Pressure effects on N₂–N₂ rototranslational Raman spectra predicted from leading spectral moments

Abstract

Non-Markovian effects having a strong influence on far-wing intensities of spectroscopic signatures by molecular gases are analyzed theoretically with the use of a non-Markovian relaxation matrix derived for rapidly colliding linear rotators (J. Chem. Phys. 149, 044305 [2018]) for the benchmark case of rototranslational Raman spectra of molecular nitrogen recorded at high densities up to very far wings (Phys. Lett. A 157, 44 [1991]). This matrix is built here on the base of the translational-spectrum model of Birnbaum and Cohen and the recently computed, from known potential energy surfaces, two leading classical spectral moments (

Energy‐corrected sudden modeling of the non‐Markovian rotational relaxation matrix for high‐pressure Raman spectra of pure nitrogen

“…At small detunings from the band center, the overall intensity is in good agreement with the experiment, albeit somewhat worse for 169 amagat for all the models. Because of the convolution, the strongly pronounced rotational structure appearing previously [17] on the curves of the spectral‐moments approach in the 200–300 cm range is no longer present and the predictions are much more in line with the experiment. Also, according to Equation (), the data are normalized to density, so the two experimental datasets coincide in the wing beyond 300 cm ; the same holds for the pairs of theoretical curves computed for different pressures with the same ECS model.…”

“…Each (except for E-ED HW1) line color and type is present twice: The upper curve corresponds to n ¼ 1 and the lower one corresponds to n ¼ 2 [Colour figure can be viewed at wileyonlinelibrary.com] Practical application of Equation ( 16) requires, however, a desymmetrization procedure to match the experimentally observed asymmetric band shapes and its choice is not unique. For the sake of homogeneity with the spectral moments approach, [17] we relate the symmetric spectral density S (r) (ω) to the observed spectral density S ðrÞ ðωÞ via a quantum asymmetry factor issued from the Boltzmann relation S ðrÞ ðÀωÞ ¼ expðÀℏω=kTÞS ðrÞ ðωÞ:…”

“…T A B L E 2 Parameters for Q lalb [Equation (14)] and Ω DP [Equation (12)] including the temperature dependence parameter N [Equation (15)] fitted on different experimental halfwidth sets at T 0 ¼ 298 K (HW1 [23] and HW2 [25] ) and 194 K [25] F I G U R E 3 Comparison of theoretical anisotropic Raman scattering spectra of pure N 2 at room temperature and 41 amagat with the experimental data. [19] Theoretical curves are from the spectral-moments approach (green [18,32] and violet [17] lines) using the potential-energy surface (PES) by Cappelletti et al, [33] the "molecule-atom" energy-corrected-sudden (ECS) P2 approach [11] (orange line) and the bimolecular ECS approach of the present work for two models (red and blue lines) fitted on the experimental data of Rosasco et al [23] All theoretical data are convoluted with the apparatus function [Colour figure can be viewed at wileyonlinelibrary.com]…”

“…Comparison of theoretical intensities for anisotropic Raman scattering spectra of pure N 2 at room temperature for 41 and 169 amagat with experimental data. [19] Theoretical curves are from the spectral-moments approach (green [18,32] and violet [17] lines) using the potential-energy surface (PES) by Cappelletti et al, [33] the "molecule-atom" energy-corrected-sudden (ECS) P2 approach [11] (orange line) and the bimolecular ECS approach of the present work (red and blue lines) for two models fitted on the experimental data of Rosasco et al [23] All theoretical data are convoluted with the apparatus function [Colour figure can be viewed at wileyonlinelibrary.com] detunings from the band center, the overall intensity is in good agreement with the experiment, albeit somewhat worse for 169 amagat for all the models. Because of the convolution, the strongly pronounced rotational structure appearing previously [17] on the curves of the spectralmoments approach in the 200-300 cm À1 range is no…”

“…Three possible ways to practical calculations were outlined: direct calculations from the known potential‐energy surfaces (PES), PES‐based spectral‐moments approach, and ECS modeling. The second way was followed with an application to Raman spectra [16–18] and revealed that the PES taken for spectral moments calculations and especially the choice for the spherical‐harmonics expansion of the “potential”‐“density matrix” products strongly influences both the halfwidths and the far‐wing intensities.…”