Fidelity, entropy, and Poincaré sections as tools to study the polyad breaking phenomenon

Bermúdez-Montaña, M.; Lemus, R.; Castaños, Octavio

doi:10.1209/0295-5075/116/13001

Cited by 17 publications

(21 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is a remarkable behaviour allowing the polyad breaking process to be studied in different ways. One possibility is to consider the local-to-normal mode transition in parametric way by introducing different tools like probability densities, fidelity, entropy and Poincaré sections [30]. Another point of view consists in considering a time dependent evolution in the parameters leading to the transition.…”

Section: Discussionmentioning

confidence: 99%

“…This phenomenon is manifested as a transition process of polyad breaking but also by the impossibility of a reasonable estimation of the force constants starting from a local scheme [29]. This local-tonormal mode transition (LNT) has been studied taking the parametric transition from H 2 O and CO 2 molecule [30]. The local polyad breaking has been detected using several concepts: probability density, fidelity, entropy and Poincaré sections.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Time-dependent local-to-normal mode transition in triatomic molecules

2017

View full text Add to dashboard Cite

Time-evolution of the vibrational states of two interacting harmonic oscillators in the local mode scheme is presented. A local-to-normal mode transition (LNT) is identified and studied from the time dependent point of view. The LNT is established as a polyad breaking phenomenon from the local point of view for the stretching degrees of freedom in a triatomic molecule. This study is carried out in the algebraic representation of bosonic operators. The dynamics of the states are determined via the solutions of the corresponding nonlinear Ermakov equation. Application of this formalism to H 2 O, CO 2 , O 3 and NO 2 molecules in the adiabatic, sudden and linear regime is considered.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time-dependent local-to-normal mode transition in triatomic molecules

2017

View full text Add to dashboard Cite

show abstract

“…A Darling–Dennison interaction is included in , although due to the fact that 2 ω 1 ≠2 ω 3 , the contribution is expected not to be relevant. On the other hand, the splitting between the stretches is around 1,064 cm −1 , large enough to expect α ≠ γ . The identification of the resonances 3 ω 1 ≈2 ω 3 and 4 ω 1 ≈2 ω 3 leads to polyad schemes

{\overset{P}{true}}_{213} = 2 {\overset{ν}{true}}_{1} + {\overset{ν}{true}}_{2} + 3 {\overset{ν}{true}}_{3},

{\overset{P}{true}}_{214} = 2 {\overset{ν}{true}}_{1} + {\overset{ν}{true}}_{2} + 4 {\overset{ν}{true}}_{3},

respectively.…”

Section: Polyad Preserving Hamiltoniansmentioning

confidence: 97%

“…On the other hand, the splitting between the stretches is around 1,064 cm −1 , large enough to expect ≠ . [22,43] The identification of the resonances 3 1 ≈ 2 3 and 4 1 ≈ 2 3 leads to polyad schemes [14], [44]- [52]…”

Section: Polyad Preserving Hamiltoniansmentioning

confidence: 99%

An algebraic alternative for the accurate simulation of CO₂ Raman spectra

Bermúdez-Montaña

Carvajal

Pérez‐Bernal

et al. 2020

J Raman Spectroscopy

View full text Add to dashboard Cite

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.

show abstract

“…This means that, at some values of potential V 0 , the systematic accidental degeneracy disappears, but near-degeneracy remains at the low lying region of the spectrum. In order to quantify this statement, we introduce parameter ζ defined as follows [58,59]. This parameter measures the relative splitting between a couple of levels E 1 and E 2 .…”

Section: Ho-dvr Pt-dvrmentioning

confidence: 99%

Algebraic DVR Approaches Applied to Piecewise Potentials: Symmetry and Degeneracy

2022

View full text Add to dashboard Cite

Algebraic discrete variable representation (DVR) methods that have been recently proposed are applied to describe 1D and 2D piecewise potentials. First, it is shown that it is possible to use a DVR approach to describe 1D square well potentials testing the wave functions with exact results. Thereafter, Morse and Pöschl-Teller (PT) potentials are described with multistep piecewise potentials in order to explore the sensibility of the potential to reproduce the transition from a pure square well energy pattern to an anharmonic energy spectrum. Once the properties of the different algebraic DVR approaches are identified, the 2D square potential as a function of the potential depth is studied. We show that this system displays natural degeneracy, accidental degeneracy and systematic accidental degeneracy. The latter appears only for a confined potential, where the symmetry group is identified and irreducible representations are constructed. One particle confined in a rectangular well potential with commensurate sides is also analyzed. It is proved that the systematic accidental degeneracy appearing in this system is removed for finite potential depth.

show abstract

Fidelity, entropy, and Poincaré sections as tools to study the polyad breaking phenomenon

Cited by 17 publications

References 40 publications

Time-dependent local-to-normal mode transition in triatomic molecules

Time-dependent local-to-normal mode transition in triatomic molecules

An algebraic alternative for the accurate simulation of CO₂ Raman spectra

Algebraic DVR Approaches Applied to Piecewise Potentials: Symmetry and Degeneracy

Contact Info

Product

Resources

About

Fidelity, entropy, and Poincaré sections as tools to study the polyad breaking phenomenon

Cited by 17 publications

References 40 publications

Time-dependent local-to-normal mode transition in triatomic molecules

Time-dependent local-to-normal mode transition in triatomic molecules

An algebraic alternative for the accurate simulation of CO2 Raman spectra

Algebraic DVR Approaches Applied to Piecewise Potentials: Symmetry and Degeneracy

Contact Info

Product

Resources

About

An algebraic alternative for the accurate simulation of CO₂ Raman spectra