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metal-organic compounds
One of the two independent Zn atoms of the polymeric title compound, [Zn3(C16H10O4)3(C10H8N2)]n, lies on a special position of site symmetry 3 and the other on a special position of site symmetry . The carboxylate ends of the 4,4′-(ethene-1,2-diyl)dibenzoate dianion, which lies on a special position of site symmetry , each bridge these two independent Zn atoms. The bipyridine-coordinated Zn atom on the threefold axis has a tetrahedral geometry, whereas the other Zn atom is coordinated by the O atoms of six different dianions in an octahedral geometry.
Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536806047532/hg2126sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S1600536806047532/hg2126Isup2.hkl |
CCDC reference: 629900
Key indicators
- Single-crystal X-ray study
- T = 293 K
- Mean (C-C) = 0.007 Å
- Disorder in main residue
- R factor = 0.062
- wR factor = 0.194
- Data-to-parameter ratio = 15.0
checkCIF/PLATON results
No syntax errors found
Alert level B ABSTM02_ALERT_3_B The ratio of expected to reported Tmax/Tmin(RR') is < 0.75 Tmin and Tmax reported: 0.421 0.791 Tmin(prime) and Tmax expected: 0.657 0.781 RR(prime) = 0.633 Please check that your absorption correction is appropriate. PLAT061_ALERT_3_B Tmax/Tmin Range Test RR' too Large ............. 0.62 PLAT301_ALERT_3_B Main Residue Disorder ......................... 27.00 Perc.
Alert level C PLAT031_ALERT_4_C Refined Extinction Parameter within Range ...... 3.25 Sigma PLAT041_ALERT_1_C Calc. and Rep. SumFormula Strings Differ .... ? PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ .... ? PLAT045_ALERT_1_C Calculated and Reported Z Differ by ............ 3.00 Ratio PLAT068_ALERT_1_C Reported F000 Differs from Calcd (or Missing)... ? PLAT242_ALERT_2_C Check Low Ueq as Compared to Neighbors for Zn1 PLAT341_ALERT_3_C Low Bond Precision on C-C bonds (x 1000) Ang ... 7
Alert level G FORMU01_ALERT_2_G There is a discrepancy between the atom counts in the _chemical_formula_sum and the formula from the _atom_site* data. Atom count from _chemical_formula_sum:C58 H38 N2 O12 Zn3 Atom count from the _atom_site data: C57.92 H37.92 N2 O12 Zn3 CELLZ01_ALERT_1_G Difference between formula and atom_site contents detected. CELLZ01_ALERT_1_G ALERT: check formula stoichiometry or atom site occupancies. From the CIF: _cell_formula_units_Z 3 From the CIF: _chemical_formula_sum C58 H38 N2 O12 Zn3 TEST: Compare cell contents of formula and atom_site data atom Z*formula cif sites diff C 174.00 173.76 0.24 H 114.00 113.76 0.24 N 6.00 6.00 0.00 O 36.00 36.00 0.00 Zn 9.00 9.00 0.00 PLAT199_ALERT_1_G Check the Reported _cell_measurement_temperature 293 K
0 ALERT level A = In general: serious problem 3 ALERT level B = Potentially serious problem 7 ALERT level C = Check and explain 4 ALERT level G = General alerts; check 7 ALERT type 1 CIF construction/syntax error, inconsistent or missing data 2 ALERT type 2 Indicator that the structure model may be wrong or deficient 4 ALERT type 3 Indicator that the structure quality may be low 1 ALERT type 4 Improvement, methodology, query or suggestion 0 ALERT type 5 Informative message, check
Computing details top
Data collection: RAPID-AUTO (Rigaku, 1998); cell refinement: RAPID-AUTO; data reduction: CrystalStructure (Rigaku/MSC, 2002); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: X-SEED (Barbour, 2001); software used to prepare material for publication: publCIF (Westrip, 2006).
Poly[(µ2-4,4'-bipyridine)tris[µ4-(E)-4,4'-(ethene-1,2-
diyl)dibenzoato]zinc(II)] top
Crystal data top
[Zn3(C16H10O4)(C10H8N2)] | Dx = 1.401 Mg m−3 |
Mr = 1151.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3 | Cell parameters from 7459 reflections |
Hall symbol: -R 3 | θ = 3.1–27.4° |
a = 16.134 (1) Å | µ = 1.37 mm−1 |
c = 18.162 (1) Å | T = 293 K |
V = 4094.1 (3) Å3 | Prism, colorless |
Z = 3 | 0.30 × 0.24 × 0.18 mm |
F(000) = 1758 |
Data collection top
Rigaku R-AXIS RAPID IP diffractometer | 2086 independent reflections |
Radiation source: fine-focus sealed tube | 1249 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.076 |
ω scans | θmax = 27.4°, θmin = 3.1° |
Absorption correction: multi-scan (ABSCOR; Higashi, 1995) | h = −20→20 |
Tmin = 0.421, Tmax = 0.791 | k = −20→20 |
13477 measured reflections | l = −21→23 |
Refinement top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | Hydrogen site location: inferred from neighbouring sites |
R[F2 > 2σ(F2)] = 0.062 | H-atom parameters constrained |
wR(F2) = 0.194 | w = 1/[σ2(Fo2) + (0.0927P)2 + 8.7373P] where P = (Fo2 + 2Fc2)/3 |
S = 1.11 | (Δ/σ)max = 0.001 |
2086 reflections | Δρmax = 0.62 e Å−3 |
139 parameters | Δρmin = −0.88 e Å−3 |
138 restraints | Extinction correction: SHELXL97, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
Primary atom site location: structure-invariant direct methods | Extinction coefficient: 0.0013 (4) |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Zn1 | 1.0000 | 0.0000 | 0.80699 (5) | 0.0509 (4) | |
Zn2 | 1.0000 | 0.0000 | 1.0000 | 0.0456 (4) | |
O1 | 1.0030 (3) | 0.1204 (3) | 0.82481 (19) | 0.0658 (10) | |
O2 | 0.9378 (3) | 0.0597 (2) | 0.93358 (18) | 0.0579 (9) | |
C1 | 0.9736 (4) | 0.1270 (3) | 0.8884 (3) | 0.0576 (13) | |
C2 | 0.9822 (3) | 0.2205 (3) | 0.9083 (2) | 0.0607 (14) | |
C5 | 1.0008 (4) | 0.3949 (3) | 0.9483 (3) | 0.086 (2) | |
C3 | 1.0506 (6) | 0.3040 (6) | 0.8738 (5) | 0.056 (2) | 0.50 |
H3 | 1.0900 | 0.3014 | 0.8376 | 0.067* | 0.50 |
C4 | 1.0595 (7) | 0.3910 (9) | 0.8940 (4) | 0.070 (3) | 0.50 |
H4 | 1.1050 | 0.4470 | 0.8711 | 0.084* | 0.50 |
C6 | 0.9321 (7) | 0.3107 (6) | 0.9821 (6) | 0.081 (3) | 0.50 |
H6 | 0.8923 | 0.3133 | 1.0180 | 0.097* | 0.50 |
C7 | 0.9225 (7) | 0.2232 (9) | 0.9626 (4) | 0.068 (3) | 0.50 |
H7 | 0.8769 | 0.1671 | 0.9854 | 0.082* | 0.50 |
C3' | 1.0228 (6) | 0.2971 (6) | 0.8597 (6) | 0.056 (2) | 0.50 |
H3' | 1.0437 | 0.2899 | 0.8136 | 0.067* | 0.50 |
C4' | 1.0324 (7) | 0.3845 (9) | 0.8796 (4) | 0.070 (3) | 0.50 |
H4' | 1.0598 | 0.4359 | 0.8471 | 0.084* | 0.50 |
C6' | 0.9606 (7) | 0.3186 (7) | 0.9973 (6) | 0.081 (3) | 0.50 |
H6' | 0.9401 | 0.3260 | 1.0435 | 0.097* | 0.50 |
C7' | 0.9510 (7) | 0.2313 (9) | 0.9772 (4) | 0.068 (3) | 0.50 |
H7' | 0.9238 | 0.1799 | 1.0097 | 0.082* | 0.50 |
C8 | 1.0152 (6) | 0.4905 (4) | 0.9684 (3) | 0.097 (2) | |
H8 | 1.0474 | 0.5404 | 0.9351 | 0.117* | |
N1 | 1.0000 | 0.0000 | 0.6929 (4) | 0.069 (2) | |
C9 | 0.9567 (12) | −0.0831 (7) | 0.6559 (7) | 0.079 (4) | 0.33 |
H9 | 0.9267 | −0.1404 | 0.6820 | 0.095* | 0.33 |
C10 | 0.9558 (13) | −0.0854 (6) | 0.5797 (7) | 0.083 (4) | 0.33 |
H10 | 0.9259 | −0.1436 | 0.5548 | 0.100* | 0.33 |
C11 | 1.0000 | 0.0000 | 0.54121 (14) | 0.080 (3) | |
C10' | 1.0455 (13) | 0.0858 (6) | 0.5798 (7) | 0.083 (4) | 0.33 |
H10' | 1.0765 | 0.1438 | 0.5547 | 0.100* | 0.33 |
C9' | 1.0444 (13) | 0.0841 (7) | 0.6563 (7) | 0.079 (4) | 0.33 |
H9' | 1.0743 | 0.1413 | 0.6824 | 0.095* | 0.33 |
Atomic displacement parameters (Å2) top
U11 | U22 | U33 | U12 | U13 | U23 | |
Zn1 | 0.0574 (5) | 0.0574 (5) | 0.0380 (5) | 0.0287 (2) | 0.000 | 0.000 |
Zn2 | 0.0500 (6) | 0.0500 (6) | 0.0368 (7) | 0.0250 (3) | 0.000 | 0.000 |
O1 | 0.086 (3) | 0.072 (3) | 0.049 (2) | 0.047 (2) | −0.0004 (18) | 0.0021 (17) |
O2 | 0.062 (2) | 0.057 (2) | 0.058 (2) | 0.0321 (19) | −0.0034 (17) | 0.0080 (16) |
C1 | 0.065 (3) | 0.068 (3) | 0.048 (3) | 0.039 (3) | −0.011 (2) | −0.001 (2) |
C2 | 0.080 (4) | 0.053 (3) | 0.055 (3) | 0.038 (3) | 0.006 (3) | 0.006 (2) |
C5 | 0.125 (5) | 0.062 (4) | 0.079 (4) | 0.053 (4) | 0.020 (4) | 0.007 (3) |
C3 | 0.064 (5) | 0.061 (3) | 0.049 (4) | 0.037 (4) | −0.011 (4) | −0.003 (3) |
C4 | 0.084 (6) | 0.063 (4) | 0.059 (4) | 0.034 (4) | 0.000 (4) | 0.007 (3) |
C6 | 0.106 (6) | 0.071 (4) | 0.070 (5) | 0.048 (4) | 0.013 (4) | 0.004 (3) |
C7 | 0.089 (6) | 0.064 (4) | 0.060 (4) | 0.044 (4) | 0.004 (4) | 0.006 (3) |
C3' | 0.064 (5) | 0.061 (3) | 0.049 (4) | 0.037 (4) | −0.011 (4) | −0.003 (3) |
C4' | 0.084 (6) | 0.063 (4) | 0.059 (4) | 0.034 (4) | 0.000 (4) | 0.007 (3) |
C6' | 0.106 (6) | 0.071 (4) | 0.070 (5) | 0.048 (4) | 0.013 (4) | 0.004 (3) |
C7' | 0.089 (6) | 0.064 (4) | 0.060 (4) | 0.044 (4) | 0.004 (4) | 0.006 (3) |
C8 | 0.141 (6) | 0.067 (4) | 0.089 (4) | 0.056 (4) | 0.028 (4) | 0.010 (3) |
N1 | 0.085 (4) | 0.085 (4) | 0.037 (4) | 0.0427 (19) | 0.000 | 0.000 |
C9 | 0.096 (7) | 0.064 (6) | 0.057 (5) | 0.025 (5) | −0.003 (4) | 0.000 (5) |
C10 | 0.107 (7) | 0.068 (6) | 0.057 (5) | 0.029 (5) | 0.003 (5) | 0.007 (5) |
C11 | 0.094 (4) | 0.094 (4) | 0.052 (5) | 0.047 (2) | 0.000 | 0.000 |
C10' | 0.107 (7) | 0.068 (6) | 0.057 (5) | 0.029 (5) | 0.003 (5) | 0.007 (5) |
C9' | 0.096 (7) | 0.064 (6) | 0.057 (5) | 0.025 (5) | −0.003 (4) | 0.000 (5) |
Geometric parameters (Å, º) top
Zn1—O1 | 1.946 (4) | C3'—C4' | 1.388 (5) |
Zn1—O1i | 1.946 (4) | C6'—C7' | 1.387 (5) |
Zn1—O1ii | 1.946 (4) | C8—C8vi | 1.342 (5) |
Zn1—N1 | 2.071 (7) | N1—C9 | 1.342 (5) |
Zn2—O2 | 2.087 (3) | N1—C9' | 1.352 (5) |
Zn2—O2i | 2.087 (3) | C9—C10 | 1.384 (5) |
Zn2—O2ii | 2.087 (3) | C10—C11 | 1.384 (5) |
Zn2—O2iii | 2.087 (3) | C11—C10' | 1.390 (5) |
Zn2—O2iv | 2.087 (3) | C11—C11vii | 1.497 (5) |
Zn2—O2v | 2.087 (3) | C10'—C9' | 1.388 (5) |
O1—C1 | 1.273 (6) | C3—H3 | 0.9300 |
O2—C1 | 1.249 (6) | C4—H4 | 0.9300 |
C1—C2 | 1.489 (4) | C6—H6 | 0.9300 |
C2—C3' | 1.388 (5) | C7—H7 | 0.9300 |
C2—C7' | 1.391 (5) | C3'—H3' | 0.9300 |
C2—C3 | 1.392 (5) | C4'—H4' | 0.9300 |
C2—C7 | 1.393 (5) | C6'—H6' | 0.9300 |
C5—C4' | 1.389 (5) | C7'—H7' | 0.9300 |
C5—C6' | 1.390 (5) | C8—H8 | 0.9300 |
C5—C4 | 1.390 (5) | C9—H9 | 0.9300 |
C5—C6 | 1.394 (5) | C10—H10 | 0.9300 |
C5—C8 | 1.486 (4) | C10'—H10' | 0.9300 |
C3—C4 | 1.387 (5) | C9'—H9' | 0.9300 |
C6—C7 | 1.388 (5) | ||
O1i—Zn1—O1 | 117.3 (1) | C3—C4—H4 | 119.8 |
O1i—Zn1—O1ii | 117.3 (1) | C5—C4—H4 | 119.8 |
O1—Zn1—O1ii | 117.3 (1) | C7—C6—C5 | 120.6 (11) |
O1i—Zn1—N1 | 99.6 (1) | C7—C6—H6 | 119.7 |
O1—Zn1—N1 | 99.6 (1) | C5—C6—H6 | 119.7 |
O1ii—Zn1—N1 | 99.6 (1) | C6—C7—C2 | 119.0 (11) |
O2iv—Zn2—O2i | 180 | C6—C7—H7 | 120.5 |
O2iv—Zn2—O2v | 89.9 (1) | C2—C7—H7 | 120.5 |
O2i—Zn2—O2v | 90.1 (1) | C4'—C3'—C2 | 120.1 (11) |
O2iv—Zn2—O2ii | 90.1 (1) | C4'—C3'—H3' | 119.9 |
O2i—Zn2—O2ii | 89.9 (1) | C2—C3'—H3' | 119.9 |
O2v—Zn2—O2ii | 180 | C3'—C4'—C5 | 119.7 (11) |
O2iv—Zn2—O2 | 90.1 (1) | C3'—C4'—H4' | 120.1 |
O2i—Zn2—O2 | 89.9 (1) | C5—C4'—H4' | 120.1 |
O2v—Zn2—O2 | 90.1 (1) | C7'—C6'—C5 | 119.7 (11) |
O2ii—Zn2—O2 | 89.9 (1) | C7'—C6'—H6' | 120.1 |
O2iv—Zn2—O2iii | 89.9 (1) | C5—C6'—H6' | 120.1 |
O2i—Zn2—O2iii | 90.1 (1) | C6'—C7'—C2 | 120.0 (11) |
O2v—Zn2—O2iii | 89.9 (1) | C6'—C7'—H7' | 120.0 |
O2ii—Zn2—O2iii | 90.1 (1) | C2—C7'—H7' | 120.0 |
O2—Zn2—O2iii | 180 | C8vi—C8—C5 | 124.1 (6) |
C1—O1—Zn1 | 114.2 (3) | C8vi—C8—H8 | 117.9 |
C1—O2—Zn2 | 131.4 (3) | C5—C8—H8 | 117.9 |
O2—C1—O1 | 123.5 (4) | C9—N1—C9' | 120.4 (10) |
O2—C1—C2 | 119.4 (4) | C9—N1—Zn1 | 120.1 (7) |
O1—C1—C2 | 117.1 (4) | C9ii—N1—Zn1 | 120.1 (7) |
C3'—C2—C7' | 120.0 (11) | C9i—N1—Zn1 | 120.1 (7) |
C7'—C2—C3 | 116.4 (5) | C9'i—N1—Zn1 | 119.5 (7) |
C3'—C2—C7 | 116.7 (5) | C9'—N1—Zn1 | 119.5 (7) |
C3—C2—C7 | 121.0 (11) | C9'ii—N1—Zn1 | 119.5 (7) |
C3'—C2—C1 | 120.7 (6) | N1—C9—C10 | 121.4 (13) |
C7'—C2—C1 | 119.2 (6) | N1—C9—H9 | 119.3 |
C3—C2—C1 | 119.8 (6) | C10—C9—H9 | 119.3 |
C7—C2—C1 | 119.2 (6) | C11—C10—C9 | 119.0 (12) |
C4'—C5—C6' | 120.4 (11) | C11—C10—H10 | 120.5 |
C6'—C5—C4 | 116.2 (5) | C9—C10—H10 | 120.5 |
C4—C5—C6 | 119.7 (11) | C10—C11—C10' | 119.3 (8) |
C4'—C5—C8 | 118.0 (6) | C10—C11—C11vii | 120.4 (6) |
C6'—C5—C8 | 121.6 (7) | C10'—C11—C11vii | 120.3 (6) |
C4—C5—C8 | 117.7 (6) | C9'—C10'—C11 | 119.3 (12) |
C6—C5—C8 | 122.6 (7) | C9'—C10'—H10' | 120.3 |
C4—C3—C2 | 119.4 (11) | C11—C10'—H10' | 120.3 |
C4—C3—H3 | 120.3 | N1—C9'—C10' | 120.5 (12) |
C2—C3—H3 | 120.3 | N1—C9'—H9' | 119.7 |
C3—C4—C5 | 120.4 (11) | C10'—C9'—H9' | 119.7 |
O1i—Zn1—O1—C1 | 52.9 (4) | C8—C5—C4'—C3' | 178.1 (6) |
O1ii—Zn1—O1—C1 | −95.0 (3) | C4'—C5—C6'—C7' | −0.6 (8) |
N1—Zn1—O1—C1 | 158.9 (3) | C4—C5—C6'—C7' | −22.5 (9) |
O2iv—Zn2—O2—C1 | 71.7 (3) | C6—C5—C6'—C7' | 83 (3) |
O2i—Zn2—O2—C1 | −108.3 (3) | C8—C5—C6'—C7' | −178.1 (7) |
O2v—Zn2—O2—C1 | 161.6 (4) | C5—C6'—C7'—C2 | 0.3 (8) |
O2ii—Zn2—O2—C1 | −18.4 (4) | C3'—C2—C7'—C6' | 0.0 (6) |
Zn2—O2—C1—O1 | 74.7 (7) | C3—C2—C7'—C6' | 22.3 (8) |
Zn2—O2—C1—C2 | −106.0 (5) | C7—C2—C7'—C6' | −86 (3) |
Zn1—O1—C1—O2 | −6.1 (7) | C1—C2—C7'—C6' | 178.4 (6) |
Zn1—O1—C1—C2 | 174.6 (3) | C4'—C5—C8—C8vi | 177.2 (10) |
O2—C1—C2—C3' | 179.1 (5) | C6'—C5—C8—C8vi | −5.4 (15) |
O1—C1—C2—C3' | −1.6 (7) | C4—C5—C8—C8vi | −160.6 (10) |
O2—C1—C2—C7' | 0.7 (8) | C6—C5—C8—C8vi | 18.9 (15) |
O1—C1—C2—C7' | 180.0 (6) | O1i—Zn1—N1—C9 | −29.9 (10) |
O2—C1—C2—C3 | 156.1 (5) | O1—Zn1—N1—C9 | −149.9 (10) |
O1—C1—C2—C3 | −24.6 (7) | O1ii—Zn1—N1—C9 | 90.1 (10) |
O2—C1—C2—C7 | −22.5 (7) | O1i—Zn1—N1—C9ii | 90.1 (10) |
O1—C1—C2—C7 | 156.8 (6) | O1—Zn1—N1—C9ii | −29.9 (10) |
C3'—C2—C3—C4 | 83 (3) | O1ii—Zn1—N1—C9ii | −149.9 (10) |
C7'—C2—C3—C4 | −22.5 (6) | O1i—Zn1—N1—C9i | −149.9 (10) |
C7—C2—C3—C4 | 0.1 (3) | O1—Zn1—N1—C9i | 90.1 (10) |
C1—C2—C3—C4 | −178.5 (4) | O1ii—Zn1—N1—C9i | −29.9 (10) |
C2—C3—C4—C5 | 0.2 (3) | O1i—Zn1—N1—C9'i | 30.6 (10) |
C4'—C5—C4—C3 | −85 (3) | O1—Zn1—N1—C9'i | −89.4 (10) |
C6'—C5—C4—C3 | 22.3 (7) | O1ii—Zn1—N1—C9'i | 150.6 (10) |
C6—C5—C4—C3 | −0.6 (6) | O1i—Zn1—N1—C9' | 150.6 (10) |
C8—C5—C4—C3 | 178.8 (6) | O1—Zn1—N1—C9' | 30.6 (10) |
C4'—C5—C6—C7 | 22.6 (9) | O1ii—Zn1—N1—C9' | −89.4 (10) |
C6'—C5—C6—C7 | −85 (3) | O1i—Zn1—N1—C9'ii | −89.4 (10) |
C4—C5—C6—C7 | 0.8 (8) | O1—Zn1—N1—C9'ii | 150.6 (10) |
C8—C5—C6—C7 | −178.7 (7) | O1ii—Zn1—N1—C9'ii | 30.6 (10) |
C5—C6—C7—C2 | −0.5 (8) | C9'—N1—C9—C10 | −0.2 (3) |
C3'—C2—C7—C6 | −22.2 (8) | Zn1—N1—C9—C10 | −179.78 (15) |
C7'—C2—C7—C6 | 83 (3) | N1—C9—C10—C11 | −0.4 (3) |
C3—C2—C7—C6 | 0.0 (6) | C9—C10—C11—C10i | 49.0 (5) |
C1—C2—C7—C6 | 178.6 (6) | C9—C10—C11—C10ii | −48.6 (5) |
C7'—C2—C3'—C4' | −0.1 (3) | C9—C10—C11—C10' | 1.1 (6) |
C3—C2—C3'—C4' | −85 (3) | C9—C10—C11—C10'i | −73.3 (9) |
C7—C2—C3'—C4' | 22.6 (6) | C9—C10—C11—C10'ii | 74.3 (9) |
C1—C2—C3'—C4' | −178.5 (5) | C9—C10—C11—C11vii | −179.79 (14) |
C2—C3'—C4'—C5 | −0.2 (3) | C9—N1—C9'—C10' | 0.2 (7) |
C6'—C5—C4'—C3' | 0.6 (6) | Zn1—N1—C9'—C10' | 179.8 (5) |
C4—C5—C4'—C3' | 84 (3) | C11—C10'—C9'—N1 | 0.4 (9) |
C6—C5—C4'—C3' | −22.2 (7) |
Symmetry codes: (i) −y+1, x−y−1, z; (ii) −x+y+2, −x+1, z; (iii) −x+2, −y, −z+2; (iv) y+1, −x+y+1, −z+2; (v) x−y, x−1, −z+2; (vi) −x+2, −y+1, −z+2; (vii) x−y, x−1, −z+1. |
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