Choice of the reduction and of the representation in centrifugal distortion analysis: A case study of dimethylsulfoxide

The millimeter-wave and submillimeter-wave spectra of dimethylsulfoxide have been measured up to 660 GHz, corresponding to maximum values of J = 70 and K_c = 68. A total of 3331 transitions (corresponding to 2133 distinct frequencies) were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although dimethylsulfoxide 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) but the least-squares system of normal equations is better conditioned with representation I^r. These results are compared to those obtained for a few typical molecules.     

The high-resolution infrared spectrum of pyrrole between 900 and 1500 cm revisited

The Fourier transform gas-phase infrared spectrum of pyrrole, C₄H₅N, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the 900-1500 cm⁻¹ spectral region. Four fundamental bands, ν₈(A₁; 1016.9 cm⁻¹), ν₂₃(B₂; 1049.1 cm⁻¹), ν₇(A₁; 1074.6 cm⁻¹), ν₂₀(B₂; 1424.4 cm⁻¹) and the overtone band 2ν₁₆(A₁; 962.7 cm⁻¹) have been analysed using the Watson model. The ν₈ and 2ν₁₆ bands are unperturbed; the ν₇ and ν₂₃ bands are locally perturbed, while the ν₂₀ band is globally perturbed by weak c-Coriolis resonance. Upper state vibrational term values, and rotational and centrifugal distortion constants, have been obtained from fits using S-reduction and I^r-representation as well as A-reduction and III^r-representation. A set of ground state rotational and centrifugal distortion constants using A-reduction was obtained from a simultaneous fit of ground state combination differences from all five bands and previous microwave and millimetre-wave data.     

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.     

The high-resolution FTIR spectrum of the ν6 band of C2H3D

The absorption spectrum of the ν₆ band of C₂H₃D centered near 1125.27674 cm⁻¹ in the 1100-1250 cm⁻¹ region was recorded with an unapodized resolution of 0.0063 cm⁻¹ using a Fourier transform infrared (FTIR) spectrometer. A total of 947 infrared transitions of the A-B hybrid-type band were assigned and fitted to upper-state (ν₆ = 1) rovibrational constants using a Watson’s A-reduced Hamiltonian in the I^r representation up to eighth-order centrifugal distortion terms. The b-type infrared transitions of the band were analyzed for the first time. The root-mean-square deviation of the fit was 0.00062 cm⁻¹. The ground-state rovibrational constants up to eighth-order terms were also obtained by a fit of 617 combination differences from the present infrared measurements, simultaneously with 21 microwave frequencies with a root-mean-square deviation of 0.00055 cm⁻¹. From this work, the upper-state (ν₆ = 1) and ground-state constants of C₂H₃D were derived with the highest accuracy, so far. The a- and b-type transitions of the hybrid ν₆ band were found to be relatively free from local frequency perturbations. The ratio of the a- to b-type vibrational dipole transition moments (μ_a/μ_b) was found to be 1.05 ± 0.10. From the ν₆ = 1 rovibrational constants obtained, the inertial defect Δ₆ was calculated to be 0.3570 ± 0.0008 μŲ.     

High-resolution FTIR spectrum of the ν12 band of ethylene-d (C2H3D)

The infrared absorption spectrum of the ν₁₂ fundamental band of ethylene-d (C₂H₃D) has been recorded with an unapodized resolution of 0.004 cm⁻¹ in the wavenumber range of 1340-1460 cm⁻¹ using the Fourier transform technique. By assigning and fitting a total of 870 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation, three rotational and five quartic centrifugal distortion constants for the upper state (v₁₂ = 1) were determined for the first time. The rms deviation of the fit was 0.00044 cm⁻¹ which is close to the experimental precision of the absorption lines. The A-type ν₁₂ band centred at 1400.762811 ± 0.000041 cm⁻¹was found to be relatively free from local frequency perturbations. The inertial defect Δ₁₂ was found to be 0.20928 ±  0.00002 μŲ.     

Improved rovibrational constants for the ν12 band of C2H3D

The Fourier transform infrared absorption spectrum of the ν₁₂ fundamental band of ethylene-d (C₂H₃D) was recorded at an unapodized resolution of 0.0063 cm⁻¹ in the 1330-1475 cm⁻¹ region. Upper state (ν₁₂ = 1) rovibrational constants inclusive of three rotational, five quartic, and four sextic centrifugal distortion constants were improved by assigning and fitting 1444 infrared transitions using Watson’s A-reduced Hamiltonian in the I^r representation. The present analysis yielded more higher-order upper state constants than previously reported. The rms deviation of the fit is 0.00055 cm⁻¹. Improved ground state rovibrational constants were also determined from the combined fit of 2026 ground state combination differences (GSCD) from the assigned infrared transitions of the ν₁₂, ν₃ and ν₆ bands and 21 microwave frequencies of C₂H₃D. The rms deviation of the GSCD fit is 0.00047 cm⁻¹. The A-type ν₁₂ band is centered at 1400.76262 ± 0.00004 cm⁻¹. Local frequency perturbations were not detected in the analysis. The calculated inertial defect Δ₁₂ is 0.20809 ± 0.00003 μŲ.     

High-resolution infrared and microwave study of the ν20 and ν21 levels near 300 cm in 1,2,4-triazine

The gas phase far-IR spectrum of the ν₂₀ (A″, 367.88 cm⁻¹) and ν₂₁ (A″, 311.28 cm⁻¹) bands of 1,2,4-triazine, a five membered ring having the point group C_s, has been studied at a resolution ranging from 0.002 to 0.003 cm⁻¹. From the MW spectrum 58 transitions in the ν₂₀ level and 64 in the ν₂₁ level have been assigned. The ν₂₀ and ν₂₁ modes which are due to non-planar motions of the ring system are found to be nearly unperturbed. From a simultaneous analysis of IR and MW transitions band centers, rotational constants, and the quartic centrifugal distortion constants , and δ_K have been obtained using the Watson Hamiltonian, A-reduction, III^r-representation.     

Ground state parameters of BiH3 from infrared and millimeter-wave spectra: ground state and equilibrium structures

Unstable, short-lived BiH₃ has been synthesized and investigated by rotational spectroscopy in the range 158 (J=1-0) to 1280 GHz (J=8-7). Quadrupole and spin-rotation hyperfine structures (eQq=584.676(96) MHz), and the A₁A₂ splitting of the K=3 ground state level, have been resolved. By merging the pure rotational data with 1764 ground state combination differences obtained from the analysis of high resolution Fourier transform infrared spectra of the ν₁-ν₄ bands [J. Mol. Spectrosc. (2004) (in press)] spanning J and K values up to 16 and 14, respectively, with 0?ΔK?9, the ground state rotational and centrifugal distortion constants up to octic and sextic terms for reductions A and B, respectively, have been determined. Of the reductions of the ground state rovibrational Hamiltonian, reduction B including ε rather than h₃ as off-diagonal element is clearly favored. An experimental r₀ structure of the very-near spherical oblate symmetric top BiH₃, r(BiH)=178.82 pm and α(HBiH)=90.320°, has been deduced from the rotational constants B₀=2.64160172(18) and C₀=2.6010403(31) cm⁻¹. The derived experimental r_e structure, r_e(BiH)=177.834(50) pm and α_e(HBiH)=90.321(10)°, was determined. This is in excellent agreement with the most recent ab initio structure, r_e(BiH)=177.84 pm, and α_e(HBiH)=90.12°.     

The harmonic force field and rz structure of HNCO

The presently available microwave, millimeter wave, and far-infrared data of five isotopic species of isocyanic acid, namely, HNCO, H¹⁵NCO, HN¹³CO, HNC¹⁸O, and DNCO, have been used to obtain improved values of the ground-state rotational constants, the five quartic distortion constants, and some higher-order distortion constants in the I^rS reduced Hamiltonian of Watson. The appropriate planarity relation among the quartic centrifugal distortion constants has been imposed in the fitting procedure. The general harmonic force field of isocyanic acid has been determined using all existing data, and assuming a trans bent equilibrium geometry of the molecule with an NCO angle of 170°. Finally an r_z structure has been obtained using the A_z, B_z, and C_z rotational constants of five isotopic species. The bending of the NCO chain is found to be 8° in the trans configuration.     

The ν12 band of ethylene-1-C (CCH4) by high-resolution FTIR spectroscopy

The Fourier transform infrared (FTIR) spectrum of the ν₁₂ fundamental band of ethylene-1-¹³C (or ¹³C¹²CH₄) was recorded with an unapodized resolution of 0.0063 cm⁻¹ in the wavenumber region of 1360-1520 cm⁻¹. Rovibrational constants for the upper state (ν₁₂ = 1) up to five quartic and two sextic centrifugal distortion terms were derived for the first time by assigning and fitting a total of 879 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation. The root-mean-square deviation of the fit was 0.00066 cm⁻¹. The ground state rovibrational constants were also determined by a fit of 523 combination-differences from the present infrared measurements, with a rms deviation of 0.00090 cm⁻¹. The A-type ν₁₂ band which is centred at 1439.34607 ± 0.00004 cm⁻¹ was found to be relatively free from local frequency perturbations. From the ν₁₂ = 1 rovibrational constants obtained, the inertial defect Δ₁₂ was found to be 0.242826 ± 0.000002 μŲ.     

High-resolution infrared study of collisionally cooled trans-1,2-dichloroethylene

A recently constructed long-path enclosive flow cooling apparatus is employed to obtain the Fourier transform gas-phase infrared absorption spectrum of natural isotopic trans-1,2-dichloroethylene with a resolution of 0.00190 cm⁻¹ in the 800-1000 cm⁻¹ spectral region. The rotational structure of the out-of-plane CH flapping fundamental has been analyzed for the isotopic analogues ³⁵Cl₂ and ³⁵Cl³⁷Cl using the Watson A-reduced Hamiltonian model and I^r-representation. A ground-state combination difference analysis for the ³⁵Cl³⁷Cl isotopomer based on 1402 assigned transitions belonging to the ν₆ band yields a band origin of 897.94493(10) cm⁻¹ and values for the ground-state rotational constants: A₀ = 1.7466454(44) cm⁻¹, B₀ = 0.05019643(82) cm⁻¹ and C₀ = 0.04877977(82) cm⁻¹ together with quartic centrifugal distortion constants. The red-shift of 0.00444(10) cm⁻¹ observed for the ν₆ band origin of ³⁵Cl³⁷Cl relative to the ³⁵Cl₂ band origin is now consistent with the Rayleigh rule.     

A high-resolution infrared study of five bands of 1,2,5-thiadiazole in the range 750-1250 cm, together with ab initio and DFT studies

The Fourier transform gas-phase IR spectrum of 1,2,5-thiadiazole, C₂H₂N₂S, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the wavenumber region 750-1250 cm⁻¹. Five fundamental bands in this region, ν₄ (A₁), ν₅ (A₁), ν₁₁ (B₁), ν₁₃ (B₁), and ν₁₄ (B₂), have been analysed by the Watson Hamiltonian model to yield ground-state rotational and quartic centrifugal distortion constants as well as upper-state spectroscopic constants. A global perturbation of the ν₄ level is explained by Fermi resonance with the 2ν₁₅ level which has been located from its resonance effect. Rotational constants, harmonic and anharmonic frequencies have been calculated using a cc-pVTZ basis, at the MP2 and B3LYP methodology levels, and compared with the experimental data.     

Ritz assignment and Watson fits of the high-resolution ring-puckering spectrum of oxetane

Oxetane is a four-membered ring molecule exhibiting a large-amplitude ring-puckering motion. In order to analyze this vibration we recorded a rotationally resolved far-infrared spectrum between 50 and 145 cm⁻¹. The analysis of the ring-puckering fundamental band with the assignment of 1108 lines, has been presented in a previous paper. In the present work we present a list of further 6531 assigned transitions between the five lowest excited ring-puckering states. The 4983 term values involved in the transitions assigned in this and in the preceding work have been evaluated by the “Ritz” program, and are now available. An A-reduced Watson Hamiltonian in any of the three representations I^r, II^r, and III^r was used to perform a fit of the assigned transitions. Precise rotational constants and quartic as well as a full set of sextic centrifugal distortion constants were obtained for the investigated ring-puckering states. For the first time, high-resolution values for the vibrational G_v parameters have been obtained, and we have added terms in x⁶ and x⁸ to the double minimum-potential well describing the ring-puckering motion, in order to reproduce their values within the experimental accuracy. The same potential still reproduces the lower resolution values of the Q-branch origins involving higher ring-puckering states up to v_rp=14 found in the previous literature.     

High-resolution FTIR measurement of the 2ν8 band of methylene fluoride (CH2F2)

A high-resolution (0.003 cm⁻¹) infrared absorption spectrum of the first overtone of the fundamental mode ν₈ of methylene fluoride (CH₂F₂) has been measured on a Bruker IFS 120-HR Fourier transform infrared spectrometer. More than 2000 ro-vibration transitions in the range of 2770-2900 cm⁻¹ with J ? 45 and K_a ? 20 have been assigned in this B-type band centered at 2838.5 cm⁻¹. Precise value for the band origin (2838.579799 cm⁻¹) and centrifugal distortion constants up to third order (Φ_JK, Φ_KJ, and Φ_K) have been obtained by fitting a total of 1474 unblended ro-vibration transitions (J ? 45 and K_a ? 13) of the 2ν₈ band with a standard deviation of 0.00029 cm⁻¹ using a Watson’s A-reduced Hamiltonian in the I^r representation. Signature of perturbations with nearby states has been seen.     

Ground-state constants, ab initio anharmonic force field, and equilibrium structure of F2BOH

The millimeterwave spectra of F₂¹⁰BOH and F₂¹¹BOH (difluorohydroxyborane) have been measured in their ground vibrational state. Accurate rotational and centrifugal distortion constants have been determined. The equilibrium geometry and anharmonic force fields have been calculated at the CCSD(T) level of theory. The ab initio centrifugal distortion constants and rotation-vibration interaction constants are compared to the experimental values. Some discrepancies are found and discussed. Particularly, it is explained why the semi-experimental structure is not reliable. The best equilibrium structure is: r_e(BF_cis) = 132.29 pm, r_e(BF_trans) = 131.29 pm, r_e(BO) = 134.48 pm, r_e(OH) = 95.74 pm, ∠_e(FBF) = 118.36°, ∠_e(F_cisBO) = 122.25°, and ∠_e(BOH) = 113.14°.     

High-resolution FTIR measurement and analysis of the ν3 band of C2H3D

The Fourier transform infrared (FTIR) spectrum of the ν₃ band of C₂H₃D was measured at an unapodized resolution of 0.0063 cm⁻¹ in the 1240-1340 cm⁻¹ region. Rovibrational constants for the upper state (ν₃ = 1) up to five quartic and two sextic centrifugal distortion terms had been obtained by assigning and fitting a total of 1037 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation. The root-mean-square deviation of the fit was 0.00051 cm⁻¹. The ground state rovibrational constants were also determined by a fit of 674 combination differences together with 21 microwave frequencies from the present infrared measurements with a root-mean-square deviation of 0.00040 cm⁻¹. The upper state (ν₃ = 1) and ground state rovibrational constants of C₂H₃D represent the most accurate values obtained so far. The A-type ν₃ band, centred at 1288.788826 ± 0.000044 cm⁻¹ was found to be relatively free from local frequency perturbations. From the ν₃ = 1 rovibrational constants obtained, the inertial defect Δ₃ was 0.1619724 ± 0.0000001 μŲ.     

Analysis of rotational structure in the high-resolution infrared spectrum and assignment of vibrational fundamentals of butadiene-2,3-C2

The 2,3-¹³C₂ isotopomer of butadiene was synthesized, and its fundamental vibrational fundamentals were assigned from a study of its infrared and Raman spectra aided with quantum chemical predictions of frequencies, intensities, and Raman depolarization ratios. For two C-type bands in the high-resolution (0.002 cm⁻¹) infrared spectrum, the rotational structure was analyzed. These bands are for ν₁₁ (a_u) at 907.17 cm⁻¹ and for ν₁₂ (a_u) at 523.37 cm⁻¹. Ground state and upper state rotational constants were fitted to Watson-type Hamiltonians with a full quartic set of centrifugal distortion constants and two sextic ones. For the ground state, A₀ = 1.3545088(7) cm⁻¹, B₀ = 0.1469404(1) cm⁻¹, and C₀ = 0.1325838(2)  cm⁻¹. The small inertial defects of butadiene and two ¹³C₂ isotopomers, as well as for five deuterium isotopomers as previously reported, confirm the planarity of the s-trans rotamer of butadiene.     

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.     

The high-resolution infrared spectrum of thiophene between 600 and 1200 cm: A spectroscopic and theoretical study of the fundamental bands ν6, ν7, ν13, and the c-Coriolis interacting dyad ν5, ν19

The Fourier transform infrared spectrum of gaseous thiophene, C₄H₄S, has been recorded in the 600-1200 cm⁻¹ spectral region with a resolution of ca. 0.0030 cm⁻¹. Five fundamental bands ν₁₃ (B₁, 712.1 cm⁻¹), ν₇ (A₁; 840.0 cm⁻¹), ν₆ (A₁; 1036.4 cm⁻¹), ν₅ (A₁; 1081.5 cm⁻¹) and ν₁₉ (B₂; 1084.0 cm⁻¹) have been analysed by the standard Watson model (A-reduction). Ground state rotational and quartic centrifugal distortion constants have been obtained from a simultaneous fit of ground state combination differences from four of these bands and previous microwave transitions. Upper state spectroscopic constants have been obtained for all five bands from single band fits using the Watson model. A strong c-Coriolis resonance perturbs the close lying ν₅ and ν₁₉ bands. We have analysed this dyad system by a model including first and second order Coriolis resonance using the theoretically predicted Coriolis coupling constant . From this analysis we locate the previously unobserved ν₁₉ band at 1083.969 cm⁻¹. 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 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.     

A study of the AΠ-XΣ and BΣ-XΣ band systems of scandium monosulfide, ScS, using Fourier transform emission spectroscopy and laser excitation spectroscopy

Emission spectra of the A²Π_3/2-X²Σ⁺ (0, 1), (0, 0), and (1, 0) bands and the B²Σ⁺-X²Σ⁺ (0, 1), (0, 0), (1, 0), (2, 0), and (3, 1) bands of ScS have been recorded in the 10 000-13 500 cm⁻¹ region at a resolution of 0.05 cm⁻¹ using a Fourier transform (FT) spectrometer. The A²Π_r-X²Σ⁺ (1, 0) band as well as the B²Σ⁺-X²Σ⁺ (0, 0) and (1, 0) bands have been recorded at high resolution (±0.001 cm⁻¹) by laser excitation spectroscopy using a supersonic molecular beam source. The FT spectral features range up to N = 148, while those recorded with the laser cover the “low-N” regions. The lines recorded with the laser exhibit splittings due to the ⁴⁵Sc (I = 7/2) magnetic hyperfine interactions, which are large (∼6.65 GHz) in the X²Σ⁺ state and much smaller in the B²Σ⁺ and A²Π states. The energy levels were modeled using a traditional ‘effective’ Hamiltonian approach, and improved spectroscopic constants were extracted and compared with previous determinations and theoretical predictions.