Anharmonic force field and vibrational frequencies of tetrafluoromethane (CF4_4) and tetrafluorosilane (SiF4_4)

Accurate quartic anharmonic force fields for CF$_4$ and SiF$_4$ have been calculated using the CCSD(T) method and basis sets of $spdf$ quality. Based on the {\it ab initio} force field with a minor empirical adjustment, the vibrational energy levels of these two molecules and their isotopomers are calculated by means of high order Canonical Van Vleck Perturbation Theory(CVPT) based on curvilinear coordinates. The calculated energies agree very well with the experimental data. The full quadratic force field of CF$_4$ is further refined to the experimental data. The symmetrization of the Cartesian basis for any combination bands of $T_d$ group molecules is discussed using the circular promotion operator for the doubly degenerate modes, together with tabulated vector coupling coefficients. The extraction of the spectroscopic constants from our second order transformed Hamiltonian in curvilinear coordinates is discussed, and compared to a similar procedure in rectilinear coordinates.Comment: (submitted to J. Chem. Phys.

Resolution of Maxwell's equations by the spectral moments method. Global approach

We present a systematic analysis, within the scope of electromagnetic theory, of the spectral moments method (SMM) and develop several ways to compute the linear response of any type of system. We show that the method can be used in diffraction studies regardless of the number, nature and form of the diffracting objects. Multiple diffraction is naturally taken into account in the computation. The method can thus be applied to determine propagation through any type of media. It is based on the computation of Green functions, solutions of discretized Maxwell's equations. Fourier transforms of Green functions are developed in continued fraction. Two approaches will be presented. In the first “global” approach, all space is discretized, the coefficients of continued fractions are computed directly from the dynamic matrix obtained by the discretization of Maxwell's equations and from sources and receivers. In the second “local” approach, only the diffracting system is discretized. This paper is devoted to the global approach. We study two important problems in electromagnetism, i.e. propagation of a plane wave through a heterogeneous layer and scattering of an isolated object. We present two computation techniques for plane wave propagation: one uses a small grid, is very rapid but the results are approximate; the other uses a large grid, is less rapid but the results are exact. We show that computing the reflectivity and/or transmissivity of photonic lattices is now a very simple problem. For scattering, we mainly report a series of tests on some canonical systems, such as cylinders or spheres, showing that SMM results are in very good agreement with the analytical results. Several types of absorbing boundary conditions are tested. We report results on backscattering cross-sections and the impulsional response of different one-, two- and three-dimensional systems

Analyse rotationnelle de la bande ν4 de 12CH4 de 1 225 à 1376 cm-1

The rotational analysis of the threefold degenerate infrared absorption band ν4 of 12CH4 has been carried out up to the fourth order of approximation, by least squares techniques, from a spectrum obtained by Botineau at O. N. E. R. A. ; 250 vibration-rotation lines have been identified (from P12 to R13), in a region between 1 225 to 1 376 cm-1. The values of 16 spectroscopic constants have been computed by considering 141 lines, 72 % of which are reproduced to better than 2 x 10-2 cm-1, and 47 % to better than 10-2 cm-1.L'analyse rotationnelle, au quatrième ordre d'approximation, de la bande fondamentale triplement dégénérée ν 4 de 12CH4 est effectuée sur un spectre à haute résolution enregistré récemment à l'O. N. E. R. A. par Botineau ; on utilise à cette fin une méthode itérative de moindres carrés avec amortissement, adaptée au calcul sur ordinateur. Dans la région de 1 225 cm-1 à 1 376 cm-1 on identifie 250 raies de vibration-rotation de P12 à R13. On détermine les valeurs de 16 constantes spectrales telles que 72 % des 141 transitions participant au calcul soient reproduites avec une erreur inférieure à 2 x 10-2 cm-1, et 47 % avec une erreur inférieure à 10-2 cm-1

Resolution of Maxwell's equations by spectral moments method. Local approach

In previous work, we have presented a computation method based on the determination of the Green functions of the electromagnetic field with the help of the spectral moments method (SMM). In this method, the Green functions are calculated in the form of continued fractions, and one determines the coefficients of their development. Two approaches have been presented: one, we call global approach, where all space is discretized in a box, the other, we call the local approach, where only the diffracting item is considered. In this work we present the results obtained for the one, two and three-dimensional cases by the local approach. We first develop the necessary tools for the computing. We establish the analytical form of the Green functions of the continuous vacuum and of the discretized vacuum, the dispersion curves and the selection rules which appear. We show that the real part of the diagonal Green functions is directly linked to the vibrational density of states and therefore perfectly determined whatever dimension the space is. Longitudinal, non physical modes are found to play a subsequent role. As regards scattering, we principally report a series of tests on some canonical systems, such as cylinders or spheres, showing that the backscattering cross- section and the impulsional response obtained with SMM are in very good agreement with the analytical results. Bi-static scattering cross section is also studied

Analyse de la bande ν2 + ν4 de 12CF 4. Coïncidences pour J' ≤ 40 avec les raies de CO 2

The ν2 + ν4 band of 12CF 4 is analysed using an interferometric spectrum (max. path diff. = 5 m). The assignment of the transitions is systematically performed up to J' = 40. Altogether 4 300 transitions are identified within 1 750 experimental lines. A theoretical model limited to the third order is used to fit the data and to adjust simultaneously the 3 ground state parameters and the 14 upper state (υ2 = υ4 = 1) parameters. The transition wavenumbers are now defined within 0.001 cm- 1, due to the accuracy of both spectrum and theoretical model. The results are then used to set up the list of all coincidences between the 12CF 4 transitions (J' ≤ 40) and the laser lines of 16 O12C16O, 18O12C18 O, 16O12C18O, 16O 13 C16 O and 18C13C18O, within a tuning range of ± 1 500 MHz.La bande ν2 + ν4 de 12CF 4 a été analysée à partir d'un spectre interférométrique (d.d.m. max = 5 m). L'attribution des transitions a été effectuée de façon systématiquejusqu'à J' = 40, soit au total 4 300 transitions correspondant à 1 750 raies expérimentales. L'analyse des données à partir d'un modèle théorique limité au 3e ordre d'approximation a permis de déterminer simultanément les 3 paramètres relatifs à l'état fondamental et les 14 paramètres relatifs à l'état υ2 = υ4 = 1. Grâce à la qualité du spectre et du modèle théorique, les nombres d'ondes des transitions sont définis avec une précision de 0,001 cm-1. Ces résultats ont été utilisés pour établir la liste complète des coïncidences entre les transitions de 12CF4(J' ≤ 40) et les raies des lasers 16O12C16O, 18O12C18O, 16O12C18 O, 16O13C16O, et 18O 13C18O, dans une plage d'accord de ± 1500 MHz

Dipole moment matrix for vibration - rotation transitions in C3v molecules

The transformed dipole moment or C3v molecules has been worked out up to second order of approximation on the basis of its invariance properties. Its dependence on the total angular momentum components has been made explicit. The dipole moment matrix has been written with a view to calculate vibration-rotation intensities in the case of strongly interacting vibrational polyads. The importance of a coherent phase system for correct intensity calculations has been emphasized.Le moment dipolaire transformé des molécules C3v a été calculé jusqu'au second ordre d'approximation sur la base de ses propriétés d'invariance. Sa dépendance par rapport aux composantes du moment angulaire total a été explicitée. La matrice moment dipolaire a été écrite pour permettre le calcul des intensités de vibration-rotation dans le cas des polyades vibrationnelles fortement interagissantes. L'importance de la cohérence des facteurs de phase pour un calcul rigoureux des intensités a été soulignée

PHOSPHINE IN THE 5μM5 \mu M OBSERVATION WINDOW OF JUPITER: LINE STRENGTHS, H2−H_{2}- AND He- BROADENED WIDTHS

Author Institution: Laboratoire d'Infrarouge, Associ\'e au CNRS, Bot 350Laboratory spectra of pure, hydrogen- and helium-broadened phosphine were recorded, near $5 \mu m$, using high resolution Fourier transform spectrometer (apodized resolution $0.0054 cm^{-1})$. The lines under study belong mainly to the $\nu^{2} + \nu^{4}$ transition. A number of lines pertaining to the neighbouring $2\nu^{2}$ and $2\nu^{4} (\bot$ and //) bands were also analyzed. A first series of spectra, of pure phosphine under low pressure ($\sim 0.3 Torr$) at 296 and 180 K, was used for vibration-rotation analysis and line strength measurements. A second set, consisting of hydrogen- and helium-broadened spectra (total pressure $\sim 120$ Torr) at temperatures ranging from 170 to 296 K, yielded collisional line widths along with their temperature dependence. The true broadening coefficients and line strenths were directly derived from the measured values of the apparent width and peak transmission of the recorded lines. For this purpose, correction tables were previously built up by convolving the instrument function of the interferometer with a series of synthetic Voigt lines of given strengths and lorentzian widths

PROGRESS IN THE ROTATIONAL ANALYSIS OF TRIPLY DEGENERATE FUNDAMENTAL BANDS OF TETRAHEDRAL XY4XY_{4} MOLECULES

Author Institution: Facult\'{e} des Sciences, Laboratoire de Spectroscopie Mol\'{e}culaireUsing the general development of AMAT and NIELSEN’s transformed Hamiltonian, expressed in a convenient form of tensorial operators by MORET-BAILLY for the tetrahedral $XY_{4}$ molecules, it becomes possible to extend to large values of J the analysis of the three-fold degenerate fundamental bands $\nu_{3}$ and $\nu_{4}$ of these molecules. Starting with the formula of MORET-BAILLY we construct. Hamiltonian matrices, the elements of which depend linearly on 19 parameters. The usual procedure is to evaluate these parameters by least squares adjustment of theoretical results in agreement with spectral data. The contribution to energy of some seven parameters may be expected to be appreciable mainly for large values of the rotational quantum number J. For these values, the bases used in MORET BAILLY’s representation become inadequate, the corresponding selection rules become less and less accurate and other lines, improperly called ``forbidden’’ lines, appear the influence of non-diagonal matrix elements, due to the increasing value of J, is so important that finally the eigen-states are a complex mixture of MORET-BAILLY’s bases and the same effect is also observed in the line intensities. In other words, most of the transitions allowed by group-theory are possible. This theory has been applied to the bands $\nu_{3}$, $\nu_{4}$ of $CH_{4}$ and $\nu_{4}$ of $CD_{4}$. Our computed results are in good agreement with the experimental data and explain entirely the fine details of the I.R. spectra of these bands

INVESTIGATION OF THE ABSORPTION SPECTRUM OF 12CF4^{12}CF_{4} AT 16 μ\mum

Author Institution:The absorption spectrum of $^{12}CF_{4}$ has been recorded at room temperature in the range $591-675 cm^{-1}$ with a resolution of about $0.010 cm^{-1}$. The rotational structure of the $\nu_{4}$ band has been analyzed up to $J^{\prime} = 70$. A total a 869 line clusters have been fitted with an overall standard deviation of $0.003 cm^{-1}$, giving rise to the following set of spectroscopic constants (in $cm^{-1}$): m = 631.20029 (27) n = 0.5215235 (66) p = 1.26242 $(85) \times 10^{-4}$ q = -6.210 $(18) \times 10^{-7}$ g = -2.6682 $(24) \times 10^{-5}$ h = 1.2981 $(38) \times 10^{-7}$ $z^{\prime} = -2.01 (26) \times 10^{-11}$ The quoted errors are one standard deviation. A number of transitions belonging to hot bands have also been identified. The analysis of the strongest of them presumably $\nu_{2} + \nu_{4} - \nu_{2}$, is presently in progress

Défauts cis-trans dans le polyacétylène

La présence de courtes séquences ris dans l’isomère trans du polyacétylène a été proposée par de nombreux auteurs. Dans ce travail nous étudions l’activité de modes infrarouge, produite par la présence d’un tel défaut. Un modèle dynamique pour les chaînes cis et trans parfaites a été élaboré en tenant compte des dernières attributions de raies, basées sur des spectres obtenus en lumière polarisée. Le défaut ris est ensuite introduit dans une séquence trans. Plusieurs géométries ont été étudiées. Nous trouvons qu’un défaut portant sur une cinquantaine de carbone permet d’expliquer l’origine d’un certain nombre de raies jusqu’à présent non attribuées dans le matériau trans