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Acta Cryst. (2007). E63, o3041
https://doi.org/10.1107/S1600536807023938
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4-Bromo-2-{α-[1-(2-thien­yl)benz­imidazol-2-yl]benz­yl}phenol

F. Yang, F. Chen and H. Xiao
In the title compound, C24H17BrN2OS, the benzimidazole ring system is planar. The dihedral angles formed by the bromo­phenol, phenyl and thienyl rings with the benzimidazole ring system are 78.4 (1), 80.2 (2) and 33.1 (1)°, respectively. The mol­ecular structure and packing are stabilized by intra- and inter­molecular O—H...N and C—H...N hydrogen-bonding inter­actions and C—H...π inter­actions.
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Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536807023938/rz2141sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536807023938/rz2141Isup2.hkl
Contains datablock I

CCDC reference: 651531

checkCIF report

Key indicators

  • Single-crystal X-ray study
  • T = 295 K
  • Mean [sigma](C-C) = 0.005 Å
  • R factor = 0.041
  • wR factor = 0.112
  • Data-to-parameter ratio = 14.7

checkCIF/PLATON results

No syntax errors found




Alert level C
PLAT066_ALERT_1_C Predicted and Reported Transmissions Identical .          ?
PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd.  #          1
              C24 H17 Br N2 O S


Alert level G
PLAT793_ALERT_1_G Check the Absolute Configuration of C7     = ...          R


   0 ALERT level A = In general: serious problem
   0 ALERT level B = Potentially serious problem
   2 ALERT level C = Check and explain
   1 ALERT level G = General alerts; check

   2 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   0 ALERT type 2 Indicator that the structure model may be wrong or deficient
   0 ALERT type 3 Indicator that the structure quality may be low
   1 ALERT type 4 Improvement, methodology, query or suggestion
   0 ALERT type 5 Informative message, check
Comment top

The benzimidazole nucleus has been of considerable interest since it was noted that it inhibits the growth of certain yeasts and bacteria (Woolley, 1944). Over the past few years, benzimidazoles have been used as antifungals, antibacterials, antihelminthics, 5-HT receptor antagonists, and thrombin receptor antagonists (Rivas et al., 2002). However, that structural modifications can produce marked effects on physiological activity has been shown by the test data on the substituted benzimidazoles. In recent chemical literature, introduction of bulky substituents in ortho to the amide groups significantly increases the barrier to racemization (Fekner et al., 2004). For this reason, the efficient synthesis of important diversely functionalized substituted benzimidazoles have attracted considerable attention. In particular, the discovery of 1,2-bisubstituted benzimidazole has increased this interest, which can be attributed not only to a good nucleophile but to their diverse biological and pharmacological properties as well (Liu et al., 2005). We describe here the structure of the title compound, I, whose ring system contains two nitrogen atoms, a tertiary basic nitrogen and the other attached to an active 2-hydroxy-5-bromophenyl)(phenyl)methyl group, bearing a chiral carbon atom.

In I, the benzimidazole ring is planar. The dihedral angles formed by the plane of the hydroxybromobenzene ring (p1) and thienyl ring (p2) with the phenyl ring are 73.6 (3) and 67.8 (2)°, respectively. The dihedral angles formed by the plane of benzimidazole with p1 and p2 are 78.4 (1) and 33.1 (1)°, respectively. The phenyl ring is almost perpendicular to the benzimidazole ring, as indicated by the dihedral angle of 80.2 (2)° between the two planes. The dihedral angle between p1 and p2 is 56.9 (2)°.

The molecular structure is stabilized by intra- and intermolecular O—H···N, C—H···N hydrogen-bonding interactions and by intermolecular C—H···π interactions (Table 2; Cg1 is the centroid of the C19—C24 ring).

Related literature top

For related literature, see: Fekner et al. (2004); Liu et al. (2005); Rivas et al. (2002); Woolley (1944).

Experimental top

5-Bromo-2-hydroxybenzophenone (HBBP) (27.7 g, 0.10 mol), 1,2-diaminobenzene (10.8 g, 0.10 mol), piperidine (10.2 g, 0.12 mol), and triethylorthoformate (12 ml) refluxed in absolute ethanol (120 ml) resulted in the red-orange product of HBBP-PHEN. The title compound was obtained by the reaction of HBBP-PHEN (22.0 g, 0.06 mol) with 2-thiopheneformaldehyde (7.3 g, 0.065 mol) and piperidine (8.5 g, 0.1 mol) in methanol (150 ml) under dry nitrogen at room temperature. The precipitated yellow solid was collected by filtration and washed twice with hot methanol. Single crystals suitable for X-ray measurements were obtained by slow evaporation of an absolute ethanol/acetic acid solution (1:1 v/v) at room temperature.

Refinement top

All H atoms were placed at calculated positions and allowed to ride on their attached atoms, with C—H = 0.93–0.98 Å and O—H = 0.82 Å, and with Uiso(H) = 1.2 Ueq(C) or 1.5 Ueq(O).

Structure description top

The benzimidazole nucleus has been of considerable interest since it was noted that it inhibits the growth of certain yeasts and bacteria (Woolley, 1944). Over the past few years, benzimidazoles have been used as antifungals, antibacterials, antihelminthics, 5-HT receptor antagonists, and thrombin receptor antagonists (Rivas et al., 2002). However, that structural modifications can produce marked effects on physiological activity has been shown by the test data on the substituted benzimidazoles. In recent chemical literature, introduction of bulky substituents in ortho to the amide groups significantly increases the barrier to racemization (Fekner et al., 2004). For this reason, the efficient synthesis of important diversely functionalized substituted benzimidazoles have attracted considerable attention. In particular, the discovery of 1,2-bisubstituted benzimidazole has increased this interest, which can be attributed not only to a good nucleophile but to their diverse biological and pharmacological properties as well (Liu et al., 2005). We describe here the structure of the title compound, I, whose ring system contains two nitrogen atoms, a tertiary basic nitrogen and the other attached to an active 2-hydroxy-5-bromophenyl)(phenyl)methyl group, bearing a chiral carbon atom.

In I, the benzimidazole ring is planar. The dihedral angles formed by the plane of the hydroxybromobenzene ring (p1) and thienyl ring (p2) with the phenyl ring are 73.6 (3) and 67.8 (2)°, respectively. The dihedral angles formed by the plane of benzimidazole with p1 and p2 are 78.4 (1) and 33.1 (1)°, respectively. The phenyl ring is almost perpendicular to the benzimidazole ring, as indicated by the dihedral angle of 80.2 (2)° between the two planes. The dihedral angle between p1 and p2 is 56.9 (2)°.

The molecular structure is stabilized by intra- and intermolecular O—H···N, C—H···N hydrogen-bonding interactions and by intermolecular C—H···π interactions (Table 2; Cg1 is the centroid of the C19—C24 ring).

For related literature, see: Fekner et al. (2004); Liu et al. (2005); Rivas et al. (2002); Woolley (1944).

Computing details top

Data collection: CAD-4 Software (Enraf–Nonius, 1989); cell refinement: CAD-4 Software; data reduction: NRCVAX (Gabe et al., 1989); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL (Sheldrick, 1990); software used to prepare material for publication: WinGX (Farrugia, 1999).

Figures top
[Figure 1] Fig. 1. The structure of the title compound showing 30% probability displacement ellipsoids and the atom-numbering scheme.
4-bromo-2-{α-[1-(2-thienyl)benzimidazol-2-yl]benzyl}phenol top
Crystal data top
C24H17BrN2OSF(000) = 936
Mr = 461.37Dx = 1.482 Mg m−3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 25 reflections
a = 13.623 (3) Åθ = 4–14°
b = 9.6472 (19) ŵ = 2.11 mm−1
c = 16.962 (3) ÅT = 295 K
β = 111.98 (3)°Block, colourless
V = 2067.2 (8) Å30.25 × 0.20 × 0.18 mm
Z = 4
Data collection top
Enraf-Nonius CAD-4
diffractometer		2509 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tubeRint = 0.033
Graphite monochromatorθmax = 25.0°, θmin = 2.5°
ω scansh = −15→16
Absorption correction: ψ scan
(North et al., 1968)		k = −11→7
Tmin = 0.609, Tmax = 0.684l = −20→18
8223 measured reflections3 standard reflections every 100 reflections
3632 independent reflections intensity decay: none
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)] = 0.042Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.112H-atom parameters constrained
S = 1.02 w = 1/[σ2(Fo2) + (0.0347P)2 + 1.0362P]
where P = (Fo2 + 2Fc2)/3
3842 reflections(Δ/σ)max < 0.001
262 parametersΔρmax = 0.37 e Å−3
0 restraintsΔρmin = −0.52 e Å−3
Crystal data top
C24H17BrN2OSV = 2067.2 (8) Å3
Mr = 461.37Z = 4
Monoclinic, P21/cMo Kα radiation
a = 13.623 (3) ŵ = 2.11 mm−1
b = 9.6472 (19) ÅT = 295 K
c = 16.962 (3) Å0.25 × 0.20 × 0.18 mm
β = 111.98 (3)°
Data collection top
Enraf-Nonius CAD-4
diffractometer		2509 reflections with I > 2σ(I)
Absorption correction: ψ scan
(North et al., 1968)		Rint = 0.033
Tmin = 0.609, Tmax = 0.6843 standard reflections every 100 reflections
8223 measured reflections intensity decay: none
3632 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0420 restraints
wR(F2) = 0.112H-atom parameters constrained
S = 1.02Δρmax = 0.37 e Å−3
3842 reflectionsΔρmin = −0.52 e Å−3
262 parameters
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
Br10.06574 (4)0.19632 (4)0.05538 (3)0.0884 (2)
S10.46731 (8)−0.60807 (12)0.37058 (7)0.0777 (3)
O10.41657 (15)−0.1640 (2)0.28505 (13)0.0519 (6)
H1A0.4732−0.12250.30190.078*
N10.39000 (19)−0.5378 (3)0.17794 (16)0.0462 (6)
N20.27450 (17)−0.3751 (2)0.18257 (14)0.0360 (5)
C10.3387 (2)−0.0780 (3)0.23568 (18)0.0425 (7)
C20.3573 (3)0.0582 (4)0.2186 (2)0.0567 (9)
H2A0.42520.09490.24320.068*
C30.2769 (3)0.1391 (4)0.1658 (2)0.0606 (9)
H3A0.29030.22940.15340.073*
C40.1762 (3)0.0858 (3)0.1314 (2)0.0510 (8)
C50.1543 (2)−0.0470 (3)0.14970 (18)0.0434 (7)
H5A0.0853−0.08040.12740.052*
C60.2360 (2)−0.1312 (3)0.20179 (17)0.0358 (6)
C70.2183 (2)−0.2816 (3)0.21980 (18)0.0366 (7)
H7A0.2518−0.29330.28150.044*
C80.1029 (2)−0.3217 (3)0.19572 (18)0.0389 (7)
C90.0459 (3)−0.2612 (4)0.2397 (2)0.0532 (8)
H9A0.0787−0.19770.28270.064*
C10−0.0591 (3)−0.2948 (4)0.2199 (3)0.0675 (10)
H10A−0.0965−0.25380.24960.081*
C11−0.1084 (3)−0.3880 (4)0.1568 (3)0.0679 (11)
H11A−0.1794−0.40960.14340.081*
C12−0.0535 (3)−0.4490 (4)0.1138 (2)0.0635 (10)
H12A−0.0872−0.51290.07120.076*
C130.0529 (2)−0.4170 (3)0.13276 (19)0.0499 (8)
H13A0.0899−0.45960.10310.060*
C140.3385 (2)−0.4836 (3)0.22301 (18)0.0384 (7)
C150.3489 (2)−0.5363 (3)0.30641 (19)0.0468 (8)
C160.2737 (3)−0.5468 (3)0.3435 (2)0.0547 (8)
H16A0.2042−0.51580.31860.066*
C170.3172 (4)−0.6111 (4)0.4243 (2)0.0753 (11)
H17A0.2790−0.62670.45890.090*
C180.4191 (4)−0.6472 (5)0.4460 (2)0.0829 (13)
H18A0.4589−0.68950.49730.099*
C190.3577 (2)−0.4605 (3)0.10344 (19)0.0419 (7)
C200.3864 (3)−0.4754 (4)0.0331 (2)0.0557 (9)
H20A0.4330−0.54460.03110.067*
C210.3433 (3)−0.3840 (4)−0.0334 (2)0.0613 (10)
H21A0.3620−0.3904−0.08070.074*
C220.2729 (3)−0.2831 (4)−0.0307 (2)0.0576 (9)
H22A0.2453−0.2229−0.07650.069*
C230.2417 (2)−0.2681 (3)0.03740 (18)0.0487 (8)
H23A0.1934−0.20050.03810.058*
C240.2862 (2)−0.3589 (3)0.10480 (17)0.0370 (7)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Br10.0952 (4)0.0492 (2)0.0888 (3)0.0169 (2)−0.0023 (2)0.0140 (2)
S10.0674 (6)0.0854 (8)0.0717 (7)0.0199 (5)0.0162 (5)0.0253 (6)
O10.0355 (11)0.0475 (13)0.0650 (14)−0.0063 (10)0.0098 (10)0.0043 (11)
N10.0377 (13)0.0423 (15)0.0585 (16)0.0047 (12)0.0180 (12)0.0007 (13)
N20.0336 (12)0.0317 (13)0.0416 (14)0.0028 (10)0.0126 (10)−0.0009 (10)
C10.0426 (17)0.0406 (17)0.0450 (17)−0.0007 (14)0.0172 (14)−0.0005 (14)
C20.0488 (19)0.0442 (19)0.075 (2)−0.0122 (16)0.0210 (17)−0.0047 (17)
C30.069 (2)0.0340 (17)0.081 (2)−0.0033 (17)0.029 (2)0.0054 (17)
C40.058 (2)0.0359 (17)0.0536 (19)0.0106 (15)0.0142 (16)0.0016 (15)
C50.0436 (17)0.0371 (16)0.0465 (17)0.0006 (14)0.0134 (14)−0.0035 (14)
C60.0383 (15)0.0311 (15)0.0395 (15)0.0004 (12)0.0162 (13)−0.0027 (12)
C70.0360 (15)0.0353 (16)0.0380 (15)0.0012 (12)0.0134 (12)−0.0021 (12)
C80.0361 (15)0.0343 (15)0.0457 (17)0.0009 (13)0.0148 (13)0.0040 (13)
C90.0472 (19)0.053 (2)0.062 (2)−0.0007 (16)0.0243 (16)−0.0044 (17)
C100.050 (2)0.072 (3)0.090 (3)0.006 (2)0.038 (2)0.010 (2)
C110.0390 (19)0.071 (3)0.090 (3)−0.0083 (19)0.020 (2)0.017 (2)
C120.053 (2)0.060 (2)0.069 (2)−0.0222 (18)0.0127 (18)−0.0024 (19)
C130.0494 (19)0.0466 (19)0.0515 (19)−0.0067 (15)0.0164 (15)−0.0014 (15)
C140.0324 (15)0.0317 (15)0.0483 (18)−0.0008 (12)0.0119 (13)−0.0020 (13)
C150.0488 (18)0.0363 (17)0.0502 (18)−0.0002 (14)0.0128 (15)0.0018 (14)
C160.060 (2)0.049 (2)0.058 (2)0.0038 (17)0.0249 (17)0.0157 (17)
C170.091 (3)0.071 (3)0.072 (3)−0.005 (2)0.040 (2)0.020 (2)
C180.098 (3)0.074 (3)0.064 (3)0.009 (2)0.015 (2)0.028 (2)
C190.0349 (16)0.0408 (17)0.0501 (18)−0.0050 (13)0.0161 (14)−0.0059 (14)
C200.0451 (19)0.062 (2)0.065 (2)0.0026 (17)0.0266 (17)−0.0123 (19)
C210.060 (2)0.080 (3)0.052 (2)−0.009 (2)0.0306 (18)−0.013 (2)
C220.063 (2)0.067 (2)0.0412 (19)0.0014 (19)0.0179 (16)0.0049 (17)
C230.0525 (19)0.0496 (19)0.0422 (18)0.0052 (15)0.0157 (15)−0.0016 (15)
C240.0339 (15)0.0379 (15)0.0373 (16)−0.0045 (13)0.0111 (13)−0.0048 (13)
Geometric parameters (Å, º) top
Br1—C41.900 (3)C9—H9A0.9300
S1—C181.686 (4)C10—C111.365 (5)
S1—C151.718 (3)C10—H10A0.9300
O1—C11.360 (3)C11—C121.360 (5)
O1—H1A0.8200C11—H11A0.9300
N1—C141.323 (4)C12—C131.396 (4)
N1—C191.389 (4)C12—H12A0.9300
N2—C141.371 (3)C13—H13A0.9300
N2—C241.396 (3)C14—C151.459 (4)
N2—C71.470 (3)C15—C161.392 (4)
C1—C21.390 (4)C16—C171.417 (5)
C1—C61.395 (4)C16—H16A0.9300
C2—C31.370 (5)C17—C181.341 (5)
C2—H2A0.9300C17—H17A0.9300
C3—C41.374 (5)C18—H18A0.9300
C3—H3A0.9300C19—C241.387 (4)
C4—C51.376 (4)C19—C201.395 (4)
C5—C61.394 (4)C20—C211.377 (5)
C5—H5A0.9300C20—H20A0.9300
C6—C71.521 (4)C21—C221.379 (5)
C7—C81.519 (4)C21—H21A0.9300
C7—H7A0.9800C22—C231.379 (4)
C8—C131.380 (4)C22—H22A0.9300
C8—C91.390 (4)C23—C241.387 (4)
C9—C101.379 (5)C23—H23A0.9300
C18—S1—C1591.77 (19)C10—C11—H11A120.1
C1—O1—H1A109.5C11—C12—C13120.8 (3)
C14—N1—C19104.9 (2)C11—C12—H12A119.6
C14—N2—C24106.4 (2)C13—C12—H12A119.6
C14—N2—C7126.1 (2)C8—C13—C12119.6 (3)
C24—N2—C7126.9 (2)C8—C13—H13A120.2
O1—C1—C2122.9 (3)C12—C13—H13A120.2
O1—C1—C6117.4 (3)N1—C14—N2112.8 (2)
C2—C1—C6119.7 (3)N1—C14—C15122.8 (3)
C3—C2—C1120.7 (3)N2—C14—C15124.3 (3)
C3—C2—H2A119.6C16—C15—C14130.0 (3)
C1—C2—H2A119.6C16—C15—S1111.1 (2)
C2—C3—C4119.4 (3)C14—C15—S1118.8 (2)
C2—C3—H3A120.3C15—C16—C17110.9 (3)
C4—C3—H3A120.3C15—C16—H16A124.5
C3—C4—C5121.2 (3)C17—C16—H16A124.5
C3—C4—Br1119.3 (3)C18—C17—C16113.2 (4)
C5—C4—Br1119.5 (2)C18—C17—H17A123.4
C4—C5—C6119.8 (3)C16—C17—H17A123.4
C4—C5—H5A120.1C17—C18—S1113.0 (3)
C6—C5—H5A120.1C17—C18—H18A123.5
C5—C6—C1119.1 (3)S1—C18—H18A123.5
C5—C6—C7122.3 (2)C24—C19—N1110.5 (2)
C1—C6—C7118.5 (2)C24—C19—C20120.6 (3)
N2—C7—C8112.4 (2)N1—C19—C20128.9 (3)
N2—C7—C6110.6 (2)C21—C20—C19117.7 (3)
C8—C7—C6114.5 (2)C21—C20—H20A121.2
N2—C7—H7A106.2C19—C20—H20A121.2
C8—C7—H7A106.2C20—C21—C22120.9 (3)
C6—C7—H7A106.2C20—C21—H21A119.6
C13—C8—C9118.8 (3)C22—C21—H21A119.6
C13—C8—C7122.6 (3)C23—C22—C21122.5 (3)
C9—C8—C7118.6 (3)C23—C22—H22A118.7
C10—C9—C8120.5 (3)C21—C22—H22A118.7
C10—C9—H9A119.8C22—C23—C24116.6 (3)
C8—C9—H9A119.8C22—C23—H23A121.7
C11—C10—C9120.5 (4)C24—C23—H23A121.7
C11—C10—H10A119.8C23—C24—C19121.7 (3)
C9—C10—H10A119.8C23—C24—N2132.9 (3)
C12—C11—C10119.8 (3)C19—C24—N2105.4 (2)
C12—C11—H11A120.1
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C13—H13A···N20.932.502.843 (4)102
O1—H1A···N1i0.821.942.753 (3)169
C3—H3A···N1ii0.932.583.449 (5)155
C12—H12A···Cg1iii0.933.153.916 (5)141
Symmetry codes: (i) −x+1, y+1/2, −z+1/2; (ii) x, y+1, z; (iii) −x, −y−1, −z.

Experimental details

Crystal data
Chemical formulaC24H17BrN2OS
Mr461.37
Crystal system, space groupMonoclinic, P21/c
Temperature (K)295
a, b, c (Å)13.623 (3), 9.6472 (19), 16.962 (3)
β (°) 111.98 (3)
V (Å3)2067.2 (8)
Z4
Radiation typeMo Kα
µ (mm−1)2.11
Crystal size (mm)0.25 × 0.20 × 0.18
Data collection
DiffractometerEnraf-Nonius CAD-4
diffractometer
Absorption correctionψ scan
(North et al., 1968)
Tmin, Tmax0.609, 0.684
No. of measured, independent and
observed [I > 2σ(I)] reflections		8223, 3632, 2509
Rint0.033
(sin θ/λ)max (Å−1)0.595
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.042, 0.112, 1.02
No. of reflections3842
No. of parameters262
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å−3)0.37, −0.52

Computer programs: CAD-4 Software (Enraf–Nonius, 1989), CAD-4 Software, NRCVAX (Gabe et al., 1989), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), SHELXTL (Sheldrick, 1990), WinGX (Farrugia, 1999).

Selected bond lengths (Å) top
Br1—C41.900 (3)N1—C191.389 (4)
S1—C181.686 (4)N2—C141.371 (3)
S1—C151.718 (3)N2—C241.396 (3)
O1—C11.360 (3)N2—C71.470 (3)
N1—C141.323 (4)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
C13—H13A···N20.932.502.843 (4)102
O1—H1A···N1i0.821.942.753 (3)169
C3—H3A···N1ii0.932.583.449 (5)155
C12—H12A···Cg1iii0.933.153.916 (5)141
Symmetry codes: (i) −x+1, y+1/2, −z+1/2; (ii) x, y+1, z; (iii) −x, −y−1, −z.
 

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