Algebraic time-reversal operation

International audience; We analyze the implementation of the time-reversal (TR) transformation in the algebraic approach to tetrahedral local molecules through the chain of groups U(5) U(4) K(4) = A(4) ^ S(4) S(4) Td. We determine the general form of the TR operation using a purely algebraic realization, based exclusively on the requirement that the irreducible representations must not be changed under the time inversion symmetry. As a result we can determine the TR behavior of purely algebraic operators.

Vibrational Spectra of Polyatomic Molecules through an Algebraic Approach

The study of molecular oscillators may be performed with algebraic methods based upon dynamical chains and their realization in terms of boson operators. From the dynamical algebra U(p+1) for p equivalent oscillators, associated with stretching modes, the local, pseudo-normal and normal limits are obtained through appropriate subgroup chains and various realizations of the U(p+1) generators. Similar technics can be applied to bending modes. Application to XY4 molecules will be presented.

The Vibrational Stretching States of the Pyramidal Molecules: Application to the Arsine and Stibine.

Algebraic Study of XYn Molecules in Vibrationaly High Excited States

Application du formalisme U(p+1) à la molécule de silane

Séminaire invité, Université de Villeneuve d'Ascq, France

The U(p+1) formalism applied to XY3 molecules in vibrationaly high excited states

Séminaire invité : Institut for Physical Research, NASA ; Ashtarak, Arménie

Rovibrational Interactions in the Local-Mode Limit: The (n000) Stretching Overtone Bands of Spherical Tops

Abstract We present a tensorial formalism adapted to the study of the ( n 000) rovibrational stretching states of spherical tops in the local mode limit. A local symmetrized rovibrational basis is built to take explicitly into account the fact that, in these states, the local symmetry is C 3ν rather than T d . Likewise, we introduce local rovibrational operators to build an effective Hamiltonian for these states. We then test our model by fitting the energy levels of 28 SiH 4 for 3 ≤ n ≤ 5.

Symmetry-adapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups

International audience; We present a short review on the tensorial formalism developed by the Dijon group to solve molecular spectroscopy problems. This approach, originally devoted to the rovibrational spectroscopy of highly symmetrical species (spherical tops) has been recently extended in several directions: quasi-spherical tops, some symmetric and asymmetric tops, and rovibronic spectroscopy of spherical tops in a degenerate electronic state. Despite its apparent complexity (heavy notations, quite complex mathematical tools), these group theoretical tensorial methods have a great advantage of flexibility: a systematic expansion of effective terms for any rovib- rational/rovibronic probl…

Vibrational Spectrum of Phosphine Molecule

Symmetrized Local States and Effective Dipole Moment within a Rovibrational Cartesian Picture.

Vibrational modes of the stibine molecule

International audience; In this paper, we use the algebraic approach to describe the vibrational modes of stibine molecule (of C3v molecular symmetry group) up to 21 quanta. As the stibine molecule exhibits stretch-bend resonances, we build an algebraic pyramidal coupling operator between stretching modes and bending modes adapted to this molecule. The standard deviation associated to the fit of the vibrational levels is 1.75 cm-1.

A local picture associated with a triply degenerate vibrational mode: vibrational and rovibrational local states

International audience; Abstract: A symmetrized basis adapted to the study of some vibrational excited states of spherical top molecules is proposed. This basis, consistent with the Cartesian picture associated with a three-dimensional mode, is then tested numerically through various XY6 and XY4 molecules. In addition, some simulations, made with 238UF6 and a simplified version of an effective Hamiltonian, clearly show that the method can be further extended through the construction of a symmetrized local rovibrational basis.

Opération de renversement du temps appliquée a un hamiltonien algébrique adapté aux molécules tétraédriques.

Nous analysons la formulation de l'opération de renversement du temps (RVT) dans le cadre de l'approche algébrique des molécules tétraèdriques locales. Cette approche est basée sur les propriétés mathématiques de la chaîne de groupes U(5) <-- U(4) <-- K(4) = A(4) ^ S(4) <-- S(4) = Td (1) adaptée au système moléculaire étudié. Nous déterminons la forme générale de la transformation RVT pour une réalisation purement algébrique de tous les opérateurs, en imposant que les représentations irréductibles associées à a la chaîne (1) soient invariantes dans la symétrie RVT. Le résultat essentiel est que nous déduisons le comportement dans l'opération RVT de tous les opérateurs de notre formalisme, n…

Le formalisme algébrique U(p+1) adapté aux modes de pliage des molécules tétraédriques.

A Tensorial Formalism Adapted to the Rovibronic Couplings in the Colored Hexafluorides: Application to the nu(5)(F(2g)) and nu(3)(F(1u)) Modes.

A tensorial formalism adapted to the case of transition-metal hexafluorides in a degenerate electronic state has been developed on the basis of preceding works about spherical-top molecules in a nondegenerate electronic state. We have introduced electronic operators constructed using group theory features and some physical considerations. Vibronic couplings (Jahn-Teller effect, etc.) have been reviewed for the triply degenerate vibrational modes nu(5)(F(2g)) and nu(3)(F(1u)) leading to the identification of the main vibronic parameters. For the first time, an effective rovibronic Hamiltonian as well as the effective transition moment operators (dipole moment and polarizability) for rovibron…

Symmetry adaptation of spherical tensor quantities in cubic point groups: comments on a paper by M. Rey et al.

We underline some inconsistencies in the work [J. Mol. Spectrosc. 219 (2003) 313] concerning symmetry adaptation in cubic groups. Also we show that some rather complicated methods presented can be easily avoided.

Generalized algebraic treatment for XY2 molecules : application to D2S.

Symmetry of molecular properties

The symmetry of coefficients in the expansion of a given molecular property are shown to be obtainable through well defined tensor methods. The analytical expansions required of various vibrational and rotational tensors are given up to the fourth degree in dynamical variables. To illustrate the method, some rovibrational properties of spherical tops are considered. The symmetry of the associated molecular constants is expressed, simultaneously, for XY4 and XY6 molecules, by algebraic relations involving the independent constants and the coupling symbols of the molecular symmetry group. To allow comparisons, some examples are given for which the symmetry of the constants has been published …

Algebraic Treatment of a Three-Oscillator System: Applications to Some Molecular Models

Abstract A new algebraic treatment of a three-oscillator system, called 3d formalism, is proposed. First, arbitrary tensor operators, expressed in terms of elementary creation and annihilation boson operators, are built within the standard algebraic chain u (3) ⊃ so (3) ⊃ so (2). Their matrix elements are next derived in a standard basis. Some applications, which require few adaptions or extensions, are proposed. They allow one to recover, for instance, Hecht's and tetrahedral Hamiltonians associated with threefold degenerate modes of spherical molecules and the vibron model Hamiltonian introduced for diatomic molecules.

Su(4) approach to fourfold degenerate electronic states of some hexafluoride molecules

Abstract We show that two appropriate realizations of the su (4) algebra allow the construction of all electronic operators needed for the study of vibronic and rovibronic interactions in a G ′ electronic state. In each case a full bosonic realization is made and all matrix elements are calculated. Illustrations of our formalism and comparisons with previous approaches are made in the case of ν 5 ( F 2 g ) and ν 3 ( F 1 u ) modes.

Vibrational interactions and resonances in XY2 molecules of C2v symmetry. Algebraic application to D2S system.

U(p+1) : Application aux états moléculaires très excités.

International audience

The local group K(4) in the algebraic approach to vibrational spectra of tetrahedral molecules: Application to silane

Abstract In a previous paper, Michelot and Moret-Bailly (J. Phys., 48, 51 (1987)) proposed an algebraic treatment of vibrational stretching modes in polyatomic molecules. They used the properties of the group chain U(p + 1) ⊃ U(p) ⊃ S(p) ⊃ G for the study of p identical oscillators. The molecule, with p equivalent bonds described as a system of p oscillators, has a symmetry group G. We develop in this paper an application to p = 4 equivalent oscillators. We show that, for a tetrahedral molecule, the group chain U(5) ⊃ U(4) ⊃ S(4) ≈ Td can be completed, in a local point of view, with a particular group K(4): U(5) ⊃ U(4) ⊃ K(4) ⊃ S(4) ≈ T d This group provides us with available labels which c…