The relaxation matrix for symmetric tops with inversion symmetry. II. Line mixing effects in the ν1 band of NH3

Line shape parameters of PH3 transitions: Theoretical studies of self-broadened widths and line mixing effects

Line mixing effects have been calculated in various parallel and perpendicular bands of self-broadened PH₃ lines and compared with recent experimental data. The theoretical approach is an extension to symmetric tops with high inversion barrier of the formalism previously developed for NH₃ [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. The model takes into account the non-diagonality of the scattering operator within the line space as well as, in a correct way, the double degeneracy of the j, k levels when k ≠ 0. Transitions between such levels should be considered as doublets whose components may be coupled by the line mixing process. It has been shown that, at low pressure, the inversion of the experimental data will strongly depend on the splitting between the two components of a doublet. When it is significant, one can measure independently both the width of one component and the intra-doublet coupling matrix element. Otherwise, one can only measure the sum of these two elements. Comparisons with measurements show that the present formalism leads to accurate predictions of the experimental line shapes.

Relaxation matrix for symmetric tops with inversion symmetry: Line coupling and line mixing effects on NH3 lines in the 𝝂4 band

Line shape parameters including the half-widths and the off-diagonal elements of the relaxation matrix have been calculated for self-broadened NH₃ lines in the perpendicular ν₄ band. As in the pure rotational and the parallel ν₁ bands, the small inversion splitting in this band causes a complete failure of the isolated line approximation. As a result, one has to use formalisms not relying on this approximation. However, due to differences between parallel and perpendicular bands of NH₃, the applicability of the formalism used in our previous studies of the ν₁ band and other parallel bands must be carefully verified. We have found that, as long as potential models only contain components with K₁ = K₂ = 0, whose matrix elements require the selection rule Δk = 0, the formalism is applicable for the ν₄ band with some minor adjustments. Based on both theoretical considerations and results from numerical calculations, the non-diagonality of the relaxation matrices in all the ^PP, ^RP, ^PQ, ^RQ, ^PR, and ^RR branches is discussed. Theoretically calculated self-broadened half-widths are compared with measurements and the values listed in HITRAN 2012. With respect to line coupling effects, we have compared our calculated intra-doublet off-diagonal elements of the relaxation matrix with reliable measurements carried out in the ^PP branch where the spectral environment is favorable. The agreement is rather good since our results do well reproduce the observed k and j dependences of these elements, thus validating our formalism.

The relaxation matrix for symmetric tops with inversion symmetry. I. Effects of line coupling on self-broadened ν1 and pure rotational bands of NH3

The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of self-broadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).