Forbidden pure rotational Raman spectra of C3v and Td molecules

Some of the pure rotational Raman transitions of polyatomic molecules that are forbidden according to rigid rotor selection rules may acquire intensity by a centrifugal distortion mechanism. These are analogous to forbidden rotational electric dipole transitions which recently have been studied extensively (1–6). A simple technique to obtain the intensity factors leading to the line strengths of such Raman transitions is presented. The intensity factors $\text{b}{}_{\mathrm{J\prime k\prime }}{}^{\mathrm{Jk}}$ and $\text{b}{}_{\mathrm{J\prime }}{}^{\mathrm{J}}$ of the Q, R, and S branches of molecules with C_3v and T_d symmetry are obtained. For C_3v molecules, in addition to the usual selection rules for J, those for k are found to be Δk = ±3 and ±6. There is a modification of intensity of the normally allowed Δk = 0 transitions. T_d molecules, which normally do not have pure rotational spectra, now give rise to weak Raman transitions due to centrifugal distortion.     

Forbidden rotational spectra of axially symmetric polar molecules

In this paper we consider the rotational transitions induced by centrifugal distortion in polar or quasipolar symmetric top molecules belonging to the point groups C_n and C_nv (n ≥ 3). It is shown that in this series only the molecules of point groups C₃, C_3v, C₄, and C_4v may possess rotational spectra induced by first-order centrifugal distortion. A general expression is given for the effective dipole moment operator and for its matrix elements. The peak absorption coefficients for some of the strongest ΔK = 3 transitions of the CH₃D molecule have been calculated and compared with the peak absorption coefficients of allowed transitions.     

Identification of forbidden vibration-rotation transitions in 15NH3

Forbidden Δ|k ? l| = 3 vibration-rotation transitions have been observed in the ν₄ band of ¹⁵NH₃. The analysis of these transitions, together with previously published data on the allowed transitions, has made it possible to determine a set of molecular parameters, including for the first time the rotational constant C as well as the centrifugal distortion constants D_K and H_KKK, which are necessary for the calculation of energy levels. Some weak forbidden transitions in the ν₂ band have also been observed.     

The forbidden (J → J + 1) spectrum of CH4 in the ground vibronic state

The pure rotational R-branch spectrum of CH₄ arising from the centrifugal distortion moment has been studied using a simple 12.10-m light-pipe cell and a conventional interferometer. Ten forbidden (J → J + 1) transitions for J = 7 to J = 16 have been observed in the spectral region 80–200 cm^?1 with a theoretical resolution of 0.5 cm^?1. The integrated intensity of the six strongest lines has been measured and was found to be of the order of twice that calculated from the distortion moment obtained earlier from a molecular beam study of the (J = 2) rotational level. In the approximation that frequency shifts due to this excess intensity are neglible, it has been determined that the rotational constant B₀ = (5.245 ± 0.004) cm^?1 and the scalar distortion constant D_S = (1.19 ± 0.09) × 10^?4 cm^?1. It is argued that the excess intensity is due to higher-order terms in the dipole moment operator and the validity of the frequency analysis is considered in this context.     

The pure rotational spectrum of Difluoroiodomethane, CHF2I

The pure rotational spectrum of CHF₂I has been recorded for the first time, in a supersonic expansion in the region 1.7-17 GHz, and at room-temperature in the region 302-318 GHz. The observed transitions span the values of J^″ from 0 up to 67. Precise rotational and centrifugal distortion constants have been determined. Furthermore, the complete iodine nuclear electric quadrupole coupling tensor, in the inertial and principal axes, has been determined. Quantum chemical calculations have been performed to aid with the analysis. Iodine quadrupole mediated perturbations have resulted in the following observations: (i) several transitions having enhanced intensities and (ii) the observation of several forbidden, ΔJ=±2, transitions. Comparisons in electronic structure are made between the series of molecules CH_3-nF_nX; and X = Cl, Br, I.     

Forbidden vibrational-rotational transitions and Herman-Wallis factors in fundamental IR bands of symmetric-top molecules

Within the theory of coupled schemes of ordering of vibrational-rotational interactions, the operator of the effective dipole moment of single-quantum vibrational transitions is represented in the form of an infinite series in vibrational (normal coordinates and conjugate momenta) or rotational variables (components of the total angular momentum). Mechanisms of activation of infrared-inactive totally symmetric vibrations in molecules of the D _2a , D _3h , C _3h , D _n (n ≥ 3), S ₄, T, T _a , and O symmetries and forbidden vibrational-rotational transitions in IR bands of active vibrations have been studied. The group-theoretic analysis of tensor parameters in higher-order effective dipole moments of single-quantum vibrational transitions in axially symmetric molecules has been performed. The strengths of allowed transitions and forbidden transitions in fundamental and hot IR bands of axially symmetric molecules are calculated with allowance for the Herman-Wallis factors. For effective dipole moments of multiquantum transitions in molecules, models are developed in the form of infinite series in rotational variables and in the form of Padé approximants.     

Microwave spectra and centrifugal distortion constants of oxetane

The microwave spectra of oxetane (trimethylene oxide) and its three symmetrically deuterated isotopic species have been observed on a Hewlett-Packard microwave spectrometer from 26.5 to 40 GHz. For the parent species, the β-d₂ and the αα′-d₄ species, about 300 lines have been assigned for each molecule, and for the d₆ species more than 600 lines have been assigned. The assignments range from v = 0 to v = 5 in the puckering vibration; although they are mostly Q transitions, either 3 or 4 R transitions have been observed for each vibrational state.The spectra have been interpreted using an effective rotational hamiltonian for each vibrational state, including five quartic distortion constants according to Watson's formulation, and a variable number of sextic distortion constants; in general, the lines are fitted to about ± 10 kHz. The distortion constants show an anomalous zig-zag dependence on the puckering vibrational quantum number, similar to that first observed for the rotational constants by Gwinn and coworkers. This is interpreted according to a simple modification of the standard theory of centrifugal distortion, involving the double minimum potential function in the puckering coordinate.     

A line list of allowed and forbidden rotational transition intensities for water

Pure rotational lines are important for monitoring water concentrations in many environments both in space and on earth. A list of line intensities of rotational transitions for H₂¹⁶O is calculated using variational nuclear-motion wave functions and an ab initio dipole moment surface. This methodology should be equally reliable for both allowed and forbidden rotational transitions. Extensive comparisons are made with available intensity data for these transitions including the HITRAN and JPL databases. Problems are identified with some of these data. A list of 555 allowed and 846 forbidden rotational transition lines within the ground vibrational state is made available.     

Perturbations in the vibration-rotation-torsion energy levels of an ethane molecule exhibiting internal rotation splittings

Various examples of perturbations in the vibration-rotation-torsion energy levels of an ethane molecule exhibiting internal rotation splittings are discussed, both from the point of view of the point group D_3d, appropriate when internal rotation tunneling effects cannot be observed, and from the point of view of the group $\text{G}{}_{36}{}^2$, appropriate when internal rotation tunneling in ethane leads to observable splittings in the spectrum. It is found, for perturbations allowed in both D_3d and $\text{G}{}_{36}{}^2$, that each of the two torsional components of the perturbed D_3d vibration-rotation level can in principle interact with a “corresponding” torsional component in the perturbing vibration-rotation level. It is found for perturbations forbidden in D_3d but allowed in $\text{G}{}_{36}{}^2$, which all occur between D_3d vibrational levels of different g, u parity, that only one of the two torsional components of the perturbed D_3d vibration-rotation level can interact with a corresponding torsional component in the perturbing vibration-rotation level. Some of the perturbations examined give intensity to otherwise forbidden transitions in such a way that perturbation-induced transitions can be used in conjunction with normally allowed transitions to determine the sum of the internal rotation splittings for two rotational levels differing in K by three units.     

Investigation of the absorptions of monoisotopic OsO4 with CO2 and N2O laser lines with saturation spectroscopy

Some absorption features of monoisotopic ^{186–190,192}OsO₄ have been studied by saturated absorption using low-pressure CO₂ and N₂O lasers. Ground-state absorptions of the ν₃ fundamental band were distinguished from hot-band absorptions by investigation of the linear absorption coefficients, and were assigned on the basis of frequency calculations. In addition the vibrational transition moment was evaluated. A few lines were found, which, due to their unusual saturation properties, were identified as forbidden transitions arising from off-diagonal terms of a sixth rank tensor in the effective Hamiltonian. Their observation permits a value of the tensor centrifugal distortion constant to be derived: D_t = (2.045 ± 0.018) × 10^-9 cm^-1.     

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.     

Origin bands of electronically forbidden spectra made allowed by centrifugal distortion

Watson’s theory of pure rotational spectra in nonpolar molecules is adapted to show that, if appropriate symmetry conditions are met, centrifugal distortion can lead to the appearance of the forbidden 0-0 origin band in an electronically forbidden spectrum. The intensity of such bands will be low; in the case of the benzene ùB_2u-¹A_1g system the maximum intensity of the forbidden origin is estimated to be about 10⁻⁷ of that of the 6¹₀ band in the main vibronic spectrum. The prospects for the experimental detection of such weak bands are discussed.     

Infrared spectrum involving forbidden transitions & coriolis interaction and identification of optically pumped far infrared laser lines in asymmetrically mono-deuterated methanol (Methanol-D1)

In this paper new type of ΔK = 2 and 0 transitions have been identified in the Fourier Transform spectrum of Methanol-D₁ (CH₂DOH). These transitions are normally forbidden but a “Coriolis” type interaction with nearby states is believed to be contributing sufficient transition strength through intensity borrowing effect. This is the first time such forbidden transitions are reported to be identified in the excited states, in this molecule. The present conjecture is supported by observation of a many strong allowed transitions to upper terminating levels which are seen to be highly perturbed. This conclusion has been reached by comparing calculated energy levels using known molecular parameters (Pearson et al., 2012; Coudert et al., 2014; El Hilali et al., 2011; Quade et al., 1998; Richard Quade, 1998, 1999; Mukhopadhyay, 1997) and the actually observed FIR lines. The upper levels are seen to be upshifted from expected position. A closer look at the calculated energy values seems to indicate a possible interaction between the above states and other proximate torsional–rotational states could occur. The possible candidates for the interacting level manifolds are narrowed down through the presence of the forbidden transition. We also take the opportunity to propose alternate rotational quantum numbers for some of the assignments recently reported in the literature (El Hilali et al., 2011). Some ambiguities are pointed out on the data and the reported analysis. There remain too many such irregularities and we propose to gather a large body assigned transitions in a future catalog. Assignments and relevant comments on optically pumped FIR laser radiation are also made.     

Fourier transform microwave spectroscopy of the reactive intermediate monoiodosilylene,HSiI and DSiI

The pure rotational spectra of three silicon isotopologues of HSiI and two isotopologues of DSiI have been recorded by pulsed-jet Fourier transform microwave (FTMW) spectroscopy. Neon was passed over dry ice cooled H₃SiI or D₃SiI and introduced into the pulsed valve of the FTMW spectrometer. The monoiodosilylenes HSiI and DSiI were produced in situ with a 1000 V DC-discharge nozzle. Only a-type transitions occur in monoiodosilylene from 6 to 26 GHz. We observe K_a = 0 a-type transitions for H²⁸SiI, H²⁹SiI, H³⁰SiI, and D²⁹SiI, and both K_a = 0 and 1 a-type transitions for D²⁸SiI. Rotational constants, centrifugal distortion constants, iodine nuclear quadrupole coupling constants, and nuclear spin–molecular rotation constants were measured.     

Forbidden transitions in homopolar isotopically unsymmetric diatomic molecules and the dipole moment of HD

The theoretical expressions for the intensities of forbidden rotational and rotation-vibration spectra of homopolar isotopically unsymmetric diatomic molecules, made allowed by the breakdown of the Born-Oppenheimer approximation, are derived. The results are applied to HD and it is shown that among the previously overlooked contributions to the dipole moment of the molecule there is one with a very significant value in the direction H^?D⁺. A rotationally dependent contribution arising from centrifugal distortion is extremely small. The intensities of the fundamental and overtone bands of HD are also considered.     

The microwave spectrum and centrifugal distortion constants of propiolic acid

The microwave spectra of propiolic acid and propiolic acid-d have been measured up to J = 30. These have enabled accurate evaluation of the rotational and centrifugal distortion constants for each species. The measured frequencies are presented, along with some predictions of transitions unmeasured in the present work, but of potential use in radioastronomy.     

Microwave spectrum of deuterated silyl isocyanate,SiD3NCO

The microwave spectrum of SiD₃NCO has been observed and analyzed for 18 different vibrational states in the ν₁₀ manifold. Some accidental resonances have been observed and analyzed. The vibrational dependence of the rotational and l-doubling constant and centrifugal distortion constant D_JK has been successfully interpreted in terms of the two-dimensional anharmonic oscillator model.     

The rotational spectrum of acrylonitrile in excited states of the two low-frequency CCN bending vibrational modes

The strongest vibrational satellites in the rotational spectrum of acrylonitrile have been assigned and frequencies of μ_a- and μ_b-type transitions in the frequency range 27–184 GHz are reported for the first two excited states in the lowest frequency in-plane CCN bending vibrational mode and the first excited state in the out-of-plane CCN bending mode. The values of the rotational constants, the quartic and sextic centrifugal distortion constants, and one octic centrifugal distortion constant are determined for each of these states. Less extensive results are also presented for the third quantum of the in-plane bend. The data set for the ground state has been extended by a number of new measurements and the improved ground state constants are used in a discussion of changes in rotational and centrifugal distortion constants with vibrational state where all constants associated with P_zⁿ and P²P_z⁽ⁿ⁻²⁾ terms in the Hamiltonian are found to reflect the common origin of the two CCN bends.     

Millimeter-wave spectrum of the C4v molecule iodine oxygen pentafluoride IOF5: K-doubling of the |k| = 2 transitions in the ground state spectrum

Measurements are reported for the rotational spectrum of the C_4v molecule IOF₅ in the ground vibrational state in the range 30–75 GHz (J7 ← 6 to J17 ← 16). The K-doubling of |k| = 2 transitions due to an off-diagonal centrifugal distortion interaction of the type (Δl, Δk) = (0, ±4) has been observed. The centrifugal distortion constants D_J, D_JK, and R₆ have been determined as 0.139(2) kHz, 0.107(4) kHz, and 21(2) Hz, respectively.     

High-precision frequency measurements of the ν1 + ν3 combination band of C2H2 in the 1.5 μm region

A pair of 1.5 μm semiconductor laser frequency standards have been developed for optical telecommunications use, stabilised to transitions of ¹²C₂H₂ and ¹³C₂H₂, using cavity-enhanced Doppler-free saturation absorption spectroscopy. The absolute frequencies of 41 lines of the ν₁ + ν₃ band of ¹²C₂H₂, covering the spectral region 1520-1545 nm, have been measured by use of a passive optical frequency comb generator, referenced to ¹³C₂H₂ transitions of known frequency. The mean experimental uncertainties (coverage factor k = 1) of the frequency values are 3.0 kHz (type A) and 10 kHz (type B). Improved values of the band origin ν₀, rotational constants B′ and B″, and centrifugal distortion coefficients D′, D″, H′, and H″ are presented.