SU(2) approximation to the coupling of Morse oscillators

Frank, A.; Lemus, R.; Carvajal, M.; Jung, Christof; Ziemniak, E.

doi:10.1016/s0009-2614(99)00576-x

Cited by 64 publications

(82 citation statements)

References 29 publications

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“…Their relation with the structure constants, however, was still lacking. Recently, it was shown that the U(2) model automatically gives the correct coupling between Morse oscillators as long as they only interact via the dominant ⌬v ϭ Ϯ1 selection rule (43). This result not only clarifies the approximation involved when considering the U(2) group, but also suggest a procedure to extend the model to obtain a description closer to the Morse oscillators results (44).…”

Section: Su(2) Approximationmentioning

confidence: 67%

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Vibrational Excitations of Methane in the Framework of a Local-Mode Anharmonic Model

Lemus

Frank

2000

Journal of Molecular Spectroscopy

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Section: Su(2) Approximationmentioning

confidence: 67%

“…where the coefficients ␤ i ⌫,␥, x are identical to the ones appearing in the coordinate projection [42]- [43]. Transformation [55] provides a realization of the tensors -Ϯ, x ⌫,␥ , and consequently of the Hamiltonian [50], in terms of local operators a i † (a i ).…”

Section: Normal-mode Descriptionmentioning

confidence: 99%

Vibrational Excitations of Methane in the Framework of a Local-Mode Anharmonic Model

Lemus

Frank

2000

Journal of Molecular Spectroscopy

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“…Here b † i (b i ) with i = 1, 2 are creation and annihilation operators acting on the Morse eigenfunctions [57]. The anhar-monization (59) is equivalent to consider the linear approximation [29,30,60] …”

Section: Force Constants In the Algebraic Approachmentioning

confidence: 99%

“…The exact connection of the U (2) model with the Morse and Pöschl-Teller potentials was established in Refs. [29,30,33]. This connection opened up the possibility of obtaining force constants from the optimized values of Hamiltonian parameters [31,32,40].…”

Section: Introductionmentioning

confidence: 99%

“…The 1D limit of the vibron model assigns a U (2) dynamical algebra to each vibrational degree of freedom [28], a description which turns out to be equivalent to the algebraic treatment of a set of interacting Morse oscillators [29,30]. Although at first Morse oscillators were considered only to be a convenient description of stretching modes, later on they were also introduced to model asymmetric bending oscillations involved in non-linear semi-rigid molecules [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

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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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An algebraic alternative for the accurate simulation of CO₂ Raman spectra

Bermúdez-Montaña

Carvajal

Pérez‐Bernal

et al. 2020

J Raman Spectroscopy

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We present an accurate simulation of the Raman spectrum of the carbon dioxide molecule in the 1150–1500 cm−1 spectral range, comparing the results obtained using the three polyad schemes found in the literature of this molecule. The description of the molecule with the algebraic U1(2)×U(3)×U2(2) local model encompasses both stretching and bending degrees of freedom. A detailed analysis of the Hamiltonian interactions for the three polyad schemes provides fittings with root mean square deviations in the range 0.14–0.20 cm−1, involving 19 parameters taking into account the 178 experimental term energies found in the literature. Using a limited subset of 9 experimental transition moments, we optimize 5 partial derivatives of the mean polarizability and simulate the Raman spectrum of CO2 for the three polyad schemes. Comparing the calculated results with the experimental spectrum, we obtain an overall good agreement for the three polyads. However, an inspection in detail of the spectrum seems to show a slight preference for polyad P212 albeit not due to the interaction characterizing the polyad but due to anharmonic effects and energy distribution. Finally, we assess the effect of the Fermi resonance over CO2 Raman line intensities.

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SU(2) approximation to the coupling of Morse oscillators

Cited by 64 publications

References 29 publications

Vibrational Excitations of Methane in the Framework of a Local-Mode Anharmonic Model

Vibrational Excitations of Methane in the Framework of a Local-Mode Anharmonic Model

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

An algebraic alternative for the accurate simulation of CO₂ Raman spectra

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SU(2) approximation to the coupling of Morse oscillators

Cited by 64 publications

References 29 publications

Vibrational Excitations of Methane in the Framework of a Local-Mode Anharmonic Model

Vibrational Excitations of Methane in the Framework of a Local-Mode Anharmonic Model

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

An algebraic alternative for the accurate simulation of CO2 Raman spectra

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An algebraic alternative for the accurate simulation of CO₂ Raman spectra