metal-organic compounds\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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Crystal structure of bis­­{N-[(di­ethyl­amino)­di­methyl­sil­yl]anilido-κ2N,N′}zinc

aDepartment of Chemistry, Taiyuan Teachers College, Taiyuan 030031, People's Republic of China
*Correspondence e-mail: chenchenj1128@163.com

Edited by E. F. C. Herdtweck, Technischen Universität München, Germany (Received 21 November 2015; accepted 28 November 2015; online 6 December 2015)

The title zinc amide, [Zn(C12H21N2Si)2], was prepared by the metathetical reaction of [LiN(SiMe2NEt2)(C6H5)]2 with zinc dichloride. It is mononuclear and the mol­ecule is generated by twofold rotation symmetry. The central ZnII atom is N,N′-chelated by each of the two N-silylated anilide ligands in a highly distorted tetra­hedral environment. Two N—Si—N ligands are arranged in a cis fashion around the ZnII atom. The Zn—Namine bonds [2.2315 (12) Å] are much longer than the Zn—Nanilide bonds [1.9367 (11) Å].

1. Related literature

For related compounds which show linear and tetra­hedral coordination, see: Schumann et al. (2000[Schumann, H., Gottfriedsen, J., Dechert, S. & Girgsdies, F. (2000). Z. Anorg. Allg. Chem. 626, 747-758.]). For applications of zinc amides, see: Armstrong et al. (2002[Armstrong, D. R., Forbes, G. C., Mulvey, R. E., Clegg, W. & Tooke, D. M. (2002). J. Chem. Soc. Dalton Trans. pp. 1656-1661.]) and for their utility in MOVCD, see Maile & Fischer (2005[Maile, E. & Fischer, R. A. (2005). Chem. Vap. Deposition, 11, 409-414.]). For a related zinc amide with a dimethylanilide ligand instead of an anilide ligand, see: Chen et al. (2007[Chen, J., Cao, K.-N. & Guo, J. (2007). Acta Cryst. E63, m3112.]).

[Scheme 1]

2. Experimental

2.1. Crystal data

  • [Zn(C12H21N2Si)2]

  • Mr = 508.19

  • Orthorhombic, F d d 2

  • a = 29.7954 (12) Å

  • b = 21.3566 (8) Å

  • c = 8.5844 (3) Å

  • V = 5462.5 (4) Å3

  • Z = 8

  • Mo Kα radiation

  • μ = 1.01 mm−1

  • T = 200 K

  • 0.20 × 0.15 × 0.15 mm

2.2. Data collection

  • Bruker SMART area-detector diffractometer

  • Absorption correction: multi-scan (SADABS; Sheldrick, 1996[Sheldrick, G. M. (1996). SADABS. University of Göttingen, Germany.]) Tmin = 0.824, Tmax = 0.864

  • 12927 measured reflections

  • 3296 independent reflections

  • 3153 reflections with I > 2σ(I)

  • Rint = 0.023

2.3. Refinement

  • R[F2 > 2σ(F2)] = 0.019

  • wR(F2) = 0.051

  • S = 1.12

  • 3296 reflections

  • 147 parameters

  • 1 restraint

  • H-atom parameters constrained

  • Δρmax = 0.23 e Å−3

  • Δρmin = −0.23 e Å−3

  • Absolute structure: Flack (1983[Flack, H. D. (1983). Acta Cryst. A39, 876-881.]), 1484 Friedel pairs

  • Absolute structure parameter: 0.028 (7)

Data collection: SMART (Bruker, 2000[Bruker (2000). SMART and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); cell refinement: SAINT (Bruker, 2000[Bruker (2000). SMART and SAINT. Bruker AXS Inc., Madison, Wisconsin, USA.]); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); molecular graphics: SHELXTL/PC (Sheldrick, 2008[Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122.]); software used to prepare material for publication: SHELXL97.

Supporting information


Comment top

Zinc amides were good transamination reagents and useful precusors for preparing the zinc thin film through the MOVCD method (Amstrong et al., 2002; Maile et al., 2005).

The title compound was prepared by metathetical reaction of [LiN(SiMe2NEt2)(C6H5)]2 with zinc dichloride. It is monomeric and similar to the reported bis[(N-trimethylsilyl)2,6-dimethylanilido]zinc (Schumann et al., 2000). The ligand fixes Zn center with the N—Si—N chelating unit, giving an N—Zn—N bite angle of 76.98°. The N—Si—N group is presumed to be a "quasi" conjugated system owing to dπ interaction between Si and N atoms, but is much more flexible in contrast to the rigid N—C—N chelating unit in the amidinate ligand. The Zn—Nanilide bonds are in the normal range. The Zn—Namine bonds are about 0.3 Å longer than the Zn—Nanilide bonds. Two N—Si—N ligands are arranged in a cis fashion around Zn, composing a highly distorted tetrahedral environment. The situation is quite different from an analgous zinc amide with the similar ligand, in which the two ligands are trans to each other (Chen et al., 2007). Two types of ligands have slightly different steric effect.

Related literature top

For related compounds which show linear and tetrahedral coordination, see: Schumann et al. (2000). For applications of zinc amides, see: Armstrong et al. (2002) and for their utility in MOVCD, see Maile et al. (2005). For an analogous zinc amide, see: Chen et al. (2007).

Experimental top

A solution of LiBun (2.2 M, 2.27 ml, 5.0 mmol) in hexane was slowly added into a solution of [NH(SiMe2NEt2)(C6H5)]2 (1.14 g, 5.0 mmol) in Et2O (30 ml) at 273 K by syringe. The mixture was stirred at room temperature for five hours and then ZnCl2 (0.56 g, 2.5 mmol) was added at 273 K. The resulting solution was stirred at room temperature overnight. The filtrate was concentrated to give the title compound as colorless crystals (yield 0.85 g, 67%).

Refinement top

The methyl H atoms were constrained to an ideal geometry, with C—H distances of 0.98 Å and Uiso(H) = 1.5Ueq(C), but each group was allowed to rotate freely along its C—C bond. The methylene H atoms were constrained with C—H distances of 0.99 Å and Uiso(H) = 1.2Ueq(C). The phenyl H atoms were placed in geometrically idealized positions and constrained to ride on their parent atoms, with C—H distances in the range 0.95 Å and Uiso(H) = 1.2Ueq(C).

Structure description top

Zinc amides were good transamination reagents and useful precusors for preparing the zinc thin film through the MOVCD method (Amstrong et al., 2002; Maile et al., 2005).

The title compound was prepared by metathetical reaction of [LiN(SiMe2NEt2)(C6H5)]2 with zinc dichloride. It is monomeric and similar to the reported bis[(N-trimethylsilyl)2,6-dimethylanilido]zinc (Schumann et al., 2000). The ligand fixes Zn center with the N—Si—N chelating unit, giving an N—Zn—N bite angle of 76.98°. The N—Si—N group is presumed to be a "quasi" conjugated system owing to dπ interaction between Si and N atoms, but is much more flexible in contrast to the rigid N—C—N chelating unit in the amidinate ligand. The Zn—Nanilide bonds are in the normal range. The Zn—Namine bonds are about 0.3 Å longer than the Zn—Nanilide bonds. Two N—Si—N ligands are arranged in a cis fashion around Zn, composing a highly distorted tetrahedral environment. The situation is quite different from an analgous zinc amide with the similar ligand, in which the two ligands are trans to each other (Chen et al., 2007). Two types of ligands have slightly different steric effect.

For related compounds which show linear and tetrahedral coordination, see: Schumann et al. (2000). For applications of zinc amides, see: Armstrong et al. (2002) and for their utility in MOVCD, see Maile et al. (2005). For an analogous zinc amide, see: Chen et al. (2007).

Computing details top

Data collection: SMART (Bruker, 2000); cell refinement: SAINT (Bruker, 2000); data reduction: SAINT (Bruker, 2000); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL/PC (Sheldrick, 2008); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. The molecular structure of the title compound, showing the atom-numbering scheme. Displacement ellipsoids are drawn at the 30% probability level. Hydrogen atoms have been omitted for clarity.
Bis{N-[(diethylamino)dimethylsilyl]anilido-κ2N,N'}zinc top
Crystal data top
[Zn(C12H21N2Si)2]F(000) = 2176
Mr = 508.19Dx = 1.236 Mg m3
Orthorhombic, Fdd2Mo Kα radiation, λ = 0.71073 Å
Hall symbol: F 2 -2dCell parameters from 9968 reflections
a = 29.7954 (12) Åθ = 2.8–28.3°
b = 21.3566 (8) ŵ = 1.01 mm1
c = 8.5844 (3) ÅT = 200 K
V = 5462.5 (4) Å3Block, colorless
Z = 80.20 × 0.15 × 0.15 mm
Data collection top
Bruker SMART area-detector
diffractometer
3296 independent reflections
Radiation source: fine-focus sealed tube3153 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.023
φ and ω scanθmax = 28.3°, θmin = 3.3°
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
h = 3936
Tmin = 0.824, Tmax = 0.864k = 2828
12927 measured reflectionsl = 1111
Refinement top
Refinement on F2Hydrogen site location: inferred from neighbouring sites
Least-squares matrix: fullH-atom parameters constrained
R[F2 > 2σ(F2)] = 0.019 w = 1/[σ2(Fo2) + (0.0141P)2 + 1.7098P]
where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.051(Δ/σ)max < 0.001
S = 1.12Δρmax = 0.23 e Å3
3296 reflectionsΔρmin = 0.23 e Å3
147 parametersExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
1 restraintExtinction coefficient: 0.00049 (6)
Primary atom site location: structure-invariant direct methodsAbsolute structure: Flack (1983), 1484 Friedel pairs
Secondary atom site location: difference Fourier mapAbsolute structure parameter: 0.028 (7)
Crystal data top
[Zn(C12H21N2Si)2]V = 5462.5 (4) Å3
Mr = 508.19Z = 8
Orthorhombic, Fdd2Mo Kα radiation
a = 29.7954 (12) ŵ = 1.01 mm1
b = 21.3566 (8) ÅT = 200 K
c = 8.5844 (3) Å0.20 × 0.15 × 0.15 mm
Data collection top
Bruker SMART area-detector
diffractometer
3296 independent reflections
Absorption correction: multi-scan
(SADABS; Sheldrick, 1996)
3153 reflections with I > 2σ(I)
Tmin = 0.824, Tmax = 0.864Rint = 0.023
12927 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.019H-atom parameters constrained
wR(F2) = 0.051Δρmax = 0.23 e Å3
S = 1.12Δρmin = 0.23 e Å3
3296 reflectionsAbsolute structure: Flack (1983), 1484 Friedel pairs
147 parametersAbsolute structure parameter: 0.028 (7)
1 restraint
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds 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 > 2sigma(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
Zn10.25000.25000.29180 (2)0.02397 (7)
Si10.247147 (12)0.121100 (17)0.32504 (4)0.02649 (10)
N20.28157 (4)0.17456 (5)0.43443 (15)0.0259 (2)
N10.22836 (4)0.17412 (5)0.19372 (15)0.0272 (2)
C10.20137 (5)0.16863 (6)0.06303 (15)0.0270 (3)
C20.19263 (5)0.11107 (7)0.01073 (18)0.0342 (3)
H20.20630.07400.02810.041*
C30.16452 (6)0.10739 (8)0.1389 (2)0.0418 (4)
H30.15920.06790.18630.050*
C60.18084 (5)0.22167 (7)0.00242 (17)0.0348 (3)
H60.18640.26160.04240.042*
C80.20082 (6)0.08844 (8)0.4469 (2)0.0443 (4)
H8A0.18450.12280.49710.066*
H8B0.21340.06080.52680.066*
H8C0.18020.06460.38070.066*
C90.32965 (5)0.17499 (7)0.38603 (19)0.0329 (3)
H9A0.33130.16810.27210.039*
H9B0.34530.13970.43750.039*
C110.27592 (6)0.17628 (8)0.60640 (19)0.0359 (3)
H11A0.24340.17680.63030.043*
H11B0.28880.21590.64580.043*
C70.28096 (6)0.05379 (8)0.2524 (3)0.0530 (5)
H7A0.26090.01920.22440.080*
H7B0.30170.04000.33420.080*
H7C0.29810.06670.16050.080*
C40.14411 (5)0.15989 (9)0.19904 (19)0.0432 (4)
H40.12450.15680.28600.052*
C120.29757 (7)0.12168 (10)0.6950 (3)0.0568 (5)
H12A0.28630.08190.65350.085*
H12B0.29000.12480.80590.085*
H12C0.33020.12340.68240.085*
C100.35400 (5)0.23565 (7)0.4258 (2)0.0401 (4)
H10A0.33830.27100.37760.060*
H10B0.38480.23370.38620.060*
H10C0.35450.24120.53910.060*
C50.15272 (6)0.21749 (8)0.12999 (19)0.0402 (4)
H50.13920.25430.17080.048*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Zn10.02833 (11)0.01733 (9)0.02623 (11)0.00051 (8)0.0000.000
Si10.0303 (2)0.01746 (17)0.0317 (3)0.00078 (13)0.00043 (17)0.00132 (13)
N20.0254 (6)0.0237 (5)0.0286 (6)0.0029 (4)0.0020 (5)0.0004 (5)
N10.0366 (7)0.0197 (5)0.0253 (5)0.0027 (5)0.0024 (5)0.0004 (5)
C10.0303 (7)0.0291 (7)0.0216 (7)0.0042 (5)0.0044 (5)0.0004 (5)
C20.0417 (8)0.0294 (7)0.0316 (7)0.0058 (6)0.0021 (6)0.0041 (6)
C30.0474 (10)0.0449 (9)0.0332 (8)0.0118 (7)0.0002 (7)0.0115 (7)
C60.0453 (9)0.0326 (7)0.0264 (7)0.0006 (6)0.0035 (6)0.0019 (6)
C80.0461 (10)0.0440 (9)0.0427 (9)0.0117 (7)0.0022 (8)0.0132 (8)
C90.0279 (7)0.0294 (7)0.0414 (8)0.0040 (5)0.0005 (6)0.0020 (6)
C110.0372 (8)0.0418 (9)0.0286 (7)0.0022 (6)0.0030 (6)0.0028 (6)
C70.0506 (10)0.0278 (7)0.0806 (15)0.0098 (7)0.0018 (10)0.0167 (9)
C40.0396 (9)0.0651 (11)0.0250 (7)0.0074 (7)0.0038 (7)0.0055 (8)
C120.0654 (12)0.0608 (12)0.0442 (10)0.0046 (9)0.0136 (10)0.0175 (9)
C100.0296 (8)0.0406 (8)0.0502 (10)0.0015 (6)0.0034 (7)0.0047 (7)
C50.0442 (9)0.0499 (10)0.0267 (7)0.0068 (7)0.0021 (6)0.0027 (7)
Geometric parameters (Å, º) top
Zn1—N11.9367 (11)C8—H8B0.9800
Zn1—N1i1.9367 (11)C8—H8C0.9800
Zn1—N2i2.2315 (12)C9—C101.524 (2)
Zn1—N22.2315 (12)C9—H9A0.9900
Zn1—Si1i2.7689 (4)C9—H9B0.9900
Si1—N11.6930 (13)C11—C121.535 (2)
Si1—N21.7993 (12)C11—H11A0.9900
Si1—C71.8628 (16)C11—H11B0.9900
Si1—C81.8669 (17)C7—H7A0.9800
N2—C111.486 (2)C7—H7B0.9800
N2—C91.4917 (18)C7—H7C0.9800
N1—C11.3854 (18)C4—C51.389 (2)
C1—C61.405 (2)C4—H40.9500
C1—C21.4070 (19)C12—H12A0.9800
C2—C31.385 (2)C12—H12B0.9800
C2—H20.9500C12—H12C0.9800
C3—C41.376 (3)C10—H10A0.9800
C3—H30.9500C10—H10B0.9800
C6—C51.382 (2)C10—H10C0.9800
C6—H60.9500C5—H50.9500
C8—H8A0.9800
N1—Zn1—N1i128.46 (8)Si1—C8—H8C109.5
N1—Zn1—N2i134.62 (5)H8A—C8—H8C109.5
N1i—Zn1—N2i76.98 (5)H8B—C8—H8C109.5
N1—Zn1—N276.98 (5)N2—C9—C10113.59 (12)
N1i—Zn1—N2134.62 (5)N2—C9—H9A108.8
N2i—Zn1—N2113.45 (6)C10—C9—H9A108.8
N1—Zn1—Si1i152.49 (4)N2—C9—H9B108.8
N1i—Zn1—Si1i37.12 (4)C10—C9—H9B108.8
N2i—Zn1—Si1i40.41 (3)H9A—C9—H9B107.7
N2—Zn1—Si1i130.41 (3)N2—C11—C12115.22 (15)
N1—Si1—N296.41 (6)N2—C11—H11A108.5
N1—Si1—C7118.18 (9)C12—C11—H11A108.5
N2—Si1—C7110.86 (7)N2—C11—H11B108.5
N1—Si1—C8112.23 (8)C12—C11—H11B108.5
N2—Si1—C8111.48 (7)H11A—C11—H11B107.5
C7—Si1—C8107.39 (9)Si1—C7—H7A109.5
C11—N2—C9112.67 (12)Si1—C7—H7B109.5
C11—N2—Si1118.00 (11)H7A—C7—H7B109.5
C9—N2—Si1113.95 (9)Si1—C7—H7C109.5
C11—N2—Zn1118.64 (10)H7A—C7—H7C109.5
C9—N2—Zn1104.34 (8)H7B—C7—H7C109.5
Si1—N2—Zn186.07 (5)C3—C4—C5118.69 (15)
C1—N1—Si1132.42 (10)C3—C4—H4120.7
C1—N1—Zn1128.03 (9)C5—C4—H4120.7
Si1—N1—Zn199.21 (6)C11—C12—H12A109.5
N1—C1—C6120.57 (12)C11—C12—H12B109.5
N1—C1—C2123.07 (13)H12A—C12—H12B109.5
C6—C1—C2116.36 (13)C11—C12—H12C109.5
C3—C2—C1121.27 (15)H12A—C12—H12C109.5
C3—C2—H2119.4H12B—C12—H12C109.5
C1—C2—H2119.4C9—C10—H10A109.5
C4—C3—C2121.25 (15)C9—C10—H10B109.5
C4—C3—H3119.4H10A—C10—H10B109.5
C2—C3—H3119.4C9—C10—H10C109.5
C5—C6—C1121.94 (15)H10A—C10—H10C109.5
C5—C6—H6119.0H10B—C10—H10C109.5
C1—C6—H6119.0C6—C5—C4120.48 (16)
Si1—C8—H8A109.5C6—C5—H5119.8
Si1—C8—H8B109.5C4—C5—H5119.8
H8A—C8—H8B109.5
N1—Si1—N2—C11129.24 (11)N1i—Zn1—N1—C140.18 (11)
C7—Si1—N2—C11107.31 (13)N2i—Zn1—N1—C172.13 (15)
C8—Si1—N2—C1112.27 (14)N2—Zn1—N1—C1177.65 (13)
N1—Si1—N2—C995.22 (10)Si1i—Zn1—N1—C17.03 (19)
C7—Si1—N2—C928.23 (13)N1i—Zn1—N1—Si1145.83 (7)
C8—Si1—N2—C9147.82 (10)N2i—Zn1—N1—Si1101.86 (7)
N1—Si1—N2—Zn18.73 (6)N2—Zn1—N1—Si18.36 (6)
C7—Si1—N2—Zn1132.18 (8)Si1i—Zn1—N1—Si1166.96 (3)
C8—Si1—N2—Zn1108.23 (7)Si1—N1—C1—C6162.62 (12)
N1—Zn1—N2—C11127.69 (11)Zn1—N1—C1—C69.3 (2)
N1i—Zn1—N2—C11100.35 (13)Si1—N1—C1—C217.0 (2)
N2i—Zn1—N2—C115.59 (10)Zn1—N1—C1—C2171.08 (11)
Si1i—Zn1—N2—C1149.47 (12)N1—C1—C2—C3178.36 (14)
N1—Zn1—N2—C9105.95 (9)C6—C1—C2—C31.3 (2)
N1i—Zn1—N2—C926.01 (12)C1—C2—C3—C40.0 (2)
N2i—Zn1—N2—C9120.77 (9)N1—C1—C6—C5178.12 (14)
Si1i—Zn1—N2—C976.89 (9)C2—C1—C6—C51.5 (2)
N1—Zn1—N2—Si17.78 (5)C11—N2—C9—C1066.02 (17)
N1i—Zn1—N2—Si1139.74 (6)Si1—N2—C9—C10156.06 (12)
N2i—Zn1—N2—Si1125.50 (5)Zn1—N2—C9—C1063.99 (14)
Si1i—Zn1—N2—Si1169.383 (19)C9—N2—C11—C1259.38 (18)
N2—Si1—N1—C1176.23 (13)Si1—N2—C11—C1276.70 (17)
C7—Si1—N1—C158.42 (16)Zn1—N2—C11—C12178.35 (12)
C8—Si1—N1—C167.40 (16)C2—C3—C4—C51.0 (2)
N2—Si1—N1—Zn110.18 (7)C1—C6—C5—C40.5 (2)
C7—Si1—N1—Zn1127.99 (8)C3—C4—C5—C60.7 (2)
C8—Si1—N1—Zn1106.18 (8)
Symmetry code: (i) x+1/2, y+1/2, z.

Experimental details

Crystal data
Chemical formula[Zn(C12H21N2Si)2]
Mr508.19
Crystal system, space groupOrthorhombic, Fdd2
Temperature (K)200
a, b, c (Å)29.7954 (12), 21.3566 (8), 8.5844 (3)
V3)5462.5 (4)
Z8
Radiation typeMo Kα
µ (mm1)1.01
Crystal size (mm)0.20 × 0.15 × 0.15
Data collection
DiffractometerBruker SMART area-detector
Absorption correctionMulti-scan
(SADABS; Sheldrick, 1996)
Tmin, Tmax0.824, 0.864
No. of measured, independent and
observed [I > 2σ(I)] reflections
12927, 3296, 3153
Rint0.023
(sin θ/λ)max1)0.667
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.019, 0.051, 1.12
No. of reflections3296
No. of parameters147
No. of restraints1
H-atom treatmentH-atom parameters constrained
Δρmax, Δρmin (e Å3)0.23, 0.23
Absolute structureFlack (1983), 1484 Friedel pairs
Absolute structure parameter0.028 (7)

Computer programs: SMART (Bruker, 2000), SAINT (Bruker, 2000), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), SHELXTL/PC (Sheldrick, 2008).

 

Acknowledgements

This work was supported by grants from the Natural Science Foundation of China (grant No. 20702029) and the Natural Science Foundation of Shanxi Province (grant No. 2008011024).

References

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