Structure and Conformational Properties of 1, 3, 3-Trimethyl-1, 3

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Structure and Conformational Properties of 1,3,3-Trimethyl-1, 3-Azasilinane: Gas Electron Diffraction, Dynamic NMR, and Theoretical Study Bagrat A. Shainyan,*,† Svetlana V. Kirpichenko,† Sergei A. Shlykov,*,‡ and Erich Kleinpeter*,§ †

A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Division of the Russian Academy of Science, 1 Favorsky Street, 664033, Irkutsk, Russian Federation ‡ Department of Physics, Ivanovo State University of Chemistry and Technology, Engels Avenue, 7, 153000, Ivanovo, Russian Federation § Chemisches Institut der Universit€at Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam (Golm), Germany

bS Supporting Information ABSTRACT: Structure and the conformational properties of 1,3,3-trimethyl1,3-azasilinane have been studied. According to gas electron diffraction (GED), the molecule exists in a slightly distorted chair conformation with the N Me group in equatorial position. High-level quantum chemical calculations excellently reproduce the experimental geometry. Employing variable temperature 1H and 13C NMR spectroscopy down to 103 K, the conformational equilibrium could be frozen and the barrier to ring inversion determined.

1. INTRODUCTION The molecular structure and the conformational equilibria in silacyclohexanes have been studied extensively for nearly 10 years, in particular, by gas phase electron diffraction (GED) and low temperature NMR spectroscopy,1 6 as well as quantum chemical calculations.7 10 The study of the molecular structure of heterosilacyclopentanes and -hexanes by GED has been restricted to 3,3-dimethyl-3-silatetrahydrofuran,11,12 3,3-dimethyl3-silathiophane,13 and 3,3-dimethyl-3-silathiane.14 Molecular structure15 and conformational analysis16 of 4,4-dimethyl-4silathianes S-oxides have been published recently. Our interest in the conformational behavior of heterosilacyclohexanes prompted us to turn attention to heterocyclic ring systems containing the silicon and/or nitrogen. At present, the chemistry of bioactive 1,4-azasilinanes, which are the isostructural analoguues of known drugs, is an intensively developing field.17 19 The molecular structure of a series of 1,4-azasilinanes has been determined by X-ray analysis.20 23 Recently, variabletemperature NMR spectroscopy was used for the conformational analysis of 1-trifluoromethylsulfonyl-4,4-dimethyl-1,4-azasilinanes.24 In the past, much less attention has been paid to the isomeric 1, 3-azasilinanes which, actually, attracted a lot of interest as potential biologically active compounds.25,26 Thus, the stereocontrolled synthesis of 2-substituted 3,3-diphenyl-1,3-azasilinanes as potential protease inhibitors has been reported.26 From the analysis of room temperature 1H NMR spectra of a series of 1,3,3trimethyl-1,3-azasilinanes it was suggested that they take a chair r 2011 American Chemical Society

conformation distorted in the case of bulky substituents such as the 5-t-butyl group.27 It is the objective of this paper to submit the first experimental and theoretical study of molecular structure and conformational behavior of 1,3,3-trimethyl-1,3-azasilinane using GED and lowtemperature NMR spectroscopy as experimental methods and high-level theoretical calculations.

2. RESULTS AND DISCUSSION 2A. Gas Phase Electron Diffraction. The molecular structure of 1,3,3-trimethyl-1,3-azasilinane determined by GED is shown in Figure 1, and the experimental geometry parameters are given in Table 1. Experimental and theoretical sM(s) curves along with their differences ΔsM(s) are given in Figure 2. The radial distribution curves f(r) with the corresponding differences Δf(r) are shown in Figure 3. The quantum chemical calculations (vide infra) predict the NMeeq conformer to be more stable when compared with the NMeax analogue (18.5 to 21.8 kJ mol 1). This makes it possible to assume the vapor phase of this compound to consist of the NMeeq conformer with negligible content of the axial conformer, at least at the temperature of the GED/MS experiment (271 K). Received: November 17, 2011 Revised: December 5, 2011 Published: December 05, 2011 784

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Table 1. Calculated and Experimental Geometry and Vibrational Parametersb for 1,3,3-Trimethyl-1,3-azasilinanea Theoretical calculationsc DFT MP2

G2

GED d

r

l

r

l

Bond Distances and Vibration Amplitudes

Figure 1. Molecular structure of 1,3,3-trimethyl-1,3-azasilinane as obtained by GED (N-Me group found in equatorial position).

The modified KCED-35 program was applied for the analysis of the electron diffraction intensities.30 The geometry model of the equatorial conformer was described using the z-matrix built on the basis of 19 parameters: four bond lengths r(C2 Si3), r(C4 C5), r(C6 N1), r(C2 H10), nine valence angles A(C2 Si3 C4), A(Si3 C4 C5), A(C4 C5 C6), A(C2 Si3 C7), A(C2 N1 C9), A(Si3 C2 H10), A(N1 C2 H10), A(H10 C2 H11), A(C5 C4 H12), and six torsion angles D(C2 Si3 C4 C5), D(Si3 C4 C5 C6), D(C5 C6 N1 C2), D(C2 Si3 C7 H18), D(C2 Si3 C8 H21), D(C2 N1 C9 H24). The other geometry parameters were described using differences with the homologous ones adopted from DFT-B3LYP/aug-cc-pVTZ calculations. Vibrational corrections, Δr = rh1 ra, and starting values for root-mean-square amplitudes were derived from a calculated force field (DFT-B3LYP/aug-cc-pVTZ) using the method of Sipachev28,29 and are included in Table 1. The structure with fixed geometric and vibrational parameters was taken from the theoretical calculation (DFT) and yielded an agreement factor between the experiment and theory of Rf = 8.3% in the case of equatorial conformer, while it was significantly higher for the axial structure, Rf = 26.5%. The refined structure (see Table 1) led to an agreement factor Rf = 3.7%. Thus, the GED data confirm the conclusion based on the energy difference between these two conformers (vide infra) that the NMeeq conformer is much more favorable than the NMeax conformer. The latter disagreement is corroborated also by the difference curves ΔsM(s) and Δf(r) (see Figures 2 and 3). Vibrational amplitudes for the closely spaced internuclear distances were refined in groups. Eight groups were formed in which the differences between amplitudes within each group were constrained to the calculated values. With these constraints, 19 independent parameters (see above) and eight groups of vibrational amplitudes were refined simultaneously. The structure of 1,3,3-trimethyl-1,3-azasilinane was calculated theoretically using the Møller Plesset second-order perturbation theory with Dunning’s augmented correlation consistent polarized valence triple-ζ basis set (MP2/aug-cc-pVTZ), the G2 level of theory, and at the DFT level (B3LYP) with aug-cc-pVTZ basis set. The NMeax and NMeeq conformers of 1 were calculated by the MP2/6-311G(d,p), MP2/aug-cc-pVTZ, B3LYP/aug-ccpVTZ, and G2 methods. All methods predict the NMeeq conformer to be more stable by 21.6 (MP2/6-311G(d,p)), 19.5 (MP2/aug-cc-pVTZ) and 18.25 (G2) kJ mol 1.

R(2,3) R(3,4)

1.894 1.882

1.901 1.891

1.902 1.891

0.053 1.896(4) 0.052(1) 0.053 1.885(4) 0.052(1)

R(3,7)

1.880

1.893

1.888

0.053 1.881(4) 0.052(1)

R(3,8)

1.879

1.891

1.887

0.053 1.881(4) 0.052(1)

R(4,5)

1.536

1.540

1.540

0.052 1.538(3) 0.053(3)

R(5,6)

1.525

1.531

1.531

0.052 1.529(3) 0.052(3)

R(1,2)

1.468

1.462

1.468

0.050 1.470(3) 0.051(3)

R(1,6)

1.461

1.456

1.463

0.050 1.465(3) 0.051(3)

R(1,9) R(2,10)

1.456 1.108

1.448 1.098

1.455 1.108

0.049 1.457(3) 0.050(3) 0.080 1.115(2) 0.085(2)

A(2,3,4)

102.1

102.7

102.6

A(2,3,7)

110.8

110.7

110.3

110.2(4)

A(3,4,5)

109.4

110.3

110.5

111.4 (4)

A(4,5,6)

113.4

114.0

114.1

112.5(6)

A(5,4,12)

110.7

110.1

110.4

110.5(10)

A(3,2,10)

110.7

110.9

110.0

112.6(9)

A(1,2,10) A(10,2,11)

110.8 106.6

111.2 106.0

111.2 106.1

115.4(10) 105.0(7)

A(2,1,9)

109.6

111.3

111.4

110.8(5)

A(2,1,6)

111.5

113.3

113.1

113.3(5)

A(6,1,9)

109.5

111.4

111.3

110.8(5)

Σ(CNC angles)

330.7

336.0

335.8

334.9(9)

D(2,3,4,5)

44.0

40.9

40.9

41.0(8)

D(2,3,7,18)

177.9

178.0

177.9

177.9(4)

Bond Angles 102.9(3)

Dihedral Angles

D(2,3,8,21) D(3,4,5,6)

173.1 54.2

174.1 51.9

175.4 52.1

175.4(4) 52.2(1)

D(2,1,9,24)

61.5

63.9

63.4

63.4(2)

a

For atom numbering, see Figure 1. b Distances and vibration amplitudes in Å, angles in degrees; theoretical (re) and experimental (rh1) structure geometric parameters. c MP2 and DFT calculations were performed with aug-cc-pVTZ basis sets. d Root mean square vibration amplitudes were estimated using the program SHRINK28,29 for the temperature of the GED/MS experiment, T = 271 K, on the base of the force field adopted from the DFT/aug-cc-pVTZ calculations.

The bond lengths of the “piperidine” part of the ring are consistent with those of piperidine itself.31 As follows from Table 2, all bond lengths are best reproduced using the aug-ccpVTZ basis set: the mean deviation is ca. 0.006 Å both for MP2 and DFT, and 0.011 Å for G2 calculations. The bond angles, however, are better reproduced by the G2 method (the mean deviation is 1.2, 1.3, and 1.6° for G2, DFT, and MP2 methods, respectively). Finally, dihedral angles are exactly reproduced by DFT (the mean deviation is 0.04°), excellently by G2 (0.46°), and slightly worse by the MP2 method (1.8°). The 1,3-azasilinane ring of the studied compound has a slightly distorted chair conformation. The dihedral angles N1C2C3C4, 785

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Table 2. 1H and 13C NMR Data of 1,3,3-Trimethyl-1,3azasilinane in the Freon Mixture CD2Cl2/CHCl2F/CHClF2 T, °K

MeSi

2-CH2 4-CH2 5-CH2

6-CH2

NMe

0.52 m 1.86 m

2.30 m

2.29 s

0.37 t 0.70 d

1.65 q 1.92 d

1.79 t 2.70 d

2.22

0.33

0.27

0.91

1

H

273

0.10 s

163 Δae = δax

ax eq δeq

1.85 s

0.03 1.43 d 0.10 2.16 d 0.13

0.73

13

C

273

3.60

49.70

11.95

25.31

60.52

52.71

113

5.48

47.58

9.95

23.73

58.62

51.45

Figure 2. Experimental (dots) and theoretical (line) molecular scattering intensities sM(s) curves along with their differences ΔsM(s) for refined structure of the N-equatorial conformer.

3.83

Scheme 1

Figure 3. Radial distribution f(r) curves: experimental (dots) and theoretical (line) and difference Δf(r) “theory experiment”: calculated, DFT/aug-cc-pVTZ, for N-equatorial (a) and N-axial (c) conformers; curves marked as (b) correspond to the refined structure of the N-equatorial conformer. The contribution of the individual terms is shown by vertical bars.

analogues of 1,3,3-trimethyl-1,3-azasilinane, e.g., in 1,3,3-trimethyl-5-t-butyl-1,3-azasilinane in which the axial and equatorial methylene protons are diastereotopic and give different signals regardless of temperature.27 The assignment of the proton signals in the low temperature NMR spectra to the corresponding directly bonded carbon atoms was made according to HSQC experiments and the chemical shift differences Δae. The largest Δae values are observed for the 2-CH2 and 6-CH2 methylene groups (Table 2) in the α-position to nitrogen,33,34 whereas for the more distant 4-CH2 and 5-CH2 methylene groups, Δae values are much smaller. A larger value of Δae for the 6-CH2 (α) methylene group, which is subject only to the effect of the nitrogen lone pair, is consistent with previous data for 1-trifluoromethyl-sulfonyl4,4-dimethyl-1,4-azasilinane in which the value of Δae for the NCH2 protons (0.63 ppm) is 5 times as large as that for the SiCH2 protons (0.12 ppm).24 The signals were further assigned to the axial or equatorial protons according to their shielding order using the same criteria as for C-ring substituted 1,3,3-trimethyl-1,3-azasilinanes:27 the low-frequency and highfrequency resonances are in expected agreement with those for the axial and equatorial protons, respectively (Table 2). An independent criterion is the splitting of the signals (only the large 3J(ax,ax) and 2J(ax,eq) were considered; the corresponding small 3J(ax,eq) and 3J(eq,eq) are not resolved due to residual low temperature broadening). The analysis of the corresponding low temperature 13C NMR study of 1,3,3-trimethyl-1,3-azasilinane (Table 2) is in complete agreement with the above results of the 1H NMR study. Only the

C2Si3C5C6 and C6N1Si3C4 are 3.6, 4.5, and 8.0° (MP2), or 3.6, 5.5, and 9.1° (G2). The flap angle C2Si3C4/N1C2C4C5 (the angle between the plane C2Si3C4 and the average plane N1C2C4C5) is 43.5 (MP2) or 40.3° (G2), and the angle C6N1C2/C2Si3C5C6 is 59.1 (MP2) or 58.0° (G2), so, the “Si-part” of the 1,3-azasilinane ring is much less folded than the “N-part”. The substantial flattening of the siliconcontaining part of the six-membered ring with respect to the “ideal” angle of 60° is fully consistent with the same effect observed recently for the Si,S-containing heterocycles.14,15,32 2B. Conformational Analysis. Similar to N-Me-piperidine and silacyclohexanes, the chair conformers of 1,3,3-trimethyl-1,3azasilinane undergo rapid ring and nitrogen inversion at room temperature (on the NMR time scale) resulting in averaging of chemical shifts and coupling constants of the participating conformers (Scheme 1). This dynamic process was investigated by variable temperature 1H and 13C NMR spectroscopy. As the temperature is lowered, the signals of all the ring protons broaden and should eventually decoalesce into two signals corresponding to the axial and equatorial protons. The averaged (room temperature) and the fully decoalesced (163 K) 1H NMR spectra are shown in Figure 4, and the NMR parameters are summarized in Table 2. It it worth noting that the values of Δae given in Table 2 are nicely consistent with the corresponding values in ring-substituted 786

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Figure 4. 1H NMR spectra of 1 in CD2Cl2/CHCl2F/CHClF2 at different temperatures.

3-azasilinane relative to 1,1-dimethylsilacyclohexane (ΔG‡ = 23.0 kJ mol 1 at 111 K).39 Likewise, on going from cyclohexane to N-methylpiperidine, a lower barrier to ring inversion was observed for the former compound (ΔG‡ = 43.1 kJ mol 1, CS2, 211 K,40 46.0 kJ mol 1, 213 K,36 and 50.2 kJ mol 1 in the gas phase at 298 K41).

SiMe2 resonance at 3.6 ppm broadens and decoalesces into a doublet of same intensity (Tc at 200 K; vide infra). The other lines corresponding to the NMe and the ring carbon atoms remain nonsplit even at 113 K, thus corroborating the fact that the NMeeq conformer is the only stable conformer. The observed conformational changes presumably refer to the ring inversion rather than the nitrogen inversion. The latter, apparently, remains fast, resulting in the averaged NMe signal corresponding to the conformational equilibrium strongly biased to the NMeeq conformer, as proved by a sharp singlet signal of the NMe group even at 113 K. As known, the Me group shows a strong preference for the equatorial position in N-methylpiperidine as well (ΔGavo = 11.3 kJ mol 1).35 37 The NMeax group in N-methylpiperidine is more crowded by the syn-axial hydrogen atoms at C-3 and C-5 than the axial Me group in cyclohexane due to the shorter C N bond (1.47 Å) in comparison with the C C bond (1.54 Å).35,37,38 The NMe group in 1,3,3-trimethylpiperidine38 occupies the equatorial position because of unfavorable 1,3-syn diaxial Me 3 3 3 Me interactions in the NMeax conformation.33,34,37 For the same reason, the NMe group in 1,3,3-trimethyl-1,3-azasilinane should occupy the equatorial position, since, in spite of a larger Si C bond length, the distance between the NMeax and the SiMeax group in the axial conformer (3.65 Å) is smaller than the sum of the effective van der Waals radii of the methyl groups (4.0 Å). The barrier to ring inversion ΔG‡ of 38.1 kJ mol 1 was calculated from the temperature of coalescence (200 K) of the H-4 proton and SiMe carbon signals. The lower barrier to ring inversion in 1,3,3-trimethyl-1,3-azasilinane as compared to that in N-methylpiperidine (ΔG‡ = 60.3 kJ mol 1, CD3OD, 245 K)34 and 1,3,3-trimethylpiperidine (ΔG‡ = 45.2 kJ mol 1, CD3OD, 245 K)33 is explained by the longer Si C bond (1.904 Å) compared to the C C bond (1.534 Å) resulting in a more flexible chair conformation in the former compound. On the other hand, replacement of the CH2 by the NMe group causes a marked increase of ΔG‡ for 1,3,3-trimethyl-1,

3. SUMMARY AND CONCLUSIONS Both experimental (GED) and theoretical (DFT, MP2, G2) analysis of the molecular structure of 1,3,3-trimethyl-1,3-azasilinane is reported. The molecule exists in a slightly distorted chair conformation with the N-Me group in equatorial position. The calculated geometric parameters (bond lengths, bond angles, dihedral angles) excellently coincide with those determined experimentally. A large energy difference between the axial and equatorial N Me conformers (∼21 kJ mol 1) favors the existence of only one stable conformer, which is confirmed by the results of the low temperature NMR spectroscopy. The barrier to ring inversion was also determined to be 38.1 kJ mol 1. 4. EXPRIMENTAL SECTION 4A. Synthetic Procedure. The preparation of 1,3,3-trimethyl1,3-azasilinane is given in the Supporting Information. 4B. GED/MS. Experimentally, the structure of the free molecule of 1,3,3-trimethyl-1,3-azasilinane was studied by a combined gasphase electron diffraction/mass spectrometric GED/MS technique described previously.42 The sample (colorless liquid) was kept in a glass vessel connected to a dosing valve of the inlet system. The molecular beam was formed by passing the vapor flow via pipe line through the effusion cell. The latter had a cylindrical shape of 7 mm inner diameter and its nozzle was of 0.6 mm inner diameter and 1.2 mm length. The ratio of the evaporation/effusion areas exceeded 500, ensuring thermodynamic equilibrium in the effusion cell. Materials of the inlet system were Teflon, stainless 787

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The Journal of Physical Chemistry A steel, glass and nickel. The effusion cell was filled with metal shavings (stainless steel in this case) in order to ensure uniform temperature of the vapor passing through by multiple hits of the molecules at the value the cell was kept, 271(3) K, as measured by W/W Re 5/20 thermocouple. The scattered electrons were collected on Kodak Electron Image films of 9  12 cm. Two camera distances, L1 = 598 (long) and L2 = 338 mm (short), were used, resulting in diffraction patterns in s-ranges of 1.4 16.7 Å 1 and 3.3 29.2 Å 1, respectively [s = (4π/λ) sin θ/2, λ is electron wavelength, and θ is scattering angle] at 85 kV of accelerating voltage. The accurate electron wavelength, 0.04049(4) Å, was measured from diffraction patterns of polycrystalline ZnO. The diffraction patterns were recorded with 0.5 0.6 μA primary electron beam intensity, 50 60 s exposure times, and a residual pressure of (1.8 2.6)  10 6 and (7.2 7.6)  10 7 Torr in the diffraction chamber and in the mass spectrometric block, respectively. Four and six diffraction patterns were recorded from short and long camera distances and were used for further treatment. The optical densities of the diffraction patterns were measured by a computer controlled MD-100 (Carl Zeiss, Jena) microdensitometer.43 The molecular scattering function, sM(s), was evaluated as sM(s) = (I(s)/G(s) 1)s, where I(s) is the total electron scattering intensity, G(s) is the experimental background.44 After crossing the fast electrons beam in the diffraction chamber, the gas beam from the effusion cell entered directly the ionization chamber of a monopole mass spectrometer attached to the GED unit. This allows real-time monitoring of the vapor composition by recording the mass spectra simultaneously with recording the diffraction patterns. The most abundant ion peaks in the electron impact (Ui = 50 V) mass spectrum of the vapor studied were 143 (28) [M]+, 142 (22) [M H]+, 128 (100) [M Me]+ , 115 (10) [M 2CH 2 ]+ , 114 (13) [M CH 3 CH 2 ]+ , 100 (42) [Me 2 SiC 2 H 4 N]+ , 86 (22) [MeHSiC2H4N]+, 73 (93) [Me2SiHN]+, 72(38) [Me2SiN]+, 59 (60) [Me2SiH]+, 45 (34) [MeSiH2]+, 44 (37) [MeSiH]+, 43 (46) [MeSi]+, 42 (41) [CH2Si]+, 41 (21) [C3H5]+. No peaks with the mass exceeding that of the molecular ion or caused by impurities, decomposition products, etc., were detected in the mass spectrum. 4C. Theoretical Calculations. High-level calculations at the DFT and MP2 levels of theory with the 6-311G(d,p) and aug-ccpVTZ basis sets, and at the G2 level of theory were performed with the Gaussian 09 computational program.45 No restrictions on the variation of geometric parameters were imposed during the optimization procedure. 4D. NMR Measurements. 1H and 13C NMR spectra were recorded on a Bruker AV-600 (at 600 and 150 MHz, respectively). Chemical shifts were determined relative to residual internal CD2Cl2 (13C, δ 53.73) and are given in ppm highfrequency to trimethylsilane (TMS). Analysis and assignment of the 1H NMR data were supported by homonuclear (COSY) and heteronuclear (HSQC 13C 1H, HMBC 13C 1H) 2D correlation experiments. A solvent mixture of CD2Cl2, CHFCl2, and CHF2Cl in a ratio of 1:1:3 was used for the low temperature measurements. The probe temperature was calibrated by means of a thermocouple PT 100 inserted into a dummy tube. The lowtemperature measurements were estimated to be accurate to (2 K. The chemical shifts difference Δνc (Hz) was determined by extrapolation of the slightly temperature dependent chemical shift differences Δν to the coalescence temperature Tc and used

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to calculate kc and the ring inversion barriers by the Eyring equation at Tc.

’ ASSOCIATED CONTENT

bS

Supporting Information. Experimental synthetic procedures, 2D{1H 13C} NMR spectrum of 1,3,3-trimethyl-1,3azasilinane, results of G2, DFT, and MP2 calculations. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (B.A.S.); [email protected] (S.A.S.); [email protected] (E.K.).

’ ACKNOWLEDGMENT The financial support of this work by the Russian Foundation for Basic Research and Deutsche Forschungsgemeinschaft (Grant RFBR-DFG No. 11-03-91334) is greatly acknowledged. We thank Dipl.-Ing (FA) Angela Krtitschka (University of Potsdam) for preparing the freon sample and recording the low-temperature NMR spectra. ’ REFERENCES (1) Arnason, I.; Kvaran, A.; Jonsdottir, S.; Gudnason, P. I.; Oberhammer, H. J. Org. Chem. 2002, 67, 3827–3831.  Arnason,  .; Jonsdottir, S.; Antonsson, E.; Wallevik, S. O.; (2) Kvaran, A I.; Belyakov, A. V.; Baskakov, A. A.; H€olbling, M.; Oberhammer, H. Organometallics 2007, 26, 6544–6550. (3) Girichev, G. V.; Giricheva, N. I.; Bodi, A.; Gudnason, P. I.; Jonsdottir, S.; Kvaran, A.; Arnason, I.; Oberhammer, H. Chem.—Eur. J. 2007, 13, 1776–1783.  Bjornsson, R.; Kvaran, A  .; Jonsdottir, S.; (4) Wallevik, S. O.; Girichev, G. V.; Giricheva, N. I.; Hassler, K.; Arnason, I. J. Mol. Struct. 2010, 978, 209–219.  Bjornsson, R.; Kvaran, A  .; Jonsdottir, S.; Arnason, (5) Wallevik, S. O.; I.; Belyakov, A. V.; Baskakov, A. A.; Hassler, K.; Oberhammer, H. J. Phys. Chem. A 2010, 114, 2127–2135. (6) Arnason, I.; Gudnason, P. I.; Bjornsson, R.; Oberhammer, H. J. Phys. Chem. A 2011, 115, 10000–10008. (7) Freeman, F.; Fang, C.; Shainyan, B. A. Int. J. Quantum Chem. 2004, 100, 720–732. (8) Weldon, A. J.; Tschumper, G. S. Int. J. Quantum Chem. 2007, 107, 2261–2265. (9) Bjornsson, R.; Arnason, I Phys. Chem. Chem. Phys. 2009, 11, 8689–8697. (10) Bodi, A.; Bjornsson, R.; Arnason, I. J. Mol. Struct. 2010, 978, 14–19. (11) Gromov, A.Yu.; Shishkov, I. F.; Skancke, A.; Vilkov, L. V.; Yesipenko, A. V.; Kirpichenko, S. V. J. Mol. Struct. 1995, 352, 115–124. (12) Gromov, A.Yu.; Shishkov, I. F.; Skancke, A.; Vilkov, L. V.; Yesipenko, A. V.; Kirpichenko, S. V. J. Struct. Chem. 1996, 37, 594–608. (13) Mastryukov, V. S.; Golubinskii, A. V.; Vilkov, L. V.; Kirpichenko, S. V.; Suslova, E. N.; Voronkov, M. G. Zh. Strukt. Khim. 1991, 32, 148–151. (14) Atavin, E. G.; Khristenko, L. V.; Lokshin, B. V.; Samdal, S.; Kirpichenko, S. V.; Vilkov, L. V. J. Struct. Chem. 2005, 46, 422–430. (Engl. Transl.). Zh. Strukt. Khim. 2005, 46, 435–443. (15) Shainyan, B. A.; Suslova, E. N.; Schilde, U. Struct. Chem. 2008, 19, 889–894. (16) Shainyan, B. A.; Suslova, E. N.; Kleinpeter, E. J. Phys. Org. Chem. 2011, 24, 1188–1192. 788

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