supplementary materials


dn2260 scheme

Acta Cryst. (2007). E63, m2935-m2936    [ doi:10.1107/S1600536807055894 ]

Di-[mu]-methoxo-bis[aquadimethoxonitrosylmolybdenum(II)]

J. Bucher, O. Blacque and H. Berke

Abstract top

The title complex, [Mo2(CH3O)6(NO)2(H2O)2], is a pseudocentrosymmetric dimer. The MoII centres are bridged by two methoxo groups and adopt distorted octahedral geometries. The crystal structure exhibits two intramolecular O-H...O contacts (O...O < 3.0 Å) between coordinated water molecules and methoxo groups. One H atom of each water molecule is disordered equally over two sites.

Comment top

The molybdenum dimer (I) exhibits a planar central four-membered Mo2O2 ring (torsional angle of 1.33 (11)°) with a Mo—Mo distance of 3.3933 (7) Å excluding any metal–metal bond. The nitrosyl ligands are nearly linear (176.7 (3) and 175.2 (3)°) and coordinated in trans positions to the methoxy bridges as observed in [Mo2(C5H5)2(OMe)2(CH2SiMe3)2(NO)2] (Hayton et al., 2002). Two terminal methoxo ligands complete the nearly planar core [Mo2(µ-OMe)2(NO)2(OMe)2] whereas the two other ones are almost perpendicular to this plane and trans to coordinated water molecules. The Mo—Oaq bond distances of 2.269 (4) Å and 2.274 (4) Å are longer than the reported unweighted mean of 2.201 Å (Orpen et al., 1989).

In this conformation we observe two intramolecular O—H···H contacts (H10A···O4 = 2.06 (3) Å, O10···O4 = 2.929 (5) Å; H5A···O8 = 2.24 (6) Å, O5···O8 = 2.991 (5) Å) between the methoxo groups and the water molecules located on the same side of the Mo2O2 plane (Fig. 1). The other water H atoms are positionally disordered and form intermolecular hydrogen bonds with oxygen atoms of the nitrosyl groups and of one terminal methoxo ligand (O···O < 3.3 Å).

Related literature top

For related di-µ-methoxo-bis(nitrosylmolybdenum) complexes, see: Hayton et al. (2002). For related di-µ-methoxo-bis(dimethoxomolybdenum) complexes, see: Kessler et al. (1993); Clegg et al. (1996); Bardina et al. (2006). For related di-µ-methoxo-bis(methoxomolybdenum) complexes, see: Hsieh & Zubieta (1987); Chilou et al. (1989). For reference bond lengths, see: Orpen et al. (1989).

Experimental top

Two equivalents of sodium hydroxide were added to a methanol solution of Mo(NO)2(Cl)2 in order to produce Mo(NO)2(OH)2(MeOH)2. The green solution was slowly added to two equivalents of 1,3,5-triaza-7-phosphaadamantate (PTA) partly dissolved in methanol and the colour of the solution turned red within one hour. The IR spectrum of the reaction solution exhibited a strong NO band at 1638 cm−1 indicating loss of one nitrosyl ligand from the molybdenum coordination sphere. Also the solid-state IR (ATR) spectrum of the soluble part revealed a ν(NO) absorption at 1640 cm-1 and a very weak one at 1620 cm−1, and additionally a strong ν(CO) band at 1037 cm−1 and a few other signals attributable to PTA and to the corresponding phosphine oxyde (OPTA). The compounds soluble in methanol were redissolved in dichloromethane and red crystals of compound [Mo(µ-OMe)(OMe)2(NO)(H2O)]2 (I) co-crystallized together with PTA and OPTA.

Refinement top

While the hydrogen atoms attached to carbon atoms were placed in geometrically calculated positions, those on water molecules were located in a difference Fourier map and then refined with the O—H distances restrained to 0.86 (2) Å. Three residual peaks could be attributed to H atoms for each coordinated water molecules. The positional disorders were refined with H5A and H10A with occupancy factors as unity and the second hydrogen atoms occupying two sites, H5B/H5C and H10B/H10C (occupancy factors of 1/2). Except H5A and H10A, all H atoms were included in the refinement with Uiso values of 1.3Ueq (parent atom).

Computing details top

Data collection: IPDS Software (Stoe & Cie, 1998); cell refinement: IPDS Software (Stoe & Cie, 1998); data reduction: X-RED (Stoe & Cie, 1998); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: WinGX (Farrugia, 1999), SHELXL97 (Sheldrick, 1997).

Figures top
[Figure 1] Fig. 1. The molecular structure of (I) with the atom-labeling scheme. Displacement ellipsoids are drawn at the 30% probability level.
Di-µ-methoxo-bis[aquadimethoxonitrosylmolybdenum(II)] top
Crystal data top
[Mo2(CH3O)6(NO)2(H2O)2]F000 = 944
Mr = 474.14Dx = 1.91 Mg m3
Monoclinic, P21/cMo Kα radiation
λ = 0.71073 Å
Hall symbol: -P 2ybcCell parameters from 7998 reflections
a = 8.7567 (13) Åθ = 2.8–30.3º
b = 15.6682 (17) ŵ = 1.56 mm1
c = 12.5488 (18) ÅT = 183 (2) K
β = 106.750 (16)ºPrism, red
V = 1648.7 (4) Å30.5 × 0.45 × 0.43 mm
Z = 4
Data collection top
Stoe IPDS
diffractometer
Rint = 0.085
φ rotation scanθmax = 28º
Absorption correction: numerical
(Coppens et al., 1965)
θmin = 3.6º
Tmin = 0.522, Tmax = 0.614h = 11→11
19216 measured reflectionsk = 0→20
3874 independent reflectionsl = 0→16
3240 reflections with I > 2σ(I)
Refinement top
Refinement on F24 restraints
Least-squares matrix: fullH atoms treated by a mixture of
independent and constrained refinement
R[F2 > 2σ(F2)] = 0.041  w = 1/[σ2(Fo2) + (0.0942P)2]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.128(Δ/σ)max < 0.001
S = 1.11Δρmax = 0.75 e Å3
3874 reflectionsΔρmin = 1.21 e Å3
207 parametersExtinction correction: none
Crystal data top
[Mo2(CH3O)6(NO)2(H2O)2]V = 1648.7 (4) Å3
Mr = 474.14Z = 4
Monoclinic, P21/cMo Kα
a = 8.7567 (13) ŵ = 1.56 mm1
b = 15.6682 (17) ÅT = 183 (2) K
c = 12.5488 (18) Å0.5 × 0.45 × 0.43 mm
β = 106.750 (16)º
Data collection top
Stoe IPDS
diffractometer
3874 independent reflections
Absorption correction: numerical
(Coppens et al., 1965)
3240 reflections with I > 2σ(I)
Tmin = 0.522, Tmax = 0.614Rint = 0.085
19216 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0414 restraints
wR(F2) = 0.128H atoms treated by a mixture of
independent and constrained refinement
S = 1.11Δρmax = 0.75 e Å3
3874 reflectionsΔρmin = 1.21 e Å3
207 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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Mo10.14909 (4)0.05522 (2)0.25247 (3)0.02109 (13)
Mo20.35941 (4)0.22983 (2)0.21836 (3)0.02114 (13)
N10.0325 (4)0.0077 (2)0.1801 (3)0.0242 (7)
O10.1556 (4)0.0263 (2)0.1254 (3)0.0327 (7)
N20.5425 (4)0.2756 (2)0.2931 (3)0.0247 (7)
O20.6664 (4)0.3052 (2)0.3518 (3)0.0359 (8)
O30.2412 (4)0.04131 (19)0.3389 (3)0.0299 (7)
C30.1717 (6)0.1235 (3)0.3376 (4)0.0337 (10)
H3A0.07490.11870.35860.044*
H3B0.24490.16020.38930.044*
H3C0.14840.14720.26410.044*
O40.0788 (4)0.11761 (19)0.3613 (3)0.0279 (6)
C40.0701 (6)0.1164 (3)0.3822 (5)0.0391 (11)
H4A0.14420.08410.32520.051*
H4B0.10850.17380.38230.051*
H4C0.05950.09050.45330.051*
O50.2715 (5)0.0038 (2)0.1292 (3)0.0407 (8)
H5A0.356 (7)0.035 (5)0.131 (8)0.09 (3)*
H5B0.30 (2)0.048 (5)0.145 (18)0.114*0.50
H5C0.21 (2)0.004 (14)0.061 (6)0.114*0.50
O60.3733 (3)0.12295 (17)0.3148 (2)0.0212 (5)
C60.4855 (6)0.1103 (3)0.4203 (4)0.0313 (9)
H6A0.59120.12010.41480.041*
H6B0.47740.05290.44470.041*
H6C0.46390.14950.47300.041*
O70.1374 (3)0.16046 (17)0.1539 (2)0.0224 (6)
C70.0167 (6)0.1784 (3)0.0530 (4)0.0312 (9)
H7A0.02750.14020.00420.041*
H7B0.02750.23620.03090.041*
H7C0.08640.17090.06430.041*
O80.4287 (4)0.16934 (19)0.1057 (3)0.0274 (6)
C80.5864 (6)0.1568 (4)0.1018 (5)0.0395 (11)
H8A0.65800.19030.15880.051*
H8B0.59490.17390.03030.051*
H8C0.61390.09750.11380.051*
O90.2601 (4)0.32633 (19)0.1369 (3)0.0307 (7)
C90.3085 (7)0.4130 (3)0.1455 (4)0.0376 (11)
H9A0.27990.43950.20600.049*
H9B0.25640.44220.07740.049*
H9C0.42200.41610.15880.049*
O100.2458 (5)0.2776 (2)0.3488 (4)0.0392 (8)
H10A0.188 (7)0.235 (3)0.363 (6)0.06 (2)*
H10B0.190 (18)0.324 (6)0.328 (14)0.081*0.50
H10C0.305 (17)0.297 (10)0.413 (7)0.081*0.50
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Mo10.0247 (2)0.02005 (19)0.0179 (2)0.00202 (12)0.00518 (15)0.00039 (11)
Mo20.0235 (2)0.01972 (19)0.0211 (2)0.00026 (11)0.00789 (15)0.00202 (12)
N10.0294 (19)0.0235 (16)0.0190 (16)0.0002 (13)0.0060 (15)0.0005 (13)
O10.0332 (18)0.0349 (17)0.0261 (16)0.0083 (13)0.0025 (14)0.0037 (13)
N20.0278 (19)0.0248 (17)0.0234 (18)0.0014 (13)0.0106 (16)0.0017 (13)
O20.0309 (17)0.0423 (19)0.0331 (18)0.0151 (15)0.0071 (15)0.0078 (15)
O30.0353 (17)0.0251 (14)0.0269 (16)0.0017 (12)0.0053 (14)0.0059 (12)
C30.047 (3)0.0226 (19)0.031 (2)0.0029 (19)0.010 (2)0.0056 (17)
O40.0303 (16)0.0289 (15)0.0273 (16)0.0050 (12)0.0126 (14)0.0034 (12)
C40.036 (3)0.044 (3)0.042 (3)0.011 (2)0.019 (2)0.018 (2)
O50.048 (2)0.0381 (19)0.038 (2)0.0015 (17)0.0153 (18)0.0040 (16)
O60.0217 (14)0.0213 (12)0.0170 (13)0.0015 (10)0.0003 (11)0.0018 (10)
C60.031 (2)0.034 (2)0.025 (2)0.0029 (18)0.0015 (19)0.0077 (17)
O70.0224 (14)0.0239 (13)0.0185 (14)0.0004 (11)0.0020 (12)0.0037 (11)
C70.029 (2)0.035 (2)0.024 (2)0.0006 (17)0.0023 (18)0.0072 (17)
O80.0312 (16)0.0298 (15)0.0243 (15)0.0002 (12)0.0128 (13)0.0014 (12)
C80.034 (3)0.050 (3)0.039 (3)0.004 (2)0.018 (2)0.008 (2)
O90.0354 (17)0.0252 (15)0.0349 (18)0.0032 (12)0.0153 (15)0.0095 (12)
C90.057 (3)0.022 (2)0.039 (3)0.004 (2)0.023 (3)0.0048 (19)
O100.043 (2)0.0349 (18)0.045 (2)0.0004 (15)0.0203 (19)0.0024 (15)
Geometric parameters (Å, °) top
Mo1—Mo23.3933 (7)O5—H5A0.89 (2)
Mo1—N11.754 (4)O5—H5B0.87 (2)
Mo1—O31.900 (3)O5—H5C0.87 (2)
Mo1—O41.919 (3)O6—C61.417 (5)
Mo1—O52.269 (4)C6—H6A0.9600
Mo1—O62.170 (3)C6—H6B0.9600
Mo1—O72.046 (3)C6—H6C0.9600
Mo2—N21.760 (4)O7—C71.425 (5)
Mo2—O62.049 (3)C7—H7A0.9600
Mo2—O72.170 (3)C7—H7B0.9600
Mo2—O81.939 (3)C7—H7C0.9600
Mo2—O91.891 (3)O8—C81.410 (6)
Mo2—O102.274 (4)C8—H8A0.9600
N1—O11.220 (5)C8—H8B0.9600
N2—O21.214 (5)C8—H8C0.9600
O3—C31.423 (5)O9—C91.418 (5)
C3—H3A0.9600C9—H9A0.9600
C3—H3B0.9600C9—H9B0.9600
C3—H3C0.9600C9—H9C0.9600
O4—C41.402 (5)O10—H10A0.89 (2)
C4—H4A0.9600O10—H10B0.87 (2)
C4—H4B0.9600O10—H10C0.88 (2)
C4—H4C0.9600
N1—Mo1—O397.48 (15)H4B—C4—H4C109.5
N1—Mo1—O498.96 (15)Mo1—O5—H5A110 (6)
O3—Mo1—O499.75 (14)Mo1—O5—H5B111 (10)
N1—Mo1—O591.86 (16)H5A—O5—H5B108 (10)
O3—Mo1—O584.29 (15)Mo1—O5—H5C117 (10)
O4—Mo1—O5167.81 (13)H5A—O5—H5C111 (10)
O7—Mo1—O579.93 (13)H5B—O5—H5C99 (10)
O6—Mo1—O582.13 (13)C6—O6—Mo2125.0 (2)
N1—Mo1—O6170.28 (14)C6—O6—Mo1125.5 (2)
O3—Mo1—O689.56 (12)Mo2—O6—Mo1107.06 (12)
O4—Mo1—O686.38 (12)O6—C6—H6A109.5
O7—Mo1—O672.90 (11)O6—C6—H6B109.5
N1—Mo1—O798.60 (14)H6A—C6—H6B109.5
O3—Mo1—O7157.76 (13)O6—C6—H6C109.5
O4—Mo1—O792.82 (12)H6A—C6—H6C109.5
N2—Mo2—O697.39 (14)H6B—C6—H6C109.5
O9—Mo2—O6155.87 (13)C7—O7—Mo1126.3 (3)
O8—Mo2—O693.05 (12)C7—O7—Mo2126.0 (2)
N2—Mo2—O7169.55 (14)Mo1—O7—Mo2107.17 (12)
O9—Mo2—O788.62 (12)O7—C7—H7A109.5
O8—Mo2—O785.31 (12)O7—C7—H7B109.5
O6—Mo2—O772.85 (11)H7A—C7—H7B109.5
N2—Mo2—O899.19 (15)O7—C7—H7C109.5
O9—Mo2—O8100.86 (14)H7A—C7—H7C109.5
N2—Mo2—O999.69 (15)H7B—C7—H7C109.5
N2—Mo2—O1090.14 (15)C8—O8—Mo2127.5 (3)
O9—Mo2—O1084.10 (14)O8—C8—H8A109.5
O8—Mo2—O10168.46 (13)O8—C8—H8B109.5
O6—Mo2—O1078.93 (12)H8A—C8—H8B109.5
O7—Mo2—O1084.40 (13)O8—C8—H8C109.5
O1—N1—Mo1176.7 (3)H8A—C8—H8C109.5
O2—N2—Mo2175.2 (3)H8B—C8—H8C109.5
C3—O3—Mo1127.2 (3)C9—O9—Mo2130.1 (3)
O3—C3—H3A109.5O9—C9—H9A109.5
O3—C3—H3B109.5O9—C9—H9B109.5
H3A—C3—H3B109.5H9A—C9—H9B109.5
O3—C3—H3C109.5O9—C9—H9C109.5
H3A—C3—H3C109.5H9A—C9—H9C109.5
H3B—C3—H3C109.5H9B—C9—H9C109.5
C4—O4—Mo1129.2 (3)Mo2—O10—H10A107 (5)
O4—C4—H4A109.5Mo2—O10—H10B112 (10)
O4—C4—H4B109.5H10A—O10—H10B113 (10)
H4A—C4—H4B109.5Mo2—O10—H10C120 (10)
O4—C4—H4C109.5H10A—O10—H10C108 (10)
H4A—C4—H4C109.5H10B—O10—H10C97 (10)
N1—Mo1—O3—C30.0 (4)O3—Mo1—O7—C7131.3 (4)
O4—Mo1—O3—C3100.5 (4)O4—Mo1—O7—C7104.0 (3)
O7—Mo1—O3—C3136.0 (4)O6—Mo1—O7—C7170.7 (4)
O6—Mo1—O3—C3173.2 (4)O5—Mo1—O7—C785.9 (3)
O5—Mo1—O3—C391.1 (4)N1—Mo1—O7—Mo2176.42 (15)
N1—Mo1—O4—C46.2 (4)O3—Mo1—O7—Mo240.6 (4)
O3—Mo1—O4—C493.0 (4)O4—Mo1—O7—Mo284.08 (14)
O7—Mo1—O4—C4105.4 (4)O6—Mo1—O7—Mo21.26 (11)
O6—Mo1—O4—C4178.1 (4)O5—Mo1—O7—Mo286.05 (15)
O5—Mo1—O4—C4158.5 (6)N2—Mo2—O7—C7168.0 (7)
N2—Mo2—O6—C612.2 (3)O9—Mo2—O7—C725.1 (3)
O9—Mo2—O6—C6122.6 (4)O8—Mo2—O7—C776.0 (3)
O8—Mo2—O6—C6111.9 (3)O6—Mo2—O7—C7170.6 (3)
O7—Mo2—O6—C6164.0 (3)O10—Mo2—O7—C7109.3 (3)
O10—Mo2—O6—C676.5 (3)N2—Mo2—O7—Mo120.0 (8)
N2—Mo2—O6—Mo1174.92 (15)O9—Mo2—O7—Mo1162.99 (15)
O9—Mo2—O6—Mo140.1 (4)O8—Mo2—O7—Mo195.99 (14)
O8—Mo2—O6—Mo185.39 (14)O6—Mo2—O7—Mo11.33 (11)
O7—Mo2—O6—Mo11.26 (11)O10—Mo2—O7—Mo178.79 (15)
O10—Mo2—O6—Mo186.24 (15)N2—Mo2—O8—C89.3 (4)
O3—Mo1—O6—C629.9 (3)O9—Mo2—O8—C8111.1 (4)
O4—Mo1—O6—C669.9 (3)O6—Mo2—O8—C888.7 (4)
O7—Mo1—O6—C6164.0 (3)O7—Mo2—O8—C8161.2 (4)
O5—Mo1—O6—C6114.2 (3)O10—Mo2—O8—C8134.2 (7)
O3—Mo1—O6—Mo2167.46 (15)N2—Mo2—O9—C98.2 (4)
O4—Mo1—O6—Mo292.74 (15)O8—Mo2—O9—C9109.6 (4)
O7—Mo1—O6—Mo21.33 (11)O6—Mo2—O9—C9126.2 (4)
O5—Mo1—O6—Mo283.16 (15)O7—Mo2—O9—C9165.4 (4)
N1—Mo1—O7—C74.5 (4)O10—Mo2—O9—C980.9 (4)
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O5—H5A···O80.89 (2)2.24 (6)2.991 (5)142 (8)
O5—H5B···O2i0.87 (2)2.31 (6)3.156 (5)165 (20)
O5—H5C···O1ii0.87 (2)2.29 (11)3.081 (5)150 (20)
O10—H10A···O40.89 (2)2.06 (3)2.929 (5)163 (7)
O10—H10C···O8iii0.88 (2)2.41 (5)3.266 (5)166 (15)
O10—H10B···O1iv0.87 (2)2.46 (11)3.212 (5)145 (15)
Symmetry codes: (i) −x+1, y−1/2, −z+1/2; (ii) −x, −y, −z; (iii) x, −y+1/2, z+1/2; (iv) −x, y+1/2, −z+1/2.
Table 1
Selected geometric parameters (Å, °)
top
Mo1—Mo23.3933 (7)Mo2—O91.891 (3)
Mo1—N11.754 (4)Mo2—O102.274 (4)
Mo1—O31.900 (3)N1—O11.220 (5)
Mo1—O41.919 (3)N2—O21.214 (5)
Mo1—O52.269 (4)O3—C31.423 (5)
Mo1—O62.170 (3)O4—C41.402 (5)
Mo1—O72.046 (3)O6—C61.417 (5)
Mo2—N21.760 (4)O7—C71.425 (5)
Mo2—O62.049 (3)O8—C81.410 (6)
Mo2—O72.170 (3)O9—C91.418 (5)
Mo2—O81.939 (3)
N1—Mo1—O397.48 (15)O6—Mo2—O772.85 (11)
N1—Mo1—O498.96 (15)N2—Mo2—O899.19 (15)
O3—Mo1—O499.75 (14)O9—Mo2—O8100.86 (14)
N1—Mo1—O591.86 (16)N2—Mo2—O999.69 (15)
O3—Mo1—O584.29 (15)N2—Mo2—O1090.14 (15)
O4—Mo1—O5167.81 (13)O9—Mo2—O1084.10 (14)
O7—Mo1—O579.93 (13)O8—Mo2—O10168.46 (13)
O6—Mo1—O582.13 (13)O6—Mo2—O1078.93 (12)
N1—Mo1—O6170.28 (14)O7—Mo2—O1084.40 (13)
O3—Mo1—O689.56 (12)O1—N1—Mo1176.7 (3)
O4—Mo1—O686.38 (12)O2—N2—Mo2175.2 (3)
O7—Mo1—O672.90 (11)C3—O3—Mo1127.2 (3)
N1—Mo1—O798.60 (14)C4—O4—Mo1129.2 (3)
O3—Mo1—O7157.76 (13)C6—O6—Mo2125.0 (2)
O4—Mo1—O792.82 (12)C6—O6—Mo1125.5 (2)
N2—Mo2—O697.39 (14)Mo2—O6—Mo1107.06 (12)
O9—Mo2—O6155.87 (13)C7—O7—Mo1126.3 (3)
O8—Mo2—O693.05 (12)C7—O7—Mo2126.0 (2)
N2—Mo2—O7169.55 (14)Mo1—O7—Mo2107.17 (12)
O9—Mo2—O788.62 (12)C8—O8—Mo2127.5 (3)
O8—Mo2—O785.31 (12)C9—O9—Mo2130.1 (3)
Table 2
Hydrogen-bond geometry (Å, °)
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D—H···AD—HH···AD···AD—H···A
O5—H5A···O80.89 (2)2.24 (6)2.991 (5)142 (8)
O5—H5B···O2i0.87 (2)2.31 (6)3.156 (5)165 (20)
O5—H5C···O1ii0.87 (2)2.29 (11)3.081 (5)150 (20)
O10—H10A···O40.89 (2)2.06 (3)2.929 (5)163 (7)
O10—H10C···O8iii0.88 (2)2.41 (5)3.266 (5)166 (15)
O10—H10B···O1iv0.87 (2)2.46 (11)3.212 (5)145 (15)
Symmetry codes: (i) −x+1, y−1/2, −z+1/2; (ii) −x, −y, −z; (iii) x, −y+1/2, z+1/2; (iv) −x, y+1/2, −z+1/2.
Acknowledgements top

The authors thank the University of Zürich and the Swiss National Science Foundation for financial support.

references
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