Semiclassical theory of molecular spectral line shapes in gases

Fitz, D. E.; Marcus, R. A.

doi:10.1063/1.1680636

Cited by 52 publications

(7 citation statements)

References 47 publications

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“…Christian.boulet@u-psud.fr or semi-classical. [8][9][10] However, it can be reasonably claimed that the calculation of the whole relaxation matrix for complex molecular systems, starting from the knowledge of the intermolecular potential remains an open problem. If one considers only the diagonal elements of W, until recently, it was believed that the ultimate refinement of the Anderson-Tsao-Curnutte theory, known as the Robert-Bonamy formalism, 11 can treat molecule-molecule systems reasonably well.…”

Section: Introductionmentioning

confidence: 99%

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N2

Boulet

Thibault

2014

The Journal of Chemical Physics

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A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N2 for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While in the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N2, opening the way to the analysis of more complex molecular systems.

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Section: Introductionmentioning

confidence: 99%

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N2

Boulet

Thibault

2014

The Journal of Chemical Physics

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“…The Hamiltonian used in the present work is a standard one (e. g., Refs,4,5). It is given in Appendix A for completeness, together with the coordinates and a definition of the other symbols and parameters.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical collision theory. Application of multidimensional uniform approximations to the atom–rigid-rotor system

Kreek

Ellis

Marcus

1975

The Journal of Chemical Physics

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The multidimensional Bessel and Airy uniform approximations developed earlier in this series for the semiclassical S matrix are applied to the atom rigid-rotor system. The need is shown for (a) using a geoemetrical criterion for determining whether a stationary phase point (s.p.pt) is a maximum, minimum, or saddle point; (b) choosing a proper quadrilateral configuration of the s.p. pts. with the phases as nearly equal as possible; and (c) choosing a unit cell to favor near-separation of variables. (a) and (b) apply both to the Airy and to the Bessel uniform approximations, and (c) to the Bessel. The use of a contour plot both to understand and to facilitate the search in new cases is noted. The case of real and complex-valued stationary phase points is also considered, and the Bessel uniform-in-pairs approximation is applied. Comparison is made with exact quantum results. As in the one-dimensional case, the Bessel is an improvment over the Airy for "k = 0" transitions, while for other transitions they give similar results. Comparison in accuracy with the results of the integral method is also given. As a whole, the agreement can be considered to be reasonable. The improvement of the present over various more approximate results is shown.

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“…To try to cast further light on the essential approximations leading to this widely used approximation, we investigate here the classical limit of the qCSA expressions for the generalized cross-sections. The use of classical S matrix theory [12,13] to obtain classical limits was applied originally to pressure-broadening cross-sections [14], and has since been extended to obtaining arbitrary GCS for atom-molecule interactions [15].…”

Section: Introductionmentioning

confidence: 99%

Classical centrifugal-sudden calculations of transport and relaxation cross-sections for Ar−N₂

Dickinson

Liu

1994

Molecular Physics

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Classical limits of the quantal centrifugal-sudden approximation to generalized cross-sections have been derived and compared with the exact classical results. Detailed comparisons between the classical centrifugal-sudden approximation (cCSA) values, the exact classical trajectory results, and the corresponding quantal calculations are then carried out for the Ar-N2 system, and contrasted with Similar comparisons for He-N 2. Above 150 K the cCSA is found to be accurate to within 1% for the temperature dependent viscosity and diffusion cross-sections and 5% for the viscomagnetic and depolarized Rayleigb lightscattering cross-sections.

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Semiclassical theory of molecular spectral line shapes in gases

Cited by 52 publications

References 47 publications

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N2

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N2

Semiclassical collision theory. Application of multidimensional uniform approximations to the atom–rigid-rotor system

Classical centrifugal-sudden calculations of transport and relaxation cross-sections for Ar−N₂

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Semiclassical theory of molecular spectral line shapes in gases

Cited by 52 publications

References 47 publications

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N2

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N2

Semiclassical collision theory. Application of multidimensional uniform approximations to the atom–rigid-rotor system

Classical centrifugal-sudden calculations of transport and relaxation cross-sections for Ar−N2

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Classical centrifugal-sudden calculations of transport and relaxation cross-sections for Ar−N₂