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metal-organic compounds\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890
Volume 68| Part 6| June 2012| Pages m768-m769
doi:10.1107/S1600536812020740

Poly[[(methanol)(μ4-2,4,5,6-tetra­fluoro­benzene-1,3-di­carboxyl­ato)copper(II)] methanol monosolvate]

Dan Yana and Qian Duana*

aSchool of Materials Science and Engineering, Changchun University of Science and Technology, Changchun 130022, People's Republic of China
*Correspondence e-mail: duanqian88@hotmail.com

(Received 14 March 2012; accepted 8 May 2012; online 16 May 2012)

In the title compound, {[Cu(C8F4O4)(CH3OH)]·CH3OH}n, two CuII atoms are bridged by four carboxyl­ate groups, forming the well known paddle-wheel secondary building unit (SBU) with axial methanol ligands. In each ligand, the dihedral angles between the benzene ring and the two carboxyl­ate groups are 80.43 (17) and 62.5 (4)°. Within each SBU, the four carboxyl­ate groups come from four symmetry-equivalent tetra­fluoro­isophthalate ligands. Each tetra­fluoro­isophthalate group connects two SBUs, forming a layered structure . In the crystal, O—H⋯O hydrogen bonds involving the free and ligated methanol mol­ecules link the mol­ecules into a three-dimensional supra­molecular network.

Related literature

For background to coordination polymers, see: Kim et al. (2001[Kim, J., Chen, B., Reineke, T. M., Li, H. L., Eddaoudi, M., Moler, D. B., O'Keeffe, M. & Yaghi, O. M. (2001). J. Am. Chem. Soc. 123, 8239-8247.]); Kitagawa et al. (2004[Kitagawa, S., Kitaura, R. & Noro, S. (2004). Angew. Chem. Int. Ed. 43, 2334-2375.]). For applications of coordination polymers, see: Wang et al. (2009[Wang, Z., Chen, G. & Ding, K. (2009). Chem. Rev. 109, 322-359.]); Dincă & Long (2008[Dincă, M. & Long, J. R. (2008). Angew. Chem. Int. Ed. 47, 6766-6779.]); Furukawa et al. (2008[Furukawa, H., Kim, J., Ockwig, N. W., O'Keeffe, M. & Yaghi, O. M. (2008). J. Am. Chem. Soc. 130, 11650-11651.]). For information on fluorinated coordination polymers, see: Yang et al. (2007[Yang, C., Wang, X. & Omary, M. A. (2007). J. Am. Chem. Soc. 129, 15454-15455.]); Hulvey et al. (2009[Hulvey, Z., Falcao, E. H. L., Eckert, J. & Cheetham, A. K. (2009). J. Mater. Chem. 19, 4307-4309.]).

[Scheme 1]

Experimental

Crystal data

  • [Cu(C8F4O4)(CH4O)]·CH4O

  • Mr = 363.70

  • Monoclinic, P 21 /n

  • a = 8.6542 (7) Å

  • b = 12.1882 (10) Å

  • c = 12.4272 (10) Å

  • β = 98.390 (1)°

  • V = 1296.78 (18) Å3

  • Z = 4

  • Mo Kα radiation

  • μ = 1.76 mm−1

  • T = 200 K

  • 0.34 × 0.22 × 0.19 mm
Data collection

  • Bruker APEXII CCD area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Sheldrick, 2003[Sheldrick, G. M. (2003). SADABS. University of Göttingen, Germany.]) Tmin = 0.621, Tmax = 0.715

  • 8122 measured reflections

  • 2575 independent reflections

  • 2365 reflections with I > 2σ(I)

  • Rint = 0.017
Refinement

  • R[F2 > 2σ(F2)] = 0.033

  • wR(F2) = 0.092

  • S = 1.07

  • 2575 reflections

  • 196 parameters

  • 1 restraint

  • H atoms treated by a mixture of independent and constrained refinement

  • Δρmax = 1.05 e Å−3

  • Δρmin = −0.40 e Å−3

Table 1
Selected bond lengths (Å)

Cu1—O2i 1.9600 (18)
Cu1—O1 1.9650 (18)
Cu1—O3ii 1.9656 (18)
Cu1—O4iii 1.9734 (17)
Cu1—O5 2.0834 (19)
Symmetry codes: (i) -x+2, -y+2, -z+1; (ii) [x+{\script{1\over 2}}, -y+{\script{5\over 2}}, z+{\script{1\over 2}}]; (iii) [-x+{\script{3\over 2}}, y-{\script{1\over 2}}, -z+{\script{1\over 2}}].

Table 2
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A D⋯A D—H⋯A
O5—H5⋯O6iv 0.84 (1) 1.80 (1) 2.637 (3) 173 (4)
O6—H6⋯O4v 0.82 2.02 2.828 (3) 169
Symmetry codes: (iv) [x+{\script{1\over 2}}, -y+{\script{3\over 2}}, z+{\script{1\over 2}}]; (v) x-1, y-1, z.

Data collection: APEX2 (Bruker, 2007[Bruker (2007). APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 2007[Bruker (2007). APEX2 and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); molecular graphics: XP in SHELXTL (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); software used to prepare material for publication: SHELXL97.

Supporting information

Crystal structure: contains datablocks I, global. DOI: 10.1107/S1600536812020740/pk2400sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536812020740/pk2400Isup2.hkl

checkCIF report


Comment top

The design and synthesis of coordination polymers is an active area of research as these compounds have potential uses in gas storage, catalysis, magnetism and so on. The Omary and Cheetham groups have both reported interesting hydrogen adsorption properties in porous coordination polymers containing fluorinated ligands (Yang et al. 2007; Hulvey et al. 2009). Indeed, most of the reports to date of coordination polymers containing perfluorinated dicarboxylates involve a second ligand, which is typically a simple, nonfluorinated, nitrogen-containing molecule. The well known paddlewheel secondary building unit (M2(O2CR)4L2, M=Cu, Zn, etc.; L=terminal ligand) has been used extensively in generating porous coordination polymers. Here, we report a perfluorinated coordination polymer (I), {[Cu(C8F4O4)(CH3OH)].CH3OH}n, which is constructed using the paddlewheel SBU Cu2(O2CR)4L2 (L=CH3OH).

The asymmetric unit is composed of one CuII center, one tetrafluoroisophthalate anion, one coordinated methanol ligand, and one methanol solvent molecule (Fig. 1). Each CuII ion is five-coordinated by four oxygen donors from four different tetrafluoroisophthalate ligands and one oxygen atom from a terminal methanol molecule. In the paddlewheel SBU, the two copper ions are separated by 2.6622 (6) Å. Each SBU connects four tetrafluoroisophthalate ligands, and each tetrafluoroisophthalate group connect two SBUs to form a two dimensional layered structure (Fig. 2). Adjacent parallel layers are connected by O—H···O hydrogen bonds between guest methanol molecules and the coordinated methanol molecules to create a three-dimensional supramolecular network.

Related literature top

For background to coordination polymers, see: Kim et al. (2001); Kitagawa et al. (2004). For applications of coordination polymers, see: Wang et al. (2009); Dincă & Long (2008); Furukawa et al. (2008). For information on fluorinated coordination polymers, see: Yang et al. (2007); Hulvey et al. (2009).

Experimental top

Compound I was obtained by layering 5 ml of a methanol solution containing 2,4,5,6-tetrafluoro-1,3-benzenedicarboxylic acid (23 mg, 0.10 mmol) and 2,6-lutidine (0.034 ml, 0.30 mmol) onto 5 ml of a methanol/nitrobenzene solution (1.5:1, v/v) containing Cu(NO3)2.2.5H2O (23 mg, 0.10 mmol). Green crystals formed at the interlayer boundary within one week. After two weeks, blue block-shaped crystals of the title compound suitable for X-ray diffraction were obtained by slow diffusion of the solvents in 26% yield (9.5 mg, based on the ligand).

Refinement top

All H atoms bound to C atoms and O—H hydrogen atoms of the free methanol molecules were assigned to calculated positions with C—H = 0.96 Å, O—H = 0.82 Å, and refined using a riding model, with Uiso(H)=1.5 Ueq(C,O). O—H hydrogen atoms of the coordinated methanol molecules were found in difference Fourier maps and refined isotropically with the distance restraint: O—H = 0.85 Å and Uiso(H) = 1.5 Ueq(O).

Computing details top

Data collection: APEX2 (Bruker, 2007); cell refinement: SAINT (Bruker, 2007); data reduction: SAINT (Bruker, 2007); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: XP in SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. An ellipsoid plot (30% probability level) of the paddlewheel SBU showing the labelled asymmetric unit. Hydrogen atoms are drawn as small arbitrary spheres.
[Figure 2] Fig. 2. A view of the two-dimensional packing of the title compound, the hydrogen bonding interactions are shown as broken lines.
Poly[[(methanol)(µ4-2,4,5,6-tetrafluorobenzene-1,3- dicarboxylato)copper(II)] methanol monosolvate] top
Crystal data top
[Cu(C8F4O4)(CH4O)]·CH4OF(000) = 724
Mr = 363.70Dx = 1.863 Mg m−3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 2575 reflections
a = 8.6542 (7) Åθ = 2.4–26.1°
b = 12.1882 (10) ŵ = 1.76 mm−1
c = 12.4272 (10) ÅT = 200 K
β = 98.390 (1)°Block, green
V = 1296.78 (18) Å30.34 × 0.22 × 0.19 mm
Z = 4
Data collection top
Bruker APEXII CCD area-detector
diffractometer		2575 independent reflections
Radiation source: fine-focus sealed tube2365 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.017
Detector resolution: 9.00 pixels mm-1θmax = 26.1°, θmin = 2.4°
ϕ and ω scansh = −10→10
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)		k = −15→14
Tmin = 0.621, Tmax = 0.715l = −13→15
8122 measured reflections
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)] = 0.033Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.092H atoms treated by a mixture of independent and constrained refinement
S = 1.07 w = 1/[σ2(Fo2) + (0.0551P)2 + 1.2274P]
where P = (Fo2 + 2Fc2)/3
2575 reflections(Δ/σ)max = 0.001
196 parametersΔρmax = 1.05 e Å−3
1 restraintΔρmin = −0.40 e Å−3
Crystal data top
[Cu(C8F4O4)(CH4O)]·CH4OV = 1296.78 (18) Å3
Mr = 363.70Z = 4
Monoclinic, P21/nMo Kα radiation
a = 8.6542 (7) ŵ = 1.76 mm−1
b = 12.1882 (10) ÅT = 200 K
c = 12.4272 (10) Å0.34 × 0.22 × 0.19 mm
β = 98.390 (1)°
Data collection top
Bruker APEXII CCD area-detector
diffractometer		2575 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 2003)		2365 reflections with I > 2σ(I)
Tmin = 0.621, Tmax = 0.715Rint = 0.017
8122 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0331 restraint
wR(F2) = 0.092H atoms treated by a mixture of independent and constrained refinement
S = 1.07Δρmax = 1.05 e Å−3
2575 reflectionsΔρmin = −0.40 e Å−3
196 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
Cu10.86874 (3)0.96498 (2)0.53265 (2)0.01964 (12)
C10.8110 (3)1.2979 (2)0.4412 (2)0.0263 (5)
C20.7454 (3)1.32560 (19)0.33704 (19)0.0244 (5)
C30.6682 (3)1.4235 (2)0.30967 (19)0.0253 (5)
C40.6579 (4)1.4958 (2)0.3942 (2)0.0364 (7)
C50.7222 (5)1.4715 (2)0.4996 (2)0.0471 (9)
C60.7980 (4)1.3732 (2)0.5220 (2)0.0412 (7)
C70.8867 (3)1.18712 (19)0.46554 (18)0.0237 (5)
C80.6012 (3)1.45109 (18)0.1942 (2)0.0239 (5)
C90.6040 (4)0.8097 (3)0.5897 (3)0.0528 (9)
H9A0.50000.81110.60790.079*
H9B0.67360.77760.64850.079*
H9C0.60530.76680.52500.079*
C100.0958 (4)0.3426 (3)0.2112 (3)0.0545 (9)
H10A0.20610.35490.21570.082*
H10B0.06240.29140.15380.082*
H10C0.07350.31320.27900.082*
F10.7529 (2)1.25055 (12)0.25928 (11)0.0331 (4)
F20.5866 (3)1.59239 (14)0.37550 (13)0.0523 (5)
F30.7098 (4)1.54384 (16)0.57961 (16)0.0796 (9)
F40.8600 (3)1.35034 (16)0.62475 (14)0.0636 (6)
O10.8026 (2)1.11737 (14)0.50171 (15)0.0307 (4)
O21.0228 (2)1.17630 (14)0.44677 (15)0.0313 (4)
O30.4671 (2)1.48965 (17)0.17844 (14)0.0319 (4)
O40.6883 (2)1.43243 (16)0.12365 (13)0.0285 (4)
O50.6524 (2)0.91720 (17)0.57154 (19)0.0400 (5)
H50.601 (4)0.960 (2)0.606 (3)0.057 (12)*
O60.0148 (3)0.4435 (2)0.1894 (2)0.0569 (7)
H6−0.07810.43130.16970.085*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Cu10.02543 (18)0.01590 (18)0.01669 (18)−0.00318 (10)0.00001 (11)0.00040 (10)
C10.0362 (13)0.0189 (11)0.0219 (12)0.0017 (10)−0.0022 (10)0.0017 (9)
C20.0350 (13)0.0201 (11)0.0173 (11)0.0010 (10)0.0014 (9)−0.0004 (9)
C30.0351 (13)0.0206 (11)0.0183 (11)0.0019 (10)−0.0023 (9)0.0010 (9)
C40.0620 (19)0.0204 (13)0.0239 (13)0.0141 (13)−0.0028 (12)0.0015 (10)
C50.088 (3)0.0274 (15)0.0208 (14)0.0171 (14)−0.0073 (15)−0.0089 (10)
C60.073 (2)0.0284 (14)0.0171 (12)0.0104 (14)−0.0107 (12)0.0024 (11)
C70.0353 (13)0.0181 (11)0.0155 (11)0.0014 (9)−0.0037 (9)0.0005 (9)
C80.0335 (13)0.0162 (11)0.0200 (12)0.0003 (9)−0.0022 (10)−0.0006 (9)
C90.0485 (19)0.0407 (18)0.070 (2)−0.0086 (14)0.0117 (17)0.0131 (16)
C100.0519 (19)0.061 (2)0.049 (2)−0.0095 (17)0.0024 (15)0.0140 (17)
F10.0550 (10)0.0226 (7)0.0197 (7)0.0083 (6)−0.0017 (6)−0.0035 (6)
F20.0966 (15)0.0268 (8)0.0287 (9)0.0282 (9)−0.0068 (9)−0.0013 (7)
F30.166 (3)0.0405 (12)0.0247 (10)0.0440 (13)−0.0131 (12)−0.0126 (8)
F40.1242 (19)0.0373 (10)0.0196 (8)0.0251 (11)−0.0217 (9)−0.0025 (7)
O10.0374 (10)0.0191 (8)0.0356 (10)0.0020 (7)0.0055 (8)0.0043 (7)
O20.0369 (10)0.0207 (8)0.0359 (10)0.0013 (7)0.0046 (8)0.0085 (7)
O30.0376 (10)0.0376 (10)0.0192 (9)0.0111 (8)0.0001 (7)0.0032 (8)
O40.0319 (9)0.0330 (9)0.0190 (8)0.0050 (8)−0.0016 (7)0.0054 (7)
O50.0375 (11)0.0297 (10)0.0566 (13)−0.0091 (8)0.0192 (10)−0.0092 (9)
O60.0374 (12)0.0643 (15)0.0666 (17)−0.0080 (11)−0.0002 (11)0.0208 (13)
Geometric parameters (Å, º) top
Cu1—O2i1.9600 (18)C7—O21.241 (3)
Cu1—O11.9650 (18)C7—O11.245 (3)
Cu1—O3ii1.9656 (18)C8—O31.240 (3)
Cu1—O4iii1.9734 (17)C8—O41.258 (3)
Cu1—O52.0834 (19)C9—O51.404 (4)
Cu1—Cu1i2.6622 (6)C9—H9A0.9600
C1—C61.377 (4)C9—H9B0.9600
C1—C21.378 (3)C9—H9C0.9600
C1—C71.512 (3)C10—O61.422 (5)
C2—F11.339 (3)C10—H10A0.9600
C2—C31.385 (3)C10—H10B0.9600
C3—C41.384 (4)C10—H10C0.9600
C3—C81.505 (3)O2—Cu1i1.9600 (18)
C4—F21.334 (3)O3—Cu1iv1.9656 (18)
C4—C51.379 (4)O4—Cu1v1.9733 (17)
C5—F31.344 (3)O5—H50.842 (10)
C5—C61.375 (4)O6—H60.8200
C6—F41.340 (3)
O2i—Cu1—O1167.50 (8)F4—C6—C5119.1 (3)
O2i—Cu1—O3ii89.55 (8)F4—C6—C1119.5 (2)
O1—Cu1—O3ii89.38 (8)C5—C6—C1121.4 (2)
O2i—Cu1—O4iii89.89 (8)O2—C7—O1128.0 (2)
O1—Cu1—O4iii88.48 (8)O2—C7—C1116.9 (2)
O3ii—Cu1—O4iii167.51 (8)O1—C7—C1115.0 (2)
O2i—Cu1—O598.84 (8)O3—C8—O4126.9 (2)
O1—Cu1—O593.64 (8)O3—C8—C3117.2 (2)
O3ii—Cu1—O598.51 (8)O4—C8—C3115.9 (2)
O4iii—Cu1—O593.91 (8)O5—C9—H9A109.5
O2i—Cu1—Cu1i84.70 (5)O5—C9—H9B109.5
O1—Cu1—Cu1i82.79 (6)H9A—C9—H9B109.5
O3ii—Cu1—Cu1i85.21 (6)O5—C9—H9C109.5
O4iii—Cu1—Cu1i82.31 (5)H9A—C9—H9C109.5
O5—Cu1—Cu1i174.85 (7)H9B—C9—H9C109.5
C6—C1—C2117.1 (2)O6—C10—H10A109.5
C6—C1—C7121.9 (2)O6—C10—H10B109.5
C2—C1—C7120.9 (2)H10A—C10—H10B109.5
F1—C2—C1117.0 (2)O6—C10—H10C109.5
F1—C2—C3118.9 (2)H10A—C10—H10C109.5
C1—C2—C3124.0 (2)H10B—C10—H10C109.5
C4—C3—C2116.4 (2)C7—O1—Cu1123.16 (17)
C4—C3—C8121.5 (2)C7—O2—Cu1i121.24 (15)
C2—C3—C8122.1 (2)C8—O3—Cu1iv121.44 (17)
F2—C4—C5117.8 (2)C8—O4—Cu1v124.10 (16)
F2—C4—C3120.6 (2)C9—O5—Cu1126.70 (19)
C5—C4—C3121.5 (2)C9—O5—H5108 (3)
F3—C5—C6120.6 (3)Cu1—O5—H5120 (3)
F3—C5—C4119.8 (3)C10—O6—H6109.5
C6—C5—C4119.6 (3)
Symmetry codes: (i) −x+2, −y+2, −z+1; (ii) x+1/2, −y+5/2, z+1/2; (iii) −x+3/2, y−1/2, −z+1/2; (iv) x−1/2, −y+5/2, z−1/2; (v) −x+3/2, y+1/2, −z+1/2.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O5—H5···O6vi0.84 (1)1.80 (1)2.637 (3)173 (4)
O6—H6···O4vii0.822.022.828 (3)169
Symmetry codes: (vi) x+1/2, −y+3/2, z+1/2; (vii) x−1, y−1, z.

Experimental details

Crystal data
Chemical formula[Cu(C8F4O4)(CH4O)]·CH4O
Mr363.70
Crystal system, space groupMonoclinic, P21/n
Temperature (K)200
a, b, c (Å)8.6542 (7), 12.1882 (10), 12.4272 (10)
β (°) 98.390 (1)
V (Å3)1296.78 (18)
Z4
Radiation typeMo Kα
µ (mm−1)1.76
Crystal size (mm)0.34 × 0.22 × 0.19
Data collection
DiffractometerBruker APEXII CCD area-detector
diffractometer
Absorption correctionMulti-scan
(SADABS; Sheldrick, 2003)
Tmin, Tmax0.621, 0.715
No. of measured, independent and
observed [I > 2σ(I)] reflections		8122, 2575, 2365
Rint0.017
(sin θ/λ)max (Å−1)0.620
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.033, 0.092, 1.07
No. of reflections2575
No. of parameters196
No. of restraints1
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å−3)1.05, −0.40

Computer programs: APEX2 (Bruker, 2007), SAINT (Bruker, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), XP in SHELXTL (Sheldrick, 2008).

Selected bond lengths (Å) top
Cu1—O2i1.9600 (18)Cu1—O4iii1.9734 (17)
Cu1—O11.9650 (18)Cu1—O52.0834 (19)
Cu1—O3ii1.9656 (18)
Symmetry codes: (i) −x+2, −y+2, −z+1; (ii) x+1/2, −y+5/2, z+1/2; (iii) −x+3/2, y−1/2, −z+1/2.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O5—H5···O6iv0.842 (10)1.800 (12)2.637 (3)173 (4)
O6—H6···O4v0.822.022.828 (3)169.0
Symmetry codes: (iv) x+1/2, −y+3/2, z+1/2; (v) x−1, y−1, z.
 

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ISSN: 2056-9890
Volume 68| Part 6| June 2012| Pages m768-m769
doi:10.1107/S1600536812020740
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