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The title compound [systematic name: 2,3,9,10-tetramethoxy-5,6,13,13a-tetrahydroisoquino[3,2-a]isoquinolin-8-one], C21H23NO5, a protoberberine-type alkaloid, was isolated from the roots of the plant Sinomenium acutum. The piperidine ring adopts an envelope conformation and the pyridinone ring is in a screw-boat conformation.
Supporting information
CCDC reference: 298395
Key indicators
- Single-crystal X-ray study
- T = 296 K
- Mean (C-C) = 0.004 Å
- R factor = 0.041
- wR factor = 0.103
- Data-to-parameter ratio = 9.3
checkCIF/PLATON results
No syntax errors found
Alert level B
PLAT220_ALERT_2_B Large Non-Solvent C Ueq(max)/Ueq(min) ... 3.85 Ratio
Alert level C
PLAT222_ALERT_3_C Large Non-Solvent H Ueq(max)/Ueq(min) ... 3.52 Ratio
Alert level G
REFLT03_ALERT_4_G Please check that the estimate of the number of Friedel pairs is
correct. If it is not, please give the correct count in the
_publ_section_exptl_refinement section of the submitted CIF.
From the CIF: _diffrn_reflns_theta_max 27.49
From the CIF: _reflns_number_total 2318
Count of symmetry unique reflns 2317
Completeness (_total/calc) 100.04%
TEST3: Check Friedels for noncentro structure
Estimate of Friedel pairs measured 1
Fraction of Friedel pairs measured 0.000
Are heavy atom types Z>Si present no
0 ALERT level A = In general: serious problem
1 ALERT level B = Potentially serious problem
1 ALERT level C = Check and explain
1 ALERT level G = General alerts; check
0 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
1 ALERT type 2 Indicator that the structure model may be wrong or deficient
1 ALERT type 3 Indicator that the structure quality may be low
1 ALERT type 4 Improvement, methodology, query or suggestion
Data collection: XSCANS (Siemens, 1994); cell refinement: XSCANS; data reduction: SHELXTL (Sheldrick, 1997b); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997a); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997a); molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.
2,3,9,10-tetramethoxy-5,6,13,13
a-tetrahydroisoquino[3,2-
a]isoquinolin-8-one
top
Crystal data top
C21H23NO5 | F(000) = 392 |
Mr = 369.40 | Dx = 1.310 Mg m−3 |
Monoclinic, P21 | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: P 2yb | Cell parameters from 33 reflections |
a = 7.875 (1) Å | θ = 3.7–14.8° |
b = 7.870 (1) Å | µ = 0.09 mm−1 |
c = 15.139 (3) Å | T = 296 K |
β = 93.335 (15)° | Block, yellow |
V = 936.7 (3) Å3 | 0.48 × 0.38 × 0.26 mm |
Z = 2 | |
Data collection top
Siemens P4 diffractometer | Rint = 0.019 |
Radiation source: normal-focus sealed tube | θmax = 27.5°, θmin = 1.4° |
Graphite monochromator | h = 0→10 |
ω scans | k = 0→10 |
2601 measured reflections | l = −19→19 |
2318 independent reflections | 3 standard reflections every 97 reflections |
1515 reflections with I > 2σ(I) | intensity decay: 1.1% |
Refinement top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | Hydrogen site location: inferred from neighbouring sites |
R[F2 > 2σ(F2)] = 0.041 | H-atom parameters constrained |
wR(F2) = 0.103 | w = 1/[σ2(Fo2) + (0.0561P)2] where P = (Fo2 + 2Fc2)/3 |
S = 0.92 | (Δ/σ)max = 0.001 |
2318 reflections | Δρmax = 0.19 e Å−3 |
249 parameters | Δρmin = −0.14 e Å−3 |
1 restraint | Extinction correction: SHELXL97 (Sheldrick, 1997a), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
Primary atom site location: structure-invariant direct methods | Extinction coefficient: 0.008 (2) |
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 | x | y | z | Uiso*/Ueq | |
O1 | 0.1582 (4) | 0.4489 (4) | 0.09476 (14) | 0.0826 (8) | |
O2 | 0.3142 (4) | 0.7033 (5) | 0.03323 (13) | 0.0914 (9) | |
O3 | 0.2758 (3) | 1.0031 (2) | 0.56790 (13) | 0.0603 (7) | |
O4 | 0.2274 (3) | 0.8467 (3) | 0.72332 (13) | 0.0550 (6) | |
O5 | 0.2325 (3) | 0.5582 (3) | 0.80954 (11) | 0.0571 (6) | |
N7 | 0.2087 (3) | 0.8574 (3) | 0.44350 (14) | 0.0405 (6) | |
C1 | 0.1574 (4) | 0.5759 (4) | 0.24272 (17) | 0.0468 (7) | |
H1 | 0.1018 | 0.4827 | 0.2654 | 0.056* | |
C2 | 0.1964 (4) | 0.5767 (5) | 0.15431 (18) | 0.0544 (8) | |
C3 | 0.2794 (4) | 0.7157 (5) | 0.12087 (19) | 0.0610 (9) | |
C4 | 0.3171 (4) | 0.8521 (5) | 0.17394 (19) | 0.0580 (8) | |
H4 | 0.3703 | 0.9459 | 0.1504 | 0.070* | |
C5 | 0.3114 (4) | 1.0098 (4) | 0.31884 (18) | 0.0523 (8) | |
H5A | 0.2959 | 1.1107 | 0.2825 | 0.063* | |
H5B | 0.4280 | 1.0081 | 0.3433 | 0.063* | |
C6 | 0.1908 (4) | 1.0144 (4) | 0.39305 (19) | 0.0482 (8) | |
H6A | 0.2170 | 1.1109 | 0.4313 | 0.058* | |
H6B | 0.0746 | 1.0262 | 0.3688 | 0.058* | |
C8 | 0.2462 (4) | 0.8664 (3) | 0.53230 (17) | 0.0369 (6) | |
C9 | 0.2420 (3) | 0.7020 (4) | 0.67474 (17) | 0.0390 (6) | |
C10 | 0.2405 (3) | 0.5464 (4) | 0.71995 (17) | 0.0414 (7) | |
C11 | 0.2468 (4) | 0.3969 (4) | 0.67366 (17) | 0.0452 (8) | |
H11 | 0.2432 | 0.2937 | 0.7034 | 0.054* | |
C12 | 0.2586 (4) | 0.3990 (3) | 0.58252 (18) | 0.0442 (8) | |
H12 | 0.2663 | 0.2969 | 0.5521 | 0.053* | |
C13 | 0.2747 (4) | 0.5575 (4) | 0.43811 (16) | 0.0436 (7) | |
H13A | 0.2391 | 0.4496 | 0.4121 | 0.052* | |
H13B | 0.3929 | 0.5754 | 0.4259 | 0.052* | |
C14 | 0.2775 (3) | 0.8548 (4) | 0.26350 (17) | 0.0444 (7) | |
C15 | 0.2007 (3) | 0.7134 (4) | 0.29786 (17) | 0.0403 (6) | |
C16 | 0.1679 (4) | 0.6984 (4) | 0.39601 (15) | 0.0381 (6) | |
H16 | 0.0475 | 0.6717 | 0.4018 | 0.046* | |
C17 | 0.2490 (3) | 0.7043 (4) | 0.58232 (16) | 0.0353 (6) | |
C18 | 0.2591 (3) | 0.5501 (4) | 0.53646 (16) | 0.0376 (6) | |
C19 | 0.0655 (6) | 0.3100 (5) | 0.1208 (2) | 0.0836 (12) | |
H19A | 0.1315 | 0.2471 | 0.1650 | 0.100* | |
H19B | 0.0387 | 0.2384 | 0.0706 | 0.100* | |
H19C | −0.0378 | 0.3483 | 0.1450 | 0.100* | |
C20 | 0.3840 (7) | 0.8456 (8) | −0.0072 (2) | 0.135 (2) | |
H20A | 0.3141 | 0.9433 | 0.0019 | 0.162* | |
H20B | 0.3891 | 0.8250 | −0.0695 | 0.162* | |
H20C | 0.4967 | 0.8659 | 0.0183 | 0.162* | |
C21 | 0.3873 (5) | 0.9198 (4) | 0.75308 (19) | 0.0702 (11) | |
H21A | 0.4575 | 0.8342 | 0.7819 | 0.084* | |
H21B | 0.3683 | 1.0101 | 0.7940 | 0.084* | |
H21C | 0.4431 | 0.9640 | 0.7033 | 0.084* | |
C22 | 0.1907 (5) | 0.4072 (5) | 0.8559 (2) | 0.0687 (10) | |
H22A | 0.0872 | 0.3600 | 0.8297 | 0.082* | |
H22B | 0.1758 | 0.4340 | 0.9168 | 0.082* | |
H22C | 0.2810 | 0.3260 | 0.8523 | 0.082* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
O1 | 0.115 (2) | 0.0868 (19) | 0.0478 (12) | −0.0279 (18) | 0.0228 (14) | −0.0213 (14) |
O2 | 0.119 (2) | 0.117 (2) | 0.0407 (11) | −0.019 (2) | 0.0277 (14) | 0.0006 (16) |
O3 | 0.1030 (19) | 0.0292 (11) | 0.0470 (12) | −0.0058 (12) | −0.0102 (12) | −0.0012 (9) |
O4 | 0.0803 (16) | 0.0386 (11) | 0.0483 (11) | 0.0004 (13) | 0.0214 (11) | −0.0071 (10) |
O5 | 0.0861 (15) | 0.0495 (12) | 0.0366 (10) | −0.0059 (13) | 0.0110 (10) | 0.0023 (10) |
N7 | 0.0538 (15) | 0.0262 (12) | 0.0411 (12) | 0.0011 (12) | −0.0004 (10) | 0.0013 (10) |
C1 | 0.0533 (17) | 0.0484 (16) | 0.0392 (14) | −0.0057 (16) | 0.0088 (13) | 0.0017 (14) |
C2 | 0.0619 (19) | 0.063 (2) | 0.0387 (15) | −0.0043 (19) | 0.0066 (14) | −0.0038 (16) |
C3 | 0.069 (2) | 0.079 (2) | 0.0355 (14) | −0.007 (2) | 0.0102 (15) | 0.0026 (18) |
C4 | 0.0563 (19) | 0.070 (2) | 0.0489 (17) | −0.011 (2) | 0.0091 (14) | 0.0132 (18) |
C5 | 0.0575 (18) | 0.0449 (17) | 0.0539 (17) | −0.0100 (16) | −0.0024 (14) | 0.0138 (15) |
C6 | 0.0599 (19) | 0.0327 (15) | 0.0506 (16) | 0.0046 (15) | −0.0092 (14) | 0.0039 (14) |
C8 | 0.0439 (16) | 0.0267 (14) | 0.0403 (15) | 0.0009 (13) | 0.0036 (12) | −0.0022 (12) |
C9 | 0.0426 (16) | 0.0346 (14) | 0.0405 (14) | 0.0004 (15) | 0.0076 (12) | −0.0040 (14) |
C10 | 0.0454 (16) | 0.0402 (16) | 0.0387 (14) | −0.0031 (16) | 0.0029 (12) | 0.0040 (14) |
C11 | 0.059 (2) | 0.0335 (15) | 0.0429 (15) | −0.0018 (14) | −0.0013 (14) | 0.0066 (13) |
C12 | 0.061 (2) | 0.0247 (14) | 0.0461 (16) | 0.0020 (13) | −0.0016 (15) | −0.0026 (12) |
C13 | 0.0596 (18) | 0.0332 (14) | 0.0382 (14) | 0.0052 (16) | 0.0044 (12) | −0.0032 (13) |
C14 | 0.0431 (16) | 0.0508 (17) | 0.0388 (14) | −0.0055 (17) | −0.0008 (12) | 0.0054 (14) |
C15 | 0.0396 (15) | 0.0461 (16) | 0.0350 (12) | 0.0052 (16) | 0.0019 (11) | 0.0035 (14) |
C16 | 0.0430 (15) | 0.0365 (13) | 0.0351 (13) | −0.0010 (15) | 0.0040 (11) | −0.0013 (13) |
C17 | 0.0384 (15) | 0.0299 (13) | 0.0381 (13) | 0.0011 (14) | 0.0064 (11) | 0.0013 (13) |
C18 | 0.0441 (15) | 0.0309 (14) | 0.0378 (14) | 0.0017 (15) | 0.0027 (11) | −0.0004 (12) |
C19 | 0.117 (3) | 0.074 (3) | 0.060 (2) | −0.017 (3) | 0.011 (2) | −0.021 (2) |
C20 | 0.179 (5) | 0.185 (6) | 0.0443 (19) | −0.078 (5) | 0.020 (3) | 0.017 (3) |
C21 | 0.109 (3) | 0.053 (2) | 0.0469 (17) | −0.019 (2) | −0.0107 (19) | −0.0074 (16) |
C22 | 0.096 (3) | 0.065 (2) | 0.0452 (16) | −0.009 (2) | 0.0064 (18) | 0.0127 (17) |
Geometric parameters (Å, º) top
O1—C2 | 1.372 (4) | C9—C17 | 1.404 (3) |
O1—C19 | 1.384 (4) | C10—C11 | 1.372 (4) |
O2—C3 | 1.374 (3) | C11—C12 | 1.388 (4) |
O2—C20 | 1.404 (6) | C11—H11 | 0.93 |
O3—C8 | 1.220 (3) | C12—C18 | 1.378 (4) |
O4—C9 | 1.364 (4) | C12—H12 | 0.93 |
O4—C21 | 1.433 (4) | C13—C18 | 1.502 (3) |
O5—C10 | 1.365 (3) | C13—C16 | 1.511 (4) |
O5—C22 | 1.428 (4) | C13—H13A | 0.97 |
N7—C8 | 1.361 (3) | C13—H13B | 0.97 |
N7—C6 | 1.455 (3) | C14—C15 | 1.383 (4) |
N7—C16 | 1.470 (3) | C15—C16 | 1.528 (3) |
C1—C2 | 1.391 (4) | C16—H16 | 0.98 |
C1—C15 | 1.397 (4) | C17—C18 | 1.402 (4) |
C1—H1 | 0.93 | C19—H19A | 0.96 |
C2—C3 | 1.386 (5) | C19—H19B | 0.96 |
C3—C4 | 1.363 (5) | C19—H19C | 0.96 |
C4—C14 | 1.409 (4) | C20—H20A | 0.96 |
C4—H4 | 0.93 | C20—H20B | 0.96 |
C5—C14 | 1.495 (4) | C20—H20C | 0.96 |
C5—C6 | 1.513 (4) | C21—H21A | 0.96 |
C5—H5A | 0.97 | C21—H21B | 0.96 |
C5—H5B | 0.97 | C21—H21C | 0.96 |
C6—H6A | 0.97 | C22—H22A | 0.96 |
C6—H6B | 0.97 | C22—H22B | 0.96 |
C8—C17 | 1.483 (4) | C22—H22C | 0.96 |
C9—C10 | 1.403 (4) | | |
| | | |
C2—O1—C19 | 119.4 (2) | C18—C13—H13A | 109.3 |
C3—O2—C20 | 118.0 (3) | C16—C13—H13A | 109.3 |
C9—O4—C21 | 113.9 (2) | C18—C13—H13B | 109.3 |
C10—O5—C22 | 117.2 (2) | C16—C13—H13B | 109.3 |
C8—N7—C6 | 118.9 (2) | H13A—C13—H13B | 107.9 |
C8—N7—C16 | 123.8 (2) | C15—C14—C4 | 118.4 (3) |
C6—N7—C16 | 117.0 (2) | C15—C14—C5 | 120.9 (2) |
C2—C1—C15 | 120.8 (3) | C4—C14—C5 | 120.6 (3) |
C2—C1—H1 | 119.6 | C14—C15—C1 | 119.7 (2) |
C15—C1—H1 | 119.6 | C14—C15—C16 | 122.0 (3) |
O1—C2—C3 | 115.4 (2) | C1—C15—C16 | 118.2 (3) |
O1—C2—C1 | 125.2 (3) | N7—C16—C13 | 108.5 (2) |
C3—C2—C1 | 119.4 (3) | N7—C16—C15 | 111.4 (2) |
C4—C3—O2 | 125.2 (3) | C13—C16—C15 | 110.2 (2) |
C4—C3—C2 | 119.8 (3) | N7—C16—H16 | 108.9 |
O2—C3—C2 | 114.9 (3) | C13—C16—H16 | 108.9 |
C3—C4—C14 | 121.8 (3) | C15—C16—H16 | 108.9 |
C3—C4—H4 | 119.1 | C18—C17—C9 | 119.3 (3) |
C14—C4—H4 | 119.1 | C18—C17—C8 | 119.4 (2) |
C14—C5—C6 | 109.6 (2) | C9—C17—C8 | 121.3 (3) |
C14—C5—H5A | 109.7 | C12—C18—C17 | 119.6 (2) |
C6—C5—H5A | 109.7 | C12—C18—C13 | 122.5 (3) |
C14—C5—H5B | 109.7 | C17—C18—C13 | 117.9 (2) |
C6—C5—H5B | 109.7 | O1—C19—H19A | 109.5 |
H5A—C5—H5B | 108.2 | O1—C19—H19B | 109.5 |
N7—C6—C5 | 108.9 (2) | H19A—C19—H19B | 109.5 |
N7—C6—H6A | 109.9 | O1—C19—H19C | 109.5 |
C5—C6—H6A | 109.9 | H19A—C19—H19C | 109.5 |
N7—C6—H6B | 109.9 | H19B—C19—H19C | 109.5 |
C5—C6—H6B | 109.9 | O2—C20—H20A | 109.5 |
H6A—C6—H6B | 108.3 | O2—C20—H20B | 109.5 |
O3—C8—N7 | 120.5 (2) | H20A—C20—H20B | 109.5 |
O3—C8—C17 | 122.4 (2) | O2—C20—H20C | 109.5 |
N7—C8—C17 | 117.1 (2) | H20A—C20—H20C | 109.5 |
O4—C9—C10 | 117.5 (2) | H20B—C20—H20C | 109.5 |
O4—C9—C17 | 122.4 (3) | O4—C21—H21A | 109.5 |
C10—C9—C17 | 119.9 (3) | O4—C21—H21B | 109.5 |
O5—C10—C11 | 124.8 (3) | H21A—C21—H21B | 109.5 |
O5—C10—C9 | 115.3 (3) | O4—C21—H21C | 109.5 |
C11—C10—C9 | 119.9 (2) | H21A—C21—H21C | 109.5 |
C10—C11—C12 | 120.3 (3) | H21B—C21—H21C | 109.5 |
C10—C11—H11 | 119.9 | O5—C22—H22A | 109.5 |
C12—C11—H11 | 119.9 | O5—C22—H22B | 109.5 |
C18—C12—C11 | 121.0 (3) | H22A—C22—H22B | 109.5 |
C18—C12—H12 | 119.5 | O5—C22—H22C | 109.5 |
C11—C12—H12 | 119.5 | H22A—C22—H22C | 109.5 |
C18—C13—C16 | 111.8 (2) | H22B—C22—H22C | 109.5 |
| | | |
C19—O1—C2—C3 | −175.8 (3) | C6—C5—C14—C4 | 153.8 (3) |
C19—O1—C2—C1 | 3.7 (5) | C4—C14—C15—C1 | −3.0 (4) |
C15—C1—C2—O1 | −179.5 (3) | C5—C14—C15—C1 | 174.6 (3) |
C15—C1—C2—C3 | 0.1 (5) | C4—C14—C15—C16 | 174.4 (2) |
C20—O2—C3—C4 | −4.4 (6) | C5—C14—C15—C16 | −8.1 (4) |
C20—O2—C3—C2 | 174.3 (4) | C2—C1—C15—C14 | 2.5 (4) |
O1—C2—C3—C4 | 177.5 (3) | C2—C1—C15—C16 | −174.9 (3) |
C1—C2—C3—C4 | −2.1 (5) | C8—N7—C16—C13 | −35.8 (3) |
O1—C2—C3—O2 | −1.2 (5) | C6—N7—C16—C13 | 150.5 (2) |
C1—C2—C3—O2 | 179.2 (3) | C8—N7—C16—C15 | −157.4 (2) |
O2—C3—C4—C14 | −179.8 (3) | C6—N7—C16—C15 | 29.0 (3) |
C2—C3—C4—C14 | 1.6 (5) | C18—C13—C16—N7 | 52.0 (3) |
C8—N7—C6—C5 | 124.4 (3) | C18—C13—C16—C15 | 174.3 (2) |
C16—N7—C6—C5 | −61.6 (3) | C14—C15—C16—N7 | 6.7 (4) |
C14—C5—C6—N7 | 56.0 (3) | C1—C15—C16—N7 | −175.9 (2) |
C6—N7—C8—O3 | −5.0 (4) | C14—C15—C16—C13 | −113.8 (3) |
C16—N7—C8—O3 | −178.6 (3) | C1—C15—C16—C13 | 63.5 (3) |
C6—N7—C8—C17 | 175.0 (2) | O4—C9—C17—C18 | −178.2 (3) |
C16—N7—C8—C17 | 1.4 (4) | C10—C9—C17—C18 | −1.7 (4) |
C21—O4—C9—C10 | 93.0 (3) | O4—C9—C17—C8 | 1.9 (4) |
C21—O4—C9—C17 | −90.4 (3) | C10—C9—C17—C8 | 178.4 (3) |
C22—O5—C10—C11 | −14.3 (4) | O3—C8—C17—C18 | −163.1 (3) |
C22—O5—C10—C9 | 165.7 (3) | N7—C8—C17—C18 | 16.8 (4) |
O4—C9—C10—O5 | −3.0 (4) | O3—C8—C17—C9 | 16.8 (4) |
C17—C9—C10—O5 | −179.6 (2) | N7—C8—C17—C9 | −163.2 (2) |
O4—C9—C10—C11 | 177.0 (3) | C11—C12—C18—C17 | 0.6 (4) |
C17—C9—C10—C11 | 0.3 (4) | C11—C12—C18—C13 | 178.9 (3) |
O5—C10—C11—C12 | −178.6 (3) | C9—C17—C18—C12 | 1.2 (4) |
C9—C10—C11—C12 | 1.5 (4) | C8—C17—C18—C12 | −178.8 (3) |
C10—C11—C12—C18 | −1.9 (5) | C9—C17—C18—C13 | −177.2 (3) |
C3—C4—C14—C15 | 1.0 (5) | C8—C17—C18—C13 | 2.8 (4) |
C3—C4—C14—C5 | −176.6 (3) | C16—C13—C18—C12 | 143.5 (3) |
C6—C5—C14—C15 | −23.7 (4) | C16—C13—C18—C17 | −38.2 (4) |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
C12—H12···O3i | 0.93 | 2.33 | 3.127 (3) | 144 |
C19—H19C···O4ii | 0.96 | 2.56 | 3.407 (5) | 147 |
C5—H5B···Cg1iii | 0.97 | 2.57 | 3.519 (3) | 165 |
C6—H6B···Cg1iv | 0.97 | 2.56 | 3.474 (3) | 157 |
C22—H22A···Cg2ii | 0.96 | 2.83 | 3.778 (4) | 167 |
Symmetry codes: (i) x, y−1, z; (ii) −x, y−1/2, −z+1; (iii) −x+1, y+1/2, −z+1; (iv) −x, y+1/2, −z+1. |
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