Subpercent agreement between ab initio and experimental collision-induced line shapes of carbon monoxide perturbed by argon

Grzegorz Kowzan, Hubert Cybulski, Piotr Wcisło, Michał Słowiński, Alexandra Viel, Piotr Masłowski, and Franck Thibault

Phys. Rev. A 102, 012821 – Published 28 July 2020

Abstract

We present fully ab initio calculations of second-overtone rovibrational line shapes of carbon monoxide perturbed by argon. The quantum mechanical scattering problem between CO and Ar is solved numerically for two different ab initio interaction potentials. We use the generalized Hess method to determine spectroscopic cross sections which describe the effect of collisions on each spectral line. Using these cross sections, we determine the line-shape parameters that we use to generate the Hartmann-Tran and speed-dependent billiard ball profiles. We compare the generated line shapes with high-quality experimental line profiles of five lines measured at five pressures between 0.01 and 1 atm. A subpercent agreement over the entire pressure range is obtained. Calculations for the P(9) line are used to inspect the effects of the two interaction potentials. The discrepancies for both the considered interaction potentials and the experiment are explained within the described theoretical framework. The presented results are the most accurate collisional line-shape calculations for a system with collision dynamics representative of atmospherically relevant species.

Received 31 May 2020
Accepted 10 July 2020

DOI:https://doi.org/10.1103/PhysRevA.102.012821

Physics Subject Headings (PhySH)

Molecular spectra Potential energy surfaces Scattering of atoms, molecules, clusters & ions

Molecules

Coupled cluster

Atomic, Molecular & Optical

Authors & Affiliations

Grzegorz Kowzan ^1,*, Hubert Cybulski ², Piotr Wcisło¹, Michał Słowiński ¹, Alexandra Viel³, Piotr Masłowski¹, and Franck Thibault ³

¹Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudziadzka 5, 87-100 Toruń, Poland
²Institute of Physics, Kazimierz Wielki University, ul. Powstańców Wielkopolskich 2, 85-090 Bydgoszcz, Poland
³Univ Rennes, CNRS, IPR (Institut de Physique de Rennes)–UMR 6251, F-35000 Rennes, France

^*grzegorz@kowzan.eu

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Issue

Vol. 102, Iss. 1 — July 2020

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Images

Figure 1
Experimental line shapes of the P(9) line (top panel) and relative differences (residuals) between the measured and ab initio line-shape profiles (a)–(g) and the fitted profile (h). In each case the plotted range is the $\pm 4 \times FWHM$ region around the experimental line peak. Rows (a)–(e) show ab initio line-shape profiles of increasing sophistication; see Sec. 2 for an explanation of the acronyms. Row (e) is the most sophisticated and physically justified model evaluated for fully ab initio parameters. Row (f) is the $β SDHCP$ , the same as row (d), but with the line-shape parameters based on our potential. Row (g) is the $β SDHCP$ , the same as row (d), but with the $Γ_{0}$ values from the qSDHCP fit [32]. Finally, row (h) shows the qSDHCP with all the parameters obtained from a multispectrum fit to the experiment. The $ε$ values for each residual are the relative root-mean-square errors expressed as percentages, which were calculated in the $\pm FWHM$ range marked in row (a), 50 Torr, by the gray rectangle.
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Figure 2
Real part (a) and imaginary part (b) of the complex Dicke parameter ${\tilde{ν}}_{opt}$ , Eq. (12). Values are plotted as a function of the initial rotational state of the transition $P (j_{a})$ . Thick blue lines capped with error bars (a) mark the range of values adopted by the $β$ -corrected [36] ab initio $Re {\tilde{ν}}_{opt}$ in the experimental pressure range, 10–700 Torr. Analogously, the open red rectangle represents the $β$ -corrected $Re {\tilde{ν}}_{opt}$ from [20]. Blue diamonds (b) show the ab initio $Im {\tilde{ν}}_{opt}$ values, and green crosses with error bars (a), (b) represent the values retrieved from fitting the qSDHCP to the experimental data.
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Figure 3
Our (solid lines) and Sumiyoshi's (dashed lines) potential energy curves for the C-O bond length $r_{CO} = 1.132 40 Å$ and $T$ -shaped (squares) or Ar-OC (triangles) alignment of C-O and Ar. Symbols are shown only on solid lines for clarity.
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Figure 4
Comparison between our and Sumiyoshi's rovibrationally averaged Legendre expansions at a small CO-Ar separation. Our potential is represented by solid lines; Sumiyoshi's, by dashed lines. Numbers by the lines label the Legendre orders. The vertical solid black line marks $R = 3.2 Å$ , which is the lower $R$ limit of Sumiyoshi's ab initio points.
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Figure 5
Spectroscopic cross sections, Eq. (A2), and average total inelastic state-to-state cross sections, Eq. (B8), for the P(9) line from scattering on both potentials. (a) The broadening cross section (blue) and the inelastic cross section (green); (b) the absolute value of the shift cross section (red); (c) the difference between the values for our potential and that of Sumiyoshi.
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Figure 6
Differences between Legendre expansion coefficients, $V_{ν, l}$ , in the lower ( $ν = 0$ ) and upper ( $ν = 3$ ) vibrational states for both potentials.
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