Centrifugal distortion analysis of the rotational spectrum of aziridine: Comparison of different Hamiltonians

Previous measurements of rotational spectrum of aziridine up to 1.85 THz have been supplemented by new data in 225-660 GHz frequency range. A total of 1465 transitions (915 of them are newly assigned ones) with maximum values of J = 59 and K_c = 50 were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although aziridine is an asymmetric oblate top, the combination (A, III^r) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination (S, III^r). It is explained that the failure of the combination (A, III^r) is due to the large value of the parameter σ=(2C-A-B)/(A-B) which makes some sextic centrifugal distortion constants much too large impeding the convergence of the Hamiltonian. It is also shown that the calculation of the centrifugal distortion constants from a force field is sometimes an ill-conditioned operation. Finally, the use of a non-reduced Hamiltonian (with six quartic centrifugal distortion constants) was successful in the particular case thanks to the method of predicate observations.     

Determination of the spin-spin centrifugal distortion parameters for deuterated selenoformaldehyde in its first excited triplet state

Recently-formulated centrifugal distortion corrections to the spin-spin Hamiltonian have been used to analyse the first excited triplet state (ã³A₂) of deuterated selenoformaldehyde. By including six spin-spin centrifugal distortion parameters, it is possible to account for the energy levels of this state using a single set of three rotational constants, A, B, and C, where previously nine spin-dependent parameters were required.     

FTIR spectra of the ν6 and ν8 bands of C formic acid molecule—Assignment of FIR-laser lines

Two interacting vibrational modes ν₆ and ν₈ of ¹³C species of formic acid have been studied with high resolution FTIR spectroscopy in the range 900-1300 cm⁻¹ with an instrumental resolution of 0.0018 cm⁻¹. More than 10 000 lines have been assigned and fitted with a RMS deviation of 0.00024 cm⁻¹. The band centers, as well as the rotational, quartic and sextic centrifugal distortion parameters and 6 interaction parameters have been determined. The obtained parameters have enabled the assignments of 24 FIR laser emissions of this molecule observed previously by Dangoisse and Glorieux [D. Dangoisse, P. Glorieux, J. Mol. Spectrosc. 92 (1982) 283-297], Luis et al. [G.M.R.S. Luis, E.M. Telles, A. Scalabrin, D. Pereira, IEEE J. Quantum. Electron. QE-34 (1998) 767-769], and Bertolini et al. [A. Bertolini, G. Carelli, C.A. Massa, A. Moretti, F. Strumia, Infrared Phys. Technol. 40 (1999) 33-36].     

The forbidden rotational Q branch of CH3SiF3: A study in internal rotation

The pure rotational spectrum driven by the small dipole moment produced perpendicular to the symmetry axis by centrifugal distortion has been investigated for CH₃SiF₃ in the ground vibrational state using a Fourier transform waveguide spectrometer. Between 10.9 and 17.0 GHz, four (k + 3 ← k) series in the Q branch have been measured in the lowest torsional state v₆ = 0 for k = 4, 5, 6, and 7 with 54 ? J ? 65. In each transition, the quantum number σ = 0, +1, −1 labelling the different torsional sub-levels is conserved. For given (J,k), splittings from ∼10 to ∼45 MHz have been observed between lines with different values of σ. The global data set includes the anticrossing molecular beam energy differences of [W.L. Meerts, I. Ozier, Chem. Phys. 71 (1982) 401-415] as well as the mm-wave R branch frequencies and (A₁ − A₂) splittings of [P. Dréan, J.-M. Colmont, J. Demaison, L. Dore, C. Degli Esposti, J. Mol. Spectrosc. 176 (1996) 23-27]). A good fit was obtained by varying 15 molecular parameters characterizing the torsion-rotation Hamiltonian H_TR for the vibrational ground state. Because of the strong correlation between two of the quartic torsion-distortion parameters (F_0,3K and D_0,Km) and a redundancy connecting the centrifugal distortion constants, four models were obtained yielding comparable fits. In each case, effective values were determined for the A-rotational constant and the height of the potential hindering the internal rotation. A high precision determination of the structural parameter ρ was made that is the same in all four models. For the off-diagonal quartic centrifugal distortion constant ε₀ and the sextic constants H_0,J, H_0,JK, H_0,KJ, and h_0,3, the differences in the values obtained in the two different reductions used have been explained in terms of the redundancy connecting these parameters. For σ = 0, +1, −1, the energy level pattern for (|k| = 3) is discussed for the case where the pure torsional energy splitting and the matrix elements off-diagonal in k are of comparable magnitude. A method is described of using an R branch study of the resulting σ-splittings for (|k| = 3) to probe the zeroth-order torsional Hamiltonian.     

Global effective Hamiltonians of OCO and OCO improved from CW-CRDS observations in the 5900-7000 cm region

The parameters of the polyad models of the effective Hamiltonian of the ¹⁶O¹³C¹⁷O and ¹⁶O¹³C¹⁸O isotopologues of carbon dioxide have been refined by the least-squares fittings to the line positions collected from the literature. Such refinement has become necessary as the observed dataset has been significantly extended by our CW-CRDS observations in the 5900-7000 cm⁻¹ region. In the case of the ¹⁶O¹³C¹⁷O isotopologue, 1151 line positions of 11 bands have been used to refine the effective Hamiltonian parameters published by Chédin [A. Chédin, J. Mol. Spectrosc. 76 (1979) 430-491]. With the obtained set of parameters, the collected line positions are reproduced with a RMS (root mean squares of the residuals) equal to 0.0013 cm⁻¹. In the case of the ¹⁶O¹³C¹⁸O isotopologue, 61 parameters of the effective Hamiltonian were fitted to more than 6410 line positions. A weighted standard deviation of χ = 1.77 and a global RMS of 0.0017 cm⁻¹, close to the experimental accuracy, were achieved. However, several rotational levels of the 31113 state (P = 10) could not be reproduced in the frame of this polyad model and were then excluded from the fit. We found that these levels are affected by an anharmonic resonance interaction with the 51106 vibrational state (P = 11) leading to energy shifts up to 0.060 cm⁻¹ and significant intensity transfer to several extra lines which could be detected. The coupling matrix element has been estimated to 0.11 cm⁻¹ from the detailed analysis of the experimental spectrum. This is the first evidence of an interpolyad resonance interaction in the case of the carbon dioxide molecule. In order to extend the input spectroscopic information, the weak lines left unassigned in our previous analysis of the CW-CRDS spectrum of the ¹³C enriched carbon dioxide [Y. Ding, P. Macko, D. Romanini, V.I. Perevalov, S.A. Tashkun, J.-L. Teffo, S.-M. Hu, A. Campargue, J. Mol. Spectrosc. 226 (2004) 146-160.] have been revisited. Thirteen ¹³C¹⁶O₂ bands, one ¹⁶O¹³C¹⁷O band and two ¹⁶O¹³C¹⁸O bands could be newly assigned together with a number of transitions corresponding to high J values of previously observed bands. The spectroscopic constants G_v, B_v, and D_v for the unperturbed bands have been fitted to the observed line positions.     

CW-cavity ring down spectroscopy of the ozone molecule in the 6625-6830 cm region

The absorption spectrum of ozone, ¹⁶O₃, has been recorded by CW-cavity ring down spectroscopy in the 6625-6830 cm⁻¹ region. The typical sensitivity of these recordings (α_min ∼ 3 × 10⁻¹⁰ cm⁻¹) allows observing very weak transitions with intensity down to 2 × 10⁻²⁸ cm/molecule. 483 and 299 transitions have been assigned to the 2ν₁ + 3ν₂ + 3ν₃A-type band and to the 2ν₁ + 4ν₂ + 2ν₃B-type band, respectively, which are the highest frequency bands of ozone recorded so far under high resolution. Rovibrational transitions with J and K_a values up to 46 and 12, respectively, could be assigned. Despite well-known difficulties to correctly reproduce the energy levels not far from the dissociation limit, it was possible to determine the parameters of an effective Hamiltonian which includes six vibrational states, four of them being dark states. The line positions analysis led to an rms deviation of 8.5 × 10⁻³ cm⁻¹ while the experimental line intensities could be satisfactorily reproduced. Additional experiments in the 5970-6021 cm⁻¹ region allows detecting the (233) ← (010) hot band reaching the same upper state as the preceding cold band. From the effective parameters of the (233) state just determined and those of the (010) level available in the literature, 329 transitions could be assigned and used for a further refinement of the rovibrational parameters of the effective Hamiltonian leading to a value of 7.6 × 10⁻³ cm⁻¹ for the global rms deviation. The complete list of the experimentally determined rovibrational energy levels of the (233), (242), and (520) states is given. The determined effective Hamiltonian and transition moment operators allowed calculating a line list (intensity cut off of 10⁻²⁸ cm/molecule at 296 K), available as Supplementary material for the 6590-6860 and 5916-6021 cm⁻¹ regions. The integrated band strength values are 1.75 × 10⁻²⁴ and 4.78 × 10⁻²⁵ cm/molecule at 296 K for the 2ν₁ + 3ν₂ + 3ν₃A-type band and to the 2ν₁ + 4ν₂ + 2ν₃B-type band, respectively, while the band intensity value of the (233) ← (010) is estimated to be 1.03 × 10⁻²⁴ cm/molecule.     

High resolution study of the 6ν1 P-H stretching band of the PHD2 molecule

The high resolution spectrum of a phosphine gas mixture containing PHD₂ was recorded at room temperature in the 12 550-12 770 cm⁻¹ region. A high sensitivity laser photoacoustic spectrometer consisting of a longitudinal resonant cell coupled to a Ti:sapphire ring laser was employed. More than 600 transitions were assigned to the 6ν₁ overtone band of PHD₂ up to J^max=20, K_a^max=6. A Hamiltonian model developed up to the octic centrifugal distortion terms was used. Seven rotational and centrifugal distortion parameters were fitted, the other ones being fixed to their values linearly extrapolated from ν₁ and 2ν₁. The derived parameters reproduce the initial data within the experimental uncertainties. The isolated character of the P-H bond is confirmed.     

Fourier transform spectroscopy of CO2 and OCO in the 3800-8500 cm region and the global modeling of the absorption spectrum of CO2

The absorption spectrum of the ¹⁸O enriched carbon dioxide has been recorded at Doppler limited resolution with a Fourier transform spectrometer in the spectral range 3800-8500 cm⁻¹. Seventeen cold bands (14Σ-Σ and 3Σ-Π) and nine hot bands (9Π-Π) of ¹²C¹⁸O₂, nineteen cold bands (18Σ-Σ and 1Σ-Π) and eighteen hot bands (6Σ-Σ, 9Π-Π and 3Δ-Δ) of ¹⁶O¹²C¹⁸O have been observed. Among them, 14 ¹²C¹⁸O₂ bands and 12 ¹⁶O¹²C¹⁸O bands are observed for the first time. The spectroscopic parameters G_v, B_v, and centrifugal distortion constants, have been determined for all observed bands. Effective Hamiltonian parameters for the ¹²C¹⁸O₂ isotopic species are retrieved from the global fitting of the observed line positions presented in this paper and collected from the literature. As the result, 65 obtained effective Hamiltonian parameters reproduce 5443 observed line positions of 73 ¹²C¹⁸O₂ bands with RMS = 0.00145 cm⁻¹.     

Spin Hamiltonian parameters and structural disorder analysis for Cr ion in YGG crystals

A new crystalline lattice distortion model has been proposed, on the basis of it, the relations between spin Hamiltonian parameters and crystal micro structure have been established. By taking into account slight magnetic interactions, including spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions, the local structure of Cr³⁺ ion in YGG crystal has been studied using complete diagonalization method (CDM). The studies show that the local structure in the YGG:Cr³⁺ crystal is of the compressed trigonal distortion. The ligand oxygen plane moved 0.0138 nm toward Cr³⁺ ion along C₃-axis. Accordingly, the SH parameters in YGG:Cr³⁺ crystal are explained successfully.     

On the determination of the reduced rotational operator for polyatomic molecules

Irreducible tensorial sets are used for constructing the reduced rotational Hamiltonian of the molecule, i.e., for obtaining the Hamiltonian with independent rotational, centrifugal distortion, and resonance parameters. General formulas are obtained which allow one to do this, and are valid for molecules of any symmetry. As an illustration of the general results, molecules of T_d symmetry are considered.     

Vibration-rotation interaction in HCNO caused by accidental resonances and enhanced by the quasilinearity of the molecule

The recent assignment of the vibrational spectrum of the quasilinear molecule HCNO revealed several near coincidences between vibrational energy levels involving the two bending modes, ν₄ (skeletal bending mode) and ν₅ (HCN-bending mode), and the lowest-lying stretching mode, ν₃ (NO stretching mode). By considering the correlation between the energy levels of a linear and a bent molecular model of HCNO, it is seen that resonance interactions which would be of third or higher order in a linear molecule Hamiltonian would be of first or second order in the Hamiltonian of a bent molecule, and thus might be significant in the quasilinear molecule HCNO. In this way we were able to identify the type of observed interaction occurring between three pairs of nearly coincident levels, (00010, 00002), (00020, 00012), and (00100, 00004). Anomalous centrifugal distortion effects had been observed and reported earlier for the pure rotational transitions arising from molecules in the 00010, 00020, and 00002 levels. Rotational transitions arising from molecules in the 00004 and 00100 vibrational states of HCNO and the 00100 state of DCNO are reported here for the first time. For two pairs of levels, (00010, 00002) and (00100, 00004), we could determine the magnitude of the coefficients of the interaction matrix elements from an analysis of the centrifugal distortion effects.     

Microwave spectra of HPO and DPO: molecular structure

Microwave spectra of the unstable phosphorus containing molecule, HPO, and its deuterated species were measured in the frequency range of 70-380 GHz. The molecule was produced by a DC-glow discharge of a gas mixture of PH₃, CO₂, and H₂(D₂). Rotational constants and centrifugal distortion constants for HPO and DPO were determined accurately. Harmonic force constants were evaluated from the centrifugal distortion constants determined in the present study, and with vibrational frequencies reported previously. The zero-point average structure for HPO was obtained by taking the isotopic difference of the PH bond length into consideration: r_z(PH)=1.473(7) Å, r_z(PO)=1.4843(9) Å, and θ_z=104.57(16)°. The errors were estimated from the residual inertial defect. Equilibrium bond lengths for the PH and PO bonds were derived as 1.455(7) and 1.4800(9) Å, respectively, by assuming anharmonic constants of the corresponding diatomic molecules.     

High resolution study of AsHD2: Ground state and the three bending fundamental bands ν3, ν4, and ν6

For the first time the infrared spectrum of the AsHD₂ molecule has been measured in the region of the bending fundamental bands ν₃, ν₄, and ν₆ on a Fourier transform spectrometer with a resolution of 0.0024 cm⁻¹ and analyzed. More than 5500 transitions with J^max = 26 have been assigned and used both to obtain “ground state combination differences” and for the determination of upper state ro-vibrational energies of the triad (001000), (000100), and (000001). Rotational parameters including centrifugal distortion coefficients up to octic terms of the ground vibrational state were calculated by fitting more than 500 “ground state combination differences” with J^max and . The obtained set of 24 parameters provides a rms-deviation of 0.00011 cm⁻¹. The upper energies were fitted with 52 parameters of an effective Hamiltonian which takes into account strong resonance interactions between all vibrational states of the triad (001000), (000100), and (000001). The rms-deviation for the energy levels considered in the fit is 0.00014 cm⁻¹.     

Breakdown of the reduction of the rovibrational Hamiltonian: The case of SO2F2

The ground state rotational spectrum of the near-spherical top molecule S¹⁸O₂F₂ (sulfuryl fluoride) has been measured from 50 to 700 GHz. As for the parent isotopologue, S¹⁶O₂F₂ [K. Sarka, J. Demaison, L. Margulès, I. Merke, N. Heineking, H. Bürger, H. Ruland, J. Mol. Spectrosc. 200 (2000) 55-64], it was necessary to use a non-reduced Hamiltonian in order to obtain a satisfactory fit. It was possible to determine six quartic centrifugal distortion constants (instead of five for a standard asymmetric top) and five sextic constants (one of them not existing in the reduced Hamiltonian) could also be determined. This ground state level has also been analysed thanks to a tensorial formalism developed in Dijon. Only two tensorial sextic constants are fixed to zero, all others have been adjusted. Although S¹⁸O₂F₂ is less spherical than S¹⁶O₂F₂, the analysis was more difficult. It is partly due to the fact that S¹⁸O₂F₂ is oblate whereas S¹⁶O₂F₂ is prolate. The experimental quartic centrifugal distortion constants were found in good agreement with those calculated from the force field, confirming the correctness of the analysis.     

CW-cavity ringdown spectroscopy of carbon dioxide isotopologues near 1.5 μm

The absorption spectra of carbon dioxide in natural isotopic abundance and with 99% enrichment in ¹³C have been recorded by CW-cavity ringdown spectroscopy in two specific spectral regions: 5957-6122 and 6745-6833 cm⁻¹. The spectra were obtained at Doppler limited resolution by using a CW-CRDS spectrometer based on fibered DFB lasers. The typical sensitivity of 5 × 10⁻¹⁰ cm⁻¹, allowed for the detection of lines with intensity as weak as 5 × 10⁻²⁹ cm/molecule. More than 2900 line positions of the six major isotopologues contributing to the spectra (¹²C¹⁶O₂, ¹⁶O¹²C¹⁷O, ¹⁶O¹²C¹⁸O, ¹³C¹⁶O₂, ¹⁶O¹³C¹⁷O and ¹⁶O¹³C¹⁸O), were measured and assigned on the basis of their respective global effective Hamiltonian models. For comparison, only 507 lines are provided by the HITRAN database in these spectral regions. The band by band analysis has led to the determination of the rovibrational parameters of a total of 52 bands, 30 of them being newly reported. Most of the observed line positions show an agreement close to the experimental uncertainty (1-2 × 10⁻³ cm⁻¹) with the predictions of their respective effective Hamiltonian models. However, the quality of the predictions degrades for the minor isotopologues reaching maximum deviations of 0.35 cm⁻¹ in one specific case. For several bands, rovibrational transitions with J values between 60 and 90 could be newly detected. While an excellent agreement is observed with the line positions predicted by the Hamiltonian models, the comparison of these observations with the line positions listed in the HITRAN database or extrapolated by using the best FTS rotational constants available in the literature has evidenced significant deviations.     

The pure rotational spectrum of TiS (XΔr) at submillimeter wavelengths

The pure rotational spectrum of TiS in its X³Δ_r ground state has been measured using millimeter-wave direct-absorption techniques in the frequency range of 313-425 GHz. This free radical was created by the reaction of titanium vapor, produced in a high-temperature Broida-type oven, with H₂S. Eight to ten rotational transitions were recorded for the main titanium isotopologue, ⁴⁸TiS, in the v = 0 and v = 1 levels, as well as for the v = 0 state of ⁴⁶TiS, observed in natural abundance (⁴⁸Ti:⁴⁶Ti = 74:8). All three Ω components were observed in almost every recorded transition, with no evidence for lambda-doubling. The data were fit with a Hund’s case(a) Hamiltonian, and rotational, spin-orbit, and spin-spin constants were determined, as well as equilibrium parameters for ⁴⁸TiS. Relatively few fine structure parameters were needed for the analysis of TiS (A, A_D, and λ), unlike other 3d metal species. The rotational pattern of the three fine structure components suggests the presence of a nearby excited ¹Δ state, lying ∼3000 cm⁻¹ higher in energy. From the equilibrium parameters, the dissociation energy for TiS was estimated to be ∼5.1 eV, in reasonable agreement with past thermochemical data.     

Fourth-order centrifugal distortion coefficients for the nonlinear XYZ molecule

Detailed expressions in terms of fundamental molecular parameters are given for the ten fourth-order centrifugal distortion constants of the nonlinear XYZ molecule. The calculation of these coefficients is based on the Darling-Dennison Hamiltonian in the Nielsen-Amat-Goldsmith expansion.     

Cyanoketene: the microwave spectrum and structure of an unstable molecule

The unstable molecule cyanoketene has been prepared by pyrolysis in a flow system, and the microwave spectra of five isotopic species, a- and b-type, have been measured in the frequency range from 8 to 40 GHz. Precise rotational constants and centrifugal distortion parameters up to the sixth order were obtained. The molecule has been shown to be planar, and a reliable structure was derived. Also the N-quadrupole coupling constants and the dipole moment components have been determined. The results could be a basis for interstellar spectroscopy of this molecule.     

Microwave spectroscopy of furfural in vibrationally excited states

The results of microwave spectrum investigation of the excited vibrational states of furfural in the frequency range between 49 and 149 GHz are reported. In total 15 excited vibrational states (9 for trans-furfural and 6 for cis-furfural) were assigned and analyzed. Six of the 15 investigated states were assigned for the first time. Accurate values of rigid rotor and quartic centrifugal distortion constants of asymmetric top Hamiltonian have been determined for 13 excited states. Also for some states several sextic and octic level constants were needed in order to fit the data within experimental accuracy. The v_t = 3 and v_s = 1, v_a = 1 states of trans-furfural were found to be strongly perturbed and only rotational transitions with low K_a values can be reliably identified in this study.     

Vibration-internal rotation-rotation Hamiltonian of an asymmetric top molecule with C3v internal rotor

An expression for the kinetic energy part of the vibration-torsion-rotation Hamiltonian of an asymmetric top molecule containing a C_3v internal rotor has been derived. The terms for various interactions in the molecule, viz. Coriolis interaction between rotation (both overall and internal rotation) and vibration, centrifugal distortion and anharmonicity of molecular vibrations induced by the internal, and overall rotation of the molecule, have been formulated. For a planar molecule with C_s symmetry we have obtained the vibrationally averaged rotation-internal rotation Hamiltonian. Diagonalization of this Hamiltonian for a particular vibrational state will yield the rotation-internal rotation energy levels and hence the transition frequencies. These data will be useful for analysis of high-resolution infrared spectra obtained by laser or Fourier transform spectroscopy of nonrigid molecules with internal rotor. We also present a set of quartic centrifugal distortion coefficients associated with rotation and internal rotation. These data will be helpful for evaluation of vibrational potential constants of the orthorhombic asymmetric top molecules.