Vibration-rotation Hamiltonian for asymmetric Cs molecules adapted to very strong Coriolis resonance : Application to the microwave reinvestigations of the ν7 and ν9 states of HCOOH and DCOOH

Formic acid is a C_s asymmetric top molecule exhibiting an exceptionally strong Coriolis resonance between its ν₇ and ν₉ vibrational states. The usual molecular model composed of two Watson Hamiltonians coupled by linear and quadratic vibration-rotation coupling terms does not allow satisfactory interpretations of such rotational spectra by microwave spectroscopy. In this case, it is necessary to perform a more complete development of the vibration-rotation coupling part of the standard Hamiltonian operator. The first part of this paper gives details of these developments, yielding a new molecular model adapted to very strong Coriolis resonance for C_s asymmetric top molecules. This new model consists of two Watson Hamiltonians developed up to the sextic centrifugal distortion coefficients and linked by 10 coupling constants. In the second part of this paper, this model has been successfully tested on H¹²COOH and D¹²COOH. From careful microwave reinvestigations of the ν₇ and ν₉ states of these two molecules, numerous new important rotational lines of various μ_b type and intervibrational transitions of μ_c type have been assigned. Various tests are performed to estimate the quality of the results. A critical discussion of the numerical investigation revealed the limits of the new molecular model proposed for strong Coriolis resonance.     

The high-resolution infrared spectra of the ν2 and ν3 bands of HOCl

The infrared spectra of the a-type transitions of the ν₂ and ν₃ bands of HO³⁵Cl and HO³⁷Cl have been obtained under high resolution. Line assignments of both bands have been made, and the spectroscopic constants have been obtained for both bands using a Watson Hamiltonian. Lines of the K_a = 5 subband of the ν₂ band of the HO³⁵Cl molecule were found to be slightly shifted by an interaction with the K_a = 4 level of the 2ν₃ vibrational state. The b-type transitions permitted for both bands were too weak to observe. Relative intensities of selected lines of both bands have been measured, and empirical Herman-Wallis factors have been determined.     

Diode Laser Spectroscopy of Trifluoroethylene in the 8.6-μm Region

The two mid-infrared bands of the CF₂=CHF molecule, ν₅centered at 1172.673 cm⁻¹and ν₆+ ν₉at 1155.105 cm⁻¹, were measured on a tunable diode laser spectrometer with a resolution near the Doppler limit. These vibrations ofA′ species give rise toa/bhybrid bands, even though our analysis has pointed out that the intensity of thea-type component is predominant. Most of theJandKstructure has been resolved in different subbranches, and the rovibrational analysis led to the assignment of about 1400 (J≤ 60,K_a≤ 22,K_c≤ 60) and 90 (J≤ 56,K_a≤ 5,K_c≤ 56) lines of the ν₅and ν₆+ ν₉bands, respectively. Using Watson'sA-reduction Hamiltonian in theI^rrepresentation, a set of accurate spectroscopic constants for the upper states has been derived from transitions free of major resonance effects. The rotational structure of the ν₅vibration also exhibits effects of Coriolis perturbation by a state identified as ν₇+ ν₁₁. Parameters for the perturber were determined from the interaction effects near the observed crossings, using a dyad model including first-orderb-Coriolis interaction.     

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 Infrared Spectroscopy of Methyl Isocyanide: The ν3, ν6, and ν7 + ν8 Bands

The vibration-rotation spectrum of methyl isocyanide (CH₃NC) has been recorded with the aid of a high-resolution Fourier transform spectrometer in the region 1370 to 1560 cm⁻¹ containing the perpendicular band of the fundamental vibration ν₆ (species E), the weaker parallel band of the ν₃ (A₁) fundamental, and the perpendicular combination band ν₇ + ν₈ (E) enhanced by Fermi resonance with ν₆. Sixteen hundred seventy well-resolved lines were assigned to 15 subbands of ν₆, 6 subbands of ν₃, and 3 subbands of ν⁻₇ + ν⁻₈. A strong x, y-Coriolis resonance between ν₃ and ν₆ and Fermi resonance between ν^±₆ and the E component ν₇ + ν₈, as well as between ν₃ and the A_1,2 components ν^±₇ + ν₈, greatly affects the spectrum. Additional weaker anharmonic interaction of ν₆ with the ν₄ + 2ν²₈ combination and higher-order rotational interactions connecting the various states were also detected in the spectrum. All of these interactions have been incorporated into a 9 × 9 Hamiltonian matrix used for modeling the upper states of the observed transitions. A set of spectroscopic constants is reported for the upper states of the bands ν₃, ν₆, and ν₇ + ν₈ and for ν₄ + 2ν²₈ which reproduces the observed lines with an overall standard deviation of 0.0012 cm⁻¹.     

Analysis of the ν9/ν10 band system of allene

The infrared spectrum of allene has been recorded with high resolution (0.002-0.004 cm⁻¹) on a Fourier transform instrument in the region 730 to 1170 cm⁻¹ containing the perpendicular bands, ν₉ and ν₁₀. A total of 21 subbands with KΔK ranging from −6 to +14 have been assigned in the ν₉ band, and 26 subbands with KΔK = −10 to +15 have been assigned in the ν₁₀ band. The bands are affected by a combination of a J_z-Coriolis and a quartic anharmonic interaction between their upper states ν₉ and ν₁₀. In addition, several other more localized perturbations are found in the spectrum. The nature of the interactions responsible for these perturbations is discussed, and five of the strongest perturbations are quantitatively accounted for by constructing a Hamiltonian matrix which includes five different perturbing states and their Coriolis and anharmonic resonances with the ν₉ and ν₁₀ upper states. A set of spectroscopic constants for the ν₉ and ν₁₀ states and for some of the perturbing states is reported.     

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).     

The High-Resolution Fourier Transform Spectrum of Dideuterated Methane CH2D2in the Region between 1900 and 2400 cm

The infrared spectrum of doubly deuterated methane CH₂D₂has been recorded in the region from 1900 to 2400 cm⁻¹at almost Doppler-limited resolution by using two high-resolution Fourier transform spectrometers. The vibrational bands observed include 2ν₄, ν₄+ ν₇, 2ν₇, ν₂, ν₈, ν₄+ ν₉, and ν₇+ ν₉, which were analyzed by taking into account Coriolis and Fermi interactions among them and also those with ν₄+ ν₅, ν₃+ ν₇, and ν₅+ ν₇. Most of the centrifugal distortion constants were constrained to appropriate values, while the vibrational term value and three rotational constants in each of the seven excited states were adjusted along with Coriolis and Fermi interaction parameters by the least-squares analysis of the observed spectrum. The vibration–rotation interaction constants α_sthus determined for the ν₂and ν₈states were combined with those of other fundamental states already published to calculate the equilibrium C–H distance.     

On the high resolution spectroscopy and intramolecular potential function of SO2

Two weak stretching bands, ν₁ + 3ν₃ and 3ν₁ + ν₃, of the sulfur dioxide molecule have been recorded at high resolution and analyzed for the first time with using a Fourier transform Bruker IFS-120 HR interferometer. About 1000 transitions with J^max. = 51, , and 900 transitions with J^max. = 53, have been assigned to the bands ν₁ + 3ν₃ and 3ν₁ + ν₃, respectively. Analysis of the recorded spectra was made using the model of isolated vibrational states. Parameters obtained from the fit reproduce the initial experimental ro-vibrational energies with the rms deviation of 0.0006 and 0.0012 cm⁻¹ for the bands, 3ν₁ + ν₃ and ν₁ + 3ν₃, respectively. The problem of determination of the intramolecular potential function of SO₂ is discussed.     

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.     

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).     

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.     

The ν2, ν5 Raman band system of CH3F

The anisotropic and isotropic components of the ν₂, ν₅ rotation-vibrational Raman bands of ¹³CH₃F were obtained separately. The two upper states are coupled by a strong second-order Coriolis resonance. The anisotropic spectrum was analyzed by means of a program system due to R. Escribano. A contour simulation and a least-squares fit of 233 assigned transitions yielded values for ν₅, ΔA₅, ΔA₂, and Aζ_{5a, 5b^(z)}. The ¹³C shifts of ν₂ and ν₅ were obtained from the isotropic spectrum.     

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.     

The ν2 and 2ν2 - ν2 bands of N O2: Electron Spin-Rotation and Hyperfine Contact Resonances in the (010) Vibrational State

High-resolution Fourier transform spectra covering the 720-920 cm⁻¹ spectral region have been used to perform a reanalysis of the ν₂ band ((010)-(000) vibrational transition) together with the first analysis of the 2ν₂ - ν₂ hot band of nitrogen dioxide ((020)-(010) vibrational transition). The high-quality spectra show that, for numerous ν₂ lines, the hyperfine structure is easily observable in the case of resonances due to the hyperfine Fermi-type operator. By performing a full treatment of the spin-rotation and of the hyperfine operators, a new line list of the ν₂ band (positions and intensities) has been generated, and it is in excellent agreement with the experimental spectrum. Also, a thorough analysis of the 2ν₂ - ν₂ hot band has been performed leading to an extended set of new (020) spin-rotation levels. These levels, together with the {(100), (020), (001)} spin-rotation levels deduced previously from the analysis of the ν₁, 2ν₂, and ν₃ cold bands performed in the 6.3- to 7.5-μm spectral range [A. Perrin, J.-M. Flaud, C. Camy-Peyret. A.-M. Vasserot, G. Guelachvili, A. Goldman, F. J. Murcray, and R. D. Blatherwick, J. Mol. Spectrosc.154, 391-406 (1992)] were least-squares fitted, allowing one to derive a new set of vibrational band centers and rotational, spin-rotation, and interaction constants for the {(l00)(020)(001)} interacting states of ¹⁴N ¹⁶O₂.     

The ν1 and ν3 stretching fundamental bands of PD3

The infrared (IR) spectrum of PD₃ has been recorded in the 1580–1800 cm⁻¹ range at a resolution of 0.0027 cm⁻¹. About 2400 rovibrational transitions with J^′=K^′22 have been measured and assigned to the ν₁ (A₁) and ν₃ (E) stretching fundamentals. These include 506 “perturbation-allowed” transitions with selection rules Δ(k−l)=±3. Splittings of the K^′′=3 lines have been observed. Effects of strong perturbations are evident in the spectrum. Therefore the rovibrational Hamiltonian adopted for the analysis explicitly takes into account the Coriolis and k-type interactions between the v₁=1 and v₃=1 states, and includes also several essential resonances within these states. The rotational structure in the v₁=1 and v₃=1 vibrational states up to J^′=K^′=18 was reproduced by fitting simultaneously all experimental data. Thirty-four parameters reproduced 1950 transitions retained in the final cycle with a standard deviation of the fit equal to 4.9 × 10⁻⁴ cm⁻¹ (about the precision of the experimental measurements).     

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.     

High-Resolution Infrared and Millimeter-Wave Study of the v(3) = 1 State of HSiF(3) and DSiF(3)

Millimeter-wave spectra of HSiF₃ and DSiF₃ in the v₃ = 1 excited state have been measured from 100 to 490 GHz. Infrared spectra have been recorded in the ν₃ regions, ν₀ 424.0301 and 420.9320 cm⁻¹ in HSiF₃ and DSiF₃, respectively, with a resolution of 2.4 × 10⁻³ cm⁻¹. Since in both species the parameters α^B₃ and α^C₃ have very similar values, no K structure could be resolved in the ^QP and ^QR clusters for low-to-medium K values. For high J the effect of the ground state D_JK term more and more dominates and spreads the J clusters into opposite directions such that medium-to-high K components, particularly those with K = 3p, are resolved. Rotational and infrared data have been fitted together using a model up to sextic centrifugal distortion constants. No perturbations were indicated. Hot bands (ν₃ + nν₆)–nν₆ with n = 1, 2, and 3 have been detected and analyzed.     

Spectroscopic Study of the v6=1 and v8=1 Vibrational States of Formic Acid, HCOOH: New Assignments of Laser Transitions

The FTIR spectra of the Coriolis-coupled ν₆ and ν₈ bands of formic acid, HCOOH, were measured with a resolution of ca. 0.003 cm⁻¹. A total of 4878 and 1203 transitions of the ν₆ and ν₈ bands with J′ values up to 70 and 44, respectively, were assigned. A combined fit of the assigned FTIR transitions together with the available microwave, laser-saturated, and newly measured millimeter- and submillimeter-wave transitions made it possible to improve significantly the parameters of these states and to determine for the first time five new coupling parameters. The RMS deviation of the infrared data was 0.00022 cm⁻¹. Thirteen previously unassigned optically pumped transitions have been identified.     

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.