Upper and lower bounds of quartic centrifugal distortion constants

Expressions are obtained for the maximum and minimum possible values of the equilibrium centrifugal distortion constants τ_αβγδ for a molecule with given structure and vibrational frequencies. The method of calculation, based on Lagrangian multipliers, is also applied to the empirical centrifugal constants (such as D_J, D_JK, D_K, or Δ_J, Δ_JK, Δ_K, δ_J, δ_K) employed in fitting the rotational structure of spectra. These formulas make it possible to test whether a set of observed centrifugal constants is consistent with the rotational constants and vibrational frequencies. When inconsistencies arise, they are probably due to zero-point vibrational effects. By means of a second method employing inequalities, simpler formulas are derived for wider bounds. These are useful in calculating approximate values of the constants, as a preliminary to deciding which terms to include in the rotational Hamiltonian of any particular molecule.     

Uniqueness of methyl fluoride force field

The uniqueness of the general harmonic force field of methyl fluoride is analyzed. The analysis is applicable to other methyl halides as well. Through the compliance scheme, it is seen that by supplementing the data employed by Aldous and Mills (i.e., vibrational frequencies ω_i, Coriolis coupling constants ζ_i and the centrifugal stretching constants D_J, D_JK of CH₃F and CD₃F molecules), with the frequencies of A′ or A″ species of either CH₂DF or CD₂HF, the force field is uniquely determined. The addition of any other extra data including the ¹²CH₃F¹³CH₃F isotopic shifts only makes the determination of the force field parameters more precise.     

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.     

Millimeter- and Submillimeter-Wave Spectra of CD2F2

The millimeter- and submillimeter-wave spectrum of ¹³CD₂F₂ present in natural abundance in methylene fluoride-d₂ (CD₂F₂) has been measured in the region 230-380 GHz. The spectrum was recorded using a frequency-modulated millimeter- and submillimeter-wave spectrometer. More than 200 rotational transitions in the ground state of ¹³CD₂F₂ with J≤45 and K_a≤8 have been assigned. A combined weighted least squares fit of the newly assigned transitions with previously reported microwave data has been carried out in the Watson's A- and S-reduced Hamiltonian. The data have been fitted with a standard deviation approaching the experimental accuracy, to provide improved values for the rotational and quartic centrifugal distortion constants, including sextic distortion constants for the ground state of ¹³CD₂F₂.     

Microwave measurements and calculations of quadrupole coupling effects in CH3I and CD3I

The transitions J = 1 ← 0, K = 0; J = 2 ← 1, K = 0; and J = 2 ← 1, K = 1 of CH₃I and CD₃I were measured using a Stark-modulated microwave spectrometer. Iodine quadrupole coupling strengths were analyzed to determine variations with deuterium substitution on the methyl group and variations with centrifugal distortion. Quadrupole coupling strengths were described by the expression $\text{eQq}{}_0\text{+ aJ(J + 1) + bK}{}^2\text{+}\text{cK}{}^4\text{J(J + 1)}$. Explicit expressions are given for a, b, and c for a symmetric top in terms of molecular parameters. For CH₃I eQq₀ = ?1934.11 ± 0.02 MHz and for CD₃I eQq₀ = ?1928.95 ± 0.04 MHz. Rotational constants obtained are B(CH₃I) = 7501.274 ± 0.002 MHz and B(CD₃I) = 6040.298 ± 0.007 MHz. The observed fractional change in halogen quadrupole coupling of 0.0027 is related to previous results for methyl chloride and methyl bromide.     

Infrared rotation-vibration spectra of ethane: The parallel band, 2ν3, of CH3CD3

The parallel band, 2ν₃, of CH₃CD₃ is measured in the region 2715 to 2780 cm^?1 under a spectral resolution of ～0.025 cm^?1, increased to ～0.015 cm^?1 by deconvolution. About 460 lines are identified in the 2ν₃ band, and about 240 lines in a hot band arising from the first excited torsional state. Least-squares analyses with Δ₂F″ combination differences yield lower-state parameters. An individual subband analysis is undertaken because of perturbations in the vibrational bands studied. Finally, band constants are derived.     

Vibration-rotation spectra and molecular force field of methylene fluoride and methylene fluoride-d2

Infrared spectra of CH₂F₂ and CD₂F₂ have been measured under a medium resolution. The vibration-rotation bands of CD₂F₂ fundamentals have been analyzed and the assignment for the fundamentals of CD₂F₂ is given. In addition, a number of overtone and combination bands are observed for CH₂F₂, which helps to clarify the vibrational assignment for CH₂F₂. A normal coordinate treatment has been carried out: The force constants in a modified Urey-Bradley as well as the general valence force fields have been determined, the vibrational frequencies and the centrifugal distortion constants obtained from microwave spectroscopy being used. The force constants of the methylene fluoride molecule are discussed in connection with those of the related molecules. Special features of the CH₂F₂ and CD₂F₂ spectra are also described.     

Application of the contact transformation method to torsional problems in methyl silane

The effect of the torsional degree of freedom on redundancies in the Hamiltonian and on the dipole operator has been investigated for methyl silane-like molecules. By applying a rotational contact transformation to the torsion-rotation Hamiltonian H_TR for the ground vibrational state, a systematic method is demonstrated for treating the redundancies that relate different terms in H_TR. In general, with this method, the experimentally accessible molecular parameters in the reduced Hamiltonian can be related to the physically significant molecular parameters in the untransformed Hamiltonian. It is shown that H_TR contains a new term which has matrix elements with selection rules (ΔK = ±3), (Δσ = 0), and Δv_T arbitrary, where v_T and σ label the torsional levels and sublevels, respectively. As a result of this term, the distortion dipole constant μ_D which characterizes (ΔK = ±3) matrix elements in C_3v molecules cannot, in systems like CH₃SiH₃, be ascribed entirely to centrifugal distortion but can contain a significant contribution from torsional effects. Furthermore, new transitions can appear in the pure torsional bands which may be strong enough to observe in low barrier molecules. By applying a vibrational contact transformation, the form is derived of the leading torsional terms in the dipole moment expansion. The four dipole distortion constants μ₀^T, μ₂^T, μ_|;^T, and μ_Λ^T which characterize these terms are related to the molecular parameters that enter the Coriolis, centrifugal distortion, and anharmonicity contributions to the vibration-torsion-rotation Hamiltonian.     

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.     

Absolute Raman intensities of CH4, CH3D,CH2D2, CHD3, and CD4

Measurements of the absolute vibrational Raman intensities and depolarization ratios for the fundamental and some overtone and combination bands of CH₄, CH₃D, CH₂D₂, CHD₃, and CD₄ are reported. Experimental aspects of these measurements are discussed. The experimental data conform satisfactorily to all isotope intensity sum rules. The measured intensities and depolarization ratios, together with the vibrational potential function for CH₄, make possible the calculation of the four independent parameters of the isotopic invariant quantities $\text{α}{}^{\mathrm{S}}\text{= |}\text{?α}\text{?S}\text{|}$. The results deduced from these agree with all 36 experimentally observed values. Values of electro-optical parameters for the CH bond are calculated and discussed.     

The millimeter-wave spectrum of methyl chloride

The millimeter-wave spectra of CH₃³⁷Cl in its ground and ν₃ vibrational states, and of CH₃³⁵Cl in its ν₃ state, have been measured and analyzed to give B, D_J, D_JK, and eQq. The values agree well with the less-precise values from high-resolution infrared spectra for the ground state of CH₃³⁷Cl.     

Vibration-rotation spectra of ethane and deuteroethanes: The ν2 band of CH3CD3

The ν₂ band of CH₃CD₃ has been measured under an effective resolution of 0.04 cm^?1. About 400 transitions observed in the region from 2130 to 2060 cm^?1 have been identified as due to the ν₂ fundamental band. The least-squares analysis of these transitions yields the band constants: ν₀ = 2089.957, B′ = 0.548937, D_J′ = 6.97 × 10^?7, D_JK′ = 1.92 × 10^?6, A′ - A″ = ?0.01158, and D_K′ - D_K″ = 1.30 × 10^?6 cm^?1. The ground-state constants B″, D_J″, and D_JK″ are fixed to the values obtained from microwave spectroscopy.     

The harmonic force fields of methylene chloride and dichlorosilane from combined microwave and infrared data

The harmonic force fields of methylene chloride and dichlorosilane have been obtained by combining the vibrational wavenumbers and centrifugal distortion constants of several isotopic species. Although enough data were available from earlier work for dichlorosilane, it was first necessary for methylene chloride to determine its distortion constants from microwave spectra. Transitions were measured up to J = 80 and J = 90 for CH₂Cl₂ and CD₂Cl₂, respectively, and the analysis gave accurate rotational constants, and quartic and sextic distortion constants. Ground-state effective, substitution, ground-state average and approximate equilibrium structures have been obtained for both molecules.     

Electro-optical parameters and Raman intensities of CH4, CH3D,CH2D2, CHD3 and CD4

The absolute Raman intensities and the depolarization ratios of the vibrational bands of gaseous CH₄, CH₃D, CH₂D₂, CHD₃ and CD₄ have been computed here using a compact formulation of the bond polarizability theory, in its zero and first-order approximations. The agreement with experimental values taken from the literature is very good for the first-order approximation, although the difference between both approximations is not very large for these molecules. The derivatives of the polarizability with respect to the symmetry coordinates of methane are given with signs that are physically meaningful.     

The microwave spectrum of 1-phosphapropyne,CH3CP: Molecular structure,dipole moment,and vibration-rotation analysis

The J = 4 ← 3 and J = 3 ← 2 rotational transitions of 1-phosphapropyne, CH₃CP, between 26.5 and 40 GHz have been studied by microwave spectroscopy. The spectrum shows the characteristic vibration-rotation satellite patterns associated with a C_3v symmetric rotor. Apart from the most abundant isotope variant, the species ¹²CD₃¹²C³¹P, ¹²CD₂H¹²C³¹P, ¹²CH₂D¹²C³¹P, ¹³CH₃¹²C³¹P, ¹²CH₃¹³C³¹P, ¹³CD₃¹²C³¹P, and ¹²CD₃¹³C³¹P have also been studied. For ¹²CH₃¹²C³¹P the rotational constants B₀ = 4991.339 ± 0.003 MHz, D_J = 0.823 ± 0.092 kHz, D_JK = 66.59 ± 0.18 kHz have been determined. From these data the following structural parameters have been derived: $\text{r}{}_{\mathrm{s}}\text{(}\text{CH}\text{) = 1.107 ± 0.001}\text{A}\text{?}$, ∠_s(HCC) = 110.30 ± 0.09°, $\text{r}{}_{\mathrm{s}}\text{(}\text{CC}\text{) = 1.465 ± 0.003}\text{A}\text{?}$, $\text{r}{}_0\text{(}\text{CP}\text{) = 1.544 ± 0.004}\text{A}\text{?}$. The dipole moment has been determined as 1.499 ± 0.001 D by analysis of the Stark effect of the J = 3 ← 2, |K| = 1 line. The vibrational satellites (v_s = 1, 2, and 3) have been studied and various vibration-rotation parameters derived.     

Internal rotation in methyl silane by avoided-crossing molecular-beam spectroscopy

The avoided-crossing molecular-beam electric-resonance technique was applied to methyl silane in the ground torsional state. A new type of anticrossing is introduced which breaks the torsional symmetry and obeys the selection rules ΔJ = 0, K = +1 /a3 ?1. For these “barrier” anticrossings, the values of the crossing fields E_c yield directly the internal rotation splittings; the E_c are independent of the difference (A-B) in the rotational constants. Such anticrossings were observed for J from 1 to 6. Studies were also conducted of several “rotational” anticrossings (J, K) = (1, ±1) /a3 (2, 0) for which E_c does depend on (A-B). The normal rotational transition (J, K) = (1, 0) ← (0, 0) was observed in the ground torsional state using the molecular beam spectrometer. The present data on CH₃²⁸SiH₃ were combined with Hirota's microwave spectra and analyzed with the torsion-rotation Hamiltonian including all quartic centrifugal distortion terms. In addition to evaluating B and several distortion constants, determinations were made of the moment of inertia of the methyl top I_α = 3.165(5) amu-Ų, the effective rotational constant A^eff = 56 189.449(32) MHz, and the effective height of the threefold barrier to internal rotation V₃^eff = 592.3359(73) cm^?1. The correlations leading to these two effective constants are discussed and the true values of A and V₃ are determined within certain approximations. For the isotopic species CH₃³⁰SiH₃, barrier and rotational anticrossings were observed. The isotopic changes in A and V₃ were determined, as well as an upper limit to the corresponding change in I_α.     

A frequency analysis of the ν9 band of CD3CD3: experiment and ab initio calculations

The infrared gaseous spectrum of CD₃CD₃ has been measured in the range of 530–670cm^?1 to investigate vibration—torsion effects in the ν₉ band. Three separate spectra all taken under different experimental conditions were recorded. The lines with (ΔK = ?1) and with high values of K show torsional splittings that are substantially larger than expected from the observed barrier height. These splittings are caused primarily by Coriolis-type interactions between the torsional stack of ν₉ = 1 and the corresponding stack for the ground vibrational state. Because of a near-degeneracy that exists between the states (ν₉ = 0, ν₄ = 3) and (ν₉ = 1, ν₄ = 0), three subbands (K, σ) = (15,1), (16,2), (17,3) are resonantly perturbed. For these cases, perturbation-allowed 3ν₄ torsional transitions have been identified. Here σ= 0, 1, 2 or 3 labels the torsional sublevels. Measurements from the ν₉ and 3ν₄ bands, frequencies from the far-infrared torsional spectra in the ground vibrational state, and lower state combination differences from the ν₉ + ν₄ ? ν₄ band were fitted to within experimental uncertainty using an effective Hamiltonian which considered three torsional stacks; one for the ground vibrational state and two for ν₉ = 1. In all, 22 parameters were determined using a total of 2001 lines. Of these, three parameters were the interstack couplings, eight are from the ground vibrational state and 11 are from the excited vibrational state. Two barrier-dependent torsion—rotation parameters, which were essential for obtaining a satisfactory fit, were calculated by ab initio methods.     

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.     

Rotation-torsion-vibration term-value mapping for CH3OH: Torsion-mediated doorways and corridors for intermode population transfer

Fourier transform infrared spectra of CH₃OH from 930-1650 cm⁻¹ have been analyzed to reveal details of the rotation-torsion-vibration energy manifold of the CO-stretching, CH₃-rocking, OH-bending and CH₃-deformation modes and their torsional combination states. Mapping of the upper-state term values as a function of the rotational quantum number J has shown the locations of numerous substate crossing resonances that give rise to J-localized spectral perturbations and substate mixing and thereby create “doorways” for collision-induced population transfer among the different modes. Other near-degenerate substates are more globally mixed over a wide range of J, corresponding to “corridors” of doorways. Where both partner substates in a doorway resonance have been identified, the perturbations have been analyzed to find estimates of the interaction matrix elements and the degree of mixing between the coupled states. Many of the resonances are between substates of differing torsional quantum number, highlighting the importance of torsion in generating the doorway channels and enhancing intermode vibrational population transfer.