Synchrotron-radiation study of the two-leg spin-ladder (VO)₂P₂O₇ at 120 K

The crystal structure of the ambient-pressure phase of vanadyl pyrophosphate, (VO)₂P₂O₇, has been precisely determined at 120 K from synchrotron X-ray diffraction data measured on a high-quality single crystal. The structure refinement unambiguously establishes the orthorhombic space group Pca2₁ as the true crystallographic symmetry. Moreover, it improves the accuracy of previously published atomic coordinates by one order of magnitude, and provides reliable anisotropic displacement parameters for all atoms. Along the a axis, the structure consists of infinite two-leg ladders of vanadyl cations, (VO)²⁺, which are separated by pyrophosphate anions, (P₂O₇)^4-. Parallel to the c axis, the unit cell comprises two alternating crystallographically inequivalent chains of edge-sharing VO₅ square pyramids bridged by PO₄ double tetrahedra. No structural phase transition has been observed in the temperature range between 300 and 120 K.

S1. Comment

Oxovanadium phosphates constitute a family of compounds with a versatile crystallochemistry that results in an intricate magnetochemistry. This diversity is due to the accessibility of several oxidation states of vanadium, the ability of phosphate and vanadium polyhedra to form a large variety of complex network structures, and the involvement of phosphate groups in the spin transfer between V ions. Vanadyl pyrophosphate, (VO)₂P₂O₇, has been extensively studied by chemists, because this compound is known to be a very efficient catalyst for selective oxydation of n-butane to maleic anhydride (Centi et al., 1988). This process is of considerable industrial importance, as it is presently the only (heterogeneously catalyzed) alkane oxidation performed on a large scale. Recently, (VO)₂P₂O₇ has attracted much attention from solid-state physicists due to its low-dimensional magnetic properties. It represents a quantum magnetic spin system of V⁴⁺ ions (3 d¹ configuration, spin S = 1/2), whose antiferromagnetic superexchange interactions give rise to a non-magnetic singlet ground state accompanied by a singlet-triplet energy gap (Barnes et al., 1993; Eccleston et al., 1994). From a crystallographic point of view, (VO)₂P₂O₇ has been widely considered to be a prototype of a two-leg spin ladder system. S = 1/2 spin ladders are of interest as an intermediate stage between one-dimensional spin chains and two-dimensional spin lattices, and it has been proposed that hole-doped spin ladders may exhibit superconductivity (Dagotto et al., 1992; Dagotto & Rice, 1996). The magnetism of (VO)₂P₂O₇ has been interpretated in a number of ways, which have been reviewed in detail by Johnston et al. (2001). Initially, magnetic susceptibility measurements and inelastic neutron scattering data were discussed in terms of a two-leg spin ladder model (Barnes & Riera, 1994; Eccleston et al., 1994) and an alternating spin chain model (Johnston et al., 1987; Barnes & Riera, 1994). Subsequent inelastic neutron scattering studies revealed that the magnetic properties are dominated by alternating spin chains, because the dispersion of magnetic excitations was found to be inconsistent with a spin ladder (Garrett, Nagler, Barnes & Sales, 1997; Garrett, Nagler, Tennant et al., 1997). Recently, high-field magnetization measurements, NMR and Raman scattering studies proved the co-existence of two magnetic subsystems associated with two different spin-gap energies (Kikuchi et al., 1999; Yamauchi et al., 1999; Kuhlmann et al., 2000).

Several studies of the crystal structure of (VO)₂P₂O₇ at room temperature have been published. Initial diffraction experiments with X-rays and electrons suggested orthorhombic symmetry with space group Pcam or Pca2₁ (Gorbunova & Linde, 1979; Bordes & Courtine, 1979), but the final R values from the structure refinement were unsatisfactory. Subsequent single-crystal X-ray structure analyses gave acceptable R values, but contradictory results: Ebner & Thompson (1991) reported space group Pca2₁ with disorder on the V sites, while Nguyen et al. (1995) found space group P112₁ with a pseudo-orthorhombic translation lattice, as indicated by a monoclinic angle of 89.975 (3)°. The P112₁ structure model seems to be doubtful, since it presents extremely distorted non-positive definite thermal vibration ellipsoids for several V and P sites, but also unusually large isotropic displacement parameters for two O sites that are shared by opposing PO₄ tetrahedra in the P₂O₇ groups. Recent diffraction studies with X-rays, neutrons and electrons on (VO)₂P₂O₇ powder samples showed systematic extinctions which are consistent with space group Pca2₁, and led to a structure model with exceptionally large isotropic displacement parameters for a number of O sites in the P₂O₇ groups also (Hiroi et al., 1999). Crystallographic disorder in (VO)₂P₂O₇ was often detected in X-ray and electron-diffraction patterns as diffuse scattering (Bordes & Courtine, 1979; Hiroi et al., 1999) and peak-broadening effects due to the introduction of stacking faults (Nguyen et al., 1996). Several studies revealed the ability of (VO)₂P₂O₇ to accomodate various disordered or polytypic structures generated by interlayer vacancies (Thompson et al., 1994) and O defect sites (Gai & Kourtakis, 1995; Gai, 1997). On the other hand, the structure of (VO)₂P₂O₇ is capable of preserving mixed-valence V⁴⁺/V⁵⁺ pairs associated with interstitial O sites in the P₂O₇ sublattice (López-Granados et al., 1993). Very recently, a high-pressure phase treated at 2–3 GPa was found to crystallize in the orthorhombic space group Pnab, with a unit cell half the size of that of the ambient-pressure phase (Azuma et al., 1999; Saito et al., 2000).

Our investigations were motivated by the fact that all previously published crystal structure data of the ambient-pressure phase of (VO)₂P₂O₇ do not provide accurate enough values for the spin-orbital interaction energies (Koo & Whangbo, 2000). Their knowledge is indispensable to conclude unambiguously which of the alternating spin chains has a larger energy gap, and which of the bridged and edge-sharing spin dimers has a stronger spin exchange interaction in the chains. The complications in earlier studies may be attributed to sample preparation conditions, poor crystal quality, and limited experimental accuracy. The present structure determination from low-temperature synchrotron X-ray data measured on a high-quality single-crystal confirms the Pca2₁ space-group assignment. Moreover, the structure refinement provides reliable anisotropic displacement parameters for all atoms, and improves the accuracy of the atomic coordinates, as given by Hiroi et al. (1999) and Gorbunova & Linde (1979), by one order of magnitude.

The asymmetric unit of (VO)₂P₂O₇ in Pca2₁ contains four V sites, four P sites and 18 O sites. Along the a axis, the crystal structure consists of infinite two-leg ladders of vanadyl cations, (VO)²⁺, which are separated by pyrophosphate anions, (P₂O₇)^4-. All V atoms show a (4 + 1) square-pyramidal coordination to five O atoms, consisting of four equatorial V—O distances ranging from 1.940 (3) to 2.083 (4) Å and one short axial V—O distance varying between 1.594 (3) and 1.612 (4) Å. In the [100] direction and nearly opposite the strong V═O bond of the vanadyl group, the V atoms are also weakly coordinated to the apical O atom belonging to the neighbouring VO₅ pyramid, with a long V—O distance ranging from 2.250 (4) to 2.341 (3) Å. Along the c axis, the unit cell of (VO)₂P₂O₇ comprises two alternating crystallographically inequivalent chains built of pairs of edge-sharing VO₅ square pyramids. They are arranged in such a way that in every VO₅ pair the V═O bonds are in trans positions, as each axial O atom is located alternately above or below the basal plane. The VO₅ double pyramids in the V1–V2 chain are bridged by tilted PO₄ double tetrahedra involving P1 and P2 [with a P1···P2 separation of 3.0112 (18) Å], while those in the V3–V4 chain are linked by untilted PO₄ double tetrahedra involving P3 and P4 [with a P3···P4 separation of 3.0873 (19) Å]. Each equatorial O atom of the VO₅ pairs shares a corner with one PO₄ group (Fig. 1). The P—O distances range from 1.487 (4) to 1.583 (3) Å, and the O–P–O bond angles within the PO₄ tetrahedra vary between 104.1 (2) and 116.9 (2)°. The P1–O6—-P2 and P3—O5—P4 bridging angles are 144.50 (18) and 157.20 (17)°, respectively. Both values fall within the typical range found for P₂O₇ groups. The shortest non-bonding V···V distances in [001] direction (i.e. along the rungs of the ladder) are d(V3···V4) = 3.2047 (12) Å and d(V1···V2) = 3.2282 (12) Å. Those in the [100] direction (i.e. along the legs of the ladder) are much longer and approximately given as a/2 = 3.85 Å. Bond-valence calculations were carried out with the program VALENCE (Brown, 1996), using bond-valence parameters according to Brese & O'Keeffe (1991). The bond-valence sums agree very well with the expected valence states V⁴⁺ and P⁵⁺ (Table 2), and exclude the presence of mixed-valence V⁴⁺/V⁵⁺ pairs for the measured crystal. The equivalent isotropic displacement parameters of O atoms are found to be significantly larger than those of V and P atoms, and the principal mean-square atomic displacements of several O sites show a pronounced anisotropy (Fig. 2). The thermal motion of these O atoms could not reasonably well described by a split-atom model.

At T = 300 K, the lattice parameters of (VO)₂P₂O₇ have been determined as a = 7.7285 (3), b = 9.5842 (4) and c = 16.5962 (6) Å. Assuming a simple linear behaviour, the coefficients of linear thermal expansion in the temperature range between 300 and 120 K are estimated as α_a=2.0 × 10 ^-5 K^-1, α_b = 3.8 × 10 ^-6 K^-1 and α_c = 4.6 × 10 ^-6 K^-1. This indicates a strong anisotropic thermal expansion, taking place mainly in the direction parallel to the legs of the ladder. The value obtained for α_a is comparable to that one resulting from Raman scattering experiments (Kuhlmann et al., 2001).

S2. Experimental

In general, the single-crystal growth of (VO)₂P₂O₇ is complicated by two features. Firstly, the phase stability and the valence state of vanadium are very sensitive to the oxygen content in the growth atmosphere (López-Granados et al., 1993; Prokofiev et al., 2000). Secondly, the melt exhibits the tendency to a glass formation during cooling due to its high viscosity. Therefore, the single-crystal growth has to be carried out with a very low growth rate and in a growth atmosphere with controlled oxygen content. (VO)₂P₂O₇ powder for the crystal growth has been prepared from the precursor vanadyl hydrogen phosphate hemihydrate, VOHPO₄·0.5H₂O, via a topotactic dehydration (Bordes et al., 1984; Torardi et al., 1995) in an argon flow at 973 K. The precursor was synthesized according to the procedure given by Centi et al. (1985). Large single crystals of (VO)₂P₂O₇ were grown using a combination of Czochralski and Kryopoulos methods, i.e. slow cooling (4–8 K per day) of the melt with simultaneous pulling (2 mm per day) of the dark-green crystals from the melt. Crystal growth was carried out in a resistance furnace under flow of a gas mixture of argon and oxygen (0.2 vol%), using a silica growth chamber and a platinum crucible. Further details of the crystal-growth technique are described by Prokofiev, Büllesfeld & Assmus (1998). No impurity phases have been detected with electron microprobe analysis, scanning electron microscopy and X-ray powder diffraction. From thermogravimetric analysis studies based on the oxidation of (VO)₂P₂O₇ to VPO₅, the oxidation state of the V ions was determined to be +4.05. Furthermore, the single crystals have been comprehensively investigated using electron spin resonance and magnetic susceptibility measurements (Prokofiev, Büllesfeld, Assmus et al., 1998), as well as Raman scattering and IR spectroscopy (Kuhlmann et al., 2000, 2001; Grove et al., 2000).

S3. Refinement

Single-crystal X-ray diffraction experiments with synchrotron radiation were performed on beamline F1 of HASYLAB at DESY Hamburg. A double-crystal Si(111) monochromator was used to select a wavelength of λ = 0.70843 Å. Reflection groups h0l (h = 2n+1), 0kl (l = 2n+1), h00 (h = 2n+1) and 00 l (l = 2n+1) were found to be systematically absent in the data collection carried out at T = 120 K, with a measuring time of 5 s per frame and a crystal-to-detector distance of 50 mm. Possible space groups consistent with the observed reflection conditions are only Pcam or Pca2₁. Indications for disorder, non-merohedral twinning or superstructure reflections were not detected. SADABS (Sheldrick, 1996) was used for corrections of variations in the primary beam intensity and for averaging symmetry-equivalent reflections. Accurate lattice parameters at 120 and 300 K were determined from laboratory four-circle diffractometer data, because several systematic errors (e.g. positions of crystal and detector) in the cell refinement procedure are not accounted for by SAINT (Siemens, 1996). We checked monoclinic cell constraints as well, but all unit-cell angles did not differ from 90° within single standard deviation.

The Flack parameter (Flack, 1983) of an initial refinement in space group Pca2₁ indicated that the crystal is twinned. The refinement model without twinning yielded a Flack parameter x = 0.27 (4) with R = 0.0308 and wR = 0.0692. Transformation to the inverse structure resulted in x = 0.54 (4) with R = 0.0316 and wR = 0.0716. Consequently, an inversion twin was added to the structure model. The final refinement gave a twin volume fraction of 34 (4)%. This value is in good agreement with a ratio of 32% determined with the program TWIN3.0 (Kahlenberg & Messner, 2000), using the procedure proposed by Britton (1972). The deviation from the expected 1:1 distribution may be caused during the cutting process of the crystals. Fixing the twin fraction at 50% had no significant influence on the structural parameters.

Due to the fact, that all V atoms are located very close to y = 0 or y = 1/2, and such pairs of related atoms in Pca2₁ do not contribute to the intensities of reflections with h = 2n+1 (Marsh et al., 1998), almost all reflections hk0 with h = 2n+1 were also found to be absent in the data collection [average I/σ(I) = 1.3, maximum I/σ(I) = 10]. This suggests the centrosymmetric space group Pcaa, which is a translation engleiche supergroup of index 2 of Pca2₁. The possible existence of an a-glide plane perpendicular to the c axis as additional pseudo-symmetry element (with 20% non-fitting atoms) has been detected by PLATON (Spek, 2001) also. When the match tolerance for pseudo-translations was reduced to 0.1 Å, the extra symmetry disappeared. Although several pairs of unique atoms in the Pca2₁ model seem to be related by an additional a-glide plane perpendicular to the c axis, five unique atoms (V3, V4, P1, P2 and O6) have no symmetry-related counterpart. Therefore, this a-glide plane may represent a pseudo-symmetry element rather than a true crystallographic one. Even though the structure could be solved in Pcaa (26 systematic absence violations, R_int = 0.063 for 1792 independent reflections) with direct methods, the refined structure model involving split-atom positions remains deficient (R = 0.129 for 142 parameters and 1443 observed reflections), and unacceptable high residuals (3.6 and -6.4 e Å^-3) lying closely to the V atoms appear in the difference Fourier map. Attempts to refine the data in Pcam (R_int = 0.063 for 1848 independent reflections) were also unsuccessful (R = 0.121 for 151 parameters and 1466 observed reflections, highest residuals 2.9 and -5.3 e Å^-3), although the statistical distribution of normalized structure factors strongly prefers a centrosymmetric space group (the values of |E²-1| are 1.273 for 0kl, 1.040 for h0l, 1.076 for hk0, and 0.947 for all other reflections). Assuming monoclinic symmetry with space group P112₁ (inversion twin, R_int = 0.057 for 5581 independent reflections), the final R values are, in comparison with those for Pca2₁, only sligthly higher (R = 0.0330, wR = 0.0758 for 471 parameters and 3882 observed reflections, highest residuals 0.79 and -0.77 e Å^-3). However, the anisotropic displacement parameters of five unique O atoms in P112₁ possess a principal axis U_max/U_min ratio of more than 15:1, and the thermal displacement ellipsoids of a further three O atoms even become non-positive definite, while those of all atoms in Pca2₁ display a physically meaningful shape.

Computing details

Data collection: SMART (Siemens, 1996); cell refinement: MACH3 in CAD-4 UNIX Software (Enraf-Nonius, 1998); data reduction: SAINT (Siemens, 1996); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: DIAMOND (Brandenburg, 1999) and ORTEP-3 (Farrugia, 1997); software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. Polyhedral representation of the crystal structure of (VO)2P2O7 viewed (a) along the [100] direction and (b) along the [010] direction. The VO5 square pyramids are drawn in dark grey, the PO4 tetrahedra in light grey. Large circles represent V atoms and medium circles represent P atoms. Small circles in (a) denote O atoms, which are not shown in (b).
	Fig. 2. View of (VO)2P2O7 with the atom-labelling scheme. Displacement ellipsoids at 120 K are drawn at the 90% probability level.

Oxovanadium(IV) diphosphate

Crystal data

(VO)2P2O7	Dx = 3.344 Mg m^−3
Mr = 307.82	Melting point: not measured K
Orthorhombic, Pca21	Synchrotron radiation, λ = 0.70843 Å
Hall symbol: P 2c -2ac	Cell parameters from 25 reflections
a = 7.7004 (4) Å	θ = 16.1–22.5°
b = 9.5777 (5) Å	µ = 3.55 mm^−1
c = 16.5825 (8) Å	T = 120 K
V = 1222.99 (11) Å^3	Rectangular prism, dark green
Z = 8	0.10 × 0.04 × 0.03 mm
F(000) = 1184

Data collection

Huber four-circle Kappa diffractometer with Siemens SMART CCD area detector and Oxford Cryostream Cooler	3149 independent reflections
Si (111) monochromator	2452 reflections with I > 2σ(I)
Detector resolution: number of pixels: 1024 x 1024 (512 x 512 in binning mode), pixel size: 60 µm x 60 µm pixels mm^-1	Rint = 0.060
ω and ϕ scans	θmax = 30.4°, θmin = 2.1°
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	h = −10→9
Tmin = 0.804, Tmax = 0.950	k = −13→13
11910 measured reflections	l = −23→23

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0302P)^2] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.031	(Δ/σ)max < 0.001
wR(F^2) = 0.068	Δρmax = 0.81 e Å^−3
S = 0.88	Δρmin = −0.67 e Å^−3
3149 reflections	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
237 parameters	Extinction coefficient: 0.0165 (6)
1 restraint	Absolute structure: Flack (1983), 1303 Friedel pairs
0 constraints	Absolute structure parameter: 0.00 (13)
Primary atom site location: structure-invariant direct methods

Special details

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.

Bond valence sums: V1 4.08 V2 4.07 V3 4.11 V4 4.13 P1 4.89 P2 4.90 P3 4.94 P4 4.91 O1 1.89 O2 1.89 O3 1.91 O4 1.88 O5 2.17 O6 2.13 O7 2.06 O8 2.05 O9 2.09 O10 2.05 O11 2.03 O12 2.00 O13 1.96 O14 1.97 O15 2.00 O16 2.00 O17 1.98 O18 2.00

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 (Ų)

	x	y	z	Uiso*/Ueq
V1	0.20343 (11)	0.00936 (7)	0.67906 (5)	0.0037 (2)
V2	0.20820 (11)	0.99768 (7)	0.36924 (5)	0.0029 (2)
V3	0.20639 (11)	0.50028 (6)	0.42979 (5)	0.0035 (2)
V4	0.20815 (11)	0.50132 (6)	0.11893 (5)	0.0031 (2)
P1	0.30947 (17)	0.79399 (12)	0.01948 (9)	0.0035 (3)
P2	0.29951 (16)	0.20942 (12)	0.51845 (9)	0.0029 (3)
P3	0.29602 (17)	0.70759 (11)	0.27490 (8)	0.0031 (3)
P4	0.30314 (17)	0.29872 (12)	0.77388 (8)	0.0028 (3)
O1	0.0006 (4)	0.0417 (3)	0.6832 (2)	0.0060 (6)
O2	0.0042 (7)	0.9676 (3)	0.3636 (2)	0.0069 (6)
O3	0.4989 (8)	0.5125 (3)	0.4331 (2)	0.0061 (7)
O4	0.4999 (5)	0.5137 (3)	0.1150 (2)	0.0070 (6)
O5	0.5041 (4)	0.3281 (2)	0.7746 (2)	0.0097 (5)
O6	0.4952 (4)	0.2136 (3)	0.49010 (16)	0.0057 (5)
O7	0.2821 (6)	0.8695 (3)	0.2747 (2)	0.0043 (9)
O8	0.2782 (7)	0.1377 (3)	0.7743 (2)	0.0057 (9)
O9	0.2463 (8)	0.3657 (3)	0.5257 (2)	0.0048 (7)
O10	0.2517 (8)	0.6384 (3)	0.0244 (2)	0.0044 (7)
O11	0.3019 (4)	0.8583 (3)	0.1010 (2)	0.0069 (8)
O12	0.2926 (4)	0.1392 (3)	0.5986 (2)	0.0052 (8)
O13	0.2858 (5)	0.8699 (3)	0.4540 (2)	0.0052 (8)
O14	0.1984 (4)	0.1434 (3)	0.4514 (2)	0.0061 (8)
O15	0.2310 (5)	0.3601 (3)	0.6981 (2)	0.0071 (7)
O16	0.2191 (4)	0.6471 (3)	0.2000 (2)	0.0059 (7)
O17	0.2308 (6)	0.3612 (4)	0.8496 (2)	0.0062 (7)
O18	0.2228 (5)	0.6521 (3)	0.3514 (2)	0.0070 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
V1	0.0050 (6)	0.0038 (4)	0.0022 (4)	−0.0001 (3)	0.0000 (4)	0.0003 (3)
V2	0.0032 (6)	0.0032 (4)	0.0023 (4)	0.0001 (3)	0.0002 (3)	−0.0001 (3)
V3	0.0037 (6)	0.0043 (4)	0.0025 (5)	0.0001 (3)	−0.0001 (4)	0.0000 (3)
V4	0.0039 (6)	0.0033 (4)	0.0020 (4)	−0.0003 (3)	−0.0002 (3)	0.0002 (3)
P1	0.0038 (8)	0.0034 (5)	0.0033 (7)	0.0000 (4)	−0.0007 (6)	0.0002 (4)
P2	0.0044 (9)	0.0029 (5)	0.0014 (6)	−0.0007 (4)	0.0000 (6)	−0.0002 (4)
P3	0.0025 (8)	0.0038 (5)	0.0030 (7)	0.0001 (4)	−0.0002 (6)	−0.0004 (4)
P4	0.0030 (7)	0.0030 (5)	0.0025 (7)	−0.0001 (4)	−0.0004 (6)	0.0001 (4)
O1	0.0105 (15)	0.0059 (13)	0.0015 (14)	−0.0013 (14)	0.0005 (14)	−0.0007 (13)
O2	0.0063 (15)	0.0077 (13)	0.0066 (16)	−0.0003 (17)	−0.0017 (18)	−0.0013 (13)
O3	0.0081 (16)	0.0068 (15)	0.0035 (16)	0.0005 (12)	−0.0021 (17)	−0.0027 (11)
O4	0.0076 (16)	0.0077 (14)	0.0057 (15)	0.0005 (12)	0.0003 (13)	−0.0015 (12)
O5	0.0064 (12)	0.0043 (11)	0.0183 (14)	−0.0002 (10)	−0.0002 (13)	−0.0016 (14)
O6	0.0072 (14)	0.0077 (13)	0.0022 (13)	−0.0009 (10)	−0.0002 (11)	0.0004 (10)
O7	0.006 (2)	0.0042 (13)	0.0023 (14)	0.0005 (11)	−0.0026 (15)	−0.0005 (12)
O8	0.008 (2)	0.0038 (13)	0.0056 (15)	−0.0003 (12)	−0.0029 (16)	−0.0007 (13)
O9	0.0065 (19)	0.0042 (14)	0.0036 (17)	0.0022 (12)	−0.0008 (13)	−0.0012 (14)
O10	0.0066 (17)	0.0028 (14)	0.0039 (17)	−0.0013 (12)	−0.0012 (13)	0.0001 (14)
O11	0.009 (2)	0.0048 (13)	0.0065 (15)	0.0010 (11)	−0.0026 (13)	−0.0026 (10)
O12	0.005 (2)	0.0072 (14)	0.0035 (14)	−0.0024 (11)	−0.0012 (13)	0.0016 (10)
O13	0.005 (2)	0.0046 (13)	0.0062 (17)	−0.0011 (11)	−0.0011 (14)	0.0000 (11)
O14	0.007 (2)	0.0046 (13)	0.0070 (17)	−0.0021 (11)	−0.0001 (13)	−0.0015 (11)
O15	0.0109 (19)	0.0058 (13)	0.0044 (16)	0.0011 (12)	−0.0011 (14)	0.0012 (11)
O16	0.004 (2)	0.0056 (13)	0.0076 (16)	−0.0012 (11)	−0.0021 (14)	−0.0015 (11)
O17	0.0098 (19)	0.0058 (16)	0.0031 (17)	−0.0017 (12)	0.0027 (14)	−0.0010 (13)
O18	0.011 (2)	0.0051 (15)	0.0043 (18)	−0.0004 (12)	0.0017 (14)	0.0000 (13)

Geometric parameters (Å, º)

V1—O1	1.594 (3)	V4—O15^vii	1.942 (3)
V1—O11^i	1.941 (3)	V4—O9^vii	2.050 (4)
V1—O12	1.949 (3)	V4—O10	2.073 (4)
V1—O7^i	2.079 (4)	V4—O4	2.250 (4)
V1—O8	2.083 (4)	P1—O11	1.487 (4)
V1—O1^ii	2.341 (3)	P1—O13^vii	1.499 (4)
V2—O2	1.600 (5)	P1—O10	1.557 (4)
V2—O14^iii	1.951 (4)	P1—O6^ix	1.583 (3)
V2—O13	1.957 (4)	P2—O12	1.490 (3)
V2—O8^iv	2.071 (4)	P2—O14	1.498 (4)
V2—O7	2.071 (4)	P2—O9	1.556 (3)
V2—O2^v	2.305 (5)	P2—O6	1.579 (3)
V3—O3^vi	1.603 (6)	P3—O18	1.487 (4)
V3—O17^vii	1.944 (4)	P3—O16	1.494 (3)
V3—O18	1.954 (4)	P3—O7	1.554 (3)
V3—O9	2.070 (4)	P3—O5^ix	1.576 (3)
V3—O10^viii	2.077 (4)	P4—O15	1.495 (4)
V3—O3	2.256 (6)	P4—O17	1.498 (4)
V4—O4^vi	1.612 (4)	P4—O8	1.554 (3)
V4—O16	1.940 (3)	P4—O5	1.573 (3)
O1—V1—O11^i	98.77 (15)	O4^vi—V4—O4	175.5 (2)
O1—V1—O12	104.49 (15)	O16—V4—O4	86.50 (12)
O11^i—V1—O12	91.53 (14)	O15^vii—V4—O4	79.38 (14)
O1—V1—O7^i	98.36 (18)	O9^vii—V4—O4	80.83 (19)
O11^i—V1—O7^i	91.67 (13)	O10—V4—O4	77.46 (19)
O12—V1—O7^i	156.15 (15)	O11—P1—O13^vii	116.0 (2)
O1—V1—O8	97.11 (19)	O11—P1—O10	109.7 (2)
O11^i—V1—O8	162.03 (15)	O13^vii—P1—O10	111.2 (2)
O12—V1—O8	92.59 (13)	O11—P1—O6^ix	109.64 (17)
O7^i—V1—O8	77.71 (13)	O13^vii—P1—O6^ix	105.33 (19)
O1—V1—O1^ii	175.8 (2)	O10—P1—O6^ix	104.1 (2)
O11^i—V1—O1^ii	83.36 (12)	O12—P2—O14	116.9 (2)
O12—V1—O1^ii	78.98 (12)	O12—P2—O9	110.8 (2)
O7^i—V1—O1^ii	77.93 (16)	O14—P2—O9	109.1 (2)
O8—V1—O1^ii	80.28 (17)	O12—P2—O6	108.12 (17)
O2—V2—O14^iii	97.56 (15)	O14—P2—O6	106.61 (18)
O2—V2—O13	103.25 (16)	O9—P2—O6	104.5 (2)
O14^iii—V2—O13	87.59 (14)	O18—P3—O16	114.9 (2)
O2—V2—O8^iv	97.0 (2)	O18—P3—O7	109.4 (2)
O14^iii—V2—O8^iv	93.98 (14)	O16—P3—O7	111.0 (2)
O13—V2—O8^iv	159.30 (17)	O18—P3—O5^ix	107.2 (2)
O2—V2—O7	96.83 (18)	O16—P3—O5^ix	107.49 (19)
O14^iii—V2—O7	164.35 (15)	O7—P3—O5^ix	106.5 (2)
O13—V2—O7	95.09 (14)	O15—P4—O17	114.2 (2)
O8^iv—V2—O7	78.15 (12)	O15—P4—O8	110.4 (2)
O2—V2—O2^v	174.0 (2)	O17—P4—O8	110.3 (2)
O14^iii—V2—O2^v	87.89 (13)	O15—P4—O5	107.6 (2)
O13—V2—O2^v	79.47 (13)	O17—P4—O5	106.8 (2)
O8^iv—V2—O2^v	79.96 (17)	O8—P4—O5	107.4 (2)
O7—V2—O2^v	77.48 (16)	V1—O1—V1^x	156.36 (16)
O3^vi—V3—O17^vii	102.66 (18)	V2—O2—V2^xi	160.47 (18)
O3^vi—V3—O18	98.27 (17)	V3^xii—O3—V3	171.92 (19)
O17^vii—V3—O18	92.23 (15)	V4^xii—O4—V4	170.90 (18)
O3^vi—V3—O9	94.2 (2)	P4—O5—P3^xiii	157.20 (17)
O17^vii—V3—O9	93.55 (13)	P2—O6—P1^xiii	144.50 (18)
O18—V3—O9	164.72 (17)	P3—O7—V2	127.5 (2)
O3^vi—V3—O10^viii	100.2 (2)	P3—O7—V1^iv	129.9 (2)
O17^vii—V3—O10^viii	156.16 (19)	V2—O7—V1^iv	102.12 (15)
O18—V3—O10^viii	91.03 (13)	P4—O8—V2^i	129.8 (2)
O9—V3—O10^viii	78.10 (13)	P4—O8—V1	128.1 (2)
O3^vi—V3—O3	176.4 (2)	V2^i—O8—V1	102.02 (15)
O17^vii—V3—O3	78.67 (15)	P2—O9—V4^viii	128.5 (3)
O18—V3—O3	85.01 (14)	P2—O9—V3	125.4 (2)
O9—V3—O3	82.27 (19)	V4^viii—O9—V3	102.13 (14)
O10^viii—V3—O3	78.1 (2)	P1—O10—V4	133.8 (2)
O4^vi—V4—O16	97.80 (15)	P1—O10—V3^vii	121.7 (3)
O4^vi—V4—O15^vii	101.85 (16)	V4—O10—V3^vii	101.11 (14)
O16—V4—O15^vii	91.31 (15)	P1—O11—V1^iv	156.3 (2)
O4^vi—V4—O9^vii	94.8 (2)	P2—O12—V1	155.6 (2)
O16—V4—O9^vii	166.26 (18)	P1^viii—O13—V2	132.4 (2)
O15^vii—V4—O9^vii	91.54 (14)	P2—O14—V2^xiv	143.2 (2)
O4^vi—V4—O10	100.8 (2)	P4—O15—V4^viii	138.8 (2)
O16—V4—O10	93.49 (13)	P3—O16—V4	150.8 (2)
O15^vii—V4—O10	156.0 (2)	P4—O17—V3^viii	139.0 (3)
O9^vii—V4—O10	78.65 (13)	P3—O18—V3	149.1 (2)
O15—P4—O5—P3^xiii	−117.8 (7)	O12—P2—O6—P1^xiii	−21.2 (4)
O17—P4—O5—P3^xiii	119.2 (7)	O14—P2—O6—P1^xiii	−147.7 (3)
O8—P4—O5—P3^xiii	0.9 (7)	O9—P2—O6—P1^xiii	96.9 (3)

Symmetry codes: (i) −x+1/2, y−1, z+1/2; (ii) x+1/2, −y, z; (iii) x, y+1, z; (iv) −x+1/2, y+1, z−1/2; (v) x+1/2, −y+2, z; (vi) x−1/2, −y+1, z; (vii) −x+1/2, y, z−1/2; (viii) −x+1/2, y, z+1/2; (ix) −x+1, −y+1, z−1/2; (x) x−1/2, −y, z; (xi) x−1/2, −y+2, z; (xii) x+1/2, −y+1, z; (xiii) −x+1, −y+1, z+1/2; (xiv) x, y−1, z.