Isolated line shapes of molecular oxygen: Requantized classical molecular dynamics calculations versus measurements

We present comparisons between measured isolated line shapes of molecular oxygen in air at various pressures and those calculated, free of any adjusted parameter, using requantized classical molecular dynamics simulations (rCMDS). The measurements have been made for the R1Q2, P9P9, P11P11, P13P13, and P15Q14 transitions in the ${\mathrm{O}}_2$ singlet-Δ band [$a{}^1{\Delta }_g\leftarrow X{}^3{\Sigma }_g^{-}(0,0)$] by the frequency-stabilized cavity ring-down spectroscopy technique. This work extends a previous study made for a single oxygen line [Phys. Rev. A 87, 032510 (2013)] and confirms the quality of this theoretical approach over broad ranges of pressure and rotational quantum number. Indeed, not only the collisional broadening coefficients but also the (small) deviations of observed line shapes with respect to the Voigt profile are accurately predicted. These results illustrate the viability of using the rCMDS method as a benchmark for the development and testing of simpler parametrized line profiles that are suitable for the analysis of underlying physical mechanisms and for atmospheric remote sensing applications.

Figure 1

Pressure normalized Lorentz HWHM ${\gamma }^0$ (see text) versus the rotational quantum number $\left|m\right|$ ($=N^{\prime \prime }$ for P lines and $N^{\prime \prime }$ + 1 for R lines). The (black) line shows the results obtained from fits of the rCMDS-calculated spectra. The symbols are data from the HITRAN database [41] (green down triangles) and Ref. [24] (red stars), and values obtained from Voigt fits of measured spectra from the present work (black circles), and Refs. [27] (magenta squares) and [42] (blue triangles). The calculations, the present measurements and the data from Ref. [41] are for the ${\mathrm{O}}_2$ singlet-Δ band [$a{}^1{\Delta }_g\leftarrow X{}^3{\Sigma }_g^{-}(0,0)$], whereas the other measurements are for the $A$ band [$b{}^1{\Sigma }_g^{+}\leftarrow X{}^3{\Sigma }_g^{-}(0,0)$]. The error bars for $\left|m\right|$ = 0 and 30 correspond to $\pm 5\%$.

Figure 2

Observed (symbols) and theoretical (lines) collisional broadening coefficient ${\Gamma }_L\left(P\right)/P$ normalized by the value at the highest pressure. The results are for the R1Q2 (blue, open circles), P9P9 (black, squares), P11P11 (red, full circles), P13P13 (olive, up triangles), and P15Q14 (magenta, down triangles) transitions of the ${\mathrm{O}}_2$ singlet-Δ band [$a{}^1{\Delta }_g\leftarrow X{}^3{\Sigma }_g^{-}(0,0)$]. The error bar on the left side corresponds to $\pm 2$%.

Figure 3

Voigt-fit residuals normalized by the absorption peak values for the P9P9 line of the ${\mathrm{O}}_2$ singlet-Δ band [$a{}^1{\Delta }_g\leftarrow X{}^3{\Sigma }_g^{-}(0,0)$] at the pressures of (a) 10 kPa, (b) 26.7 kPa, and (c) 60 kPa, corresponding to values of ${\Gamma }_L/{\Gamma }_D\approx$ 0.5, 1.5, and 4.3, respectively. The (black) circles were obtained from measured spectra while the (blue) lines result from fits of rCMDS-calculated spectra. Note that the relative standard uncertainty of the measured absorption coefficient is 0.03%, which nominally corresponds to the symbol radius.

Figure 4

Observed (symbols) and theoretical (lines) relative amplitude $A_W/\alpha \left({\sigma }_0\right)$ of the W-shaped Voigt-fit residuals. The results are for the R1Q2 (blue, open circles), P9P9 (black, squares), P11P11 (red, full circles), P13P13 (olive, up triangles), and P15Q14 (magenta, down triangles) transitions of the ${\mathrm{O}}_2$ singlet-Δ band [$a{}^1{\Delta }_g\leftarrow X{}^3{\Sigma }_g^{-}(0,0)$]. The error bar on the left side corresponds to $\pm 0.2$%.