l-Phenyl­alanine l-phenyl­alaninium malonate

Alagar, M.; Krishnakumar, R.V.; Parimala Devi, P.; Natarajan, S.

doi:10.1107/S1600536805007014

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L-Phenylalanine L-phenylalaninium malonate

M. Alagar, R. V. Krishnakumar, P. Parimala Devi and S. Natarajan

The asymmetric unit of the title compound, C₉H₁₁NO₂·C₉H₁₂NO₂⁺·C₃H₃O₄⁻, consists of two phenylalanine molecules, one as a zwitterion (P) and the other as a cation (P⁺), in addition to a malonate anion (Mal⁻). The phenylalaninium and phenylalanine molecules are linked by a very short syn–syn carboxyl–carboxylate (–COO⁻

HOOC–) hydrogen bond [O

O = 2.429 (4) Å]. The Mal⁻ anion is stabilized by a strong intramolecular O—H

O hydrogen bond. The aggregation of P and P⁺ is mediated through Mal⁻, leading to an infinite double chain along the c axis.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536805007014/wn6334sup1.cif Contains datablocks global, I
	Structure factor file (CIF format) https://doi.org/10.1107/S1600536805007014/wn6334Isup2.hkl Contains datablock I

CCDC reference: 270569

checkCIF report

Key indicators

Single-crystal X-ray study
T = 293 K
Mean (C-C) = 0.006 Å
R factor = 0.035
wR factor = 0.101
Data-to-parameter ratio = 6.9

checkCIF/PLATON results

No syntax errors found



Alert level B
PLAT029_ALERT_3_B _diffrn_measured_fraction_theta_full Low .......       0.96

Alert level C
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ ....          ?
PLAT089_ALERT_3_C Poor Data / Parameter Ratio (Zmax .LT. 18) .....       6.86
PLAT199_ALERT_1_C Check the Reported cell_measurement_temperature         293
PLAT200_ALERT_1_C Check the Reported cell_ambient_temperature ....        293
PLAT220_ALERT_2_C Large Non-Solvent    C     Ueq(max)/Ueq(min) ...       2.73 Ratio
PLAT242_ALERT_2_C Check Low       Ueq as Compared to Neighbors for        C10
PLAT242_ALERT_2_C Check Low       Ueq as Compared to Neighbors for        C12
PLAT250_ALERT_2_C Large U3/U1 Ratio for Average U(i,j) Tensor ....       2.22
PLAT340_ALERT_3_C Low Bond Precision on C-C bonds (x 1000) Ang ...          6

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           25.03
           From the CIF: _reflns_number_total               2032
           Count of symmetry unique reflns         2123
           Completeness (_total/calc)             95.71%
           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
   1 ALERT level B = Potentially serious problem
   9 ALERT level C = Check and explain
   1 ALERT level G = General alerts; check

   3 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   4 ALERT type 2 Indicator that the structure model may be wrong or deficient
   3 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: CAD-4 EXPRESS (Enraf–Nonius, 1994); cell refinement: CAD-4 EXPRESS; data reduction: XCAD4 (Harms & Wocadlo, 1996); program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: PLATON (Spek, 2003); software used to prepare material for publication: SHELXL97.

L-Phenylalaninium malonate L-phenylalanine top

Crystal data top

C₉H₁₂NO₂⁺·C₃H₃O₄⁻·C₉H₁₁NO₂	F(000) = 460
M_r = 434.44	D_x = 1.340 Mg m⁻³ D_m = 1.35 Mg m⁻³ D_m measured by flotation in a mixture of xylene and bromoform
Monoclinic, P2₁	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2yb	Cell parameters from 25 reflections
a = 14.031 (3) Å	θ = 7.4–16.3°
b = 5.5082 (10) Å	µ = 0.10 mm⁻¹
c = 14.601 (3) Å	T = 293 K
β = 107.412 (3)°	Block cut from a needle, colourless
V = 1076.7 (4) Å³	0.30 × 0.22 × 0.15 mm
Z = 2

Data collection top

Nonius MACH3 four-circle diffractometer	1921 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	R_int = 0.049
Graphite monochromator	θ_max = 25.0°, θ_min = 2.4°
ω/2θ scans	h = −1→16
Absorption correction: ψ scans (North et al., 1968)	k = −1→5
T_min = 0.89, T_max = 0.98	l = −17→16
2761 measured reflections	3 standard reflections every 60 min min
2032 independent reflections	intensity decay: none

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)] = 0.035	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.101	H atoms treated by a mixture of independent and constrained refinement
S = 1.06	w = 1/[σ²(F_o²) + (0.0587P)² + 0.0894P] where P = (F_o² + 2F_c²)/3
2032 reflections	(Δ/σ)_max < 0.001
296 parameters	Δρ_max = 0.16 e Å⁻³
1 restraint	Δρ_min = −0.17 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
O1A	0.58881 (16)	−0.0208 (4)	0.67715 (16)	0.0451 (6)
O2A	0.69402 (18)	0.0977 (5)	0.59800 (15)	0.0516 (6)
N1A	0.58236 (18)	0.4156 (5)	0.75437 (17)	0.0398 (6)
H5	0.5865	0.5664	0.7771	0.060*
H6	0.6008	0.3114	0.8031	0.060*
H7	0.5197	0.3848	0.7197	0.060*
C1A	0.6407 (2)	0.1314 (7)	0.65476 (18)	0.0350 (7)
C2A	0.6491 (2)	0.3891 (6)	0.6933 (2)	0.0367 (7)
H8	0.6247	0.4988	0.6384	0.044*
C3A	0.7560 (2)	0.4637 (7)	0.7471 (2)	0.0445 (8)
H9	0.7945	0.4673	0.7019	0.053*
H10	0.7549	0.6273	0.7713	0.053*
C4A	0.8083 (2)	0.3008 (7)	0.8296 (2)	0.0419 (8)
C5A	0.8034 (2)	0.3435 (8)	0.9211 (2)	0.0517 (9)
H11	0.7689	0.4782	0.9328	0.062*
C6A	0.8496 (3)	0.1871 (10)	0.9961 (3)	0.0637 (12)
H12	0.8449	0.2157	1.0573	0.076*
C7A	0.9020 (3)	−0.0091 (9)	0.9792 (3)	0.0670 (12)
H13	0.9335	−0.1127	1.0295	0.080*
C8A	0.9083 (3)	−0.0533 (9)	0.8897 (3)	0.0648 (11)
H14	0.9437	−0.1872	0.8786	0.078*
C9A	0.8618 (2)	0.1018 (8)	0.8150 (3)	0.0518 (9)
H15	0.8667	0.0713	0.7539	0.062*
O1B	0.59595 (16)	0.8585 (4)	0.38890 (14)	0.0454 (6)
O2B	0.6945 (2)	0.7031 (5)	0.52394 (15)	0.0511 (7)
N1B	0.59996 (19)	0.4656 (6)	0.28503 (18)	0.0498 (8)
H16	0.6046	0.3242	0.2572	0.075*
H17	0.6260	0.5824	0.2578	0.075*
H18	0.5360	0.4985	0.2778	0.075*
C1B	0.6462 (2)	0.6927 (6)	0.4353 (2)	0.0351 (7)
C2B	0.6554 (2)	0.4516 (6)	0.3888 (2)	0.0405 (8)
H19	0.6226	0.3286	0.4174	0.049*
C3B	0.7628 (3)	0.3704 (7)	0.4048 (2)	0.0509 (9)
H20	0.7948	0.3542	0.4733	0.061*
H21	0.7620	0.2110	0.3763	0.061*
C4B	0.8251 (2)	0.5363 (7)	0.3644 (2)	0.0476 (9)
C5B	0.8746 (3)	0.7326 (8)	0.4152 (3)	0.0642 (11)
H22	0.8697	0.7637	0.4763	0.077*
C6B	0.9320 (3)	0.8860 (10)	0.3767 (4)	0.0876 (16)
H23	0.9642	1.0193	0.4116	0.105*
C7B	0.9407 (4)	0.8400 (12)	0.2874 (5)	0.0956 (17)
H24	0.9800	0.9402	0.2622	0.115*
C8B	0.8923 (3)	0.6490 (13)	0.2360 (4)	0.0869 (16)
H25	0.8972	0.6196	0.1749	0.104*
C9B	0.8359 (3)	0.4981 (10)	0.2742 (3)	0.0669 (12)
H26	0.8039	0.3661	0.2382	0.080*
O3	0.5881 (2)	1.1472 (6)	−0.07408 (19)	0.0589 (7)
O4	0.6056 (3)	0.7746 (8)	−0.1150 (2)	0.0960 (12)
O5	0.6289 (2)	0.9821 (7)	0.20181 (17)	0.0725 (9)
O6	0.6179 (3)	1.2600 (6)	0.0918 (2)	0.0754 (9)
C10	0.6087 (3)	0.9229 (7)	−0.0535 (2)	0.0469 (9)
C11	0.6397 (3)	0.8519 (7)	0.0501 (2)	0.0479 (9)
C12	0.6273 (3)	1.0375 (8)	0.1209 (2)	0.0478 (9)
H2B	0.695 (4)	0.846 (15)	0.555 (4)	0.13 (2)*
H3	0.598 (3)	1.232 (8)	−0.008 (3)	0.063 (11)*
H1	0.604 (4)	0.698 (12)	0.059 (4)	0.11 (2)*
H2	0.708 (4)	0.807 (12)	0.070 (3)	0.105 (17)*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O1A	0.0550 (12)	0.0316 (14)	0.0560 (13)	−0.0036 (12)	0.0278 (11)	−0.0049 (12)
O2A	0.0749 (15)	0.0458 (16)	0.0456 (12)	−0.0093 (13)	0.0357 (12)	−0.0124 (11)
N1A	0.0482 (13)	0.0373 (17)	0.0323 (12)	0.0061 (13)	0.0096 (11)	−0.0065 (11)
C1A	0.0459 (17)	0.0327 (18)	0.0250 (13)	0.0024 (16)	0.0085 (13)	−0.0034 (13)
C2A	0.0483 (16)	0.0340 (19)	0.0269 (13)	0.0018 (15)	0.0096 (12)	−0.0004 (13)
C3A	0.0563 (18)	0.0312 (19)	0.0460 (17)	−0.0034 (17)	0.0153 (14)	−0.0025 (15)
C4A	0.0368 (15)	0.040 (2)	0.0457 (17)	−0.0087 (16)	0.0072 (13)	−0.0068 (15)
C5A	0.0463 (17)	0.059 (3)	0.0474 (18)	−0.0030 (19)	0.0107 (15)	−0.007 (2)
C6A	0.054 (2)	0.088 (4)	0.0429 (18)	−0.015 (3)	0.0056 (16)	0.007 (2)
C7A	0.053 (2)	0.062 (3)	0.072 (3)	−0.010 (2)	−0.0036 (19)	0.018 (2)
C8A	0.0488 (19)	0.048 (3)	0.085 (3)	0.005 (2)	0.0011 (19)	−0.001 (2)
C9A	0.0449 (19)	0.048 (3)	0.058 (2)	−0.0039 (18)	0.0087 (16)	−0.0093 (19)
O1B	0.0553 (13)	0.0359 (14)	0.0387 (11)	0.0027 (12)	0.0043 (10)	−0.0048 (12)
O2B	0.0826 (17)	0.0414 (17)	0.0278 (11)	0.0128 (13)	0.0142 (11)	−0.0024 (11)
N1B	0.0542 (15)	0.052 (2)	0.0478 (15)	−0.0084 (16)	0.0228 (13)	−0.0249 (15)
C1B	0.0439 (16)	0.0304 (19)	0.0356 (16)	−0.0026 (15)	0.0190 (13)	−0.0022 (14)
C2B	0.0567 (18)	0.0299 (18)	0.0424 (16)	−0.0015 (17)	0.0261 (14)	−0.0059 (14)
C3B	0.071 (2)	0.032 (2)	0.0549 (19)	0.0120 (19)	0.0274 (17)	−0.0018 (17)
C4B	0.0406 (16)	0.042 (2)	0.058 (2)	0.0114 (17)	0.0115 (15)	−0.0048 (17)
C5B	0.052 (2)	0.057 (3)	0.082 (3)	0.005 (2)	0.017 (2)	−0.015 (2)
C6B	0.055 (2)	0.067 (3)	0.139 (4)	−0.012 (3)	0.027 (3)	−0.028 (3)
C7B	0.073 (3)	0.083 (4)	0.148 (5)	−0.002 (3)	0.059 (3)	0.009 (4)
C8B	0.075 (3)	0.104 (5)	0.094 (3)	0.000 (3)	0.046 (3)	0.004 (4)
C9B	0.060 (2)	0.079 (3)	0.068 (2)	−0.009 (3)	0.0290 (19)	−0.013 (2)
O3	0.0733 (17)	0.0552 (19)	0.0512 (14)	0.0043 (15)	0.0234 (13)	0.0085 (14)
O4	0.137 (3)	0.097 (3)	0.0601 (17)	−0.001 (2)	0.0377 (18)	−0.040 (2)
O5	0.0910 (18)	0.093 (2)	0.0364 (12)	−0.003 (2)	0.0235 (12)	−0.0102 (15)
O6	0.122 (3)	0.0373 (18)	0.079 (2)	−0.0065 (17)	0.0494 (19)	−0.0192 (15)
C10	0.0553 (19)	0.046 (3)	0.0431 (18)	−0.0014 (19)	0.0206 (15)	−0.0072 (17)
C11	0.067 (2)	0.035 (2)	0.0446 (18)	0.006 (2)	0.0211 (17)	−0.0050 (17)
C12	0.0516 (19)	0.058 (3)	0.0367 (17)	−0.0084 (19)	0.0176 (14)	−0.0102 (18)

Geometric parameters (Å, º) top

O1A—C1A	1.217 (4)	N1B—H17	0.8900
O2A—C1A	1.285 (3)	N1B—H18	0.8900
N1A—C2A	1.480 (4)	C1B—C2B	1.514 (4)
N1A—H5	0.8900	C2B—C3B	1.521 (5)
N1A—H6	0.8900	C2B—H19	0.9800
N1A—H7	0.8900	C3B—C4B	1.502 (5)
C1A—C2A	1.519 (5)	C3B—H20	0.9700
C2A—C3A	1.526 (4)	C3B—H21	0.9700
C2A—H8	0.9800	C4B—C5B	1.376 (6)
C3A—C4A	1.505 (5)	C4B—C9B	1.387 (5)
C3A—H9	0.9700	C5B—C6B	1.397 (7)
C3A—H10	0.9700	C5B—H22	0.9300
C4A—C5A	1.378 (4)	C6B—C7B	1.368 (8)
C4A—C9A	1.381 (5)	C6B—H23	0.9300
C5A—C6A	1.391 (6)	C7B—C8B	1.351 (8)
C5A—H11	0.9300	C7B—H24	0.9300
C6A—C7A	1.371 (6)	C8B—C9B	1.375 (7)
C6A—H12	0.9300	C8B—H25	0.9300
C7A—C8A	1.358 (6)	C9B—H26	0.9300
C7A—H13	0.9300	O3—C10	1.284 (5)
C8A—C9A	1.386 (6)	O3—H3	1.05 (4)
C8A—H14	0.9300	O4—C10	1.204 (5)
C9A—H15	0.9300	O5—C12	1.213 (4)
O1B—C1B	1.226 (4)	O6—C12	1.291 (5)
O2B—C1B	1.271 (4)	C10—C11	1.496 (5)
O2B—H2B	0.91 (8)	C11—C12	1.501 (5)
N1B—C2B	1.484 (4)	C11—H1	1.01 (6)
N1B—H16	0.8900	C11—H2	0.95 (5)

C2A—N1A—H5	109.5	O1B—C1B—C2B	121.2 (3)
C2A—N1A—H6	109.5	O2B—C1B—C2B	113.9 (3)
H5—N1A—H6	109.5	N1B—C2B—C1B	108.9 (3)
C2A—N1A—H7	109.5	N1B—C2B—C3B	111.4 (2)
H5—N1A—H7	109.5	C1B—C2B—C3B	113.8 (3)
H6—N1A—H7	109.5	N1B—C2B—H19	107.5
O1A—C1A—O2A	125.7 (3)	C1B—C2B—H19	107.5
O1A—C1A—C2A	122.0 (3)	C3B—C2B—H19	107.5
O2A—C1A—C2A	112.3 (3)	C4B—C3B—C2B	115.3 (3)
N1A—C2A—C1A	108.8 (3)	C4B—C3B—H20	108.4
N1A—C2A—C3A	111.4 (2)	C2B—C3B—H20	108.4
C1A—C2A—C3A	113.4 (3)	C4B—C3B—H21	108.4
N1A—C2A—H8	107.7	C2B—C3B—H21	108.4
C1A—C2A—H8	107.7	H20—C3B—H21	107.5
C3A—C2A—H8	107.7	C5B—C4B—C9B	116.8 (4)
C4A—C3A—C2A	114.8 (3)	C5B—C4B—C3B	121.7 (3)
C4A—C3A—H9	108.6	C9B—C4B—C3B	121.5 (4)
C2A—C3A—H9	108.6	C4B—C5B—C6B	121.1 (4)
C4A—C3A—H10	108.6	C4B—C5B—H22	119.4
C2A—C3A—H10	108.6	C6B—C5B—H22	119.4
H9—C3A—H10	107.5	C7B—C6B—C5B	119.9 (5)
C5A—C4A—C9A	118.1 (3)	C7B—C6B—H23	120.0
C5A—C4A—C3A	121.4 (3)	C5B—C6B—H23	120.0
C9A—C4A—C3A	120.5 (3)	C8B—C7B—C6B	120.0 (5)
C4A—C5A—C6A	120.7 (4)	C8B—C7B—H24	120.0
C4A—C5A—H11	119.6	C6B—C7B—H24	120.0
C6A—C5A—H11	119.6	C7B—C8B—C9B	120.0 (5)
C7A—C6A—C5A	119.7 (4)	C7B—C8B—H25	120.0
C7A—C6A—H12	120.1	C9B—C8B—H25	120.0
C5A—C6A—H12	120.1	C8B—C9B—C4B	122.2 (5)
C8A—C7A—C6A	120.4 (4)	C8B—C9B—H26	118.9
C8A—C7A—H13	119.8	C4B—C9B—H26	118.9
C6A—C7A—H13	119.8	C10—O3—H3	105 (2)
C7A—C8A—C9A	119.8 (4)	C12—O6—H3	101.9 (19)
C7A—C8A—H14	120.1	O4—C10—O3	121.6 (4)
C9A—C8A—H14	120.1	O4—C10—C11	120.7 (4)
C4A—C9A—C8A	121.2 (4)	O3—C10—C11	117.7 (3)
C4A—C9A—H15	119.4	C10—C11—C12	117.4 (3)
C8A—C9A—H15	119.4	C10—C11—H1	110 (3)
C1B—O2B—H2B	118 (4)	C12—C11—H1	108 (3)
C2B—N1B—H16	109.5	C10—C11—H2	110 (3)
C2B—N1B—H17	109.5	C12—C11—H2	107 (3)
H16—N1B—H17	109.5	H1—C11—H2	104 (5)
C2B—N1B—H18	109.5	O5—C12—O6	122.0 (4)
H16—N1B—H18	109.5	O5—C12—C11	121.8 (4)
H17—N1B—H18	109.5	O6—C12—C11	116.2 (3)
O1B—C1B—O2B	124.9 (3)

O1A—C1A—C2A—N1A	−2.7 (4)	O1B—C1B—C2B—C3B	127.3 (3)
O2A—C1A—C2A—N1A	177.6 (2)	O2B—C1B—C2B—C3B	−52.6 (4)
O1A—C1A—C2A—C3A	121.9 (3)	N1B—C2B—C3B—C4B	61.7 (4)
O2A—C1A—C2A—C3A	−57.8 (3)	C1B—C2B—C3B—C4B	−61.7 (4)
N1A—C2A—C3A—C4A	66.9 (4)	C2B—C3B—C4B—C5B	85.8 (4)
C1A—C2A—C3A—C4A	−56.3 (3)	C2B—C3B—C4B—C9B	−94.5 (4)
C2A—C3A—C4A—C5A	−90.0 (4)	C9B—C4B—C5B—C6B	0.5 (5)
C2A—C3A—C4A—C9A	89.3 (4)	C3B—C4B—C5B—C6B	−179.7 (4)
C9A—C4A—C5A—C6A	−1.3 (5)	C4B—C5B—C6B—C7B	−0.9 (7)
C3A—C4A—C5A—C6A	178.0 (3)	C5B—C6B—C7B—C8B	1.2 (8)
C4A—C5A—C6A—C7A	1.2 (6)	C6B—C7B—C8B—C9B	−1.3 (8)
C5A—C6A—C7A—C8A	−0.7 (6)	C7B—C8B—C9B—C4B	1.0 (8)
C6A—C7A—C8A—C9A	0.3 (6)	C5B—C4B—C9B—C8B	−0.6 (6)
C5A—C4A—C9A—C8A	0.9 (5)	C3B—C4B—C9B—C8B	179.7 (4)
C3A—C4A—C9A—C8A	−178.4 (3)	O4—C10—C11—C12	−171.2 (4)
C7A—C8A—C9A—C4A	−0.4 (6)	O3—C10—C11—C12	10.4 (5)
O1B—C1B—C2B—N1B	2.4 (4)	C10—C11—C12—O5	163.4 (3)
O2B—C1B—C2B—N1B	−177.4 (3)	C10—C11—C12—O6	−18.7 (5)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1A—H5···O4ⁱ	0.89	1.90	2.699 (4)	148
N1A—H6···O3ⁱⁱ	0.89	2.06	2.889 (4)	154
N1A—H7···O1Bⁱⁱⁱ	0.89	1.90	2.757 (3)	160
N1B—H16···O5^iv	0.89	2.12	3.005 (4)	174
N1B—H17···O5	0.89	2.35	3.167 (5)	152
N1B—H18···O1A^v	0.89	2.05	2.864 (3)	152
O2B—H2B···O2A^vi	0.91 (8)	1.53 (8)	2.429 (4)	175 (6)
O3—H3···O6	1.04 (4)	1.41 (4)	2.413 (4)	160 (4)

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

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