





Supporting information
![]() | Crystallographic Information File (CIF) https://doi.org/10.1107/S205698901500122X/su5068sup1.cif |
![]() | Structure factor file (CIF format) https://doi.org/10.1107/S205698901500122X/su5068Isup2.hkl |
![]() | Chemical Markup Language (CML) file https://doi.org/10.1107/S205698901500122X/su5068Isup3.cml |
CCDC reference: 1044361
Key indicators
- Single-crystal X-ray study
- T = 293 K
- Mean
(C-C) = 0.003 Å
- R factor = 0.050
- wR factor = 0.236
- Data-to-parameter ratio = 20.9
checkCIF/PLATON results
No syntax errors found
Alert level C PLAT242_ALERT_2_C Low Ueq as Compared to Neighbors for ..... C12 Check
Alert level G PLAT005_ALERT_5_G No _iucr_refine_instructions_details in the CIF Please Do ! PLAT066_ALERT_1_G Predicted and Reported Tmin&Tmax Range Identical ? Check PLAT072_ALERT_2_G SHELXL First Parameter in WGHT Unusually Large. 0.20 Report PLAT199_ALERT_1_G Reported _cell_measurement_temperature ..... (K) 293 Check PLAT200_ALERT_1_G Reported _diffrn_ambient_temperature ..... (K) 293 Check PLAT793_ALERT_4_G The Model has Chirality at C4 (Centro SPGR) R Verify PLAT793_ALERT_4_G The Model has Chirality at C12 (Centro SPGR) R Verify PLAT793_ALERT_4_G The Model has Chirality at C15 (Centro SPGR) S Verify PLAT899_ALERT_4_G SHELXL97 is Deprecated and Succeeded by SHELXL 2014 Note PLAT912_ALERT_4_G Missing # of FCF Reflections Above STh/L= 0.600 20 Note
0 ALERT level A = Most likely a serious problem - resolve or explain 0 ALERT level B = A potentially serious problem, consider carefully 1 ALERT level C = Check. Ensure it is not caused by an omission or oversight 10 ALERT level G = General information/check it is not something unexpected 3 ALERT type 1 CIF construction/syntax error, inconsistent or missing data 2 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 5 ALERT type 4 Improvement, methodology, query or suggestion 1 ALERT type 5 Informative message, check
Piperidine and their derivatives are significant heterocyclic compounds found in natural substances (Jain et al., 2005). They have been observed to exhibit a wide range of biological activities, such as anti-fungal, anti-malarial, anti-bacterial and anti-viral activities (Aridoss et al., 2007; Mobio et al., 1989). They also show a highly favourable antiviral activity against a range of primary HIV-1 isolates (Palani et al., 2002).
The molecular structure of the title compound is illustrated in Fig. 1. The sum of the bond angles around atom N1 is 359.85 (1) °, indicating sp2 hybridization. The dihedral angle between the phenyl rings (C5—C10 and C16—C21) is 84.91 (7) °. They are linked by an intramolecular C—H···π interaction (Table 1). The piperidine ring adopts a twist-boat conformation.
In the crystal, molecules are linked via C—H···O hydrogen bonds forming helical chains along [010], see Table 1 and Fig. 2. The chains are linked by C—H···π interactions forming sheets parallel to (100), see Table 1.
A mixture of t-3-methyl-r-2,c-6-diphenylpiperidine (5 mmol), chloroacetyl chloride (20 mmol) and triethylamine (20 mmol) in anhydrous benzene (20 ml) was stirred at rt. The precipitated ammonium salt was filtered and the resulting solution was washed with water and bicarbonate solution (4 × 10 ml). Finally, the benzene solution was dried over anhydrous sodium sulfate and concentrated. The pasty mass was purified by crystallization from pet-ether (333-353 K) and ethyl acetate in the ratio of 95: 5, and yielded colourless block-like crystals.
Data collection: APEX2 (Bruker, 2008); cell refinement: SAINT (Bruker, 2008); data reduction: SAINT (Bruker, 2008); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2015); molecular graphics: ORTEP-3 for Windows (Farrugia, 2012); software used to prepare material for publication: SHELXL97 (Sheldrick, 2015) and PLATON (Spek, 2009).
C20H22ClNO | F(000) = 696 |
Mr = 327.84 | Dx = 1.238 Mg m−3 |
Monoclinic, P21/n | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -P 2yn | Cell parameters from 4353 reflections |
a = 8.7146 (3) Å | θ = 2.1–28.2° |
b = 12.3963 (4) Å | µ = 0.22 mm−1 |
c = 16.6117 (6) Å | T = 293 K |
β = 101.523 (2)° | Block, colourless |
V = 1758.37 (10) Å3 | 0.25 × 0.23 × 0.23 mm |
Z = 4 |
Bruker APEXII CCD diffractometer | 4353 independent reflections |
Radiation source: fine-focus sealed tube | 3075 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.026 |
ω and ϕ scan | θmax = 28.2°, θmin = 2.1° |
Absorption correction: multi-scan (SADABS; Bruker, 2008) | h = −11→11 |
Tmin = 0.946, Tmax = 0.950 | k = −16→14 |
16473 measured reflections | l = −22→16 |
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)] = 0.050 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.236 | H-atom parameters constrained |
S = 0.92 | w = 1/[σ2(Fo2) + (0.2P)2] where P = (Fo2 + 2Fc2)/3 |
4353 reflections | (Δ/σ)max < 0.001 |
208 parameters | Δρmax = 0.47 e Å−3 |
0 restraints | Δρmin = −0.38 e Å−3 |
C20H22ClNO | V = 1758.37 (10) Å3 |
Mr = 327.84 | Z = 4 |
Monoclinic, P21/n | Mo Kα radiation |
a = 8.7146 (3) Å | µ = 0.22 mm−1 |
b = 12.3963 (4) Å | T = 293 K |
c = 16.6117 (6) Å | 0.25 × 0.23 × 0.23 mm |
β = 101.523 (2)° |
Bruker APEXII CCD diffractometer | 4353 independent reflections |
Absorption correction: multi-scan (SADABS; Bruker, 2008) | 3075 reflections with I > 2σ(I) |
Tmin = 0.946, Tmax = 0.950 | Rint = 0.026 |
16473 measured reflections |
R[F2 > 2σ(F2)] = 0.050 | 0 restraints |
wR(F2) = 0.236 | H-atom parameters constrained |
S = 0.92 | Δρmax = 0.47 e Å−3 |
4353 reflections | Δρmin = −0.38 e Å−3 |
208 parameters |
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. |
x | y | z | Uiso*/Ueq | ||
C17 | 0.6269 (2) | 0.82630 (15) | 0.42412 (12) | 0.0533 (5) | |
H17 | 0.6507 | 0.8995 | 0.4264 | 0.064* | |
C1 | 0.3083 (2) | 0.97610 (15) | 0.30256 (11) | 0.0498 (4) | |
C2 | 0.2026 (2) | 0.88094 (17) | 0.31112 (13) | 0.0579 (5) | |
H2A | 0.1400 | 0.8972 | 0.3517 | 0.069* | |
H2B | 0.2657 | 0.8177 | 0.3293 | 0.069* | |
C3 | 0.4639 (5) | 1.0949 (3) | 0.11267 (17) | 0.1078 (11) | |
H3A | 0.4508 | 1.1680 | 0.1290 | 0.162* | |
H3B | 0.3657 | 1.0575 | 0.1062 | 0.162* | |
H3C | 0.4991 | 1.0943 | 0.0615 | 0.162* | |
C4 | 0.53945 (19) | 1.05108 (12) | 0.26296 (10) | 0.0426 (4) | |
H4 | 0.4660 | 1.1118 | 0.2571 | 0.051* | |
C5 | 0.67052 (19) | 1.08102 (12) | 0.33476 (10) | 0.0415 (4) | |
C6 | 0.6292 (2) | 1.13399 (16) | 0.40066 (12) | 0.0548 (5) | |
H6 | 0.5240 | 1.1470 | 0.4003 | 0.066* | |
C7 | 0.7409 (3) | 1.16786 (19) | 0.46692 (14) | 0.0678 (6) | |
H7 | 0.7102 | 1.2039 | 0.5102 | 0.081* | |
C8 | 0.8963 (3) | 1.14864 (17) | 0.46926 (15) | 0.0674 (6) | |
H8 | 0.9713 | 1.1707 | 0.5142 | 0.081* | |
C9 | 0.9404 (2) | 1.09646 (16) | 0.40468 (14) | 0.0615 (5) | |
H9 | 1.0458 | 1.0829 | 0.4061 | 0.074* | |
C10 | 0.8292 (2) | 1.06365 (14) | 0.33729 (12) | 0.0507 (4) | |
H10 | 0.8610 | 1.0297 | 0.2934 | 0.061* | |
C12 | 0.5843 (2) | 1.03897 (16) | 0.17806 (11) | 0.0548 (5) | |
H12 | 0.6843 | 1.0764 | 0.1807 | 0.066* | |
C13 | 0.6075 (3) | 0.92372 (16) | 0.15453 (13) | 0.0677 (6) | |
H13A | 0.5134 | 0.8986 | 0.1178 | 0.081* | |
H13B | 0.6929 | 0.9205 | 0.1250 | 0.081* | |
C14 | 0.6440 (3) | 0.84909 (14) | 0.22878 (13) | 0.0555 (5) | |
H14A | 0.7360 | 0.8750 | 0.2666 | 0.067* | |
H14B | 0.6661 | 0.7772 | 0.2111 | 0.067* | |
C15 | 0.5053 (2) | 0.84491 (12) | 0.27212 (11) | 0.0446 (4) | |
H15 | 0.4208 | 0.8059 | 0.2360 | 0.053* | |
C16 | 0.54725 (18) | 0.78122 (13) | 0.35133 (10) | 0.0439 (4) | |
C18 | 0.6713 (2) | 0.76237 (18) | 0.49382 (13) | 0.0601 (5) | |
H18 | 0.7253 | 0.7932 | 0.5423 | 0.072* | |
C19 | 0.6364 (3) | 0.65523 (18) | 0.49162 (15) | 0.0633 (5) | |
H19 | 0.6673 | 0.6130 | 0.5383 | 0.076* | |
C20 | 0.5549 (3) | 0.60920 (16) | 0.41981 (15) | 0.0660 (6) | |
H20 | 0.5300 | 0.5362 | 0.4184 | 0.079* | |
C21 | 0.5101 (2) | 0.67207 (14) | 0.34978 (13) | 0.0533 (5) | |
H21 | 0.4551 | 0.6410 | 0.3016 | 0.064* | |
N1 | 0.44797 (15) | 0.95570 (11) | 0.28196 (8) | 0.0429 (4) | |
O1 | 0.25929 (16) | 1.06617 (12) | 0.31359 (10) | 0.0666 (4) | |
Cl1 | 0.07878 (7) | 0.85512 (5) | 0.21470 (4) | 0.0825 (3) |
U11 | U22 | U33 | U12 | U13 | U23 | |
C17 | 0.0562 (11) | 0.0472 (10) | 0.0536 (11) | −0.0082 (8) | 0.0041 (8) | 0.0001 (8) |
C1 | 0.0431 (9) | 0.0574 (10) | 0.0479 (9) | 0.0011 (7) | 0.0069 (7) | 0.0009 (8) |
C2 | 0.0448 (9) | 0.0684 (12) | 0.0604 (12) | −0.0021 (8) | 0.0106 (8) | 0.0106 (9) |
C3 | 0.156 (3) | 0.112 (2) | 0.0510 (14) | 0.046 (2) | 0.0100 (16) | 0.0171 (14) |
C4 | 0.0463 (8) | 0.0389 (8) | 0.0431 (9) | 0.0000 (6) | 0.0101 (7) | 0.0021 (6) |
C5 | 0.0471 (8) | 0.0327 (7) | 0.0455 (9) | −0.0017 (6) | 0.0110 (7) | 0.0004 (6) |
C6 | 0.0509 (10) | 0.0632 (11) | 0.0518 (11) | 0.0061 (8) | 0.0138 (8) | −0.0084 (8) |
C7 | 0.0716 (14) | 0.0793 (14) | 0.0506 (11) | 0.0073 (11) | 0.0079 (10) | −0.0165 (10) |
C8 | 0.0613 (12) | 0.0715 (13) | 0.0623 (13) | −0.0037 (10) | −0.0046 (10) | −0.0086 (10) |
C9 | 0.0477 (10) | 0.0570 (11) | 0.0772 (14) | −0.0019 (8) | 0.0062 (9) | −0.0096 (10) |
C10 | 0.0494 (9) | 0.0437 (9) | 0.0601 (11) | −0.0015 (7) | 0.0139 (8) | −0.0070 (8) |
C12 | 0.0668 (12) | 0.0546 (11) | 0.0447 (10) | −0.0038 (8) | 0.0151 (8) | 0.0025 (8) |
C13 | 0.0993 (16) | 0.0601 (12) | 0.0502 (11) | 0.0033 (11) | 0.0305 (11) | −0.0054 (9) |
C14 | 0.0698 (12) | 0.0449 (9) | 0.0578 (11) | 0.0054 (8) | 0.0269 (9) | −0.0036 (8) |
C15 | 0.0472 (9) | 0.0385 (8) | 0.0465 (9) | −0.0035 (6) | 0.0057 (7) | −0.0045 (6) |
C16 | 0.0395 (8) | 0.0427 (8) | 0.0496 (9) | −0.0013 (6) | 0.0089 (7) | −0.0017 (7) |
C18 | 0.0521 (10) | 0.0715 (13) | 0.0528 (11) | −0.0055 (9) | 0.0014 (8) | 0.0043 (9) |
C19 | 0.0608 (12) | 0.0658 (12) | 0.0648 (13) | 0.0057 (9) | 0.0159 (10) | 0.0212 (10) |
C20 | 0.0820 (15) | 0.0449 (10) | 0.0749 (14) | −0.0032 (9) | 0.0245 (12) | 0.0103 (9) |
C21 | 0.0600 (11) | 0.0424 (9) | 0.0580 (11) | −0.0060 (7) | 0.0134 (9) | −0.0014 (8) |
N1 | 0.0422 (7) | 0.0418 (7) | 0.0445 (8) | −0.0020 (5) | 0.0081 (6) | 0.0003 (6) |
O1 | 0.0523 (8) | 0.0640 (9) | 0.0863 (11) | 0.0095 (6) | 0.0205 (7) | −0.0041 (7) |
Cl1 | 0.0729 (4) | 0.0820 (5) | 0.0812 (5) | −0.0188 (3) | −0.0121 (3) | −0.0008 (3) |
C17—C16 | 1.386 (2) | C8—H8 | 0.9300 |
C17—C18 | 1.393 (3) | C9—C10 | 1.387 (3) |
C17—H17 | 0.9300 | C9—H9 | 0.9300 |
C1—O1 | 1.222 (2) | C10—H10 | 0.9300 |
C1—N1 | 1.352 (2) | C12—C13 | 1.505 (3) |
C1—C2 | 1.521 (3) | C12—H12 | 0.9800 |
C2—Cl1 | 1.773 (2) | C13—C14 | 1.524 (3) |
C2—H2A | 0.9700 | C13—H13A | 0.9700 |
C2—H2B | 0.9700 | C13—H13B | 0.9700 |
C3—C12 | 1.518 (3) | C14—C15 | 1.526 (3) |
C3—H3A | 0.9600 | C14—H14A | 0.9700 |
C3—H3B | 0.9600 | C14—H14B | 0.9700 |
C3—H3C | 0.9600 | C15—N1 | 1.482 (2) |
C4—N1 | 1.495 (2) | C15—C16 | 1.515 (2) |
C4—C5 | 1.523 (2) | C15—H15 | 0.9800 |
C4—C12 | 1.544 (2) | C16—C21 | 1.390 (2) |
C4—H4 | 0.9800 | C18—C19 | 1.361 (3) |
C5—C6 | 1.384 (2) | C18—H18 | 0.9300 |
C5—C10 | 1.392 (2) | C19—C20 | 1.384 (3) |
C6—C7 | 1.381 (3) | C19—H19 | 0.9300 |
C6—H6 | 0.9300 | C20—C21 | 1.390 (3) |
C7—C8 | 1.368 (3) | C20—H20 | 0.9300 |
C7—H7 | 0.9300 | C21—H21 | 0.9300 |
C8—C9 | 1.372 (3) | ||
C16—C17—C18 | 120.23 (17) | C13—C12—C3 | 110.9 (2) |
C16—C17—H17 | 119.9 | C13—C12—C4 | 113.64 (15) |
C18—C17—H17 | 119.9 | C3—C12—C4 | 110.11 (19) |
O1—C1—N1 | 124.60 (17) | C13—C12—H12 | 107.3 |
O1—C1—C2 | 117.28 (17) | C3—C12—H12 | 107.3 |
N1—C1—C2 | 118.11 (16) | C4—C12—H12 | 107.3 |
C1—C2—Cl1 | 109.05 (13) | C14—C13—C12 | 112.53 (17) |
C1—C2—H2A | 109.9 | C14—C13—H13A | 109.1 |
Cl1—C2—H2A | 109.9 | C12—C13—H13A | 109.1 |
C1—C2—H2B | 109.9 | C14—C13—H13B | 109.1 |
Cl1—C2—H2B | 109.9 | C12—C13—H13B | 109.1 |
H2A—C2—H2B | 108.3 | H13A—C13—H13B | 107.8 |
C12—C3—H3A | 109.5 | C13—C14—C15 | 110.24 (17) |
C12—C3—H3B | 109.5 | C13—C14—H14A | 109.6 |
H3A—C3—H3B | 109.5 | C15—C14—H14A | 109.6 |
C12—C3—H3C | 109.5 | C13—C14—H14B | 109.6 |
H3A—C3—H3C | 109.5 | C15—C14—H14B | 109.6 |
H3B—C3—H3C | 109.5 | H14A—C14—H14B | 108.1 |
N1—C4—C5 | 112.06 (13) | N1—C15—C16 | 114.54 (14) |
N1—C4—C12 | 111.04 (13) | N1—C15—C14 | 109.68 (13) |
C5—C4—C12 | 116.84 (14) | C16—C15—C14 | 110.55 (15) |
N1—C4—H4 | 105.3 | N1—C15—H15 | 107.2 |
C5—C4—H4 | 105.3 | C16—C15—H15 | 107.2 |
C12—C4—H4 | 105.3 | C14—C15—H15 | 107.2 |
C6—C5—C10 | 117.60 (16) | C17—C16—C21 | 118.86 (17) |
C6—C5—C4 | 117.51 (15) | C17—C16—C15 | 122.65 (15) |
C10—C5—C4 | 124.82 (15) | C21—C16—C15 | 118.43 (15) |
C7—C6—C5 | 121.42 (18) | C19—C18—C17 | 120.6 (2) |
C7—C6—H6 | 119.3 | C19—C18—H18 | 119.7 |
C5—C6—H6 | 119.3 | C17—C18—H18 | 119.7 |
C8—C7—C6 | 120.4 (2) | C18—C19—C20 | 119.92 (19) |
C8—C7—H7 | 119.8 | C18—C19—H19 | 120.0 |
C6—C7—H7 | 119.8 | C20—C19—H19 | 120.0 |
C7—C8—C9 | 119.4 (2) | C19—C20—C21 | 120.01 (18) |
C7—C8—H8 | 120.3 | C19—C20—H20 | 120.0 |
C9—C8—H8 | 120.3 | C21—C20—H20 | 120.0 |
C8—C9—C10 | 120.65 (19) | C20—C21—C16 | 120.33 (19) |
C8—C9—H9 | 119.7 | C20—C21—H21 | 119.8 |
C10—C9—H9 | 119.7 | C16—C21—H21 | 119.8 |
C5—C10—C9 | 120.56 (18) | C1—N1—C15 | 122.79 (14) |
C5—C10—H10 | 119.7 | C1—N1—C4 | 116.78 (14) |
C9—C10—H10 | 119.7 | C15—N1—C4 | 120.28 (13) |
O1—C1—C2—Cl1 | 88.83 (19) | C18—C17—C16—C15 | −175.86 (17) |
N1—C1—C2—Cl1 | −90.01 (18) | N1—C15—C16—C17 | −41.6 (2) |
N1—C4—C5—C6 | −75.98 (19) | C14—C15—C16—C17 | 82.9 (2) |
C12—C4—C5—C6 | 154.28 (16) | N1—C15—C16—C21 | 141.29 (16) |
N1—C4—C5—C10 | 107.24 (18) | C14—C15—C16—C21 | −94.20 (19) |
C12—C4—C5—C10 | −22.5 (2) | C16—C17—C18—C19 | −0.4 (3) |
C10—C5—C6—C7 | −0.4 (3) | C17—C18—C19—C20 | −0.5 (3) |
C4—C5—C6—C7 | −177.46 (19) | C18—C19—C20—C21 | 0.7 (3) |
C5—C6—C7—C8 | −0.7 (3) | C19—C20—C21—C16 | 0.2 (3) |
C6—C7—C8—C9 | 0.8 (4) | C17—C16—C21—C20 | −1.1 (3) |
C7—C8—C9—C10 | 0.3 (3) | C15—C16—C21—C20 | 176.11 (18) |
C6—C5—C10—C9 | 1.5 (3) | O1—C1—N1—C15 | 177.72 (17) |
C4—C5—C10—C9 | 178.23 (16) | C2—C1—N1—C15 | −3.5 (3) |
C8—C9—C10—C5 | −1.4 (3) | O1—C1—N1—C4 | −6.8 (3) |
N1—C4—C12—C13 | −30.7 (2) | C2—C1—N1—C4 | 171.99 (14) |
C5—C4—C12—C13 | 99.5 (2) | C16—C15—N1—C1 | −69.0 (2) |
N1—C4—C12—C3 | 94.4 (2) | C14—C15—N1—C1 | 166.04 (16) |
C5—C4—C12—C3 | −135.4 (2) | C16—C15—N1—C4 | 115.63 (16) |
C3—C12—C13—C14 | −146.8 (2) | C14—C15—N1—C4 | −9.3 (2) |
C4—C12—C13—C14 | −22.1 (3) | C5—C4—N1—C1 | 101.09 (17) |
C12—C13—C14—C15 | 63.8 (2) | C12—C4—N1—C1 | −126.23 (17) |
C13—C14—C15—N1 | −46.3 (2) | C5—C4—N1—C15 | −83.27 (17) |
C13—C14—C15—C16 | −173.53 (16) | C12—C4—N1—C15 | 49.41 (19) |
C18—C17—C16—C21 | 1.3 (3) |
Cg1 is the centroid of the C5–C10 ring. |
D—H···A | D—H | H···A | D···A | D—H···A |
C17—H17···Cg1 | 0.93 | 2.98 | 3.879 (2) | 164 |
C21—H21···O1i | 0.93 | 2.57 | 3.472 (3) | 165 |
C14—H14b···Cg1ii | 0.98 | 2.84 | 3.751 (2) | 156 |
Symmetry codes: (i) −x+1/2, y−1/2, −z+1/2; (ii) −x+3/2, y−1/2, −z+1/2. |
Cg1 is the centroid of the C5–C10 ring. |
D—H···A | D—H | H···A | D···A | D—H···A |
C17—H17···Cg1 | 0.93 | 2.98 | 3.879 (2) | 164 |
C21—H21···O1i | 0.93 | 2.57 | 3.472 (3) | 165 |
C14—H14b···Cg1ii | 0.98 | 2.84 | 3.751 (2) | 156 |
Symmetry codes: (i) −x+1/2, y−1/2, −z+1/2; (ii) −x+3/2, y−1/2, −z+1/2. |