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.     

The Forbidden RotationalQ-Branch of CH3CF3: Torsional Properties and (A1−A2) Splittings

The pure rotational spectrum driven by the small distortion dipole moment perpendicular to the symmetry axis has been investigated between 8 and 18 GHz for CH₃CF₃in the ground vibrational state using a pulsed Fourier transform waveguide spectrometer. This molecule has been selected as a prototype for the case of a symmetric top with small (∼500 kHz) torsional energy splittings in the ground torsional state (ν₆= 0). In this state, six (k± 3 ←k)Q-branch series have been measured for lower stateK= |k| between 3 and 8 with 27 ≤J≤ 75. For (ν₆= 1), three series with lower stateKbetween 5 and 7 with 49 ≤J≤ 66 have been observed. In two of these series, the torsional fine structure extending over ∼6.8 MHz has been fully resolved. The (A₁−A₂) splitting has been measured in the (ν₆= 0) series (K= 6 ← 3) for 37 ≤J≤ 74. The global data set of 443 frequencies included avoided-crossing molecular-beam splittings of Meerts and Ozier (1991.Chem. Phys.152, 241–259) and mm-waveR-branch measurements of Bocquetet al.(1994.J. Mol. Spectrosc.165, 494–499). In a weighted least-squares analysis, a good fit was obtained by varying 18 parameters in a Hamiltonian that represented both the torsional effects and the sextic splittings. Effective values have been determined for both rotational constants, eight torsional parameters including the barrier height, six diagonal centrifugal distortion constants, and two centrifugal distortion constants (? and ?_J) that characterize the (Δk= ±3) matrix elements. The difficulties are discussed that arise in defining a unique model for the torsional terms in the Hamiltonian when a high barrier symmetric top is investigated by distortion moment spectroscopy. The redundancies are investigated that exist in the quartic and sextic Hamiltonian for a near-spherical top such as CH₃CF₃.     

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.     

Microwave spectrum of CH3OD

The microwave spectrum of CH₃OD has been observed in the frequency region between 14 and 92 GHz. All the ground-state transitions with J ≤ 8 and J = 2 ← 1, a-type transitions in the excited torsional states (v = 1 and v = 2) have been observed. The spectrum has been analyzed and rotational constants, torsional constants, torsion-vibration-rotation interaction constants, and centrifugal distortion constants have been evaluated. The Stark effect measurements have been made and the dipole moment components have been determined as μ_a = 0.833 ± 0.008 D and μ_b = 1.488 ± 0.015 D.     

The ν3 bands of HOBr around 16 μm measured by high-resolution Fourier-transform spectroscopy

The ν₃ bands of HOBr around 16 μm have been recorded using high-resolution Fourier-transform absorption spectroscopy. More than 800 lines of the two main isotopomers, HO⁷⁹Br and HO⁸¹Br, with K_a values up to 4 and J values up to 41 have been assigned. Rotational and centrifugal distortion constants of the v₃=1 states were determined from a non-linear least-squares fit using an A-reduced Watson-type Hamiltonian. The results improve Hamiltonian constants determined previously from microwave spectroscopy, and accurate vibrational band centers are determined for the first time: 620.22855 (25) and 618.90606 (25) cm⁻¹ for the HO⁷⁹Br and HO⁸¹Br isotopomers, respectively.     

Millimeter-wave spectrum of 3-butynenitrile: Dipole moment and centrifugal distortion constants

The molecular rotational spectrum of 3-butynenitrile (3BN, propargyl cyanide), HCCCH₂CN, has been investigated in the vibrational ground state. A total of 222 transitions up to J = 69 have been measured between 8 and 300 GHz. The Hamiltonian used for the spectral analysis was required to include all centrifugal terms of fourth and sixth orders and one term of eighth order in the angular momentum components in order to reproduce the transition frequencies within the experimental error. Significant values for the respective distortion coefficients could be determined. The molecular dipole moment components were calculated from measured Stark effect shifts as |μ_a| = (3.23 ± 0.05) D, |μ_b| = (2.34 ± 0.02) D; μ_tot = (3.99 ± 0.05) D.     

Microwave spectrum of chlorine nitrate (ClNO3)

Microwave spectra of chlorine nitrate (³⁵ClNO₃ and ³⁷ClNO₃) in the ground and first excited vibrational states have been analyzed in detail. Rotational constants and centrifugal distortion parameters are reported for each species. The permanent electric dipole moment in ClNO₃ was found to have two components, μ_a = 0.72 ± 0.07 D and μ_b = 0.28 ± 0.02 D.     

Study of the torsion-rotation Hamiltonian for symmetric tops using the millimeter wave spectrum of methyl silane

The torsion-rotation Hamiltonian for symmetric tops has been tested in methyl silane by combining recent anticrossing molecular beam measurements in the ground torsional state (v = 0) with pure rotational spectra taken for v as high as 4. The earlier microwave data set which consisted of J = 1 ← 0 and 2 ← 1 has been greatly extended by studying millimeter transitions for J = 4 ← 3, 5 ← 4, and 13 ← 12. An analysis of the 72 rotational frequencies for v ≤ 2 and the 15 anticrossing data for v = 0 yielded an excellent fit using 14 rotational, torsional, and distortion constants including the effective values for the A rotational constant and the barrier height V₃. No satisfactory fit could be obtained when the data set was extended to include measurements for (v = 3) or (v = 4). For each of these higher torsional levels, the difference between the observed frequencies and the predictions based on the best (v ≤ 2) constants can be expressed in terms of a shift δB_v in the B rotational constant, where δB_v is a smooth function of the torsional energy. This disagreement is of particular interest because it may result from the fact that the molecule passes from hindered to free rotation as v is increased from 2 to 4. The possibility of perturbation by a low-lying vibrational level is considered briefly. The information contained in the different types of spectra is discussed; the redundancy relations are treated and a Fourier expansion of the diagonal torsional matrix elements is introduced. For ¹²CH₃²⁹SiH₃, ¹²CH₃³⁰SiH₃, and ¹³CH₃²⁸SiH₃ pure rotational spectra for v = 0 were studied briefly in natural abundance. The results were combined with existing data for two deuterated symmetric rotors to obtain a structure based only on symmetric top rotational constants.     

Infrared diode laser spectroscopy of the ν2 fundamental band of SH3+

The high-resolution absorption spectrum of the ν₂ fundamental band of SH₃⁺ has been observed with the magnetic field modulation technique. The ions were generated in a hollow cathode discharge through a mixture of H₂ and H₂S. The molecular constants in the excited vibrational state are determined through a least-squares fit of the data to a standard symmetric top energy level expression. The anomalous sign of the centrifugal distortion constants is explained by the Coriolis interaction between the v₂ = 1 and v₄ = 1 states.     

Torsion—rotation interactions in monodeuterated acetaldehyde

This paper presents an analysis of previously observed rotational transitions up to J = 17 of the sym and asym rotamers of monodeuterated acetaldehyde using a three-level Hamiltonian incorporating connections between rotational states of the v_sym = 0, v_asym = 0⁺ and v_asym = 0 ^? torsional energy level manifolds. Rotational transitions observed to be significantly perturbed in earlier studies, where the spectrum was fitted using a single-level Hamiltonian for the v_sym = 0 torsional state and a separate two-level Hamiltonian for the non-rigid asym states, are now fitted satisfactorily. It is confirmed that the perturbations detected in the earlier studies and tentatively attributed there to torsion-rotation interactions between the energetically distinct sym and asym manifolds do indeed arise as a consequence of such interactions. Rotational and quartic centrifugal distortion constants are given for each torsional state, together with torsion-rotation coupling constants primarily responsible for the perturbations noted in the earlier studies. Tunnelling between the energetically distinct sym and asym potential wells of the torsional potential energy function is also discussed.     

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 measurements of the 1 ← 0 infrared absorption band of hydrogen iodide

The ν₁ fundamental band of FNO has been studied by the technique of CO laser Stark spectroscopy. The band origin was determined to be 1844.099 cm^?1, and values for the rotational and centrifugal distortion constants of the (100) excited vibrational state were found. The ground state dipole moment components were determined to be μ_a = 1.690 and μ_b = 0.370 D, for a total dipole moment of 1.730 D, and a relatively large reduction (5%) was found in μ for the (100) state relative to the ground state.     

Microwave spectrum,dipole moment,and structure of anti-vinyl alcohol

The rotational spectra of the anti conformer of vinyl alcohol (ethenol, H₂CCHOH) and its OD modification have been studied by microwave spectroscopy. The compounds have been generated by very-low-pressure pyrolyses of the appropriate isotopic species of 3-thietanol. In both cases the 25 measured μ_a- and μ_b-type transitions allowed the rotational constants and all five quartic centrifugal distortion constants to be determined. Stark effect measurements have yielded the electic dipole moment: μ_a = 0.547(2), μ_b = 1.702(1), and μ = 1.788(1) D. By relative intensity measurements it has been found that the vibrational ground state of the anti conformer lies 4.5±0.6 kJ mol^?1 above the syn conformer. In addition, ab initio calculations at the 6–31G⁷ level have been performed to obtain the structure, relative energy, and dipole moment of both rotamers.     

The rotational a-type sepctra of 15N-labeled diazirine,H2CN2

The rotational a-type spectra of isotopically enriched diazirine isotopomers, H₂¹²C¹⁴N¹⁵N and H₂¹²C¹⁵N₂, have been recorded in the region between 8 and 300 GHZ; the latter isotopomer has been observed for the first time. Using Watson's A-reduced Hamiltonian, the rotational constants and the quartic and some sextic centrifugal distortion constants have been determined for the ground vibrational states.     

Forbidden rotational spectra of polyatomic molecules

Some of the pure rotational transitions of polyatomic molecules that are forbidden according to the rigid rotor selection rules may acquire intensity by a centrifugal distortion mechanism, in which the intensity depends on the dipole derivatives and on the displacements in the normal coordinates produced by centrifugal distortion. The structures of the predicted spectra are discussed for nonpolar molecules belonging to the point groups D_3h, D_n (n > 2), D_2d, and T_d. Some of the calculated R-branch lines of methane are stronger than some of the lines of HD already observed in the same frequency range. For polar molecules extra contributions to the intensity must be considered and are exemplified for the Δk = ±3 transitions of C_3v molecules. These forbidden rotational transitions may have some astrophysical importance.     

The potential function and rotation-vibration energy levels of the methyl radical CH3

The equilibrium bond length and the shape of the complete potential energy curve for the methyl radical CH₃ are determined. This is done by fitting the experimental data [mainly from C. Yamada, E. Hirota, and K. Kawaguchi, J. Chem. Phys.75, 5256–5264 (1981)] using the nonrigid invertor Hamiltonian and a model anharmonic potential function. As a result the v₂ (out-of-plane bending) dependence of the rotational constants is explained and the v₂ dependence of the spin-rotation coupling constants is modeled. In addition, some of the vibrational energies and rotational, centrifugal distortion, and spin-rotation constants are predicted for the ¹³CH₃, ¹²CD₃, and ¹²CT₃ isotopes.     

A planarity relation for sextic centrifugal distortion constants

The relations between the molecular parameters of a planar molecule are used to derive a planarity relation for the sextic centrifugal distortion constants from the recently published expressions [Aliev and Watson, J. Mol. Spectrosc.61, 29 (1976)]. This relation, which contains only the rotational constants and the quartic and sextic distortion constants, is strictly valid only for the equilibrium constants, but will be useful as a constraint in the fitting of rotational energies if the experimental error is larger than the vibrational defect. The planarity relation is compared with the observed constants for the SO₂, O₃, NO₂, H₂O, and H₂S molecules. There appears to be a significant defect for SO₂ and for H₂O and its isotopes. The defect for SO₂ may be too large to be genuine, and possibly results from truncation of the Hamiltonian at the sextic terms.     

High-resolution spectroscopy on the c1Π ← a1Δ transition in NH

The spectrum of the c¹Π, v = 0 ← a¹Δ, v = 0 band of the NH molecule at λ = 324 nm has been investigated under high resolution by laser-induced fluorescence in a molecular beam. From an analysis of the spectra we obtained: the magnetic dipole interaction constants a_N,H and the electric quadrupole constants eQq_1,2 for both electronic states, the improved values for the Λ-doubling constants q_π, q_π^D, and q_π^H for the c¹Π state, and rotational constants for both electronic states up to a third-order centrifugal distortion. Also, the Λ-doubling in the a¹Δ state could be determined.     

Effective Hamiltonian for polyatomic linear molecules

The leading terms of an effective Hamiltonian for a linear molecule in a given vibrational state are presented up to κ¹⁰T_v order of magnitude, whereby higher-order l-dependent terms such as $\text{H}\text{?}{}_{12.0}$, $\text{H}\text{?}{}_{8.0}$, and $\text{H}\text{?}{}_{8.2}$ have been neglected because in spectroscopic application they are of minor importance. This Hamiltonian therefore includes all those l-type interactions which could contribute to the fitting procedure, within a vibrational state where one or more bending vibrations are excited.     

1-Butyne microwave spectrum,barrier to internal rotation,and molecular dipole moment

Measurements of rotational transitions of 1-butyne have been made in the range of ～20–130 GHz. Both a-type transitions up to J = 46 and b-type transitions up to J = 42 have been measured and fitted to a rotational Hamiltonian which includes centrifugal distortion terms. In addition to the five quartic centrifugal distortion constants, three sextic coefficients had to be included to reproduce the observed frequencies to within experimental error. The results of the analysis are sufficient for the prediction of all strong transitions throughout the millimeterwave range. A barrier to internal rotation of the methyl group of 3.260 kcal/mole (1 kcal/mole = 4.18 kJ/mole) has been derived from the first excited torsional state. Analysis of the second-order Stark effect has led to an accurate determination of both μ_a and μ_b with μ_a = 0.763(3) D and μ_b = 0.170(4) D.