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In the title compound, [Cu(C19H11N4)2(H2O)]·2H2O or [Cu(L)2(H2O)]·2H2O, where HL is 2-phenyl-1H-1,3,7,8,-tetra­azacyclo­penta­[l]phenanthrene, the CuII atom is five-coord­inated by four N atoms from two L ligands and one O atom from one water mol­ecule. A three-dimensional supra­molecular structure is formed through π–π and hydrogen-bonding inter­actions.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536806019532/rz2035sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536806019532/rz2035Isup2.hkl
Contains datablock I

CCDC reference: 613800

Key indicators

  • Single-crystal X-ray study
  • T = 292 K
  • Mean [sigma](C-C) = 0.007 Å
  • R factor = 0.069
  • wR factor = 0.152
  • Data-to-parameter ratio = 15.2

checkCIF/PLATON results

No syntax errors found



Alert level B PLAT420_ALERT_2_B D-H Without Acceptor O2W - HW22 ... ?
Alert level C RINTA01_ALERT_3_C The value of Rint is greater than 0.10 Rint given 0.113 PLAT020_ALERT_3_C The value of Rint is greater than 0.10 ......... 0.11 PLAT042_ALERT_1_C Calc. and Rep. MoietyFormula Strings Differ .... ? PLAT094_ALERT_2_C Ratio of Maximum / Minimum Residual Density .... 2.18 PLAT220_ALERT_2_C Large Non-Solvent C Ueq(max)/Ueq(min) ... 2.79 Ratio PLAT232_ALERT_2_C Hirshfeld Test Diff (M-X) Cu1 - O1W .. 9.81 su PLAT341_ALERT_3_C Low Bond Precision on C-C bonds (x 1000) Ang ... 7 PLAT720_ALERT_4_C Number of Unusual/Non-Standard Label(s) ........ 6 PLAT790_ALERT_4_C Centre of Gravity not Within Unit Cell: Resd. # 2 H2 O
0 ALERT level A = In general: serious problem 1 ALERT level B = Potentially serious problem 9 ALERT level C = Check and explain 0 ALERT level G = General alerts; check 1 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 2 ALERT type 4 Improvement, methodology, query or suggestion

Computing details top

Data collection: PROCESS-AUTO (Rigaku, 1998); cell refinement: PROCESS-AUTO; data reduction: PROCESS-AUTO; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL-Plus (Sheldrick, 1990); software used to prepare material for publication: SHELXL97.

aquabis(2-phenyl-1,3,7,8-tetraazacyclopenta[l]phenanthrene)copper(II) dihydrate top
Crystal data top
[Cu(C19H11N4)2(H2O)]·2H2OF(000) = 1460
Mr = 708.22Dx = 1.471 Mg m3
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -p2ybcCell parameters from total reflections
a = 9.2897 (19) Åθ = 3.0–27.5°
b = 11.466 (2) ŵ = 0.74 mm1
c = 30.189 (6) ÅT = 292 K
β = 95.85 (3)°Block, blue
V = 3198.9 (11) Å30.33 × 0.26 × 0.18 mm
Z = 4
Data collection top
Rigaku R-AXIS RAPID
diffractometer
7231 independent reflections
Radiation source: rotor target3942 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.113
Detector resolution: 10.0 pixels mm-1θmax = 27.5°, θmin = 3.0°
ω scansh = 1212
Absorption correction: multi-scan
(ABSCOR; Higashi, 1995)
k = 1412
Tmin = 0.777, Tmax = 0.875l = 3939
29006 measured reflections
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)] = 0.069Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.152H atoms treated by a mixture of independent and constrained refinement
S = 1.02 w = 1/[σ2(Fo2) + (0.0471P)2 + 3.7579P]
where P = (Fo2 + 2Fc2)/3
7231 reflections(Δ/σ)max = 0.001
475 parametersΔρmax = 0.96 e Å3
2 restraintsΔρmin = 0.44 e Å3
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
C10.7248 (5)0.8971 (4)0.69241 (16)0.0491 (12)
H10.63280.86560.68610.059*
C20.8093 (6)0.8568 (4)0.72909 (18)0.0596 (14)
H20.77370.80040.74720.072*
C30.9475 (5)0.9001 (4)0.73900 (17)0.0508 (12)
H31.00600.87250.76360.061*
C40.9985 (4)0.9863 (4)0.71150 (14)0.0367 (10)
C50.9036 (4)1.0232 (3)0.67469 (13)0.0330 (9)
C60.9444 (4)1.1141 (3)0.64585 (13)0.0308 (9)
C71.0821 (4)1.1668 (3)0.65205 (13)0.0300 (9)
C81.1119 (4)1.2565 (4)0.62286 (14)0.0361 (10)
H81.20131.29380.62620.043*
C91.0104 (5)1.2888 (4)0.58969 (15)0.0423 (11)
H91.02971.34820.57010.051*
C100.8771 (5)1.2327 (4)0.58514 (15)0.0423 (11)
H100.80781.25610.56250.051*
C111.1783 (4)1.1253 (3)0.68828 (13)0.0316 (9)
C121.1385 (4)1.0396 (4)0.71764 (14)0.0356 (10)
C131.3551 (4)1.0924 (4)0.73696 (13)0.0344 (10)
C141.5004 (4)1.0992 (4)0.76121 (14)0.0378 (10)
C151.5988 (5)1.1813 (5)0.74913 (17)0.0583 (14)
H151.57101.23440.72660.070*
C161.7371 (6)1.1849 (6)0.7701 (2)0.0729 (17)
H161.80311.23830.76080.087*
C171.7785 (6)1.1105 (5)0.8045 (2)0.0698 (16)
H171.87211.11340.81870.084*
C181.6821 (6)1.0327 (5)0.8177 (2)0.0702 (17)
H181.70910.98390.84170.084*
C191.5447 (5)1.0246 (5)0.79622 (18)0.0600 (14)
H191.48100.96890.80520.072*
C200.7850 (5)0.9992 (4)0.52006 (16)0.0467 (12)
H200.85241.05850.52630.056*
C210.7940 (5)0.9326 (5)0.48241 (16)0.0538 (13)
H210.86490.94830.46360.065*
C220.6984 (5)0.8436 (4)0.47296 (15)0.0458 (11)
H220.70530.79680.44810.055*
C230.5893 (4)0.8232 (4)0.50106 (14)0.0349 (9)
C240.5869 (4)0.8966 (3)0.53835 (14)0.0327 (9)
C250.4797 (4)0.8820 (4)0.56909 (14)0.0351 (10)
C260.3891 (5)0.9466 (4)0.63305 (16)0.0527 (13)
H260.39210.99910.65660.063*
C270.2835 (5)0.8606 (4)0.62987 (18)0.0575 (14)
H270.21760.85580.65100.069*
C280.2770 (5)0.7834 (4)0.59558 (17)0.0516 (13)
H280.20800.72430.59360.062*
C290.3753 (4)0.7931 (4)0.56301 (14)0.0374 (10)
C300.3792 (4)0.7202 (3)0.52528 (14)0.0351 (10)
C310.4815 (4)0.7346 (4)0.49543 (14)0.0354 (10)
C320.3483 (5)0.5896 (4)0.47534 (15)0.0397 (10)
C330.2857 (5)0.4883 (4)0.45006 (16)0.0445 (11)
C340.3454 (6)0.4476 (5)0.41263 (18)0.0602 (14)
H340.42770.48300.40370.072*
C350.2827 (8)0.3543 (5)0.3885 (2)0.0824 (19)
H350.32240.32870.36320.099*
C360.1631 (7)0.2995 (5)0.4016 (2)0.083 (2)
H360.12210.23660.38550.100*
C370.1047 (7)0.3389 (5)0.4388 (2)0.0773 (18)
H370.02350.30190.44780.093*
C380.1641 (5)0.4323 (4)0.46305 (18)0.0576 (13)
H380.12270.45780.48810.069*
N10.8451 (4)1.1468 (3)0.61198 (11)0.0347 (8)
N20.7675 (4)0.9791 (3)0.66526 (12)0.0379 (8)
N30.6842 (4)0.9830 (3)0.54798 (12)0.0386 (9)
N40.4866 (4)0.9573 (3)0.60373 (12)0.0404 (9)
N51.2512 (4)1.0181 (3)0.74866 (12)0.0391 (9)
N61.3182 (3)1.1586 (3)0.70067 (11)0.0317 (8)
N70.2930 (4)0.6268 (3)0.51256 (12)0.0402 (9)
N80.4619 (4)0.6514 (3)0.46291 (12)0.0393 (9)
O1W0.5551 (4)1.2090 (3)0.62895 (13)0.0636 (10)
O2W1.2242 (4)0.8751 (4)0.82334 (14)0.0642 (11)
O3W0.7077 (5)0.5618 (4)0.42491 (13)0.0658 (11)
Cu10.65735 (5)1.06285 (5)0.608656 (18)0.03804 (17)
HW110.473 (4)1.202 (6)0.6443 (19)0.11 (2)*
HW120.624 (4)1.255 (4)0.6459 (16)0.081 (19)*
HW211.239 (7)0.922 (6)0.803 (2)0.10 (2)*
HW221.158 (5)0.923 (4)0.8393 (15)0.051 (14)*
HW310.627 (7)0.594 (6)0.437 (2)0.11 (2)*
HW320.748 (8)0.505 (7)0.439 (3)0.13 (3)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
C10.049 (3)0.045 (3)0.053 (3)0.013 (2)0.005 (2)0.010 (2)
C20.063 (3)0.055 (3)0.060 (4)0.016 (3)0.003 (3)0.020 (3)
C30.049 (3)0.054 (3)0.049 (3)0.001 (2)0.003 (2)0.018 (2)
C40.043 (2)0.033 (2)0.034 (2)0.0005 (19)0.004 (2)0.0033 (19)
C50.039 (2)0.028 (2)0.032 (2)0.0034 (18)0.0062 (19)0.0026 (18)
C60.035 (2)0.028 (2)0.029 (2)0.0025 (18)0.0031 (18)0.0018 (17)
C70.032 (2)0.031 (2)0.027 (2)0.0011 (18)0.0054 (17)0.0018 (17)
C80.035 (2)0.035 (2)0.039 (3)0.0063 (19)0.0049 (19)0.0060 (19)
C90.046 (3)0.038 (3)0.042 (3)0.003 (2)0.002 (2)0.011 (2)
C100.043 (2)0.041 (3)0.042 (3)0.002 (2)0.003 (2)0.014 (2)
C110.032 (2)0.032 (2)0.030 (2)0.0005 (18)0.0035 (18)0.0009 (18)
C120.036 (2)0.039 (2)0.032 (2)0.0011 (19)0.0045 (19)0.0044 (19)
C130.037 (2)0.038 (2)0.028 (2)0.0025 (19)0.0028 (18)0.0042 (18)
C140.038 (2)0.040 (3)0.034 (2)0.004 (2)0.0020 (19)0.0035 (19)
C150.051 (3)0.070 (4)0.050 (3)0.015 (3)0.014 (2)0.015 (3)
C160.056 (3)0.091 (5)0.066 (4)0.021 (3)0.016 (3)0.019 (3)
C170.042 (3)0.080 (4)0.083 (5)0.001 (3)0.014 (3)0.004 (3)
C180.058 (3)0.080 (4)0.067 (4)0.017 (3)0.020 (3)0.013 (3)
C190.049 (3)0.059 (3)0.069 (4)0.003 (3)0.005 (3)0.020 (3)
C200.040 (2)0.052 (3)0.050 (3)0.014 (2)0.008 (2)0.008 (2)
C210.048 (3)0.067 (3)0.049 (3)0.010 (3)0.016 (2)0.009 (3)
C220.047 (3)0.053 (3)0.037 (3)0.004 (2)0.005 (2)0.007 (2)
C230.033 (2)0.035 (2)0.035 (2)0.0029 (19)0.0017 (19)0.0003 (19)
C240.031 (2)0.029 (2)0.037 (2)0.0006 (18)0.0013 (18)0.0006 (18)
C250.034 (2)0.033 (2)0.037 (2)0.0011 (19)0.0025 (19)0.0042 (19)
C260.051 (3)0.059 (3)0.052 (3)0.005 (3)0.021 (2)0.021 (3)
C270.052 (3)0.062 (3)0.062 (3)0.019 (3)0.026 (3)0.019 (3)
C280.051 (3)0.051 (3)0.056 (3)0.016 (2)0.015 (2)0.011 (3)
C290.035 (2)0.037 (2)0.039 (3)0.0011 (19)0.000 (2)0.001 (2)
C300.041 (2)0.029 (2)0.035 (2)0.0007 (19)0.000 (2)0.0013 (19)
C310.038 (2)0.032 (2)0.034 (2)0.0021 (19)0.0046 (19)0.0037 (19)
C320.043 (2)0.030 (2)0.043 (3)0.003 (2)0.011 (2)0.002 (2)
C330.056 (3)0.027 (2)0.047 (3)0.002 (2)0.016 (2)0.003 (2)
C340.070 (3)0.052 (3)0.056 (3)0.006 (3)0.003 (3)0.011 (3)
C350.105 (5)0.066 (4)0.072 (4)0.001 (4)0.010 (4)0.036 (3)
C360.092 (5)0.051 (4)0.098 (5)0.012 (3)0.030 (4)0.020 (4)
C370.072 (4)0.059 (4)0.095 (5)0.016 (3)0.018 (4)0.009 (4)
C380.059 (3)0.046 (3)0.064 (3)0.007 (3)0.011 (3)0.006 (3)
N10.0372 (18)0.0311 (19)0.035 (2)0.0008 (16)0.0005 (16)0.0039 (16)
N20.0371 (19)0.035 (2)0.041 (2)0.0099 (16)0.0039 (17)0.0001 (16)
N30.0347 (19)0.040 (2)0.040 (2)0.0035 (16)0.0013 (17)0.0030 (17)
N40.0368 (19)0.042 (2)0.043 (2)0.0002 (16)0.0043 (17)0.0114 (18)
N50.0382 (19)0.042 (2)0.036 (2)0.0015 (17)0.0024 (17)0.0079 (17)
N60.0351 (18)0.0328 (19)0.0269 (18)0.0021 (15)0.0010 (15)0.0008 (15)
N70.046 (2)0.033 (2)0.041 (2)0.0031 (17)0.0016 (18)0.0015 (17)
N80.041 (2)0.037 (2)0.038 (2)0.0003 (17)0.0043 (17)0.0051 (17)
O1W0.058 (2)0.067 (3)0.066 (3)0.008 (2)0.008 (2)0.010 (2)
O2W0.071 (3)0.064 (3)0.057 (3)0.007 (2)0.005 (2)0.026 (2)
O3W0.084 (3)0.055 (2)0.063 (3)0.012 (2)0.028 (2)0.006 (2)
Cu10.0344 (3)0.0368 (3)0.0428 (3)0.0057 (2)0.0035 (2)0.0054 (3)
Geometric parameters (Å, º) top
C1—N21.334 (5)C22—H220.9300
C1—C21.371 (7)C23—C241.407 (6)
C1—H10.9300C23—C311.425 (6)
C2—C31.380 (7)C24—N31.353 (5)
C2—H20.9300C24—C251.439 (5)
C3—C41.404 (6)C25—N41.352 (5)
C3—H30.9300C25—C291.406 (6)
C4—C51.411 (6)C26—N41.335 (5)
C4—C121.432 (6)C26—C271.388 (6)
C5—N21.364 (5)C26—H260.9300
C5—C61.434 (5)C27—C281.359 (6)
C6—N11.358 (5)C27—H270.9300
C6—C71.410 (5)C28—C291.413 (6)
C7—C81.400 (5)C28—H280.9300
C7—C111.422 (5)C29—C301.416 (6)
C8—C91.356 (6)C30—N71.368 (5)
C8—H80.9300C30—C311.385 (5)
C9—C101.390 (6)C31—N81.367 (5)
C9—H90.9300C32—N71.352 (5)
C10—N11.328 (5)C32—N81.356 (5)
C10—H100.9300C32—C331.476 (6)
C11—N61.369 (5)C33—C341.389 (7)
C11—C121.398 (5)C33—C381.391 (6)
C12—N51.354 (5)C34—C351.388 (7)
C13—N61.348 (5)C34—H340.9300
C13—N51.361 (5)C35—C361.368 (8)
C13—C141.471 (6)C35—H350.9300
C14—C151.386 (6)C36—C371.373 (8)
C14—C191.389 (6)C36—H360.9300
C15—C161.374 (7)C37—C381.381 (7)
C15—H150.9300C37—H370.9300
C16—C171.369 (8)C38—H380.9300
C16—H160.9300N1—Cu11.986 (3)
C17—C181.353 (8)N2—Cu12.129 (4)
C17—H170.9300N3—Cu12.086 (4)
C18—C191.375 (7)N4—Cu11.989 (3)
C18—H180.9300O1W—Cu12.051 (4)
C19—H190.9300O1W—HW110.94 (2)
C20—N31.335 (5)O1W—HW120.94 (2)
C20—C211.379 (6)O2W—HW210.84 (7)
C20—H200.9300O2W—HW220.99 (5)
C21—C221.364 (6)O3W—HW310.94 (7)
C21—H210.9300O3W—HW320.85 (8)
C22—C231.406 (6)
N2—C1—C2123.5 (4)N4—C25—C24116.3 (4)
N2—C1—H1118.2C29—C25—C24120.9 (4)
C2—C1—H1118.2N4—C26—C27122.8 (4)
C1—C2—C3119.8 (5)N4—C26—H26118.6
C1—C2—H2120.1C27—C26—H26118.6
C3—C2—H2120.1C28—C27—C26119.5 (4)
C2—C3—C4119.2 (5)C28—C27—H27120.3
C2—C3—H3120.4C26—C27—H27120.3
C4—C3—H3120.4C27—C28—C29119.8 (4)
C3—C4—C5117.1 (4)C27—C28—H28120.1
C3—C4—C12125.5 (4)C29—C28—H28120.1
C5—C4—C12117.4 (4)C25—C29—C28116.9 (4)
N2—C5—C4123.0 (4)C25—C29—C30117.3 (4)
N2—C5—C6116.1 (4)C28—C29—C30125.8 (4)
C4—C5—C6120.9 (4)N7—C30—C31109.3 (4)
N1—C6—C7121.2 (4)N7—C30—C29128.7 (4)
N1—C6—C5117.2 (4)C31—C30—C29121.9 (4)
C7—C6—C5121.6 (4)N8—C31—C30109.5 (4)
C8—C7—C6117.8 (4)N8—C31—C23128.6 (4)
C8—C7—C11125.5 (4)C30—C31—C23121.9 (4)
C6—C7—C11116.7 (3)N7—C32—N8116.0 (4)
C9—C8—C7119.9 (4)N7—C32—C33121.0 (4)
C9—C8—H8120.0N8—C32—C33123.0 (4)
C7—C8—H8120.0C34—C33—C38118.5 (4)
C8—C9—C10119.5 (4)C34—C33—C32121.1 (4)
C8—C9—H9120.3C38—C33—C32120.4 (4)
C10—C9—H9120.3C35—C34—C33120.3 (5)
N1—C10—C9122.4 (4)C35—C34—H34119.8
N1—C10—H10118.8C33—C34—H34119.8
C9—C10—H10118.8C36—C35—C34120.8 (6)
N6—C11—C12109.1 (4)C36—C35—H35119.6
N6—C11—C7128.4 (4)C34—C35—H35119.6
C12—C11—C7122.4 (4)C35—C36—C37119.0 (6)
N5—C12—C11109.3 (3)C35—C36—H36120.5
N5—C12—C4129.8 (4)C37—C36—H36120.5
C11—C12—C4120.9 (4)C36—C37—C38121.3 (6)
N6—C13—N5115.8 (4)C36—C37—H37119.4
N6—C13—C14121.3 (4)C38—C37—H37119.4
N5—C13—C14122.9 (4)C37—C38—C33120.1 (5)
C15—C14—C19117.8 (4)C37—C38—H38120.0
C15—C14—C13120.1 (4)C33—C38—H38120.0
C19—C14—C13122.1 (4)C10—N1—C6119.2 (4)
C16—C15—C14120.7 (5)C10—N1—Cu1125.4 (3)
C16—C15—H15119.7C6—N1—Cu1115.4 (3)
C14—C15—H15119.7C1—N2—C5117.4 (4)
C17—C16—C15120.6 (5)C1—N2—Cu1131.5 (3)
C17—C16—H16119.7C5—N2—Cu1111.1 (3)
C15—C16—H16119.7C20—N3—C24117.6 (4)
C18—C17—C16119.4 (5)C20—N3—Cu1130.3 (3)
C18—C17—H17120.3C24—N3—Cu1111.9 (3)
C16—C17—H17120.3C26—N4—C25118.2 (4)
C17—C18—C19121.1 (5)C26—N4—Cu1126.6 (3)
C17—C18—H18119.5C25—N4—Cu1114.9 (3)
C19—C18—H18119.5C12—N5—C13103.0 (3)
C18—C19—C14120.5 (5)C13—N6—C11102.8 (3)
C18—C19—H19119.8C32—N7—C30102.6 (3)
C14—C19—H19119.8C32—N8—C31102.5 (3)
N3—C20—C21123.3 (4)Cu1—O1W—HW11120 (4)
N3—C20—H20118.4Cu1—O1W—HW12108 (3)
C21—C20—H20118.4HW11—O1W—HW12109 (5)
C22—C21—C20119.6 (4)HW21—O2W—HW2299 (5)
C22—C21—H21120.2HW31—O3W—HW32116 (6)
C20—C21—H21120.2N1—Cu1—N4171.32 (14)
C21—C22—C23119.5 (4)N1—Cu1—O1W91.15 (15)
C21—C22—H22120.2N4—Cu1—O1W97.45 (15)
C23—C22—H22120.2N1—Cu1—N394.25 (14)
C22—C23—C24117.0 (4)N4—Cu1—N380.38 (14)
C22—C23—C31126.0 (4)O1W—Cu1—N3136.21 (15)
C24—C23—C31117.0 (4)N1—Cu1—N280.23 (13)
N3—C24—C23123.0 (4)N4—Cu1—N295.73 (14)
N3—C24—C25116.0 (4)O1W—Cu1—N2109.16 (15)
C23—C24—C25121.0 (4)N3—Cu1—N2114.58 (14)
N4—C25—C29122.8 (4)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1W—HW11···N6i0.94 (2)2.39 (3)3.292 (5)162 (6)
O1W—HW12···O2Wii0.94 (2)2.12 (2)3.050 (5)172 (5)
O2W—HW21···N50.84 (7)1.98 (7)2.819 (5)171 (7)
O3W—HW31···N80.94 (7)1.91 (7)2.849 (6)177 (6)
O3W—HW32···N7iii0.85 (8)2.16 (7)2.871 (5)141 (7)
Symmetry codes: (i) x1, y, z; (ii) x+2, y+1/2, z+3/2; (iii) x+1, y+1, z+1.
 

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