INTRODUCTION

The ozone molecule, which absorbs the light nearly everywhere from the microwave (MW) to the infrared (IR) and ultra-violet ranges [1–4], plays the major role in the atmospheric physics and chemistry with an impact on climate, ecosystems and human health. One of incentives for the study of absorption spectra of the isotopically substitutes ozone was a discovery of isotopic anomalies in atmospheric conditions and laboratory experiments [5–8]. Another one is the experimental validation of ab initio potential energy surfaces (PES) which are used for the modeling of the ozone formation [9] and isotopic exchange reactions [10–12].

After the main isotopic species of ozone 16O3, its most abundant isotopomers are 16O16O18O and 16O18O16O with the statistical natural abundances of 0.00389 and 0.00199 correspondingly [13]. Available information for the line lists are collected in HITRAN [14], GEISA [15], and S&MPO (Spectroscopy and Molecular Properties of Ozone) [13] databases partly accessible via European VAMDC portal [16]. Analyses of infrared spectra of these species measured with Fourier Transform Spectroscopy (FTS) techniques were reported in [17–21], whereas spectra at higher energy ranges measured with Cavity-ring-down Spectroscopy (CRDS) techniques were reported in [22–24].

Ozone has a large permanent dipole moment and exhibits a strong absorption in the MW, THz and far-infrared (FIR) range corresponding to the ν2 fundamental band. For the purely rotational bands of 16O16O18O and 16O18O16O only quite sparse but very accurate measurements have been reported by Depannemaecker [25] and Chiu [26] using microwave techniques. For the ν2 band, the previous FTS measurements have been published by Flaud et al. [27].

The aim of this work is to report the results of the analysis of two new series of experimental FTS spectra recorded with the experimental SOLEIL equipment [28–30] of the CNRS (National Center of Scientific Research of France) and of their simultaneous treatment with available microwave data [25, 26].

The longwave range between 1.2–6 THz (30–200 cm–1) spectra were recorded using Synchrotron light source of the SOLEIL setup that permitted to measure a large number of rotational lines including “hot” bands, due to the exceptional brightness of the Synchrotron radiation, sensitivity of measurements and improved signal-to-noise ratio. For the ν2 band, the supplementary measurements were carried out with better spectral resolutions that the previously available ones [27].

1 EXPERIMENT

The experimental setup of measurements of ozone spectra using SOLEIL CNRS equipment has been described by Manceron et al. [31, 32]. Here, we only summarize the main features of the experiments. Some more technical details can be found in the work [33] devoted to the study of the principle isotopologue 16O3, which was using a similar setup.

The ozone was synthesized using electric discharge from batches of 7 to 20 Torr of high purity oxygen (99.9995%) and heavy 18O-labelled oxygen (99% 18O). Mixtures using different proportions of the diatomic oxygen 16O2 + 18O2 produced then six isotopic forms of ozone 16O3, 16O16O18O, 16O18O16O, 16O18O18O, 18O16O18O and 18O3, which for brevity will be denoted using simplified commonly used 666, 668, 686, 688, 868 and 888 labels.

As outlined in the Introduction, two series of experimental spectra were recorded with two different mixtures of 18O enriched ozone isotopomers. Both of them were recorded using a Bruker IFS125HR Fourier transform spectrometer.

For the first series of experiments in the range 1.2– 6 THz (30–200 cm–1), the spectrometer was linked to the AILES Beamline at the Synchrotron SOLEIL setup [28–30].The maximum optical path difference (MOPD) was set to 450 cm (giving a sinc function width of about 0.00134 cm–1). The Synchrotron source was operated with 500 mA in the most stable, multi-bunch mode and the synchrotron effective source size is compatible with the highest resolution over the whole spectral domain [30]. For this first series of measurement in the terahertz range the ozone isotopic species were generated from a 16O2 (62.5%) + 18O2 (37.5%) mixture giving the total ozone pressure of 1.725 Torr with the optical pathlength of 816 cm.

The second series was carried out at higher wavenumber range between 550 and 880 cm–1 using classical glowbar source with a 1.3 mm entrance iris diameter. The MOPD was set to 882 cm, giving a sinc function width of about 0.00068 cm–1. Table 1 gives the summary of the experimental conditions. An overview of analyzed spectra with demonstration on small areas of 0.3 cm–1 width is shown in Fig. 1.

Table 1.   Summary of the experimental conditions
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Fig. 1.
figure 1

Overview of the spectra of ozone enriched with oxygen 18O recorded using SOLEIL setup.

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The spectra were calibrated with residual CO2 lines observed in the spectrum with their wavenumbers taken from HITRAN [14]. The resulting accuracy is ± 0.00005 cm–1 for well isolated lines. In this experiment for the ν2 band region, the optical path length was set to 2.8 m ozone (spectrum d20326.1) and the total pressure, generated from a 16O2 (47.93%) + 18O2 (52.07%) mixture giving the total was 2.376 Torr.

2 ANALYSIS AND MODELLING

To work with these spectra, we have used the following programs: MultiFit [34] to visualize experimental and calculated spectra and determine the positions of experimental lines using graphical peak-finder tools; and ASSIGN [35] to identify series of transitions to the same vibrational-rotational (VR) level using combinational differences. The series of VR transitions were calculated with the computational code GIP [36] for both symmetry groups CS and C2V. Identification was carried out iteratively, series by series, as the quantum numbers J and Ka increased, using extrapolation based on an initial effective Hamiltonian model.

The effective Hamiltonian (H eff) in the representation of rotation operators described in [37] (and references therein) was used to fit experimental data:

$$\begin{gathered} {{H}^{{{\text{eff}}}}} = \sum\limits_{lm} {{{b}_{{Lm0}}}{\kern 1pt} {{{\mathbf{J}}}^{{2l}}}J_{z}^{m}} \\ + \,\,\sum\limits_{lm} {{{b}_{{Lm2}}}{\kern 1pt} {{{\mathbf{J}}}^{{2l}}}\left\{ {J_{ + }^{2}{{{({{J}_{z}} + 1)}}^{m}} + {{{({{J}_{z}} + 1)}}^{m}}J_{ - }^{2}} \right\}} , \\ \end{gathered} $$
(1)

where \({{J}_{z}}\) is the component of the angular momentum along the A-axis in I r representation [38] and \({{J}_{ \pm }}\) are the ladder combinations of \({{J}_{x}},{{J}_{y}}\) components in the molecular Eckart frame, and J2 is the square of the total angular momentum with the low case index notation L = 2l.

In this work, we did not proceed to the intensity measurement of experimental lines to refine the parameters of the effective dipole transition moments [39, 40]. Previously published effective parameters of the dipole transition moment of the bands {(000)–(000), (010)–(010), (010)–(000)} from the S&MPO database [13] were used to calculate the synthetic spectra and evaluate the correctness of the identification performed using the MultiFit program of the studied isotopic species of ozone.

Spectroscopic parameters of the ground and first excited vibrational states of the ozone isotopomers 16O16O18O and 16O18O16O were previously obtained by Flaud et al. in [27]. The authors of [27] analyzed Fourier spectra in the range of the ν2 band recorded in 1985 at room temperature with a resolution of 0.005 cm–1 using the McMath solar telescope complex at Kitt Peak National Observatory. Note that this paper [27] did not contain information about the set of experimental data which had been obtained from the analysis of the band ν2, including the number of VR transitions and the maximum values of rotational quantum numbers. It was only pointed out that for identifying and modelling series of transitions with Ka > 11, they carried out simultaneous processing IR and microwave data [25] in order to improve parameters of the ground state (000). As a result of the modelling, they obtained the parameters of the effective Watson Hamiltonian [41] to calculate the line lists [42] for the ν2 bands up to the maximum values of J = 65, Ka = 17 and Emax = 1750 cm–1. Their intensity cut off was 0.25 × 10–22 and 0.50 × 10–22 cm/molec at 296 K for 16O16O18O and 16O18O16O, respectively. The calculated lists were included in the HITRAN and S&MPO databases, and the obtained ground state parameters were taken as “reference” ones when analysing all the following bands and for corresponding calculations.

The spectra recorded in the range of 30–200 cm–1 with the SOLEIL synchrotron facility allowed us to expand the set of experimentally observed rotational transitions of the bands (000)–(000) and (010)–(010) for each isotopic modification with respect to the line lists available in the databases. Graphically, this comparison is presented in Figs. 2a, 2c and 3a, 3c for 16O16O18O and 16O18O16O, respectively. In addition, the comparison shows a significant discrepancy between the positions of our experimental lines versus HITRAN2020, particularly for transitions with high J and Ka values (Figs. 2b, 2d and 3b, 3d). For example, despite a small standard deviation (RMS) equal to 1.53 × 10–3 cm–1 for the band ν2 16O16O18O, the difference in the positions of the HITRAN2020 lines from the experimental ones for transitions with Ka = 19 reaches 11.8 × 10–3 cm–1.

Fig. 2.
figure 2

A comparative diagram of the maximum rotational quantum numbers J and Ka for the 16O16O18O bands (000)–(000) (a) and (010)–(000) (c) experimentally observed in our work versus the HITRAN2020 line lists [14], which have been calculated using the parameters [27]; the differences between the observed line positions of the (000)–(000) (b) and (010)–(000) (d) bands and the HITRAN2020 data.

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Fig. 3.
figure 3

Same as in Fig. 2, but for 16О18О16О.

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2.1 Isotopomer 16О16О18О

With the initial parameters of Flaud et al. [27] it was possible to identify purely rotational transitions of the ground state in the spectrum of d20318.3 for small values of quantum numbers up to J = 25 and Ka = 8. By adjusting the H eff parameters iteratively in the modelling process we were able to identify 2051 transitions of this band up to J = 67 and Ka = 18. The parameters obtained in the weighted fit of experimental transition frequencies together with microwave data [25] allowed us to model rotational microwave transitions of the band (000)–(000) with a standard deviation of 0.2 × 10–5 cm–1. This includes the fit of experimental transitions measured in our work with RMS = 0.171 × 10–3 cm–1, and the entire set of transitions with weighted standard deviation of 1.284 (Table 2).

Table 2.   Overall statistics of experimental transitions of 16O18O16O and 16O16O18O ozone isotopomers included in the simultaneous fit. Treatment results
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At the next stage, we fixed the obtained parameters of the ground state and varied only the parameters of the (010) bending state during the simultaneous fit of three data sets. These sets include the rotational transitions ν2–ν2 obtained from the microwave spectra [26] and the SOLEIL spectrum (d20318.3) in the range of 30–200 cm–1, as well as VR transitions of the ν2 band assigned in the range of 550–880 cm–1 in the spectrum d20326.1. The final set of the (010) state parameters for the isotopomer 16O16O18O, given in Table 3, permitted modelling the entire set of 4597 transitions with a weighted standard deviation of 0.908.

Table 3.   Spectroscopic parameters of Heff for the (000) and (010) states of the 16O18O16O and 16O16O18O ozone isotopomers, obtained in a simultaneous fit of the observed line positions in the MW, FIR and THz ranges
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2.2 Isotopomer 16О18О16О

The lines of the isotopomer 16O18O16O were identified using a similar procedure. In total, 729 purely rotational ground state transitions up to J = 62 and Ka = 18 were identified in the spectra studied in our work. Despite the fact that the information obtained on the Jmax and \({{K}_{{{{a}_{{\max }}}}}}\) only slightly exceeds the set of quantum numbers of this band in HITRAN2020 (Fig. 3a), the difference between the line positions of the experimental transitions and those calculated in HITRAN2020 increases with increasing energy and reaches 12.5 × 10–3 cm–1 for the Ka = 18 series (Fig. 3b). Using the simultaneous fit with microwave data [27], we obtained a weighted standard deviation of 1.168.

For the ν2 band, the set of vibrational-rotational transitions was significantly expanded compared to published literature data (Fig. 3c): in total, 2229 transitions of the ν2 band up to J = 61 and Ka = 19 were identified in the spectrum. Their simultaneous fit (Table 2) with the transitions of the hot band ν2–ν2 obtained from the SOLEIL spectra in our work and with the microwave spectra [26] permitted to obtain more accurate set of effective Hamiltonian parameters for 16O18O16O given in Table 3.

3 RESULTS

The detailed line statistics of the 16O18O16O and 16O16O18O ozone isotopomers assigned in the SOLEIL spectra, as well as the MW data [25, 26], included in the simultaneous fit are collected in Tables 2. The resulting parameters of the (000) and (010) states are presented in Table 3.

Using the parameters of the effective Hamiltonians of the (000) and (010) states obtained in our work, as well as the parameters of the effective dipole moments of the bands from the S&MPO database [13], the lists of lines for 16O18O16O and 16O16O18O, including transitions (000)–(000), (010)–(000), and (010)–(010) were calculated. The partition function Q(T) was taken [13] equal 7565.675 and 3647.080 for 16O16O18O and 16O18O16O, respectively. The calculated spectra constructed using these lists gave good agreement with the experiment. Figs. 4 and 5 show such a comparison in the ranges 75.8 and 719.2 cm–1, respectively.

Fig. 4.
figure 4

Comparison of the experimental ozone spectrum (d20318.3) recorded using the SOLEIL synchrotron setup with the calculated spectrum in the region of 75.8 cm–1. The left-hand panel (a) shows an example of the dominant contribution of the Q-branch rotational band of the isotopomer 16O16O18O, the right-hand panel (b) – of the isotopomer 16O18O16O.

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Fig. 5.
figure 5

Comparison of the experimental spectrum of ozone (d20326.1) registered in the far- infrared range of about 719.2 cm–1 (low panel) with the calculated in this work spectrum (upper panel).

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The line lists for the main isotopic modification of ozone was taken from the work [33] devoted to the study of 16O3 spectra recorded at SOLEIL. In the future, it is planned to perform theoretical calculations of line intensities using ab initio dipole moment [43].

CONCLUSIONS

The FTS spectra of ozone isotopically enriched with oxygen 18O recorded using the light source of AILES Beamline facility of the SOLEIL synchrotron in the range 1–6 THz (30–200 cm−1), combined with new experimental spectra of the ν2 bands recorded using glowbar source in the far-infrared range (550–880 cm−1), allowed us to significantly expand the set of observed VR transitions up to Jmax = 67, \({{K}_{{{{a}_{{\max }}}}}}\) = 19. As a result of their simultaneous fit with MW transitions, new parameters of the effective Hamiltonian of the states (000) and (010) of the isotopomers 16O16O18O and 16O18O16O were obtained. The accuracy of calculated spectra with the obtained parameters was significantly improved compared to the previously used reference parameters of J.M. Flaud et al. [27].

In the future work, we plan to use the obtained parameters, as well as theoretical calculations of line intensities using ab initio dipole moment to construct complete transition line lists for the studied bands and to fill the spectroscopy databases HITRAN, GEISA, S&MPO.