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In the title compound, C21H25NO10, the six-membered pyranosyl ring adopts a chair conformation. The crystal structure contains intra- and inter­molecular hydrogen-bonding inter­actions.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536806011329/sg2019sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536806011329/sg2019Isup2.hkl
Contains datablock I

CCDC reference: 608483

Key indicators

  • Single-crystal X-ray study
  • T = 296 K
  • Mean [sigma](C-C) = 0.005 Å
  • R factor = 0.041
  • wR factor = 0.102
  • Data-to-parameter ratio = 9.7

checkCIF/PLATON results

No syntax errors found



Alert level C PLAT029_ALERT_3_C _diffrn_measured_fraction_theta_full Low ....... 0.97 PLAT066_ALERT_1_C Predicted and Reported Transmissions Identical . ? PLAT241_ALERT_2_C Check High Ueq as Compared to Neighbors for C4 PLAT242_ALERT_2_C Check Low Ueq as Compared to Neighbors for C1 PLAT242_ALERT_2_C Check Low Ueq as Compared to Neighbors for C13 PLAT242_ALERT_2_C Check Low Ueq as Compared to Neighbors for C15 PLAT242_ALERT_2_C Check Low Ueq as Compared to Neighbors for C17 PLAT242_ALERT_2_C Check Low Ueq as Compared to Neighbors for C20 PLAT340_ALERT_3_C Low Bond Precision on C-C bonds (x 1000) Ang ... 5 PLAT720_ALERT_4_C Number of Unusual/Non-Standard Label(s) ........ 1
Alert level G REFLT03_ALERT_4_G Please check that the estimate of the number of Friedel pairs is correct. If it is not, please give the correct count in the _publ_section_exptl_refinement section of the submitted CIF. From the CIF: _diffrn_reflns_theta_max 27.51 From the CIF: _reflns_number_total 2894 Count of symmetry unique reflns 2970 Completeness (_total/calc) 97.44% TEST3: Check Friedels for noncentro structure Estimate of Friedel pairs measured 0 Fraction of Friedel pairs measured 0.000 Are heavy atom types Z>Si present no
0 ALERT level A = In general: serious problem 0 ALERT level B = Potentially serious problem 10 ALERT level C = Check and explain 1 ALERT level G = General alerts; check 1 ALERT type 1 CIF construction/syntax error, inconsistent or missing data 6 ALERT type 2 Indicator that the structure model may be wrong or deficient 2 ALERT type 3 Indicator that the structure quality may be low 2 ALERT type 4 Improvement, methodology, query or suggestion

Computing details top

Data collection: X-AREA (Stoe & Cie, 2002); cell refinement: X-AREA; data reduction: X-RED32 (Stoe & Cie, 2002); 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).

2,3,4,6-Tetra-O-acetyl-N-(2-hydroxybenzylidene)-β-D-galactopyranosylamine top
Crystal data top
C21H25NO10F(000) = 952
Mr = 451.42Dx = 1.319 Mg m3
Orthorhombic, P212121Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2abCell parameters from 16444 reflections
a = 7.8014 (4) Åθ = 1.7–27.4°
b = 15.2381 (11) ŵ = 0.11 mm1
c = 19.1271 (10) ÅT = 296 K
V = 2273.8 (2) Å3Prism, colorless
Z = 40.57 × 0.50 × 0.45 mm
Data collection top
Stoe IPDS-2
diffractometer
2894 independent reflections
Radiation source: sealed X-ray tube, 12 x 0.4 mm long-fine focus2002 reflections with I > 2σ(I)
Plane graphite monochromatorRint = 0.091
Detector resolution: 6.67 pixels mm-1θmax = 27.5°, θmin = 2.1°
ω scansh = 1010
Absorption correction: integration
(X-RED32; Stoe & Cie, 2002)
k = 1919
Tmin = 0.942, Tmax = 0.954l = 2424
16920 measured reflections
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.041H atoms treated by a mixture of independent and constrained refinement
wR(F2) = 0.102 w = 1/[σ2(Fo2) + (0.0555P)2]
where P = (Fo2 + 2Fc2)/3
S = 0.98(Δ/σ)max < 0.001
2894 reflectionsΔρmax = 0.14 e Å3
298 parametersΔρmin = 0.15 e Å3
0 restraintsExtinction correction: SHELXL97, FC*=KFC[1+0.001XFC2Λ3/SIN(2Θ)]-1/4
Primary atom site location: structure-invariant direct methodsExtinction coefficient: 0.0146 (18)
Special details top

Geometry. Bond distances, angles etc. have been calculated using the rounded fractional coordinates. All su's are estimated from the variances of the (full) variance-covariance matrix. The cell e.s.d.'s are taken into account in the estimation of distances, angles and torsion angles

Refinement. Refinement on F2 for ALL reflections except those flagged by the user for potential systematic errors. Weighted R-factors wR and all goodnesses of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The observed criterion of F2 > σ(F2) is used only for calculating -R-factor-obs etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
O10.2683 (3)0.69455 (16)0.85467 (14)0.0977 (9)
O20.78910 (19)0.86100 (11)0.79170 (9)0.0626 (5)
O30.5878 (2)0.67966 (10)0.69770 (10)0.0658 (6)
O40.3390 (2)0.74805 (14)0.67811 (13)0.0892 (8)
O50.8122 (2)0.74932 (12)0.59644 (9)0.0672 (6)
O60.9913 (4)0.6366 (2)0.58817 (15)0.1320 (12)
O70.85338 (18)0.91263 (11)0.64846 (9)0.0601 (5)
O81.0448 (3)0.91674 (19)0.56098 (14)0.1038 (9)
O91.1984 (2)0.95461 (13)0.74765 (11)0.0765 (7)
O101.1346 (3)1.07594 (17)0.69024 (18)0.1147 (12)
N10.5476 (2)0.77608 (14)0.82324 (11)0.0629 (6)
C10.2302 (3)0.7639 (2)0.89524 (15)0.0726 (9)
C20.0753 (4)0.7631 (3)0.9314 (2)0.0992 (13)
C30.0312 (6)0.8324 (4)0.9713 (3)0.1263 (19)
C40.1383 (6)0.9048 (4)0.9777 (3)0.1333 (19)
C50.2921 (5)0.9053 (3)0.94259 (19)0.1027 (14)
C60.3397 (3)0.83622 (18)0.90047 (14)0.0690 (9)
C70.5013 (3)0.83824 (17)0.86228 (14)0.0639 (8)
C80.7073 (3)0.77898 (16)0.78504 (13)0.0599 (7)
C90.6734 (3)0.76214 (14)0.70773 (13)0.0574 (7)
C100.8438 (3)0.75784 (15)0.67004 (12)0.0570 (7)
C110.9438 (3)0.84211 (15)0.68264 (14)0.0579 (7)
C120.9561 (3)0.86178 (18)0.75977 (14)0.0627 (8)
C130.4191 (3)0.68175 (19)0.68112 (16)0.0717 (9)
C140.3534 (5)0.5926 (3)0.6687 (3)0.129 (2)
C150.9013 (3)0.6890 (2)0.56006 (17)0.0751 (10)
C160.8781 (4)0.6991 (3)0.48453 (18)0.0980 (13)
C170.9135 (3)0.94171 (17)0.58662 (16)0.0688 (9)
C180.7963 (4)1.0058 (2)0.55449 (19)0.0918 (11)
C191.0281 (3)0.9502 (2)0.77726 (17)0.0741 (9)
C201.2325 (4)1.0185 (2)0.70322 (17)0.0764 (10)
C211.4055 (4)1.0074 (3)0.6720 (2)0.1074 (15)
HO10.370 (5)0.711 (2)0.830 (2)0.102 (11)*
H20.002600.714900.928000.1190*
H30.072900.831800.995000.1510*
H40.106400.952201.005300.1600*
H50.365300.953100.947400.1230*
H70.572300.886900.866900.0770*
H80.783700.733100.803000.0720*
H90.603700.809800.688300.0690*
H100.910000.707400.686800.0680*
H111.059100.836600.662800.0700*
H121.027100.816700.782000.0750*
H14A0.281200.575400.707000.1930*
H14B0.447800.552400.665000.1930*
H14C0.288300.591700.626200.1930*
H16A0.987700.707300.462700.1470*
H16B0.806800.749200.475500.1470*
H16C0.824500.647400.465900.1470*
H18A0.861701.050800.531600.1370*
H18B0.725801.031800.590100.1370*
H18C0.724900.976700.520800.1370*
H19A0.956400.996100.757800.0890*
H19B1.033200.957900.827600.0890*
H21A1.394400.993400.623300.1610*
H21B1.464700.960800.695500.1610*
H21C1.469201.061000.677100.1610*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0866 (13)0.0907 (15)0.1159 (18)0.0226 (11)0.0256 (13)0.0028 (14)
O20.0543 (8)0.0642 (9)0.0694 (10)0.0047 (7)0.0100 (7)0.0065 (8)
O30.0580 (8)0.0557 (9)0.0838 (12)0.0023 (7)0.0048 (8)0.0003 (8)
O40.0636 (10)0.0901 (14)0.1139 (16)0.0087 (11)0.0110 (10)0.0012 (13)
O50.0657 (9)0.0730 (11)0.0629 (9)0.0074 (8)0.0004 (8)0.0072 (9)
O60.135 (2)0.151 (2)0.110 (2)0.077 (2)0.0270 (17)0.0502 (19)
O70.0498 (7)0.0607 (9)0.0699 (10)0.0052 (7)0.0088 (7)0.0039 (8)
O80.0814 (13)0.1268 (18)0.1031 (16)0.0311 (13)0.0400 (12)0.0292 (14)
O90.0532 (9)0.0781 (12)0.0982 (14)0.0047 (8)0.0104 (9)0.0063 (11)
O100.0914 (14)0.0868 (14)0.166 (3)0.0134 (13)0.0034 (16)0.0195 (17)
N10.0595 (10)0.0632 (11)0.0659 (12)0.0014 (8)0.0102 (9)0.0054 (10)
C10.0661 (14)0.0819 (18)0.0697 (15)0.0050 (13)0.0128 (12)0.0175 (15)
C20.0767 (18)0.119 (3)0.102 (2)0.0001 (18)0.0246 (17)0.033 (2)
C30.105 (3)0.151 (4)0.123 (3)0.024 (3)0.062 (2)0.028 (3)
C40.134 (3)0.146 (4)0.120 (3)0.015 (3)0.066 (3)0.024 (3)
C50.111 (2)0.112 (3)0.085 (2)0.001 (2)0.032 (2)0.020 (2)
C60.0698 (14)0.0808 (17)0.0565 (13)0.0078 (13)0.0121 (12)0.0118 (13)
C70.0646 (12)0.0642 (14)0.0628 (14)0.0028 (11)0.0041 (12)0.0003 (12)
C80.0566 (12)0.0556 (12)0.0674 (14)0.0015 (9)0.0052 (10)0.0022 (11)
C90.0530 (10)0.0495 (11)0.0697 (14)0.0022 (9)0.0032 (10)0.0010 (11)
C100.0560 (11)0.0547 (12)0.0603 (13)0.0085 (10)0.0008 (9)0.0016 (11)
C110.0462 (10)0.0583 (12)0.0693 (14)0.0059 (9)0.0050 (10)0.0017 (11)
C120.0497 (11)0.0684 (14)0.0700 (15)0.0008 (10)0.0039 (10)0.0054 (12)
C130.0627 (13)0.0739 (17)0.0786 (17)0.0057 (13)0.0071 (12)0.0041 (14)
C140.105 (3)0.091 (2)0.190 (5)0.033 (2)0.058 (3)0.017 (3)
C150.0511 (12)0.0918 (19)0.0823 (18)0.0007 (13)0.0029 (12)0.0265 (16)
C160.0828 (18)0.136 (3)0.0751 (19)0.0123 (19)0.0024 (15)0.037 (2)
C170.0580 (13)0.0671 (14)0.0813 (18)0.0030 (11)0.0125 (12)0.0060 (13)
C180.0864 (18)0.093 (2)0.096 (2)0.0201 (16)0.0157 (17)0.0276 (18)
C190.0533 (12)0.0834 (17)0.0855 (18)0.0089 (12)0.0101 (12)0.0149 (15)
C200.0683 (15)0.0708 (17)0.090 (2)0.0170 (14)0.0001 (14)0.0079 (16)
C210.0793 (19)0.124 (3)0.119 (3)0.0302 (19)0.0304 (18)0.024 (2)
Geometric parameters (Å, º) top
O1—C11.344 (4)C12—C191.498 (4)
O2—C81.409 (3)C13—C141.471 (5)
O2—C121.439 (3)C15—C161.464 (5)
O3—C91.436 (3)C17—C181.472 (4)
O3—C131.354 (3)C20—C211.486 (5)
O4—C131.189 (3)C2—H20.9300
O5—C101.435 (3)C3—H30.9300
O5—C151.346 (3)C4—H40.9300
O6—C151.192 (4)C5—H50.9300
O7—C111.442 (3)C7—H70.9300
O7—C171.347 (3)C8—H80.9800
O8—C171.198 (4)C9—H90.9800
O9—C191.446 (3)C10—H100.9800
O9—C201.319 (4)C11—H110.9800
O10—C201.188 (4)C12—H120.9800
O1—HO10.96 (4)C14—H14A0.9600
N1—C81.445 (3)C14—H14B0.9600
N1—C71.259 (3)C14—H14C0.9600
C1—C21.392 (4)C16—H16A0.9600
C1—C61.398 (4)C16—H16B0.9600
C2—C31.348 (7)C16—H16C0.9600
C3—C41.389 (8)C18—H18A0.9600
C4—C51.375 (6)C18—H18B0.9600
C5—C61.377 (5)C18—H18C0.9600
C6—C71.457 (3)C19—H19A0.9700
C8—C91.524 (4)C19—H19B0.9700
C9—C101.514 (3)C21—H21A0.9600
C10—C111.522 (3)C21—H21B0.9600
C11—C121.509 (4)C21—H21C0.9600
O1···N12.579 (3)C20···C113.529 (4)
O1···C18i3.398 (4)C20···O3vii3.404 (4)
O2···O72.894 (2)C1···H3ix2.9800
O3···O52.818 (2)C1···H12iii2.8000
O3···C20ii3.404 (4)C2···H12iii3.0000
O3···N12.833 (3)C4···H19Biii3.0900
O4···C11iii3.401 (3)C5···H19Biii3.0900
O4···N13.246 (3)C7···HO12.28 (3)
O4···C16iv3.228 (4)C8···HO12.96 (4)
O5···O32.818 (2)C13···HO12.91 (4)
O5···O72.699 (2)C19···H14Aviii3.0900
O5···C173.042 (3)C21···H18Bv2.9700
O5···O83.203 (3)HO1···N11.71 (4)
O6···C14v3.287 (5)HO1···C72.28 (3)
O7···O52.699 (2)HO1···C82.96 (4)
O7···O22.894 (2)HO1···C132.91 (4)
O8···C16vi3.261 (4)H3···C1x2.9800
O8···O53.203 (3)H4···H21Axi2.4000
O10···C173.330 (4)H5···H72.4500
O10···C8vii3.364 (4)H7···O22.2600
O1···H18Bi2.7000H7···H52.4500
O2···H72.2600H7···H14Bviii2.6000
O4···H11iii2.5800H8···H102.4600
O4···H92.2800H8···H122.3200
O5···H16Aiv2.8500H8···O10ii2.4800
O6···H14Cv2.5200H9···O42.2800
O6···H102.2600H9···O72.6100
O7···H19A2.5800H9···H21Biii2.5500
O7···H92.6100H10···O62.2600
O8···H16Cvi2.4500H10···H82.4600
O8···H112.3000H11···O4v2.5800
O9···H112.6500H11···O82.3000
O10···H19A2.2500H11···O92.6500
O10···H8vii2.4800H12···C1v2.8000
N1···O12.579 (3)H12···C2v3.0000
N1···O32.833 (3)H12···H82.3200
N1···O43.246 (3)H14A···C19i3.0900
N1···C133.234 (4)H14A···H19Ai2.3100
N1···HO11.71 (4)H14B···H7i2.6000
C8···O10ii3.364 (4)H14C···O6iii2.5200
C11···O4v3.401 (3)H16A···O5vi2.8500
C11···C203.529 (4)H16C···O8iv2.4500
C13···N13.234 (4)H18B···C21iii2.9700
C14···O6iii3.287 (5)H18B···O1viii2.7000
C16···O8iv3.261 (4)H19A···O72.5800
C16···O4vi3.228 (4)H19A···O102.2500
C17···O103.330 (4)H19A···H14Aviii2.3100
C17···C203.541 (4)H19B···C4v3.0900
C17···O53.042 (3)H19B···C5v3.0900
C18···O1viii3.398 (4)H21A···H4xii2.4000
C20···C173.541 (4)H21B···H9v2.5500
C8—O2—C12112.27 (18)C3—C4—H4120.00
C9—O3—C13117.56 (19)C5—C4—H4120.00
C10—O5—C15118.7 (2)C4—C5—H5119.00
C11—O7—C17118.21 (18)C6—C5—H5119.00
C19—O9—C20118.2 (2)N1—C7—H7119.00
C1—O1—HO1105 (2)C6—C7—H7119.00
C7—N1—C8121.6 (2)O2—C8—H8109.00
O1—C1—C2118.2 (3)N1—C8—H8109.00
C2—C1—C6120.1 (3)C9—C8—H8109.00
O1—C1—C6121.7 (2)O3—C9—H9110.00
C1—C2—C3119.7 (4)C8—C9—H9110.00
C2—C3—C4121.2 (4)C10—C9—H9110.00
C3—C4—C5119.1 (5)O5—C10—H10110.00
C4—C5—C6121.1 (4)C9—C10—H10110.00
C1—C6—C5118.7 (3)C11—C10—H10110.00
C5—C6—C7120.7 (3)O7—C11—H11110.00
C1—C6—C7120.6 (2)C10—C11—H11110.00
N1—C7—C6122.0 (2)C12—C11—H11110.00
O2—C8—C9108.40 (19)O2—C12—H12109.00
N1—C8—C9109.63 (19)C11—C12—H12109.00
O2—C8—N1111.83 (19)C19—C12—H12109.00
O3—C9—C10107.87 (18)C13—C14—H14A109.00
C8—C9—C10108.48 (19)C13—C14—H14B109.00
O3—C9—C8110.96 (19)C13—C14—H14C110.00
O5—C10—C11108.65 (19)H14A—C14—H14B109.00
C9—C10—C11109.77 (19)H14A—C14—H14C109.00
O5—C10—C9108.68 (19)H14B—C14—H14C110.00
O7—C11—C10107.83 (19)C15—C16—H16A109.00
C10—C11—C12110.8 (2)C15—C16—H16B109.00
O7—C11—C12109.05 (19)C15—C16—H16C109.00
O2—C12—C11110.85 (19)H16A—C16—H16B110.00
C11—C12—C19114.9 (2)H16A—C16—H16C109.00
O2—C12—C19104.6 (2)H16B—C16—H16C109.00
O3—C13—C14110.8 (3)C17—C18—H18A110.00
O4—C13—C14126.4 (3)C17—C18—H18B109.00
O3—C13—O4122.8 (2)C17—C18—H18C110.00
O5—C15—C16112.0 (3)H18A—C18—H18B109.00
O6—C15—C16126.1 (3)H18A—C18—H18C109.00
O5—C15—O6121.9 (3)H18B—C18—H18C110.00
O7—C17—C18111.6 (2)O9—C19—H19A110.00
O8—C17—C18124.8 (3)O9—C19—H19B110.00
O7—C17—O8123.6 (3)C12—C19—H19A110.00
O9—C19—C12107.4 (2)C12—C19—H19B110.00
O9—C20—C21111.0 (3)H19A—C19—H19B108.00
O10—C20—C21125.7 (3)C20—C21—H21A109.00
O9—C20—O10123.3 (3)C20—C21—H21B109.00
C1—C2—H2120.00C20—C21—H21C109.00
C3—C2—H2120.00H21A—C21—H21B110.00
C2—C3—H3119.00H21A—C21—H21C110.00
C4—C3—H3119.00H21B—C21—H21C109.00
C12—O2—C8—C964.9 (2)O1—C1—C2—C3178.5 (4)
C12—O2—C8—N1174.17 (19)C1—C2—C3—C40.6 (7)
C8—O2—C12—C1160.3 (3)C2—C3—C4—C50.1 (8)
C8—O2—C12—C19175.3 (2)C3—C4—C5—C61.2 (7)
C13—O3—C9—C10135.4 (2)C4—C5—C6—C7178.7 (4)
C9—O3—C13—C14176.7 (3)C4—C5—C6—C11.6 (5)
C9—O3—C13—O43.8 (4)C1—C6—C7—N10.5 (4)
C13—O3—C9—C8105.9 (2)C5—C6—C7—N1179.8 (3)
C15—O5—C10—C11106.8 (2)O2—C8—C9—C1062.4 (2)
C10—O5—C15—O68.2 (4)N1—C8—C9—O356.9 (2)
C10—O5—C15—C16169.6 (2)N1—C8—C9—C10175.23 (19)
C15—O5—C10—C9133.8 (2)O2—C8—C9—O3179.23 (17)
C17—O7—C11—C12137.8 (2)O3—C9—C10—O564.5 (2)
C11—O7—C17—C18173.0 (2)C8—C9—C10—C1156.6 (2)
C17—O7—C11—C10101.8 (2)C8—C9—C10—O5175.25 (18)
C11—O7—C17—O85.7 (4)O3—C9—C10—C11176.82 (19)
C19—O9—C20—O105.6 (5)O5—C10—C11—C12170.96 (18)
C20—O9—C19—C12122.7 (3)O5—C10—C11—O751.7 (2)
C19—O9—C20—C21173.6 (3)C9—C10—C11—C1252.2 (3)
C7—N1—C8—O26.2 (3)C9—C10—C11—O767.0 (2)
C8—N1—C7—C6179.4 (2)C10—C11—C12—C19170.9 (2)
C7—N1—C8—C9126.4 (2)C10—C11—C12—O252.6 (3)
O1—C1—C6—C5179.5 (3)O7—C11—C12—C1952.4 (3)
C2—C1—C6—C7179.3 (3)O7—C11—C12—O265.9 (2)
C6—C1—C2—C30.2 (5)C11—C12—C19—O959.4 (3)
C2—C1—C6—C50.9 (4)O2—C12—C19—O9178.9 (2)
O1—C1—C6—C70.7 (4)
Symmetry codes: (i) x+1, y1/2, z+3/2; (ii) x+2, y1/2, z+3/2; (iii) x1, y, z; (iv) x1/2, y+3/2, z+1; (v) x+1, y, z; (vi) x+1/2, y+3/2, z+1; (vii) x+2, y+1/2, z+3/2; (viii) x+1, y+1/2, z+3/2; (ix) x+1/2, y+3/2, z+2; (x) x1/2, y+3/2, z+2; (xi) x+3/2, y+2, z+1/2; (xii) x+3/2, y+2, z1/2.
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—HO1···N10.96 (4)1.71 (4)2.579 (3)150 (3)
C7—H7···O20.932.262.643 (3)104
C8—H8···O10ii0.982.483.364 (4)150
C9—H9···O40.982.282.678 (3)103
C10—H10···O60.982.262.681 (4)104
C11—H11···O4v0.982.583.401 (3)141
C11—H11···O80.982.302.707 (4)104
C14—H14C···O6iii0.962.523.287 (5)137
C16—H16C···O8iv0.962.453.261 (4)143
C19—H19A···O100.972.252.671 (4)105
Symmetry codes: (ii) x+2, y1/2, z+3/2; (iii) x1, y, z; (iv) x1/2, y+3/2, z+1; (v) x+1, y, z.
 

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