The crystal structures of the isostructural title compounds poly[(μ-benzene-1,4-dithiolato)dithallium], Tl2(SC6H4S), and poly[(μ-benzene-1,4-diselenolato)dithallium], Tl2(SeC6H4Se), were solved by simulated annealing from high-resolution synchrotron X-ray powder diffraction. Rietveld refinements of an initial structure with one formula unit per triclinic cell gave satisfactory agreement with the data, but led to a structure with impossibly close non-bonded contacts. A disordered model was proposed to alleviate this problem, but an alternative supercell structure leads to slightly improved agreement with the data. The isostructural superlattice structures were confirmed for both compounds through additional data collection, with substantially better counting statistics, which revealed the presence of very weak superlattice peaks not previously seen. Overall, each structure contains Tl—S or Tl—Se two-dimensional networks, connected by phenylene bridges. The sulfur (or selenium) coordination sphere around each thallium is a highly distorted square pyramid or a `see-saw' shape, depending upon how many Tl—S or Tl—Se interactions are considered to be bonds. In addition, the two compounds contain pairs of TlI ions that interact through a closed-shell `thallophilic' interaction: in the sulfur compound there are two inequivalent pairs of Tl atoms with Tl—Tl distances of 3.49 and 3.58 Å, while in the selenium compound those Tl—Tl interactions are at 3.54 and 3.63 Å.
Supporting information
CCDC references: 849841; 849842
For both compounds, data collection: spec; cell refinement: TOPAS-Academic (Coelho, 2007); data reduction: X16C beamline software; program(s) used to solve structure: TOPAS-Academic (Coelho, 2007); program(s) used to refine structure: TOPAS-Academic (Coelho, 2007); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997) and Mercury (Version 2.2; Macrae et al., 2006); software used to prepare material for publication: publCIF (Westrip, 2009).
Crystal data top
Tl2·(SC6H2S) | V = 404.85 (9) Å3 |
Mr = 549.0 | Z = 4 |
Triclinic, P1 | Synchrotron radiation, λ = 0.698163 Å |
Hall symbol: P-1 | µ = 37 mm−1 |
a = 6.5525 (3) Å | T = 298 K |
b = 6.8444 (3) Å | Particle morphology: fine powder |
c = 9.5265 (2) Å | yellow |
α = 71.798 (2)° | cylinder, 8 × 0.7 mm |
β = 85.988 (2)° | Specimen preparation: Prepared at 298 K and 101.325 kPa, cooled at 0 K min−1 |
γ = 89.219 (2)° | |
Data collection top
Huber diffractometer | Data collection mode: transmission |
Radiation source: synchrotron, NSLS Beamline X16C | Scan method: step |
Si (111) monochromator | 2θmin = 2°, 2θmax = 30°, 2θstep = 0.005° |
Specimen mounting: Sample was mounted in a thin walled glass capillary of nominal diameter 0.7 mm. | |
Refinement top
Rp = 0.070 | 57 parameters |
Rwp = 0.080 | 0 restraints |
Rexp = 0.065 | H-atom parameters not refined |
RBragg = 0.019 | Weighting scheme based on measured s.u.'s |
χ2 = 1.484 | (Δ/σ)max = 0.0001 |
5601 data points | Background function: Chebyshev polynomial with 8 coeffecients plus 1/(2theta) term |
Excluded region(s): none | Preferred orientation correction: none |
Profile function: Simple_Axial_Model(width parameter 8.80/300) function with Rp=9999,Rs=300
in TOPAS-Academic | |
Crystal data top
Tl2·(SC6H2S) | γ = 89.219 (2)° |
Mr = 549.0 | V = 404.85 (9) Å3 |
Triclinic, P1 | Z = 4 |
a = 6.5525 (3) Å | Synchrotron radiation, λ = 0.698163 Å |
b = 6.8444 (3) Å | µ = 37 mm−1 |
c = 9.5265 (2) Å | T = 298 K |
α = 71.798 (2)° | cylinder, 8 × 0.7 mm |
β = 85.988 (2)° | |
Data collection top
Huber diffractometer | Scan method: step |
Specimen mounting: Sample was mounted in a thin walled glass capillary of nominal diameter 0.7 mm. | 2θmin = 2°, 2θmax = 30°, 2θstep = 0.005° |
Data collection mode: transmission | |
Refinement top
Rp = 0.070 | 5601 data points |
Rwp = 0.080 | 57 parameters |
Rexp = 0.065 | 0 restraints |
RBragg = 0.019 | H-atom parameters not refined |
χ2 = 1.484 | |
Special details top
Experimental. In order to decrease sample absorption, the sample was mixed with finely ground cork before loading into the capillary. This diluted the sample to prevent absorption corrections as well as ensuring no preferred orientation. |
Geometry. Bond distances, angles etc. have been calculated using the rounded fractional coordinates. All suś are estimated from the variances of the (full) variance-covariance matrix. The cell e.s.d.'s are taken into account in the estimation of distances, angles and torsion angles |
Refinement. The two S(C6H4)S moieties were refined as z-matrices, with planar regula hexagonal symmetry imposed for the aromatic rings, located at inversion centers. S-C bond lengths were refined, but S atoms were fixed in the planes of the hexagons, with S-C—C bond angles fixed at 60 °. |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Tl2 | 0.0132 (4) | 0.6150 (6) | 0.6442 (4) | 0.0385 (7)* | |
S1 | 0.05050 | 0.06291 | −0.34303 | 0.006 (3)* | |
C1 | 0.02217 | 0.02761 | −0.15058 | 0.006 (3)* | |
C2 | −0.11884 | 0.14282 | −0.09585 | 0.006 (3)* | |
C3 | −0.14101 | 0.11521 | 0.05473 | 0.006 (3)* | |
Tl1 | 0.4572 (4) | 0.8920 (6) | 0.3612 (3) | 0.0385 (7)* | |
S1A | 0.53129 | 0.52569 | −0.33719 | 0.006 (3)* | |
C1A | 0.51373 | 0.51128 | −0.14802 | 0.006 (3)* | |
C2A | 0.35925 | 0.39595 | −0.05277 | 0.006 (3)* | |
C3A | 0.34552 | 0.38467 | 0.09525 | 0.006 (3)* | |
H2 | −0.21154 | 0.25423 | −0.17062 | 0.006 (3)* | |
H3 | −0.25100 | 0.20508 | 0.09742 | 0.006 (3)* | |
H2A | 0.24946 | 0.31479 | −0.09393 | 0.006 (3)* | |
H3A | 0.22501 | 0.29471 | 0.16955 | 0.006 (3)* | |
Geometric parameters (Å, º) top
Tl2—S1i | 3.0752 | C2—H2 | 1.0800 |
Tl1—S1Aii | 2.9379 | C3—H3 | 1.0800 |
S1—C1 | 1.7695 | C1A—C2A | 1.3845 |
S1A—C1A | 1.7695 | C1A—C3Aii | 1.3845 |
C1—C3iii | 1.3845 | C2A—C3A | 1.3845 |
C1—C2 | 1.3845 | C2A—H2A | 1.0800 |
C2—C3 | 1.3845 | C3A—H3A | 1.0800 |
| | | |
Tl1···S1Aiv | 3.9216 | S1···Tl2xii | 3.1193 |
Tl1···S1i | 3.3483 | S1···Tl2xiii | 3.7477 |
Tl1···S1ii | 3.2321 | S1A···Tl1xiii | 3.2309 |
Tl1···C2i | 3.5408 | S1A···Tl2xiii | 3.4481 |
Tl1···C1i | 3.7868 | S1A···Tl2xiv | 3.2067 |
Tl1···C1ii | 3.7908 | S1A···S1Axv | 3.2829 |
Tl1···C3v | 3.7466 | S1A···Tl1iv | 3.9216 |
Tl1···Tl2 | 3.897 (4) | C1···Tl1ii | 3.7908 |
Tl1···S1Avi | 3.2309 | C1···Tl1i | 3.7868 |
Tl1···C3Avii | 3.6304 | C1A···C2xvi | 3.4091 |
Tl2···Tl1 | 3.897 (4) | C1A···Tl2xiv | 3.6622 |
Tl2···C2vi | 3.4788 | C2···C3Ai | 3.5418 |
Tl2···S1vi | 3.7477 | C2···C1Axvii | 3.4091 |
Tl2···C2Avi | 3.7206 | C2···Tl1i | 3.5408 |
Tl2···S1viii | 3.1193 | C2···Tl2xiii | 3.4788 |
Tl2···S1Aix | 3.2067 | C2A···Tl2xiii | 3.7206 |
Tl2···S1Avi | 3.4481 | C3···C3Ai | 3.5555 |
Tl2···C1Aix | 3.6622 | C3···Tl1xviii | 3.7466 |
Tl2···C3Ax | 3.2974 | C3A···Tl2x | 3.2974 |
S1···S1xi | 3.4678 | C3A···C3i | 3.5555 |
S1···Tl1i | 3.3483 | C3A···C2i | 3.5418 |
S1···Tl1ii | 3.2321 | C3A···Tl1xix | 3.6304 |
| | | |
Tl2i—S1—C1 | 141.47 | C1iii—C3—H3 | 120.00 |
Tl1ii—S1A—C1A | 109.38 | S1A—C1A—C2A | 120.00 |
S1—C1—C2 | 120.00 | S1A—C1A—C3Aii | 120.00 |
S1—C1—C3iii | 120.00 | C2A—C1A—C3Aii | 120.00 |
C2—C1—C3iii | 120.00 | C1A—C2A—C3A | 120.00 |
C1—C2—C3 | 120.00 | C1Aii—C3A—C2A | 120.00 |
C1iii—C3—C2 | 120.00 | C1A—C2A—H2A | 120.00 |
C1—C2—H2 | 120.00 | C3A—C2A—H2A | 120.00 |
C3—C2—H2 | 120.00 | C2A—C3A—H3A | 120.00 |
C2—C3—H3 | 120.00 | C1Aii—C3A—H3A | 120.00 |
| | | |
Tl2i—S1—C1—C2 | 24.88 | C2—C1—C3iii—C2iii | 0.00 |
Tl2i—S1—C1—C3iii | −155.12 | C1—C2—C3—C1iii | 0.00 |
Tl1ii—S1A—C1A—C3Aii | 126.01 | S1A—C1A—C2A—C3A | 180.00 |
Tl1ii—S1A—C1A—C2A | −53.99 | C3Aii—C1A—C2A—C3A | −0.02 |
C3iii—C1—C2—C3 | 0.00 | S1A—C1A—C3Aii—C2Aii | 180.00 |
S1—C1—C2—C3 | 179.98 | C2A—C1A—C3Aii—C2Aii | 0.02 |
S1—C1—C3iii—C2iii | −179.98 | C1A—C2A—C3A—C1Aii | 0.00 |
Symmetry codes: (i) −x, −y+1, −z; (ii) −x+1, −y+1, −z; (iii) −x, −y, −z; (iv) −x+1, −y+2, −z; (v) x+1, y+1, z; (vi) x, y, z+1; (vii) x, y+1, z; (viii) x, y+1, z+1; (ix) x−1, y, z+1; (x) −x, −y+1, −z+1; (xi) −x, −y, −z−1; (xii) x, y−1, z−1; (xiii) x, y, z−1; (xiv) x+1, y, z−1; (xv) −x+1, −y+1, −z−1; (xvi) x+1, y, z; (xvii) x−1, y, z; (xviii) x−1, y−1, z; (xix) x, y−1, z. |
Crystal data top
Tl2·(SeC6H2Se) | γ = 88.659 (3)° |
Mr = 642.8 | V = 426.72 (1) Å3 |
Triclinic, P1 | Z = 4 |
Hall symbol: P-1 | Synchrotron radiation, λ = 0.699855 Å |
a = 6.67438 (8) Å | T = 298 K |
b = 6.84998 (8) Å | Particle morphology: fine powder |
c = 9.82649 (10) Å | red-orange |
α = 72.513 (2)° | flat sheet, 8 × 17 mm |
β = 84.790 (2)° | Specimen preparation: Prepared at 298 K and 101.325 kPa, cooled at 0 K min−1 |
Data collection top
Huber diffractometer | Data collection mode: reflection |
Radiation source: synchrotron, NSLS Beamline X16C | Scan method: step |
Si (111) monochromator | 2θmin = 3°, 2θmax = 40°, 2θstep = 0.005° |
Specimen mounting: Flat plate geometry on zero-background holder. | |
Refinement top
Rp = 0.049 | 94 parameters |
Rwp = 0.056 | 0 restraints |
Rexp = 0.020 | H-atom parameters not refined |
RBragg = 0.026 | Weighting scheme based on measured s.u.'s |
χ2 = 7.756 | (Δ/σ)max = 0.0001 |
7401 data points | Background function: Chebyshev polynomial with 8 coeffecients plus 1/(2theta) term |
Excluded region(s): none | Preferred orientation correction: March-Dollase parameter 0.797(1) in (001) direction |
Profile function: Simple_Axial_Model(width parameter 6.96/300) function with Rp=9999,Rs=300
in TOPAS-Academic | |
Crystal data top
Tl2·(SeC6H2Se) | β = 84.790 (2)° |
Mr = 642.8 | γ = 88.659 (3)° |
Triclinic, P1 | V = 426.72 (1) Å3 |
a = 6.67438 (8) Å | Z = 4 |
b = 6.84998 (8) Å | Synchrotron radiation, λ = 0.699855 Å |
c = 9.82649 (10) Å | T = 298 K |
α = 72.513 (2)° | flat sheet, 8 × 17 mm |
Data collection top
Huber diffractometer | Scan method: step |
Specimen mounting: Flat plate geometry on zero-background holder. | 2θmin = 3°, 2θmax = 40°, 2θstep = 0.005° |
Data collection mode: reflection | |
Refinement top
Rp = 0.049 | 7401 data points |
Rwp = 0.056 | 94 parameters |
Rexp = 0.020 | 0 restraints |
RBragg = 0.026 | H-atom parameters not refined |
χ2 = 7.756 | |
Special details top
Experimental. In order to decrease sample absorption, the sample was mixed with finely ground cork before loading into the capillary. This diluted the sample to prevent absorption corrections as well as ensuring no preferred orientation. |
Geometry. Bond distances, angles etc. have been calculated using the rounded fractional coordinates. All suś are estimated from the variances of the (full) variance-covariance matrix. The cell e.s.d.'s are taken into account in the estimation of distances, angles and torsion angles |
Refinement. The two Se(C6H4)Se moieties were refined as z-matrices, with planar regula hexagonal symmetry imposed for the aromatic rings, located at inversion centers. Se—C bond lengths were refined, but Se atoms were fixed in the planes of the hexagons, with Se—C—C bond angles fixed at 60 °. |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Tl1 | 0.4477 (3) | 0.9039 (3) | 0.3539 (2) | 0.0500* | |
Tl2 | 0.0419 (3) | 0.5890 (3) | 0.6465 (2) | 0.0500* | |
Se1 | 0.06968 | 0.05017 | −0.34935 | 0.0015 (7)* | |
Se1A | 0.54913 | 0.55701 | −0.35070 | 0.0015 (7)* | |
C1 | 0.03022 | 0.02176 | −0.15151 | 0.0015 (7)* | |
C1A | 0.52131 | 0.52473 | −0.15209 | 0.0015 (7)* | |
C2 | 0.15899 | −0.11212 | −0.05330 | 0.0015 (7)* | |
C2A | 0.38131 | 0.37526 | −0.05822 | 0.0015 (7)* | |
C3 | 0.12877 | −0.13388 | 0.09821 | 0.0015 (7)* | |
C3A | 0.36000 | 0.35053 | 0.09387 | 0.0015 (7)* | |
H2 | 0.27768 | −0.19582 | −0.09309 | 0.0015 (7)* | |
H2A | 0.29270 | 0.28213 | −0.10169 | 0.0015 (7)* | |
H3 | 0.22490 | −0.23382 | 0.17152 | 0.0015 (7)* | |
H3A | 0.25548 | 0.23894 | 0.16394 | 0.0015 (7)* | |
Geometric parameters (Å, º) top
Tl1—Se1i | 3.2388 | C1A—C3Ai | 1.4467 |
Tl1—Se1Ai | 3.1664 | C2—C3 | 1.4467 |
Tl2—Se1ii | 3.1815 | C2A—C3A | 1.4467 |
Se1—C1 | 1.8891 | C2—H2 | 1.0800 |
Se1A—C1A | 1.8891 | C2A—H2A | 1.0800 |
C1—C2 | 1.4467 | C3—H3 | 1.0800 |
C1—C3iii | 1.4467 | C3A—H3A | 1.0800 |
C1A—C2A | 1.4467 | | |
| | | |
Tl1···Tl2 | 3.923 (3) | Se1···Tl1vii | 3.4633 |
Tl1···Se1ii | 4.0217 | Se1···Tl2vii | 3.3408 |
Tl1···Se1Aiv | 3.2660 | Se1···Se1xiii | 3.4433 |
Tl1···C3v | 3.5070 | Se1A···Tl2xiv | 3.2984 |
Tl1···C3Av | 3.4237 | Se1A···Tl1xii | 3.2660 |
Tl1···Se1Avi | 3.6839 | Se1A···Tl2xii | 3.3895 |
Tl1···C1vii | 3.8545 | Se1A···Tl1vi | 3.6839 |
Tl1···Se1vii | 3.4633 | Se1A···Se1Axv | 3.3765 |
Tl1···C1Avi | 3.8201 | C1···Tl2xii | 3.7940 |
Tl2···Se1vii | 3.3408 | C1···Tl1vii | 3.8545 |
Tl2···C3viii | 3.5010 | C1···C3Aiii | 3.5752 |
Tl2···C2Aiv | 3.7656 | C1A···C3xvi | 3.4616 |
Tl2···Tl1 | 3.923 (3) | C1A···Tl1vi | 3.8201 |
Tl2···Se1iv | 3.6794 | C1A···Tl2xiv | 3.8056 |
Tl2···Se1Aix | 3.2984 | C2A···Tl2xii | 3.7656 |
Tl2···Se1Aiv | 3.3895 | C3···Tl1xvii | 3.5070 |
Tl2···C1iv | 3.7940 | C3···Tl2viii | 3.5010 |
Tl2···C1Aix | 3.8056 | C3···C1Axvi | 3.4616 |
Tl2···C3Ax | 3.6354 | C3A···Tl2x | 3.6354 |
Se1···Tl1xi | 4.0217 | C3A···C1iii | 3.5752 |
Se1···Tl2xii | 3.6794 | C3A···Tl1xvii | 3.4237 |
| | | |
Se1i—Tl1—Se1Ai | 96.33 | C1A—C2A—C3A | 120.00 |
Tl2xi—Se1—C1 | 102.20 | C1iii—C3—C2 | 120.00 |
Tl1i—Se1—C1 | 92.41 | C1Ai—C3A—C2A | 120.00 |
Tl1i—Se1—Tl2xi | 100.07 | C1—C2—H2 | 120.00 |
Tl1i—Se1A—C1A | 101.56 | C3—C2—H2 | 120.00 |
Se1—C1—C2 | 120.00 | C1A—C2A—H2A | 120.00 |
Se1—C1—C3iii | 120.00 | C3A—C2A—H2A | 120.00 |
C2—C1—C3iii | 120.00 | C2—C3—H3 | 120.00 |
Se1A—C1A—C2A | 120.00 | C1iii—C3—H3 | 120.00 |
Se1A—C1A—C3Ai | 120.00 | C2A—C3A—H3A | 120.00 |
C2A—C1A—C3Ai | 120.00 | C1Ai—C3A—H3A | 120.00 |
C1—C2—C3 | 120.00 | | |
| | | |
Tl2xi—Se1—C1—C2 | 55.60 | Se1—C1—C3iii—C2iii | −180.00 |
Tl2xi—Se1—C1—C3iii | −124.40 | C2—C1—C3iii—C2iii | 0.00 |
Tl1i—Se1—C1—C2 | −45.24 | Se1A—C1A—C2A—C3A | 180.00 |
Tl1i—Se1—C1—C3iii | 134.76 | C3Ai—C1A—C2A—C3A | 0.00 |
Tl1i—Se1A—C1A—C2A | −42.83 | Se1A—C1A—C3Ai—C2Ai | 180.00 |
Tl1i—Se1A—C1A—C3Ai | 137.17 | C2A—C1A—C3Ai—C2Ai | 0.00 |
Se1—C1—C2—C3 | 180.00 | C1—C2—C3—C1iii | 0.00 |
C3iii—C1—C2—C3 | 0.00 | C1A—C2A—C3A—C1Ai | 0.02 |
Symmetry codes: (i) −x+1, −y+1, −z; (ii) x, y+1, z+1; (iii) −x, −y, −z; (iv) x, y, z+1; (v) x, y+1, z; (vi) −x+1, −y+2, −z; (vii) −x, −y+1, −z; (viii) −x, −y, −z+1; (ix) x−1, y, z+1; (x) −x, −y+1, −z+1; (xi) x, y−1, z−1; (xii) x, y, z−1; (xiii) −x, −y, −z−1; (xiv) x+1, y, z−1; (xv) −x+1, −y+1, −z−1; (xvi) −x+1, −y, −z; (xvii) x, y−1, z. |
Experimental details
| (Tl2SC6H4S) | (Tl2SeC6H4Se) |
Crystal data |
Chemical formula | Tl2·(SC6H2S) | Tl2·(SeC6H2Se) |
Mr | 549.0 | 642.8 |
Crystal system, space group | Triclinic, P1 | Triclinic, P1 |
Temperature (K) | 298 | 298 |
a, b, c (Å) | 6.5525 (3), 6.8444 (3), 9.5265 (2) | 6.67438 (8), 6.84998 (8), 9.82649 (10) |
α, β, γ (°) | 71.798 (2), 85.988 (2), 89.219 (2) | 72.513 (2), 84.790 (2), 88.659 (3) |
V (Å3) | 404.85 (9) | 426.72 (1) |
Z | 4 | 4 |
Radiation type | Synchrotron, λ = 0.698163 Å | Synchrotron, λ = 0.699855 Å |
µ (mm−1) | 37 | – |
Specimen shape, size (mm) | Cylinder, 8 × 0.7 | Flat sheet, 8 × 17 |
|
Data collection |
Diffractometer | Huber diffractometer | Huber diffractometer |
Specimen mounting | Sample was mounted in a thin walled glass capillary of nominal diameter 0.7 mm. | Flat plate geometry on zero-background holder. |
Data collection mode | Transmission | Reflection |
Scan method | Step | Step |
2θ values (°) | 2θmin = 2 2θmax = 30 2θstep = 0.005 | 2θmin = 3 2θmax = 40 2θstep = 0.005 |
|
Refinement |
R factors and goodness of fit | Rp = 0.070, Rwp = 0.080, Rexp = 0.065, RBragg = 0.019, χ2 = 1.484 | Rp = 0.049, Rwp = 0.056, Rexp = 0.020, RBragg = 0.026, χ2 = 7.756 |
No. of data points | 5601 | 7401 |
No. of parameters | 57 | 94 |
H-atom treatment | H-atom parameters not refined | H-atom parameters not refined |
Selected geometric parameters (Å, º) for (Tl2SC6H4S) topTl2—S1i | 3.0752 | S1—C1 | 1.7695 |
Tl1—S1Aii | 2.9379 | S1A—C1A | 1.7695 |
| | | |
Tl2i—S1—C1 | 141.47 | S1—C1—C3iii | 120.00 |
Tl1ii—S1A—C1A | 109.38 | S1A—C1A—C2A | 120.00 |
S1—C1—C2 | 120.00 | S1A—C1A—C3Aii | 120.00 |
Symmetry codes: (i) −x, −y+1, −z; (ii) −x+1, −y+1, −z; (iii) −x, −y, −z. |
Selected geometric parameters (Å, º) for (Tl2SeC6H4Se) topTl1—Se1i | 3.2388 | Se1—C1 | 1.8891 |
Tl1—Se1Ai | 3.1664 | Se1A—C1A | 1.8891 |
Tl2—Se1ii | 3.1815 | | |
| | | |
Se1i—Tl1—Se1Ai | 96.33 | Se1—C1—C2 | 120.00 |
Tl2iii—Se1—C1 | 102.20 | Se1—C1—C3iv | 120.00 |
Tl1i—Se1—C1 | 92.41 | Se1A—C1A—C2A | 120.00 |
Tl1i—Se1—Tl2iii | 100.07 | Se1A—C1A—C3Ai | 120.00 |
Tl1i—Se1A—C1A | 101.56 | | |
Symmetry codes: (i) −x+1, −y+1, −z; (ii) x, y+1, z+1; (iii) x, y−1, z−1; (iv) −x, −y, −z. |