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The crystal structure of the title compound, 2C9H12NO2+·SO42-·H2O, consists of two protonated phenyl­alaninium cations linked together by hydrogen bonding with the water mol­ecule and the sulfate anion. The aggregation of the hydro­phobic zone is along (10\overline 1) and of the hydro­philic zone is along (20\overline 2). The phenyl­alaninium mol­ecules show sterically least favourable g+ or g- conformations.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S160053680101234X/ci6038sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S160053680101234X/ci6038Isup2.hkl
Contains datablock I

CCDC reference: 170924

Key indicators

  • Single-crystal X-ray study
  • T = 293 K
  • Mean [sigma](C-C) = 0.004 Å
  • R factor = 0.046
  • wR factor = 0.119
  • Data-to-parameter ratio = 13.1

checkCIF results

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ADDSYM reports no extra symmetry








Comment top

The crystal structures of amino acids and their complexes have provided a wealth of interesting features pertaining to their patterns of aggregation and their ionic interactions (Vijayan, 1988; Prasad & Vijayan, 1993). The crystal structures of L-phenylalanine hydrochloride (Gurskaya & Vainshtein, 1963; Al-Karaghouli & Koetzle, 1975), L-phenylalanine L-phenylalaninium formate (Gorbitz & Etter, 1992), bis(L-phenylalanine) nitrate (Srikrishnan et al., 1984), bis(L-phenylalanine) sulfate monohydrate (Nagashima et al., 1992), L-phenylalanine L-phenylalaninium perchlorate (Srinivasan & Rajaram, 1997) have been reported. In the present study, the structure of DL-phenylalaninium sulfate monohydrate, (I), has been investigated (Fig. 1 and Table 1).

The asymmetric unit of (I) contains two crystallographically independent protonated phenylalaninium units (molecules A and B), one sulfate ion and a water molecule. The two phenylalaninium molecules A and B show sterically least favourable g+ and g- conformation (Benedetti et al., 1983; Suresh et al., 1994) with χ1 values of 56.2 (3) and -58.1 (3)°, respectively, and has striking similarities with that of L-phenylalnine L-phenylalaninium formate (Gorbitz & Etter, 1992).

A chelated bifurcated hydrogen bond is observed in the case of (i) the amino N atom of molecule A with sulfate O atoms O1 and O4 and (ii) the amino N atom of molecule B with the sulfate O4 atom and the carboxyl O2A atom (Jeffrey & Saenger, 1991). The O4 atom of the sulfate anion acts as acceptor in hydrogen bonded with the water molecule and the amino N atom of molecules A and B. Interestingly, phenylalaninium molecule A forms a hydrogen bond with the sulfate anion only, while molecule B is hydrogen bonded to the sulfate anion, a carboxyl O atom and the water O atom. The sulfate anion links the phenylalaninium molecules into chains running along the b axis through hydrogen bonds with (i) the amino N atom of molecule A and (ii) the amino N and carboxyl O atoms of molecule B. The packing arrangement leads to the formation of a hydrophobic zone by phenyl rings along (101) and a hydrophilic zone along (202) (Fig. 2).

Experimental top

The title compound, (I), was crystallized from an aqueous solution of DL-phenylalanine and sulfuric acid by slow evaporation.

Refinement top

The H atoms of the water molecule were located and refined using DFIX. All other H atoms were fixed by HFIX and allowed to ride on the parent atom.

Computing details top

Data collection: CAD-4 Software (Enraf-Nonius, 1989); cell refinement: CAD-4 Software; data reduction: CAD-4 Software; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: PLATON (Spek, 1999); software used to prepare material for publication: SHELXL97.

Figures top
[Figure 1] Fig. 1. The molecular structure of (I) showing the atomic numbering scheme and 50% probability displacement ellipsoids (Johnson, 1976).
[Figure 2] Fig. 2. Packing of the molecules viewed down the b axis.
(I) top
Crystal data top
2C9H12NO2+·O4S2·H2OF(000) = 944
Mr = 446.47Dx = 1.396 Mg m3
Dm = 1.39 Mg m3
Dm measured by flotation in a mixture of bromoform and xylene
Monoclinic, P21/nMo Kα radiation, λ = 0.71069 Å
a = 14.560 (2) ÅCell parameters from 25 reflections
b = 6.6000 (12) Åθ = 8.0–15.8°
c = 22.115 (4) ŵ = 0.21 mm1
β = 90.70 (2)°T = 293 K
V = 2124.9 (6) Å3Needles, colorless
Z = 40.4 × 0.2 × 0.1 mm
Data collection top
Enraf-Nonius sealed tube
diffractometer
2806 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tubeRint = 0.021
Graphite monochromatorθmax = 25.0°, θmin = 2.8°
ω–2θ scansh = 017
Absorption correction: ψ scan
(North et al., 1968)
k = 07
Tmin = 0.951, Tmax = 0.980l = 2626
3825 measured reflections25 standard reflections every 3 reflections
3671 independent reflections intensity decay: none
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.046Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.119H atoms treated by a mixture of independent and constrained refinement
S = 1.05 w = 1/[σ2(Fo2) + (0.053P)2 + 1.5922P]
where P = (Fo2 + 2Fc2)/3
3671 reflections(Δ/σ)max < 0.001
281 parametersΔρmax = 0.52 e Å3
2 restraintsΔρmin = 0.26 e Å3
Crystal data top
2C9H12NO2+·O4S2·H2OV = 2124.9 (6) Å3
Mr = 446.47Z = 4
Monoclinic, P21/nMo Kα radiation
a = 14.560 (2) ŵ = 0.21 mm1
b = 6.6000 (12) ÅT = 293 K
c = 22.115 (4) Å0.4 × 0.2 × 0.1 mm
β = 90.70 (2)°
Data collection top
Enraf-Nonius sealed tube
diffractometer
2806 reflections with I > 2σ(I)
Absorption correction: ψ scan
(North et al., 1968)
Rint = 0.021
Tmin = 0.951, Tmax = 0.98025 standard reflections every 3 reflections
3825 measured reflections intensity decay: none
3671 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0462 restraints
wR(F2) = 0.119H atoms treated by a mixture of independent and constrained refinement
S = 1.05Δρmax = 0.52 e Å3
3671 reflectionsΔρmin = 0.26 e Å3
281 parameters
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
xyzUiso*/Ueq
S0.27906 (4)0.20427 (9)0.10666 (3)0.02978 (17)
O10.32429 (11)0.2919 (3)0.05195 (7)0.0369 (4)
O20.19967 (12)0.0864 (3)0.08762 (9)0.0530 (6)
O30.34514 (12)0.0639 (3)0.13478 (8)0.0468 (5)
O40.25546 (17)0.3665 (3)0.14796 (10)0.0673 (7)
OW0.57935 (17)0.4282 (4)0.18734 (12)0.0684 (7)
H10.628 (2)0.513 (6)0.1784 (18)0.101 (14)*
H20.539 (2)0.445 (6)0.1566 (13)0.081 (12)*
O1A0.50678 (12)0.3299 (3)0.04872 (8)0.0447 (5)
O1B0.49823 (11)0.1962 (3)0.04434 (8)0.0433 (5)
H1B0.44390.22780.04250.065*
C110.54087 (16)0.2536 (3)0.00510 (11)0.0318 (5)
C120.64337 (15)0.2134 (4)0.00081 (10)0.0317 (5)
H120.65290.06720.00370.038*
N110.68793 (14)0.2804 (3)0.05773 (9)0.0344 (5)
H11A0.74810.25770.05590.052*
H11B0.66470.21160.08860.052*
H11C0.67790.41220.06300.052*
C130.68506 (17)0.3202 (4)0.05313 (12)0.0404 (6)
H13A0.65620.26920.08980.048*
H13B0.67150.46380.05050.048*
C140.78803 (17)0.2929 (4)0.05764 (11)0.0380 (6)
C150.8272 (2)0.1050 (5)0.06414 (16)0.0612 (9)
H150.79000.00950.06600.073*
C160.9219 (2)0.0849 (6)0.06797 (17)0.0706 (10)
H160.94780.04310.07190.085*
C170.9768 (2)0.2511 (6)0.06595 (14)0.0621 (10)
H171.04020.23690.06860.075*
C180.9391 (2)0.4382 (6)0.06004 (13)0.0557 (9)
H180.97670.55210.05930.067*
C190.84491 (19)0.4598 (5)0.05507 (12)0.0451 (7)
H190.81980.58810.05000.054*
O2A0.19852 (14)0.2220 (3)0.20968 (9)0.0572 (6)
O2B0.10045 (13)0.1978 (4)0.13422 (10)0.0584 (6)
H2B0.13280.10150.12420.088*
C210.13276 (16)0.2795 (4)0.18392 (11)0.0352 (6)
C220.07529 (15)0.4580 (4)0.20500 (11)0.0323 (5)
H220.05970.54230.17010.039*
N210.13195 (13)0.5768 (3)0.24707 (9)0.0334 (5)
H21A0.10010.68340.26030.050*
H21B0.14740.49950.27830.050*
H21C0.18260.61920.22800.050*
C230.01357 (16)0.3814 (4)0.23563 (14)0.0441 (7)
H23A0.00240.28940.26800.053*
H23B0.04870.30560.20630.053*
C240.07292 (15)0.5482 (4)0.26114 (12)0.0366 (6)
C250.11920 (18)0.6813 (5)0.22420 (12)0.0465 (7)
H250.11330.66860.18240.056*
C260.1739 (2)0.8323 (5)0.24803 (14)0.0577 (8)
H260.20400.92180.22250.069*
C270.1840 (2)0.8505 (6)0.31019 (15)0.0611 (9)
H270.22190.95020.32660.073*
C280.1380 (2)0.7217 (5)0.34712 (13)0.0555 (8)
H280.14380.73550.38880.067*
C290.08293 (18)0.5708 (5)0.32339 (13)0.0463 (7)
H290.05220.48340.34920.056*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S0.0282 (3)0.0276 (3)0.0333 (3)0.0037 (3)0.0074 (2)0.0020 (3)
O10.0336 (9)0.0384 (10)0.0387 (10)0.0027 (8)0.0090 (7)0.0088 (8)
O20.0362 (10)0.0633 (14)0.0597 (13)0.0206 (10)0.0064 (9)0.0188 (11)
O30.0380 (10)0.0588 (13)0.0439 (11)0.0020 (9)0.0019 (8)0.0149 (9)
O40.0854 (16)0.0513 (13)0.0644 (14)0.0018 (12)0.0350 (12)0.0122 (11)
OW0.0604 (15)0.0556 (15)0.0889 (19)0.0116 (12)0.0160 (13)0.0189 (13)
O1A0.0376 (10)0.0548 (12)0.0418 (11)0.0040 (9)0.0065 (8)0.0005 (9)
O1B0.0291 (9)0.0482 (11)0.0523 (11)0.0011 (9)0.0069 (8)0.0123 (9)
C110.0314 (12)0.0225 (12)0.0415 (14)0.0014 (10)0.0002 (11)0.0022 (11)
C120.0298 (12)0.0311 (12)0.0340 (12)0.0016 (11)0.0032 (9)0.0026 (10)
N110.0346 (11)0.0331 (11)0.0353 (11)0.0014 (9)0.0041 (9)0.0002 (9)
C130.0345 (13)0.0487 (17)0.0379 (14)0.0009 (12)0.0001 (11)0.0058 (12)
C140.0337 (13)0.0482 (16)0.0322 (13)0.0026 (13)0.0024 (10)0.0021 (12)
C150.0512 (18)0.0501 (19)0.083 (2)0.0004 (16)0.0156 (16)0.0005 (17)
C160.054 (2)0.068 (2)0.090 (3)0.0240 (19)0.0210 (18)0.014 (2)
C170.0317 (15)0.104 (3)0.0508 (18)0.0092 (18)0.0026 (13)0.0097 (19)
C180.0393 (16)0.085 (3)0.0431 (17)0.0165 (16)0.0020 (12)0.0015 (16)
C190.0449 (15)0.0493 (17)0.0412 (15)0.0031 (13)0.0005 (12)0.0034 (13)
O2A0.0453 (11)0.0670 (14)0.0597 (12)0.0273 (11)0.0167 (10)0.0143 (11)
O2B0.0465 (12)0.0628 (14)0.0664 (14)0.0218 (10)0.0188 (10)0.0313 (11)
C210.0258 (12)0.0417 (14)0.0381 (13)0.0018 (11)0.0002 (10)0.0030 (12)
C220.0242 (11)0.0385 (14)0.0342 (13)0.0021 (10)0.0015 (9)0.0029 (11)
N210.0280 (10)0.0395 (12)0.0325 (11)0.0024 (9)0.0003 (8)0.0006 (9)
C230.0266 (13)0.0415 (15)0.0641 (18)0.0007 (11)0.0047 (12)0.0060 (14)
C240.0205 (11)0.0451 (15)0.0441 (15)0.0028 (11)0.0005 (10)0.0046 (12)
C250.0371 (14)0.066 (2)0.0359 (14)0.0110 (14)0.0009 (11)0.0085 (14)
C260.0496 (17)0.068 (2)0.0553 (19)0.0253 (16)0.0070 (14)0.0048 (16)
C270.0469 (17)0.075 (2)0.061 (2)0.0210 (17)0.0007 (15)0.0251 (18)
C280.0464 (16)0.080 (2)0.0401 (15)0.0041 (16)0.0038 (13)0.0153 (16)
C290.0351 (14)0.0601 (19)0.0436 (15)0.0010 (13)0.0005 (11)0.0047 (14)
Geometric parameters (Å, º) top
S—O41.446 (2)C18—C191.385 (4)
S—O21.4597 (19)C18—H180.93
S—O31.4782 (19)C19—H190.93
S—O11.4876 (17)O2A—C211.183 (3)
OW—H10.92 (2)O2B—C211.316 (3)
OW—H20.90 (2)O2B—H2B0.82
O1A—C111.201 (3)C21—C221.516 (3)
O1B—C111.307 (3)C22—N211.476 (3)
O1B—H1B0.82C22—C231.538 (3)
C11—C121.520 (3)C22—H220.98
C12—N111.477 (3)N21—H21A0.89
C12—C131.519 (3)N21—H21B0.89
C12—H120.98N21—H21C0.89
N11—H11A0.89C23—C241.505 (4)
N11—H11B0.89C23—H23A0.97
N11—H11C0.89C23—H23B0.97
C13—C141.515 (3)C24—C251.381 (4)
C13—H13A0.97C24—C291.391 (4)
C13—H13B0.97C25—C261.377 (4)
C14—C151.373 (4)C25—H250.93
C14—C191.379 (4)C26—C271.386 (4)
C15—C161.389 (4)C26—H260.93
C15—H150.93C27—C281.361 (5)
C16—C171.358 (5)C27—H270.93
C16—H160.93C28—C291.378 (4)
C17—C181.358 (5)C28—H280.93
C17—H170.93C29—H290.93
O4—S—O2113.20 (14)C14—C19—C18120.6 (3)
O4—S—O3110.44 (14)C14—C19—H19119.7
O2—S—O3108.01 (12)C18—C19—H19119.7
O4—S—O1108.98 (12)C21—O2B—H2B109.5
O2—S—O1108.47 (11)O2A—C21—O2B124.8 (2)
O3—S—O1107.57 (10)O2A—C21—C22123.3 (2)
H1—OW—H2105 (4)O2B—C21—C22111.9 (2)
C11—O1B—H1B109.5N21—C22—C21107.22 (19)
O1A—C11—O1B126.7 (2)N21—C22—C23111.7 (2)
O1A—C11—C12122.6 (2)C21—C22—C23109.8 (2)
O1B—C11—C12110.7 (2)N21—C22—H22109.4
N11—C12—C13110.8 (2)C21—C22—H22109.4
N11—C12—C11108.42 (19)C23—C22—H22109.4
C13—C12—C11111.7 (2)C22—N21—H21A109.5
N11—C12—H12108.6C22—N21—H21B109.5
C13—C12—H12108.6H21A—N21—H21B109.5
C11—C12—H12108.6C22—N21—H21C109.5
C12—N11—H11A109.5H21A—N21—H21C109.5
C12—N11—H11B109.5H21B—N21—H21C109.5
H11A—N11—H11B109.5C24—C23—C22113.6 (2)
C12—N11—H11C109.5C24—C23—H23A108.8
H11A—N11—H11C109.5C22—C23—H23A108.8
H11B—N11—H11C109.5C24—C23—H23B108.8
C14—C13—C12113.7 (2)C22—C23—H23B108.8
C14—C13—H13A108.8H23A—C23—H23B107.7
C12—C13—H13A108.8C25—C24—C29118.2 (2)
C14—C13—H13B108.8C25—C24—C23121.7 (2)
C12—C13—H13B108.8C29—C24—C23120.1 (3)
H13A—C13—H13B107.7C26—C25—C24121.2 (3)
C15—C14—C19118.4 (2)C26—C25—H25119.4
C15—C14—C13121.8 (3)C24—C25—H25119.4
C19—C14—C13119.8 (3)C25—C26—C27119.7 (3)
C14—C15—C16120.4 (3)C25—C26—H26120.1
C14—C15—H15119.8C27—C26—H26120.1
C16—C15—H15119.8C28—C27—C26119.6 (3)
C17—C16—C15120.4 (3)C28—C27—H27120.2
C17—C16—H16119.8C26—C27—H27120.2
C15—C16—H16119.8C27—C28—C29120.8 (3)
C18—C17—C16119.9 (3)C27—C28—H28119.6
C18—C17—H17120.0C29—C28—H28119.6
C16—C17—H17120.0C28—C29—C24120.5 (3)
C17—C18—C19120.2 (3)C28—C29—H29119.7
C17—C18—H18119.9C24—C29—H29119.7
C19—C18—H18119.9
O1A—C11—C12—N110.8 (3)O2A—C21—C22—N2118.5 (4)
O1B—C11—C12—N11179.8 (2)O2B—C21—C22—N21161.7 (2)
O1A—C11—C12—C13121.6 (3)O2A—C21—C22—C23103.1 (3)
O1B—C11—C12—C1357.8 (3)O2B—C21—C22—C2376.7 (3)
N11—C12—C13—C1456.2 (3)N21—C22—C23—C2458.1 (3)
C11—C12—C13—C14177.2 (2)C21—C22—C23—C24176.9 (2)
C12—C13—C14—C1560.9 (4)C22—C23—C24—C2570.0 (3)
C12—C13—C14—C19119.0 (3)C22—C23—C24—C29110.5 (3)
C19—C14—C15—C160.1 (5)C29—C24—C25—C260.1 (4)
C13—C14—C15—C16179.8 (3)C23—C24—C25—C26179.5 (3)
C14—C15—C16—C170.7 (6)C24—C25—C26—C270.8 (5)
C15—C16—C17—C180.1 (5)C25—C26—C27—C281.5 (5)
C16—C17—C18—C191.0 (5)C26—C27—C28—C291.2 (5)
C15—C14—C19—C181.1 (4)C27—C28—C29—C240.4 (5)
C13—C14—C19—C18179.0 (2)C25—C24—C29—C280.3 (4)
C17—C18—C19—C141.7 (4)C23—C24—C29—C28179.2 (3)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1B—H1B···O10.821.802.614 (2)170
O2B—H2B···O2i0.821.772.575 (3)168
N11—H11A···O2ii0.892.492.992 (3)116
N11—H11B···O3ii0.892.092.884 (3)148
N11—H11C···O1iii0.891.972.831 (3)163
N11—H11C···O4iii0.892.563.170 (3)126
N21—H21A···OWiv0.892.012.836 (3)154
N21—H21C···O4v0.892.052.843 (3)147
N21—H21C···O2Avi0.892.332.826 (3)115
N21—H21B···O3vii0.891.972.797 (3)154
OW—H1···O4iii0.92 (2)2.00 (2)2.904 (3)165 (4)
OW—H2···O1A0.90 (2)2.54 (3)3.295 (3)142 (3)
Symmetry codes: (i) x, y, z; (ii) x+1, y, z; (iii) x+1, y+1, z; (iv) x+1/2, y+1/2, z+1/2; (v) x, y+1, z; (vi) x1/2, y+1/2, z+1/2; (vii) x1/2, y+1/2, z+1/2.

Experimental details

Crystal data
Chemical formula2C9H12NO2+·O4S2·H2O
Mr446.47
Crystal system, space groupMonoclinic, P21/n
Temperature (K)293
a, b, c (Å)14.560 (2), 6.6000 (12), 22.115 (4)
β (°) 90.70 (2)
V3)2124.9 (6)
Z4
Radiation typeMo Kα
µ (mm1)0.21
Crystal size (mm)0.4 × 0.2 × 0.1
Data collection
DiffractometerEnraf-Nonius sealed tube
diffractometer
Absorption correctionψ scan
(North et al., 1968)
Tmin, Tmax0.951, 0.980
No. of measured, independent and
observed [I > 2σ(I)] reflections
3825, 3671, 2806
Rint0.021
(sin θ/λ)max1)0.594
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.046, 0.119, 1.05
No. of reflections3671
No. of parameters281
No. of restraints2
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.52, 0.26

Computer programs: CAD-4 Software (Enraf-Nonius, 1989), CAD-4 Software, SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), PLATON (Spek, 1999), SHELXL97.

Selected geometric parameters (Å, º) top
O1A—C111.201 (3)O2A—C211.183 (3)
O1B—C111.307 (3)O2B—C211.316 (3)
O1A—C11—C12—N110.8 (3)O2A—C21—C22—N2118.5 (4)
N11—C12—C13—C1456.2 (3)N21—C22—C23—C2458.1 (3)
C11—C12—C13—C14177.2 (2)C21—C22—C23—C24176.9 (2)
C12—C13—C14—C1560.9 (4)C22—C23—C24—C2570.0 (3)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1B—H1B···O10.821.802.614 (2)170
O2B—H2B···O2i0.821.772.575 (3)168
N11—H11A···O2ii0.892.492.992 (3)116
N11—H11B···O3ii0.892.092.884 (3)148
N11—H11C···O1iii0.891.972.831 (3)163
N11—H11C···O4iii0.892.563.170 (3)126
N21—H21A···OWiv0.892.012.836 (3)154
N21—H21C···O4v0.892.052.843 (3)147
N21—H21C···O2Avi0.892.332.826 (3)115
N21—H21B···O3vii0.891.972.797 (3)154
OW—H1···O4iii0.92 (2)2.00 (2)2.904 (3)165 (4)
OW—H2···O1A0.90 (2)2.54 (3)3.295 (3)142 (3)
Symmetry codes: (i) x, y, z; (ii) x+1, y, z; (iii) x+1, y+1, z; (iv) x+1/2, y+1/2, z+1/2; (v) x, y+1, z; (vi) x1/2, y+1/2, z+1/2; (vii) x1/2, y+1/2, z+1/2.
 

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