Composantes cubiques normales des tenseurs spheriques

Champion, Jean‐Paul; Pierre, G.; Michelot, F.; Moret-Bailly, Jacques

doi:10.1139/p77-070

Cited by 106 publications

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“…A detailed description of the main theoretical features can be found in the original paper [10] and in subsequent reviews [14,25]. This approach has been already successfully applied to complex band systems of symmetric top molecules like CH 3 D [26,27,28] and CH 3 Cl [29,30].…”

Section: Theoretical Modelmentioning

confidence: 99%

“…In fact, apart from degeneracy considerations, due to the quasi spherical character of the inertia tensor of the molecule and to specic quasi coincidences among its vibrational fundamental frequencies, the vibrational pattern of the phosphine molecule is quite similar to that of the methane molecule. The phosphine molecule was then a good candidate for the global approach successfully developed for spherical tops [10,11] and extensively applied to other complex band systems encountered in polyatomic molecules [12,13,14]. The vibrational spectrum of PH 3 and its isotopomers has also been investigated by ab initio calculations [15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

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Global modeling of the lower three polyads of PH3: Preliminary results

Nikitin

Champion

Butler

et al. 2009

Journal of Molecular Spectroscopy

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In order to model the high-resolution infrared spectrum of the phosphine molecule in the 3 µm region, a global approach involving the lower three polyads of the molecule (Dyad, Pentad and Octad) as been applied using an eective hamiltonian in the form of irreducible tensors. This model allowed to describe all the 15 vibrational states involved and to consider explicitly all relevant ro-vibrational interactions that cannot be accounted for by conventional perturbation approaches.2245 levels (up to J = 14) observed through transitions arising from 34 cold and hot bands including all available existing data as well as new experimental data have been tted simultaneously using a unique set of eective hamiltonian parameters.The rms achieved is 0.63 × 10 µm by dividing the rms reported by previous works by a factor 6. A preliminary intensity analysis based on consistent sets of eective dipole moment operators for cold and hot bands has been simultaneously undertaken for direct comparison between observed and modeled absorption from 700 to 3500 cm −1 .Keywords : Phosphine ; PH 3 ; Vibrational polyads ; Global modeling ; Near infrared ; High-resolution ; Positions ; Intensities IntroductionAs part of extensive eorts to support remote sensing of Jupiter and Saturn many works have been devoted to the high-resolution infrared spectrum of phosphine [1,2,3, 4, 5, 6, 7]. Recent works focused on the 3 µm region reported experimental measurements and assignments [5, 7], but so far no comprehensive modeling was reported.1 hal-00355701, version 1 -23 Jan 2009 At present, the line parameters of phosphine (positions and intensities) in the 3 µm region rely essentially on the empirical database reported in Ref. [7] and included in HITRAN [8] and GEISA [9]. In the spectral region from 2700 to 3500 cm −1 , the HITRAN compilation contains over 3000 unassigned PH 3 lines with intensities ranging from 1. × 10 −25 to 1.5 × 10 −22 cm×molecule −1 . Moreover, only one hot band arising from the upper state of ν 2 is included. The main reason for this lack of modeling is the fundamental limitation of conventional perturbation approaches. So far, only weakly interacting features could be tted using isolated band models while strongly interacting states were left out. In fact, apart from degeneracy considerations, due to the quasi spherical character of the inertia tensor of the molecule and to specic quasi coincidences among its vibrational fundamental frequencies, the vibrational pattern of the phosphine molecule is quite similar to that of the methane molecule. The phosphine molecule was then a good candidate for the global approach successfully developed for spherical tops [10,11] and extensively applied to other complex band systems encountered in polyatomic molecules [12,13,14]. The vibrational spectrum of PH 3 and its isotopomers has also been investigated by ab initio calculations [15,16,17,18]. Recent works have reported ab initio vibrational energies [19,20] and theoretical transition moments [21]. The experimental data involv...

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Section: Theoretical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global modeling of the lower three polyads of PH3: Preliminary results

Nikitin

Champion

Butler

et al. 2009

Journal of Molecular Spectroscopy

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“…More generally, state vectors (1.1) with j integer or half of an odd integer are of considerable interest in electronic spectroscopy of paramagnetic ions in finite symmetry [4,5] and/or in rotational-vibrational spectroscopy of molecules [6,7].…”

Section: Introductionmentioning

confidence: 99%

SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases

Albouy¹

2007

SIGMA

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Abstract. This paper deals with bases in a finite-dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU 2 corresponding to an irreducible representation of SU 2 . The representation theory of SU 2 is reconsidered via the use of two truncated deformed oscillators. This leads to replacement of the familiar scheme {j 2 , j z } by a scheme {j 2 , v ra }, where the two-parameter operator v ra is defined in the universal enveloping algebra of the Lie algebra su 2 . The eigenvectors of the commuting set of operators {j 2 , v ra } are adapted to a tower of chains SO 3 ⊃ C 2j+1 (2j ∈ N * ), where C 2j+1 is the cyclic group of order 2j + 1. In the case where 2j + 1 is prime, the corresponding eigenvectors generate a complete set of mutually unbiased bases. Some useful relations on generalized quadratic Gauss sums are exposed in three appendices.

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“…Appropriate theoretical models for such symmetric tops [7] and [8] are already available from formalisms developed for spherical rotors [9] and [10]. Accurate representation of the positions and intensities of this molecule requires that the polyad scheme be used.…”

Section: Introductionmentioning

confidence: 99%

Preliminary analysis of CH3D from 3250 to 3700cm−1

Nikitin

Champion

Brown

2006

Journal of Molecular Spectroscopy

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The infrared spectrum of CH3D from 3250 to 3700 cm =1 was studied for the rst time to assign transitions involving the ν2+ν3, ν2+ν5, ν2+ν6, ν3+2ν6 and 3ν6 vibrational states. Line positions and intensities were measured at 0.011 cm =1 resolution using Fourier transform spectra recorded at Kitt Peak with isotopically enriched samples.Some 2852 line positions (involving over 900 upper state levels) and 874 line intensities were reproduced with RMS values of 0.0009 cm =1 and 4.6%, respectively. The strongest bands were found to be ν2 + ν3 at 3499.7 cm =1 and ν2 + ν6 at 3342.5 cm =1 with integrated strengths, respectively, of 8.17 Ö 10 =20 and 2.44 Ö 10 =20 (cm =1 /molecule · cm =2 ) at 296 K (for 100% CH3D). The eective Hamiltonian was expressed in terms of irreducible tensor operators and adapted to symmetric top molecules. Its present conguration in the MIRS package permitted simultaneous consideration of the four lowest polyads of CH3D: the Ground State (G.S.), the Triad from 6.3 to 9.5 mm, the Nonad from 3.1 to 4.8 mm and now the Enneadecad (19 bands) from 2.2 to 3.1 mm. The CH3D line parameters for this interval were calculated to create a new database for the 3 mm region.

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Composantes cubiques normales des tenseurs spheriques

Cited by 106 publications

References 0 publications

Global modeling of the lower three polyads of PH3: Preliminary results

Global modeling of the lower three polyads of PH3: Preliminary results

SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases

Preliminary analysis of CH3D from 3250 to 3700cm−1

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Composantes cubiques normales des tenseurs spheriques

Cited by 106 publications

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Global modeling of the lower three polyads of PH3: Preliminary results

Global modeling of the lower three polyads of PH3: Preliminary results

SU2 Nonstandard Bases: Case of Mutually Unbiased Bases

Preliminary analysis of CH3D from 3250 to 3700cm−1

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SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases