A study of the Raman spectrum of CO2 using an algebraic approach

Sánchez-Castellanos, Mariano; Lemus, R.; Carvajal, M.; Pérez‐Bernal, F.; Fernández, J. M.

doi:10.1016/j.cplett.2012.09.075

Cited by 17 publications

(26 citation statements)

References 22 publications

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“…using the linear approximation. 93 In general, there is a good agreement between our results and the experimental polarizability derivatives, in particular for the first three derivatives (∂ᾱ/∂S 1 ), (∂ 2ᾱ /∂S 2 1 ), and (∂ 2ᾱ /∂S 2 3 ). For the derivative (∂ 3ᾱ /∂S 1 ∂S 2 2a ), a slightly different value is obtained, but significant discrepancies appear in the bending polarizability derivatives (∂ 2ᾱ /∂S 2 2a ).…”

Section: The Raman Spectrumsupporting

confidence: 81%

“…In cases with a heavy mixing of the basis elements, ambiguity arises and quite a few states may carry the same quantum labels. 77,93 Truncating the expansion (10) at the linear approximation in the coordinates, the vibrational spectrum of the 12 CO 2 molecule has been described in Refs. 76 and 77 using the Hamiltonian (41).…”

Section: The Matrix Representation Of the Hamiltonian (41) Can Be Obtmentioning

confidence: 99%

“…This case was previously considered by the authors to estimate the derivatives of the polarizability as well as to calculate the Raman spectrum. 93 In the present work we investigate nonlinearity effects in this analysis. If nonlinear terms are taken into account, substituting Eq.…”

Section: The Raman Spectrummentioning

confidence: 99%

“…The analysis of the carbon dioxide molecule using rectilinear coordinates has already been reported in a letter form. 93 In this work we include previously neglected nonlinear effects and we present the approach from a more general perspective, emphasizing the effect of the nonlinear contributions. In addition to this, the CO 2 polarizability transition moments are predicted, and used to simulate the Raman spectrum close to experimental accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Simulation of the Raman spectra of CO2: Bridging the gap between algebraic models and experimental spectra

Lemus

Sánchez-Castellanos

Pérez‐Bernal

et al. 2014

The Journal of Chemical Physics

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The carbon dioxide Raman spectrum is simulated within an algebraic approach based on curvilinear coordinates in a local representation. The two main advantages of the present algebraic approach are a possible connection with configuration space and the correct description of systems with either local or normal mode character. The system Hamiltonian and polarizability tensor are expanded in terms of curvilinear coordinates. The curvilinear coordinates are in turn expanded into normal coordinates, obtaining an algebraic representation in terms of normal bosonic operators. A canonical transformation maps the operators into a local algebraic representation. The final step is an anharmonization procedure to local operators. The Raman spectrum of CO2 has been simulated, obtaining results close to experimental accuracy, and polarizability transition moments for the Raman spectral lines between 1150 cm(-1) and 1500 cm(-1) are reported. The comparison between experimental and simulated spectra has provided six new CO2 experimental vibrational terms.

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Section: The Raman Spectrumsupporting

confidence: 81%

Section: The Matrix Representation Of the Hamiltonian (41) Can Be Obtmentioning

confidence: 99%

Section: The Raman Spectrummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simulation of the Raman spectra of CO2: Bridging the gap between algebraic models and experimental spectra

Lemus

Sánchez-Castellanos

Pérez‐Bernal

et al. 2014

The Journal of Chemical Physics

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“…The present work results for the polyad schemes, P 212 , P 213 , and P 214 , labeled as

false| M_{i f}^{false(calc false)} false|

, are shown in the sixth, seventh, and eighth columns, respectively. These were computed by fitting the first 9 experimental transition moments minimizing a rms deviation between experimental

false| M_{i f}^{false(e x p false)} false|

and calculated

false| M_{i f}^{false(calc false)} false|

transition moments defined as

r m s = \sqrt{\sum_{β} {((), \log false| M_{β}^{false(e x p false)} false| - \log false| M_{β}^{false(c a l c false)} false|)}^{2}} .

…”

Section: Raman Spectrum Simulationmentioning

confidence: 99%

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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The potential energy surface of CO₂ from an algebraic approach

Sánchez-Castellanos

Lemus

Carvajal

et al. 2012

Int J of Quantum Chemistry

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The potential energy surface for the ground state of the 12 C 16 O 2 molecule is estimated through an algebraic approach based on unitary groups. It is shown that a purely algebraic approach may lead to a unphysical surface even when the fit turns out to be of a remarkable high quality. The vibrational description is obtained in the framework of the U (2) × U (3) × U (2) model, where the U (2) algebras are associated with the CO bond stretching and the U (3) algebra with the OCO bending. The algebraic representation of the Hamiltonian is obtained through the connection between the coordinates and momenta and the generators of the dynamical algebra. It is shown that through this connection is possible to choose the appropriate set of spectroscopic parameters leading to the right Potential Energy Surface (PES). The fit from which the PES is estimated involves 101 energy levels with an standard deviation of rms = 0.53 cm −1 .

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A study of the Raman spectrum of CO2 using an algebraic approach

Abstract: The vibrational Raman spectrum of CO 2 is calculated by means of the alge-

Cited by 17 publications

References 22 publications

Simulation of the Raman spectra of CO2: Bridging the gap between algebraic models and experimental spectra

Simulation of the Raman spectra of CO2: Bridging the gap between algebraic models and experimental spectra

An algebraic alternative for the accurate simulation of CO₂ Raman spectra

The potential energy surface of CO₂ from an algebraic approach

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A study of the Raman spectrum of CO2 using an algebraic approach

Abstract: The vibrational Raman spectrum of CO 2 is calculated by means of the alge-

Cited by 17 publications

References 22 publications

Simulation of the Raman spectra of CO2: Bridging the gap between algebraic models and experimental spectra

Simulation of the Raman spectra of CO2: Bridging the gap between algebraic models and experimental spectra

An algebraic alternative for the accurate simulation of CO2 Raman spectra

The potential energy surface of CO2 from an algebraic approach

Contact Info

Product

Resources

About

An algebraic alternative for the accurate simulation of CO₂ Raman spectra

The potential energy surface of CO₂ from an algebraic approach