Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536805013292/lh6415sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S1600536805013292/lh6415Isup2.hkl |
CCDC reference: 274577
Key indicators
- Single-crystal X-ray study
- T = 294 K
- Mean (C-C) = 0.012 Å
- R factor = 0.065
- wR factor = 0.167
- Data-to-parameter ratio = 7.9
checkCIF/PLATON results
No syntax errors found
Alert level A PLAT027_ALERT_3_A _diffrn_reflns_theta_full (too) Low ............ 64.97 Deg.
Author Response: ...'see _exptl_special_details' |
Alert level B PLAT340_ALERT_3_B Low Bond Precision on C-C bonds (x 1000) Ang ... 12
Alert level C REFNR01_ALERT_3_C Ratio of reflections to parameters is < 8 for a non-centrosymmetric structure, where ZMAX < 18 sine(theta)/lambda 0.5877 Proportion of unique data used 1.0000 Ratio reflections to parameters 7.9170 STRVA01_ALERT_4_C Flack test results are ambiguous. From the CIF: _refine_ls_abs_structure_Flack 0.450 From the CIF: _refine_ls_abs_structure_Flack_su 0.080 THETM01_ALERT_3_C The value of sine(theta_max)/wavelength is less than 0.590 Calculated sin(theta_max)/wavelength = 0.5877 PLAT023_ALERT_3_C Resolution (too) Low [sin(th)/Lambda < 0.6]..... 64.97 Deg. PLAT033_ALERT_2_C Flack Parameter Value Deviates from Zero ....... 0.45 PLAT089_ALERT_3_C Poor Data / Parameter Ratio (Zmax .LT. 18) ..... 7.92 PLAT128_ALERT_4_C Non-standard setting of Space group Pca21 .... Pbc21 PLAT242_ALERT_2_C Check Low Ueq as Compared to Neighbors for N8B PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 4 Cl
Alert level G REFLT03_ALERT_4_G WARNING: Large fraction of Friedel related reflns may be needed to determine absolute structure From the CIF: _diffrn_reflns_theta_max 64.97 From the CIF: _reflns_number_total 1908 Count of symmetry unique reflns 1908 Completeness (_total/calc) 100.00% TEST3: Check Friedels for noncentro structure Estimate of Friedel pairs measured 0 Fraction of Friedel pairs measured 0.000 Are heavy atom types Z>Si present yes
1 ALERT level A = In general: serious problem 1 ALERT level B = Potentially serious problem 9 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 2 ALERT type 2 Indicator that the structure model may be wrong or deficient 6 ALERT type 3 Indicator that the structure quality may be low 4 ALERT type 4 Improvement, methodology, query or suggestion
Data collection: Picker Operating Manual (Picker, 1967); cell refinement: Picker; data reduction: DATRDN (Stewart, 1976); program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: SHELXL97.
C11H14N+·Cl− | Dx = 1.176 Mg m−3 |
Mr = 195.68 | Cu Kα radiation, λ = 1.54178 Å |
Orthorhombic, Pbc21 | Cell parameters from 32 reflections |
a = 5.958 (2) Å | θ = 22–37° |
b = 11.039 (3) Å | µ = 2.68 mm−1 |
c = 33.596 (5) Å | T = 294 K |
V = 2209.6 (10) Å3 | Needle, colorless |
Z = 8 | 0.31 × 0.07 × 0.03 mm |
F(000) = 832 |
Picker FACS-1 four-circle diffractometer | 1636 reflections with I > 2σ(I) |
Radiation source: fine-focus sealed tube | Rint = 0.000 |
Ni filtered radiation monochromator | θmax = 65.0°, θmin = 2.6° |
ω/2θ scans | h = 0→7 |
Absorption correction: ψ scan (North et al., 1968) | k = 0→12 |
Tmin = 0.794, Tmax = 0.919 | l = 0→39 |
1908 measured reflections | 3 standard reflections every 100 reflections |
1908 independent reflections | intensity decay: 1.2% |
Refinement on F2 | Hydrogen site location: inferred from neighbouring sites |
Least-squares matrix: full | H-atom parameters constrained |
R[F2 > 2σ(F2)] = 0.065 | w = 1/[σ2(Fo2) + (0.1152P)2 + 0.9636P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.167 | (Δ/σ)max < 0.001 |
S = 0.98 | Δρmax = 0.49 e Å−3 |
1908 reflections | Δρmin = −0.39 e Å−3 |
241 parameters | Extinction correction: SHELXL97, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
1 restraint | Extinction coefficient: 0.0071 (9) |
Primary atom site location: structure-invariant direct methods | Absolute structure: Flack (1983), 0 Friedel pairs |
Secondary atom site location: difference Fourier map | Absolute structure parameter: 0.45 (8) |
Experimental. PICKER FACS-1 mechanical limit does not allow for data collection above θ = 65° |
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 | ||
C1A | 0.3868 (11) | 0.4459 (6) | 0.2602 (2) | 0.0556 (15) | |
C2A | 0.1829 (12) | 0.3982 (7) | 0.2471 (2) | 0.0655 (17) | |
H2A | 0.1347 | 0.3230 | 0.2562 | 0.089 (5)* | |
C3A | 0.0531 (14) | 0.4630 (9) | 0.2206 (3) | 0.082 (2) | |
H3A | −0.0810 | 0.4300 | 0.2115 | 0.089 (5)* | |
C4A | 0.1170 (16) | 0.5736 (9) | 0.2077 (3) | 0.086 (2) | |
H4A | 0.0254 | 0.6161 | 0.1902 | 0.089 (5)* | |
C5A | 0.3153 (16) | 0.6241 (7) | 0.2201 (3) | 0.076 (2) | |
H5A | 0.3578 | 0.7006 | 0.2113 | 0.089 (5)* | |
C6A | 0.4522 (13) | 0.5595 (7) | 0.2460 (2) | 0.0670 (18) | |
H6A | 0.5886 | 0.5924 | 0.2541 | 0.089 (5)* | |
C7A | 0.5291 (12) | 0.3767 (6) | 0.2885 (2) | 0.0581 (16) | |
H71A | 0.4669 | 0.2960 | 0.2914 | 0.089 (5)* | |
H72A | 0.6779 | 0.3684 | 0.2771 | 0.089 (5)* | |
N8A | 0.5508 (8) | 0.4318 (4) | 0.32872 (17) | 0.0467 (11) | |
H8A | 0.6288 | 0.5022 | 0.3261 | 0.089 (5)* | |
C9A | 0.6825 (14) | 0.3504 (6) | 0.3543 (3) | 0.067 (2) | |
H91A | 0.5968 | 0.2788 | 0.3599 | 0.079 (9)* | |
H92A | 0.7179 | 0.3909 | 0.3788 | 0.079 (9)* | |
H93A | 0.8190 | 0.3283 | 0.3410 | 0.079 (9)* | |
C10A | 0.3273 (10) | 0.4616 (6) | 0.3467 (2) | 0.0502 (14) | |
H10A | 0.2456 | 0.5147 | 0.3289 | 0.089 (5)* | |
H11A | 0.2409 | 0.3877 | 0.3498 | 0.089 (5)* | |
C11A | 0.3496 (10) | 0.5205 (6) | 0.3856 (2) | 0.0519 (15) | |
C12A | 0.3669 (11) | 0.5675 (7) | 0.4162 (2) | 0.0586 (16) | |
H12A | 0.3807 | 0.6053 | 0.4408 | 0.089 (5)* | |
C1B | 0.0797 (12) | 0.3558 (6) | 0.5816 (2) | 0.0579 (16) | |
C2B | 0.2807 (13) | 0.4022 (8) | 0.5956 (3) | 0.0723 (19) | |
H2B | 0.3327 | 0.4766 | 0.5864 | 0.089 (5)* | |
C3B | 0.4024 (16) | 0.3382 (10) | 0.6229 (3) | 0.095 (3) | |
H3B | 0.5373 | 0.3692 | 0.6324 | 0.089 (5)* | |
C4B | 0.3261 (18) | 0.2281 (11) | 0.6364 (3) | 0.098 (3) | |
H4B | 0.4112 | 0.1840 | 0.6546 | 0.089 (5)* | |
C5B | 0.1224 (18) | 0.1826 (9) | 0.6231 (3) | 0.095 (3) | |
H5B | 0.0693 | 0.1090 | 0.6328 | 0.089 (5)* | |
C6B | 0.0002 (15) | 0.2459 (7) | 0.5958 (2) | 0.0702 (18) | |
H6B | −0.1361 | 0.2155 | 0.5867 | 0.089 (5)* | |
C7B | −0.0506 (12) | 0.4273 (6) | 0.5509 (2) | 0.0584 (16) | |
H71B | −0.2013 | 0.4406 | 0.5609 | 0.089 (5)* | |
H72B | 0.0198 | 0.5060 | 0.5478 | 0.089 (5)* | |
N8B | −0.0661 (8) | 0.3685 (4) | 0.51102 (17) | 0.0458 (11) | |
H8B | −0.1444 | 0.2984 | 0.5144 | 0.089 (5)* | |
C9B | −0.1956 (13) | 0.4436 (7) | 0.4829 (3) | 0.069 (2) | |
H91B | −0.3382 | 0.4636 | 0.4944 | 0.079 (9)* | |
H92B | −0.2187 | 0.3993 | 0.4586 | 0.079 (9)* | |
H93B | −0.1141 | 0.5166 | 0.4773 | 0.079 (9)* | |
C10B | 0.1625 (11) | 0.3336 (7) | 0.4948 (3) | 0.0577 (19) | |
H10B | 0.2552 | 0.4055 | 0.4925 | 0.089 (5)* | |
H11B | 0.2354 | 0.2785 | 0.5132 | 0.089 (5)* | |
C11B | 0.1434 (10) | 0.2764 (5) | 0.4564 (2) | 0.0506 (14) | |
C12B | 0.1338 (12) | 0.2300 (6) | 0.4252 (2) | 0.0607 (17) | |
H12B | 0.1261 | 0.1930 | 0.4004 | 0.089 (5)* | |
Cl1A | 0.8653 (2) | 0.64654 (12) | 0.32272 (6) | 0.0543 (5) | |
Cl2B | −0.3734 (3) | 0.15049 (12) | 0.51852 (6) | 0.0557 (5) |
U11 | U22 | U33 | U12 | U13 | U23 | |
C1A | 0.065 (4) | 0.052 (3) | 0.050 (3) | −0.002 (3) | 0.009 (3) | 0.002 (3) |
C2A | 0.071 (4) | 0.065 (4) | 0.060 (4) | −0.008 (3) | −0.001 (3) | −0.003 (3) |
C3A | 0.071 (5) | 0.115 (7) | 0.061 (4) | −0.006 (5) | −0.009 (4) | −0.001 (5) |
C4A | 0.105 (7) | 0.105 (6) | 0.048 (4) | 0.016 (5) | −0.007 (4) | 0.005 (4) |
C5A | 0.109 (6) | 0.064 (4) | 0.056 (4) | −0.002 (4) | 0.008 (4) | 0.009 (4) |
C6A | 0.080 (5) | 0.057 (4) | 0.064 (4) | −0.008 (4) | −0.005 (4) | −0.007 (3) |
C7A | 0.056 (4) | 0.050 (3) | 0.068 (4) | 0.004 (3) | 0.008 (3) | −0.006 (3) |
N8A | 0.042 (2) | 0.039 (2) | 0.059 (3) | 0.0024 (19) | −0.004 (2) | −0.007 (2) |
C9A | 0.066 (4) | 0.050 (4) | 0.087 (6) | 0.017 (3) | −0.006 (4) | 0.006 (3) |
C10A | 0.040 (3) | 0.055 (3) | 0.055 (3) | 0.003 (3) | 0.005 (3) | −0.008 (3) |
C11A | 0.052 (4) | 0.049 (3) | 0.055 (4) | 0.004 (2) | 0.008 (3) | 0.002 (3) |
C12A | 0.063 (4) | 0.066 (4) | 0.047 (4) | 0.007 (3) | 0.003 (3) | −0.002 (3) |
C1B | 0.066 (4) | 0.056 (4) | 0.051 (4) | −0.005 (3) | 0.001 (3) | −0.015 (3) |
C2B | 0.068 (4) | 0.087 (5) | 0.062 (4) | −0.012 (4) | 0.000 (4) | −0.003 (4) |
C3B | 0.088 (6) | 0.127 (8) | 0.070 (5) | −0.009 (5) | −0.020 (4) | 0.010 (5) |
C4B | 0.124 (7) | 0.108 (8) | 0.061 (5) | 0.011 (6) | −0.030 (5) | 0.002 (5) |
C5B | 0.152 (10) | 0.077 (5) | 0.056 (5) | −0.012 (5) | −0.017 (5) | 0.003 (4) |
C6B | 0.100 (5) | 0.062 (4) | 0.049 (3) | −0.008 (4) | −0.006 (4) | −0.002 (3) |
C7B | 0.066 (4) | 0.053 (3) | 0.056 (4) | 0.002 (3) | 0.004 (3) | −0.012 (3) |
N8B | 0.042 (2) | 0.044 (2) | 0.051 (3) | 0.005 (2) | 0.003 (2) | 0.006 (2) |
C9B | 0.069 (4) | 0.060 (4) | 0.080 (5) | 0.013 (3) | −0.005 (4) | 0.015 (4) |
C10B | 0.040 (3) | 0.058 (4) | 0.074 (5) | 0.005 (3) | 0.001 (3) | −0.009 (3) |
C11B | 0.051 (3) | 0.046 (3) | 0.055 (4) | 0.002 (2) | 0.003 (3) | −0.003 (3) |
C12B | 0.070 (4) | 0.057 (4) | 0.055 (4) | −0.001 (3) | 0.002 (3) | 0.003 (3) |
Cl1A | 0.0500 (9) | 0.0477 (8) | 0.0651 (11) | −0.0031 (5) | −0.0054 (7) | −0.0007 (7) |
Cl2B | 0.0544 (9) | 0.0494 (9) | 0.0634 (11) | −0.0048 (6) | −0.0074 (7) | −0.0027 (7) |
C1A—C2A | 1.395 (9) | C1B—C2B | 1.385 (10) |
C1A—C6A | 1.397 (9) | C1B—C6B | 1.386 (10) |
C1A—C7A | 1.486 (10) | C1B—C7B | 1.511 (10) |
C2A—C3A | 1.380 (11) | C2B—C3B | 1.367 (13) |
C2A—H2A | 0.9300 | C2B—H2B | 0.9300 |
C3A—C4A | 1.350 (12) | C3B—C4B | 1.374 (15) |
C3A—H3A | 0.9300 | C3B—H3B | 0.9300 |
C4A—C5A | 1.371 (13) | C4B—C5B | 1.388 (14) |
C4A—H4A | 0.9300 | C4B—H4B | 0.9300 |
C5A—C6A | 1.389 (11) | C5B—C6B | 1.365 (12) |
C5A—H5A | 0.9300 | C5B—H5B | 0.9300 |
C6A—H6A | 0.9300 | C6B—H6B | 0.9300 |
C7A—N8A | 1.486 (9) | C7B—N8B | 1.493 (8) |
C7A—H71A | 0.9700 | C7B—H71B | 0.9700 |
C7A—H72A | 0.9700 | C7B—H72B | 0.9700 |
N8A—C9A | 1.471 (9) | N8B—C9B | 1.475 (9) |
N8A—C10A | 1.499 (7) | N8B—C10B | 1.517 (8) |
N8A—H8A | 0.9100 | N8B—H8B | 0.9100 |
C9A—H91A | 0.9600 | C9B—H91B | 0.9600 |
C9A—H92A | 0.9600 | C9B—H92B | 0.9600 |
C9A—H93A | 0.9600 | C9B—H93B | 0.9600 |
C10A—C11A | 1.465 (10) | C10B—C11B | 1.442 (11) |
C10A—H10A | 0.9700 | C10B—H10B | 0.9700 |
C10A—H11A | 0.9700 | C10B—H11B | 0.9700 |
C11A—C12A | 1.155 (10) | C11B—C12B | 1.166 (9) |
C12A—H12A | 0.9300 | C12B—H12B | 0.9300 |
C2A—C1A—C6A | 118.4 (7) | C2B—C1B—C6B | 120.1 (7) |
C2A—C1A—C7A | 120.3 (6) | C2B—C1B—C7B | 118.8 (6) |
C6A—C1A—C7A | 121.3 (6) | C6B—C1B—C7B | 121.1 (6) |
C1A—C2A—C3A | 119.7 (7) | C1B—C2B—C3B | 119.7 (8) |
C1A—C2A—H2A | 120.2 | C1B—C2B—H2B | 120.2 |
C3A—C2A—H2A | 120.2 | C3B—C2B—H2B | 120.2 |
C2A—C3A—C4A | 121.2 (8) | C2B—C3B—C4B | 120.2 (9) |
C2A—C3A—H3A | 119.4 | C2B—C3B—H3B | 119.9 |
C4A—C3A—H3A | 119.4 | C4B—C3B—H3B | 119.9 |
C5A—C4A—C3A | 120.8 (8) | C5B—C4B—C3B | 120.2 (9) |
C5A—C4A—H4A | 119.6 | C5B—C4B—H4B | 119.9 |
C3A—C4A—H4A | 119.6 | C3B—C4B—H4B | 119.9 |
C6A—C5A—C4A | 119.2 (8) | C4B—C5B—C6B | 119.9 (10) |
C6A—C5A—H5A | 120.4 | C4B—C5B—H5B | 120.1 |
C4A—C5A—H5A | 120.4 | C6B—C5B—H5B | 120.1 |
C5A—C6A—C1A | 120.7 (7) | C1B—C6B—C5B | 119.8 (8) |
C5A—C6A—H6A | 119.7 | C1B—C6B—H6B | 120.1 |
C1A—C6A—H6A | 119.7 | C5B—C6B—H6B | 120.1 |
N8A—C7A—C1A | 115.0 (5) | N8B—C7B—C1B | 114.6 (5) |
N8A—C7A—H71A | 108.5 | N8B—C7B—H71B | 108.6 |
C1A—C7A—H71A | 108.5 | C1B—C7B—H71B | 108.6 |
N8A—C7A—H72A | 108.5 | N8B—C7B—H72B | 108.6 |
C1A—C7A—H72A | 108.5 | C1B—C7B—H72B | 108.6 |
H71A—C7A—H72A | 107.5 | H71B—C7B—H72B | 107.6 |
C7A—N8A—C9A | 109.2 (5) | C9B—N8B—C7B | 111.3 (5) |
C7A—N8A—C10A | 112.3 (5) | C9B—N8B—C10B | 112.5 (6) |
C9A—N8A—C10A | 111.8 (6) | C7B—N8B—C10B | 112.2 (5) |
C7A—N8A—H8A | 107.8 | C9B—N8B—H8B | 106.8 |
C9A—N8A—H8A | 107.8 | C7B—N8B—H8B | 106.8 |
C10A—N8A—H8A | 107.8 | C10B—N8B—H8B | 106.8 |
N8A—C9A—H91A | 109.5 | N8B—C9B—H91B | 109.5 |
N8A—C9A—H92A | 109.5 | N8B—C9B—H92B | 109.5 |
H91A—C9A—H92A | 109.5 | H91B—C9B—H92B | 109.5 |
N8A—C9A—H93A | 109.5 | N8B—C9B—H93B | 109.5 |
H91A—C9A—H93A | 109.5 | H91B—C9B—H93B | 109.5 |
H92A—C9A—H93A | 109.5 | H92B—C9B—H93B | 109.5 |
C11A—C10A—N8A | 112.1 (5) | C11B—C10B—N8B | 111.2 (6) |
C11A—C10A—H10A | 109.2 | C11B—C10B—H10B | 109.4 |
N8A—C10A—H10A | 109.2 | N8B—C10B—H10B | 109.4 |
C11A—C10A—H11A | 109.2 | C11B—C10B—H11B | 109.4 |
N8A—C10A—H11A | 109.2 | N8B—C10B—H11B | 109.4 |
H10A—C10A—H11A | 107.9 | H10B—C10B—H11B | 108.0 |
C12A—C11A—C10A | 179.7 (8) | C12B—C11B—C10B | 178.3 (7) |
C11A—C12A—H12A | 180.0 | C11B—C12B—H12B | 180.0 |
C6A—C1A—C2A—C3A | 0.5 (10) | C6B—C1B—C2B—C3B | 1.2 (12) |
C7A—C1A—C2A—C3A | −179.6 (7) | C7B—C1B—C2B—C3B | −179.2 (8) |
C1A—C2A—C3A—C4A | −1.5 (12) | C1B—C2B—C3B—C4B | 0.1 (15) |
C2A—C3A—C4A—C5A | 1.0 (13) | C2B—C3B—C4B—C5B | −1.5 (16) |
C3A—C4A—C5A—C6A | 0.5 (13) | C3B—C4B—C5B—C6B | 1.6 (15) |
C4A—C5A—C6A—C1A | −1.6 (12) | C2B—C1B—C6B—C5B | −1.2 (11) |
C2A—C1A—C6A—C5A | 1.0 (10) | C7B—C1B—C6B—C5B | 179.3 (7) |
C7A—C1A—C6A—C5A | −178.8 (7) | C4B—C5B—C6B—C1B | −0.2 (13) |
C2A—C1A—C7A—N8A | −112.8 (7) | C2B—C1B—C7B—N8B | 113.6 (7) |
C6A—C1A—C7A—N8A | 67.1 (8) | C6B—C1B—C7B—N8B | −66.8 (8) |
C1A—C7A—N8A—C9A | 176.2 (6) | C1B—C7B—N8B—C9B | 179.9 (6) |
C1A—C7A—N8A—C10A | 51.6 (7) | C1B—C7B—N8B—C10B | −53.0 (7) |
C7A—N8A—C10A—C11A | −177.5 (5) | C9B—N8B—C10B—C11B | −53.9 (8) |
C9A—N8A—C10A—C11A | 59.3 (7) | C7B—N8B—C10B—C11B | 179.7 (6) |
D—H···A | D—H | H···A | D···A | D—H···A |
N8A—H8A···Cl1A | 0.91 | 2.13 | 3.029 (5) | 169 |
N8B—H8B···Cl2B | 0.91 | 2.13 | 3.034 (5) | 171 |
C6B—H6B···Cl2B | 0.93 | 2.79 | 3.578 (8) | 144 |
C10A—H10A···Cl1Ai | 0.97 | 2.70 | 3.521 (7) | 143 |
C10B—H11B···Cl2Bii | 0.97 | 2.73 | 3.516 (7) | 138 |
C12A—H12A···Cl2Biii | 0.93 | 2.66 | 3.559 (8) | 163 |
C12B—H12B···Cl1Aiv | 0.93 | 2.66 | 3.565 (8) | 165 |
C7A—H71A···Cl1Aiv | 0.97 | 2.78 | 3.647 (7) | 149 |
C7B—H72B···Cl2Biii | 0.97 | 2.82 | 3.693 (7) | 150 |
C9B—H91B···Cl2Bv | 0.96 | 2.80 | 3.639 (8) | 146 |
C9A—H93A···Cl1Avi | 0.96 | 2.82 | 3.667 (8) | 148 |
Symmetry codes: (i) x−1, y, z; (ii) x+1, y, z; (iii) −x, y+1/2, z; (iv) −x+1, y−1/2, z; (v) −x−1, y+1/2, z; (vi) −x+2, y−1/2, z. |
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