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.

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.

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

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.

Unitary Approach to Vibrational Spectra of Tetrahedral Molecules: Generalized Infrared Intensity Model.

International audience; In this paper we further extend a previous formalism, the construction of a dipole function adapted to tetrahedral molecules. The extension is based on an algebraic construction of symmetrized tensor operators through unitary algebra and point group symmetry. We prove that this generalization allows us to find the particular formalism that has been established and satisfactorily tested in a previous paper (C. Leroy et al., J. Mol. Spectrosc. 175, 289–295 (1996)).

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.

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.