A General Algebraic Model for Molecular Vibrational Spectroscopy

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

doi:10.1006/aphy.1996.0129

Cited by 80 publications

(72 citation statements)

References 18 publications

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“…Physically, these contributions arise from the anharmonic character of the interatomic interactions, and seem to play an important role when dealing with molecular anharmonicities, especially at higher number of quanta. This conclusion is supported by our other applications of the symmetry-adapted model to the Be 4 cluster [16] and the H + 3 , Be 3 and Na + 3 molecules [19], as well as our study of two isotopes of the ozone molecule [20].…”

Section: Discussionsupporting

confidence: 74%

“…(13,15) and carry out the building up procedure to construct the Hamiltonian and states with a higher number of quanta with the appropriate projection operators and Clebsch-Gordan coefficients [19].…”

Section: H Triatomic Moleculesmentioning

confidence: 99%

“…In the case of Be 4 we present a comparison with ab initio calculations, while for CH 4 we present a detailed comparison with experiment. The application of these techniques to other molecules, as well as a more complete presentation can be found in references [16,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

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A Symmetry Adapted Algebraic Approach to Molecular Spectroscopy

Frank

Lemus

Bijker

et al. 1997

Symmetries in Science IX

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Section: Discussionsupporting

confidence: 74%

Section: H Triatomic Moleculesmentioning

confidence: 99%

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A Symmetry Adapted Algebraic Approach to Molecular Spectroscopy

Frank

Lemus

Bijker

et al. 1997

Symmetries in Science IX

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“…In particular, a one-to-one correspondence can be established between eigenstates of the Morse-Schrödinger equation, h͉͘ϭ͉͘ with hϭ p 2 /2m ϩV(x), and the representations of U(2), ͉N,͘, the latter being characterized by two quantum numbers which specify the total number of bound levels, 1ϩN/2 or 1ϩ(NϪ1)/2 ͑N even or N odd͒, and the vibrational index, , such that ϭ0,1...N/2 or (NϪ1)/2. When recast in the U(2) basis, the Morse Hamiltonian assumes the simple form hϭ 0 ϩAC where 0 and A signify constant modeling parameters while C is related to the invariant quadratic Casimir operator C of the subalgebra O(2) ͓with eigenvalues m 2 ϭ(NϪ2) 2 ͔ by means of: 65,66 Cϭ…”

Section: Lie Algebraic Analyses a Lie Algebraic Realization Of Tmentioning

confidence: 99%

The vibronically-resolved emission spectrum of disulfur monoxide (S2O): An algebraic calculation and quantitative interpretation of Franck–Condon transition intensities

Müller

Vaccaro

Pérez‐Bernal

et al. 1999

The Journal of Chemical Physics

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Emission spectra obtained from jet-cooled disulfur monoxide (S 2 O) molecules have been interpreted by means of a novel Lie algebraic formalism that makes possible the facile evaluation of multidimensional Franck-Condon factors. Fluorescence accompanying selective excitation of isolated vibronic bands in the S 2 O C 1 AЈ-X 1 AЈ(*-) absorption system has been dispersed under moderate spectral resolution, allowing assignment of ground state levels possessing up to 20 quanta of vibration in the 2 S-S stretching mode ͓E vib (X )р13 900 cm Ϫ1 ͔. Aside from providing a rigorous and economical description for the inherently anharmonic nature of highly-excited polyatomic species, our algebraic approach enables quantitative information on molecular wavefunctions to be extracted directly from spectroscopic data. The emerging picture of S 2 O vibrational dynamics suggests that the X 1 AЈ potential surface is substantially more ''local'' in character than the C 1 AЈ manifold. While the observed pattern of X 1 AЈ vibrational energies could be reproduced well through use of model Hamiltonians that include only diagonal anharmonicities in the local algebraic basis, successful treatment of the C 1 AЈ state necessitated explicit incorporation of off-diagonal anharmonicities that lead to pervasive mixing of local vibrational character. This disparate behavior is manifest strongly in measured C -X transition strengths, thereby allowing detailed investigations of Franck-Condon intensities to discern the underlying dynamics. Structural parameters deduced from algebraic analyses are in good accord with previous predictions of the change in S 2 O geometry accompanying *-excitation.

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“…However, in molecular systems, if the Hamiltonian goes beyond one and two-body operators, the number of interactions is greater than the number of invariant operators [59]. Consequently another prescription should be used to construct the Hamiltonian.…”

Section: Algebraic Approach To Triatomic Moleculesmentioning

confidence: 99%

A novel connection between algebraic spectroscopic parameters and force constants in the description of vibrational excitations of linear triatomic molecules

Sánchez-Castellanos

Lemus

Carvajal

et al. 2009

Journal of Molecular Spectroscopy

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A connection between an algebraic approach to the dynamics of triatomic molecules based on the U (2) × U (3) × U (2) Lie algebra and the traditional description in configuration space is presented. The connection is established in four steps. First, the molecular Hamiltonian is expanded in symmetrized local coordinates. Second, the Hamiltonian is transformed into an algebraic representation by introducing the realization of coordinates and momenta in terms of bosonic creation and annihilation operators of normal character. The third step is to perform a canonical transformation applied to the bosons associated with the stretching degrees of freedom in order to obtain a unified representation in a local scheme. Finally, an anharmonization procedure is applied to identify the U (2) × U (3) × U (2) dynamical algebra. The main advantage of the proposed approach is that it provides relations between the spectroscopic parameters and the molecular structure and force constants. As an application, the analysis of the vibrational excitations of CO 2 in its ground electronic state is considered. In this scheme, each stretching degree of freedom is identified as an interacting Morse oscillator, with an associated U (2) dynamical algebra, and the doubly degenerate bending degree of freedom is modelled with a U (3) dynamical algebra, obtaining as a final result a reasonable set of force constants.

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A General Algebraic Model for Molecular Vibrational Spectroscopy

Cited by 80 publications

References 18 publications

A Symmetry Adapted Algebraic Approach to Molecular Spectroscopy

A Symmetry Adapted Algebraic Approach to Molecular Spectroscopy

The vibronically-resolved emission spectrum of disulfur monoxide (S2O): An algebraic calculation and quantitative interpretation of Franck–Condon transition intensities

A novel connection between algebraic spectroscopic parameters and force constants in the description of vibrational excitations of linear triatomic molecules

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