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Featured researches published by R. Lemus.


Annals of Physics | 1996

A general algebraic model for molecular vibrational spectroscopy

A. Frank; R. Lemus; R. Bijker; F. Pérez-Bernal; J. M. Arias

Abstract We introduce the anharmonic oscillator symmetry model to describe vibrational excitations in molecular systems exhibiting a high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and configuration space formulations, leading to new interactions in the algebraic model. This approach incorporates the full power of group theoretical techniques and provides reliable spectroscopic predictions. We illustrate the method for the case of D 3h-triatomic molecules.


Journal of Molecular Spectroscopy | 1991

Vibrational spectra of linear triatomic molecules in the vibron model

F. Iachello; S. Oss; R. Lemus

Abstract We report results of calculations of five linear triatomic molecules, N 2 O, C 12 O 2 , C 13 O 2 , OCS, and HCN, with average r.m.s. deviations of 1–5 cm −1 within the framework of the vibron model. The corresponding algebraic force field constants are derived. Calculations of intensities of stretching vibrations in CO 2 and HCN are also presented.


Chemical Physics Letters | 1999

SU(2) approximation to the coupling of Morse oscillators

A. Frank; R. Lemus; M. Carvajal; C. Jung; E. Ziemniak

Abstract We show that the SU(2) vibron model automatically gives the correct coupling between Morse oscillators as long as they only interact via the dominant Δv=±1 selection rule. We compare the SU(2) approximation with the model introduced by Child and Lawton, where the coupling is harmonic. The well-known harmonically coupled anharmonic oscillator model (HCAO) can thus be modified to consistently incorporate anharmonicity maintaining an analytic framework. We also discuss the classical phase space for the Morse oscillator case and its relation to the harmonic and SU(2) approximations.


Chemical Physics | 2000

An extended SU(2) model for coupled Morse oscillators

M. Carvajal; R. Lemus; A. Frank; C. Jung; E. Ziemniak

Abstract The SU(2) vibron model has been shown to correspond to an approximation where only the dominant Δv =±1 interaction between Morse oscillators is taken into account [A. Frank, R. Lemus, M. Carvajal, C. Jung, E. Ziemniak, Chem. Phys. Lett. 308 (1999) 91]. We extend the algebraic model in order to incorporate higher-order couplings for the Morse oscillators, thus, providing a means to establish an exact quantum-mechanical connection with traditional phase-space descriptions of molecular vibrations. Results for the energy spectrum for two coupled Morse oscillators are compared with both the traditional and extended SU(2) models, as well as with the Child–Lawton model. The wave functions corresponding to the different models are also examined. A classical analysis is carried out in order to further explore the interrelations between these models.


Journal of Chemical Physics | 1994

ALGEBRAIC APPROACH TO VIBRATIONAL SPECTRA OF TETRAHEDRAL MOLECULES : APPLICATION TO METHANE

R. Lemus; A. Frank

We present an algebraic approach to describe the vibrational excitations of polyatomic molecules. The model is based on the coupling of anharmonic oscillators and is characterized by combining the strengths of the Lie‐algebraic methods with those of point symmetry techniques. We illustrate the algebraic method for tetrahedral molecules and apply it to the construction of the complete vibrational spectra of methane up to four quanta.


Journal of Molecular Spectroscopy | 1997

Symmetry-Adapted Algebraic Description of Stretching and Bending Vibrations of Ozone

F. Pérez-Bernal; J. M. Arias; A. Frank; R. Lemus; R. Bijker

Abstract The vibrational excitations of ozone, including both bending and stretching vibrations, are studied in the framework of a symmetry-adapted algebraic approach. This method is based on the isomorphism between the U (2) algebra and the one-dimensional Morse oscillator, and the introduction of point group symmetry techniques. The use of symmetry-adapted interactions, which in the harmonic limit have a clear physical interpretation, makes it possible to systematically include higher-order terms and anharmonicities. A least-squares fit to all published experimental levels (up to 10 quanta) of 16 O 3 and 18 O 3 yields rms deviations of 2.5 and 1.0 cm −1 , respectively.


Chemical Physics | 2002

Connection of the vibron model with the modified Pöschl–Teller potential in configuration space

R. Lemus; R. Bernal

Abstract The modified Poschl–Teller (MPT) potential is analyzed by a realization of its dynamical group in configuration space. The expansions of the coordinate and momentum in terms of the creation and annihilation operators are obtained from this realization. A system of two MPT oscillators interacting via a potential coupling bilinear in the coordinate x is studied. This analysis allows to establish an exact quantum-mechanical connection between the su(2) vibron model and the traditional description of molecular vibrations. It is shown that the su(2) vibron model corresponds to taking the dominant Δv =±1 interaction in an approximate fashion. The energy spectrum for the system of coupled oscillators is compared with both the su(2) vibron model and the more general approach of considering higher-order terms of the expansions in the algebraic space. In addition, a two oscillator system with an interacting potential in terms of the variables u i =tanh( αx i ) is analyzed. Comparison of the spectrum generated by this system with previous results in the space ( p , x ) suggests that u is the natural variable to describe the Poschl–Teller systems.


Molecular Physics | 2003

A general method to obtain vibrational symmetry adapted bases in a local scheme

R. Lemus

A general approach to obtain symmetry adapted bases from a local set of states is presented. The approach is based on the identification of the invariant subspaces which, when projected by means of the eigenfunction method developed by Chen (1989, Group Representation Theory for Physicists Singapore, World Scientific), allow the generation of a symmetry adapted basis. The symmetrized functions so obtained are further taken as a basis to diagonalize simultaneously a set of normal number operators, which provides a set of normal states expanded in terms of the symmetry adapted local basis. In this approach the normal number operators are generated implicitly from the one quantum space through a tensorial formalism. Although the normal operators are defined in a harmonic basis, the locality of the basis allows the approach to be extended to anharmonic functions. This approach has the additional advantage of allowing the elimination of the spurious states, a common problem in a local coordinate representation. An important advantage of this symmetrization method is that it allows generation of a code to analyse any molecular system with a minimum set of input data.


Molecular Physics | 2011

Equivalent rotations associated with the permutation inversion group revisited: symmetry projection of the rovibrational functions of methane

O. Álvarez-Bajo; R. Lemus; M. Carvajal; F. Pérez-Bernal

In this work the analysis of the equivalent rotations from the permutation inversion group formalism is revisited. We emphasize that explicit knowledge of changes in the Euler angles are not required in order to determine the transformation that a given symmetry operation causes to the rotational functions when dealing with the permutation inversion group formalism. Indeed, matrix elements of the equivalent rotations are provided by a single Wigners D (j)(R) function. Taking advantage of this, we propose a symmetry projection approach to build the rovibrational functions of methane. This approach focuses on the relevance of the isomorphism between permutations and equivalent rotations. In our method, symmetry adapted functions are obtained by simultaneous diagonalization of a set of commuting operators, whose representation is given in terms of direct products of Wigners D functions and vibrational matrix representations provided by a local scheme. The proposed approach is general and permits us to obtain in a systematic fashion an orthonormal set of symmetry-projected functions, with good total angular momentum, and carrying the irreducible representations of the molecular symmetry group.


Chemical Physics Letters | 1996

On the relation between algebraic and configuration space calculations of molecular vibrations

F. Pérez-Bernal; R. Bijker; A. Frank; R. Lemus; J. M. Arias

Abstract The relation between algebraic and traditional calculations of molecular vibrations is investigated. An explicit connection between interactions in configuration space and the corresponding algebraic interactions is established.

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A. Frank

National Autonomous University of Mexico

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J. M. Arias

National Autonomous University of Mexico

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M. Sánchez-Castellanos

National Autonomous University of Mexico

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R. Bijker

National Autonomous University of Mexico

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C.A. Amezcua-Eccius

National Autonomous University of Mexico

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R. D. Santiago

National Autonomous University of Mexico

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