A combined ab initio, Fourier transform microwave and Fourier transform infrared spectroscopic investigation of β-propiolactone: The ν8 and ν12 bands

The pure rotational spectrum of β-propiolactone (c-C₂H₄COO) has been recorded between 7 and 21 GHz using a pulsed jet Fourier transform microwave spectrometer. The resulting ground state spectroscopic constants guided the analysis of the rotationally-resolved infrared spectra of two bands that were collected using the far infrared beamline at the Canadian Light Source synchrotron. The observed modes correspond to motions best described as ring deformation (ν₁₂) at 747.2 cm⁻¹ and CO ring stretching (ν₈) at 1095.4 cm⁻¹. A global fit of 4430 a- and b-type transitions from the microwave spectrum and the two infrared bands provided an accurate set of ground state and excited state spectroscopic parameters. To complement the experimental results, the harmonic and anharmonic vibrational frequencies of all 21 infrared active modes of β-propiolactone have been calculated using the DFT B3LYP method (6-311+G(d,p), 6-311++G(2d,3p) basis sets).     

Line Positions and Intensities of the ν1+ ν2+ 3ν3, ν2+ 4ν3, and 3ν1+ 2ν2Bands of Ozone

Using a Fourier transform spectrometer, we have recorded the spectra of ozone in the region of 4600 cm⁻¹, with a resolution of 0.008 cm⁻¹. The strongest absorption in this region is due to the ν₁+ ν₂+ 3ν₃band which is in Coriolis interaction with the ν₂+ 4ν₃band. We have been able to assign more than 1700 transitions for these two bands. To correctly reproduce the calculation of energy levels, it has been necessary to introduce the (320) state which strongly perturbs the (113) and (014) states through Coriolis- and Fermi-type resonances. Seventy transitions of the 3ν₁+ 2ν₂band have also been observed. The final fit on 926 energy levels withJ_max= 50 andK_max= 16 gives RMS = 3.1 × 10⁻³cm⁻¹and provides a satisfactory agreement of calculated and observed upper levels for most of the transitions. The following values for band centers are derived: ν₀(ν₁+ ν₂+ 3ν₃) = 4658.950 cm⁻¹, ν₀(3ν₁+ 2ν₂) = 4643.821 cm⁻¹, and ν₀(ν₂+ 4ν₃) = 4632.888 cm⁻¹. Line intensities have been measured and fitted, leading to the determination of transition moment parameters for the two bands ν₁+ ν₂+ 3ν₃and ν₂+ 4ν₃. Using these parameters we have obtained the following estimations for the integrated band intensities,S_V(ν₁+ ν₂+ 3ν₃) = 8.84 × 10⁻²²,S_V(ν₂+ 4ν₃) = 1.70 × 10⁻²², andS_V(3ν₁+ 2ν₂) = 0.49 × 10⁻²²cm⁻¹/molecule cm⁻²at 296 K, which correspond to a cutoff of 10⁻²⁶cm⁻¹/molecule cm⁻².     

High resolution Fourier transform infrared spectroscopy on CH2DI and CHD2I: evaluation of the ground state constants and analyses of the C-I stretching bands ν3

Abstract

The high resolution (0.0010cm^?1) Fourier transform infrared spectra of the partially deuterated methyl iodide molecules CH₂DI and CHD₂1 have been recorded and analysed in the ν₃ band regions around 510cm^?1. The fundamental band ν₃ is associated with the stretching of the C-I bond and the spectra appear therefore as an asymmetric rotor hybrid a/b-type band and hybrid a/c-type band for CH₂DI and CHD₂I, respectively. About 4700 transitions in the case of CH₂DI and about 3900 transitions in the case of CHD₂I have been assigned. The ground state rotational constants of CH₂DI and CHD₂I have been obtained using the ground state combination differences calculated from the assigned ν₃ transitions and 16 microwave transitions from literature. The S reduced Watson's Hamiltonian has been used in the calculations. In addition, the upper state parameters describing the v₃=1 vibrational states of these molecules have been determined. The obtained ground state constants as well as the upper state parameters have been compared to the corresponding constants of the symmetric top species CH₃I and CD₃I     

Millimeter-Wave and High-Resolution Infrared Spectra of Monoisotopic SCSe: Equilibrium, Ground State, and ν1, mν2, and nν3 Rovibrational Parameters

The Fourier transform infrared spectrum of monoisotopic SC⁸⁰Se has been investigated in the ν₂, ν₃, 2ν₂, 2ν₃, and ν₁ regions with a resolution between 3 and 4 × 10⁻³ cm⁻¹. In addition, the millimeter-wave spectrum has been studied in the region 150 to 320 GHz, and ground and ν₂ = 1 excited state transitions have been measured. Ground state constants, B₀ = 2043.285 4(4) MHz and D₀ = 146.53(5) Hz, have been determined from a merge of millimeter-wave data and ground state combination differences spanning J values up to 77 and 143, respectively. The band centers ν₂ = 352.341 075(9) cm⁻¹ and ν₃ = 505.480 06(5)cm⁻¹ have been determined. The rovibrational parameters of numerous overtone and combination levels (ν₁ν^l2₂ν₃) = 02⁰0, 02²0, 03¹0, 03³0, 04⁰0, 04²0, 00⁰2, and 00⁰3 have been obtained from polynomial analyses whose standard deviations ranged from 0.7 to 3.5 × 10⁻⁴ cm⁻¹. The 10⁰0 level, ν_eff 1435.840 cm⁻¹, is anharmonically perturbed by the 04⁰0 level, with an avoided crossing at J = 55, and W₁₂₂₂₂ = 0.963 09(1) cm⁻¹. Transitions to both the upper (E⁺) and lower (E⁻) sublevels of the dyad were observed for 1 ≤ J′ ≤ 117 and 4 ≤ J′ ≤ 171, respectively, and the deperturbed wavenumbers ν₁ = 1435.542 76(2) and 4ν⁰₂ = 1432.725 00(3) cm⁻¹ were derived. Furthermore, a local crossing of the E⁻ and 04²0 levels involving l-type resonance was observed at J = 91.     

CO2: Global Treatment of Vibrational–Rotational Spectra and First Observation of the 2ν1 + 5ν3 and ν1 + 2ν2 + 5ν3 Absorption Bands

The effective operator approach is applied to the calculation of both line positions and line intensities of the ¹³C¹⁶O₂ molecule. About 11 000 observed line positions of ¹³C¹⁶O₂ selected from the literature have been used to derive 84 parameters of a reduced effective Hamiltonian globally describing all known vibrational–rotational energy levels in the ground electronic state. The standard deviation of the fit is 0.0015 cm⁻¹. The eigenfunctions of this effective Hamiltonian have then been used in fittings of parameters of an effective dipole-moment operator to more than 600 observed line intensities of the cold and hot bands covering the ν₂ and 3ν₂ regions. The standard deviations of the fits are 3.2 and 12.0% for these regions, respectively. The quality of the fittings and the extrapolation properties of the fitted parameters are discussed. A comparison of calculated line parameters with those provided by the HITRAN database is given. Finally, the first observations of the 2ν₁ + 5ν₃ and ν₁ + 2ν₂ + 5ν₃ absorption bands by means of photoacoustic spectroscopy (PAS) is presented. The deviations of predicted line positions from observed ones is found to be less than 0.1 cm⁻¹, and most of them lie within the experimental accuracy (0.007 cm⁻¹) once the observed line positions are included in the global fit.     

Analysis of the ν3 band of NO2

The rotational structure of the ν₃ fundamental of ¹⁴N¹⁶O₂ has been recorded by employing a vacuum grating infrared spectrograph. The analysis has led to the assignment of over 500 R- and P-branch transitions in the spectral region 1562–1650 cm⁻¹. Molecular constants for the upper state, 001, have been presented. No Q-branch transitions were used in the evaluation of these constants. The presently obtained and the band center ν₀ = 1616.846 cm⁻¹ differ significantly from previous determinations. Spin splitting was observed but no information was extracted about upper state spin splitting parameters.     

A new electronic transition of antimony chloride in the visible region

The emission spectrum of SbCl has been photographed at high resolution in the region 400 to 640 nm. In addition to bands of two previously reported transitions in this region, A₁-X and A₂-X, 36 bands of a new system have been identified. A vibrational analysis has been made with ν₀₀ ≈ 20 679 cm⁻¹, and 7 of the bands have been rotationally analyzed. The electronic transition has ΔΩ = 0 with lower state constants which match published data for the ground state X³Σ⁻(0⁺). The upper state is characterized by the following ¹²¹Sb³⁵Cl molecular parameters: B′₀ = 0.0922 cm⁻¹, D′₀ = 3.1 × 10⁻⁸ cm⁻¹.     

High-resolution infrared and theoretical study of four fundamental bands of gaseous 1,3,4-oxadiazole between 800 and 1600 cm

The Fourier transform infrared spectrum of gaseous 1,3,4-oxadiazole, C₂H₂N₂O, has been recorded in the 800–1600 cm⁻¹ wavenumber region with a resolution around 0.0030 cm⁻¹. The four fundamental bands ν₉(B₁; 852.5 cm⁻¹), ν₁₄(B₂; 1078.5 cm⁻¹), ν₄(A₁; 1092.6 cm⁻¹), and ν₂(A₁; 1534.9 cm⁻¹) are analyzed by the standard Watson model. Ground state rotational and quartic centrifugal distortion constants are obtained from a simultaneous fit of ground state combination differences from three of these bands and previous microwave transitions. Upper state spectroscopic constants are obtained for all four bands from single band fits using the Watson model. The ν₄ and ν₁₄ bands form a c-Coriolis interacting dyad, and the two bands are analyzed simultaneously by a model including first and second order Coriolis resonance using the ab initio predicted Coriolis coupling constant . An extended local resonance in ν₂ is explained as higher order b-Coriolis type resonance with ν₆ + ν₁₀, which is further perturbed globally by the ν₁₅ + ν₁₀ level. A fit of selected low-J transitions to a triad model including ν₂(A₁), ν₆ + ν₁₀(B₁), and ν₁₅ + ν₁₀(A₂) using an ab initio calculated Coriolis coupling constant is performed.The rotational constants, ground state quartic centrifugal distortion constants, anharmonic frequencies, and vibration–rotational constants (α-constants) predicted by quantum chemical calculations using a cc-pVTZ and TZ2P basis with B3LYP methodology, are compared with the present experimental data, where there is generally good agreement. A complete set of anharmonic frequencies and α-constants for all fundamental levels of the molecule is given.     

High Resolution Study of Deuterated Hydrogen Sulfide in the Region 2400-3000 cm

High resolution Fourier transform spectra of deuterated hydrogen sulfide have been recorded in the region 2400-3000 cm⁻¹. Rotational structures of the ν₁ + ν₂, ν₂ + ν₃ bands of D₂³²S, of the ν₃ and ν₁ + ν₂ bands of HD³²S, and of the ν₁ + ν₂ band of HD³⁴S were analyzed. Band centers and rotational, centrifugal distortion, and resonance parameters were obtained, which reproduce the initial values of the upper energy levels within a mean accuracy of 1.39 × 10⁻⁴ cm⁻¹ for the states (110) and (011) of D₂³²S, 1.61 × 10⁻⁴ cm⁻¹ and 1.82 × 10⁻⁴ cm⁻¹ for the states (001) and (110) of HD³²S, and 2.09 × 10⁻⁴ cm⁻¹ for the state (110) of HD³⁴S, respectively.     

Analysis of high resolution fourier transform and diode laser spectra of the ν9 band of ethane

Fourier transform measurements with an apodized apparatus function up to 0.002 cm⁻¹ are reported for the ν₉ band (ρ_u) of ethane in the 12-μm region, together with an integrated band strength obtained from intensity measurements on selected Q-branch lines recorded using a diode laser spectrometer. Since the ν₉ band falls in an atmospheric window, these data may be useful in studies of the ethane concentration in the atmosphere of Jupiter and other outer planets. Torsional splittings in the ν₉ level caused by a higher-order Coriolis interaction with the close lying 3ν₄ state (a_1u) have been analyzed in a global least squares fit of 2206 Fourier transform lines and 58 diode splittings to a molecular Hamiltonian containing 20 parameters, with a standard deviation of 0.35 × 10⁻³ cm⁻¹. Rotational levels of one component of the torsionally split 3ν₄ state cross interacting rotational levels of the ν₉ state for K = 17, and the spectrum is followed to K = 19 on the ^pP subband side to permit inclusion of ν₉ levels beyond this crossing. No transitions to 3ν₄ levels were observed. The theoretical treatment presented here makes use of standard symmetric top formalism and of the G₃₆^† double-group formalism for ethane.     

CW-Cavity Ring Down Spectroscopy of O3. Part 3: Analysis of the 6490–6900 cm region and overview comparison with the O3 main isotopologue

This paper is devoted to the third part of the analysis of the very weak absorption spectrum of the ¹⁸O₃ isotopologue of ozone recorded by CW-Cavity Ring Down Spectroscopy between 5930 and 6900 cm⁻¹. In the two first parts [A. Campargue, A. Liu, S. Kassi, D. Romanini, M.-R. De Backer-Barilly, A. Barbe, E. Starikova, S.A. Tashkun, Vl.G. Tyuterev, J. Mol. Spectrosc. (2009), doi: 10.1016/j.jms.2009.02.012 and E. Starikova, M.-R. De Backer-Barilly, A. Barbe, Vl.G. Tyuterev, A. Campargue, A.W.Liu, S. Kassi, J. Mol. Spectrosc. (2009) doi: 10.1016/j.jms.2009.03.013], the effective operators approach was used to model the spectrum in the 6200–6400 and 5930–6080 cm⁻¹ regions, respectively. The analysis of the whole investigated region is completed by the present investigation of the 6490–6900 cm⁻¹ upper range. Three sets of interacting states have been treated separately. The first one falls in the 6490–6700 cm⁻¹ region, where 1555 rovibrational transitions were assigned to three A-type bands: 3ν₂ + 5ν₃, 5ν₁ + ν₂ + ν₃ and 2ν₁ + 3ν₂ + 3ν₃ and one B-type band: ν₁ + 3ν₂ + 4ν₃. The corresponding line positions were reproduced with an rms deviation of 18.4 × 10⁻³ cm⁻¹ by using an effective Hamiltonian (EH) model involving eight vibrational states coupled by resonance interactions. In the highest spectral region – 6700–6900 cm⁻¹ – 389 and 183 transitions have been assigned to the ν₁ + 2ν₂ + 5ν₃ and 4ν₁ + 3ν₂ + ν₃ A-type bands, respectively. These very weak bands correspond to the most excited upper vibrational states observed so far in ozone. The line positions of the ν₁ + 2ν₂ + 5ν₃ band were reproduced with an rms deviation of 7.3 × 10⁻³ cm⁻¹ by using an EH involving the {(054), (026), (125)} interacting states. The coupling of the (431) upper state with the (502) dark state was needed to account for the observed line positions of the 4ν₁ + 3ν₂ + ν₃ band (rms = 5.7 × 10⁻³ cm⁻¹).The dipole transition moment parameters were determined for the different observed bands. The obtained set of parameters and the experimentally determined energy levels were used to generate a complete line list provided as Supplementary Materials.The results of the analyses of the whole 5930–6900 cm⁻¹ spectral region were gathered and used for a comparison of the band centres to their calculated values. The agreement achieved for both ¹⁸O₃ and ¹⁶O₃ (average difference on the order of 1 cm⁻¹) indicates that the used potential energy surface provides accurate predictions up to a vibrational excitation approaching 80% of the dissociation energy. The comparison of the ¹⁸O₃ and ¹⁶O₃ band intensities is also discussed, opening a field of questions concerning the variation of the dipole moments and resonance intensity borrowing by isotopic substitution.     

Millimeter-Wave Spectroscopy, High-Resolution Infrared Spectrum, ab Initio Calculations, and Molecular Geometry of FPS

The transient thiophosphenous fluoride FPS was produced by pyrolysis of 2.5% F₂PSPF₂ in Ar at 1300–1800°C. High-resolution (≥0.004 cm⁻¹) Fourier transform infrared spectra of the a-type ν₁ and b-type ν₂ bands, centered respectively at 803.249 and 726.268 cm⁻¹, were measured and fitted to rotational and quartic centrifugal distortion parameters. The millimeter-wave spectrum, essentially b-type, was measured between 300 and 370 GHz in the ground state and in the ν₃ excited state for FP³²S and in the ground state for FP³⁴S. The frequencies were fitted to a Watson-type A-reduced Hamiltonian up to sextic distortion terms. High level ab initio calculations with large basis sets were performed on FPS and supported the first identification of its infrared and millimeter wave spectra. The calculated anharmonic force field provided precise ab initio rovibrational α constants which were combined with the experimental molecular parameters to determine an accurate equilibrium structure of the molecule: r_e(PS)=188.86 pm, r_e(PF)=158.70 pm, θ(FPS)=109.28°. The collision-controlled 1/e lifetime measured in a 10-Pa (1 : 20) F₂PSPF₂/Ar mixture was 2 s, more than two orders of magnitude larger than that of FPO under the same experimental conditions.     

The Hot Bands of Methane between 5 and 10 μm

Experimental line intensities of 1727 transitions arising from nine hot bands in the pentad–dyad system of methane are fitted to first and second order using the effective dipole moment expansion in the polyad scheme. The observed bands are ν₃− ν₂, ν₃− ν₄, ν₁− ν₂, ν₁− ν₄, 2ν₄− ν₄, ν₂+ ν₄− ν₂, ν₂+ ν₄− ν₄, 2ν₂− ν₂, and 2ν₂− ν₄, and the intensities are obtained from long-path spectra recorded with the Fourier transform spectrometer located at Kitt Peak National Observatory. For the second order model, some of the 27 intensity parameters are not linearly independent, and so two methods (extrapolation and effective parameters) are proposed to model the intensities of the hot bands. In order to obtain stable values for three of these parameters, 1206 dyad (ν₄, ν₂) intensities are refitted simultaneously with the hot band lines. The simultaneous fits to first and second order lead to rms values respectively of 21.5% and 5.0% for the 1727 hot band lines and 6.5% and 3.0% for the 1206 dyad lines. The band intensities of all 10 pentad–dyad hot bands are predicted in units of cm⁻²atm⁻¹at 296 K to range from 0.931 (for 2ν₄− ν₄) to 7.67 × 10⁻⁵(for 2ν₄− ν₂). The total intensities are also estimated to first order for two other hot band systems (octad–pentad and tetradecad–octad) that give rise to weak transitions between 5 and 10 μm.     

The hot bands of silane between 2120 and 2270 cm

The infrared spectrum of the SiH₄ molecule has been recorded between 2040 and 2320 cm⁻¹ using the high-resolution Fourier interferometer of the Laboratoire de Photophysique Moléculaire (Orsay, France). The resolution was 5.4 × 10⁻³ cm⁻¹. In this region, many lines were previously analyzed and assigned to the ν₁/ν₃ stretching dyad of ²⁸SiH₄, ²⁹SiH₄, and ³⁰SiH₄ molecules [J. Mol. Spectrosc. 143 (1990) 35]. However, several lines in the spectrum were not assigned. The results obtained in our previous study [J. Mol. Spectrosc. 197 (1999) 307] of the infrared spectrum of ²⁸SiH₄, in the bending-stretching tetrad region at 3100 cm⁻¹, enabled us to assign 204 of the observed transitions to hot bands (the ν₁ + ν₂/ν₁ + ν₄/ν₂ + ν₃/ν₃ + ν₄ bending-stretching tetrad minus the ν₂/ν₄ bending dyad). These transitions were used to refine the set of the Hamiltonian parameters of the bending-stretching tetrad. The analysis is performed using the tensorial formalism developed in Dijon for tetrahedral molecules and implemented in the STDS software (http://www.u-bourgogne.fr/LPUB/shTDS.html).     

The ν9 Band of Propyne-d3

A high-resolution Fourier transform spectrum of the ν₉ band of CD₃CCH has been recorded at an apodized resolution of 0.004 cm−1 and analyzed. More than 1700 lines in the spectrum have been assigned and the parameters of the ν₉ state derived. The standard deviation of the fit was 0.00034 cm⁻¹. In order to achieve this fit it was necessary to include l-type doubling interaction and Fermi resonance between ν₉ and the E component of 2ν₁₀.     

Measurement and analysis of the ν4 band of silane

The ν₄ band of silane has been recorded with a resolution of about 0.06 cm⁻¹ in the region from 850 to 950 cm⁻¹. Assignments of all allowed transitions in this range with J′ ≤ 12 have been made on the basis of frequency and relative intensity. Qualitative agreement with theory is good but quantitative agreement begins to break down above J′ = 8. The breakdown is attributed to the effects of the strong Coriolis interaction with nearby ν₂.Lines of ²⁹SiH₄ and ³⁰SiH₄ have been observed in the R branch with constant isotope shifts of −1.334 cm⁻¹ and −2.600 cm⁻¹.     

Fourier transform infrared spectrum of the ν3 band of HCO

The ν₃ fundamental band of the formyl radical, HCO, in the 5.3-μm region has been observed at high resolution (0.0025 cm⁻¹, unapodized) using a Fourier transform spectrometer. The HCO radicals were formed by the reaction of F atoms with H₂CO in a fast-flow multiple-traversal absorption cell. A total of 298 lines were measured with an accuracy of about 0.0004 cm⁻¹ and assigned to transitions with values of the rotational quantum numbers N and K_a up to 20 and 5, respectively. These data greatly improve the knowledge of the HCO ν₃ line positions and (v₁v₂v₃) = (001) vibrational state molecular parameters as compared to earlier laser magnetic resonance studies of this band, especially for higher values of N. The ν₁ fundamental band of HCO was also observed and an analysis of these data agrees well with the recent study of Dane et al. [J. Chem. Phys. 88, 2121–2128 (1988)].     

Diborane : High resolution infrared rovibration studies of B2H6 and B2D6

Ground state rotation and quartic distortion constants were obtained for ¹¹B₂D₆ from the analysis of high resolution (0.05 cm⁻¹) Fourier transform infrared spectra. The bands studied comprised the ν₁₇, ν₁₈ type A, and ν₁₄, ν₉ + ν₁₅ type C bands of ¹¹B₂H₆ and the ν₁₆, ν₁₇, ν₁₈ type A, ν₈ type B, and ν₁₄ type C bands of ¹¹B₂D₆. In the case of ¹¹B₂H₆, the authors' ground state data were combined with those of Lafferty et al. obtained from a previous study (J. Mol. Spectrosc. 33, 345–367 (1970)) at comparable resolution of the ν₁₆ type A and ν₈ type B fundamentals. Information on the ground state rotational energy manifold of ¹¹B₂H₆ was accumulated up to J = 23, K_a = 18, and of ¹¹B₂D₆ up to J = 32, K_a = 22. This permitted rather precise determination of the distortion constants Δ_J⁰, Δ_JK⁰, Δ_K⁰, although δ_J⁰ and δ_K⁰ proved to be too small (< 10⁻⁷ cm⁻¹) and were constrained to values calculated from the force field. Sets of upper state parameters were determined for all vibrational levels studied. Although these appear to be essentially unperturbed globally, several localized perturbations were observed and identified.     

The ν1 and ν3 Bands of the OOO Isotopomer of Ozone

Using 0.002 cm⁻¹ resolution Fourier transform absorption spectra of an ¹⁷O-enriched ozone sample, an extensive analysis of the ν₃ band together with a partial identification of the ν₁ band of the ¹⁷O¹⁶O¹⁷O isotopomer of ozone has been performed for the first time. As for other C_2v-type ozone isotopomers [J.-M. Flaud and R. Bacis, Spectrochim. Acta, Part A 54, 3–16 (1998)], the (001) rotational levels are involved in a Coriolis-type resonance with the levels of the (100) vibrational state. The experimental rotational levels of the (001) and (100) vibrational states have been satisfactorily reproduced using a Hamiltonian matrix which takes into account the observed rovibrational resonances. In this way precise vibrational energies and rotational and coupling constants were deduced and the following band centers ν₀(ν₃) = 1030.0946 cm⁻¹ and ν₀(ν₁) = 1086.7490 cm⁻¹ were obtained for the ν₃ and ν₁ bands, respectively.     

Microwave and low-frequency vibrational spectra of bullvalene

The microwave spectrum of bullvalene has been investigated in the region 18–40 GHz. In addition to transitions in the ground vibrational state, transitions arising from five excited vibrational states below 600 cm⁻¹ have also been observed. A combination of microwave intensity measurements and infrared and Raman data has been utilized to assign these vibrations. Three of the vibrations are E-type modes at 241, 355, and 588 cm⁻¹. One is an A₁-type mode at 445 cm⁻¹, and another is an A₂-type at 266 cm⁻¹. The microwave spectrum indicates the presence of a first-order Coriolis interaction for the E modes at 241 and 588 cm⁻¹. The first-order Coriolis coupling constant q = 0.557 MHz for the 241 cm⁻¹ vibration. The spectral results are consistent with C_3v symmetry for bullvalene.