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.     

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.     

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.     

Ground state rotational energies of C3v quasi-spherical top molecules: Applications to 16OPF3 and PH3

Rotational spectra of the quasi-spherical symmetric molecules, ¹⁶OPF₃ and PH₃, are analyzed with all the data currently available. In both cases the current formulation that uses rotational contact transformations to completely diagonalize the ground state energy matrix appears to be inadequate, due to the smallness of the quantity |;A₀ ? B₀|. This quantity represents only 5% of A₀ or B₀ in the case of OPF₃ and 11% in the case of PH₃. Thus, both analyses require the resonance terms in ΔK = ±3 and/or ΔK = ±6 to be taken into account through diagonalization of the energy matrix. The ground state parameters as well as the ground state energies are given for both molecules.     

“Forbidden” rotational spectra of symmetric-top molecules: PH3 and PD3

A millimeter-wave spectrometer having a sensitivity of 4 × 10^?10 cm^?1 in the 2-mm region has been constructed for observation of extremely weak millimeter-wave spectra of gases. It has been used to measure J → J, K = 0 ← 3 transitions in PH₃ and J → J, K = 0 ← 3 as well as K = ±1 ← ±4 transitions in PD₃. The B₀ and C₀ spectral constants (in MHz) are: for PH₃, B₀ = 133 480.15 ± 0.12 and C₀ = 117 488.85 ± 0.16; for PD₃, B₀ = 69 471.10 ± 0.03 and C₀ = 58 974.37 ± 0.05. The effective ground-state values obtained for the bond angle and bond length are: for PH₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.420}{}_0$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.34}{}_5$; for PD₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.417}{}_6$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.35}{}_9$. The corresponding zero-point-average values were calculated to be: for PH₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4269}{}_9\text{± 0.0002}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.228}{}_7$; for PD₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4226}{}_5\text{± 0.0001}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.256}{}_7\text{± 0.004}$. For both species, the equilibrium values are $\text{r}{}_{\mathrm{e}}\text{(}\text{A}\text{?}\text{) = 1.4115}{}_9\text{± 0.0006}$ and $\text{α}{}_{\mathrm{e}}\text{(}{}^{\mathrm{o}}\text{) = 93.32}{}_8\text{± 0.02}$.     

Raman spectra of HfS3

We report the first order Raman spectra of a one-dimensional semiconducting compound HfS₃ at 300 and 77 K. The detected phonons are associated with the different point group symmetries involved in the crystal's structure.     

Spectroscopy of XY3Z (C3v) molecules: A tensorial formalism adapted to the O (3) ⊃ C∞v ⊃ C3v group chain

A tensorial formalism adapted to the case of XY₃Z symmetric tops has been developed. We use the O (3) ⊃ C_∞v ⊃ C_3v group chain. All the coupling coefficients and formulas for the computation of the matrix elements are given for this chain. Such relations are also deduced in C_3v group itself.     

Raman spectra of ZrS3

We report the first order Raman spectra of a one-dimensional semiconducting compound ZrS₃ at 300 and 77 K. Four phonons have been detected and associated with the crystal's symmetry.     

Etude par spectroscopies Raman et infra-rouge des vibrations de valence vOH du glycerol cristallise

The v_OH stretching vibrations of crystalline glycerol have been investigated at various temperatures by infra-red and Raman spectroscopy. The temperature and crystal field effects are discussed.     

The analysis of symmetric rotor Raman spectra: The pure rotational spectrum of 11BF3

The pure rotational Raman spectrum of ¹¹BF₃ has been photographed. Great care was taken in the analysis to consider all the unresolved components under each observed Raman line profile. If this is ignored, systematic errors result. The final set of molecular constants obtained was B₀ = 0.34502(±3 × 10^?5)cm^?1, D_J = 4.38(±0.10) × 10^?7cm^?1, and D_JK = ?9.1(±1.0) × 10^?7cm^?1.     

Intensities of rotational lines in combination 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 combination bands of axially symmetric molecules of the group C_3v. The calculation utilizes the contact transformation method through first order of approximation as outlined by Hanson and Nielsen. General formulas for the intensities of the lines in the parallel combination band (ν_n + ν_n′) and perpendicular combination band (ν_m + ν_n) are obtained. It is found that to this order of approximation the usual selection rules ΔJ = 0, ±1 and ΔK = 0 are observed for the parallel combination band. For the perpendicular combination band the selection rules are more complicated, being ΔJ = 0, ±1, Δl_m = +1 and ΔK = +1 or ?2, Δl_m = ?1 and ΔK = ?1 or +2, Δl_m = ±3 and ΔK = 0. Specific intensity formulas are then given for the (ν₁ + ν₃) parallel and (ν₂ + ν₃) perpendicular combination bands of ammonia.     

The vt=1 Rovibrational Hamiltonian for C3v Symmetric Top Molecules Containing One Quadrupolar Nucleus: Reductions and Application to AsF3

The reduction of the effective Hamiltonian has been derived for C_3v symmetric top molecules in the v_tequals;1 state with extension to nuclear quadrupole coupling. The theory has been applied to the hyperfine structures of rotational transitions observed for AsF₃ (v₄equals;1) [H. Bürger, J. Demaison, P. Dréan, C. Gerke, L. Halonen, H. Harder, H. Mäder, J. Radtke, and H. Ruland, J. Mol. Spectrosc.180, 85-99 (1996)]. The data have been analyzed using two reduced forms of the effective Hamiltonian which follow the reductions Q and D [E. I. Lobodenko, O. N. Sulakshina, V. I. Perevalov, and Vl. G. Tyuterev, J. Mol. Spectrosc.126, 159-170 (1987)] in the pure rovibrational case. The unitary equivalence of the derived parameter sets has been demonstrated.     

Formation of Sim and SimCn clusters by C60 sputtering of Si

The secondary ion mass spectrum of silicon sputtered by high energy C₆₀⁺ ions in sputter equilibrium is found to be dominated by Si clusters and we report the relative yields of Si_m⁺ (1 ≤ m ≤ 15) and various Si_mC_n⁺ clusters (1 ≤ m ≤ 11 for n = 1; 1 ≤ m ≤ 6 for n = 2; 1 ≤ m ≤ 4 for n = 3). The yields of Si_m⁺ clusters up to Si₇⁺ are significant (between 0.1 and 0.6 of the Si⁺ yield) with even numbered clusters Si₄⁺ and Si₆⁺ having the highest probability of formation. The abundances of cluster ions between Si₈⁺ and Si₁₁⁺ are still significant (>1% relative to Si⁺) but drop by a factor of ∼100 between Si₁₁⁺ and Si₁₃⁺. The probability of formation of clusters Si₁₃⁺-Si₁₅⁺ is approximately constant at ∼5 × 10⁻⁴ relative to Si⁺ and rising a little for Si₁₅⁺, but clusters beyond Si₁₅ are not detected (Si_m≥16⁺/Si⁺ < 1 × 10⁻⁴). The probability of formation of Si_m⁺ and Si_mC_n⁺ clusters depends only very weakly on the C₆₀⁺ primary ion energy between 13.5 keV and 37.5 keV. The behaviour of Si_m⁺ and Si_mC_n⁺ cluster ions was also investigated for impacts onto a fresh Si surface to study the effects that saturation of the surface with C₆₀⁺ in reaching sputter equilibrium may have had on the measured abundances. By comparison, there are very minor amounts of pure Si_m⁺ clusters produced during C₆₀⁺ sputtering of silica (SiO₂) and various silicate minerals. The abundances for clusters heavier than Si₂⁺ are very small compared to the case where Si is the target.The data reported here suggest that Si_m⁺ and Si_mC_n⁺ cluster abundances may be consistent in a qualitative way with theoretical modelling by others which predicts each carbon atom to bind with 3-4 Si atoms in the sample. This experimental data may now be used to improve theoretical modelling.     

Microwave spectrum and molecular force field of tetratomic C2v molecules: NO2Cl

The rotational constants and quartic centrifugal distortion constants for NO₂³⁵Cl and NO₂³⁷Cl have been determined from an analysis of rotational transitions in the microwave and millimeter wave regions between 8.2–40 and 90–120 GHz, respectively.The values of the in-plane force constants in the general harmonic potential field have been obtained by combination of infrared and microwave data. Vibrational frequencies of ¹⁴NO₂Cl and ¹⁵NO₂Cl, inertia defects of NO₂³⁵Cl in the excited vibrational states v₃ = 1 and v₅ = 1, and first-order centrifugal distortion constants of NO₂³⁷Cl are the experimental data used in the least-squares fitting determination of force constants.     

Some Raman bands of C3O2

The ν₁, ν₅, 2ν₅, and 2ν₆ Raman band accumulations of carbon suboxide, C₃O₂, have been photographed with a resolution of 0.2–0.3 cm^?1. Each band accumulation consists, in addition to the main band, of a large number of “hot” bands due to the extremely low, highly anharmonic ν₇ fundamental vibration. In the 2ν₆ band accumulation a few series of unresolved Q branches have been assigned. In the ν₁ and 2ν₅ band accumulations most Q branches almost coincide, forming a very intense peak, whereas the dominating feature of the ν₅ band accumulation is a minimum, in agreement with the expectation of an extremely weak Q branch for a Π_g fundamental band. Tentative values of ν₁ = 2196.9 ± 0.1 cm^?1 and ν₅ = 580.2 ± 0.5 cm^?1 as well as several energy values in the ν₇ manifold of the 2ν₆⁰ state are obtained. Further, improved exposures of the ν₂ + 2ν₇⁰ band accumulation yield some levels in the ν₇ manifold of the ν₂ state, in addition to those determined previously.     

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.     

掺钐和掺镧铁酸铋的拉曼光谱

本文对Bi1-xSmxFeO3和Bi1-xLaxFeO3样品的拉曼光谱进行了研究, 结果表明当掺Sm量达15%时, 170 cm-1和272 cm-1模消失, 287 cm-1新模出现, Bi1-xSmxFeO3样品发生了三角到三斜的结构相变; 而当La量达30%时, 175 cm-1、219 cm-1和348 cm-1模消失, Bi1-xLaxFeO3样品才发生三角到正交的结构相变。这归因于Sm的有效离子半径与Bi的差别较大。掺杂导致的拉曼峰蓝移归因于离子间的作用增强。     

Effect of substitution-type disorder in GaS1-xSex layer solid solutions on Raman scattering spectra

An experimental study has been carried out to investigate Raman scattering spectra of GaS_1-xSe_x solid solutions in which a one-dimensional localization of interlayer mode due to a disorder in the layer stacking was observed.