Third-order theory of the line intensities in the allowed and forbidden vibrational-rotational bands of C3v molecules

A third-order theory of the intensities of the allowed and “forbidden” (perturbation-allowed) transitions to the fundamental vibrational levels of C_3v semirigid molecules has been worked out by using the method of contact transformations applied to the electric dipole moment operator. Explicit expressions have been obtained for the linestrengths of the allowed (Δk = 0, ±1) as well as forbidden (Δk = ±2, ±3, ±4) transitions from the ground vibronic state to the fundamental vibrational levels of C_3v molecules. The treatment takes into account all the important Coriolis and anharmonic interactions in a C_3v molecule, including the effect of the “2, 2” and “2, −1” l-type interactions and the Δk = ±3 interactions on the intensities of the allowed and forbidden vibrational-rotational transitions. The expressions for the linestrengths of the allowed and forbidden transitions are given here in a form suitable to fit the experimental data on the intensities in the vibrational-rotational spectra of C_3v molecules.     

Microwave l-type resonance transitions of the v6 = 1 state in CHF3 and CDF3: Accidental degeneracy and molecular structure

Observations of the direct l-type resonance transitions in the microwave spectrum of the v₆ = 1 state of CHF₃ and CDF₃ have been extended to J = 37. Accidental degeneracies were found between J = 34, $\text{K}\text{= 3}\text{and}\text{0}$ in both molecules enabling the C rotational constants of CHF₃ and CDF₃ to be determined, using 118 observed frequencies for CHF₃ and 104 for CDF₃. After suitable correction the B and C rotational constants were used to determine the r₀, r₂, and r_e structures for CHF₃ and CDF₃.The equilibrium structure was determined to be $\text{CH}\text{= 1.091 ± 0.014}\text{A}\text{?}$, $\text{CF}\text{= 1.3284 ± 0.0031}\text{A}\text{?}$ and ∠FCF = 108.58 ± 0.34°.     

ΔK = 2 transitions in H2CO and D2CO

Weak transitions of the type ΔJ = ± 1, $\text{Δ}\text{K}{}_{\mathrm{a}}\text{= ? 2}$, ΔK_c = ± 3 have been observed in H₂CO and D₂CO by the millimeterwave double resonance method and also by direct absorption with a Stark modulated spectrometer. The addition of these new transitions in a least-squares analysis, in which all previously known microwave and millimeterwave data are also included, results in an improved set of rotational and distortion constants.     

Intensities of rotational lines in first overtone bands for axially symmetric molecules of the group C3v

The interaction of vibration and rotation is considered in the computation of the intensities of rotational lines in the first overtone bands of axially symmetric molecules of the group C_3v. The calculation utilizes the contact transformation method through first order of approximation as outlines by Hanson and Nielsen. General formulas for the intensities of the lines in the first overtone bands 2ν_n and 2ν_m are obtained, where n and m denote normal modes of species A₁ and E, respectively. It is found that to this order of approximation the usual selection rules ΔJ = 0, ±1 and ΔK = 0 are observed for the parallel overtone band 2ν_n. For the overtone band 2ν_m, the selection rules are more complicated, being ΔJ = 0, ±1; Δl_m = 0 and ΔK = 0, Δl_m = ±2 and $\text{Δ}\text{K = ?1}$, or Δl_m = ±2 and ΔK = ±2.     

Rotational analysis of the 7390- and 7937-Å bands of NO2 by means of Fourier transform spectroscopy

We have extended to higher N and to K_a = 3 and 4 the rotational analysis of the 7390-Å band of NO₂ performed by K. E. Hallin and A. J. Merer (Canad. J. Phys.55, 2101–2112 (1977)). The lines belong to a perturbed parallel band for which Hallin and others have proposed the vibrational assignment (2 13 1)-(0 0 0) within the electronic ground state. These authors presumed that this band borrows its intensity through a vibronic coupling (spin-orbit and/or Coriolis coupling) from the stronger (0 2 0)-(0 0 0) band of the $\text{A}\text{?}\text{-}\text{X}\text{?}$ electronic system at 7460 Å. We have observed about 900 transitions belonging to the K_a = 0, 1, 2, 3, 4 subbands of the (2 13 1)-(0 0 0) band for N values going up to about 23, and 300 lines of the “hot” band (2 13 1)-(0 1 0). We have also looked for spin-orbit-induced transitions and we have detected about 400 transitions with ΔN ≠ ΔJ. Among them ΔN = ±2 transitions with ΔK_a = 0 or ± 2 have been observed, indicating that N and K_a are no longer good quantum numbers, and demonstrating clearly the existence of rovibronic interactions perturbing the upper levels of the transitions.     

Spin forbidden transitions in the Ka = 0 subband of NO2 in the λ = 592.5 nm region

In a high resolution laser excitation spectrum of NO₂, lines were recorded which do not follow the selection rule ΔN = ΔJ = ΔF of “spin allowed” transitions. Line positions and intensities of these “spin forbidden” lines were investigated for all rotational lines up to N″ = 12 of the K_a = 0 subband around λ = 592.5 nm. While the observed line intensities of “spin allowed” transitions can be well described by the J-coupling scheme, neither the J- nor the G-coupling scheme sufficiently describes the “spin forbidden” transitions. The observations can be fitted satisfactorily by perturbation theory, in which the Fermi interaction in ²A₁ is treated as the perturber. This looks similar to a superposition of J and G scheme in the ²A₁ ground state.     

Infrared-microwave double resonance in CF3I; Microwave spectroscopy in emission and absorption

From the double resonance effects observed on the microwave spectrum of CF₃I it has been shown that the R(16) CO₂ laser line of the 9.4 μm band is coincident with the R(7), K = 2, $\text{F =}\text{19}\text{2}\text{→}\text{21}\text{2}$ transition of the CF₃, symmetric stretch (ν₁ band) of CF₃I. Using this laser line, 50 double resonance signals all with K = 2 were observed ranging from J = 4 → 5 to J = 12 → 13 transition. The fact that double resonance effects were observable over such a large range of J was explained as being caused by very strong ΔJ = ± 1, ΔK = 0 collisional transitions.Extremely large pumping effects were produced using 6 W of laser radiation, which caused relative changes in intensity ($\text{Δ}\text{I}\text{I}$) in ground state lines of up to 25. The population transfer into the excited state was so large that many excited state lines, which had previously been undetectable, produced signals up to 30 times more intense than the corresponding undisturbed ground state lines (i.e., values of $\text{Δ}\text{I}\text{I}$ of ～6000 were achieved). Population inversions were produced by the laser pump in many of the K = 2 microwave transitions, not only in those with levels directly pumped by the laser but also in some connected only by collisional transitions. The results was that many of the signals were observed as stimulated emissions rather than absorptions.The rotational constant and quadrupole coupling constants of CF₃I in the v₁ excited state are calculated and an estimation of the center of the ν₁ band is made. The absolute population shifts produced by the laser pump are estimated and the rate constants of the collisional transitions are discussed.     

Pure rotational spectrum of cyanopropyne in the v12 = 1 vibrational state

The micoowave and millimeter-wave spectrum of cyanopropyne, CH₃CCCN, in the lowest excited vibrational state, v₁₂ = 1 (E), has been observed in the frequency range from 8 to 220 GHz. The measurements up to the J = 53−52 transitions allowed us to determine the Coriolis coupling term and the l-type interaction term very precisely in addition to some of the sextic centrifugal terms. The contribution of the r-type interaction (Δk = ±1, Δl = ±2) has been found to be correlated with that of η_J, a centrifugal correction term to the first-order Coriolis interaction.     

Millimeter wave spectrum of acetonitrile oxide,CH3CNO,in the ν10 vibrational manifold: The ground state and the state v10 = 1

The pure rotational spectrum of CH₃CNO was measured in the frequency range 75 to 230 GHz. For the ground state, transitions were measured for J between 9 and 28 and for K from 0 to 12. In the v₁₀ = 1 state the measurements range from J = 0 to 19 and from K = 0 to 11. Numerous perturbations are observed, apparently due to accidental resonances with levels in other vibrational states. The contributions due to ΔK = 2, Δl = 2 matrix elements (l-type resonance and l-type doubling) are accounted for by matrix diagonalization, and the effects due to accidental resonances are presented graphically.     

The microwave spectrum of 14NH3 in the v = 000011 state

The frequencies and assignments of 50 lines in the pure inversion spectrum of ¹⁴NH₃ in the 0001¹ vibrational state are reported in the microwave frequency region 18–53 GHz and in selected regions up to 58 GHz.The J = 0 inversion frequency, K-type doubling constant K, l = 2, ?1 and molecular dipole moment in this state are 32 904.7 ± 2.0 MHz, 1.958 ± 0.040 MHz and 1.459 ± 0.002 D, respectively, where model inadequacies are included in the uncertainties of the first two parameters. The dipole moment measurements for this and the ground state are in excellent agreement with Stark laser measurements. An expression containing the effective l-type doubling constant is obtained from the combination of frequencies $\text{[ν(1, 1, 1) ? ν(1, 1, ?1) ? ν(2, 1, 1) + ν(2, 1, ?1)]}\text{8}\text{= 10 361.894 ± 0.004}\text{MHz}$. A preliminary value for the l-type doubling constant is 10 655 ± 20 MHz.     

Far infrared spectrum and spectroscopic constants of AsH3 in the ground state

The far ir spectrum of arsine, AsH₃, was recorded in the range 25–100 cm^?1 with a resolution of approximately 0.004 cm^?1. ΔJ = +1, ΔK = 0 rotational transitions were measured and assigned up to J″ = 12. These transitions, together with the presently available microwave and submillimeter-wave data and ground state combination differences, were analyzed on the basis of a rotational Hamiltonian which includes Δk = ±3 and Δk = ±6 interaction terms. The derived ground state molecular parameters reproduced the transition frequencies of both allowed and “perturbation allowed” transitions within the accuracy of the measurements. The equilibrium structure was determined for the AsH₃ molecule.     

The ν4 state inversion spectra of 15NH3 and 14NH3

The frequencies and assignments of 45 inversion transitions of ¹⁵NH₃ and 15 additional inversion transitions of ¹⁴NH₃ in the ν₄ state are reported. The J = 0 inversion frequency and K-type doubling constant for K,l = 2, ?1 are 31 602.72 MHz and 2.000 MHz for ¹⁵NH₃. The expression containing the effective l-type doubling constant, q₀ - 5q_J - Δη…, is calculated from the (J,K,l) = (1,1,1), (1,1,?1), (2,1,1), and (2,1,?1) transitions as 10 166.022 MHz. The contribution to this expression from the Coriolis coupling with 2ν₂ is estimated for ¹⁴NH₃.     

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” millimeter-wave transitions in arsine

A millimeter-wave spectrometer having a sensitivity of 4 × 10^?10 cm^?1 in the 2-mm region has been used for observation of the “forbidden” transitions J → J, K = ±4 → ±1 and J → J, K = ±5 → ±2 in AsH₃. A comprehensive computer analysis was made of the frequencies measured in this work together with available microwave frequencies of other transitions. This analysis provides accurate values of the rotational constants, nuclear quadrupole couplings, and effective structural parameters of the molecule. The spectral constants B₀ and C₀ (in MHz) are 112 470.597 and 104 884.665, respectively.     

The Rotational Spectrum of SiHF3 in the Vibrational State υ6=2: Observation of Direct l-Type Resonance Transitions

The υ₆=2 vibrational state of the main isotopomer of trifluorosilane, ²⁸SiHF₃, has been investigated in the centimeter- and millimeter-wave ranges. Rotational spectra following the Δ J=1, Δk=Δ l=0 selection rule have been measured up to J=24 and K=23 and for both values of ∣l∣. Two types of direct l-type resonance transitions induced by the (Δ l=Δk=±2) interaction could be observed by means of waveguide Fourier transform microwave spectroscopy in the range 8-26 GHz: 252 transitions following the Δ J=0, Δl=Δk=±2 selection rule covering values of J=7-39 and G=∣k-l∣ from 1 to 18 and 90 transitions following the Δ J=0, Δl=Δ k=±4 selection rule covering values of J=17-52 and G from 1 to 4. Due to the strong (2,2) resonance, 18 A₁-A₂ splittings of the k=l=±2 states from J=36-53 could also be observed. Accidental near-degeneracies lead to strong perturbations due to Δ (k-l)=±3 interactions, enabling the observation of perturbation-allowed transitions with selection rules k=±3(l=±2)↔±4(±2), ±2(±2), A₊↔ ±1(?2), A₋ and ± 1(0)↔± 6(±2). In a multiple-fit analysis the experimental data have been refined using five reduced forms of the effective Hamiltonian as proposed by Sarka and Harder [J. Mol. Spectrosc.197, 254-261 (1999)]. Parameters up to seventh order have been determined including the axial rotational constant C for both values of ∣l∣ and the vibrational separation of the ∣l∣=0 and 2 states. The unitary equivalence of the determined parameter sets has been demonstrated up to fifth order. Differences of the rotational constants in the various parameter sets have been explained by the theory of reduction. Sign relations of the fitted parameters and general features of the direct l-type resonance spectrum in a υ_t=2 level are discussed.     

l-type doubling transitions in Δ states of OCS

Molecular beam electric resonance spectroscopy has been used to measure the l-type doubling transitions in carbonyl sulfide. Transitions in J = 4 to J = 20 have been observed for the (02²0) vibrational state and for J = 1 and J = 2 for the (03¹0) state. The data has been analyzed to give the v = 2 energy separation $\text{E}{}_{\mathrm{<mtext>\Delta </mtext>}}{}^0\text{- E}{}_{\mathrm{<mtext>\Sigma </mtext>}}{}^0\text{= ?5.7861(2) + 8.36(1) × 10}{}^{\mathrm{?5}}\text{J(J + 1)}\text{cm}{}^{\mathrm{?1}}$, and the vibrational dependence of q to be 86.52(9)(v₂ + 1) KHz. The dipole moment of the (02²0) vibrational state is 0.6936(3) D.     

The bonded water molecule3ĪII: 180° Flips and diffusion

The proton spin-lattice relaxation time, T₁, is measured as a function of temperature in α -(COOH)₂·-2H₂O, K₂HgCl₄· H₂O and LiCHO·H₂O. The relaxation is caused by 180° flips of the water molecules about their 2-fold axes and good agreement is obtained between calculated and observed values of T₁. Empiricly the flip rate follows a classical Arrhenius equation: P· exp $\text{(? ΔH}\text{(RT))}$. A literature survey of values of P and ΔH obtained from similar investigations on other hydrates is given. The survey shows that the preexponential factor, P, is a function of the activation enthalpy, ΔH. P increases from 10¹² to 10¹⁷ Hz when ΔH changes from 2 to 17 $\text{kcal}\text{mole}$. Using a dynamical rate theory as formulated by Feit, we find the flip rate is given by: K₂· √(ΔH)· exp (K₁ΔH)· exp $\text{(?ΔH}\text{(RT>))}$. This expression can be fitted to the observed data using K₁ = 0.69 $\text{mole}\text{kcal}$ and K₂ = 2 × 10¹¹ Hz · $\text{(kcal}\text{mole)}$$\text{?1}\text{2}$. Thus both the frequency factor, K₂√ (ΔH), and the entropic factor, exp (K₁ΔH), have been obtained for flipping water molecules in hydrates. The values of K₁ and K₂ are shown to be physically reasonable.     

The ν2 + ν4 band of 12CF4

From a high-resolution diode laser spectrum of cooled ¹²CF₄, line assignments in ν₂ + ν₄ at 1066.4 cm^?1 have been made for tetrahedral subspecies to J = 20, and in many cases to higher J. Spectroscopic constants have been obtained from a least-squares fit of the Hamiltonian, and the relative intensities of the assigned lines have been calculated. The ground- and excited-state rotational constants, Coriolis constant, and splitting of the F₁ and F₂ vibrational substates have the values a.The CF bond length in the ground vibrational state is thus $\text{r}{}_0\text{= 1.31752 ± 0.00007}\text{A}\text{?}$. The analysis of a combination band such as this provides a method of obtaining ground-state spectroscopic constants of spherical-top molecules directly from the infrared spectrum, without the necessity of measuring weak “forbidden” transitions. The assignments allow accurate predictions of the frequencies emitted by the CO₂-pumped CF₄ laser.     

Microwave spectrum of the C4v molecule IF5 in the excited vibrational states v5(B1) = 1 and v9(E) = 1: Analysis of the ν5-ν9 Coriolis resonance

Measurements of the microwave spectrum of the C_4v molecule IF₅ in the excited vibrational states v₅(B₁) = 1 and v₉(E) = 1 are reported for the transitions J4 → 5, 5 → 6, 6 → 7, 8 → 9, and 9 → 10 (27–55 GHz). The Coriolis resonance interaction between these two states is analyzed by diagonalization of Hamiltonian matrices of dimension 3 × (2J + 1) in which all (Δl,Δk) = (±2, ±2)(q⁺), (±2, ±2)(q^?), and (0, ±4)(R₆) interactions are included as off-diagonal terms in addition to the v₅ = 1 ? v₉ = 1, l₉ = ±1(R₅₉) Coriolis interaction. In the v₉ = 1 state spectra, the $\text{B}{}_1\text{B}{}_2$l-doubling of the kl = ?1 transitions and $\text{A}{}_1\text{A}{}_2$ splittings of the kl = ?3 transitions and $\text{B}{}_1\text{B}{}_2$ splittings of the kl = +3 transitions, all enhanced by the Coriolis resonance, have been observed and measured. Least-squares refined rovibrational parameters for the v₅ = 1 and v₉ = 1 states are reported and a preliminary value for the rotational constant C₉ has been obtained.     

Doppler-limited dye laser excitation spectroscopy of HCCl

The cw dye laser excitation spectrum of the $\text{A}\text{?}{}^1\text{A″(050) ←}\text{X}\text{?}{}^1\text{A′(000)}$ vibronic band of HCCl was observed between 16 539 and 16 656 cm^?1 with the Doppler-limited resolution, 0.03 cm^?1. The HCCl molecule was generated by the reaction of discharged CF₄ with CH₃Cl. The observed spectra were assigned to c-type transitions with ΔK_a = ±1 and also to axis-switching transitions with ΔK_a = 0 or ?2, but all with K′_a = 0, both for HC³⁵Cl and HC³⁷Cl. A rotational analysis yielded the rotational constants and quartic centrifugal distortion constants for the ground vibronic state and the band origin. A weak vibronic band, about one-third as intense as the main band, was found at about 57 cm^?1 to the violet of the main band for both isotopic species, and was ascribed to a transition from the ground vibronic state to a vibrational level, possibly (041), of the à state. The rotational levels of HC³⁵Cl in the à state showed a large perturbation; the J′ = 8, 9, and 10 levels were found to be split into two components. A normal coordinate analysis was carried out to calculate the centrifugal distortion constants and the inertia defect, which were in fair agreement with the observed values. The molecular structure of HCCl in the ground vibronic state was recalculated from the rotational constants of the two isotopic species combined with the 0.75B₀ + 0.25C₀ value previously reported for DC³⁵Cl.