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A topological analysis of the experimental electron density in racemic ethylenebis(1-indenyl)zirconium dichloride, C20H16Cl2Zr, measured at 100 (1) K, has been performed. The atomic charges calculated by the numerical integration of the electron density over the zero-flux atomic basins demonstrate the charge transfer of 2.25 e from the Zr atom to the two indenyl ligands (0.19 e to each) and two Cl atoms (0.93 e to each). All the atomic interactions were quantitatively characterized in terms of the electron density and the electronic energy-density features at the bond critical points. The Zr—C2 bond paths significantly curved towards the C1—C2 bond were found; no other bond paths connecting the Zr atom and indenyl ligand were located. At the same time, the π-electrons of the C1—C2 bond are significantly involved in the metal–ligand interaction. The electron density features indicate that the indenyl coordination can be approximately described as η1 with slippage towards η2. The `ligand-opposed' charge concentrations around the Zr atom were revealed using the Laplacian of the electron density and the one-particle potential; they were linked to the orbital representations. Bonds in the indenyl ligand were characterized using the Cioslowski–Mixon bond-order indices calculated directly from the experimental electron density.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768105014114/bs5015sup1.cif
Contains datablock zrsh

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768105014114/bs5015sup2.fcf
Contains datablock zrsh

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S0108768105014114/bs5015sup3.pdf
Atomic coordinates, data from multipole refinement and electron density figures

CCDC reference: 280357

Computing details top

Program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
[Figure 6]
Ethylenebis(1-indenyl)zirconium dichloride top
Crystal data top
C20H16Cl2ZrF(000) = 840
Mr = 418.45Dx = 1.696 Mg m3
Monoclinic, C2/cMo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2ycCell parameters from 40 reflections
a = 15.3870 (5) Åθ = 30.0–35.0°
b = 10.5120 (5) ŵ = 0.99 mm1
c = 11.9270 (5) ÅT = 100 K
β = 121.85 (1)°Sphere, colourless
V = 1638.7 (2) Å30.09 mm (radius)
Z = 4
Data collection top
MacScience four-circle
diffractometer
6151 reflections with I > 2σ(I)
Radiation source: rotating anodeRint = 0.020
Graphite monochromatorθmax = 50.0°, θmin = 2.5°
ω/2θ? scansh = 3328
Absorption correction: for a sphere
Interpolation using Int.Tab. Vol. C (1992) p. 523,Tab. 6.3.3.3 for values of muR in the range 0-2.5, and Int.Tab. Vol.II (1959) p.302; Table 5.3.6 B for muR in the range 2.6-10.0. The interpolation procedure of C.W.Dwiggins Jr (Acta Cryst.(1975) A31,146-148) is used with some modification.
k = 2218
Tmin = 0.861, Tmax = 0.863l = 1925
10224 measured reflections3 standard reflections every 30 reflections
6602 independent reflections intensity decay: 1.5%
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)] = 0.030Hydrogen site location: difference Fourier map
wR(F2) = 0.072All H-atom parameters refined
S = 1.02 w = 1/[σ2(Fo2) + (0.0356P)2 + 1.3284P]
where P = (Fo2 + 2Fc2)/3
6602 reflections(Δ/σ)max = 0.002
137 parametersΔρmax = 1.37 e Å3
0 restraintsΔρmin = 1.44 e Å3
Crystal data top
C20H16Cl2ZrV = 1638.7 (2) Å3
Mr = 418.45Z = 4
Monoclinic, C2/cMo Kα radiation
a = 15.3870 (5) ŵ = 0.99 mm1
b = 10.5120 (5) ÅT = 100 K
c = 11.9270 (5) Å0.09 mm (radius)
β = 121.85 (1)°
Data collection top
MacScience four-circle
diffractometer
6151 reflections with I > 2σ(I)
Absorption correction: for a sphere
Interpolation using Int.Tab. Vol. C (1992) p. 523,Tab. 6.3.3.3 for values of muR in the range 0-2.5, and Int.Tab. Vol.II (1959) p.302; Table 5.3.6 B for muR in the range 2.6-10.0. The interpolation procedure of C.W.Dwiggins Jr (Acta Cryst.(1975) A31,146-148) is used with some modification.
Rint = 0.020
Tmin = 0.861, Tmax = 0.8633 standard reflections every 30 reflections
10224 measured reflections intensity decay: 1.5%
6602 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0300 restraints
wR(F2) = 0.072All H-atom parameters refined
S = 1.02Δρmax = 1.37 e Å3
6602 reflectionsΔρmin = 1.44 e Å3
137 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
Zr0.00000.271052 (11)0.25000.01012 (2)
Cl0.136622 (17)0.42390 (2)0.18359 (2)0.01786 (4)
C10.00110 (7)0.07448 (8)0.13263 (9)0.01541 (12)
C20.09921 (7)0.13235 (10)0.05610 (9)0.01863 (14)
C30.09025 (8)0.24789 (10)0.00163 (9)0.01878 (15)
C3A0.01377 (7)0.26199 (9)0.04028 (8)0.01545 (12)
C40.06545 (10)0.35219 (10)0.00658 (10)0.02057 (16)
C50.16749 (10)0.33535 (11)0.05609 (12)0.02325 (18)
C60.22272 (9)0.23071 (12)0.13963 (12)0.02224 (16)
C70.17584 (8)0.14142 (10)0.17323 (10)0.01779 (13)
C7A0.06909 (7)0.15477 (8)0.12271 (8)0.01380 (11)
C80.02332 (10)0.04865 (9)0.20705 (11)0.02108 (16)
H20.1615 (16)0.102 (2)0.040 (2)0.029 (5)*
H30.1394 (15)0.301 (2)0.047 (2)0.025 (5)*
H40.0289 (15)0.4190 (19)0.0500 (19)0.020 (4)*
H50.2021 (18)0.390 (2)0.038 (2)0.039 (6)*
H60.2965 (17)0.222 (2)0.169 (2)0.027 (5)*
H70.2130 (16)0.070 (2)0.222 (2)0.028 (5)*
H810.1003 (15)0.0621 (19)0.2686 (19)0.022 (4)*
H820.0010 (15)0.118 (2)0.1477 (19)0.026 (5)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Zr0.00990 (4)0.01098 (4)0.00911 (4)0.0000.00476 (3)0.000
Cl0.01714 (8)0.02022 (9)0.01815 (8)0.00735 (6)0.01064 (7)0.00518 (6)
C10.0193 (3)0.0130 (3)0.0150 (3)0.0007 (2)0.0098 (3)0.0019 (2)
C20.0166 (3)0.0210 (4)0.0153 (3)0.0029 (3)0.0063 (3)0.0051 (3)
C30.0182 (3)0.0229 (4)0.0105 (2)0.0050 (3)0.0044 (2)0.0001 (2)
C3A0.0210 (3)0.0149 (3)0.0115 (2)0.0032 (2)0.0093 (2)0.0012 (2)
C40.0350 (5)0.0151 (3)0.0189 (3)0.0030 (3)0.0192 (4)0.0025 (3)
C50.0342 (5)0.0204 (4)0.0270 (4)0.0036 (4)0.0243 (4)0.0019 (3)
C60.0233 (4)0.0247 (4)0.0262 (4)0.0007 (3)0.0182 (3)0.0026 (4)
C70.0192 (3)0.0184 (3)0.0185 (3)0.0044 (3)0.0118 (3)0.0008 (3)
C7A0.0178 (3)0.0128 (3)0.0125 (2)0.0019 (2)0.0091 (2)0.0003 (2)
C80.0338 (5)0.0120 (3)0.0253 (4)0.0018 (3)0.0209 (4)0.0003 (3)
Geometric parameters (Å, º) top
Zr—Cli2.4230 (5)C1—C21.4241 (15)
Zr—Cl2.4230 (5)C1—C7A1.4240 (13)
Zr—C22.4655 (12)C1—C81.5008 (14)
Zr—C2i2.4655 (12)C2—C31.4180 (16)
Zr—C12.4910 (9)C3—C3A1.4204 (15)
Zr—C1i2.4910 (9)C3A—C41.4250 (14)
Zr—C32.5341 (12)C3A—C7A1.4415 (12)
Zr—C3i2.5341 (12)C4—C51.3664 (18)
Zr—C7Ai2.5754 (9)C5—C61.4253 (18)
Zr—C7A2.5754 (9)C6—C71.3664 (15)
Zr—C3A2.6210 (9)C7—C7A1.4269 (13)
Zr—C3Ai2.6210 (9)C8—C8i1.530 (2)
Cli—Zr—Cl96.92 (2)C2i—Zr—C3A123.49 (3)
Cli—Zr—C2134.40 (3)C1—Zr—C3A54.09 (3)
Cl—Zr—C294.85 (4)C1i—Zr—C3A121.75 (3)
Cli—Zr—C2i94.85 (4)C3—Zr—C3A31.93 (3)
Cl—Zr—C2i134.40 (3)C3i—Zr—C3A147.32 (3)
C2—Zr—C2i107.49 (6)C7Ai—Zr—C3A144.26 (3)
Cli—Zr—C1118.76 (3)C7A—Zr—C3A32.20 (3)
Cl—Zr—C1128.24 (3)Cli—Zr—C3Ai101.84 (3)
C2—Zr—C133.39 (3)Cl—Zr—C3Ai80.97 (3)
C2i—Zr—C181.59 (4)C2—Zr—C3Ai123.49 (3)
Cli—Zr—C1i128.24 (3)C2i—Zr—C3Ai53.50 (3)
Cl—Zr—C1i118.76 (3)C1—Zr—C3Ai121.75 (3)
C2—Zr—C1i81.59 (4)C1i—Zr—C3Ai54.09 (3)
C2i—Zr—C1i33.39 (3)C3—Zr—C3Ai147.32 (3)
C1—Zr—C1i67.90 (4)C3i—Zr—C3Ai31.93 (3)
Cli—Zr—C3106.95 (4)C7Ai—Zr—C3Ai32.20 (3)
Cl—Zr—C380.55 (4)C7A—Zr—C3Ai144.26 (3)
C2—Zr—C332.92 (4)C3A—Zr—C3Ai175.83 (4)
C2i—Zr—C3136.54 (4)C2—C1—C7A106.71 (8)
C1—Zr—C354.99 (3)C2—C1—C8126.68 (9)
C1i—Zr—C3114.47 (3)C7A—C1—C8126.60 (9)
Cli—Zr—C3i80.55 (4)C2—C1—Zr72.32 (6)
Cl—Zr—C3i106.95 (4)C7A—C1—Zr76.97 (5)
C2—Zr—C3i136.54 (4)C8—C1—Zr117.24 (6)
C2i—Zr—C3i32.92 (4)C3—C2—C1109.46 (9)
C1—Zr—C3i114.47 (3)C3—C2—Zr76.20 (6)
C1i—Zr—C3i54.99 (3)C1—C2—Zr74.29 (6)
C3—Zr—C3i168.97 (5)C2—C3—C3A107.82 (8)
Cli—Zr—C7Ai132.75 (3)C2—C3—Zr70.88 (5)
Cl—Zr—C7Ai87.17 (3)C3A—C3—Zr77.41 (6)
C2—Zr—C7Ai91.63 (3)C3—C3A—C4132.75 (9)
C2i—Zr—C7Ai53.86 (3)C3—C3A—C7A107.37 (8)
C1—Zr—C7Ai93.16 (3)C4—C3A—C7A119.74 (9)
C1i—Zr—C7Ai32.59 (3)C3—C3A—Zr70.66 (6)
C3—Zr—C7Ai120.10 (4)C4—C3A—Zr125.68 (6)
C3i—Zr—C7Ai53.65 (3)C7A—C3A—Zr72.16 (5)
Cli—Zr—C7A87.17 (3)C5—C4—C3A118.48 (9)
Cl—Zr—C7A132.75 (3)C4—C5—C6121.83 (10)
C2—Zr—C7A53.86 (3)C7—C6—C5121.52 (10)
C2i—Zr—C7A91.63 (3)C6—C7—C7A118.48 (9)
C1—Zr—C7A32.59 (3)C1—C7A—C7131.38 (8)
C1i—Zr—C7A93.16 (3)C1—C7A—C3A108.62 (8)
C3—Zr—C7A53.65 (3)C7—C7A—C3A119.92 (8)
C3i—Zr—C7A120.10 (4)C1—C7A—Zr70.44 (5)
C7Ai—Zr—C7A123.33 (4)C7—C7A—Zr122.61 (6)
Cli—Zr—C3A80.97 (3)C3A—C7A—Zr75.64 (5)
Cl—Zr—C3A101.84 (3)C1—C8—C8i109.67 (7)
C2—Zr—C3A53.50 (3)
Symmetry code: (i) x, y, z+1/2.

Experimental details

Crystal data
Chemical formulaC20H16Cl2Zr
Mr418.45
Crystal system, space groupMonoclinic, C2/c
Temperature (K)100
a, b, c (Å)15.3870 (5), 10.5120 (5), 11.9270 (5)
β (°) 121.85 (1)
V3)1638.7 (2)
Z4
Radiation typeMo Kα
µ (mm1)0.99
Crystal size (mm)0.09 (radius)
Data collection
DiffractometerMacScience four-circle
diffractometer
Absorption correctionFor a sphere
Interpolation using Int.Tab. Vol. C (1992) p. 523,Tab. 6.3.3.3 for values of muR in the range 0-2.5, and Int.Tab. Vol.II (1959) p.302; Table 5.3.6 B for muR in the range 2.6-10.0. The interpolation procedure of C.W.Dwiggins Jr (Acta Cryst.(1975) A31,146-148) is used with some modification.
Tmin, Tmax0.861, 0.863
No. of measured, independent and
observed [I > 2σ(I)] reflections
10224, 6602, 6151
Rint0.020
(sin θ/λ)max1)1.077
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.030, 0.072, 1.02
No. of reflections6602
No. of parameters137
H-atom treatmentAll H-atom parameters refined
Δρmax, Δρmin (e Å3)1.37, 1.44

Computer programs: SHELXS97 (Sheldrick, 1990), SHELXL97 (Sheldrick, 1997).

 

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