An extended SU(2) model for coupled Morse oscillators

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

doi:10.1016/s0301-0104(00)00258-5

Cited by 64 publications

(82 citation statements)

References 35 publications

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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: 98%

“…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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Section: Force Constants In the Algebraic Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…For simplicity, we have assumed that the system is one dimensional (x and E point in the same direction) and neglected the transverse nature of the electromagnetic field and any magnetic effects. By identifying the number states |n with the Morse eigenfunctions φ n (x) and comparing the matrix elements [13] φ n+α |x|φ n and φ n+α |p|φ n of the position x and the momentum p operators with those of the deformed boson operators n + α|(A † ) α |n and n − α|A α |n we may obtain expressions for x and p in terms ofn, A and A † ,…”

Section: Interaction With a Driving Fieldmentioning

confidence: 99%

“…The coefficients f ij , g ij , are functions of the excitation number operatorn and are given by [13] …”

Section: Interaction With a Driving Fieldmentioning

confidence: 99%

Nonlinear response of a deformed oscillator

Récamier

Mochán

Maytorena

2005

Int J of Quantum Chemistry

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We analize the response of a single anharmonic diatomic molecule to a monochromatic time dependent electric field E ω (t) and evaluate the temporal evolution of the dipole moment, phase space trajectories and several transition probabilities as a function of the intensity of the field. We define deformed boson operators A † = f (n)a † , A = af (n) in terms of the usual harmonic oscillator creation and annihilation operators a, a † ,n = a † a and choose the number operator function f (n) such that the energy spectrum of a harmonic oscillator-type Hamiltonian written in terms of the deformed operators yield an energy spectra similar to that of a Morse potential. TheoryMuch work has been devoted to the study of the optical linear and nonlinear response of harmonic systems to time dependent electric and magnetic fields either with classical [1] or quantum mechanical treatments [2,3]. Laser pulses with well controlled temporal characteristics of amplitude and frequency have a high potential for selective manipulation of the internal state of atoms and molecules [4,5,6]. Cooling techniques have allowed the trapping and manipulation of atoms by optical means, however, fluctuations of the electromagnetic fields used to trap or to modify the quantum state lead to decoherence in ion traps and limits the trap stability [7]. A study involving multiple photon excitation for a linearly driven anharmonic oscillator using 1

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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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An extended SU(2) model for coupled Morse oscillators

Cited by 64 publications

References 35 publications

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

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

Nonlinear response of a deformed oscillator

An algebraic alternative for the accurate simulation of CO₂ Raman spectra

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An extended SU(2) model for coupled Morse oscillators

Cited by 64 publications

References 35 publications

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

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

Nonlinear response of a deformed oscillator

An algebraic alternative for the accurate simulation of CO2 Raman spectra

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Product

Resources

About

An algebraic alternative for the accurate simulation of CO₂ Raman spectra