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In the title complex, (C2H10N2)2[Cd(C7H3NO4)3]·6H2O, the CdII atom is nine-coordinated by three pyridine-2,6-dicarboxylate ligands via six O atoms and three N atoms in a distorted tricapped trigonal prismatic structure. A crystallographic twofold rotation axis passes through the Cd atom and three atoms of one pyridine ring, viz. N, the C in the p-position and its attached H atom. The pyridine-2,6-dicarboxylate ligands, ethylenediammonium cations and uncoordinated water molecules contribute to the formation of intermolecular hydrogen bonds, forming a three-dimensional network.
Supporting information
CCDC reference: 193863
Key indicators
- Single-crystal X-ray study
- T = 298 K
- Mean (C-C) = 0.003 Å
- R factor = 0.028
- wR factor = 0.067
- Data-to-parameter ratio = 12.5
checkCIF/PLATON results
No syntax errors found
Alert level C
PLAT029_ALERT_3_C _diffrn_measured_fraction_theta_full Low ....... 0.97
PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ .... ?
PLAT125_ALERT_4_C No _symmetry_space_group_name_Hall Given ....... ?
PLAT164_ALERT_4_C Nr. of Refined C-H H-Atoms in Heavy-At Struct... 9
PLAT222_ALERT_3_C Large Non-Solvent H Ueq(max)/Ueq(min) ... 3.15 Ratio
PLAT232_ALERT_2_C Hirshfeld Test Diff (M-X) Cd1 - O1 .. 5.75 su
PLAT232_ALERT_2_C Hirshfeld Test Diff (M-X) Cd1 - O5 .. 5.43 su
PLAT731_ALERT_1_C Bond Calc 0.87(3), Rep 0.867(10) ...... 3.00 su-Rat
O7 -H17 1.555 1.555
PLAT731_ALERT_1_C Bond Calc 0.88(3), Rep 0.876(10) ...... 3.00 su-Rat
O8 -H19 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.87(3), Rep 0.867(10) ...... 3.00 su-Rat
O7 -H17 1.555 1.555
PLAT735_ALERT_1_C D-H Calc 0.88(3), Rep 0.876(10) ...... 3.00 su-Rat
O8 -H19 1.555 1.555
PLAT736_ALERT_1_C H...A Calc 1.81(3), Rep 1.804(13) ...... 2.31 su-Rat
H19 -O3 1.555 3.655
0 ALERT level A = In general: serious problem
0 ALERT level B = Potentially serious problem
12 ALERT level C = Check and explain
0 ALERT level G = General alerts; check
6 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
2 ALERT type 3 Indicator that the structure quality may be low
2 ALERT type 4 Improvement, methodology, query or suggestion
Data collection: SMART (Bruker,1997); cell refinement: SMART; data reduction: SAINT (Bruker, 1997); program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL (Bruker, 1997); software used to prepare material for publication: SHELXTL.
Bis(ethylenediammonium)
tris(pyridine-2,6-dicarboxylato-
κ3O,
O',
N)cadmium(II)
hexahydrate
top
Crystal data top
(C2H10N2)2[Cd(C7H3NO4)3]·6H2O | Dx = 1.705 Mg m−3 |
Mr = 840.05 | Mo Kα radiation, λ = 0.71073 Å |
Orthorhombic, Pbcn | Cell parameters from 5899 reflections |
a = 16.250 (3) Å | θ = 2.4–26.6° |
b = 10.0614 (15) Å | µ = 0.76 mm−1 |
c = 20.021 (3) Å | T = 298 K |
V = 3273.4 (9) Å3 | Block, colourless |
Z = 4 | 0.40 × 0.30 × 0.15 mm |
F(000) = 1728 | |
Data collection top
Bruker SMART 1000 CCD area-detector diffractometer | 3930 independent reflections |
Radiation source: fine-focus sealed tube | 2680 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.033 |
φ and ω scans | θmax = 28.3°, θmin = 2.0° |
Absorption correction: multi-scan (SADABS; Sheldrick, 1996) | h = −21→20 |
Tmin = 0.751, Tmax = 0.895 | k = −13→12 |
19430 measured reflections | l = −23→25 |
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)] = 0.028 | Hydrogen site location: difmap and geom |
wR(F2) = 0.067 | H atoms treated by a mixture of independent and constrained refinement |
S = 0.95 | w = 1/[σ2(Fo2) + (0.035P)2] where P = (Fo2 + 2Fc2)/3 |
3930 reflections | (Δ/σ)max < 0.001 |
314 parameters | Δρmax = 0.46 e Å−3 |
6 restraints | Δρmin = −0.41 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 | Uiso*/Ueq | |
Cd1 | 1.0000 | 0.62545 (2) | 0.2500 | 0.02407 (7) | |
N1 | 0.88153 (10) | 0.74815 (16) | 0.21056 (8) | 0.0263 (4) | |
N2 | 1.0000 | 0.3872 (2) | 0.2500 | 0.0227 (5) | |
N3 | 0.16046 (14) | 0.9064 (2) | 0.08264 (11) | 0.0369 (5) | |
N4 | 0.09979 (14) | 0.6123 (2) | 0.04394 (12) | 0.0350 (5) | |
O1 | 1.03209 (9) | 0.79277 (14) | 0.15859 (8) | 0.0352 (4) | |
O2 | 0.97935 (10) | 0.92180 (18) | 0.07915 (8) | 0.0429 (4) | |
O3 | 0.86523 (9) | 0.55836 (14) | 0.30265 (8) | 0.0374 (4) | |
O4 | 0.73626 (10) | 0.61870 (15) | 0.32455 (9) | 0.0477 (5) | |
O5 | 0.96419 (10) | 0.52147 (14) | 0.13657 (7) | 0.0335 (4) | |
O6 | 0.98238 (10) | 0.33841 (16) | 0.07528 (8) | 0.0398 (4) | |
O7 | 0.11138 (12) | 0.15613 (17) | 0.02829 (9) | 0.0446 (4) | |
O8 | 0.17597 (11) | 0.35586 (19) | 0.11868 (9) | 0.0442 (4) | |
O9 | 0.15520 (13) | 0.60130 (18) | 0.45670 (10) | 0.0515 (5) | |
C1 | 0.97305 (14) | 0.8521 (2) | 0.13053 (11) | 0.0288 (5) | |
C2 | 0.88875 (13) | 0.8380 (2) | 0.16159 (10) | 0.0281 (5) | |
C3 | 0.82353 (15) | 0.9143 (2) | 0.13942 (13) | 0.0397 (6) | |
C4 | 0.74713 (16) | 0.8951 (3) | 0.16806 (13) | 0.0463 (7) | |
C5 | 0.73832 (15) | 0.8001 (3) | 0.21722 (13) | 0.0396 (6) | |
C6 | 0.80723 (13) | 0.7297 (2) | 0.23776 (10) | 0.0295 (5) | |
C7 | 0.80186 (13) | 0.6271 (2) | 0.29296 (11) | 0.0303 (5) | |
C8 | 0.97850 (12) | 0.3997 (2) | 0.12971 (11) | 0.0266 (5) | |
C9 | 0.99116 (12) | 0.3189 (2) | 0.19282 (10) | 0.0251 (4) | |
C10 | 0.99175 (15) | 0.1819 (2) | 0.19087 (12) | 0.0399 (6) | |
C11 | 1.0000 | 0.1132 (3) | 0.2500 | 0.0437 (9) | |
C12 | 0.15909 (17) | 0.8350 (2) | 0.01798 (12) | 0.0379 (6) | |
C13 | 0.17388 (15) | 0.6884 (3) | 0.02502 (14) | 0.0375 (6) | |
H1 | 0.8347 (14) | 0.974 (2) | 0.1046 (13) | 0.044 (7)* | |
H2 | 0.7011 (14) | 0.949 (2) | 0.1574 (12) | 0.042 (7)* | |
H3 | 0.6901 (15) | 0.785 (2) | 0.2407 (11) | 0.038 (7)* | |
H4 | 0.9864 (12) | 0.137 (2) | 0.1460 (13) | 0.033 (6)* | |
H5 | 1.0000 | 0.020 (5) | 0.2500 | 0.104 (19)* | |
H6 | 0.2156 (18) | 0.900 (2) | 0.0988 (13) | 0.055 (8)* | |
H7 | 0.1212 (17) | 0.869 (2) | 0.1088 (14) | 0.054 (8)* | |
H8 | 0.1488 (16) | 0.991 (3) | 0.0757 (13) | 0.056 (9)* | |
H9 | 0.1070 (14) | 0.8535 (19) | −0.0078 (11) | 0.028 (6)* | |
H10 | 0.2037 (16) | 0.868 (2) | −0.0078 (12) | 0.038 (7)* | |
H11 | 0.1917 (14) | 0.654 (2) | −0.0164 (12) | 0.032 (6)* | |
H12 | 0.2143 (16) | 0.671 (2) | 0.0557 (13) | 0.050 (7)* | |
H13 | 0.1095 (16) | 0.527 (3) | 0.0450 (14) | 0.059 (9)* | |
H14 | 0.0660 (18) | 0.626 (2) | 0.0137 (15) | 0.056 (9)* | |
H15 | 0.0808 (17) | 0.633 (2) | 0.0812 (14) | 0.050 (9)* | |
H16 | 0.0773 (14) | 0.126 (2) | −0.0012 (11) | 0.063 (10)* | |
H17 | 0.0838 (18) | 0.207 (3) | 0.0550 (13) | 0.095 (12)* | |
H18 | 0.1856 (17) | 0.2836 (19) | 0.1417 (13) | 0.074 (11)* | |
H19 | 0.167 (2) | 0.415 (3) | 0.1499 (13) | 0.097 (12)* | |
H20 | 0.139 (2) | 0.671 (2) | 0.4777 (14) | 0.083 (11)* | |
H21 | 0.1103 (11) | 0.586 (3) | 0.4340 (12) | 0.057 (9)* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Cd1 | 0.02507 (12) | 0.02111 (11) | 0.02603 (11) | 0.000 | −0.00007 (9) | 0.000 |
N1 | 0.0307 (10) | 0.0223 (9) | 0.0261 (10) | 0.0010 (7) | 0.0001 (7) | −0.0028 (7) |
N2 | 0.0208 (11) | 0.0239 (12) | 0.0235 (11) | 0.000 | −0.0003 (10) | 0.000 |
N3 | 0.0320 (12) | 0.0304 (12) | 0.0484 (14) | −0.0046 (9) | −0.0045 (10) | −0.0007 (10) |
N4 | 0.0407 (13) | 0.0341 (12) | 0.0304 (12) | −0.0032 (10) | −0.0027 (10) | 0.0004 (10) |
O1 | 0.0308 (8) | 0.0366 (9) | 0.0381 (9) | 0.0004 (7) | −0.0003 (7) | 0.0087 (7) |
O2 | 0.0440 (10) | 0.0511 (10) | 0.0335 (10) | −0.0070 (8) | −0.0018 (7) | 0.0156 (8) |
O3 | 0.0283 (8) | 0.0345 (9) | 0.0494 (10) | 0.0016 (7) | 0.0034 (7) | 0.0124 (8) |
O4 | 0.0372 (10) | 0.0495 (10) | 0.0565 (12) | 0.0061 (8) | 0.0171 (8) | 0.0153 (8) |
O5 | 0.0424 (9) | 0.0269 (8) | 0.0311 (9) | 0.0019 (7) | −0.0047 (7) | 0.0008 (7) |
O6 | 0.0535 (11) | 0.0407 (9) | 0.0253 (9) | 0.0081 (7) | −0.0064 (7) | −0.0063 (7) |
O7 | 0.0588 (13) | 0.0344 (10) | 0.0407 (11) | −0.0004 (9) | −0.0073 (9) | −0.0066 (8) |
O8 | 0.0397 (10) | 0.0481 (12) | 0.0447 (11) | 0.0034 (8) | −0.0017 (8) | −0.0149 (10) |
O9 | 0.0584 (13) | 0.0413 (11) | 0.0547 (13) | 0.0043 (10) | −0.0186 (10) | −0.0066 (9) |
C1 | 0.0356 (12) | 0.0229 (11) | 0.0278 (12) | −0.0063 (9) | −0.0031 (9) | −0.0050 (9) |
C2 | 0.0324 (12) | 0.0277 (11) | 0.0243 (11) | 0.0015 (9) | −0.0009 (9) | −0.0001 (9) |
C3 | 0.0440 (15) | 0.0400 (14) | 0.0350 (14) | 0.0078 (11) | 0.0009 (11) | 0.0089 (11) |
C4 | 0.0400 (15) | 0.0586 (18) | 0.0404 (15) | 0.0197 (12) | −0.0035 (11) | 0.0071 (13) |
C5 | 0.0321 (14) | 0.0517 (16) | 0.0350 (14) | 0.0070 (11) | 0.0016 (11) | 0.0040 (13) |
C6 | 0.0285 (12) | 0.0283 (11) | 0.0317 (14) | 0.0013 (9) | −0.0005 (9) | −0.0012 (9) |
C7 | 0.0305 (12) | 0.0278 (11) | 0.0325 (12) | −0.0037 (10) | 0.0004 (9) | −0.0019 (10) |
C8 | 0.0231 (11) | 0.0330 (13) | 0.0238 (11) | −0.0019 (8) | −0.0016 (8) | 0.0003 (9) |
C9 | 0.0263 (11) | 0.0230 (10) | 0.0260 (11) | −0.0018 (8) | −0.0002 (8) | −0.0014 (8) |
C10 | 0.0630 (18) | 0.0263 (11) | 0.0304 (13) | −0.0028 (11) | −0.0046 (11) | −0.0029 (10) |
C11 | 0.077 (3) | 0.0185 (15) | 0.0361 (18) | 0.000 | 0.0011 (18) | 0.000 |
C12 | 0.0343 (14) | 0.0433 (14) | 0.0362 (14) | −0.0066 (11) | 0.0016 (11) | 0.0051 (11) |
C13 | 0.0321 (14) | 0.0417 (14) | 0.0386 (15) | −0.0007 (11) | 0.0007 (11) | −0.0059 (12) |
Geometric parameters (Å, º) top
Cd1—N2 | 2.397 (2) | O7—H16 | 0.864 (10) |
Cd1—N1i | 2.4194 (17) | O7—H17 | 0.867 (10) |
Cd1—N1 | 2.4194 (17) | O8—H18 | 0.874 (10) |
Cd1—O3 | 2.5225 (15) | O8—H19 | 0.876 (10) |
Cd1—O3i | 2.5225 (15) | O9—H20 | 0.861 (10) |
Cd1—O1i | 2.5408 (15) | O9—H21 | 0.872 (10) |
Cd1—O1 | 2.5408 (15) | C1—C2 | 1.511 (3) |
Cd1—O5 | 2.5671 (15) | C2—C3 | 1.382 (3) |
Cd1—O5i | 2.5671 (15) | C3—C4 | 1.381 (3) |
N1—C6 | 1.337 (3) | C3—H1 | 0.94 (2) |
N1—C2 | 1.339 (3) | C4—C5 | 1.379 (4) |
N2—C9i | 1.343 (2) | C4—H2 | 0.95 (2) |
N2—C9 | 1.343 (2) | C5—C6 | 1.387 (3) |
N3—C12 | 1.481 (3) | C5—H3 | 0.93 (2) |
N3—H6 | 0.95 (3) | C6—C7 | 1.515 (3) |
N3—H7 | 0.91 (3) | C8—C9 | 1.516 (3) |
N3—H8 | 0.88 (3) | C9—C10 | 1.380 (3) |
N4—C13 | 1.476 (3) | C10—C11 | 1.377 (3) |
N4—H13 | 0.88 (3) | C10—H4 | 1.01 (2) |
N4—H14 | 0.83 (3) | C11—C10i | 1.377 (3) |
N4—H15 | 0.83 (3) | C11—H5 | 0.94 (5) |
O1—C1 | 1.262 (3) | C12—C13 | 1.501 (3) |
O2—C1 | 1.249 (3) | C12—H9 | 1.01 (2) |
O3—C7 | 1.255 (2) | C12—H10 | 0.95 (2) |
O4—C7 | 1.242 (3) | C13—H11 | 0.94 (2) |
O5—C8 | 1.255 (2) | C13—H12 | 0.92 (3) |
O6—C8 | 1.254 (3) | | |
| | | |
N2—Cd1—N1i | 120.68 (4) | H14—N4—H15 | 112 (3) |
N2—Cd1—N1 | 120.68 (4) | C1—O1—Cd1 | 118.54 (14) |
N1i—Cd1—N1 | 118.64 (8) | C7—O3—Cd1 | 120.02 (13) |
N2—Cd1—O3 | 74.48 (3) | C8—O5—Cd1 | 116.93 (13) |
N1i—Cd1—O3 | 133.71 (5) | H16—O7—H17 | 107 (3) |
N1—Cd1—O3 | 65.30 (5) | H18—O8—H19 | 103 (3) |
N2—Cd1—O3i | 74.48 (3) | H20—O9—H21 | 98 (3) |
N1i—Cd1—O3i | 65.30 (5) | O2—C1—O1 | 124.7 (2) |
N1—Cd1—O3i | 133.71 (5) | O2—C1—C2 | 117.8 (2) |
O3—Cd1—O3i | 148.95 (7) | O1—C1—C2 | 117.5 (2) |
N2—Cd1—O1i | 131.50 (3) | N1—C2—C3 | 122.9 (2) |
N1i—Cd1—O1i | 65.81 (5) | N1—C2—C1 | 116.37 (18) |
N1—Cd1—O1i | 74.55 (5) | C3—C2—C1 | 120.7 (2) |
O3—Cd1—O1i | 72.43 (5) | C4—C3—C2 | 118.6 (2) |
O3i—Cd1—O1i | 131.04 (5) | C4—C3—H1 | 124.8 (14) |
N2—Cd1—O1 | 131.50 (3) | C2—C3—H1 | 116.6 (14) |
N1i—Cd1—O1 | 74.55 (5) | C5—C4—C3 | 119.1 (2) |
N1—Cd1—O1 | 65.81 (5) | C5—C4—H2 | 118.4 (14) |
O3—Cd1—O1 | 131.04 (5) | C3—C4—H2 | 122.3 (14) |
O3i—Cd1—O1 | 72.43 (5) | C4—C5—C6 | 118.8 (2) |
O1i—Cd1—O1 | 97.01 (7) | C4—C5—H3 | 124.2 (15) |
N2—Cd1—O5 | 65.95 (3) | C6—C5—H3 | 116.7 (15) |
N1i—Cd1—O5 | 132.61 (5) | N1—C6—C5 | 122.5 (2) |
N1—Cd1—O5 | 74.86 (5) | N1—C6—C7 | 116.33 (18) |
O3—Cd1—O5 | 93.66 (5) | C5—C6—C7 | 121.2 (2) |
O3i—Cd1—O5 | 73.62 (5) | O4—C7—O3 | 126.0 (2) |
O1i—Cd1—O5 | 149.40 (5) | O4—C7—C6 | 117.84 (19) |
O1—Cd1—O5 | 71.30 (5) | O3—C7—C6 | 116.15 (19) |
N2—Cd1—O5i | 65.95 (3) | O6—C8—O5 | 125.8 (2) |
N1i—Cd1—O5i | 74.86 (5) | O6—C8—C9 | 117.00 (19) |
N1—Cd1—O5i | 132.61 (5) | O5—C8—C9 | 117.21 (19) |
O3—Cd1—O5i | 73.62 (5) | N2—C9—C10 | 122.3 (2) |
O3i—Cd1—O5i | 93.66 (5) | N2—C9—C8 | 116.79 (18) |
O1i—Cd1—O5i | 71.30 (5) | C10—C9—C8 | 120.9 (2) |
O1—Cd1—O5i | 149.40 (5) | C11—C10—C9 | 118.5 (2) |
O5—Cd1—O5i | 131.90 (6) | C11—C10—H4 | 123.3 (12) |
C6—N1—C2 | 118.10 (18) | C9—C10—H4 | 118.1 (13) |
C6—N1—Cd1 | 120.98 (14) | C10i—C11—C10 | 119.8 (3) |
C2—N1—Cd1 | 120.92 (13) | C10i—C11—H5 | 120.09 (15) |
C9i—N2—C9 | 118.5 (2) | C10—C11—H5 | 120.09 (15) |
C9i—N2—Cd1 | 120.77 (12) | N3—C12—C13 | 113.1 (2) |
C9—N2—Cd1 | 120.77 (12) | N3—C12—H9 | 111.7 (12) |
C12—N3—H6 | 106.0 (16) | C13—C12—H9 | 111.4 (11) |
C12—N3—H7 | 107.0 (16) | N3—C12—H10 | 107.1 (14) |
H6—N3—H7 | 116 (2) | C13—C12—H10 | 105.7 (13) |
C12—N3—H8 | 109.0 (18) | H9—C12—H10 | 107.3 (19) |
H6—N3—H8 | 109 (2) | N4—C13—C12 | 113.8 (2) |
H7—N3—H8 | 110 (2) | N4—C13—H11 | 106.5 (13) |
C13—N4—H13 | 111.6 (18) | C12—C13—H11 | 109.3 (13) |
C13—N4—H14 | 105.2 (19) | N4—C13—H12 | 108.3 (16) |
H13—N4—H14 | 108 (2) | C12—C13—H12 | 111.4 (15) |
C13—N4—H15 | 113.9 (18) | H11—C13—H12 | 107 (2) |
H13—N4—H15 | 107 (2) | | |
| | | |
N3—C12—C13—N4 | 81.9 (3) | | |
Symmetry code: (i) −x+2, y, −z+1/2. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
N3—H6···O8ii | 0.95 (3) | 1.86 (3) | 2.801 (3) | 168 (2) |
N3—H7···O1iii | 0.91 (3) | 1.92 (3) | 2.823 (3) | 176 (2) |
N3—H8···O7iv | 0.88 (3) | 2.01 (3) | 2.852 (3) | 160 (2) |
N4—H13···O9v | 0.88 (3) | 2.31 (3) | 2.912 (3) | 126 (2) |
N4—H14···O6vi | 0.83 (3) | 1.98 (3) | 2.779 (3) | 162 (3) |
N4—H15···O1iii | 0.83 (3) | 2.37 (3) | 3.126 (3) | 151 (2) |
O7—H16···O2vi | 0.86 (1) | 1.88 (1) | 2.723 (3) | 167 (3) |
O7—H17···O6iii | 0.87 (1) | 2.15 (2) | 2.940 (2) | 151 (3) |
O8—H18···O4vii | 0.87 (1) | 1.97 (1) | 2.819 (2) | 163 (3) |
O8—H19···O3viii | 0.88 (1) | 1.80 (1) | 2.661 (2) | 165 (3) |
O9—H20···O7ix | 0.86 (1) | 2.06 (1) | 2.919 (3) | 175 (3) |
O9—H21···O5viii | 0.87 (1) | 1.97 (1) | 2.810 (2) | 161 (3) |
Symmetry codes: (ii) −x+1/2, y+1/2, z; (iii) x−1, y, z; (iv) x, y+1, z; (v) x, −y+1, z−1/2; (vi) −x+1, −y+1, −z; (vii) x−1/2, y−1/2, −z+1/2; (viii) −x+1, y, −z+1/2; (ix) x, −y+1, z+1/2. |
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