(+)-(1S,2S,3S,4R,5R)-N-(1,3-Di­hydroxy­prop-2-yl)-2,3,4-tri­hydroxy-5-(hydroxy­methyl)-1-cyclo­hexanaminium picrate

Zhu, J.; Chang, H.; Feng, X.-L.

doi:10.1107/S1600536805012419

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(+)-(1S,2S,3S,4R,5R)-N-(1,3-Dihydroxyprop-2-yl)-2,3,4-trihydroxy-5-(hydroxymethyl)-1-cyclohexanaminium picrate

J. Zhu, H. Chang and X.-L. Feng

In the title compound, C₁₀H₂₂NO₆⁺·C₆H₂N₃O₇^-, the cyclohexane ring has a slightly distorted chair conformation. Molecules are linked into chains by hydrogen bonds.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536805012419/fl6157sup1.cif Contains datablocks global, I
	Structure factor file (CIF format) https://doi.org/10.1107/S1600536805012419/fl6157Isup2.hkl Contains datablock I

CCDC reference: 271876

checkCIF report

Key indicators

Single-crystal X-ray study
T = 293 K
Mean (C-C) = 0.004 Å
R factor = 0.037
wR factor = 0.103
Data-to-parameter ratio = 7.8

checkCIF/PLATON results

No syntax errors found



Alert level C
PLAT089_ALERT_3_C Poor Data / Parameter Ratio (Zmax .LT. 18) .....       7.84
PLAT220_ALERT_2_C Large Non-Solvent    O     Ueq(max)/Ueq(min) ...       3.18 Ratio
PLAT242_ALERT_2_C Check Low       Ueq as Compared to Neighbors for         N2
PLAT242_ALERT_2_C Check Low       Ueq as Compared to Neighbors for         N4

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           27.03
           From the CIF: _reflns_number_total               2383
           Count of symmetry unique reflns         2394
           Completeness (_total/calc)             99.54%
           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
   4 ALERT level C = Check and explain
   1 ALERT level G = General alerts; check

   0 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   3 ALERT type 2 Indicator that the structure model may be wrong or deficient
   1 ALERT type 3 Indicator that the structure quality may be low
   1 ALERT type 4 Improvement, methodology, query or suggestion

Computing details top

Data collection: SMART (Bruker,1999); cell refinement: SAINT-Plus (Bruker, 1999); data reduction: SAINT-Plus; program(s) used to solve structure: SHELXTL (Bruker, 1999); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.

(+)-(1S,2S,3S,4R,5R)-N-(1,3-Dihydroxyprop-2-yl)-2,3,4-trihydroxy- 5-(hydroxymethyl)-1-cyclohexanaminium picrate top

Crystal data top

C₁₀H₂₂NO₆⁺·C₆H₂N₃O₇⁻	F(000) = 504
M_r = 480.39	D_x = 1.586 Mg m⁻³
Monoclinic, P2₁	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2yb	Cell parameters from 966 reflections
a = 8.7362 (11) Å	θ = 3.2–26.8°
b = 6.8235 (8) Å	µ = 0.14 mm⁻¹
c = 16.957 (2) Å	T = 293 K
β = 95.769 (2)°	Block, yellow
V = 1005.7 (2) Å³	0.33 × 0.25 × 0.19 mm
Z = 2

Data collection top

Bruker SMART 1000 CCD diffractometer	2383 independent reflections
Radiation source: fine-focus sealed tube	2138 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.021
ω scans	θ_max = 27.0°, θ_min = 1.2°
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	h = −10→11
T_min = 0.884, T_max = 0.974	k = −8→7
6583 measured reflections	l = −21→21

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.037	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.103	H-atom parameters constrained
S = 1.05	w = 1/[σ²(F_o²) + (0.0581P)² + 0.2641P] where P = (F_o² + 2F_c²)/3
2383 reflections	(Δ/σ)_max = 0.006
304 parameters	Δρ_max = 0.41 e Å⁻³
7 restraints	Δρ_min = −0.27 e Å⁻³

Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

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 (Å²) top

	x	y	z	U_iso*/U_eq
C1	0.1457 (3)	0.4600 (4)	0.17641 (14)	0.0292 (5)
H1	0.1677	0.5153	0.2297	0.035*
C2	0.1553 (3)	0.6253 (4)	0.11585 (14)	0.0292 (5)
H2	0.2543	0.6926	0.1268	0.035*
C3	0.1422 (3)	0.5455 (4)	0.03067 (13)	0.0266 (5)
H3	0.0437	0.4767	0.0209	0.032*
C4	0.2704 (3)	0.3976 (4)	0.02347 (14)	0.0288 (5)
H4	0.3682	0.4644	0.0389	0.035*
C5	0.2589 (3)	0.2261 (4)	0.08035 (15)	0.0299 (5)
H5A	0.1606	0.1592	0.0664	0.036*
C6	0.2628 (3)	0.2994 (5)	0.16567 (14)	0.0328 (6)
H6A	0.2434	0.1899	0.1998	0.039*
H6B	0.3650	0.3489	0.1824	0.039*
C7	−0.0920 (3)	0.3454 (5)	0.24305 (14)	0.0337 (6)
H7	−0.0754	0.4598	0.2778	0.040*
C8	−0.0211 (4)	0.1681 (5)	0.28631 (15)	0.0397 (7)
H8A	0.0869	0.1928	0.3021	0.048*
H8B	−0.0717	0.1451	0.3339	0.048*
C9	−0.2638 (3)	0.3258 (6)	0.21829 (17)	0.0430 (7)
H9A	−0.2834	0.2050	0.1888	0.052*
H9B	−0.3189	0.3201	0.2651	0.052*
C10	0.3889 (3)	0.0791 (4)	0.07363 (17)	0.0356 (6)
H10A	0.4856	0.1493	0.0750	0.043*
H10B	0.3950	−0.0082	0.1190	0.043*
C11	0.2983 (3)	0.2813 (4)	0.63925 (15)	0.0361 (6)
C12	0.2020 (3)	0.2824 (5)	0.56480 (17)	0.0437 (7)
C13	0.2573 (4)	0.2997 (5)	0.49253 (17)	0.0501 (8)
H13	0.1896	0.3049	0.4466	0.060*
C14	0.4129 (4)	0.3093 (5)	0.48800 (16)	0.0454 (7)
C15	0.5167 (4)	0.3100 (5)	0.55580 (16)	0.0400 (6)
H15	0.6220	0.3188	0.5523	0.048*
C16	0.4589 (3)	0.2972 (4)	0.62796 (15)	0.0361 (6)
O13	0.2480 (2)	0.2740 (4)	0.70600 (11)	0.0459 (5)
N1	−0.0189 (2)	0.3849 (4)	0.16770 (12)	0.0289 (5)
H1A	−0.0777	0.4729	0.1391	0.035*
H1B	−0.0214	0.2730	0.1395	0.035*
N2	0.0343 (3)	0.2637 (6)	0.56562 (19)	0.0616 (9)
N3	0.4723 (5)	0.3204 (6)	0.41135 (16)	0.0643 (9)
N4	0.5720 (3)	0.3039 (5)	0.69756 (14)	0.0450 (6)
O1	0.0346 (2)	0.7629 (3)	0.12117 (11)	0.0404 (5)
H1C	0.0542	0.8315	0.1606	0.061*
O2	0.1443 (2)	0.6993 (3)	−0.02586 (10)	0.0351 (4)
H2A	0.2161	0.7736	−0.0127	0.053*
O3	0.2735 (2)	0.3321 (4)	−0.05605 (10)	0.0409 (5)
H3A	0.1852	0.3234	−0.0773	0.061*
O4	0.3681 (2)	−0.0348 (3)	0.00280 (12)	0.0395 (5)
H4A	0.3535	0.0384	−0.0356	0.059*
O5	−0.0362 (3)	0.0001 (3)	0.23740 (12)	0.0437 (5)
H5	−0.0980	−0.0757	0.2542	0.066*
O6	−0.3177 (3)	0.4873 (4)	0.17053 (12)	0.0486 (6)
H6C	−0.3328	0.5810	0.1990	0.073*
O7	−0.0172 (3)	0.1647 (7)	0.61563 (17)	0.0829 (11)
O8	−0.0457 (4)	0.3472 (10)	0.5156 (3)	0.145 (2)
O9	0.3797 (4)	0.3431 (7)	0.35258 (14)	0.0988 (13)
O10	0.6105 (4)	0.3101 (7)	0.40870 (16)	0.0864 (10)
O11	0.6939 (3)	0.3832 (6)	0.69244 (17)	0.0843 (12)
O12	0.5427 (3)	0.2238 (6)	0.75837 (14)	0.0756 (10)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
C1	0.0280 (12)	0.0360 (14)	0.0231 (10)	−0.0061 (11)	−0.0005 (9)	0.0000 (11)
C2	0.0274 (12)	0.0318 (13)	0.0278 (11)	−0.0032 (10)	0.0004 (9)	0.0010 (10)
C3	0.0240 (11)	0.0302 (12)	0.0253 (11)	−0.0036 (9)	0.0014 (8)	0.0034 (10)
C4	0.0258 (11)	0.0344 (13)	0.0259 (11)	−0.0017 (10)	0.0016 (9)	0.0009 (10)
C5	0.0236 (11)	0.0329 (14)	0.0326 (12)	−0.0009 (10)	0.0007 (9)	0.0020 (11)
C6	0.0298 (12)	0.0395 (15)	0.0283 (11)	0.0008 (11)	−0.0010 (9)	0.0063 (12)
C7	0.0382 (13)	0.0400 (15)	0.0245 (11)	−0.0063 (12)	0.0117 (10)	−0.0036 (11)
C8	0.0470 (16)	0.0468 (18)	0.0257 (12)	−0.0054 (14)	0.0059 (11)	0.0017 (12)
C9	0.0385 (15)	0.0516 (18)	0.0409 (14)	−0.0026 (14)	0.0132 (11)	0.0030 (15)
C10	0.0298 (13)	0.0346 (15)	0.0416 (14)	0.0013 (11)	−0.0002 (10)	0.0019 (12)
C11	0.0412 (14)	0.0330 (14)	0.0330 (12)	0.0053 (12)	−0.0013 (10)	−0.0008 (12)
C12	0.0449 (16)	0.0432 (17)	0.0410 (14)	−0.0021 (14)	−0.0059 (12)	0.0049 (14)
C13	0.066 (2)	0.0474 (18)	0.0334 (13)	−0.0081 (17)	−0.0107 (13)	0.0079 (15)
C14	0.069 (2)	0.0382 (16)	0.0293 (12)	−0.0088 (15)	0.0051 (12)	0.0014 (13)
C15	0.0481 (16)	0.0344 (15)	0.0379 (13)	−0.0014 (13)	0.0072 (12)	0.0005 (13)
C16	0.0419 (14)	0.0332 (14)	0.0325 (12)	0.0010 (12)	−0.0007 (10)	−0.0013 (12)
O13	0.0445 (11)	0.0574 (14)	0.0361 (10)	0.0120 (11)	0.0053 (8)	0.0037 (10)
N1	0.0308 (10)	0.0338 (12)	0.0227 (9)	−0.0027 (9)	0.0048 (7)	−0.0018 (9)
N2	0.0471 (16)	0.069 (2)	0.0645 (18)	−0.0005 (16)	−0.0165 (14)	0.0181 (18)
N3	0.101 (3)	0.0586 (19)	0.0352 (14)	−0.019 (2)	0.0161 (15)	0.0004 (15)
N4	0.0401 (13)	0.0552 (16)	0.0384 (12)	−0.0028 (13)	−0.0020 (10)	−0.0021 (13)
O1	0.0485 (11)	0.0368 (11)	0.0356 (9)	0.0082 (9)	0.0032 (8)	−0.0056 (9)
O2	0.0364 (10)	0.0383 (11)	0.0298 (9)	−0.0017 (9)	−0.0013 (7)	0.0090 (9)
O3	0.0435 (11)	0.0514 (12)	0.0281 (9)	0.0061 (11)	0.0060 (8)	−0.0020 (9)
O4	0.0371 (10)	0.0376 (11)	0.0447 (10)	0.0031 (9)	0.0082 (8)	−0.0006 (9)
O5	0.0496 (12)	0.0406 (12)	0.0434 (11)	−0.0024 (10)	0.0170 (9)	−0.0048 (10)
O6	0.0463 (12)	0.0588 (15)	0.0412 (11)	0.0114 (12)	0.0072 (9)	−0.0007 (11)
O7	0.0517 (15)	0.131 (3)	0.0652 (16)	−0.0129 (19)	−0.0001 (12)	0.019 (2)
O8	0.068 (2)	0.195 (5)	0.165 (4)	−0.007 (3)	−0.032 (2)	0.108 (4)
O9	0.138 (3)	0.125 (3)	0.0306 (12)	−0.044 (3)	−0.0038 (15)	0.0111 (18)
O10	0.105 (3)	0.104 (3)	0.0566 (15)	−0.009 (2)	0.0374 (16)	0.0035 (19)
O11	0.0512 (14)	0.135 (3)	0.0651 (15)	−0.0321 (19)	−0.0026 (12)	−0.006 (2)
O12	0.0600 (15)	0.119 (3)	0.0441 (13)	−0.0126 (18)	−0.0140 (11)	0.0231 (16)

Geometric parameters (Å, º) top

C1—N1	1.520 (3)	C10—H10A	0.9700
C1—C6	1.523 (4)	C10—H10B	0.9700
C1—C2	1.534 (4)	C11—O13	1.256 (3)
C1—H1	0.9800	C11—C16	1.440 (4)
C2—O1	1.421 (3)	C11—C12	1.445 (4)
C2—C3	1.537 (3)	C12—C13	1.367 (4)
C2—H2	0.9800	C12—N2	1.471 (4)
C3—O2	1.423 (3)	C13—C14	1.371 (5)
C3—C4	1.522 (4)	C13—H13	0.9300
C3—H3	0.9800	C14—C15	1.391 (4)
C4—O3	1.423 (3)	C14—N3	1.449 (4)
C4—C5	1.527 (4)	C15—C16	1.372 (4)
C4—H4	0.9800	C15—H15	0.9300
C5—C10	1.528 (4)	C16—N4	1.461 (4)
C5—C6	1.528 (4)	N1—H1A	0.9000
C5—H5A	0.9800	N1—H1B	0.9000
C6—H6A	0.9700	N2—O8	1.189 (4)
C6—H6B	0.9700	N2—O7	1.207 (4)
C7—N1	1.509 (3)	N3—O10	1.215 (5)
C7—C8	1.515 (4)	N3—O9	1.229 (4)
C7—C9	1.523 (4)	N4—O11	1.205 (4)
C7—H7	0.9800	N4—O12	1.217 (4)
C8—O5	1.413 (4)	O1—H1C	0.8200
C8—H8A	0.9700	O2—H2A	0.8200
C8—H8B	0.9700	O3—H3A	0.8200
C9—O6	1.420 (4)	O4—H4A	0.8200
C9—H9A	0.9700	O5—H5	0.8200
C9—H9B	0.9700	O6—H6C	0.8200
C10—O4	1.427 (4)

N1—C1—C6	112.7 (2)	C7—C9—H9A	109.5
N1—C1—C2	107.34 (19)	O6—C9—H9B	109.5
C6—C1—C2	111.5 (2)	C7—C9—H9B	109.5
N1—C1—H1	108.4	H9A—C9—H9B	108.1
C6—C1—H1	108.4	O4—C10—C5	112.8 (2)
C2—C1—H1	108.4	O4—C10—H10A	109.0
O1—C2—C1	110.6 (2)	C5—C10—H10A	109.0
O1—C2—C3	107.94 (19)	O4—C10—H10B	109.0
C1—C2—C3	111.4 (2)	C5—C10—H10B	109.0
O1—C2—H2	108.9	H10A—C10—H10B	107.8
C1—C2—H2	108.9	O13—C11—C16	123.8 (2)
C3—C2—H2	108.9	O13—C11—C12	124.2 (3)
O2—C3—C4	112.08 (19)	C16—C11—C12	111.9 (2)
O2—C3—C2	111.5 (2)	C13—C12—C11	123.8 (3)
C4—C3—C2	108.94 (19)	C13—C12—N2	117.3 (3)
O2—C3—H3	108.1	C11—C12—N2	118.9 (3)
C4—C3—H3	108.1	C12—C13—C14	119.8 (3)
C2—C3—H3	108.1	C12—C13—H13	120.1
O3—C4—C3	111.6 (2)	C14—C13—H13	120.1
O3—C4—C5	111.5 (2)	C13—C14—C15	121.4 (3)
C3—C4—C5	111.22 (19)	C13—C14—N3	119.9 (3)
O3—C4—H4	107.4	C15—C14—N3	118.6 (3)
C3—C4—H4	107.4	C16—C15—C14	118.0 (3)
C5—C4—H4	107.4	C16—C15—H15	121.0
C4—C5—C10	111.1 (2)	C14—C15—H15	121.0
C4—C5—C6	110.5 (2)	C15—C16—C11	125.0 (2)
C10—C5—C6	109.9 (2)	C15—C16—N4	116.1 (3)
C4—C5—H5A	108.4	C11—C16—N4	118.9 (2)
C10—C5—H5A	108.4	C7—N1—C1	117.03 (19)
C6—C5—H5A	108.4	C7—N1—H1A	108.0
C1—C6—C5	113.4 (2)	C1—N1—H1A	108.0
C1—C6—H6A	108.9	C7—N1—H1B	108.0
C5—C6—H6A	108.9	C1—N1—H1B	108.0
C1—C6—H6B	108.9	H1A—N1—H1B	107.3
C5—C6—H6B	108.9	O8—N2—O7	122.4 (4)
H6A—C6—H6B	107.7	O8—N2—C12	117.8 (3)
N1—C7—C8	111.5 (2)	O7—N2—C12	119.8 (3)
N1—C7—C9	105.7 (2)	O10—N3—O9	123.6 (3)
C8—C7—C9	114.0 (2)	O10—N3—C14	118.5 (3)
N1—C7—H7	108.5	O9—N3—C14	117.9 (4)
C8—C7—H7	108.5	O11—N4—O12	121.7 (3)
C9—C7—H7	108.5	O11—N4—C16	119.1 (3)
O5—C8—C7	110.8 (2)	O12—N4—C16	119.2 (3)
O5—C8—H8A	109.5	C2—O1—H1C	109.5
C7—C8—H8A	109.5	C3—O2—H2A	109.5
O5—C8—H8B	109.5	C4—O3—H3A	109.5
C7—C8—H8B	109.5	C10—O4—H4A	109.5
H8A—C8—H8B	108.1	C8—O5—H5	109.5
O6—C9—C7	110.5 (3)	C9—O6—H6C	109.5
O6—C9—H9A	109.5

N1—C1—C2—O1	49.8 (3)	C16—C11—C12—N2	178.9 (3)
C6—C1—C2—O1	173.7 (2)	C11—C12—C13—C14	2.6 (6)
N1—C1—C2—C3	−70.3 (2)	N2—C12—C13—C14	−177.3 (3)
C6—C1—C2—C3	53.6 (3)	C12—C13—C14—C15	−2.7 (5)
O1—C2—C3—O2	55.8 (3)	C12—C13—C14—N3	177.8 (3)
C1—C2—C3—O2	177.42 (19)	C13—C14—C15—C16	1.1 (5)
O1—C2—C3—C4	−180.0 (2)	N3—C14—C15—C16	−179.3 (3)
C1—C2—C3—C4	−58.3 (3)	C14—C15—C16—C11	0.6 (5)
O2—C3—C4—O3	−50.5 (3)	C14—C15—C16—N4	−178.4 (3)
C2—C3—C4—O3	−174.4 (2)	O13—C11—C16—C15	−178.4 (3)
O2—C3—C4—C5	−175.7 (2)	C12—C11—C16—C15	−0.6 (5)
C2—C3—C4—C5	60.4 (3)	O13—C11—C16—N4	0.5 (5)
O3—C4—C5—C10	55.4 (3)	C12—C11—C16—N4	178.3 (3)
C3—C4—C5—C10	−179.4 (2)	C8—C7—N1—C1	−70.2 (3)
O3—C4—C5—C6	177.6 (2)	C9—C7—N1—C1	165.4 (2)
C3—C4—C5—C6	−57.2 (3)	C6—C1—N1—C7	100.1 (3)
N1—C1—C6—C5	70.2 (3)	C2—C1—N1—C7	−136.8 (2)
C2—C1—C6—C5	−50.6 (3)	C13—C12—N2—O8	−33.1 (6)
C4—C5—C6—C1	52.1 (3)	C11—C12—N2—O8	147.0 (5)
C10—C5—C6—C1	175.0 (2)	C13—C12—N2—O7	146.3 (4)
N1—C7—C8—O5	−58.1 (3)	C11—C12—N2—O7	−33.7 (5)
C9—C7—C8—O5	61.5 (3)	C13—C14—N3—O10	−173.1 (4)
N1—C7—C9—O6	−50.6 (3)	C15—C14—N3—O10	7.3 (6)
C8—C7—C9—O6	−173.4 (2)	C13—C14—N3—O9	8.0 (6)
C4—C5—C10—O4	−73.6 (3)	C15—C14—N3—O9	−171.6 (4)
C6—C5—C10—O4	163.8 (2)	C15—C16—N4—O11	24.8 (5)
O13—C11—C12—C13	176.8 (3)	C11—C16—N4—O11	−154.2 (3)
C16—C11—C12—C13	−1.0 (5)	C15—C16—N4—O12	−152.8 (3)
O13—C11—C12—N2	−3.3 (5)	C11—C16—N4—O12	28.2 (5)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1A···O6	0.90	2.22	2.707 (3)	114
N1—H1A···O1	0.90	2.24	2.751 (3)	115
N1—H1B···O2ⁱ	0.90	2.17	2.839 (3)	131
O1—H1C···O5ⁱⁱ	0.82	1.96	2.671 (3)	144
O2—H2A···O4ⁱⁱ	0.82	1.86	2.676 (3)	171
O3—H3A···O1ⁱ	0.82	2.03	2.844 (3)	171
O4—H4A···O3	0.82	2.14	2.790 (3)	136
O4—H4A···O6ⁱ	0.82	2.30	2.932 (3)	134
O5—H5···O13ⁱⁱⁱ	0.82	1.84	2.662 (3)	175
O6—H6C···O13^iv	0.82	2.15	2.885 (3)	149
O6—H6C···O12^iv	0.82	2.26	2.898 (4)	135

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

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