organic compounds
Bis(creatininium) 3-nitrophthalate monohydrate
aDepartment of Physics, Presidency college, Chennai 600 005, Tamil Nadu, India, and bDepartment of Physics & Nano Technology, SRM University, SRM Nagar, Kattankulathur, Kancheepuram Dist, Chennai 603 203 Tamil Nadu, India
*Correspondence e-mail: ppkpresidency@gmail.com, phdguna@gmail.com
In the title hydrated molecular salt, 2C4H8N3O+·C8H3NO62−·H2O, the dihedral angles between the benzene ring and the nitro group and the carboxylate groups are 48.0 (2), 55.3 (2) and 60.7 (2)°, respectively. In the crystal, the components are linked by N—H⋯O, O—H⋯O and C—H⋯O hydrogen bonds, generating a two-dimensional network parallel to (102).
CCDC reference: 1486234
Structure description
Creatinine (systematic name: 2-imino-1-methylimidazolidin-4-one) and its derivatives display a range of biological activity. In particular, creatinine is an indicator of renal function. In understanding renal dysfunction, the determination of creatinine is more important than that of urea (Sharma et al., 2004). Creatinine clearance is used to determine the glomerular filtration rate (GFR) of the kidneys (Mădăraş & Buck, 1996) and various disease states in biological fluids can be indicated by an abnormal level of creatinine (Narayanan & Appleton, 1980). We report here the structure of the protonated creatinine derivative bis-creatininium 3-nitrophthalate that crystallizes as a monohydrate.
The ). The geometric parameters of the title molecule agree well with those reported for similar similar structures (Jahubar Ali et al., 2011, 2012). The packing features N—H⋯O, O—H⋯O and C—H⋯O hydrogen bonds, which generate a two-dimensional network parallel to (102) (Table 1, Fig. 2).
of the title compound comprises two protonated creatinine cations, one doubly deprotonated 3-nitrophthalic acid anion and a water molecule of crystallization (Fig. 1Synthesis and crystallization
Creatinine and 3-nitrophthalic acid in 2:1 molar ratio were dissolved in deionized water. The solution was stirred well, filtered and kept in a dust-free environment. Crystals were obtained from the mother solution after 10 d (yield 95%).
Refinement
Crystal data, data collection and structure .
details are summarized in Table 2
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Structural data
CCDC reference: 1486234
10.1107/S2414314616009895/sj4041sup1.cif
contains datablocks C3NP, I. DOI:Structure factors: contains datablock I. DOI: 10.1107/S2414314616009895/sj4041Isup2.hkl
Supporting information file. DOI: 10.1107/S2414314616009895/sj4041Isup3.cml
Data collection: APEX2 (Bruker, 2008); cell
SAINT (Bruker, 2008); data reduction: SAINT (Bruker, 2008); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: PLATON (Spek, 2009); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).2C4H8N3O+·C8H3NO62−·H2O | F(000) = 952 |
Mr = 455.40 | Dx = 1.471 Mg m−3 |
Monoclinic, P21/c | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: -P 2ybc | Cell parameters from 3032 reflections |
a = 7.6682 (3) Å | θ = 2.5–25.0° |
b = 16.5504 (6) Å | µ = 0.12 mm−1 |
c = 16.2358 (7) Å | T = 295 K |
β = 93.775 (1)° | Block, colourless |
V = 2056.04 (14) Å3 | 0.30 × 0.25 × 0.20 mm |
Z = 4 |
Bruker APEXII CCD diffractometer | 3620 independent reflections |
Radiation source: fine-focus sealed tube | 3202 reflections with I > 2σ(I) |
Graphite monochromator | Rint = 0.023 |
Detector resolution: 0 pixels mm-1 | θmax = 25.0°, θmin = 2.5° |
ω and φ scans | h = −9→9 |
Absorption correction: multi-scan (SADABS; Sheldrick, 1996) | k = −19→19 |
Tmin = 0.964, Tmax = 0.975 | l = −19→19 |
30566 measured reflections |
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)] = 0.034 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.097 | H atoms treated by a mixture of independent and constrained refinement |
S = 1.04 | w = 1/[σ2(Fo2) + (0.0511P)2 + 0.6212P] where P = (Fo2 + 2Fc2)/3 |
3620 reflections | (Δ/σ)max < 0.001 |
299 parameters | Δρmax = 0.23 e Å−3 |
3 restraints | Δρmin = −0.19 e Å−3 |
x | y | z | Uiso*/Ueq | ||
O4 | 0.31739 (13) | 0.24338 (6) | 0.37689 (7) | 0.0426 (3) | |
O2 | −0.20496 (15) | 0.39851 (6) | 0.44152 (7) | 0.0468 (3) | |
O1 | −0.05094 (16) | 0.36012 (6) | 0.33692 (7) | 0.0500 (3) | |
O7 | −0.12906 (18) | −0.00022 (8) | 0.32383 (8) | 0.0623 (4) | |
O3 | 0.26695 (14) | 0.34371 (6) | 0.46389 (7) | 0.0455 (3) | |
O8 | 0.37908 (18) | −0.23485 (8) | 0.30455 (8) | 0.0650 (4) | |
N4 | 0.04747 (17) | 0.14441 (7) | 0.19650 (8) | 0.0411 (3) | |
N5 | 0.50199 (16) | −0.15212 (7) | 0.21091 (8) | 0.0382 (3) | |
H5 | 0.5431 | −0.1882 | 0.1794 | 0.046* | |
C1 | −0.09432 (17) | 0.26573 (8) | 0.44182 (8) | 0.0292 (3) | |
C5 | 0.08351 (17) | 0.15554 (8) | 0.48841 (8) | 0.0306 (3) | |
O6 | 0.36494 (17) | 0.16305 (9) | 0.54522 (9) | 0.0698 (4) | |
N1 | 0.25658 (17) | 0.12099 (8) | 0.50719 (9) | 0.0455 (3) | |
N7 | 0.43615 (16) | −0.03075 (8) | 0.25712 (7) | 0.0392 (3) | |
N2 | 0.15811 (18) | 0.06240 (8) | 0.09368 (8) | 0.0446 (3) | |
H2A | 0.1982 | 0.1028 | 0.0675 | 0.054* | |
H2B | 0.1711 | 0.0141 | 0.0755 | 0.054* | |
C6 | 0.07245 (17) | 0.23258 (7) | 0.45540 (7) | 0.0275 (3) | |
N6 | 0.59974 (16) | −0.04045 (7) | 0.13985 (8) | 0.0406 (3) | |
H6A | 0.6065 | 0.0111 | 0.1343 | 0.049* | |
H6B | 0.6479 | −0.0718 | 0.1057 | 0.049* | |
N3 | 0.01716 (15) | 0.01224 (7) | 0.20550 (7) | 0.0367 (3) | |
H3A | 0.0275 | −0.0380 | 0.1932 | 0.044* | |
O5 | 0.28472 (18) | 0.05264 (8) | 0.48399 (11) | 0.0811 (5) | |
C2 | −0.24056 (18) | 0.22093 (9) | 0.45977 (9) | 0.0357 (3) | |
H2 | −0.3512 | 0.2436 | 0.4513 | 0.043* | |
C14 | 0.07773 (18) | 0.07435 (8) | 0.16086 (8) | 0.0341 (3) | |
C4 | −0.05969 (19) | 0.11000 (8) | 0.50609 (9) | 0.0364 (3) | |
H4 | −0.0464 | 0.0584 | 0.5282 | 0.044* | |
C8 | 0.23328 (17) | 0.27727 (8) | 0.43044 (8) | 0.0314 (3) | |
C3 | −0.22333 (19) | 0.14322 (9) | 0.49004 (9) | 0.0387 (3) | |
H3 | −0.3224 | 0.1132 | 0.4997 | 0.046* | |
C7 | −0.11757 (18) | 0.34859 (8) | 0.40421 (9) | 0.0338 (3) | |
C9 | 0.3674 (2) | −0.08763 (10) | 0.31486 (9) | 0.0468 (4) | |
H9A | 0.2420 | −0.0815 | 0.3172 | 0.056* | |
H9B | 0.4229 | −0.0807 | 0.3698 | 0.056* | |
C11 | 0.51691 (17) | −0.07093 (8) | 0.19967 (8) | 0.0333 (3) | |
C10 | 0.4126 (2) | −0.16844 (10) | 0.27923 (10) | 0.0445 (4) | |
C13 | −0.0626 (2) | 0.04049 (10) | 0.27279 (9) | 0.0423 (4) | |
C15 | 0.4564 (2) | 0.05471 (10) | 0.27549 (11) | 0.0492 (4) | |
H15A | 0.5508 | 0.0621 | 0.3166 | 0.074* | |
H15B | 0.3502 | 0.0752 | 0.2958 | 0.074* | |
H15C | 0.4814 | 0.0833 | 0.2262 | 0.074* | |
C12 | −0.0482 (2) | 0.13135 (10) | 0.26946 (10) | 0.0480 (4) | |
H12A | −0.1627 | 0.1564 | 0.2638 | 0.058* | |
H12B | 0.0155 | 0.1524 | 0.3185 | 0.058* | |
C16 | 0.0946 (3) | 0.22366 (10) | 0.16828 (11) | 0.0602 (5) | |
H16A | 0.1949 | 0.2195 | 0.1361 | 0.090* | |
H16B | 0.1217 | 0.2580 | 0.2150 | 0.090* | |
H16C | −0.0013 | 0.2462 | 0.1349 | 0.090* | |
O9W | −0.3299 (2) | 0.38052 (7) | 0.59774 (8) | 0.0656 (4) | |
H9WA | −0.302 (3) | 0.3802 (13) | 0.5476 (7) | 0.090 (8)* | |
H9WB | −0.358 (3) | 0.3319 (8) | 0.6078 (13) | 0.100 (9)* |
U11 | U22 | U33 | U12 | U13 | U23 | |
O4 | 0.0439 (6) | 0.0355 (5) | 0.0506 (6) | −0.0020 (4) | 0.0200 (5) | −0.0028 (5) |
O2 | 0.0563 (7) | 0.0333 (6) | 0.0528 (6) | 0.0121 (5) | 0.0187 (5) | 0.0086 (5) |
O1 | 0.0735 (8) | 0.0375 (6) | 0.0411 (6) | 0.0100 (5) | 0.0192 (5) | 0.0112 (5) |
O7 | 0.0802 (9) | 0.0622 (8) | 0.0472 (7) | 0.0035 (7) | 0.0254 (6) | 0.0062 (6) |
O3 | 0.0558 (7) | 0.0379 (6) | 0.0445 (6) | −0.0188 (5) | 0.0165 (5) | −0.0095 (5) |
O8 | 0.0799 (9) | 0.0548 (8) | 0.0619 (8) | −0.0041 (6) | 0.0164 (7) | 0.0222 (6) |
N4 | 0.0553 (8) | 0.0328 (6) | 0.0353 (7) | 0.0030 (5) | 0.0038 (6) | −0.0046 (5) |
N5 | 0.0414 (7) | 0.0341 (7) | 0.0400 (7) | 0.0036 (5) | 0.0093 (5) | 0.0023 (5) |
C1 | 0.0342 (7) | 0.0271 (7) | 0.0267 (6) | 0.0014 (5) | 0.0042 (5) | 0.0002 (5) |
C5 | 0.0335 (7) | 0.0272 (7) | 0.0317 (7) | 0.0031 (5) | 0.0064 (5) | 0.0003 (5) |
O6 | 0.0455 (7) | 0.0771 (9) | 0.0840 (10) | 0.0088 (7) | −0.0164 (7) | 0.0045 (8) |
N1 | 0.0419 (7) | 0.0367 (7) | 0.0590 (8) | 0.0083 (6) | 0.0114 (6) | 0.0131 (6) |
N7 | 0.0424 (7) | 0.0408 (7) | 0.0352 (6) | 0.0059 (5) | 0.0086 (5) | −0.0018 (5) |
N2 | 0.0640 (9) | 0.0340 (7) | 0.0374 (7) | −0.0006 (6) | 0.0153 (6) | −0.0025 (5) |
C6 | 0.0337 (7) | 0.0244 (6) | 0.0247 (6) | −0.0016 (5) | 0.0049 (5) | −0.0023 (5) |
N6 | 0.0464 (7) | 0.0322 (6) | 0.0452 (7) | −0.0007 (5) | 0.0177 (6) | −0.0027 (5) |
N3 | 0.0438 (7) | 0.0333 (6) | 0.0334 (6) | 0.0011 (5) | 0.0052 (5) | −0.0034 (5) |
O5 | 0.0613 (8) | 0.0378 (7) | 0.1471 (15) | 0.0172 (6) | 0.0299 (9) | 0.0047 (8) |
C2 | 0.0308 (7) | 0.0379 (8) | 0.0388 (8) | 0.0019 (6) | 0.0050 (6) | 0.0017 (6) |
C14 | 0.0377 (7) | 0.0343 (7) | 0.0298 (7) | 0.0011 (6) | −0.0026 (6) | −0.0021 (6) |
C4 | 0.0458 (8) | 0.0231 (6) | 0.0418 (8) | −0.0001 (6) | 0.0133 (6) | 0.0031 (6) |
C8 | 0.0330 (7) | 0.0298 (7) | 0.0317 (7) | −0.0012 (5) | 0.0037 (5) | 0.0018 (5) |
C3 | 0.0374 (8) | 0.0354 (8) | 0.0445 (8) | −0.0078 (6) | 0.0130 (6) | 0.0005 (6) |
C7 | 0.0357 (7) | 0.0311 (7) | 0.0344 (7) | 0.0015 (6) | 0.0023 (6) | 0.0048 (6) |
C9 | 0.0486 (9) | 0.0593 (10) | 0.0334 (8) | 0.0110 (8) | 0.0093 (7) | 0.0081 (7) |
C11 | 0.0293 (7) | 0.0360 (7) | 0.0347 (7) | 0.0029 (5) | 0.0020 (5) | −0.0006 (6) |
C10 | 0.0438 (9) | 0.0494 (9) | 0.0404 (8) | 0.0025 (7) | 0.0039 (7) | 0.0123 (7) |
C13 | 0.0460 (8) | 0.0488 (9) | 0.0322 (8) | 0.0065 (7) | 0.0036 (6) | −0.0006 (7) |
C15 | 0.0487 (9) | 0.0476 (9) | 0.0517 (9) | 0.0067 (7) | 0.0064 (7) | −0.0135 (8) |
C12 | 0.0629 (10) | 0.0468 (9) | 0.0350 (8) | 0.0098 (8) | 0.0073 (7) | −0.0077 (7) |
C16 | 0.0952 (15) | 0.0345 (9) | 0.0512 (10) | −0.0020 (9) | 0.0069 (9) | −0.0022 (7) |
O9W | 0.1076 (11) | 0.0374 (7) | 0.0546 (8) | 0.0013 (7) | 0.0266 (8) | −0.0016 (6) |
O4—C8 | 1.2491 (16) | C6—C8 | 1.5159 (18) |
O2—C7 | 1.2458 (17) | N6—C11 | 1.2970 (18) |
O1—C7 | 1.2508 (17) | N6—H6A | 0.8600 |
O7—C13 | 1.2065 (19) | N6—H6B | 0.8600 |
O3—C8 | 1.2459 (17) | N3—C14 | 1.3573 (19) |
O8—C10 | 1.2072 (19) | N3—C13 | 1.3690 (19) |
N4—C14 | 1.3232 (18) | N3—H3A | 0.8600 |
N4—C16 | 1.443 (2) | C2—C3 | 1.380 (2) |
N4—C12 | 1.450 (2) | C2—H2 | 0.9300 |
N5—C11 | 1.3617 (18) | C4—C3 | 1.379 (2) |
N5—C10 | 1.369 (2) | C4—H4 | 0.9300 |
N5—H5 | 0.8600 | C3—H3 | 0.9300 |
C1—C2 | 1.3911 (19) | C9—C10 | 1.507 (2) |
C1—C6 | 1.3957 (18) | C9—H9A | 0.9700 |
C1—C7 | 1.5070 (18) | C9—H9B | 0.9700 |
C5—C4 | 1.3775 (19) | C13—C12 | 1.509 (2) |
C5—C6 | 1.3836 (18) | C15—H15A | 0.9600 |
C5—N1 | 1.4587 (18) | C15—H15B | 0.9600 |
O6—N1 | 1.2200 (19) | C15—H15C | 0.9600 |
N1—O5 | 1.2161 (18) | C12—H12A | 0.9700 |
N7—C11 | 1.3311 (18) | C12—H12B | 0.9700 |
N7—C15 | 1.452 (2) | C16—H16A | 0.9600 |
N7—C9 | 1.452 (2) | C16—H16B | 0.9600 |
N2—C14 | 1.3028 (19) | C16—H16C | 0.9600 |
N2—H2A | 0.8600 | O9W—H9WA | 0.855 (9) |
N2—H2B | 0.8600 | O9W—H9WB | 0.852 (9) |
C14—N4—C16 | 127.06 (14) | O4—C8—C6 | 115.68 (12) |
C14—N4—C12 | 109.84 (12) | C4—C3—C2 | 120.23 (13) |
C16—N4—C12 | 123.07 (13) | C4—C3—H3 | 119.9 |
C11—N5—C10 | 110.75 (12) | C2—C3—H3 | 119.9 |
C11—N5—H5 | 124.6 | O2—C7—O1 | 125.96 (13) |
C10—N5—H5 | 124.6 | O2—C7—C1 | 117.35 (12) |
C2—C1—C6 | 120.02 (12) | O1—C7—C1 | 116.65 (12) |
C2—C1—C7 | 119.63 (12) | N7—C9—C10 | 103.02 (12) |
C6—C1—C7 | 120.29 (11) | N7—C9—H9A | 111.2 |
C4—C5—C6 | 123.75 (12) | C10—C9—H9A | 111.2 |
C4—C5—N1 | 117.95 (12) | N7—C9—H9B | 111.2 |
C6—C5—N1 | 118.29 (12) | C10—C9—H9B | 111.2 |
O5—N1—O6 | 123.96 (15) | H9A—C9—H9B | 109.1 |
O5—N1—C5 | 118.51 (14) | N6—C11—N7 | 127.13 (13) |
O6—N1—C5 | 117.52 (13) | N6—C11—N5 | 122.26 (13) |
C11—N7—C15 | 125.62 (13) | N7—C11—N5 | 110.61 (12) |
C11—N7—C9 | 109.51 (12) | O8—C10—N5 | 125.80 (16) |
C15—N7—C9 | 122.51 (13) | O8—C10—C9 | 128.18 (15) |
C14—N2—H2A | 120.0 | N5—C10—C9 | 106.03 (13) |
C14—N2—H2B | 120.0 | O7—C13—N3 | 126.04 (15) |
H2A—N2—H2B | 120.0 | O7—C13—C12 | 128.05 (14) |
C5—C6—C1 | 117.10 (12) | N3—C13—C12 | 105.90 (13) |
C5—C6—C8 | 121.54 (12) | N7—C15—H15A | 109.5 |
C1—C6—C8 | 121.27 (11) | N7—C15—H15B | 109.5 |
C11—N6—H6A | 120.0 | H15A—C15—H15B | 109.5 |
C11—N6—H6B | 120.0 | N7—C15—H15C | 109.5 |
H6A—N6—H6B | 120.0 | H15A—C15—H15C | 109.5 |
C14—N3—C13 | 110.74 (12) | H15B—C15—H15C | 109.5 |
C14—N3—H3A | 124.6 | N4—C12—C13 | 102.71 (12) |
C13—N3—H3A | 124.6 | N4—C12—H12A | 111.2 |
C3—C2—C1 | 120.78 (13) | C13—C12—H12A | 111.2 |
C3—C2—H2 | 119.6 | N4—C12—H12B | 111.2 |
C1—C2—H2 | 119.6 | C13—C12—H12B | 111.2 |
N2—C14—N4 | 127.26 (14) | H12A—C12—H12B | 109.1 |
N2—C14—N3 | 121.98 (13) | N4—C16—H16A | 109.5 |
N4—C14—N3 | 110.74 (12) | N4—C16—H16B | 109.5 |
C5—C4—C3 | 118.06 (12) | H16A—C16—H16B | 109.5 |
C5—C4—H4 | 121.0 | N4—C16—H16C | 109.5 |
C3—C4—H4 | 121.0 | H16A—C16—H16C | 109.5 |
O3—C8—O4 | 126.73 (13) | H16B—C16—H16C | 109.5 |
O3—C8—C6 | 117.58 (12) | H9WA—O9W—H9WB | 105.1 (14) |
C4—C5—N1—O5 | 49.1 (2) | C1—C6—C8—O4 | −117.14 (14) |
C6—C5—N1—O5 | −132.09 (15) | C5—C4—C3—C2 | −2.1 (2) |
C4—C5—N1—O6 | −131.17 (15) | C1—C2—C3—C4 | 2.6 (2) |
C6—C5—N1—O6 | 47.61 (19) | C2—C1—C7—O2 | 55.03 (18) |
C4—C5—C6—C1 | 1.80 (19) | C6—C1—C7—O2 | −127.68 (14) |
N1—C5—C6—C1 | −176.91 (12) | C2—C1—C7—O1 | −123.06 (15) |
C4—C5—C6—C8 | −174.78 (13) | C6—C1—C7—O1 | 54.23 (18) |
N1—C5—C6—C8 | 6.51 (19) | C11—N7—C9—C10 | −2.97 (16) |
C2—C1—C6—C5 | −1.31 (19) | C15—N7—C9—C10 | −166.41 (14) |
C7—C1—C6—C5 | −178.58 (12) | C15—N7—C11—N6 | −14.4 (2) |
C2—C1—C6—C8 | 175.28 (12) | C9—N7—C11—N6 | −177.21 (14) |
C7—C1—C6—C8 | −2.00 (18) | C15—N7—C11—N5 | 165.78 (14) |
C6—C1—C2—C3 | −0.8 (2) | C9—N7—C11—N5 | 2.98 (16) |
C7—C1—C2—C3 | 176.46 (13) | C10—N5—C11—N6 | 178.51 (13) |
C16—N4—C14—N2 | 1.0 (3) | C10—N5—C11—N7 | −1.67 (17) |
C12—N4—C14—N2 | 179.12 (15) | C11—N5—C10—O8 | 179.93 (16) |
C16—N4—C14—N3 | 179.08 (16) | C11—N5—C10—C9 | −0.30 (17) |
C12—N4—C14—N3 | −2.76 (17) | N7—C9—C10—O8 | −178.31 (17) |
C13—N3—C14—N2 | −179.73 (14) | N7—C9—C10—N5 | 1.93 (16) |
C13—N3—C14—N4 | 2.03 (16) | C14—N3—C13—O7 | 179.98 (16) |
C6—C5—C4—C3 | −0.1 (2) | C14—N3—C13—C12 | −0.45 (16) |
N1—C5—C4—C3 | 178.63 (13) | C14—N4—C12—C13 | 2.32 (17) |
C5—C6—C8—O3 | −121.68 (14) | C16—N4—C12—C13 | −179.43 (15) |
C1—C6—C8—O3 | 61.89 (17) | O7—C13—C12—N4 | 178.47 (16) |
C5—C6—C8—O4 | 59.29 (17) | N3—C13—C12—N4 | −1.08 (16) |
D—H···A | D—H | H···A | D···A | D—H···A |
O9W—H9WA···O2 | 0.86 (1) | 1.94 (2) | 2.7856 (18) | 168 (2) |
O9W—H9WB···O8i | 0.85 (1) | 2.16 (2) | 2.9241 (18) | 149 (2) |
N2—H2A···O3ii | 0.86 | 2.00 | 2.7899 (17) | 152 |
N2—H2B···O2iii | 0.86 | 1.95 | 2.8000 (17) | 168 |
N3—H3A···O1iii | 0.86 | 1.77 | 2.6275 (15) | 177 |
N5—H5···O4iv | 0.86 | 1.84 | 2.6836 (16) | 166 |
N6—H6A···O9Wv | 0.86 | 1.96 | 2.7952 (17) | 163 |
N6—H6B···O3iv | 0.86 | 1.94 | 2.7900 (16) | 171 |
C4—H4···O5i | 0.93 | 2.59 | 3.2071 (19) | 124 |
C9—H9B···O6vi | 0.97 | 2.47 | 3.212 (2) | 133 |
Symmetry codes: (i) −x, −y, −z+1; (ii) x, −y+1/2, z−1/2; (iii) −x, y−1/2, −z+1/2; (iv) −x+1, y−1/2, −z+1/2; (v) x+1, −y+1/2, z−1/2; (vi) −x+1, −y, −z+1. |
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