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

Abstract

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.

Line mixing effects in isotropic Raman spectra of pure N2: A classical trajectory study

“…Note that a similar result was obtained from the semi-classical approach of Ref. 24, corroborating the necessity of taking into account the translational-rotational coupling in such cases of high inelasticity.…”

“…24 where it was not possible to obtain relaxation matrix elements verifying at the same time detailed balance and the sum rule.…”

“…13,24,26,29,31 The molecules were treated as rigid rotors, so the PES is fourdimensional. It has been developed over bispherical harmonics and the expansion retained 30 angular functions.…”

Recent advances in collisional effects on spectra of molecular gases and their practical consequences

“…At the same time, a slightly different approach was proposed [227], based on the coordinate representation. It was first applied to isotropic Raman transitions of pure N 2 [227,228] for which a comparison with benchmark quantum results [195,229] was possible. This analysis showed that accounting for the line coupling reduces the line widths by about 15 % with a much better agreement with the quantum results.…”

An experimental and theoretical study of nitrogen-broadened acetylene lines

“…More recently, Ma et al [20] have shown that by considering effects from the line coupling in the standard [12] RB method, one is able to obtain a much better agreement with experimental values at least for self-perturbed nitrogen isotropic Raman lines. The latter study has been completed by a comparison of the full relaxation matrix as obtained with this refined method with quantum dynamical calculations [24,25]. Meanwhile, this refined version of semi-classical RB model has been adapted to the case of IR lines [26].…”