Structure of toluene6.4-ZSM-5 and the toluene disproportionation reaction on ZSM-5

The structure of a high-loading complex of ZSM-5 with 6.4 toluene molecules per unit cell has been determined by single-crystal X-ray diffraction. At least three kinds of toluene molecules were identified in the unit cell. Two disordered toluene molecules were located at the intersection of the straight and sinusoidal channels, the third in the sinusoidal channel. One (TOL1) of the two toluene orientations at the intersection was similar to that of p-dichlorobenzene at the intersection in high-loaded H-ZSM-5/p-xylene (hereafter 8PARA) and high-loaded H-ZSM-5/p-dichlorobenzene (hereafter 8PDCB) complexes, respectively. The other toluene orientation (TOL2) at the intersection was similar to those of p-xylene or p-dichlorobenzene at the intersection in the low-loaded p-dichlorobenzene complex (hereafter 2.6PDCB). A third toluene orientation (TOL3) existed in the sinusoidal channel; its orientation was similar to those of p-xylene and p-dichlorobenzene in the sinusoidal channels in 8PARA and 8PDCB complexes, respectively. If the occupancy of TOL2 at the intersection increases with temperature, TOL2 will connect with TOL3 in the sinusoidal channel and form the intermediate diphenylmethane

1. Introduction

The aluminosilicate ZSM-5 has been of interest due to its wide applicability as a shape-selective catalyst (Eylem et al., 1996). The sorbate-ZSM-5 structure has been investigated by X-ray single-crystal diffraction and X-ray powder diffraction (Olson et al., 1981; Price et al., 1982; van Koningsveld, 1987; Yokomori & Idaka, 1999; van Koningsveld et al., 1989, 1996; van Koningsveld & Jansen, 1996; Reck et al., 1996; Mentzen, 1989). At present, aromatic sorbate-ZSM-5 structures may be grouped into two classes:

• (i) Low-loading group (4 or less sorbate per unit cell), space group Pnma or Pn2₁a; α2 (the angle between the positive a axis and the normal to the benzene ring plane) ≃ 45°. Structures that fall into this category include 2.6PDCB (van Koningsveld, Jansen & Man, 1996), p-nitroaniline3.7-ZSM-5 (Reck et al., 1996), naphthalene3.7-ZSM-5 (Klein et al., 1994; van Koningsveld & Jansen, 1996).

• (ii) High-loading group (over 4 sorbate per unit cell); space group P2₁2₁2₁; α2 ≃ 150°. This category includes 8PARA (van Koningsveld et al., 1989) and 8PDCB (van Koningsveld, Jansen & van Bekkum, 1996).

The acid-catalyzed disproportionation of toluene to benzene and xylenes has been extensively investigated in ZSM-5 zeolite (Chen et al., 1979; Kaeding, 1985; Kaeding et al., 1981; Young et al., 1982; Meshram, 1987). At present, the two widely accepted mechanisms for toluene disproportionation on ZSM-5 are:

• (i) intermolecular methyl transfer and

• (ii) a bimolecular reaction invoking a diphenylmethane-type intermediate.

However, these mechanisms are poorly understood and have been the subject of continuing speculation (Xiong et al., 1995). We have investigated the toluene-ZSM-5 structure by X-ray single-crystal diffraction. In the process we have determined the new high-loaded toluene6.4-ZSM-5 structure and shown three distinct locations of toluene in the crystal with different occupancies and have begun to understand the toluene disproportionation mechanism in the ZSM-5 crystal field. Here we report, for the first time, the new high-loaded toluene6.4-ZSM-5 structure and show the toluene disproportionation reaction in ZSM-5 zeolite.

2. Experimental

2.1. Preparation of ZSM-5

The ZSM-5 crystals were synthesized by Lermer's method (Lermer et al., 1985). The formal molar composition of the reaction mixture was SiO₂:NaAlO₂:NaOH:TPABr:H₂O = 12:1:40:40:2000. The samples were cooled, washed and dried at 388 K for 1 d. Cubic crystals were obtained. The Si/Al ratio was found to be over 183 by EDX (Horiba Co. Ltd, EMAX-5770W) and Na⁺ content was not measured. The crystals were treated by NaClO₄ and calcined at 823 K for 12 h. Calcination started at room temperature; the temperature was raised to 823 K at a rate of 2 K min⁻¹ and after a 12 h hold, lowered down to room temperature at the same rate.

2.2. Preparation of toluene6.4-ZSM-5

A freshly prepared ZSM-5 was exposed in a closed vacuum vessel to saturated toluene vapour at room temperature for 2 d. The crystal selected for X-ray analysis measured 0.10 × 0.07 × 0.05 mm.

2.3. Analysis of toluene6.4-ZSM-5

Cell constants were obtained at 293 K on a DIP-3200 X-ray diffractometer (Bruker AXS Co. Ltd) with an imaging plate, Cu Kα radiation and an Ni filter. Full experimental details are given in Table 1.¹ The chemical composition of the toluene 6.4-ZSM-5 sample was (CH₃C₆H₅)_6.432[Si₉₆O₁₉₂], Z = 4. The 17 509 reflections were collected with an imaging plate from the sphere of reflection (−24 → h → 24, −23 → k → 24, −16 → l → 16), and was corrected for Lorentz polarization and absorption effects but not for the extinction effect. The structure was solved with direct methods (SIR97; Altomare et al., 1999) in the space group P2₁2₁2₁ (No. 19) and later refined the structure. It is necessary to shift the origin in the standard P2₁2₁2₁ setting to (0, 0, )² for easy comparison with the high-loading groups 8PARA (van Koningsveld et al., 1989) and 8PDCB (van Koningsveld, Jansen & van Bekkum, 1996). The structure was refined by the full-matrix least-squares method (SHELXL97; Sheldrick, 1997) using 8477 observations with |I| ≥ 2σ(I). Σw||F_o| − |F_c||² was minimized; w = 1/[σ²(F_o²) + (0.1099P)² + 4.6477P], where P = (F_o² + 2F_c²)/3. All T (T = Si, Al) atoms were treated as silicon and H atoms were included in the calculations. In the final few cycles, three independent toluene molecules were restrained to avoid deformation, i.e. all seven C atoms of toluene were located in a plane and each methyl carbon of toluene was located the same distance from the attached carbon and the two nearest C atoms of the benzene ring. The final difference map showed a peak height of +0.81 (3) e Å⁻³. The final R value was 0.058 and the final goodness-of-fit parameter (S) was 1.048 with anisotropic displacement factors. All calculations were performed on the computer system of the National Defense Academy.

Table 1
Experimental details

Crystal data
Chemical formula	O48Si24·C7·0.614C7H12.80
Mr	1590.25
Cell setting, space group	Orthorhombic, P212121
a, b, c (Å)	20.0990 (4), 19.8440 (3), 13.4240 (2)
V (Å^3)	5354.1 (2)
Z	4
Dx (Mg m^−3)	1.973
Radiation type	Cu Kα
No. of reflections for cell parameters	5636
θ range (°)	0.6–0.7
μ (mm^−1)	6.49
Temperature (K)	293
Crystal form, colour	Cube, colourless
Crystal size (mm)	0.10 × 0.07 × 0.05
Data collection
Diffractometer	DIP Image plate
Data collection method	Image plate
Absorption correction	Empirical (using intensity measurements)
Tmin	0.609
Tmax	0.723
No. of measured, independent and observed reflections	17 530, 9878, 8477
Criterion for observed reflections	I > 2σ(I)
Rint	0.033
θmax (°)	70.2
Range of h, k, l	−24 → h → 24
	−23 → k → 24
	−16 → l → 16
Refinement
Refinement on	F^2
R[F^2 > 2σ(F^2)], wR(F^2), S	0.058, 0.173, 1.05
No. of reflections	9878
No. of parameters	737
H-atom treatment	Only coordinates refined
Weighting scheme	w = 1/[σ^2(Fo^2) + (0.1099P)^2 + 4.6477P], where P = (Fo^2 + 2Fc^2)/3
(Δ/σ)max	0.041
Δρmax, Δρmin (e Å^−3)	0.62, −0.72
Computer programs: DIP Image plate, Scalepack (HKL), maXus (Mackay et al., 1999), SHELXL97 (Sheldrick, 1997).

3. Results and discussion

3.1. Results

Final positional and equivalent isotropic displacement parameters of high-loaded toluene 6.4-ZSM-5 have been deposited. Figs. 1(a) and (b) show the ZSM-5 zeolite framework and adsorbed toluene molecules at 293 K. Fig. 2 shows an ORTEP3 (Burnett & Johnson, 1996) drawing in which the three types of toluene molecules in the ZSM-5 framework are highlighted in colour. Two kinds of toluene molecule (TOL1 and TOL2) are located at the intersection of straight and sinusoidal channels, and the other toluene molecule (TOL3) is located in the sinusoidal channel of ZSM-5. In the case of 8PARA or 8PDCB, an additional adsorbed molecule is located at the intersection, while another molecule is located in the sinusoidal channel of ZSM-5. However, the toluene molecule is smaller than the p-xylene or p-dichlorobenzene molecule, thus two kinds of toluene molecules (TOL1, TOL2) are located in disorder around the intersection. The occupancy factors of TOL1, TOL2 and TOL3 were 0.65 (1), 0.33 (1) and 0.62 (1), respectively, as shown in Fig. 1(a). TOL2 and TOL3 do not form a bond because the shortest distance between the two C atoms is 2.00 Å.

Figure 1 ORTEP3 drawings (Burnett & Johnson, 1996) of Tol6.4-ZSM-5. (a) View down the straight channel axis. Tol1 and Tol2 are at the intersection of the channels; Tol3 is in the sinusoidal channel. The occupancy factors are 0.65, 0.33 and 0.62, respectively. (b) View approximately along [001]. H atoms are not shown. The ellipsoids are drawn at 50% probability.

Figure 2 ORTEP (Burnett & Johnson, 1996) drawing of three kinds of toluene molecule in ZSM-5.

3.2. Disordering of toluene

Two kinds of toluene molecules (TOL1 and TOL2) are located in disorder around the intersection. The occupancy factors of TOL1 and TOL2 are 0.65 and 0.33, respectively, as shown in Fig. 1(a). The TOL1 orientation at the intersection is similar to that of p-dichlorobenzene at the intersection in 2.6PDCB. The angle with the positive a axis and the normal on the toluene ring plane (α2) is 52.7°. The α2 values for 2.6PDCB (van Koningsveld, Jansen & Man, 1996), p-nitroaniline3.7-ZSM-5 (Reck et al., 1996) and naphthalene3.7-ZSM-5 (van Koningsveld & Jansen, 1996) are 47.1, 44.3 and 40.5°, respectively. The TOL1 orientation with a high occupancy factor (0.65) is the first example in the high-loaded group. The TOL2 orientation at the intersection is formally similar to those of p-xylene or p-dichlorobenzene at the intersection in 8PARA (van Koningsveld et al., 1989) and 8PDCB (van Koningsveld, Jansen & van Bekkum, 1996), respectively. The α2 angle of TOL2, 8PARA and 8PDCB is 171.4, 149.0 and 153.8°, respectively. However, the occupancy factor of the TOL2 orientation is only 0.33 in the present high-loaded toluene/ZSM-5. Table 2 gives the fractional coordinates (x, y, z) and the corresponding α2 of TOL1 and TOL2 at the intersection, together with those of 2.6PDCB, 8PARA and 8PDCB. The TOL2 orientation has a high α2 value (171.4) and a very low z value (−0.0560). This means that TOL2 approaches TOL3 in the sinusoidal channel. However, we question whether or not TOL2 and TOL3 can be occupied simultaneously. The answer is no because the occupancy factor of TOL3 located in the sinusoidal channel is 0.62. That is, the contribution of the TOL1 and TOL3 orientations is ca 65%, while that of TOL2 and the vacant TOL3 space is ca 33%. The shortest bond distance between the two C atoms of TOL2 and TOL3 is 2.00 Å. This is too long for TOL2 and TOL3 to bond with each other.

Table 2
Orientation of molecules at the intersection of channels in MFI

	TOL1	TOL2	2.6PDCB	8PARA	8PDCB
x	0.4742	0.5081	0.4860	0.5105	0.5113
y	0.2465	0.2495	0.2400	0.2390	0.2419
z	−0.0370	−0.0560	−0.0188	−0.0188	−0.0253
α2 (°)	52.7	171.4	47.1	149.0	153.8

3.3. Toluene disproportionation

It is tempting to speculate on the dynamics of the toluene disproportionation reaction in the ZSM-5 framework. The reaction consists of four steps.

• (i) Toluene molecules are adsorbed on ZSM-5, diffuse into the straight channel and are confined at the intersection. This is TOL1 in Figs. 1(a) and (b).

• (ii) Toluene molecules diffuse into the sinusoidal channel and are confined there. This is TOL3.

• (iii) TOL1 partially transforms into TOL2.

• (iv) If the reaction temperature increases, the proportion of TOL2 increases above 33%. TOL2 and TOL3 become occupied simultaneously and bond with each other.

The combined molecule (TOL2–TOL3) is a diphenylmethane- or diphenylmethane-type cation (Chen et al., 1989). Wu et al. (1998) varied contact time over a wide range to determine which isomer of xylene is the primary product of toluene disproportionation on ZSM-5 and other zeolites. Unfortunately, the results for only ZSM-5 did not reveal which m- or p-xylene isomer is preferred. Fig. 2 shows that m-xylene is a primary product of toluene disproportionation on ZSM-5.

Supporting information

Computing details

Data collection: Bruker FRAMBO; cell refinement: Bruker FRAMBO; data reduction: Bruker SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: Bruker SHELXTL; software used to prepare material for publication: Bruker SHELXTL.

Figures

(tol_zsm5)

Crystal data

C11.33H12.95O48Si24	F(000) = 3203.8
Mr = 1591.33	Dx = 2.018 Mg m^−3
Orthorhombic, P212121	Cu Kα radiation, λ = 1.54178 Å
a = 20.0990 (4) Å	µ = 6.49 mm^−1
b = 19.8440 (3) Å	T = 293 K
c = 13.4240 (2) Å	Cubic, colorless
V = 5354.09 (16) Å^3	0.10 × 0.07 × 0.05 mm
Z = 4

Data collection

DIP Image plate diffractometer	10206 independent reflections
Radiation source: roter	5636 reflections with I > 2σ(I)
Ni filter monochromator	Rint = 0.044
phi and ω scans	θmax = 70.2°, θmin = 3.1°
Absorption correction: empirical (using intensity measurements) ?	h = −24→24
Tmin = 0.609, Tmax = 0.723	k = −23→24
17509 measured reflections	l = −16→16

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F^2 > 2σ(F^2)] = 0.058	Ride
wR(F^2) = 0.172	w = 1/[σ^2(Fo^2) + (0.1099P)^2 + 4.6477P] where P = (Fo^2 + 2Fc^2)/3
S = 1.05	(Δ/σ)max = 0.060
5636 reflections	Δρmax = 0.79 e Å^−3
700 parameters	Δρmin = −0.72 e Å^−3
15 restraints	Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: 0.43 (4)

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.

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	Occ. (<1)
C11	0.0110 (10)	0.6854 (7)	0.2209 (16)	0.158 (13)*	0.607 (12)
C12	0.0634 (9)	0.7062 (9)	0.1608 (14)	0.184 (13)*	0.607 (12)
H12	0.0881	0.6746	0.1256	0.221*	0.607 (12)
C13	0.0789 (9)	0.7743 (11)	0.1533 (14)	0.186 (13)*	0.607 (12)
H13	0.1139	0.7882	0.1130	0.223*	0.607 (12)
C14	0.0419 (10)	0.8216 (8)	0.2059 (17)	0.160 (11)*	0.607 (12)
H14	0.0522	0.8671	0.2009	0.192*	0.607 (12)
C15	−0.0105 (10)	0.8008 (8)	0.2661 (16)	0.176 (14)*	0.607 (12)
H15	−0.0352	0.8324	0.3013	0.212*	0.607 (12)
C16	−0.0260 (9)	0.7327 (9)	0.2736 (15)	0.136 (9)*	0.607 (12)
H16	−0.0610	0.7188	0.3138	0.163*	0.607 (12)
C17	0.0016 (15)	0.6124 (14)	0.239 (3)	0.219 (18)*	0.607 (12)
H17A	−0.0115	0.5906	0.1785	0.263*	0.607 (12)
H17B	−0.0323	0.6060	0.2887	0.263*	0.607 (12)
H17C	0.0426	0.5932	0.2625	0.263*	0.607 (12)
C21	−0.0031 (9)	0.8150 (13)	0.2296 (19)	0.18 (2)*	0.378 (12)
C22	0.0015 (13)	0.7606 (15)	0.294 (2)	0.18 (2)*	0.378 (12)
H22	0.0073	0.7678	0.3622	0.215*	0.378 (12)
C23	−0.0026 (15)	0.6952 (14)	0.258 (3)	0.128 (14)*	0.378 (12)
H23	0.0004	0.6588	0.3009	0.154*	0.378 (12)
C24	−0.0112 (15)	0.6843 (15)	0.156 (3)	0.28 (4)*	0.378 (12)
H24	−0.0140	0.6406	0.1315	0.336*	0.378 (12)
C25	−0.0158 (18)	0.739 (2)	0.091 (2)	0.29 (4)*	0.378 (12)
H25	−0.0216	0.7315	0.0235	0.342*	0.378 (12)
C26	−0.0117 (15)	0.8042 (17)	0.1281 (19)	0.23 (3)*	0.378 (12)
H26	−0.0147	0.8406	0.0848	0.278*	0.378 (12)
C27	0.0011 (14)	0.8790 (16)	0.264 (3)	0.125 (14)*	0.378 (12)
H27A	−0.0001	0.9099	0.2093	0.150*	0.378 (12)
H27B	0.0421	0.8846	0.3001	0.150*	0.378 (12)
H27C	−0.0357	0.8879	0.3079	0.150*	0.378 (12)
C31	−0.1164 (6)	0.7546 (6)	−0.0757 (10)	0.221 (15)*	0.634 (9)
C32	−0.1694 (8)	0.7759 (6)	−0.0171 (9)	0.123 (8)*	0.634 (9)
H32	−0.1616	0.7930	0.0464	0.148*	0.634 (9)
C33	−0.2340 (7)	0.7718 (7)	−0.0534 (12)	0.186 (12)*	0.634 (9)
H33	−0.2695	0.7861	−0.0142	0.223*	0.634 (9)
C34	−0.2457 (6)	0.7464 (6)	−0.1483 (13)	0.140 (8)*	0.634 (9)
H34	−0.2889	0.7436	−0.1726	0.168*	0.634 (9)
C35	−0.1927 (8)	0.7251 (6)	−0.2069 (9)	0.132 (8)*	0.634 (9)
H35	−0.2005	0.7081	−0.2704	0.158*	0.634 (9)
C36	−0.1280 (7)	0.7292 (6)	−0.1706 (10)	0.123 (8)*	0.634 (9)
H36	−0.0926	0.7149	−0.2098	0.148*	0.634 (9)
C37	−0.0556 (13)	0.7563 (11)	−0.0428 (18)	0.204 (14)*	0.634 (9)
H37A	−0.0261	0.7389	−0.0928	0.245*	0.634 (9)
H37B	−0.0523	0.7293	0.0163	0.245*	0.634 (9)
H37C	−0.0436	0.8020	−0.0276	0.245*	0.634 (9)
O1	0.3729 (2)	1.0609 (2)	0.5190 (3)	0.0381 (11)
O2	0.3104 (2)	1.0524 (2)	0.6866 (3)	0.0349 (9)
O3	0.2017 (2)	1.0557 (2)	0.7910 (4)	0.0512 (12)
O4	0.0976 (2)	1.0572 (2)	0.6793 (3)	0.0416 (11)
O5	0.11524 (19)	1.0632 (2)	0.4875 (3)	0.0289 (9)
O6	0.2434 (2)	1.0601 (2)	0.5216 (3)	0.0408 (11)
O7	0.3717 (2)	0.8385 (2)	0.5249 (4)	0.0425 (12)
O8	0.3071 (3)	0.8521 (2)	0.6885 (3)	0.0379 (10)
O9	0.1953 (2)	0.84545 (18)	0.7864 (3)	0.0372 (10)
O10	0.0870 (3)	0.8440 (3)	0.6827 (4)	0.0524 (14)
O11	0.1152 (2)	0.8358 (2)	0.4936 (4)	0.0408 (12)
O12	0.2421 (2)	0.8416 (3)	0.5221 (4)	0.0443 (12)
O13	0.3093 (3)	0.9508 (2)	0.5591 (3)	0.0535 (13)
O14	0.0823 (2)	0.9500 (2)	0.5708 (4)	0.0420 (11)
O15	0.4181 (2)	1.13557 (18)	0.3739 (4)	0.0355 (11)
O16	0.4052 (2)	1.0060 (2)	0.3475 (4)	0.0433 (12)
O17	0.4022 (2)	0.8747 (2)	0.3425 (3)	0.0390 (11)
O18	0.1934 (2)	1.13676 (17)	0.3822 (3)	0.0320 (9)
O19	0.1943 (3)	1.00733 (18)	0.3569 (3)	0.0430 (11)
O20	0.1933 (3)	0.87689 (18)	0.3481 (3)	0.0416 (11)
O21	−0.00340 (18)	1.0484 (2)	0.5553 (3)	0.0310 (9)
O22	−0.0059 (2)	0.8535 (2)	0.5512 (4)	0.0346 (11)
O23	0.4250 (2)	0.7529 (2)	0.3998 (3)	0.0401 (11)
O24	0.1921 (2)	0.75217 (17)	0.4010 (3)	0.0360 (10)
O25	0.2826 (2)	0.74721 (18)	0.8004 (3)	0.0334 (10)
O26	0.10991 (19)	0.74639 (18)	0.8060 (3)	0.0295 (9)
O27	0.8708 (2)	1.0555 (3)	0.5119 (3)	0.0463 (12)
O28	0.8033 (2)	1.06653 (17)	0.3503 (3)	0.0310 (9)
O29	0.7001 (2)	1.0621 (2)	0.2294 (3)	0.0474 (11)
O30	0.5988 (2)	1.06642 (19)	0.3496 (3)	0.0322 (10)
O31	0.61457 (19)	1.0509 (2)	0.5421 (3)	0.0309 (9)
O32	0.7428 (2)	1.0466 (3)	0.5184 (4)	0.0505 (13)
O33	0.8712 (2)	0.8446 (3)	0.5022 (4)	0.0472 (13)
O34	0.8052 (3)	0.8389 (2)	0.3400 (3)	0.0477 (12)
O35	0.6968 (2)	0.84893 (18)	0.2369 (3)	0.0390 (10)
O36	0.5905 (2)	0.8330 (2)	0.3465 (4)	0.0435 (12)
O37	0.6155 (2)	0.8463 (2)	0.5359 (4)	0.0370 (12)
O38	0.7424 (3)	0.8526 (3)	0.5067 (4)	0.0595 (16)
O39	0.8112 (3)	0.9506 (2)	0.4366 (4)	0.0654 (15)
O40	0.5771 (2)	0.9499 (2)	0.4296 (3)	0.0378 (10)
O41	0.9191 (2)	1.1211 (2)	0.6641 (4)	0.0407 (12)
O42	0.9110 (2)	0.9913 (2)	0.6741 (3)	0.0406 (11)
O43	0.9017 (2)	0.86075 (18)	0.6896 (3)	0.0325 (10)
O44	0.6898 (2)	1.12399 (19)	0.6541 (3)	0.0401 (11)
O45	0.6886 (2)	0.99435 (18)	0.6782 (3)	0.0347 (10)
O46	0.6953 (3)	0.86324 (17)	0.6878 (3)	0.0359 (10)
O47	0.49674 (18)	1.0519 (2)	0.4676 (3)	0.0290 (9)
O48	0.4953 (2)	0.8517 (2)	0.4736 (3)	0.0341 (11)
Si1	0.42311 (7)	1.06305 (7)	0.42713 (11)	0.0192 (3)
Si2	0.30852 (8)	1.03054 (6)	0.57164 (11)	0.0212 (3)
Si3	0.28056 (7)	1.05625 (7)	0.79564 (11)	0.0214 (3)
Si4	0.12313 (7)	1.05806 (7)	0.79019 (10)	0.0189 (3)
Si5	0.07261 (7)	1.02917 (7)	0.57396 (11)	0.0181 (3)
Si6	0.18717 (8)	1.06630 (7)	0.43703 (11)	0.0209 (3)
Si7	0.42334 (7)	0.82965 (7)	0.43516 (11)	0.0191 (3)
Si8	0.30749 (9)	0.87135 (7)	0.57311 (11)	0.0205 (3)
Si9	0.27272 (7)	0.82642 (7)	0.78820 (11)	0.0195 (3)
Si10	0.11852 (8)	0.82536 (7)	0.78673 (11)	0.0199 (3)
Si11	0.06951 (8)	0.87090 (7)	0.57441 (11)	0.0191 (3)
Si12	0.18594 (8)	0.82715 (6)	0.44067 (10)	0.0199 (3)
Si13	0.92364 (7)	1.05334 (7)	0.60133 (10)	0.0186 (3)
Si14	0.80721 (8)	1.02965 (6)	0.45506 (11)	0.0218 (3)
Si15	0.77953 (7)	1.06781 (6)	0.23623 (11)	0.0196 (3)
Si16	0.62220 (7)	1.06911 (7)	0.23581 (11)	0.0194 (3)
Si17	0.57204 (7)	1.02937 (7)	0.44683 (11)	0.0173 (3)
Si18	0.68470 (7)	1.05379 (7)	0.59752 (10)	0.0205 (3)
Si19	0.92315 (7)	0.82630 (7)	0.58549 (11)	0.0194 (3)
Si20	0.80734 (9)	0.87189 (6)	0.44695 (11)	0.0216 (3)
Si21	0.77343 (7)	0.82920 (7)	0.23258 (12)	0.0209 (3)
Si22	0.61928 (8)	0.82846 (7)	0.23530 (12)	0.0202 (3)
Si23	0.56992 (8)	0.87071 (7)	0.44605 (11)	0.0195 (3)
Si24	0.68649 (8)	0.82708 (6)	0.58150 (11)	0.0209 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.024 (2)	0.048 (3)	0.042 (3)	−0.007 (2)	0.0121 (19)	−0.003 (2)
O2	0.033 (2)	0.047 (2)	0.0246 (19)	−0.005 (2)	0.0049 (19)	−0.0030 (18)
O3	0.011 (2)	0.078 (3)	0.065 (3)	0.002 (2)	−0.001 (2)	−0.002 (3)
O4	0.053 (3)	0.047 (3)	0.025 (2)	0.002 (2)	−0.008 (2)	−0.006 (2)
O5	0.021 (2)	0.036 (2)	0.030 (2)	−0.0007 (17)	0.0065 (16)	0.0143 (18)
O6	0.026 (2)	0.056 (3)	0.040 (3)	0.007 (2)	−0.0101 (19)	0.009 (2)
O7	0.028 (3)	0.053 (3)	0.046 (3)	0.005 (2)	0.017 (2)	0.001 (2)
O8	0.041 (3)	0.047 (2)	0.026 (2)	−0.004 (2)	0.002 (2)	0.0113 (17)
O9	0.019 (2)	0.033 (2)	0.060 (3)	−0.0001 (18)	0.001 (2)	−0.0059 (19)
O10	0.059 (4)	0.058 (3)	0.040 (3)	−0.006 (2)	−0.020 (3)	0.018 (2)
O11	0.029 (3)	0.039 (3)	0.054 (3)	0.0013 (19)	0.014 (2)	−0.020 (2)
O12	0.033 (3)	0.053 (3)	0.046 (3)	−0.009 (2)	−0.007 (2)	−0.009 (2)
O13	0.088 (4)	0.019 (2)	0.053 (3)	0.003 (3)	−0.003 (3)	0.003 (2)
O14	0.039 (3)	0.019 (2)	0.068 (3)	0.0008 (19)	0.001 (2)	0.004 (2)
O15	0.042 (3)	0.017 (2)	0.048 (3)	0.0002 (16)	−0.019 (2)	0.0088 (18)
O16	0.059 (3)	0.031 (2)	0.040 (3)	−0.011 (2)	−0.010 (2)	−0.008 (2)
O17	0.054 (3)	0.027 (2)	0.036 (3)	0.009 (2)	−0.008 (2)	0.0113 (19)
O18	0.042 (2)	0.0191 (18)	0.035 (2)	−0.0032 (18)	0.010 (2)	0.0062 (15)
O19	0.064 (3)	0.0218 (19)	0.044 (2)	0.006 (2)	0.010 (3)	−0.0102 (18)
O20	0.063 (3)	0.0230 (18)	0.039 (2)	−0.010 (2)	−0.001 (3)	0.0087 (18)
O21	0.019 (2)	0.041 (2)	0.033 (2)	0.0033 (18)	0.0056 (16)	0.003 (2)
O22	0.018 (2)	0.046 (3)	0.040 (3)	−0.0071 (18)	−0.0002 (19)	0.000 (2)
O23	0.064 (3)	0.0164 (19)	0.040 (3)	0.003 (2)	−0.012 (2)	−0.0055 (18)
O24	0.055 (3)	0.0141 (17)	0.039 (2)	0.000 (2)	0.019 (2)	−0.0038 (16)
O25	0.044 (2)	0.0148 (17)	0.041 (2)	−0.0007 (17)	−0.0062 (19)	−0.0054 (17)
O26	0.044 (2)	0.0135 (17)	0.031 (2)	0.0005 (17)	0.0027 (18)	−0.0003 (16)
O27	0.026 (2)	0.069 (3)	0.043 (3)	−0.008 (2)	−0.012 (2)	0.010 (3)
O28	0.043 (2)	0.0276 (19)	0.0225 (19)	−0.0063 (19)	−0.0039 (19)	0.0052 (15)
O29	0.025 (2)	0.066 (3)	0.051 (3)	0.002 (2)	0.000 (2)	0.008 (2)
O30	0.043 (2)	0.030 (2)	0.024 (2)	−0.0014 (18)	0.0093 (18)	0.0054 (17)
O31	0.022 (2)	0.039 (2)	0.032 (2)	−0.0023 (18)	−0.0100 (16)	−0.009 (2)
O32	0.025 (2)	0.082 (4)	0.044 (3)	0.010 (3)	0.015 (2)	0.011 (3)
O33	0.037 (3)	0.062 (3)	0.043 (3)	0.009 (2)	−0.016 (2)	0.003 (2)
O34	0.048 (3)	0.063 (3)	0.032 (2)	0.007 (3)	−0.012 (2)	−0.022 (2)
O35	0.021 (2)	0.0329 (19)	0.063 (3)	−0.0013 (18)	0.001 (2)	−0.0049 (19)
O36	0.062 (3)	0.030 (2)	0.039 (3)	−0.001 (2)	0.014 (2)	−0.013 (2)
O37	0.025 (3)	0.038 (2)	0.049 (3)	0.0056 (18)	−0.014 (2)	0.004 (2)
O38	0.039 (3)	0.088 (4)	0.052 (3)	−0.015 (3)	0.013 (3)	0.012 (3)
O39	0.103 (4)	0.016 (2)	0.077 (4)	−0.003 (3)	0.007 (4)	0.004 (2)
O40	0.047 (3)	0.023 (2)	0.043 (2)	−0.002 (2)	0.003 (2)	0.001 (2)
O41	0.044 (3)	0.024 (2)	0.054 (3)	0.0023 (19)	0.016 (2)	−0.012 (2)
O42	0.052 (3)	0.027 (2)	0.042 (3)	−0.0030 (19)	0.011 (2)	0.0074 (19)
O43	0.040 (3)	0.018 (2)	0.039 (3)	0.0010 (16)	0.006 (2)	−0.0025 (17)
O44	0.047 (3)	0.0233 (19)	0.050 (3)	−0.004 (2)	−0.016 (2)	−0.0100 (18)
O45	0.042 (3)	0.0229 (18)	0.039 (2)	0.0065 (19)	−0.005 (2)	0.0082 (16)
O46	0.053 (3)	0.0198 (18)	0.036 (2)	−0.0058 (19)	−0.008 (3)	−0.0101 (16)
O47	0.0153 (19)	0.037 (2)	0.035 (2)	0.0055 (17)	−0.0004 (16)	0.000 (2)
O48	0.021 (2)	0.047 (3)	0.034 (3)	−0.0085 (19)	0.0039 (18)	−0.0023 (19)
Si1	0.0178 (7)	0.0141 (7)	0.0258 (7)	−0.0005 (5)	−0.0010 (6)	0.0034 (6)
Si2	0.0203 (8)	0.0185 (6)	0.0249 (7)	0.0010 (6)	0.0021 (7)	0.0013 (5)
Si3	0.0212 (7)	0.0170 (6)	0.0258 (7)	0.0004 (5)	0.0000 (5)	−0.0031 (6)
Si4	0.0183 (7)	0.0163 (6)	0.0222 (7)	−0.0009 (6)	−0.0001 (5)	−0.0032 (6)
Si5	0.0168 (7)	0.0158 (6)	0.0215 (7)	0.0000 (5)	0.0011 (6)	0.0013 (5)
Si6	0.0195 (7)	0.0174 (6)	0.0258 (7)	0.0009 (5)	0.0049 (6)	0.0041 (5)
Si7	0.0190 (8)	0.0120 (6)	0.0265 (7)	0.0008 (5)	0.0009 (6)	0.0005 (5)
Si8	0.0215 (8)	0.0165 (6)	0.0235 (7)	0.0001 (6)	0.0024 (7)	−0.0008 (5)
Si9	0.0219 (8)	0.0129 (6)	0.0237 (7)	−0.0018 (5)	−0.0001 (6)	−0.0011 (6)
Si10	0.0238 (8)	0.0115 (6)	0.0244 (7)	0.0011 (6)	0.0003 (6)	−0.0006 (6)
Si11	0.0180 (8)	0.0161 (6)	0.0233 (7)	0.0007 (5)	0.0005 (6)	−0.0005 (5)
Si12	0.0210 (8)	0.0122 (6)	0.0265 (7)	−0.0014 (6)	0.0033 (6)	−0.0021 (5)
Si13	0.0159 (7)	0.0156 (6)	0.0242 (7)	0.0006 (6)	0.0012 (5)	0.0000 (6)
Si14	0.0214 (8)	0.0188 (6)	0.0251 (7)	0.0010 (6)	0.0008 (7)	0.0023 (5)
Si15	0.0208 (7)	0.0155 (7)	0.0225 (7)	0.0006 (5)	0.0008 (6)	0.0035 (5)
Si16	0.0195 (7)	0.0168 (7)	0.0218 (7)	0.0002 (5)	0.0008 (6)	0.0013 (5)
Si17	0.0171 (7)	0.0155 (6)	0.0194 (7)	0.0001 (5)	−0.0021 (6)	0.0005 (5)
Si18	0.0190 (7)	0.0185 (6)	0.0239 (7)	0.0003 (6)	−0.0031 (6)	−0.0033 (6)
Si19	0.0177 (8)	0.0132 (6)	0.0273 (7)	0.0021 (5)	−0.0023 (6)	−0.0026 (6)
Si20	0.0235 (8)	0.0158 (6)	0.0254 (7)	−0.0018 (6)	−0.0033 (7)	0.0010 (5)
Si21	0.0245 (8)	0.0119 (6)	0.0263 (8)	−0.0009 (5)	0.0000 (6)	−0.0008 (6)
Si22	0.0215 (8)	0.0108 (6)	0.0281 (8)	0.0019 (5)	−0.0007 (6)	−0.0012 (6)
Si23	0.0179 (8)	0.0153 (6)	0.0252 (7)	0.0003 (5)	0.0002 (6)	−0.0020 (5)
Si24	0.0233 (8)	0.0142 (6)	0.0251 (7)	0.0003 (6)	−0.0050 (7)	−0.0003 (5)

Geometric parameters (Å, º)

C11—C12	1.3900	O18—Si9^i	1.609 (4)
C11—C16	1.3900	O19—Si3^i	1.589 (4)
C11—C17	1.48 (3)	O19—Si6	1.596 (4)
C12—C13	1.3900	O20—Si3^i	1.591 (4)
C12—H12	0.9300	O20—Si12	1.594 (4)
C13—C14	1.3900	O21—Si13^ii	1.594 (4)
C13—H13	0.9300	O21—Si5	1.594 (4)
C14—C15	1.3900	O22—Si11	1.585 (4)
C14—H14	0.9300	O22—Si19^ii	1.593 (4)
C15—C16	1.3900	O23—Si19^iii	1.585 (4)
C15—H15	0.9300	O23—Si7	1.595 (4)
C16—H16	0.9300	O24—Si12	1.585 (3)
C17—H17A	0.9600	O24—Si24^iii	1.594 (3)
C17—H17B	0.9600	O25—Si21^iii	1.590 (4)
C17—H17C	0.9600	O25—Si9	1.593 (4)
C21—C27	1.35 (4)	O26—Si22^iii	1.596 (4)
C21—C22	1.3900	O26—Si10	1.598 (4)
C21—C26	1.3900	O27—Si14	1.575 (4)
C22—C23	1.3900	O27—Si13	1.603 (4)
C22—H22	0.9300	O28—Si14	1.587 (4)
C23—C24	1.3900	O28—Si15	1.605 (4)
C23—H23	0.9300	O29—Si16	1.575 (5)
C24—C25	1.3900	O29—Si15	1.603 (5)
C24—H24	0.9300	O30—Si17	1.592 (4)
C25—C26	1.3900	O30—Si16	1.599 (4)
C25—H25	0.9300	O31—Si18	1.595 (4)
C26—H26	0.9300	O31—Si17	1.597 (4)
C27—H27A	0.9600	O32—Si18	1.585 (4)
C27—H27B	0.9600	O32—Si14	1.585 (4)
C27—H27C	0.9600	O33—Si19	1.572 (5)
C31—C37	1.30 (3)	O33—Si20	1.579 (5)
C31—C32	1.3900	O34—Si20	1.579 (4)
C31—C36	1.3900	O34—Si21	1.589 (4)
C32—C33	1.3900	O35—Si21	1.591 (5)
C32—H32	0.9300	O35—Si22	1.610 (5)
C33—C34	1.3900	O36—Si23	1.586 (4)
C33—H33	0.9300	O36—Si22	1.604 (5)
C34—C35	1.3900	O37—Si23	1.590 (5)
C34—H34	0.9300	O37—Si24	1.599 (4)
C35—C36	1.3900	O38—Si20	1.580 (5)
C35—H35	0.9300	O38—Si24	1.589 (5)
C36—H36	0.9300	O39—Si20	1.570 (4)
C37—H37A	0.9600	O39—Si14	1.590 (4)
C37—H37B	0.9600	O40—Si23	1.593 (4)
C37—H37C	0.9600	O40—Si17	1.598 (4)
O1—Si2	1.593 (4)	O41—Si22^iv	1.584 (4)
O1—Si1	1.594 (4)	O41—Si13	1.590 (4)
O2—Si3	1.584 (4)	O42—Si13	1.591 (4)
O2—Si2	1.603 (4)	O42—Si16^iv	1.604 (4)
O3—Si4	1.579 (4)	O43—Si16^iv	1.598 (4)
O3—Si3	1.587 (4)	O43—Si19	1.614 (4)
O4—Si4	1.575 (4)	O44—Si21^iv	1.588 (4)
O4—Si5	1.600 (4)	O44—Si18	1.590 (4)
O5—Si5	1.593 (4)	O45—Si15^iv	1.594 (4)
O5—Si6	1.598 (4)	O45—Si18	1.603 (4)
O6—Si2	1.584 (4)	O46—Si15^iv	1.597 (4)
O6—Si6	1.606 (4)	O46—Si24	1.607 (4)
O7—Si8	1.585 (5)	O47—Si1	1.592 (4)
O7—Si7	1.599 (5)	O47—Si17	1.602 (4)
O8—Si9	1.591 (4)	O48—Si23	1.590 (4)
O8—Si8	1.595 (4)	O48—Si7	1.596 (4)
O9—Si10	1.593 (5)	Si3—O19^v	1.589 (4)
O9—Si9	1.602 (5)	Si3—O20^v	1.591 (4)
O10—Si10	1.578 (5)	Si4—O16^v	1.592 (4)
O10—Si11	1.588 (5)	Si4—O17^v	1.592 (4)
O11—Si11	1.583 (4)	Si9—O18^v	1.609 (4)
O11—Si12	1.599 (4)	Si10—O15^v	1.585 (4)
O12—Si8	1.595 (5)	Si13—O21^vi	1.594 (4)
O12—Si12	1.597 (5)	Si15—O45^vii	1.594 (4)
O13—Si8	1.588 (4)	Si15—O46^vii	1.597 (4)
O13—Si2	1.592 (4)	Si16—O43^vii	1.598 (4)
O14—Si5	1.583 (4)	Si16—O42^vii	1.604 (4)
O14—Si11	1.591 (4)	Si19—O23^viii	1.585 (4)
O15—Si10^i	1.585 (4)	Si19—O22^vi	1.593 (4)
O15—Si1	1.610 (4)	Si21—O44^vii	1.588 (4)
O16—Si4^i	1.592 (4)	Si21—O25^viii	1.590 (4)
O16—Si1	1.598 (4)	Si22—O41^vii	1.584 (4)
O17—Si7	1.589 (4)	Si22—O26^viii	1.596 (4)
O17—Si4^i	1.592 (4)	Si24—O24^viii	1.594 (3)
O18—Si6	1.585 (4)
C12—C11—C16	120.0	O2—Si3—O3	110.0 (3)
C12—C11—C17	118.9 (8)	O2—Si3—O19^v	108.6 (2)
C16—C11—C17	120.5 (8)	O3—Si3—O19^v	109.5 (3)
C13—C12—C11	120.0	O2—Si3—O20^v	108.9 (2)
C13—C12—H12	120.0	O3—Si3—O20^v	110.6 (3)
C11—C12—H12	120.0	O19^v—Si3—O20^v	109.1 (2)
C12—C13—C14	120.0	O4—Si4—O3	109.4 (3)
C12—C13—H13	120.0	O4—Si4—O16^v	109.4 (3)
C14—C13—H13	120.0	O3—Si4—O16^v	109.3 (3)
C15—C14—C13	120.0	O4—Si4—O17^v	108.8 (3)
C15—C14—H14	120.0	O3—Si4—O17^v	109.9 (3)
C13—C14—H14	120.0	O16^v—Si4—O17^v	110.0 (2)
C14—C15—C16	120.0	O14—Si5—O5	109.6 (2)
C14—C15—H15	120.0	O14—Si5—O21	110.5 (2)
C16—C15—H15	120.0	O5—Si5—O21	107.4 (2)
C15—C16—C11	120.0	O14—Si5—O4	109.3 (3)
C15—C16—H16	120.0	O5—Si5—O4	109.1 (2)
C11—C16—H16	120.0	O21—Si5—O4	110.9 (2)
C11—C17—H17A	109.5	O18—Si6—O19	109.1 (2)
C11—C17—H17B	109.5	O18—Si6—O5	107.6 (2)
H17A—C17—H17B	109.5	O19—Si6—O5	109.8 (3)
C11—C17—H17C	109.5	O18—Si6—O6	109.9 (3)
H17A—C17—H17C	109.5	O19—Si6—O6	110.9 (3)
H17B—C17—H17C	109.5	O5—Si6—O6	109.5 (2)
C27—C21—C22	120.7 (9)	O17—Si7—O23	108.0 (2)
C27—C21—C26	119.3 (8)	O17—Si7—O48	110.0 (3)
C22—C21—C26	120.0	O23—Si7—O48	109.7 (2)
C21—C22—C23	120.0	O17—Si7—O7	110.7 (3)
C21—C22—H22	120.0	O23—Si7—O7	110.0 (3)
C23—C22—H22	120.0	O48—Si7—O7	108.4 (3)
C24—C23—C22	120.0	O7—Si8—O13	110.0 (3)
C24—C23—H23	120.0	O7—Si8—O12	110.0 (3)
C22—C23—H23	120.0	O13—Si8—O12	109.6 (3)
C25—C24—C23	120.0	O7—Si8—O8	107.6 (3)
C25—C24—H24	120.0	O13—Si8—O8	110.6 (2)
C23—C24—H24	120.0	O12—Si8—O8	109.0 (3)
C26—C25—C24	120.0	O8—Si9—O25	110.4 (2)
C26—C25—H25	120.0	O8—Si9—O9	109.5 (3)
C24—C25—H25	120.0	O25—Si9—O9	110.8 (2)
C25—C26—C21	120.0	O8—Si9—O18^v	109.3 (2)
C25—C26—H26	120.0	O25—Si9—O18^v	108.4 (2)
C21—C26—H26	120.0	O9—Si9—O18^v	108.4 (2)
C21—C27—H27A	109.5	O10—Si10—O15^v	110.6 (3)
C21—C27—H27B	109.5	O10—Si10—O9	109.1 (3)
H27A—C27—H27B	109.5	O15^v—Si10—O9	109.2 (2)
C21—C27—H27C	109.5	O10—Si10—O26	109.3 (3)
H27A—C27—H27C	109.5	O15^v—Si10—O26	108.1 (2)
H27B—C27—H27C	109.5	O9—Si10—O26	110.5 (2)
C37—C31—C32	121.3 (8)	O11—Si11—O22	108.9 (3)
C37—C31—C36	118.6 (8)	O11—Si11—O10	110.6 (3)
C32—C31—C36	120.0	O22—Si11—O10	108.6 (3)
C33—C32—C31	120.0	O11—Si11—O14	108.6 (3)
C33—C32—H32	120.0	O22—Si11—O14	111.3 (2)
C31—C32—H32	120.0	O10—Si11—O14	108.9 (3)
C32—C33—C34	120.0	O24—Si12—O20	108.2 (2)
C32—C33—H33	120.0	O24—Si12—O12	110.0 (3)
C34—C33—H33	120.0	O20—Si12—O12	110.9 (3)
C33—C34—C35	120.0	O24—Si12—O11	108.7 (2)
C33—C34—H34	120.0	O20—Si12—O11	111.2 (3)
C35—C34—H34	120.0	O12—Si12—O11	107.8 (3)
C36—C35—C34	120.0	O41—Si13—O42	108.7 (2)
C36—C35—H35	120.0	O41—Si13—O21^vi	108.1 (2)
C34—C35—H35	120.0	O42—Si13—O21^vi	109.7 (2)
C35—C36—C31	120.0	O41—Si13—O27	109.7 (3)
C35—C36—H36	120.0	O42—Si13—O27	112.0 (3)
C31—C36—H36	120.0	O21^vi—Si13—O27	108.7 (2)
C31—C37—H37A	109.5	O27—Si14—O32	109.5 (3)
C31—C37—H37B	109.5	O27—Si14—O28	108.6 (2)
H37A—C37—H37B	109.5	O32—Si14—O28	109.7 (3)
C31—C37—H37C	109.5	O27—Si14—O39	110.8 (3)
H37A—C37—H37C	109.5	O32—Si14—O39	109.5 (3)
H37B—C37—H37C	109.5	O28—Si14—O39	108.6 (2)
Si2—O1—Si1	150.1 (3)	O45^vii—Si15—O46^vii	109.7 (2)
Si3—O2—Si2	153.4 (3)	O45^vii—Si15—O29	108.5 (2)
Si4—O3—Si3	177.3 (4)	O46^vii—Si15—O29	110.6 (3)
Si4—O4—Si5	160.3 (3)	O45^vii—Si15—O28	109.5 (2)
Si5—O5—Si6	144.3 (3)	O46^vii—Si15—O28	107.9 (2)
Si2—O6—Si6	155.5 (3)	O29—Si15—O28	110.5 (2)
Si8—O7—Si7	151.8 (4)	O29—Si16—O43^vii	110.8 (2)
Si9—O8—Si8	153.6 (4)	O29—Si16—O30	110.0 (2)
Si10—O9—Si9	151.9 (3)	O43^vii—Si16—O30	108.2 (2)
Si10—O10—Si11	168.0 (4)	O29—Si16—O42^vii	108.7 (3)
Si11—O11—Si12	150.2 (3)	O43^vii—Si16—O42^vii	109.0 (2)
Si8—O12—Si12	160.5 (4)	O30—Si16—O42^vii	110.2 (2)
Si8—O13—Si2	167.0 (3)	O30—Si17—O31	110.6 (2)
Si5—O14—Si11	163.4 (3)	O30—Si17—O40	108.4 (2)
Si10^i—O15—Si1	142.6 (3)	O31—Si17—O40	110.3 (2)
Si4^i—O16—Si1	165.9 (4)	O30—Si17—O47	109.4 (2)
Si7—O17—Si4^i	154.5 (3)	O31—Si17—O47	107.0 (2)
Si6—O18—Si9^i	142.9 (3)	O40—Si17—O47	111.1 (2)
Si3^i—O19—Si6	163.7 (4)	O32—Si18—O44	110.6 (3)
Si3^i—O20—Si12	153.1 (3)	O32—Si18—O31	109.6 (3)
Si13^ii—O21—Si5	146.6 (3)	O44—Si18—O31	108.1 (2)
Si11—O22—Si19^ii	150.8 (4)	O32—Si18—O45	110.5 (2)
Si19^iii—O23—Si7	155.4 (3)	O44—Si18—O45	108.6 (2)
Si12—O24—Si24^iii	150.6 (3)	O31—Si18—O45	109.4 (2)
Si21^iii—O25—Si9	153.9 (3)	O33—Si19—O23^viii	109.5 (3)
Si22^iii—O26—Si10	147.5 (3)	O33—Si19—O22^vi	108.1 (3)
Si14—O27—Si13	153.1 (3)	O23^viii—Si19—O22^vi	110.5 (2)
Si14—O28—Si15	150.2 (3)	O33—Si19—O43	109.9 (3)
Si16—O29—Si15	168.8 (3)	O23^viii—Si19—O43	108.6 (2)
Si17—O30—Si16	153.9 (3)	O22^vi—Si19—O43	110.2 (2)
Si18—O31—Si17	148.9 (3)	O39—Si20—O33	110.0 (3)
Si18—O32—Si14	168.6 (4)	O39—Si20—O34	109.4 (3)
Si19—O33—Si20	162.4 (4)	O33—Si20—O34	107.9 (3)
Si20—O34—Si21	152.4 (4)	O39—Si20—O38	109.1 (3)
Si21—O35—Si22	151.0 (3)	O33—Si20—O38	110.5 (3)
Si23—O36—Si22	154.8 (3)	O34—Si20—O38	109.9 (3)
Si23—O37—Si24	151.3 (4)	O44^vii—Si21—O34	110.1 (3)
Si20—O38—Si24	169.2 (5)	O44^vii—Si21—O25^viii	108.6 (2)
Si20—O39—Si14	164.8 (4)	O34—Si21—O25^viii	108.8 (2)
Si23—O40—Si17	161.4 (3)	O44^vii—Si21—O35	109.4 (2)
Si22^iv—O41—Si13	151.9 (3)	O34—Si21—O35	109.1 (3)
Si13—O42—Si16^iv	164.1 (3)	O25^viii—Si21—O35	110.9 (2)
Si16^iv—O43—Si19	141.8 (3)	O41^vii—Si22—O26^viii	108.7 (2)
Si21^iv—O44—Si18	149.3 (3)	O41^vii—Si22—O36	110.5 (3)
Si15^iv—O45—Si18	156.8 (3)	O26^viii—Si22—O36	109.5 (2)
Si15^iv—O46—Si24	141.1 (3)	O41^vii—Si22—O35	108.7 (2)
Si1—O47—Si17	149.0 (3)	O26^viii—Si22—O35	110.7 (2)
Si23—O48—Si7	147.6 (3)	O36—Si22—O35	108.8 (3)
O47—Si1—O1	108.7 (2)	O36—Si23—O37	110.2 (3)
O47—Si1—O16	109.8 (2)	O36—Si23—O48	109.2 (3)
O1—Si1—O16	110.9 (2)	O37—Si23—O48	107.1 (3)
O47—Si1—O15	109.5 (2)	O36—Si23—O40	108.9 (2)
O1—Si1—O15	109.1 (3)	O37—Si23—O40	110.7 (2)
O16—Si1—O15	108.8 (2)	O48—Si23—O40	110.6 (2)
O6—Si2—O13	109.3 (3)	O38—Si24—O24^viii	110.9 (3)
O6—Si2—O1	110.1 (2)	O38—Si24—O37	108.2 (3)
O13—Si2—O1	108.8 (3)	O24^viii—Si24—O37	110.8 (2)
O6—Si2—O2	109.1 (2)	O38—Si24—O46	109.9 (3)
O13—Si2—O2	111.8 (2)	O24^viii—Si24—O46	107.6 (2)
O1—Si2—O2	107.8 (2)	O37—Si24—O46	109.4 (3)

Symmetry codes: (i) −x+1/2, −y+2, z−1/2; (ii) x−1, y, z; (iii) x−1/2, −y+3/2, −z+1; (iv) −x+3/2, −y+2, z+1/2; (v) −x+1/2, −y+2, z+1/2; (vi) x+1, y, z; (vii) −x+3/2, −y+2, z−1/2; (viii) x+1/2, −y+3/2, −z+1.

 

Footnotes

¹Supplementary data for this paper are available from the IUCr electronic archives (Reference: BS5009 ). Services for accessing these data are described at the back of the journal.

²The symmetry operations in P2₁2₁2₁ become: x, y, z; ; ; .