Anharmonic resonances between the v 1 + v ±1 6, v 3 + v ±1 5 + 2v 0 6 and v 3 + v ∓1 5 + 2v ±2 6 vibrational bands of CH3 79Br

The 22 K sub-bands, belonging to the v ₁ + v ^±1 ₆, v ₃ + v ^± ₅ + 2v ⁰ ₆ and v ₃ + v ^±1 ₅ + 2v ^±2 ₆ rovibrational bands of monoisotopic CH₃ ⁷⁹Br, have been identified. An RMS standard deviation of about 0·020 cm^-1 has been achieved by a least squares fit over 619 lines belonging to these 22 sub-bands. For this purpose, a model taking into account (a) anharmonic resonances between (i) v ₁ + v ^±1 ₆, and v ₃ + v ^±1 ₅ + 2v ⁰ ₆, (ii) v ₁ + v ^±1 ₆ and v ₃ + v ^?1 ₅ + 2v ^±2 ₆ and (iii) v ₃ + v ^±1 ₅ + 2v ⁰ ₆ and v ₂ + 2v ₃ + v ^±1 ₅ and (b) Coriolis resonances between the v ₂ and v ₅ modes, was used.     

Study of the spectrum of CH335C1 between 4250 and 4600 CM?1: thev2+v4 andv4+v5 rovibrational bands

About 2500 lines of CH₃ ³⁵Cl have been assigned. The strong xy Coriolis resonance between thev ₂ andv ₅ modes is quite visible between thev ₄+v ₄ ^±1 perpendicular band, centered around 4383 cm^–1, and thev ₄ ^±1 +v ₅ ^±1 perpendicular component, centered around 4475 cm^–1, with a crossing of upper energy levels allowing the observation of lines which are normally forbidden. Although not yet observed with certainty, because of the great density of lines of the spectrum, thev ₄ ¹ +v ₅ ^±1 parallel component is nevertheless detectable by its effects onv ₂+v ₄ ^±1 which is linked by Coriolis resonance to both components ofv ₄+v ₅. Moreover the spectrum is much complicated by many other resonances with weak bands which occur at level crossings: it is the case ofv ₂+3v ₆ ^±1 , connected tov ₂+v ₄ ^±1 by the well known Darling Dennison resonance which couplesv ₄ ^±1 and 3v ₆ ^±1 , and also ofv ₅ ^±1 +3v ₆ ^±1 connected tov ₄ ^±1 +v ₅ ^±1 by the same resonance; but this last case is complicated by an anharmonic resonance betweenv ₅ ^±1 +3v ₆ ^±1 and 2v ₃+3v ₆ ¹ . Two more perturbations occur on the K=–1 side ofv ₂+v ₄: a weak Coriolis resonance gives rise to one subband ofv ₁+v ₂ at a level crossing withv ₂+v ₄, and thev ₁+v ₅ band (linked of course tov ₁+v ₂ by the Coriolis resonance between thev ₂ andv ₅ modes) is quite visible and perturbs several subbands ofv ₂+v ₄ of high values of K through an anharmonic resonance. Moreover, the complex (3v ₅ ^±1 ,v+2v ₅ ⁰ , 2v ₂+v ₅ ^±1 , 3v ₂,v ₂+2v ₅ ^±2 , 3v ₅ ^±3 ) system of Coriolis-connected bands is linked to the bands studied in the present work by two Fermi resonances: one betweenv ₂+2v ₅ ⁰ andv ₁+v ₂, and the other one betweenv ₁+v ₅ and 3v ₅ ^±1 , whose several subbands have been observed on the low part of the spectrum. The values of all the band centres and of the different coupling constants have been estimated, but all these interactions make the line assignments and the interpretation of the spectrum very difficult.     

Rotational analysis of the v 2 + v 6 ±1, v 5 ∓1 + v 6 ∓1 and v 5 ∓1 + v 6 ±1 interacting infrared bands of methyl bromide

The rotational analysis of the infrared absorption spectrum of CH₃ ⁷⁹Br and CH₃ ⁸¹Br between 2150 and 2510 cm^-1 was performed on a Fourier transform spectrum with a resolution of 0·007 cm^-1. The bands v ₂ + v ₆(E) and v ₅ + v ₆(A ₁ + A ₂ + E) occur in this region, giving rise to several perturbations as in the corresponding system of methyl chloride [3]. Forbidden transitions, observed in correspondence of the level crossing of the x-y Coriolis coupling between v ₂ + v ₆ and v ₅ + v ₆(E), enabled us to estimate the value of A″ - 225D″_K at 5·16186 cm^-1 for CH₃ ⁷⁹Br and 5·16173 cm^-1 for CH₃ ⁸¹Br. The parallel system of v ₅ + v ₆ exhibits a perpendicular structure, and an l-type resonance couples those levels of the parallel and perpendicular components of v ₅ + v ₆ involved in transitions from the K″ = 0 levels of the ground state. The ^QQ ₀ branches of the A ₂ component of v ₅ + v ₆, made active by this resonance, are observed for both isotopic species.     

Vibration-rotation bands in ethane

The absorption spectrum of ethane was recorded at 0.014 cm^?1 resolution in the range 4500–6500 cm^?1 using a Fourier transform spectrometer and at room temperature. Eighteen bands could be identified and their type assigned. Upper state rotational constants are provided for the band at 5948.338 cm^?1 and Coriolis constants are obtained for most perpendicular bands. Vibrational assignments are suggested for the bands at 5948 cm^?1 (v7 + v10), 5914 cm^?1(v8 + v ₁₀+ v ₁₁), and 5852cm^?1 (v ₅+v ₁₀). All vibrational bands reported in the literature are gathered.     

Spin-flip laser spectra of ethylene in the 2000 cm-1 region

With the use of a Q-switched spin-flip Raman laser rovibrational lines of ethylene in the 2000 cm^-1 region have been measured with an accuracy of the order of 0·005 cm^-1. On the basis of these data and previous conventional high resolution spectra an analysis of v ₇ + v ₈, v ₄ + v ₈ and v ₁₀ + v ₈ has been performed. The results permit calculation of the harmonic and anharmonic contributions to the rotational constants of v ₇ and v ₇ + v ₈, and allow the v ₈ rotational constants to be estimated.     

N.M.R. investigation of critical orientational order fluctuations below the nematic-isotropic transition in liquid crystals

The high-resolution infra-red spectrum of SiH₄ in the region 2101 cm^-1 to 2265 cm^-1 has been analysed. Most of the lines observed have been assigned to transitions of the v ₃ and v ₁ bands of the abundant isotopic species ²⁸SiH₄. The v ₁ band is formally forbidden in the infra-red, but a vibration-rotation interaction between v ₁ and v ₃ lends intensity to the v ₁ transitions. The spectrum has been fitted by diagonalizing the v ₃ = 1 and v ₁ = 1 hamiltonians coupled by the vibration-rotation interaction term. 500 transitions have been fitted with an overall standard deviation of 0·007 cm^-1, using only 15 adjustable parameters (ten in the v ₃ = 1 hamiltonian, four in the v ₁ = 1 hamiltonian, and one interaction coefficient). The calculated intensities are also in good agreement with experiment. Transitions of the other isotopic species ²⁹SiH₄ and ³⁰SiH₄ have also been observed, but these spectra have not been analysed in detail.     

Higher ro-vibrational levels of H2O deduced from high resolution oxygen-hydrogen flame spectra between 6200 and 9100 cm-1

The spectra of hydrogen-oxygen and acetylene-oxygen flames have been recorded on a Fourier transform spectrometer in the region 6200–9100 cm^-1 with a resolution of 0·015 cm^-1. In this region, we have performed a detailed analysis of the 2v ₂ + v ₃, v ₁ + v ₃, v ₁ + v ₂ + v ₃ - v ₂ and v ₁ + v ₂ + v ₃ bands. A primary motive for this study was to obtain higher rotational energy levels for the (021), (101) and (111) vibrational states. Moreover an extensive set of rotational levels of the (010) vibrational state has been deduced from the combined study of hot bands involving the (011), (021) and (111) vibrational states. A room-temperature absorption spectrum of water recorded on a Fourier transform spectrometer in the region 1750–2300 cm^-1 (resolution 0·005 cm^-1) has also been used to confirm the analysis.     

High-resolution FTIR spectroscopy of the v11 and v2 + v7 bands of ethylene-d4

The Fourier transform infrared spectrum of the v₁₁ band of ethylene-d₄ (C₂D₄) has been recorded with an unapodized resolution of 0.006 cm^?1 in the frequency range 2150 to 2250cm^?1. The v₁₁ band, with a band centre of about 2201 cm^?1, was found to be perturbed by the nearby v₂ + v₇ band centred at about 2235 cm^?1 by a b-type Coriolis interaction. By fitting a total of 772 infrared transitions of v₁₁ using a Watson's A-reduced Hamiltonian in the I^r representation with the inclusion of b-type Coriolis interaction term, two sets of constants, up to quartic distortion constants for the v₁₁ = 1 state, and principal rotational constants for the v₂ + v₇ = 1 dark state, were derived. The inertia defect of the v₁₁ state was found to be 0.0693 ± 0.0004u Ų.     

High-resolution infrared and microwave study of 10BF2 OH and 11BF2OH: the 5, 6l, 71, 8l, 91 and 81 91 vibrationally excited states

Abstract

High-resolution (≤2.4×10^?3cm^?1) Fourier transform infrared spectra of gas-phase ¹⁰B-enriched isotopic and natural samples of BF₂OH (difluoroboric acid) were recorded in the 400–4000 cm^?1 spectral range. Starting from the results of a previous study [Collet, D., Perrin, A., Burger, H., and Flaud, J.-M., 2002, J. Molec. Spectrosc. 212, 118], which involved the v ₈ ¹⁰BF₂ out-of-plane bending) and v₉ (OH torsion) bands of ¹¹BF₂OH, it has been possible to perform the first rovibrational analysis of the v ₅ ¹⁰BF₂ bending), v ₈ , v ₉ and v ₈+v ₉ bands of’¹¹BF₂OH, and of the v ₇ (F₂BO in-plane bending), v ₅, and v ₈+v₉ bands of ¹¹BF₂OH up to very high rotational quantum numbers. In addition, microwave transitions within the 5¹, 6¹, 7¹ and 8¹ vibrational states of ¹¹BF₂OH were measured using predictions from ab initio calculations [Breidung, J., Demaison, J., D'Eu, J.-F., Margules, L., Collet, D., Mkadmi, E. B., Perrtn, A., And Thiel, W., 2004, J. Mol. S ectrosc. (in press)]. The v ₅, v ₈, v ₉ and v ₈+v ₉ bands of’ bands of ¹⁰BF₂OH and the v ₈+v ₉ band of'BF₂OH are not significantly affected by ptrturbations, and the experimental 5¹, 8¹ and 9¹ of ¹⁰BF₂OH and the 8¹9¹ energy levels of BF20H and ¹⁰BF₂OH could be reproduced using a simple Watson-type Hamiltonian. For the v ₅ and v ₇ bands of ¹¹BF₂OH, C-type Coriolis interactions coupling the 5¹ and 7¹ energy levels with those of the 7² and 6¹ dark states, respectively, were accounted for in the calculation. In addition, an updated set of rotational parameters was provided for the unperturbed 8¹ and 9¹ vibrational states of ¹¹BF₂OH using the data from our previous analysis. In all these cases, the upper state parameters derived in this work enabled the reproduction of both the infrared and microwave data to within experimental uncertainties.     

Line strength measurements of carbonyl sulfide (OCS) in the 2v3, v1+2v2+v3, and 4v2+v3 bands

To support planetary studies of the Venus atmosphere, we measured line strengths of the 2v₃, v₁+2v₂+v₃, and 4v₂+v₃ bands of the primary isotopologue of carbonyl sulfide (¹⁶O¹²C³²S), whose band centers are located at 4101.387, 3937.427, and 4141.212 cm⁻¹, respectively. For this, infrared absorption spectra in normal carbonyl sulfide (OCS) sample gas were recorded at an unapodized resolution of 0.0033 cm⁻¹ at ambient room temperatures using a Bruker Fourier transform spectrometer (FTS) at the Jet Propulsion Laboratory. The FTS instrumental line shape (ILS) function was investigated, which revealed no significant instrumental line broadening or distortions. Various custom-made short cells and a multi-pass White cell were employed to achieve optical densities sufficient to observe the strong 2v₃ and the weaker bands in the region. Gas sample impurities and the isotopic abundances were determined from mass spectrum analysis. Line strengths were retrieved spectrum by spectrum using a non-linear curve fitting algorithm adopting a standard Voigt line profile, from which Herman–Wallis factors were derived for the three bands. The band strengths of 2v₃, v₁+2v₂+v₃, and 4v₂+v₃ of ¹⁶O¹²C³²S (normalized at 100% of isotopologue) are observed to be 6.315(13)×10⁻¹⁹, 1.570(2)×10⁻²⁰, and 7.949(20)×10⁻²¹ cm⁻¹/molecule cm⁻², respectively, at 296 K. These results are compared with earlier measurements and the HITRAN 2004 database.     

The rotational spectrum of 13C2HD in the ground and excited bending states

The pure rotational spectrum of ¹³C₂HD was recorded in the range 100–700 GHz. Lines belonging to the ground vibrational state were observed from J^″ = 1 to J^″ = 11. Several absorption lines were also detected in the bending states v₄ = 1 (Π), v₅ = 1 (Π), v₄ = 2 (Σ⁺ and Δ), v₅ = 2 (Σ⁺ and Δ), v₄ = v₅ = 1 (Σ^?, Σ⁺ and Δ), v₄ = 3 (Π and Φ) and v₅ = 3 (Π and Φ). The transition frequencies measured in this work were fitted together with all the infrared lines available in the literature. The global fit allowed a very accurate determination of the vibrational, rotational and ?-type interaction parameters for the bending states of this molecule.     

High-resolution infrared spectrum of acetylene in the region of the bending fundamental v 5

The infrared spectrum of C₂H₂ in the region of the bending fundamental v ₅ has been studied at a resolution of about 0·015 cm^-1. The molecular constants G ₀(v ₅=1) = 730·3341 (1) cm^-1 and B ₀ = 1·176641 (2) cm^-1 have been derived. In addition to the fundamental, all the hot bands starting from the levels v ₄ and v ₅ have been investigated. The vibrational, vibration-rotation coupling and centrifugal constants for the excited vibrational states v ₅ = 2 and v ₄ = v ₅ = 1 have been derived using the vibration-rotation energy matrix.     

Self-diffusion at grain boundaries with a disordered atomic structure

A change in the free energy of a grain boundary is analyzed in the case when lattice vacancies come to the boundary and are then delocalized in its disordered atomic structure. It is shown that the free energy of the boundary is minimized at some excess atomic volume Δv _b =Δv _b ^* , whose value depends on the energy of vacancy formation in the crystal lattice and the boundary energy. The formation of a metastable localized grain-boundary vacancy as a result of thermal fluctuations of the density in a group of n ₀=\gM_v/Δv _b atoms (\gM_v is the vacancy volume), followed by the jump of an adjacent atom into this vacancy, is taken as an elementary event of grain-boundary diffusion. Expressions for the activation energy of diffusion and the diffusion coefficient are derived for equilibrium (Δv _b =Δv _b ^* ) and nonequilibrium (Δv _b >Δv _b ^* ) boundaries.     

The infra-red spectrum of 13CH3F and the general harmonic force field of methyl fluoride

Analyses of the v ₃, 2v ₃, and (predominantly) v ₁ parallel bands, and of the v ₄ and v ₆ perpendicular fundamentals have been made for ¹³CH₃F in terms of the rotational structure observed with a resolution of ～0·2 cm^-1. In addition, the band centres of the strongly Coriolis-interacting v ₂ and v ₅ fundamentals are accurately located. Some elucidation of the complex Fermi resonance interactions in the 3000 cm^-1 region is achieved through study of spectra of crystalline samples. This enables all three components of the v ₁, 2v ₂, 2v ₅ ⁰ triad to be observed for both ¹²CH₃F and ¹³CH₃F, and estimates to be made for the unperturbed vibration frequencies.

The ¹³C frequency shifts determined for all six fundamentals are used in conjunction with existing frequency, Coriolis ζ, and centrifugal distortion data for CH₃F, CD₃F, CHD₂F and CH₂DF, to determine the general harmonic force field for methyl fluoride. The extra shift data enable all 12 parameters of the force field to be fixed within narrow limits for the first time. The disagreement with predictions of the hybrid orbital model in the A₁ species can be attributed to the effect of trans repulsions arising from the fluorine lone-pair electrons, an effect which contributes to the longer CH bond in methyl fluoride compared with the other methyl halides.     

Vibration-inversion-rotation spectra of ammonia: Centrifugal distortion, Coriolis interactions, and force field in NH3, NH3, ND3, and NT3

An effective inversion-rotation Hamiltonian has been developed for NH₃ which avoids the necessity of having to include high powers of the inversion motion coordinate in the Taylor expansions of the potential energy and the inverse moment of inertia tensor. This nonrigid bender Hamiltonian describes the centrifugal distortion and the Coriolis interactions in the ground and excited inversion states. It also describes the inversion doublings in the ground and excited vibration-inversion states of ammonia. A least-squares procedure that includes the numerical integration of the Schrödinger wave equation has been used to determine the harmonic force field and the double-minimum inversion potential function for (¹⁴NH₃, ¹⁵NH₃) and for (¹⁴ND₃ and ¹⁴NT₃).The anomalous rotational dependence of the inversion doublings in the (±l) components of the v₄ = 1 state of ¹⁴NH₃ has been explained by the Coriolis interactions between v₂=1, v₄ = 1, v₂ = 2, v₂ = 1, v₄ = 1, and v₂ = 3 vibration-inversion states.     

High resolution study of the v 7 + v 8 band of ethylene (C2H4) at 1889 cm-1

The v ₇ + v ₈ A-type band of C₂H₄ has been recorded between 1932 and 1847 cm^-1 with a resolution of 0·06 cm^-1. The transitions with K _-1 ? 8> and J ? 2>5 have been assigned. Although slight Coriolis resonances perturb the band, the analysis has been made easy through the use of an elaborate set of asymmetric top computer programmes. The band centre and a set of upper state constants have been obtained. With these constants, 288 observed upper state energy levels have been fitted with a standard deviation of 0·021 cm^-1.

Using very simple expressions, we have predicted all the resonance effects perturbing the levels of ethylene near 2000 cm^-1. This led us to the identification of the v ₄ + v ₈ and v ₈ + v ₁₀ combination bands in low resolution spectra.     

Franck-Condon Factors and r-Centroids for the (B [sbnd] X) and (C [sbnd] X) Bands of the 107Ag 109Ag Molecule

Arrays of Franck-Condon factors q(v′, v″) and r-centroids r(v′, v″) were computed using Morse potentials for C¹Π [sbnd] X¹Σ⁺ _g and B O⁺ _u [sbnd] X¹Σ⁺ _g bands of the ¹⁰⁷Ag ¹⁰⁹Ag molecule.     

Electric field gradients created by near neighbour impurity atoms in a cubic silver host

The electric quadrupole interactions produced by near neighbour impurity atoms of Cu, Au, Zn, In, Sn and Bi on¹¹¹Cd probe nuclei in a cubic Ag lattice were studied by the TDPAC method. The effects of the type of impurity and its concentration have been investigated. The results show the presence of a high-frequency interactionv _Q ^h superimposed to a smeared out low frequencyv _Q ^l . The high frequency interaction, in the range 20 to 600 MHz, is attributed to impurity atoms located in nearest neighbour sites, while the low frequency interaction, in the range 2 to 12 MHz, is generated by impurities distributed at various different atomic distances from the probe nuclei. Bothv _Q ^h andv _Q ^l increase with impurity concentration leaving the ratiov _Q ^h /v _Q ^l almost constant. The results show that the high frequencyv _Q ^h is linearly dependent on the solute valence, and a logarithmic function of the impurity concentration, in the range 0.5 to 4.5 at. %. Large size effects have been observed in CuAg and BiAg alloys. Instead for ZnAg and SnAg, thev _Q ^h andv _Q ^l variation is attributed basically to charge effects.Work supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Financiadora de Estudos e Projetos (FINEP).     

2H-NMR Study of ammonium ion rotational tunneling and reorientation in (ND4)2SnCl6 single crystal

Because of the quadrupole interaction, the²H-NMR spectra of a tunneling ND ₄ ⁺ ion depend on the Larmor frequencyv ₀ and the tunneling frequencyv _t , when both frequencies are less than 20 MHz. Calculated single crystal spectra visualize features to be expected. Significant broadening and asymmetry are observed at level crossing regions aroundv _t =v ₀ orv _t =2v ₀. Angular, frequency and temperature dependences of the spectra are studied using an (ND₄)₂SnCl₆ single crystal. Experimental spectra obtained for different frequencies at 4.2K are fitted withv _t as a parameter. The tunneling frequency is also checked by measurements of the deuteron spin-lattice relaxation timeT ₁ as a fuction ofv ₀. Both methods give consistentlyv _t =7.15±0.10 MHz.     

4 Ag ↔2 Eg Transition of Mn4+ in Cs2TiF6: MnF6 2-

We report and interpret the ⁴ A_2g ?² E_g absorption, emission, linear dichroism, MCD and MCE of the MnF₆ ^2- octahedra at sites of D_3d symmetry in single crystals of Cs₂TiF₆. The spectra show many sharp features but a simplified calculation using cubic basis functions successfully accounts for all of the major features and much of the detailed structure. The electronic levels are not split by the trigonal field in first order but trigonal distortion splits the three-fold degenerate v ₆(t_2u ) vibration of the octahedron into a two-fold degenerate v ₆(e_u ) and a non-degenerate v ₆(a_1u ) vibration and these two vibrational modes give rise to the features 213 cm^-1 and 246 cm^-1 from the zero-phonon line respectively. Similarly the v ₄(t_1u ) vibration is split into a v ₄(a_2u ) and v ₄(e_u ) vibration and give the features at 313 cm^-1 and 340 cm^-1 respectively.

Several transitions involving two or more quanta of vibration are clearly seen in the emission and MCE spectrum. At an energy shift of greater than 700 cm^-1 from the zero-phonon transition these features are found to consist of progressions in the v ₁(a_1g ) breathing mode and the v ₂(e_g ) two-fold degenerate Jahn-Teller active mode. This structure can again be explained, with one exception, in terms of a calculation which assumes cubic basis functions. The exception is the reversal in sign of the MCE at a frequency v ₆(e_u ) + v ₂(e_g ) compared with that at v ₆(e_u ) which is not fully understood.