An approach for the description of vibrational excitations: Application to 11BF3

Amezcua-Eccius, C.A.; Lemus, R.

doi:10.1016/j.jms.2009.12.007

Cited by 17 publications

(29 citation statements)

References 52 publications

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“…This means that we should proceed to extract the force constants from a normal mode formulation, following the approach presented in the previous section [15][16][17]. Later on we shall come back to the calculation of x f to check the consistency.…”

Section: Force Field Constantsmentioning

confidence: 99%

“…We may thus use these ratios to estimate the degree of locality of a set of oscillators [15][16][17].…”

Section: Force Field Constantsmentioning

confidence: 99%

“…It is thus convenient to count on a criterion to discriminate normal from local behavior. The Child's parameter represents a useful criterion [11], but recently it has been noticed that such criterion may involve both geometric and dynamic parameters [15][16][17]. This means that from the Wilson matrix elements it is possible to quantitatively estimate 0022-2852/$ -see front matter Ó 2011 Elsevier Inc. All rights reserved.…”

Section: Introductionmentioning

confidence: 99%

“…doi:10.1016/j.jms.2011.01.005 the behavior of vibrational modes, which is crucial to extract the correct force constants. In addition, from that analysis it follows that a local mode model can be used by starting with a symmetry adapted coordinates (isomorphic to the normal modes) through a canonical transformation keeping the possibility of obtaining the correct force constants [16,17]. This approach will be followed in this work to extract the force constants of Formaldehyde.…”

Section: Introductionmentioning

confidence: 99%

“…This approach has a clear correspondence between the generators and the creation and annihilation operators of the Morse and/or Pöschl-Teller functions [19][20][21]. This feature makes possible to set up the correspondence between effective Hamiltonians and the description in configuration space, allowing the force constants to be calculated [15,16,[22][23][24]. This algebraic approach together with the symmetry adapted formulation of the Hamiltonian will be used to obtain the force constants of Formaldehyde.…”

Section: Introductionmentioning

confidence: 99%

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Force field constants for Formaldehyde obtained from an algebraic approach

Sánchez-Castellanos

Lemus

2011

Journal of Molecular Spectroscopy

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Section: Force Field Constantsmentioning

confidence: 99%

“…We may thus use these ratios to estimate the degree of locality of a set of oscillators [15][16][17].…”

Section: Force Field Constantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Force field constants for Formaldehyde obtained from an algebraic approach

Sánchez-Castellanos

Lemus

2011

Journal of Molecular Spectroscopy

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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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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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An approach for the description of vibrational excitations: Application to 11BF3

Cited by 17 publications

References 52 publications

Force field constants for Formaldehyde obtained from an algebraic approach

Force field constants for Formaldehyde obtained from an algebraic approach

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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An approach for the description of vibrational excitations: Application to 11BF3

Cited by 17 publications

References 52 publications

Force field constants for Formaldehyde obtained from an algebraic approach

Force field constants for Formaldehyde obtained from an algebraic approach

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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Product

Resources

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An algebraic alternative for the accurate simulation of CO₂ Raman spectra

The potential energy surface of CO₂ from an algebraic approach