Orthogonal transformations in the line space and modelling of rotational relaxation in the Raman spectra of linear tops

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

“…Impact-limit values are shown for the present spectral-moments approach at 41 amagat and for the ECS approach at 169 amagat [Colour figure can be viewed at wileyonlinelibrary.com] 1 Impact-limit values are easily obtained in the frame of both ECS and spectral-moments approaches by setting ω = ω fi or ω f 0 i 0 depending on the considered term in the expression of the relaxation matrix element (see eq. (13)(14) of Buldyreva and Bonamy [11] and Equation (3) of the present work).…”

“…Here, the summation is made over the pairs of (vib) rotational transitions i!f, i 0 !f 0 coupled by line-mixing effects,L a is the free-active-molecule Liouvillian leading in the transition-operators basis to the diagonal matrix of proper rotational frequencies ω fi , n is the density of molecules, and the squared A ðrÞ if values give the intensities of isolated lines. With the specific symmetric metric in the LS [14] introduced to avoid all spurious effects in spectra calculations, the relaxation matrix Γ(ω) satisfies automatically all fundamental properties resulting from fundamental principles (matrix symmetry, time-reversal symmetry, double-sided sum rules, and dispersive relations) and provides a symmetric spectral density S(ω). The weighting factors A ðrÞ if read in this case [3] A…”

“…According to the formalism developed by Zwanzig, Fano and Mori, [13] the unit‐area‐normalized spectral density S ( r ) ( ω ) is determined by the super‐operator containing all “active molecule”–“bath” interactions: Here, the summation is made over the pairs of (vib)rotational transitions i → f , i ′ → f ′ coupled by line‐mixing effects, is the free‐active‐molecule Liouvillian leading in the transition‐operators basis to the diagonal matrix of proper rotational frequencies ω fi , n is the density of molecules, and the squared values give the intensities of isolated lines. With the specific symmetric metric in the LS [14] introduced to avoid all spurious effects in spectra calculations, the relaxation matrix Γ( ω ) satisfies automatically all fundamental properties resulting from fundamental principles (matrix symmetry, time‐reversal symmetry, double‐sided sum rules, and dispersive relations) and provides a symmetric spectral density S ( ω ). The weighting factors read in this case [3] …”

Infrared absorption by pure CO 2 near 3340 cm −1 : Measurements and analysis of collisional coefficients and line-mixing effects at subatmospheric pressures

“…The Energy-Corrected Sudden approach based on a symmetric definition of the scalar product in the Liouville space yields the symmetric spectral density S ðrÞ ðνÞ as a function of the rotational wavenumber ν [45][46][47]:…”

“…Owing to the chosen symmetric metric of the Liouville space, the relaxation matrix satisfies all fundamental relations obtained from first principles (see [45][46][47] for more details), including the symmetry relation and the doublesided sum rules:…”