Search results for "algebraic approach"

STUDY OF THE INTERNAL DYNAMICS OF NON PLANAR PYRAMIDAL MOLECULES IN VIBRATIONALY VERY EXCITED STATES.

2007

From the U (p+1) formalism, we built a Hamiltonian adapted to the stretching modes of nonplanar XY3 molecules having the C3v group of geometrical invariance. This Hamiltonian is then coupled with two possible Hamiltonians describing the bending modes of these molecular system: a) based on the U (p+1) approach, a bending Hamiltonian is developed and the interaction between the bending and the stretching modes is taking into account through adapted 2:1 resonance coupling operator defined as a Us(4) x Ub(4) enveloping algebra operator ; b) based on the standard normal modes formalism, a bending modes Hamiltonian is expanded and the 2:1 interaction is taken into account as a tensorial product o…

Vibrational Spectra of Polyatomic Molecules through an Algebraic Approach

1987

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.

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

1997

Vibrational modes of the stibine molecule

2005

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.

Algebraic study of pyramidal molecules in the very excited vibrational states.

2005

In the frame of the algebraic formalism U(p+1), we developed the method to build a vibrational Hamiltonian corresponding to a set of three identical oscillators. In order to test the model, we apply it to the molecules of stibine and arsine. We introduce a supplementary intermediate group K(3) inspired by the similar formalism used in nuclear physics. This group K(3) gives additional labels for classification of the energy levels. The eigenvalues of these invariant operators distinguish the local states of the molecule. Then we study the coupling of the vibrational modes of stretching and bending for the non plane XY3 molecules. We present the construction of an algebraic operator of coupli…

Rovibrational interactions in the local-mode limit. The (n000) stretching overtone bands of spherical tops.

1993

Théorie des spectres rovibroniques des molécules octaédriques : Hamiltonien et moments de transition

2002

This thesis is devoted to the treatment of rovibronic couplings of octahedral species for which the Born-Oppenheimer approximation is broken down. By using the octahedral formalism, a full effective rovibronic model is extended from works about molecules in a non-degenerate electronic state. This effective model is dedicated to molecules with an odd or an even number of electrons and it has been successfully applied to V(CO)6 and ReF6. For both of them we have four interacting vibronic sublevels attributed to a dynamical Jahn-Teller effect and giving rise to very complicated spectra. This model is validated by the overall agreement between predicted and observed band profiles. Moreover, an …

?Almost? mean-field ising model: An algebraic approach

1991

We study the thermodynamic limit of the algebraic dynamics for an "almost" mean-field Ising model, which is a slight generalization of the Ising model in the mean-field approximation. We prove that there exists a family of "relevant" states on which the algebraic dynamics αt can be defined. This αt defines a group of automorphisms of the algebra obtained by completing the standard spin algebra with respect to the quasiuniform topology defined by our states. © 1991 Plenum Publishing Corporation.

Algebraic approach to vibrational spectra of tetrahedral molecules. First order infrared intensity model.

1995

International audience; The algebraic approach we have proposed to describe the vibrational stretching modes of polyatomic molecules (Leroy and Michelot, J. Mol. Spectrosc. 151, 71–96 (1992); Can. J. Phys. 72, 274–289 (1994)) is applied to the silane molecule for up to seven quanta. We then suggest a form of the dipole operator adapted to the (n000) local states by combining the strength of group theory method with the necessity of a compact formulation.