supplementary materials


hb2681 scheme

Acta Cryst. (2008). E64, m338-m339    [ doi:10.1107/S1600536807068651 ]

[1,2-Bis(dimethylphosphino)ethane]carbonyl([eta]5-cyclopentadienyl)iron(II) diphenylphosphinoylborate

K. Lee, A. J. Lough and I. Manners

Abstract top

In the title compound, [Fe(C5H5)(C6H16P2)(CO)](C12H13BOP), the FeII ion adopts a three-legged piano-stool geometry, with Fe...Cg = 1.721 (5)Å (Cg = the centroid defined by the C atoms of the cyclopentadienyl ring). The 1,2-bis(dimethylphosphino)ethane (dmpe) ligand chelates to form a five-membered C2P2Fe ring which is in a pseudo-half-chair conformation. In the crystal structure, associations of one cation and two anions are formed via weak intermolecular C-H...O hydrogen bonds, giving rise to R42(9) rings.

Comment top

The mechanism for the metal catalyzed dehydrocoupling of phosphine-borane adducts has been studied by investigating the synthesis and reactivity of model complexes. The P—H bond oxidative addition of RPhPH-BH3 to Pt(PEt3)3 has been reported as well as the phosphine-borane ligand-exchange reaction at the Pt centre of cis-[PtH(PPh2.BH3) (depe)] (Jaska et al., 2003). Model complexes such as cis-[PtH(PPhH.BH3)(dcype)] [dcype = 1,2-bis(dicyclohexylphosphino)ethane] have been synthesized via dehydrocoupling routes involving Pt—H and P—H bonds of cis-[PtH2(dcype)] and PhPH2.BH3 respectively (Jaska et al., 2005). The reactivity of CpFe(CO)2PPh2.BH3, (I), (Kuckmann et al., 2007) [see Fig. 3] was probed as a potential model complex in the study of the mechanism of the dehydrocoupling of phosphine-borane adducts: the CO ligands might dissociate to promote a reaction with phosphine-borane adducts. Before reacting (I) with phosphine-borane adducts, dmpe (1,2-bis(dimethylphosphino)ethane) was added in excess to (I) to observe the lability of the CO ligands. When adventitious air was also introduced to this reaction in THF, the title compound, (II), (Fig. 1), was formed. A similar complex, Cp*Fe(dmpe)X (X = H, CH3 or Cl) was reported earlier (Paciello et al., 1990).

The Fe atom in (II) is bonded to a cyclopentadienyl (cp) ring with Fe···Cg = 1.721 (5)Å (Cg = the centroid of C1—C5), a carbonyl group and the bis-chelating (dimethylphosphino)ethane (dmpe) ligand (Table 1). In the crystal of (II), weak intermolecular C—H···O hydrogen bonds (Table 2) form rings with graph set assignment R24(9) (Bernstein et al., 1995) created in a three component cluster of two anions and one cation (Fig. 2).

Related literature top

For related literature, see: Jaska et al. (2003, 2005); Kuckmann et al. (2007); Paciello et al. (1990). For background on graph-set theory, see: Bernstein et al. (1995).

Experimental top

The complex CpFe(CO)2PPh2.BH3 (200 mg, 0.532 mmol) was dissolved in 1.8 ml THF in a round bottom Schlenk flask. This yellow solution turned orange upon addition of dmpe (0.150 ml, 0.899 mmol). After 8 days of stirring at 293 K, orange precipitate was observed in the solution. The solution was filter cannulated into a new flask and then the volatile components of the reaction mixture were removed in vacuo overnight. The product was purified by chromatography with a column of celite (0.5 cm × 1.5 cm) supported on glass wool with hexanes (4 ml), Et2O (5 ml) and then THF (4 ml). The product in THF afforded pale yellow needles of (II) due to adventitious air.

Refinement top

All hydrogen atoms bonded to C were placed in calculated positions with C—H = 0.95–1.00 Å and refined as riding with Uiso(H) = 1.2Ueq(C) or 1.5Ueq(Cmethyl). The H atoms bonded to B1 were refined independently with isotropic displacement parameters.

Computing details top

Data collection: Collect (Nonius, 1997-2002); cell refinement: DENZO-SMN (Otwinowski & Minor, 1997); data reduction: DENZO-SMN (Otwinowski & Minor, 1997); program(s) used to solve structure: SIR92 (Altomare et al., 1994); program(s) used to refine structure: SHELXTL (Sheldrick, 2001); molecular graphics: PLATON (Spek, 2003) and SHELXTL (Sheldrick, 2001); software used to prepare material for publication: SHELXTL (Sheldrick, 2001).

Figures top
[Figure 1] Fig. 1. The molecular structure of (II) with displacement ellipsoids drawn at the 30% probability level. H atoms bonded to C atoms are not shown.
[Figure 2] Fig. 2. Part of the crystal structure of (II) showing hydrogen bonds as thin lines. Only the H atoms bonded to B atoms and those involved in hydrogen bonding are shown.
[Figure 3] Fig. 3. The reaction scheme.
[1,2-Bis(dimethylphosphino)ethane]carbonyl(η5-cyclopentadienyl)iron(II) diphenylphosphinoylborate top
Crystal data top
[Fe(C5H5)(C6H16P2)(CO)](C12H13BOP)Z = 2
Mr = 514.08F000 = 540
Triclinic, P1Dx = 1.341 Mg m3
Hall symbol: -P 1Mo Kα radiation
λ = 0.71073 Å
a = 9.0244 (5) ÅCell parameters from 8558 reflections
b = 11.4671 (4) Åθ = 2.6–25.0º
c = 14.0568 (7) ŵ = 0.80 mm1
α = 67.491 (3)ºT = 150 (1) K
β = 81.155 (2)ºCut needle, pale yellow
γ = 71.497 (3)º0.20 × 0.14 × 0.12 mm
V = 1273.50 (11) Å3
Data collection top
Nonius KappaCCD
diffractometer
4217 independent reflections
Radiation source: fine-focus sealed tube2935 reflections with I > 2σ(I)
Monochromator: graphiteRint = 0.091
Detector resolution: 9 pixels mm-1θmax = 25.0º
T = 150(1) Kθmin = 2.6º
φ scans and ω scans with κ offsetsh = 10→10
Absorption correction: multi-scan
(SORTAV; Blessing, 1995)
k = 12→13
Tmin = 0.521, Tmax = 0.943l = 16→16
8558 measured reflections
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.058H atoms treated by a mixture of
independent and constrained refinement
wR(F2) = 0.176  w = 1/[σ2(Fo2) + (0.0844P)2 + 1.3773P]
where P = (Fo2 + 2Fc2)/3
S = 1.05(Δ/σ)max = 0.002
4217 reflectionsΔρmax = 0.81 e Å3
296 parametersΔρmin = 0.79 e Å3
Primary atom site location: structure-invariant direct methodsExtinction correction: none
Crystal data top
[Fe(C5H5)(C6H16P2)(CO)](C12H13BOP)γ = 71.497 (3)º
Mr = 514.08V = 1273.50 (11) Å3
Triclinic, P1Z = 2
a = 9.0244 (5) ÅMo Kα
b = 11.4671 (4) ŵ = 0.80 mm1
c = 14.0568 (7) ÅT = 150 (1) K
α = 67.491 (3)º0.20 × 0.14 × 0.12 mm
β = 81.155 (2)º
Data collection top
Nonius KappaCCD
diffractometer
4217 independent reflections
Absorption correction: multi-scan
(SORTAV; Blessing, 1995)
2935 reflections with I > 2σ(I)
Tmin = 0.521, Tmax = 0.943Rint = 0.091
8558 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.058296 parameters
wR(F2) = 0.176H atoms treated by a mixture of
independent and constrained refinement
S = 1.05Δρmax = 0.81 e Å3
4217 reflectionsΔρmin = 0.79 e Å3
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
Fe10.22249 (8)0.31967 (6)0.79005 (5)0.0227 (2)
P10.03606 (15)0.38455 (12)0.78938 (10)0.0256 (3)
P20.20337 (15)0.11946 (11)0.82546 (10)0.0231 (3)
O10.2462 (5)0.3727 (4)0.5707 (3)0.0444 (10)
C10.4180 (6)0.3862 (5)0.7772 (4)0.0339 (13)
H1A0.48620.41080.71390.041*
C20.4403 (6)0.2587 (5)0.8551 (4)0.0294 (12)
H2A0.52700.17790.85680.035*
C30.3203 (6)0.2692 (5)0.9321 (4)0.0319 (13)
H3A0.30630.19650.99740.038*
C40.2271 (6)0.4001 (5)0.9012 (4)0.0305 (12)
H4A0.13360.43570.94090.037*
C50.2834 (6)0.4729 (5)0.8063 (4)0.0326 (13)
H5A0.24000.56910.76740.039*
C60.1017 (6)0.2512 (5)0.7849 (4)0.0328 (12)
H6A0.21340.26310.80710.039*
H6B0.08930.25060.71380.039*
C70.0015 (6)0.1229 (5)0.8573 (4)0.0301 (12)
H7A0.02120.04710.84920.036*
H7B0.02750.11720.92970.036*
C80.1254 (7)0.5297 (5)0.6827 (4)0.0397 (14)
H8A0.23940.54770.69020.060*
H8B0.08910.51490.61780.060*
H8C0.09610.60520.68240.060*
C90.1446 (6)0.4183 (6)0.9003 (4)0.0372 (13)
H9A0.25440.42330.89770.056*
H9B0.13770.50220.89960.056*
H9C0.10030.34760.96360.056*
C100.2542 (6)0.0595 (5)0.7200 (4)0.0337 (13)
H10A0.22840.02370.73980.051*
H10B0.36650.04530.70310.051*
H10C0.19520.12440.65960.051*
C110.3108 (6)0.0181 (5)0.9308 (4)0.0318 (12)
H11A0.28590.09840.93800.048*
H11B0.28120.00010.99500.048*
H11C0.42330.03000.91630.048*
C120.2342 (6)0.3517 (4)0.6586 (4)0.0275 (12)
P30.21995 (16)0.08074 (12)0.22685 (10)0.0265 (3)
O20.3092 (5)0.0325 (4)0.1455 (3)0.0482 (11)
C130.3424 (6)0.1487 (4)0.2728 (4)0.0246 (11)
C140.4211 (6)0.2322 (5)0.1986 (4)0.0287 (12)
H14A0.40800.25340.12760.034*
C150.5184 (6)0.2844 (5)0.2277 (4)0.0346 (13)
H15A0.57140.34120.17650.042*
C160.5383 (6)0.2541 (5)0.3308 (4)0.0332 (12)
H16A0.60640.28860.35050.040*
C170.4598 (6)0.1742 (5)0.4046 (4)0.0328 (13)
H17A0.47210.15500.47540.039*
C180.3619 (6)0.1208 (5)0.3767 (4)0.0283 (12)
H18A0.30820.06530.42850.034*
C200.2031 (6)0.0630 (4)0.3411 (4)0.0249 (11)
C210.0648 (6)0.0653 (5)0.4012 (4)0.0303 (12)
H21A0.02290.01070.38580.036*
C220.0560 (7)0.1787 (5)0.4833 (4)0.0355 (13)
H22A0.03840.18000.52380.043*
C230.1819 (7)0.2897 (5)0.5070 (4)0.0348 (13)
H23A0.17410.36720.56310.042*
C240.3195 (6)0.2878 (5)0.4489 (4)0.0351 (13)
H24A0.40720.36370.46590.042*
C250.3308 (6)0.1761 (5)0.3662 (4)0.0310 (12)
H25A0.42570.17610.32620.037*
B10.0223 (8)0.2119 (6)0.1944 (5)0.0338 (14)
H10.045 (6)0.298 (5)0.132 (4)0.030 (13)*
H20.037 (7)0.166 (6)0.160 (5)0.062 (18)*
H30.020 (6)0.244 (5)0.265 (4)0.043 (15)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Fe10.0241 (4)0.0196 (4)0.0260 (4)0.0091 (3)0.0030 (3)0.0068 (3)
P10.0240 (7)0.0230 (7)0.0301 (7)0.0048 (5)0.0049 (6)0.0097 (6)
P20.0233 (7)0.0193 (7)0.0280 (7)0.0083 (5)0.0021 (5)0.0077 (5)
O10.061 (3)0.040 (2)0.027 (2)0.012 (2)0.0033 (19)0.0081 (17)
C10.033 (3)0.037 (3)0.037 (3)0.023 (3)0.003 (2)0.007 (2)
C20.030 (3)0.024 (3)0.037 (3)0.008 (2)0.011 (2)0.009 (2)
C30.045 (3)0.032 (3)0.029 (3)0.024 (3)0.007 (3)0.008 (2)
C40.034 (3)0.036 (3)0.035 (3)0.015 (2)0.001 (2)0.024 (2)
C50.034 (3)0.026 (3)0.046 (3)0.015 (2)0.007 (3)0.014 (2)
C60.018 (3)0.039 (3)0.052 (3)0.012 (2)0.002 (2)0.025 (3)
C70.025 (3)0.028 (3)0.045 (3)0.013 (2)0.001 (2)0.017 (2)
C80.034 (3)0.033 (3)0.038 (3)0.004 (2)0.011 (3)0.006 (2)
C90.029 (3)0.050 (3)0.038 (3)0.011 (3)0.005 (2)0.024 (3)
C100.040 (3)0.024 (3)0.039 (3)0.010 (2)0.003 (3)0.013 (2)
C110.037 (3)0.021 (3)0.034 (3)0.009 (2)0.005 (2)0.004 (2)
C120.031 (3)0.017 (3)0.034 (3)0.008 (2)0.007 (2)0.005 (2)
P30.0302 (8)0.0211 (7)0.0302 (7)0.0117 (6)0.0063 (6)0.0059 (5)
O20.058 (3)0.043 (2)0.048 (3)0.021 (2)0.001 (2)0.0176 (19)
C130.027 (3)0.017 (3)0.028 (3)0.003 (2)0.006 (2)0.007 (2)
C140.032 (3)0.025 (3)0.029 (3)0.012 (2)0.004 (2)0.006 (2)
C150.036 (3)0.030 (3)0.042 (3)0.017 (2)0.002 (3)0.011 (2)
C160.034 (3)0.030 (3)0.044 (3)0.016 (2)0.007 (3)0.014 (2)
C170.037 (3)0.027 (3)0.035 (3)0.007 (2)0.012 (2)0.009 (2)
C180.029 (3)0.021 (3)0.032 (3)0.009 (2)0.002 (2)0.007 (2)
C200.028 (3)0.027 (3)0.028 (3)0.015 (2)0.008 (2)0.011 (2)
C210.025 (3)0.029 (3)0.038 (3)0.008 (2)0.003 (2)0.012 (2)
C220.032 (3)0.037 (3)0.038 (3)0.015 (3)0.004 (2)0.012 (2)
C230.048 (4)0.030 (3)0.027 (3)0.021 (3)0.002 (3)0.005 (2)
C240.036 (3)0.028 (3)0.038 (3)0.005 (2)0.011 (3)0.008 (2)
C250.031 (3)0.029 (3)0.033 (3)0.008 (2)0.000 (2)0.012 (2)
B10.034 (4)0.029 (3)0.039 (4)0.010 (3)0.007 (3)0.010 (3)
Geometric parameters (Å, °) top
Fe1—C121.733 (5)C10—H10A0.9800
Fe1—P12.2129 (15)C10—H10B0.9800
Fe1—P22.2133 (13)C10—H10C0.9800
Fe1—C22.093 (5)C11—H11A0.9800
Fe1—C12.093 (5)C11—H11B0.9800
Fe1—C52.097 (5)C11—H11C0.9800
Fe1—C32.105 (5)P3—O21.477 (4)
Fe1—C42.107 (5)P3—C201.837 (5)
P1—C81.811 (5)P3—C131.844 (5)
P1—C91.815 (5)P3—B11.917 (6)
P1—C61.831 (5)C13—C181.396 (7)
P2—C101.804 (5)C13—C141.396 (7)
P2—C111.818 (5)C14—C151.388 (7)
P2—C71.826 (5)C14—H14A0.9500
O1—C121.160 (6)C15—C161.382 (7)
C1—C51.422 (7)C15—H15A0.9500
C1—C21.426 (7)C16—C171.369 (7)
C1—H1A1.0000C16—H16A0.9500
C2—C31.418 (7)C17—C181.394 (7)
C2—H2A1.0000C17—H17A0.9500
C3—C41.401 (7)C18—H18A0.9500
C3—H3A1.0000C20—C211.397 (7)
C4—C51.394 (7)C20—C251.401 (7)
C4—H4A1.0000C21—C221.385 (7)
C5—H5A1.0000C21—H21A0.9500
C6—C71.521 (7)C22—C231.377 (8)
C6—H6A0.9900C22—H22A0.9500
C6—H6B0.9900C23—C241.379 (7)
C7—H7A0.9900C23—H23A0.9500
C7—H7B0.9900C24—C251.381 (7)
C8—H8A0.9800C24—H24A0.9500
C8—H8B0.9800C25—H25A0.9500
C8—H8C0.9800B1—H11.09 (5)
C9—H9A0.9800B1—H21.12 (6)
C9—H9B0.9800B1—H31.15 (5)
C9—H9C0.9800
C12—Fe1—C2113.6 (2)P2—C7—H7A110.1
C12—Fe1—C190.6 (2)C6—C7—H7B110.1
C2—Fe1—C139.84 (19)P2—C7—H7B110.1
C12—Fe1—C5105.3 (2)H7A—C7—H7B108.4
C2—Fe1—C566.7 (2)P1—C8—H8A109.5
C1—Fe1—C539.7 (2)P1—C8—H8B109.5
C12—Fe1—C3153.0 (2)H8A—C8—H8B109.5
C2—Fe1—C339.5 (2)P1—C8—H8C109.5
C1—Fe1—C366.1 (2)H8A—C8—H8C109.5
C5—Fe1—C365.9 (2)H8B—C8—H8C109.5
C12—Fe1—C4143.2 (2)P1—C9—H9A109.5
C2—Fe1—C465.7 (2)P1—C9—H9B109.5
C1—Fe1—C465.4 (2)H9A—C9—H9B109.5
C5—Fe1—C438.7 (2)P1—C9—H9C109.5
C3—Fe1—C438.9 (2)H9A—C9—H9C109.5
C12—Fe1—P191.01 (17)H9B—C9—H9C109.5
C2—Fe1—P1155.10 (15)P2—C10—H10A109.5
C1—Fe1—P1142.78 (15)P2—C10—H10B109.5
C5—Fe1—P1104.63 (15)H10A—C10—H10B109.5
C3—Fe1—P1115.69 (16)P2—C10—H10C109.5
C4—Fe1—P192.67 (15)H10A—C10—H10C109.5
C12—Fe1—P291.92 (15)H10B—C10—H10C109.5
C2—Fe1—P295.99 (14)P2—C11—H11A109.5
C1—Fe1—P2130.86 (15)P2—C11—H11B109.5
C5—Fe1—P2159.26 (15)H11A—C11—H11B109.5
C3—Fe1—P293.58 (14)P2—C11—H11C109.5
C4—Fe1—P2124.82 (15)H11A—C11—H11C109.5
P1—Fe1—P286.24 (5)H11B—C11—H11C109.5
C8—P1—C9102.6 (3)O1—C12—Fe1178.2 (5)
C8—P1—C6106.0 (3)O2—P3—C20107.9 (2)
C9—P1—C6103.3 (3)O2—P3—C13108.6 (2)
C8—P1—Fe1117.0 (2)C20—P3—C13101.9 (2)
C9—P1—Fe1118.65 (19)O2—P3—B1118.6 (3)
C6—P1—Fe1107.95 (17)C20—P3—B1111.6 (3)
C10—P2—C11102.7 (2)C13—P3—B1106.9 (2)
C10—P2—C7104.4 (2)C18—C13—C14118.5 (4)
C11—P2—C7104.9 (2)C18—C13—P3124.1 (4)
C10—P2—Fe1115.38 (18)C14—C13—P3117.5 (4)
C11—P2—Fe1119.88 (17)C15—C14—C13120.6 (5)
C7—P2—Fe1108.14 (16)C15—C14—H14A119.7
C5—C1—C2108.0 (5)C13—C14—H14A119.7
C5—C1—Fe170.3 (3)C16—C15—C14120.2 (5)
C2—C1—Fe170.1 (3)C16—C15—H15A119.9
C5—C1—H1A126.0C14—C15—H15A119.9
C2—C1—H1A126.0C17—C16—C15120.0 (5)
Fe1—C1—H1A126.0C17—C16—H16A120.0
C3—C2—C1107.2 (5)C15—C16—H16A120.0
C3—C2—Fe170.7 (3)C16—C17—C18120.5 (5)
C1—C2—Fe170.1 (3)C16—C17—H17A119.7
C3—C2—H2A126.4C18—C17—H17A119.7
C1—C2—H2A126.4C17—C18—C13120.2 (5)
Fe1—C2—H2A126.4C17—C18—H18A119.9
C4—C3—C2107.8 (4)C13—C18—H18A119.9
C4—C3—Fe170.7 (3)C21—C20—C25118.8 (4)
C2—C3—Fe169.8 (3)C21—C20—P3122.2 (4)
C4—C3—H3A126.1C25—C20—P3118.9 (4)
C2—C3—H3A126.1C22—C21—C20119.7 (5)
Fe1—C3—H3A126.1C22—C21—H21A120.1
C5—C4—C3109.6 (5)C20—C21—H21A120.1
C5—C4—Fe170.3 (3)C23—C22—C21121.0 (5)
C3—C4—Fe170.5 (3)C23—C22—H22A119.5
C5—C4—H4A125.2C21—C22—H22A119.5
C3—C4—H4A125.2C22—C23—C24119.6 (5)
Fe1—C4—H4A125.2C22—C23—H23A120.2
C4—C5—C1107.3 (5)C24—C23—H23A120.2
C4—C5—Fe171.0 (3)C23—C24—C25120.5 (5)
C1—C5—Fe170.0 (3)C23—C24—H24A119.8
C4—C5—H5A126.3C25—C24—H24A119.8
C1—C5—H5A126.3C24—C25—C20120.4 (5)
Fe1—C5—H5A126.3C24—C25—H25A119.8
C7—C6—P1107.3 (3)C20—C25—H25A119.8
C7—C6—H6A110.3P3—B1—H1107 (3)
P1—C6—H6A110.3P3—B1—H2101 (3)
C7—C6—H6B110.3H1—B1—H2107 (4)
P1—C6—H6B110.3P3—B1—H3107 (3)
H6A—C6—H6B108.5H1—B1—H3106 (4)
C6—C7—P2108.1 (3)H2—B1—H3127 (4)
C6—C7—H7A110.1
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
C2—H2A···O2i1.002.413.389 (7)167
C3—H3A···O2ii1.002.203.197 (7)172
C11—H11B···O2ii0.982.353.281 (7)159
C11—H11C···O2i0.982.433.403 (7)171
Symmetry codes: (i) −x+1, −y, −z+1; (ii) x, y, z+1.
Table 1
Selected geometric parameters (Å)
top
Fe1—C121.733 (5)Fe1—P22.2133 (13)
Fe1—P12.2129 (15)
Table 2
Hydrogen-bond geometry (Å, °)
top
D—H···AD—HH···AD···AD—H···A
C2—H2A···O2i1.002.413.389 (7)167
C3—H3A···O2ii1.002.203.197 (7)172
C11—H11B···O2ii0.982.353.281 (7)159
C11—H11C···O2i0.982.433.403 (7)171
Symmetry codes: (i) −x+1, −y, −z+1; (ii) x, y, z+1.
Acknowledgements top

IM thanks the EPSRC, the University of Bristol for start-up funds, the European Union for a Marie Curie Chair and the Royal Society for a Wolfson Research Merit Award for financial support. AJL acknowledges NSERC Canada and the University of Toronto for funding.

references
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