 (4)
C13	0.0319 (2)	0.2851 (3)	−0.21764 (10)	0.0242 (4)
H13	−0.0372	0.3325	−0.1974	0.029*
N1	0.1472 (2)	0.2922 (4)	0.44496 (10)	0.0537 (7)
H1A	0.2143	0.3404	0.4631	0.064*
H1B	0.0937	0.2416	0.4655	0.064*
C6	0.0353 (2)	0.1913 (3)	0.27101 (10)	0.0268 (5)
H6	−0.0302	0.1307	0.2484	0.032*
C5	0.0426 (2)	0.1937 (3)	0.34055 (11)	0.0326 (5)
H5	−0.0199	0.1340	0.3650	0.039*
N3	0.1540 (2)	0.2500 (3)	−0.38711 (9)	0.0324 (4)
H3A	0.0772	0.2451	−0.4051	0.039*
H3B	0.2181	0.2073	−0.4059	0.039*
C10	0.2395 (2)	0.1511 (3)	−0.27810 (11)	0.0272 (5)
H10	0.3100	0.1073	−0.2981	0.033*
C9	0.2312 (2)	0.1375 (3)	−0.20921 (11)	0.0255 (4)
H9	0.2964	0.0849	−0.1833	0.031*
C2	0.2233 (2)	0.3625 (3)	0.26928 (11)	0.0280 (5)
H2A	0.2847	0.4187	0.2456	0.034*
C3	0.2321 (2)	0.3649 (3)	0.33879 (11)	0.0314 (5)
H3	0.2996	0.4215	0.3613	0.038*
O6	0.4080 (2)	0.2162 (4)	0.02767 (13)	0.0874 (9)
H6A	0.3381	0.2481	0.0425	0.105*
H6B	0.4146	0.3256	0.0198	0.105*
N4	0.16524 (16)	0.0421 (2)	−0.07437 (8)	0.0211 (4)
H4	0.2273	−0.0089	−0.0923	0.025*
O4	0.12774 (13)	−0.01100 (19)	−0.01141 (6)	0.0209 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Co1	0.02660 (16)	0.01796 (14)	0.01431 (13)	−0.00035 (11)	0.00260 (10)	−0.00054 (10)
O1	0.0365 (9)	0.0277 (8)	0.0183 (7)	−0.0102 (7)	−0.0017 (6)	−0.0001 (6)
O3	0.0322 (8)	0.0240 (7)	0.0171 (7)	0.0064 (6)	0.0044 (6)	0.0008 (6)
O2	0.0339 (9)	0.0311 (8)	0.0165 (7)	−0.0052 (7)	0.0030 (6)	0.0001 (6)
N2	0.0336 (10)	0.0317 (10)	0.0188 (9)	−0.0110 (8)	0.0008 (7)	−0.0033 (7)
C8	0.0241 (10)	0.0198 (10)	0.0172 (9)	−0.0028 (8)	0.0035 (7)	0.0008 (8)
O5	0.0352 (9)	0.0211 (7)	0.0231 (8)	0.0015 (6)	0.0055 (6)	0.0016 (6)
C14	0.0226 (10)	0.0187 (10)	0.0171 (9)	−0.0031 (8)	0.0016 (7)	−0.0011 (7)
C7	0.0248 (10)	0.0210 (10)	0.0196 (10)	0.0012 (8)	0.0006 (8)	−0.0010 (8)
C4	0.0310 (12)	0.0380 (13)	0.0206 (10)	0.0021 (10)	−0.0029 (9)	−0.0011 (9)
C12	0.0271 (11)	0.0321 (12)	0.0210 (10)	0.0018 (9)	0.0024 (8)	0.0057 (9)
C11	0.0287 (11)	0.0253 (11)	0.0183 (10)	−0.0047 (9)	0.0058 (8)	0.0010 (8)
C1	0.0231 (10)	0.0221 (11)	0.0177 (9)	0.0004 (8)	−0.0012 (7)	−0.0014 (8)
C13	0.0233 (11)	0.0280 (11)	0.0220 (10)	0.0030 (9)	0.0059 (8)	0.0013 (8)
N1	0.0495 (14)	0.093 (2)	0.0175 (10)	−0.0225 (14)	−0.0037 (9)	−0.0022 (11)
C6	0.0274 (11)	0.0310 (11)	0.0214 (10)	−0.0051 (9)	−0.0030 (8)	−0.0029 (9)
C5	0.0322 (12)	0.0444 (14)	0.0212 (10)	−0.0109 (11)	0.0009 (9)	0.0019 (10)
N3	0.0341 (11)	0.0459 (12)	0.0177 (9)	−0.0006 (9)	0.0065 (8)	0.0020 (8)
C10	0.0262 (11)	0.0305 (12)	0.0258 (11)	0.0030 (9)	0.0087 (9)	0.0005 (9)
C9	0.0261 (11)	0.0276 (11)	0.0230 (10)	0.0050 (9)	0.0025 (8)	0.0030 (9)
C2	0.0258 (11)	0.0341 (12)	0.0241 (11)	−0.0061 (9)	0.0018 (8)	−0.0017 (9)
C3	0.0264 (12)	0.0399 (13)	0.0270 (11)	−0.0069 (10)	−0.0061 (9)	−0.0062 (10)
O6	0.0394 (13)	0.137 (3)	0.0859 (18)	−0.0009 (15)	0.0076 (12)	−0.0290 (18)
N4	0.0234 (9)	0.0241 (9)	0.0163 (8)	0.0018 (7)	0.0046 (6)	0.0012 (7)
O4	0.0279 (8)	0.0221 (7)	0.0129 (6)	0.0004 (6)	0.0023 (5)	0.0021 (5)

Geometric parameters (Å, º) top

Co1—O2	2.0741 (15)	C11—N3	1.394 (3)
Co1—O1	2.0742 (14)	C11—C10	1.395 (3)
Co1—O3	2.0975 (14)	C1—C6	1.392 (3)
Co1—O4	2.1021 (14)	C1—C2	1.398 (3)
Co1—O4ⁱ	2.1198 (15)	C13—H13	0.9300
Co1—O5	2.1655 (15)	N1—H1A	0.8628
O1—C7	1.259 (2)	N1—H1B	0.8150
O3—C14	1.270 (2)	C6—C5	1.380 (3)
O2—N2	1.381 (2)	C6—H6	0.9300
N2—C7	1.323 (3)	C5—H5	0.9600
N2—H2	0.8600	N3—H3A	0.8745
C8—C9	1.396 (3)	N3—H3B	0.8598
C8—C13	1.396 (3)	C10—C9	1.380 (3)
C8—C14	1.478 (3)	C10—H10	0.9300
O5—H5A	0.8500	C9—H9	0.9300
O5—H5B	0.8500	C2—C3	1.379 (3)
C14—N4	1.317 (3)	C2—H2A	0.9300
C7—C1	1.477 (3)	C3—H3	0.9300
C4—N1	1.377 (3)	O6—H6A	0.8499
C4—C5	1.397 (3)	O6—H6B	0.8501
C4—C3	1.398 (3)	N4—O4	1.394 (2)
C12—C13	1.384 (3)	N4—H4	0.8600
C12—C11	1.395 (3)	O4—Co1ⁱ	2.1199 (15)
C12—H12	0.9300

O2—Co1—O1	78.69 (6)	N3—C11—C12	120.6 (2)
O2—Co1—O3	92.65 (6)	C10—C11—C12	118.77 (19)
O1—Co1—O3	171.07 (6)	C6—C1—C2	117.76 (18)
O2—Co1—O4	96.76 (6)	C6—C1—C7	118.68 (18)
O1—Co1—O4	104.87 (6)	C2—C1—C7	123.52 (19)
O3—Co1—O4	78.10 (5)	C12—C13—C8	120.90 (19)
O2—Co1—O4ⁱ	172.41 (5)	C12—C13—H13	119.5
O1—Co1—O4ⁱ	94.15 (5)	C8—C13—H13	119.5
O3—Co1—O4ⁱ	94.60 (6)	C4—N1—H1A	115.7
O4—Co1—O4ⁱ	82.56 (6)	C4—N1—H1B	118.6
O2—Co1—O5	92.56 (6)	H1A—N1—H1B	125.2
O1—Co1—O5	87.39 (6)	C5—C6—C1	121.6 (2)
O3—Co1—O5	90.87 (5)	C5—C6—H6	119.2
O4—Co1—O5	165.83 (5)	C1—C6—H6	119.2
O4ⁱ—Co1—O5	89.58 (6)	C6—C5—C4	120.3 (2)
C7—O1—Co1	112.97 (13)	C6—C5—H5	120.0
C14—O3—Co1	112.10 (12)	C4—C5—H5	119.7
N2—O2—Co1	107.85 (11)	C11—N3—H3A	105.8
C7—N2—O2	119.88 (17)	C11—N3—H3B	119.9
C7—N2—H2	120.1	H3A—N3—H3B	123.5
O2—N2—H2	120.1	C9—C10—C11	120.6 (2)
C9—C8—C13	118.33 (18)	C9—C10—H10	119.7
C9—C8—C14	123.36 (18)	C11—C10—H10	119.7
C13—C8—C14	118.04 (18)	C10—C9—C8	120.9 (2)
Co1—O5—H5A	109.5	C10—C9—H9	119.6
Co1—O5—H5B	109.8	C8—C9—H9	119.6
H5A—O5—H5B	92.2	C3—C2—C1	121.2 (2)
O3—C14—N4	120.23 (18)	C3—C2—H2A	119.4
O3—C14—C8	121.16 (18)	C1—C2—H2A	119.4
N4—C14—C8	118.54 (18)	C2—C3—C4	120.6 (2)
O1—C7—N2	119.28 (18)	C2—C3—H3	119.7
O1—C7—C1	120.88 (18)	C4—C3—H3	119.7
N2—C7—C1	119.83 (18)	H6A—O6—H6B	82.3
N1—C4—C5	121.3 (2)	C14—N4—O4	119.12 (17)
N1—C4—C3	120.2 (2)	C14—N4—H4	120.4
C5—C4—C3	118.5 (2)	O4—N4—H4	120.4
C13—C12—C11	120.4 (2)	N4—O4—Co1	107.06 (11)
C13—C12—H12	119.8	N4—O4—Co1ⁱ	108.24 (10)
C11—C12—H12	119.8	Co1—O4—Co1ⁱ	97.44 (6)
N3—C11—C10	120.5 (2)

Co1—O2—N2—C7	10.8 (2)	C2—C1—C6—C5	1.9 (3)
Co1—O3—C14—N4	5.4 (2)	C7—C1—C6—C5	179.7 (2)
Co1—O3—C14—C8	−177.58 (14)	C1—C6—C5—C4	−0.3 (4)
C9—C8—C14—O3	164.1 (2)	N1—C4—C5—C6	177.8 (2)
C13—C8—C14—O3	−21.9 (3)	C3—C4—C5—C6	−1.7 (4)
C9—C8—C14—N4	−18.8 (3)	N3—C11—C10—C9	177.3 (2)
C13—C8—C14—N4	155.16 (19)	C12—C11—C10—C9	1.5 (3)
Co1—O1—C7—N2	−5.6 (3)	C11—C10—C9—C8	0.1 (3)
Co1—O1—C7—C1	173.90 (15)	C13—C8—C9—C10	−2.0 (3)
O2—N2—C7—O1	−3.8 (3)	C14—C8—C9—C10	171.9 (2)
O2—N2—C7—C1	176.66 (18)	C6—C1—C2—C3	−1.4 (3)
C13—C12—C11—N3	−177.0 (2)	C7—C1—C2—C3	−179.1 (2)
C13—C12—C11—C10	−1.2 (3)	C1—C2—C3—C4	−0.6 (4)
O1—C7—C1—C6	−11.9 (3)	N1—C4—C3—C2	−177.3 (2)
N2—C7—C1—C6	167.6 (2)	C5—C4—C3—C2	2.2 (4)
O1—C7—C1—C2	165.8 (2)	O3—C14—N4—O4	9.8 (3)
N2—C7—C1—C2	−14.7 (3)	C8—C14—N4—O4	−167.29 (17)
C11—C12—C13—C8	−0.7 (3)	C14—N4—O4—Co1	−18.85 (19)
C9—C8—C13—C12	2.3 (3)	C14—N4—O4—Co1ⁱ	85.25 (17)
C14—C8—C13—C12	−172.0 (2)

Symmetry code: (i) −x, −y, −z.

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
O5—H5A···O2ⁱⁱ	0.85	1.85	2.681 (2)	164
N1—H1B···O6ⁱⁱⁱ	0.81	2.41	3.106 (3)	144
N1—H1A···O4^iv	0.86	2.20	3.060 (3)	174
O5—H5B···O3ⁱⁱ	0.85	2.05	2.817 (2)	150
N3—H3A···O6^v	0.87	2.20	3.047 (3)	163
N3—H3B···O5^vi	0.86	2.24	3.103 (2)	178
O6—H6A···O2	0.85	1.99	2.822 (3)	164
O6—H6A···N2	0.85	2.58	3.392 (3)	160
N4—H4···N3^vii	0.86	2.28	3.063 (3)	152

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

Acknowledgements

This research was supported by Doctoral Fund Project of Huanggang Normal University (grant No. 2015001803).

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