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Acta Cryst. (2009). E65, o1505-o1506    [ doi:10.1107/S1600536809020819 ]

N'-(5-Chloro-2-hydroxybenzylidene)nicotinohydrazide

C.-G. Ren

Abstract top

There are two independent Schiff base molecules in the asymmetric unit of the title compound, C13H10ClN3O2. The dihedral angles between the benzene and pyridine rings are 12.8 (2) and 1.9 (2)° in the two molecules. Intramolecular O-H...N hydrogen bonds are observed. Molecules are linked into centrosymmetric R44(26) motifs by N-H...O and N-H...N interactions.

Comment top

The Schiff base compounds show excellent biological properties (Jeewoth et al., 1999; Ren et al., 2002; Eltayeb et al., 2008; Sinha et al., 2008). Moreover, the Schiff base compounds have been widely used as versatile ligands in coordination chemistry (Shivakumar et al., 2008; Prabhakaran et al., 2006; Dhar et al., 2005). We report here the crystal structure of the title compound .In the title compound, Fig. 1, there two independent molecules in the symmetric unit.The dihedral angles between the benzene and pyridine rings are 12.8 (2) and 1.9 (2)°, respectively. All the bond lengths are within normal values (Allen et al., 1987) and comparable to those in other similar compounds (Cui et al., 2007; Jing et al., 2007; Ma et al., 2008; Salhin et al., 2007; Lin et al., 2007; Alhadi et al., 2008; Xue et al., 2008; Wang et al., 2008; Lu, 2008; Diao et al., 2008; Qiu, 2009; Lair et al., 2009a,b). The molecules of the title compound are linked into centrosymmetric R44(26) motifs by N–H···O and N–H···N interactions (Table 1, Fig. 2) (Bernstein et al., 1995).

Related literature top

For the biological properties of Schiff base compounds, see: Jeewoth et al. (1999); Ren et al. (2002); Eltayeb et al. (2008); Sinha et al. (2008). For metal complexes of Schiff base compounds, see: Shivakumar et al. (2008); Prabhakaran et al. (2006); Dhar et al. (2005). For related structures, see: Cui et al. (2007); Jing et al. (2007); Ma et al. (2008); Salhin et al. (2007); Lin et al. (2007); Alhadi et al. (2008); Xue et al. (2008); Wang et al. (2008); Lu (2008); Diao et al. (2008); Qiu (2009); Mohd Lair et al. (2009a,b). For reference structural data, see: Allen et al. (1987). For hydrogen-bond motifs, see: Bernstein et al. (1995).

Experimental top

All the starting materials were obtained with AR grade from Lancaster. 5-Chloro-2-hydroxybenzaldehyde (1.0 mmol, 157.1 mg) and nicotinohydrazide (1.0 mmol, 137.1 mg) were refluxed in a 30 ml methanol solution for 30 min to give a clear yellow solution. Yellow block-shaped single crystals of the compound were obtained by slow evaporation of the solution for five days at room temperature.

Refinement top

H2 and H5 were located from a difference Fourier map and refined isotropically, with the N–H distance restrained to 0.90 (1) Å, and with Uiso restrained to 0.08 Å2. Other H atoms were constrained to ideal geometries, with d(C–H) = 0.93 Å, d(O–H) = 0.82 Å, and with Uiso(H) = 1.2Ueq(C) and 1.5Ueq(O).

Computing details top

Data collection: SMART (Bruker, 2002); cell refinement: SAINT (Bruker, 2002); data reduction: SAINT (Bruker, 2002); 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: SHELXL97 (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. The molecular structure of the compound with 30% probability ellipsoids. The intramolecular O–H···N hydrogen bonds are shown as dashed lines.
[Figure 2] Fig. 2. Molecular packing of the compound with hydrogen bonds drawn as dashed lines. Hydrogen atoms not involved in hydrogen bonding have been omitted.
(I) top
Crystal data top
C13H10ClN3O2F(000) = 1136
Mr = 275.69Dx = 1.476 Mg m−3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 2236 reflections
a = 9.792 (2) Åθ = 2.6–24.5°
b = 23.358 (3) ŵ = 0.31 mm−1
c = 10.926 (2) ÅT = 298 K
β = 96.848 (2)°Block, yellow
V = 2481.2 (8) Å30.30 × 0.30 × 0.27 mm
Z = 8
Data collection top
Bruker SMART CCD area-detector
diffractometer		5342 independent reflections
Radiation source: fine-focus sealed tube3193 reflections with I > 2σ(I)
graphiteRint = 0.042
ω scansθmax = 27.0°, θmin = 1.7°
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)		h = −12→12
Tmin = 0.913, Tmax = 0.921k = −29→27
14387 measured reflectionsl = −12→13
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)] = 0.049Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.115H atoms treated by a mixture of independent and constrained refinement
S = 1.01 w = 1/[σ2(Fo2) + (0.0466P)2]
where P = (Fo2 + 2Fc2)/3
5342 reflections(Δ/σ)max < 0.001
351 parametersΔρmax = 0.22 e Å−3
2 restraintsΔρmin = −0.24 e Å−3
Crystal data top
C13H10ClN3O2V = 2481.2 (8) Å3
Mr = 275.69Z = 8
Monoclinic, P21/nMo Kα radiation
a = 9.792 (2) ŵ = 0.31 mm−1
b = 23.358 (3) ÅT = 298 K
c = 10.926 (2) Å0.30 × 0.30 × 0.27 mm
β = 96.848 (2)°
Data collection top
Bruker SMART CCD area-detector
diffractometer		5342 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)		3193 reflections with I > 2σ(I)
Tmin = 0.913, Tmax = 0.921Rint = 0.042
14387 measured reflectionsθmax = 27.0°
Refinement top
R[F2 > 2σ(F2)] = 0.049H atoms treated by a mixture of independent and constrained refinement
wR(F2) = 0.115Δρmax = 0.22 e Å−3
S = 1.01Δρmin = −0.24 e Å−3
5342 reflectionsAbsolute structure: ?
351 parametersFlack parameter: ?
2 restraintsRogers parameter: ?
Special details top

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
Cl1−0.31666 (7)0.15824 (3)0.49570 (7)0.0648 (2)
Cl20.67723 (7)−0.10226 (3)0.57393 (6)0.0648 (2)
N10.28860 (19)0.22587 (8)0.70899 (16)0.0414 (5)
N20.4128 (2)0.20261 (8)0.75424 (18)0.0421 (5)
N30.7948 (2)0.13722 (8)0.92250 (17)0.0438 (5)
N40.29718 (18)0.00154 (8)0.94498 (16)0.0387 (4)
N50.2156 (2)−0.01091 (8)1.03441 (16)0.0402 (5)
N6−0.0434 (2)−0.04219 (10)1.3111 (2)0.0659 (6)
O10.13564 (17)0.31528 (6)0.65672 (16)0.0520 (4)
H10.20750.29810.67840.078*
O20.50725 (19)0.29034 (7)0.76057 (19)0.0755 (6)
O30.39503 (17)0.07872 (6)0.81707 (15)0.0486 (4)
H30.34840.06580.86820.073*
O40.17570 (18)0.08396 (7)1.05029 (15)0.0598 (5)
C10.0545 (2)0.21766 (9)0.63088 (19)0.0368 (5)
C20.0344 (2)0.27712 (9)0.62187 (19)0.0394 (5)
C3−0.0937 (3)0.29868 (10)0.5765 (2)0.0496 (6)
H3A−0.10720.33810.57150.059*
C4−0.2008 (3)0.26227 (11)0.5390 (2)0.0504 (6)
H4−0.28650.27700.50880.060*
C5−0.1810 (2)0.20380 (10)0.5461 (2)0.0438 (6)
C6−0.0555 (2)0.18151 (10)0.59222 (19)0.0415 (6)
H6−0.04390.14200.59770.050*
C70.1862 (2)0.19285 (10)0.6792 (2)0.0411 (6)
H70.19570.15340.68820.049*
C80.5195 (2)0.23961 (10)0.7816 (2)0.0444 (6)
C90.6530 (2)0.21501 (9)0.83757 (19)0.0359 (5)
C100.7653 (3)0.25086 (10)0.8548 (2)0.0483 (6)
H100.75670.28900.83040.058*
C110.8900 (3)0.23037 (11)0.9080 (2)0.0585 (7)
H110.96580.25450.92240.070*
C120.9001 (3)0.17355 (11)0.9395 (2)0.0509 (6)
H120.98490.15970.97460.061*
C130.6739 (2)0.15881 (9)0.8743 (2)0.0425 (6)
H130.59850.13430.86490.051*
C140.4402 (2)−0.02227 (9)0.79497 (18)0.0357 (5)
C150.4588 (2)0.03497 (9)0.7643 (2)0.0380 (5)
C160.5456 (2)0.04896 (10)0.6773 (2)0.0476 (6)
H160.55790.08720.65720.057*
C170.6134 (2)0.00709 (10)0.6205 (2)0.0464 (6)
H170.67240.01690.56320.056*
C180.5936 (2)−0.04957 (10)0.6489 (2)0.0446 (6)
C190.5080 (2)−0.06441 (9)0.7344 (2)0.0414 (6)
H190.4951−0.10280.75230.050*
C200.3537 (2)−0.03840 (9)0.88893 (19)0.0395 (5)
H200.3400−0.07670.90760.047*
C210.1567 (2)0.03509 (10)1.0846 (2)0.0419 (6)
C220.0660 (2)0.02299 (9)1.18211 (19)0.0401 (5)
C230.0067 (3)0.06862 (11)1.2362 (2)0.0538 (7)
H230.02360.10591.21240.065*
C24−0.0774 (3)0.05834 (13)1.3256 (2)0.0651 (8)
H24−0.11930.08851.36240.078*
C25−0.0986 (3)0.00294 (14)1.3595 (2)0.0657 (8)
H25−0.1554−0.00341.42060.079*
C260.0382 (3)−0.03068 (10)1.2238 (2)0.0542 (7)
H260.0790−0.06161.18870.065*
H50.206 (3)−0.0477 (5)1.053 (2)0.080*
H20.411 (3)0.1663 (5)0.779 (2)0.080*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Cl10.0444 (4)0.0649 (5)0.0827 (5)−0.0128 (3)−0.0025 (4)0.0037 (4)
Cl20.0697 (5)0.0567 (4)0.0709 (5)0.0172 (4)0.0197 (4)−0.0037 (3)
N10.0369 (12)0.0387 (11)0.0479 (11)0.0041 (9)0.0020 (9)0.0047 (9)
N20.0351 (12)0.0342 (11)0.0552 (12)0.0012 (9)−0.0016 (10)0.0047 (9)
N30.0362 (12)0.0371 (11)0.0574 (13)0.0001 (9)0.0023 (10)0.0029 (9)
N40.0374 (12)0.0354 (11)0.0432 (11)−0.0026 (9)0.0048 (9)0.0047 (9)
N50.0422 (12)0.0333 (11)0.0465 (11)0.0001 (9)0.0116 (10)0.0040 (9)
N60.0726 (17)0.0628 (15)0.0674 (15)0.0088 (13)0.0299 (13)0.0101 (12)
O10.0514 (11)0.0317 (9)0.0697 (11)−0.0002 (8)−0.0060 (10)0.0021 (8)
O20.0604 (13)0.0346 (11)0.1240 (16)−0.0032 (9)−0.0194 (12)0.0196 (10)
O30.0549 (11)0.0292 (9)0.0649 (11)−0.0015 (8)0.0206 (9)0.0034 (7)
O40.0713 (13)0.0321 (10)0.0788 (12)0.0011 (9)0.0205 (10)0.0045 (9)
C10.0369 (14)0.0353 (13)0.0390 (13)0.0020 (10)0.0073 (10)0.0041 (10)
C20.0432 (15)0.0366 (13)0.0387 (13)−0.0007 (11)0.0057 (11)0.0002 (10)
C30.0506 (17)0.0368 (14)0.0600 (16)0.0088 (12)0.0013 (13)0.0051 (11)
C40.0419 (16)0.0554 (17)0.0527 (16)0.0080 (13)0.0008 (12)0.0060 (12)
C50.0358 (15)0.0476 (15)0.0481 (14)−0.0051 (11)0.0056 (11)0.0018 (11)
C60.0430 (15)0.0354 (13)0.0467 (14)−0.0024 (11)0.0079 (11)0.0033 (10)
C70.0426 (15)0.0326 (13)0.0482 (14)0.0022 (11)0.0052 (12)0.0025 (10)
C80.0445 (16)0.0353 (14)0.0523 (15)0.0002 (11)0.0012 (12)0.0038 (11)
C90.0376 (14)0.0289 (12)0.0410 (12)−0.0028 (10)0.0042 (10)−0.0003 (9)
C100.0498 (17)0.0308 (13)0.0635 (16)−0.0067 (11)0.0035 (13)0.0037 (11)
C110.0433 (16)0.0477 (16)0.0815 (19)−0.0131 (13)−0.0043 (14)0.0003 (14)
C120.0367 (15)0.0520 (17)0.0625 (16)0.0016 (12)0.0000 (12)0.0000 (12)
C130.0338 (14)0.0358 (13)0.0571 (15)−0.0048 (11)0.0027 (12)0.0019 (11)
C140.0332 (13)0.0330 (12)0.0399 (13)−0.0017 (10)−0.0006 (10)0.0050 (10)
C150.0335 (13)0.0355 (13)0.0444 (13)−0.0027 (10)0.0020 (11)0.0005 (10)
C160.0530 (16)0.0365 (14)0.0542 (15)−0.0072 (12)0.0097 (13)0.0051 (11)
C170.0454 (16)0.0496 (15)0.0457 (14)−0.0044 (12)0.0121 (12)0.0040 (12)
C180.0449 (15)0.0427 (14)0.0455 (14)0.0065 (11)0.0029 (12)0.0007 (11)
C190.0445 (15)0.0330 (13)0.0459 (13)0.0020 (11)0.0025 (11)0.0062 (10)
C200.0417 (14)0.0281 (12)0.0482 (14)−0.0016 (10)0.0037 (11)0.0049 (10)
C210.0393 (14)0.0365 (14)0.0484 (14)−0.0008 (11)−0.0004 (11)−0.0002 (11)
C220.0367 (14)0.0385 (14)0.0439 (13)0.0042 (10)0.0005 (11)−0.0027 (10)
C230.0542 (17)0.0453 (15)0.0622 (17)0.0041 (13)0.0073 (14)−0.0108 (12)
C240.0600 (19)0.068 (2)0.0687 (19)0.0135 (15)0.0139 (15)−0.0213 (15)
C250.0514 (18)0.094 (2)0.0538 (17)0.0100 (17)0.0166 (14)−0.0020 (16)
C260.0606 (18)0.0439 (16)0.0619 (16)0.0083 (13)0.0230 (14)−0.0006 (12)
Geometric parameters (Å, °) top
Cl1—C51.740 (2)C7—H70.9300
Cl2—C181.736 (2)C8—C91.491 (3)
N1—C71.276 (3)C9—C101.376 (3)
N1—N21.369 (2)C9—C131.381 (3)
N2—C81.361 (3)C10—C111.375 (3)
N2—H20.892 (10)C10—H100.9300
N3—C121.332 (3)C11—C121.372 (3)
N3—C131.336 (3)C11—H110.9300
N4—C201.278 (3)C12—H120.9300
N4—N51.365 (2)C13—H130.9300
N5—C211.365 (3)C14—C151.396 (3)
N5—H50.891 (10)C14—C191.397 (3)
N6—C251.324 (3)C14—C201.456 (3)
N6—C261.342 (3)C15—C161.388 (3)
O1—C21.354 (3)C16—C171.371 (3)
O1—H10.8200C16—H160.9300
O2—C81.210 (2)C17—C181.378 (3)
O3—C151.361 (2)C17—H170.9300
O3—H30.8200C18—C191.373 (3)
O4—C211.223 (2)C19—H190.9300
C1—C61.394 (3)C20—H200.9300
C1—C21.405 (3)C21—C221.493 (3)
C1—C71.455 (3)C22—C261.372 (3)
C2—C31.387 (3)C22—C231.380 (3)
C3—C41.375 (3)C23—C241.372 (3)
C3—H3A0.9300C23—H230.9300
C4—C51.380 (3)C24—C251.369 (4)
C4—H40.9300C24—H240.9300
C5—C61.374 (3)C25—H250.9300
C6—H60.9300C26—H260.9300
C7—N1—N2119.29 (19)N3—C12—C11123.3 (2)
C8—N2—N1116.92 (19)N3—C12—H12118.3
C8—N2—H2125.2 (17)C11—C12—H12118.3
N1—N2—H2116.2 (18)N3—C13—C9124.5 (2)
C12—N3—C13116.7 (2)N3—C13—H13117.7
C20—N4—N5120.75 (18)C9—C13—H13117.7
C21—N5—N4115.52 (18)C15—C14—C19118.6 (2)
C21—N5—H5127.1 (17)C15—C14—C20121.4 (2)
N4—N5—H5117.4 (17)C19—C14—C20120.05 (19)
C25—N6—C26115.5 (2)O3—C15—C16117.57 (19)
C2—O1—H1109.5O3—C15—C14122.55 (19)
C15—O3—H3109.5C16—C15—C14119.9 (2)
C6—C1—C2118.8 (2)C17—C16—C15120.7 (2)
C6—C1—C7119.2 (2)C17—C16—H16119.6
C2—C1—C7122.0 (2)C15—C16—H16119.6
O1—C2—C3117.5 (2)C16—C17—C18119.7 (2)
O1—C2—C1122.7 (2)C16—C17—H17120.2
C3—C2—C1119.8 (2)C18—C17—H17120.2
C4—C3—C2120.5 (2)C19—C18—C17120.6 (2)
C4—C3—H3A119.8C19—C18—Cl2120.18 (18)
C2—C3—H3A119.8C17—C18—Cl2119.23 (18)
C3—C4—C5119.9 (2)C18—C19—C14120.5 (2)
C3—C4—H4120.1C18—C19—H19119.7
C5—C4—H4120.1C14—C19—H19119.7
C6—C5—C4120.6 (2)N4—C20—C14118.06 (19)
C6—C5—Cl1120.01 (19)N4—C20—H20121.0
C4—C5—Cl1119.37 (19)C14—C20—H20121.0
C5—C6—C1120.4 (2)O4—C21—N5121.7 (2)
C5—C6—H6119.8O4—C21—C22121.3 (2)
C1—C6—H6119.8N5—C21—C22116.94 (19)
N1—C7—C1119.2 (2)C26—C22—C23116.9 (2)
N1—C7—H7120.4C26—C22—C21124.6 (2)
C1—C7—H7120.4C23—C22—C21118.4 (2)
O2—C8—N2121.6 (2)C24—C23—C22119.3 (2)
O2—C8—C9121.2 (2)C24—C23—H23120.4
N2—C8—C9117.3 (2)C22—C23—H23120.4
C10—C9—C13116.8 (2)C25—C24—C23118.8 (2)
C10—C9—C8117.9 (2)C25—C24—H24120.6
C13—C9—C8125.3 (2)C23—C24—H24120.6
C11—C10—C9120.0 (2)N6—C25—C24124.2 (3)
C11—C10—H10120.0N6—C25—H25117.9
C9—C10—H10120.0C24—C25—H25117.9
C12—C11—C10118.5 (2)N6—C26—C22125.3 (2)
C12—C11—H11120.8N6—C26—H26117.4
C10—C11—H11120.8C22—C26—H26117.4
C7—N1—N2—C8178.3 (2)C8—C9—C13—N3178.8 (2)
C20—N4—N5—C21−177.7 (2)C19—C14—C15—O3178.9 (2)
C6—C1—C2—O1−179.7 (2)C20—C14—C15—O3−2.0 (3)
C7—C1—C2—O10.3 (3)C19—C14—C15—C16−1.3 (3)
C6—C1—C2—C30.8 (3)C20—C14—C15—C16177.9 (2)
C7—C1—C2—C3−179.2 (2)O3—C15—C16—C17179.9 (2)
O1—C2—C3—C4179.7 (2)C14—C15—C16—C170.1 (3)
C1—C2—C3—C4−0.7 (3)C15—C16—C17—C181.0 (4)
C2—C3—C4—C5−0.2 (4)C16—C17—C18—C19−0.8 (4)
C3—C4—C5—C61.0 (3)C16—C17—C18—Cl2178.62 (18)
C3—C4—C5—Cl1−178.88 (18)C17—C18—C19—C14−0.5 (3)
C4—C5—C6—C1−1.0 (3)Cl2—C18—C19—C14−179.87 (17)
Cl1—C5—C6—C1178.92 (16)C15—C14—C19—C181.5 (3)
C2—C1—C6—C50.1 (3)C20—C14—C19—C18−177.7 (2)
C7—C1—C6—C5−179.9 (2)N5—N4—C20—C14−179.66 (18)
N2—N1—C7—C1−179.88 (18)C15—C14—C20—N4−1.5 (3)
C6—C1—C7—N1176.7 (2)C19—C14—C20—N4177.7 (2)
C2—C1—C7—N1−3.3 (3)N4—N5—C21—O40.5 (3)
N1—N2—C8—O2−3.9 (3)N4—N5—C21—C22179.61 (18)
N1—N2—C8—C9176.60 (18)O4—C21—C22—C26178.9 (2)
O2—C8—C9—C10−5.6 (3)N5—C21—C22—C26−0.2 (3)
N2—C8—C9—C10173.9 (2)O4—C21—C22—C23−2.0 (3)
O2—C8—C9—C13174.2 (2)N5—C21—C22—C23178.9 (2)
N2—C8—C9—C13−6.3 (3)C26—C22—C23—C24−1.1 (4)
C13—C9—C10—C11−0.9 (3)C21—C22—C23—C24179.7 (2)
C8—C9—C10—C11178.9 (2)C22—C23—C24—C250.8 (4)
C9—C10—C11—C122.0 (4)C26—N6—C25—C240.2 (4)
C13—N3—C12—C11−1.3 (4)C23—C24—C25—N6−0.4 (4)
C10—C11—C12—N3−0.8 (4)C25—N6—C26—C22−0.6 (4)
C12—N3—C13—C92.5 (3)C23—C22—C26—N61.1 (4)
C10—C9—C13—N3−1.3 (3)C21—C22—C26—N6−179.8 (2)
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O1—H1···N10.821.882.594 (2)145
O3—H3···N40.821.822.538 (2)146
N5—H5···N3i0.89 (1)2.11 (1)2.991 (3)171 (2)
N2—H2···O30.89 (1)2.10 (1)2.984 (2)173 (2)
Symmetry codes: (i) −x+1, −y, −z+2.
Table 1
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O1—H1···N10.821.882.594 (2)145
O3—H3···N40.821.822.538 (2)146
N5—H5···N3i0.89 (1)2.11 (1)2.991 (3)171 (2)
N2—H2···O30.89 (1)2.10 (1)2.984 (2)173 (2)
Symmetry codes: (i) −x+1, −y, −z+2.
Acknowledgements top

The author acknowledges Zaozhuang University for funding this study.

references
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