Thibault D'halluin

Célia Lepeytre

Antoine Leydier

Carine Julcour
email: carine.julcour@ensiacet.fr

Degradation mechanism of tributyl phosphate by UV/H 2 O 2 treatment and parameters optimization towards the design of a pilot reactor

Keywords: Water treatment, organophosphates, AOP, photo-oxidation, degradation mechanism

While activated sludge treatment is currently the preferred process for the removal of tributyl phosphate (TBP) at the mg.L -1 level, it is well known that this recalcitrant molecule is incompletely degraded, stimulating research into alternative approaches, such as advanced oxidation. The aim of this study was to characterize the degradation mechanism of TBP during ultraviolet/H 2 O 2 treatment using 31 P NMR, ionic chromatography and total organic carbon analysis. The effects of initial pH, amount of oxidant and pollutant concentration were also assessed using an experimental design approach. The results of this parametric study show that ultraviolet/H 2 O 2 photo-oxidation efficiently degrades TBP at concentrations up to 600 mg.L -1 , with >90% phosphate release and up to 95% removal of total organic carbon within 1 h. The data also show that the main reaction intermediates are short carboxylic acids, resulting from the released alkyl groups, meaning that an interesting application of this process may be to rapidly pre-treat industrial effluent upstream of activated sludge reactors.

Introduction

Tributyl phosphate is an organophosphorus compound mainly used as flame retardant in the aircraft and automobile industry, and as an extraction agent for lanthanides in the nuclear industry in PUREX Process (Plutonium Uranium Refining by EXtraction). This process involves liquid-liquid extraction between TBP/ dodecane (30/70) mixture and nitric acid solution. During the phases contacting, a hundred mg.L -1 of TBP can be solubilized into the aqueous phase [START_REF] Velavendan | Studies on solubility of TBP in aqueous solutions of fuel reprocessing[END_REF], which has to be subsequently treated before discharge.

TBP has recently been identified and classified as a hazardous substance with harmful effects on aquatic life and humans, in whom it acts as an endocrine disruptor [START_REF]Tributyl phosphatesubstance information -ECHA[END_REF]. The limit in France for TBP release into rivers is therefore 50 µg.L -1 with a long-term flow threshold of 5 g per day. As this threshold is set to be reduced, new solutions for TBP degradation are required to reduce the concentration of pollutant out from the industry. Activated sludge treatment is the classical approach used in industrial effluent processing plants to degrade organic pollutants dissolved in water. A recent study on its application to OrganoPhosphorus Flame Retardants (OPFRs) in industrial effluent [START_REF] Cristale | Can activated sludge treatments and advanced oxidation processes remove organophosphorus flame retardants?[END_REF] highlighted the fact that these molecules are particularly bio-recalcitrant. New bacteria such as Serratia odorifera [START_REF] Berne | Tributyl phosphate degradation by Serratia odorifera[END_REF] and Pseudomas pseudalcaligenes [START_REF] Chaudhari | Tributyl phosphate degradation in batch and continuous processes using pseudomonas pseudoalcaligenes MHF ENV[END_REF] have been screened for their ability to degrade TBP: in 1-3 days of treatment from starting concentrations of 75-500 mg.L -1 , these strains were able to remove 31% to 73% of the TBP, respectively. This long and incomplete degradation, along with uncertainties regarding future threshold concentrations for bio-remediation and the fate of this compound in the environment, emphasize the requirement for complementary or alternative approaches.

Advanced Oxidation Processes (AOPs) are attractive in this context as their efficiency for the removal of refractory organic compounds is proven. The highly reactive and non-selective oxygen species such as hydroxyl radicals ( • OH) generated in AOPs decompose the target compounds into non-toxic intermediates, such as short carboxylic acids, yielding CO 2 , H 2 O and mineral acids as final compounds. This contrasts with other powerful treatments such as chlorination, which produce toxic halides. Applying AOPs to industrial effluent treatment seems therefore to be a promising solution [START_REF] Parsons | Advanced oxidation processes for water treatment: fundamentals and applications[END_REF]. For TBP and similar molecules in particular, Cristale et al. [START_REF] Cristale | Can activated sludge treatments and advanced oxidation processes remove organophosphorus flame retardants?[END_REF] have shown for instance that an initial ozone concentration of 25 mg.L -1 can reduce the total OPFR content of industrial effluent treatment plant effluents by 25% to 50%. Similarly, using ultraviolet (UV)-C photocatalyzed β-Ga 2 O 3 , Seshadri and Sinha [START_REF] Seshadri | Photocatalytic performance of combustion synthesized β-Ga 2 O 3 for the degradation of tri-n-butyl phosphate in aqueous solution[END_REF] were able to degrade 95% of the TBP in a 400 mg.L -1 solution in 30 min. Effective but slower removal was also achieved with a classical catalyst (TiO 2 ), with an equivalent degradation yield reached in 70 min [START_REF] Seshadri | Photocatalytic performance of combustion synthesized β-Ga 2 O 3 for the degradation of tri-n-butyl phosphate in aqueous solution[END_REF][START_REF] Drinks | UV-a photocatalytic degradation of the radionuclide complexants tributylphosphate and dibutylphosphate[END_REF], while Drinks et al. [START_REF] Drinks | UV-a photocatalytic degradation of the radionuclide complexants tributylphosphate and dibutylphosphate[END_REF] degraded 87.5% of the TBP in a 100 mg.L -1 solution in 80 min using 0.5 g.L -1 TiO 2 and UV-A irradiation. The combination of UV light and H 2 O 2 is a particularly interesting method of generating radicals because of its low cost and the easy availability of hydrogen peroxide. According to the review of Miklos et al. [START_REF] Miklos | Evaluation of advanced oxidation processes for water and wastewater treatmenta critical review[END_REF] UV/H 2 O 2 appears among the most energy-efficient AOPs with E EO (electrical energy per order) values in the order of 1 kWh/m 3 (compared to 100 kWh/m 3 or more for UVbased photocatalysis or ultrasound). Their study also revealed that this figure was influenced to some extent by water quality (median E EO values ranging from 0.63 kWh/m 3 for drinking water to 2.2 kWh/m 3 for wastewater and 2.7 kWh/m 3 for ground water) and was reduced with an increase in scale (from 2.2 kWh/m 3 at lab-scale to 0.68 kWh/m 3 for pilot-scale and 0.5 kWh/ m 3 for full-scale applications) [START_REF] Miklos | Evaluation of advanced oxidation processes for water and wastewater treatmenta critical review[END_REF]. Furthermore, the process is simple to manage, adaptable to changes in the influent [START_REF] Parsons | Advanced oxidation processes for water treatment: fundamentals and applications[END_REF][START_REF] Miklos | Evaluation of advanced oxidation processes for water and wastewater treatmenta critical review[END_REF] and industrial scale systems are available (Calgon Carbon's Peroxpure™ and Rayox® systems for drinking water treatment for instance).

There have been a few studies on the performance of the UV/H 2 O 2 process for TBP remediation [START_REF] Cristale | Can activated sludge treatments and advanced oxidation processes remove organophosphorus flame retardants?[END_REF][START_REF] Watts | Photooxidation and subsequent biodegradability of recalcitrant tri-alkyl phosphates TCEP and TBP in water[END_REF][START_REF] Watts | Advanced oxidation kinetics of aqueous trialkyl phosphate flame retardants and plasticizers[END_REF][START_REF] Santoro | Modeling hydroxyl radical distribution and trialkyl phosphates oxidation in UV-H 2 O 2 photoreactors using computational fluid dynamics[END_REF], but focussing on the disappearance of the molecule rather on its ultimate fate and the degradation process. The aim of the work reported here was to determine the degradation mechanism in full, as well as to examine the influence of key process parameters, such as the initial concentration of TBP, initial H 2 O 2 concentration and initial pH.

Materials and methods

Reagents

The aqueous effluents originating from the nuclear fuel treatment contain the classical ions found in every water (bicarbonates, nitrates, sulphates, etc.). That is why all the experiments were performed in Evian water (composition in Table 1) to approximate the mineral content typically found in such industrial effluents and to insure a constant composition of the matrix.

Tributyl phosphate was purchased from Fluka with a purity of 99.8%. Hydrogen peroxide (H 2 O 2 ) was purchased as a 35% w/w solution from Alfa Aesar.

Dibutyl phosphate (DBP) (≥97.0% purity, Sigma-Aldrich), a 1:1 DBP:MBP (mono butylphosphate) mixture (Alfa Aesar, molar ratio), phosphate, formate and acetate standards (1000 mg.L -1 supplied by Sigma Aldrich) were used to calibrate the quantitative 31 P NMR and ion chromatography analyses. All chemicals were used as received.

Experimental set-up and procedure

The laboratory scale photo-reactor used in this study consisted of a 1 L annular reactor (length: 38.2 cm; diameter: 6.3 cm) equipped with an immersion lamp in a quartz sleeve, and a recirculation loop. The content of the reactor was stirred magnetically at 450 rpm and the recycle flow rate was set to 164 L.h -1 , to ensure adequate mixing. The temperature inside the reactor was kept at 20°C using a water-cooled jacket. The light source for the UV/H 2 O 2 treatment was a low pressure mercury UV-C lamp (wavelength: 254 nm; radiation length: 33.7 cm; diameter: 2.3 cm) supplied by Heraeus. The photonic power of the lamp was measured with a UV radiometer using the Keitz method [START_REF] Rekab | H 2 O 2 and/or photocatalysis under UV-C irradiation for the removal of EDTA, a chelating agent present in nuclear waste waters[END_REF], resulting in a value of about 13 W. In complement, the photon flux entering the reactor was measured with the same captor, but directly at the quartz lamp holder wall, giving a value of 1.63⋅10 -5 ein.s -1 .

For the parametric study, the initial pH of the TBP solution was varied by adding H 2 SO 4 or NaOH (1 M solutions). During the tests, pH value was not controlled, but its evolution was followed.

Tributyl phosphate is known be stable under acidic conditions (as in the PUREX process) and has been shown to remain stable for more than 30 days in slightly alkaline solutions [START_REF] Wright | Review of physical and chemical properties of tributyl phosphate/diluent/nitric acid systems[END_REF]. The hydrolytic degradation of TBP was therefore assumed to be negligible over the pH range considered here.

The lamp was turned on 5 min before the injection of H 2 O 2 to ensure the irradiation remained constant during the oxidation process. Samples (10 mL) were taken every 5 min for the first 30 min of the reaction, then at t = 45, 60, 150 and 360 min, and analysed using the methods described below.

Analytical methods

31 P NMR

The organophosphorus species in the samples (TBP, DBP and MBP) were identified and quantified by 31 P NMR. NMR spectra were recorded on a Bruker 400 UltraShield VS spectrometer (161.976 MHz for 31 P) using deuterated water as the solvent with a dilution factor of 5. A total of 5632 scans were co-added for each sample. Internal calibration was performed from 5 to 100 mg.L -1 for DBP and from 1 to 100 mg.L -1 for the other phosphorous species. The precision of the analyses for TBP, DBP and MBP was 2% of the respective ranges.

Ion chromatography

Concentrations of phosphate and short-chain organic acids were measured using a Metrohm 930 Compact IC Flex ion chromatograph. The aliquots from the reactor were diluted 10-fold and 100 µL samples were injected into the device. The compounds were separated on a Metrosep A Supp 5 column maintained at 30°C and with the conductimetry detector set to 40°C. The mobile phase was 1 mM NaHCO 3 and 3.2 mM Na 2 CO 3 in isocratic mode with a flow rate of 0.7 mL.min -1 . Calibration was performed using standards from 0.5 to 10 mg.L -1 . The overall uncertainty of the technique was estimated to be 2% over this concentration range.

Total organic carbon analysis

The mineralization of TBP was determined by measuring the residual total organic carbon (TOC) content of the samples, using a Shimadzu TOC-V device. The TOC data were also used to evaluate the contributions of identified organic compounds. The non-purgeable organic carbon method was used given the high concentrations of inorganic carbon, but the results were similar to the default (total carboninorganic carbon) method, ruling out any significant loss of light organic compounds during the measurements. Prior to injection (81 µL) the samples were diluted 10-fold, and 2% of a 2 M HCl solution was added to remove the inorganic carbon. The coefficient of variation between successive TOC measurements (three repetitions) was 5%.

Mass spectrometry

Mass spectrometry was used to identify other potential oxidation by-products such as butanol. The samples (500 µL) were injected directly at 500 µL.min -1 into a TSQ Quantum Access Max quadrupole device. The capillary temperature was 380°C and the electrospray temperature, 350°C. The analyses to detect butanol were performed in positive mode at a voltage of 2500 V.

Titration of remaining H 2 O 2

The evolution of hydrogen peroxide concentration during the oxidation was followed by Eisenberg's method [START_REF] Eisenberg | Colorimetric determination of hydrogen peroxide[END_REF], where H 2 O 2 forms a pertitanic acid complex with titanium (IV) salt under acidic conditions. Pertitanic acid is stable for a few hours and exhibits a yellow colour. This feature enables its concentration to be measured with a UV-Vis spectrometer set at 410 nm. Under these conditions, the molar absorption coefficient of pertitanic acid is 742 L.mol -1 .cm -1 .

In the course of the reaction, samples were withdrawn and diluted with ultra-pure water when required. Then, 50 mg of TiO 2 were mixed with 5 mL of H 2 SO 4 at 98% and heated at 150°C for 16 h in order to obtain Ti 4+ at 6.6 mmol.L -1 . 1 mL of this solution was mixed with 2 mL from the sample and produced the yellow complex.

This method allows the measurement of hydrogen peroxide concentration between 0.5 and 4.5 mM, the detection limit being 0.1 mM.

Results and discussion

Synergistic effect

No phosphate release was observed after 2.5 h when UV or H 2 O 2 were used alone. The synergistic effects of UV and H 2 O 2 on the degradation of TBP were then evaluated in terms of TOC removal, using apparent first-order constants (k). These experiments were performed at neutral initial pH with 100 mg.L -1 TBP and a H 2 O 2 /TBP molar ratio of 10. The synergy factor S was defined as shown in Equation [START_REF] Velavendan | Studies on solubility of TBP in aqueous solutions of fuel reprocessing[END_REF].

S = k UV/H 2 O 2 k UV + k H 2 O 2 (1)
The values obtained for k H 2 O 2 , k UV , and k UV/H 2 O 2 were respectively ∼0, 0.017, and 0.069 min -1 , with S ≈ 4, highlighting the strong beneficial effect of combining UV and oxidant treatment. The facts that there was no TOC removal using H 2 O 2 alone and minimal TBP photolysis prove that TBP degradation is mainly mediated by the photo-decomposition of H 2 O 2 into radicals [START_REF] Da Silva | Antibiotics mineralization by electrochemical and UV-based hybrid processes: evaluation of the synergistic effect[END_REF]. The absorption spectrum of 100 mg.L -1 TBP in Evian water (Figure S1, Supplementary Material), shows a molar absorption coefficient of 0.13 L.mol -1 .cm -1 at 254 nm (compared with about 20 L.mol -1 .cm -1 for H 2 O 2 ).

Evolution of hydrogen peroxide concentration

The consumption of H 2 O 2 concentration during TBP oxidation was followed for different oxidant amounts (from 10 to 60 molar equivalents with respect to TBP) starting with a TBP concentration of 100 mg.L -1 and an initial pH of 7.5. Figure 1 shows a similar time-conversion profile of the oxidant regardless of its initial concentration. Indeed, there should be a marginal competition for the photons in between TBP (poorly absorbing at 254 nm) and H 2 O 2 . In addition, the consumption of H 2 O 2 was found almost complete after 30 min of oxidation and its possible scavenging effect should thus mainly prevail at the very beginning of the oxidation.

Degradation mechanism of TBP during UV/ H 2 O 2 treatment

The evolution of a typical 31 P NMR spectrum during oxidation is shown in Figure 2a. The chemical shifts of TBP, DBP, MBP and phosphate relative to 85% H 3 PO 4 are -0.17, 0.9, 2.2 ± 0.2 and 3.4 ± 0.4 ppm, respectively. The small variation in the position of the MBP and phosphate peaks is an effect of initial pH changes during the reaction. Figure 2b shows that the concentration of TBP drops down to ∼0 ppm in about 5 min, which is also when the concentration of MBP and DBP are maximal (∼16 and ∼10 ppm, respectively).

Figure 3a shows the typical evolution of the chromatograms during UV/H 2 O 2 treatment. At first, only the ions present in the Evian water are detected, namely chloride (rt = 8.5 min), nitrate (rt = 14.3 min) and sulphate (rt = 23 min), and their concentration remains stable throughout the reaction (Figure 3b). Under these operating conditions, acetate (rt = 6.5 min) and formate (rt = 7 min) ions appear within the first 15 min. Subsequently, oxalate ions (rt = 27 min) are formed and finally degraded, as the corresponding peak is no longer visible after 1 h. The molar absorption coefficients measured at 254 nm for the oxalate, acetate and formate reaction intermediates were 21.23, 0.02 and 0.12 L.mol -1 .cm -1 , respectively, while for TBP the value obtained was 0.13 L.mol -1 .cm -1 . Note that DBP, MBP and phosphate do not absorb at 254 nm. Oxalic acid has thus the same absorption coefficient as hydrogen peroxide, and might be readily photolyzed.

The pH showed a maximum variation by one pH unit from its initial value (cf. Figure 3b). This minimum corresponded to the highest concentration of formed carboxylic acids.

As mentioned in the introduction, the degradation/ stability of TBP has already been studied under various treatments. The mechanism identified using alpha or gamma radiolysis by [START_REF] Williams | Radiolysis of tri-n-butyl phosphate[END_REF][START_REF] Burger | Abstract of the American Chemical Society Meeting[END_REF][START_REF] Burr | The radiolysis of tributyl phosphate[END_REF], with DBP and MBP as stable intermediates, has subsequently been observed under hydrolysis [START_REF] Davids | Aqueous-phase decomposition of TBP at 35-75°C in nitric acid solutions[END_REF][START_REF] David | Accelerated hydrolysis of industrial organophosphates in water and soil using sodium perborate[END_REF], thermal decomposition [START_REF] Powell | Compounds of hexavalent uranium and dibutylphosphate in nitric acid systems[END_REF][START_REF] Patil | Thermal decomposition of nitrated Tri-n-butyl phosphate in a flow reactor[END_REF] and biodegradation [START_REF] Chaudhari | Tributyl phosphate degradation in batch and continuous processes using pseudomonas pseudoalcaligenes MHF ENV[END_REF][START_REF] Nancharaiah | Biodegradation of tributyl phosphate, an organosphate triester, by aerobic granular biofilms[END_REF]. Three butyl chains are detached one after the other, as shown in Figure 4 [START_REF] Drinks | UV-a photocatalytic degradation of the radionuclide complexants tributylphosphate and dibutylphosphate[END_REF]. In aqueous solutions, the butyl phosphate species yield phosphate ions as the final phosphorus compound.

The fact that the corresponding species were all identified here (Figure 2a), confirms that the same mechanism applies under photo-oxidation. Regarding the fate of the carbon chains, butanol was only detected at trace levels by mass spectrometry (concentration < 0.1 mg.L -1 ) in the early stages of process (at sampling times < 1 min). Among the six carboxylic acids targeted by ion chromatography, only acetic, oxalic and formic acid were identified (pyruvic, lactic and butyric acids were not found). The elemental balances of phosphorus and carbon were calculated (Equations ( 2) and (3), respectively) to confirm that the main oxidation intermediates had not gone undetected:

P balance = [TBP] t mol + [DBP] t mol + [MBP] t mol + [PO 3- 4 ] t mol [TBP] 0 mol (2)
C balance = TOC identified species TOC measured

The values obtained at the different measurement times are listed in Table 2 at conditions yielding an intermediate oxidation rate. The phosphorus and carbon balances are both close to 100% at all the reaction times, confirming that that all major stable intermediates are identified. The small deviations from 100% are especially due to difficulties quantifying DBP below 5 mg.L -1 .

Figure 5 illustrates the mechanism proposed on the basis of these results for the oxidation of TBP during UV/H 2 O 2 treatment. The alkyl chains detached from TBP are rapidly transformed into shorter C1-C2 carboxylic acids. As their concentration increases, the initial pH of the solution is slightly reduced, by about one unit at most. Oxalic acid appears last, probably from the oxidation of acetic acid. The concentration of acetic acid is the highest because of its low reactivity with hydroxyl radicals. Note that in their study of the UV-A photocatalysis of TBP, Drinks et al. [START_REF] Drinks | UV-a photocatalytic degradation of the radionuclide complexants tributylphosphate and dibutylphosphate[END_REF] did not detect oxalic acid, but did identify C3-C4 acids (2-ketobutyric, propionic, lactic and pyruvic acid) not observed here. These differences can be ascribed to the stronger oxidizing conditions with UV/H 2 O 2 .

Inhibition effect of hydrogen peroxide

Ultraviolet light activates the decomposition of H 2 O 2 into • OH radicals, which can subsequently oxidize organic compounds through different mechanisms. Several species, such as carbonate and phosphate ions [START_REF] Santoro | Modeling hydroxyl radical distribution and trialkyl phosphates oxidation in UV-H 2 O 2 photoreactors using computational fluid dynamics[END_REF][START_REF] Sillanpää | Degradation of chelating agents in aqueous solution using advanced oxidation process (AOP)[END_REF][START_REF] Muruganandham | Recent developments in homogeneous advanced oxidation processes for water and wastewater treatment[END_REF], can compete with the pollutant for • OH radicals, as can H 2 O 2 itself when in large excess, according to the following reactions:

• OH + H 2 O 2 HO • 2 + H 2 O (4) HO • 2 + • OH +H 2 O + O 2 (5)
The hydroperoxyl radicals (HO • 2 ) formed in the first reaction and consumed in the second one have a lower oxidation potential than • OH (1.65 V vs. 2.8 V). There is therefore usually an optimal H 2 O 2 concentration for peroxide-based AOPs and for UV/H 2 O 2 process in particular [START_REF] Li | Organic pollutant degradation in water by the vacuum-ultraviolet/ultraviolet/H 2 O 2 process: inhibition and enhancement roles of H 2 O 2[END_REF].

To identify suitable boundaries for the experimental design optimization, a preliminary study was carried out to determine the maximum concentration of oxidant before inhibition occurs. The corresponding assays were performed at neutral initial pH (Evian water) with 100 mg.L -1 of TBP. Figure 6 shows the percentage of phosphate released as a function of the initial H 2 O 2 concentration, expressed as H 2 O 2 /TBP molar ratio. Phosphate release levels off at 40 molar equivalents of H 2 O 2 , indicating that adding more hydrogen peroxide does not improve the degradation of TBP. At higher concentrations, the supplementary hydroxyl radicals are readily scavenged by the excess of peroxide and do not react with the pollutant [START_REF] Cater | UV/H 2 O 2 treatment of methyl tert-butyl ether in contaminated waters[END_REF][START_REF] Lopez-Alvarez | Degradation of a toxic mixture of the pesticides carbofuran and iprodione by UV/H 2 O 2 : evaluation of parameters and implications of the degradation pathways on the synergistic effects[END_REF][START_REF] Liu | Combining ozone with UV and H 2 O 2 for the degradation of micropollutants from different origins: lab-scale analysis and optimization[END_REF][START_REF] Somathilake | Influence of UV dose on the UV/H 2 O 2 process for the degradation of carbamazepine in wastewater[END_REF]. The rate constant of the reaction between H 2 O 2 and • OH is 1.7-4.5 × 10 7 L.mol -1 .s -1 , which is about hundred times less than for the oxidation of TBP by • OH (6.4 × 10 9 L.mol -1 .s -1 [START_REF] Watts | Advanced oxidation kinetics of aqueous trialkyl phosphate flame retardants and plasticizers[END_REF]), explaining the order of magnitude of excess concentration required for the competition effect to be observed.

Parametric study

The degradation process was optimized using a full factorial design with three factors (initial pH, initial TBP concentration and initial H 2 O 2 concentration) and three levels for each [START_REF] Córdova | Removal of organic matter and ammoniacal nitrogen from landfill leachate using the UV/H 2 O 2 photochemical process[END_REF]. Two assays were duplicated (5 and 9) and three additional intermediate conditions (I1-I3) were investigated. The parameter ranges covered were chosen based on preliminary observations or tests: the initial pH could not be increased above 8.5 because the magnesium ions in the Evian water precipitated as magnesium oxide, and the solubility limit of TBP was found to be above 1000 mg.L -1 . As discussed above, the reaction rate plateaued at H 2 O 2 concentrations above 40 molar equivalents (Figure 6). Note that this concentration is only slightly more than the stoichiometric quantity required to mineralize the TBP according to:

PO(OC 4 H 9 ) 3 + 36 H 2 O 2 = 3 H + + PO 3- 4 + 12 CO 2 + 48 H 2 O (6)
The selected limits of the parameters for the experimental design study are summarized in Table 3.

The degradation of TBP was assessed for each parameter combination by measuring the release of phosphate and the mineralization yield after 5, 15 and 60 min. These reaction times were selected based on the kinetics observed in preliminary experiments. The results obtained are shown in Table 4.

The fact that the absolute difference between replicates (5 vs 5R and 9 vs 9R) is less than 3% for the mineralization yields and less than 2.5% for phosphate release, shows that the results are reproducible.

The initial pH has a small to moderate effect on phosphate release and mineralization, with neutral or basic initial pH being preferable. Regardless of the initial pH or H 2 O 2 concentration, the degradation process is usually less effective at higher pollutant concentrations, as is typically observed in AOPs [START_REF] Watts | Photooxidation and subsequent biodegradability of recalcitrant tri-alkyl phosphates TCEP and TBP in water[END_REF][START_REF] Watts | Advanced oxidation kinetics of aqueous trialkyl phosphate flame retardants and plasticizers[END_REF][START_REF] Li | Organic pollutant degradation in water by the vacuum-ultraviolet/ultraviolet/H 2 O 2 process: inhibition and enhancement roles of H 2 O 2[END_REF]. This might be explained by some competition in between H 2 O 2 and the formed by-products for the photons or by an increased amount of bicarbonate and phosphate ions formed during the mineralization.

The degradation efficiency is more strongly correlated with the H 2 O 2 to TBP molar ratio. With an H 2 O 2 /TBP molar ratio of one, TBP is not significantly oxidized at any of the initial pH and initial concentrations investigated here. This may be because Evian water already contains a relatively high concentration of bicarbonate ions ([HCO - 3 ] = 360 mg.L -1 ), which can compete with TBP for • OH groups at low radical concentrations. Note however that these ions should be removed at low initial pH, whereas as mentioned above, the process was actually more effective at neutral and basic initial pH.

To quantify the influence of the parameters more precisely and elucidate possible interaction effects, the responses were fitted with a quadratic model using the software Design Expert 11. The responses considered were phosphate release (Y PO 4 ) and TOC removal (X) after 60 min, which vary substantially over the investigated range of operating conditions at this reaction time (Table 4).

The optimization led to the following equations for the percentages of phosphate release and TOC removal, respectively:

Y PO 4 (60 min) = 2.133 + 0.022 • pH -0.0015 • C TBP + 0.479 • D H 2 O 2 -0.0067 • D 2 H 2 O 2 (7) X (60 min) = -25.403 + 15.574 • pH + 0.092 • C TBP + 0.244 • D H 2 O 2 -0.0041 • pH • C TBP -5.31 • 10 -4 • C TBP • D H 2 O 2 -1.179 • pH 2 -6.90 • 10 -5 • C 2 TBP + 0.033 • D 2 H 2 O 2 (8)
where D H 2 O 2 is the H 2 O 2 /TBP molar ratio and C TBP is the pollutant concentration in mg.L -1 . Accurate fits were obtained (see Figs S2 andS3, Supplementary Material) with adjusted coefficients of determination (which take into account the number of parameters in the equations) of 0.9772 and 0.9576 respectively, and predicted coefficients of determination of 0.9697 and 0.9358, respectively. The latter parameter is a cross-validation of the model, calculated by sequentially removing each of the data points and assessing how well the model fitted to the remaining data fits the missing point. The small differences (<0.03) between the adjusted and predicted coefficients show that the model is predictive and not overfit. Furthermore the high signal to noise ratio of the data ('Adeq Precision' > 20) and the low p-values of the models (<0.001) show that they are statistically significant and can be used over the design space.

The model for Y PO 4 confirms that increasing the TBP concentration has a negative effect on the degradation efficiency while higher initial pH and especially higher H 2 O 2 concentrations are favourable. The model for X TOC is more complex, with a greater number of interaction and quadratic terms.

The iso-response curves in Figure 7a reveal the influence of initial pH and TBP concentration on the degradation performance of the process at the maximum H 2 O 2 /TBP molar ratio. They confirm the positive effects of higher initial pH and lower TBP concentrations and show that complete phosphate removal can be achieved in 1 h for initial TBP concentrations up to 600 mg.L -1 (at neutral initial pH). Note that while much stronger scavenging effects are expected for carbonate than for bicarbonate ions, since the rate constant of their reaction with • OH is almost two orders of magnitude higher: 3.9 × 10 8 vs. 8.5 × 10 6 L.mol -1 .s -1 [START_REF] Buxton | Critical review of rate constants for reactions of hydrated electrons, hydrogen atoms and hydroxyl radicals ( • OH/ • O -) in aqueous solution[END_REF] the maximum initial pH considered here is two units lower than the pKa of carbonate (10.3), which was therefore presumably not involved in these reactions. Likewise for the equilibrium between H 2 O 2 and HO 2 -(whose molar absorptivity is much higher: 240 vs. 19.6 L.mol -1 .cm -1 ), the former should predominate under the conditions investigated here because the pKa of HO - 2 is 11.6 [START_REF] Sillanpää | Degradation of chelating agents in aqueous solution using advanced oxidation process (AOP)[END_REF][START_REF] Muruganandham | Recent developments in homogeneous advanced oxidation processes for water and wastewater treatment[END_REF]. Figure 7b shows the predictions of the model at neutral pH 0 (the most relevant in practice because modifying the pH of industrial effluent is costly and it promotes the conversion of TBP to DBP and MBP). Comparing the two parts of Figure 7 highlights the fact that the H 2 O 2 /TBP molar ratio has a much stronger effect on the TBP degradation efficiency than the pH 0 does. Increasing the H 2 O 2 concentration always improves phosphate release regardless of the initial TBP concentration. The ideal parameter combinations to optimize phosphate release in 1 h are therefore a low TBP concentration (below 600 mg.L -1 ) and a high H 2 O 2 /TBP molar ratio (35-40 eq).

The results for TOC removal (Figure 8) are similar. The effect of initial pH is stronger than it is for phosphate release (Figure 8a vs. Figure 7a), but as for the latter, the process is optimal (>90% TOC removal) for TBP concentrations below 600 mg.L -1 . The H 2 O 2 /TBP molar ratio has a stronger effect on carbon mineralization than the initial pH does (Figure 8a vs. Figure 8b). The optimal conditions at neutral initial pH are likewise a TBP concentration below 600 mg.L -1 and an H 2 O 2 /TBP molar ratio close to 40 eq.

The optimal ranges of the parameters are reported in Table 5 for all the investigated responses.

Degradation of TBP under optimal conditions

A 6 h validation test was performed with the optimal parameter combination (Figure 9). Under these conditions, the model predicted total phosphate release and a TOC removal of about 95% after 1 h. The experimental results are in accordance with these predictions (accounting for measurement uncertainties), with about 95% phosphate release and 90% TOC removal at a reaction time of 1 h. From the above analysis (Figure 3b), the residual carbon after 1 h is probably in the form of acetic and formic acids. Figure 9 shows that phosphate release is particularly rapid, reaching 75% in just 15 min. As the remaining carbon species are light carboxylic acids, which are easily digested by microorganisms, this process could be used as a short pretreatment before activated sludge processing. It may therefore be more relevant to focus only on the phosphate release.

High levels of phosphate release (>80%) could then be achieved in 1 h using a lower H 2 O 2 /TBP molar ratio (30 eq, Figure 10a). On the other hand, the fit of the phosphate response after 15 min (see also Figure S4, Supplementary Material) indicates that a yield of about 70% would be achieved for [TBP] 0 < 400 mg.L -1 and [H 2 O 2 ] 0 /[TBP] 0 = 40 (Figure 10b). This is an interesting perspective for future biodegradability analyses and ongoing initiatives to reduce oxidant usage, processing times, and thereby the cost of the treatment.

Conclusion

Ultraviolet/H 2 O 2 treatment has been confirmed as a promising method for the removal of tributyl phosphate and is likely similarly effective for other organophosphorus compounds. Chromatography, NMR and TOC data show that after rapid phosphate release (∼80% after 15 min under optimal conditions), the main organic intermediates are light carboxylic acids (acetic, formic and oxalic acid). The concentration of H 2 O 2 was the parameter that had the greatest effect on the efficiency of the process, with an H 2 O 2 /TBP molar ratio of 40 being optimal for both phosphate release and TOC removal, while avoiding wastage in competing reactions. Acidifying the reaction conditions did not prove beneficial and there was therefore little inhibition from bicarbonate ions. The process was shown to remain effective over a large range of TBP concentrations, up to 600 mg.L -1 , with more than two-thirds of the phosphate content released within 1 h. Phosphate release is achieved sooner than carbon mineralization for oxidant concentration near the stoichiometry, and lower H 2 O 2 concentrations (e.g. a molar ratio of ∼30) are required to achieve yields high enough to expedite subsequent sludge treatment, reducing operational costs. Having delineating the operating zone of interest in this study, biodegradability tests at different reaction times and operating conditions are in progress to help finalize the analysis.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Sum of

Figure 1 .

 1 Figure 1. Consumption of H 2 O 2 during the oxidation of 100 mg.L -1 TBP at pH 0 = 7.5 for different initial concentrations of H 2 O 2 (expressed in molar equivalents with respect to TBP).

Figure 2 .

 2 Figure 2. (a) 31 P NMR spectra of samples withdrawn at different times (red, 0 min; blue, 1 min; black, 2 min) during the oxidation of 100 mg.L -1 TBP at neutral initial pH and 20 molar equivalents of H 2 O 2 ([H 2 O 2 ] 0 :[TBP] 0 = 20); (b) corresponding time-evolution of the concentration of the identified organophorphorus species (TBP, tributyl phosphate; DBP, dibutyl phosphate; MBP, monobutyl phosphate).

Figure 3 .

 3 Figure 3. (a) Ion chromatograms of phosphate ions and light organic acids in samples withdrawn at different times (black, 0 min; red, 5 min; green, 10 min; yellow, 20 min; blue, 60 min) during the oxidation of 100 mg.L -1 TBP at a neutral initial pH and 20 molar equivalents of H 2 O 2 ([H 2 O 2 ] 0 :[TBP] 0 = 20); (b) corresponding time-evolution of the concentration of carboxylic acids and phosphate.

Figure 4 .

 4 Figure 4. Structural formulas showing the sequence of four stages in the hydrolysis of tributyl phosphate.

Figure 5 .

 5 Figure 5. Structural formulas illustrating the proposed mechanism of tributyl phosphate degradation during UV/H 2 O 2 treatment.

Figure 6 .

 6 Figure 6. Percentage of phosphate released at different reaction times during the degradation of tributyl phosphate (TBP initial concentration: 100 mg.L -1 ) by UV/H 2 O 2 process at neutral initial pH: effect of the initial concentration of H 2 O 2 .

Figure 7 .

 7 Figure 7. Influence of the design parameters on phosphate release after 1 h of TBP oxidation by UV/H 2 O 2 process: (a) with the H 2 O 2 / TBP molar ratio set to 40 eq and (b) with pH 0 = 7.

Figure 8 .

 8 Figure 8. Influence of the design parameters on total organic carbon (TOC) removal after 1 h of TBP oxidation by UV/H 2 O 2 process: (a) with the H 2 O 2 /TBP molar ratio set to 40 eq and (b) with pH 0 = 7.

Figure 9 .

 9 Figure 9. Evolution of phosphorus and carbon mineralization yields over 6 h during photo-oxidation of tributyl phosphate (TBP) starting with an initial concentration of 300 mg.L -1 , a neutral pH and H 2 O 2 /TBP molar ratio set at 40 eq.

Figure 10 .

 10 Figure 10. Phosphate release during TBP oxidation by UV/H 2 O 2 process: (a) after 1 h with an H 2 O 2 /TBP molar ratio of 30; (b) after 15 min with an H 2 O 2 /TBP molar ratio of 40.

Table 1 .

 1 Mineral content of the Evian water used in the study.

	Mineral	Concentration (mg.L -1 )
	-HCO 3 Ca 2+	360 80
	Cl -	10
	Mg 2+ -NO 3 K +	26 3.8 1
	SiO 2 Na +	15 6.5
	SO 4 2-

Table 2 .

 2 Phosphorus and carbon balances during TBP oxidation by UV/H 2 O 2 process (100 mg.L -1 TBP, neutral initial pH, 20 molar equivalents of H 2 O 2 ).

	t (min)	P balance	C balance (TOC)
	0	100%	100%
	5	80%	85%
	10	84%	91%
	15	90%	95%
	20	93%	99%
	25	96%	94%
	30	98%	100%
	45	98%	100%
	60	99%	100%
	150	98%	100%
	360	99%	100%

Table 3 .

 3 Parameters and selected levels for the experimental design study.

	Initial TBP concentration (mg.L -1 )	Initial pH	Initial H 2 O 2 concentration (molar equivalent with respect to TBP)
	100	2.15	1
	500	7.5	20
	1000	8.4

Table 4 .

 4 Experimental results of the parametric study performed to optimize TBP degradation under UV/H 2 O 2 .

					Phosphate release (%)	Carbon mineralization yield (%)
	Test n°Initial pH	[TBP] 0 (mg.L -1 )	[ H 2 O 2 ] 0 / [TBP] 0 (molar ratio)	5 min	15 min	60 min	5 min	15 min	60 min
	1	7	100	1	5.6	6.0	9.5	15.0	25.1	30.9
	2	7	100	20	29.0	53.5	75.7	13.1	30.0	40.6
	3	7	100	40	69.0	94.9	>99.9	28.3	70.5	95.2
	4	7	500	1	1.1	1.2	1.9	15.7	26.3	43.9
	5	7	500	20	9.6	36.0	76.2	25.3	36.7	57.2
	5R	7	500	20	9.2	36.1	76.1	25.8	39.7	57.1
	6	7	500	40	14.2	68.9	99.4	26.6	38.1	92.0
	7	7	1000	1	1.0	1.4	2.2	2.1	13.8	19.9
	8	7	1000	20	4.3	16.4	59.0	9.6	22.1	34.6
	9	7	1000	40	11.0	42.2	98.3	3.9	34.0	55.8
	9R	7	1000	40	13.2	40.1	99.4	5.4	36.5	58.2
	10	2.15	100	1	2.5	4.8	10.8	2.2	9.8	13.9
	11	2.15	100	20	13.1	58.1	81.3	20.1	25.5	33.3
	12	2.15	100	40	41.6	87.7	>99.9	0.3	29.8	67.4
	13	2.15	500	1	0.6	1.6	3.6	10.6	12.8	22.3
	14	2.15	500	20	3.3	20.7	74.2	15.1	17.5	33.4
	15	2.15	500	40	13.9	53.1	99.5	19.1	20.8	80.1
	16	2.15	1000	1	0.0	0.2	0.3	2.0	7.4	20.1
	17	2.15	1000	20	1.7	9.0	8.4	15.5	18.7	30.4
	18	2.15	1000	40	12.5	37.6	97.6	9.5	34.4	55.2
	19	8.4	100	1	3.6	5.4	8.1	16.9	29.0	32.1
	20	8.4	100	20	21.8	70.2	98.8	15.1	31.7	40.0
	21	8.4	100	40	58.3	88.6	99.5	24.7	64.0	86.5
	22	8.4	500	1	0.6	1.2	2.2	26.5	30.7	31.4
	23	8.4	500	20	6.7	36.5	76.4	29.4	38.7	45.0
	24	8.4	500	40	14.6	67.0	99.2	14.2	26.0	94.4
	25	8.4	1000	1	0.3	0.8	1.6	3.0	6.7	7.5
	26	8.4	1000	20	3.3	15.2	50.4	13.1	13.7	18.7
	27	8.4	1000	40	18.8	42.1	96.8	4.4	33.8	54.8
	I1	7	300	40	39.8	74.6	93.6	15.4	45.8	93.6
	I2	8.4	300	20	13.2	45.4	82.6	21.8	31.0	35.7
	I3	2.15	100	10	0.85	4.6	5.4	8.8	13.1	25.3

Table 5 .

 5 Optimal ranges of parameters from response surface methodology. Up to 500 mg.L -1 500 mg.L -1 300 mg.L -1 300 mg.L -1 Initial H 2 O 2 concentration (with respect to TBP)

	Phosphate release	TOC removal

  (60 min) = -25.403 + 15.574 ⋅ 𝑝𝐻 + 0.092 ⋅ 𝐶 𝑇𝐵𝑃 + 0.244 ⋅ 𝐷 𝐻 2 𝑂 2 -0.0041 ⋅ 𝑝𝐻 ⋅ 𝐶 𝑇𝐵𝑃 -5.31 ⋅ 10 -4 ⋅ 𝐶 𝑇𝐵𝑃 ⋅ 𝐷 𝐻 2 𝑂 2 -1.179 ⋅ 𝑝𝐻 2

	Source	Squares	df	Mean Square		F Value	p-value Prob > F
	Model	16595.9600	8	2074.4950	74.4900	0.0001
	A-pH	211.4400	1	211.4400	7.5900	0.0130
	B-Conc TBP	199.4400	1	199.4400	7.1600	0.0154
	C-Eq H2O2	11243.8900	1	11243.8900	403.7200	0.0001
	AB	433.6300	1	433.6300	15.5700	0.0009
	BC	261.2500	1	261.2500	9.3800	0.0067
	A 2	349.2100	1	349.2100	12.5400	0.0023
	B 2	1125.3700	1	1125.3700	40.4100	0.0001
	C 2	935.8000	1	935.8000	33.6000	0.0001
	Residual	501.3200 18	27.8511
	Cor Total	17097.2800 26
	Std. Dev.	5.2800	R-Squared	0.9707
	Mean	45.8100	Adj R-Squared	0.9576
	C.V. %	11.5200	Pred R-Squared	0.9358
				Adeq Precision	26.8683
				Model	Significant
	TOC removal 60min	=			A-pH	Significant
	-25.402910			B-Conc TBP	Significant
	15.574030 * pH		C-Eq H2O2	Significant
	0.092403 * Conc TBP			AB	Significant
	0.244197 * Eq H2O2			BC	Significant
	-0.004065 * pH * Conc TBP			A 2	Significant
	-0.000531 * Conc TBP * Eq H2O2		B 2	Significant
	-1.179240 * pH ²			C 2	Significant
	-6.90E-05 * Conc TBP ²		Std. deviation	Non Significant
	0.032868 * Eq H2O2 ²		Adequation	Significant
				Precision	Significant
		-6.90 ⋅ 10 -5 ⋅ 𝐶 𝑇𝐵𝑃 2	+ 0.033 ⋅ 𝐷 𝐻 2 𝑂 2

𝑋 2 Fig. S3. Output of the fitting software Design Expert 11 for the reduced quadratic model of TOC removal after 1h.

Funding

This work was supported by the French Alternative Energies and Atomic Energy Commission (CEA) [grant number 2017-THE-018-DE2D/SEAD/LPSD] and Occitania Region [grant number ALDOCT-000152].

Supplementary Material


V E Zuev
email: alain.campargue@univ-grenoble-alpes.fr

) upper vibrational levels are the most excited levels measured so far by absorption spectroscopy. The spectrum analysis allowed for the experimental determination of 240 of their rotational levels. Their energy ranges between 93.1 and 96.6 % of the dissociation threshold. The line positions and line intensity of the two bands were modelled using the effective operator approach. Synthetic line lists of the transitions are provided with line positions empirically corrected according to the experimental value of the upper energy levels and line intensities computed using fitted parameter values of the effective dipole moment. The fitted values of the band centres and rotational constants show a very good agreement with variational predictions based on an ab initio potential energy surface. Recent results indicate that if the calculations are not constrained to bound levels within one potential well, they give rise to three identical potential wells separated by barriers leading to deviations of some of the energy level values predicted by the 1-well and 3-well approaches, near the dissociation threshold. A better agreement of the (163) experimentally determined energy value with the 3-well predicted value is tentatively interpreted as an evidence of the 3-well effect.

I. INTRODUCTION

Various physical and chemical processes involved in the formation and depletion of ozone in the atmosphere have attracted attention over the years [1][2][3][4][5][6][7][8][9][10][11][12][13]. In this context, several aspects of the ozone dynamics remain to be understood for an accurate modeling at the molecular level. This concerns in particular, the knowledge of the highly excited quantum states and associated transition probabilities, near the dissociation threshold, D0. These excited states have attracted increasing interest in various fields, in particular for a reliable interpretation of satellite measurements of the ozone absorption/emission in the upper atmosphere [14][15][16] in non-local thermodynamic equilibrium (non-LTE) conditions [17,18].

These are challenging tasks both for experiments and theory because of the complicated electronic structure of this unstable molecule [19][20][21][22][23][24][25][26][27][28][29]. Many related aspects, which are of interest for fundamental molecular physics, would benefit from extended experimental information. Among them, there are issues related to possible tunneling between potential wells [30,31], non-adiabatic coupling with excited electronic states [20][21][22]29], isotopic exchange reactions [32][33][34][35][36], unusual properties related to isotopic anomalies of the ozone formation [11,37,38], which are not yet fully understood at the molecular level.

Environmental applications and climate research impact were incentive for many laboratory studies of high-resolution spectra of ozone isotopic species ([39-47] and references therein). The most relevant information concerning absorption spectra is included in the HITRAN [48] and GEISA spectroscopic databases [49] and collected in the web-accessible information system "Spectroscopy & Molecular Properties of Ozone" (SMPO) [50].

Most of spectra in the infra-red ranging from fundamental to relatively strong overtone and combination bands with low and moderate vibration excitation are accessible by Fourier Transform spectroscopy (FTS) [39][40][41]50]. In terms of normal mode quantum numbers, ʋi, this was limited to

6   i i 
i. e. to band centers below 5600 cm -1 (ʋi=1-3 are the conventional vibrational normal modes quantum numbers corresponding to the symmetric stretching, bending and antisymmetric stretching modes, respectively. The corresponding fundamental wavenumbers are about 1103, 701 and 1042 cm -1 , respectively). Due to the rapid decrease of absorption intensities of the vibrational bands at increasing wavenumbers (see Fig 2 of Ref. [52]), the FTS technique does not provide the required sensitivity to access vibrational levels approaching the dissociation threshold, D0, evaluated around 8560 cm -1 (as cited in [23,26]) from thermochemical measurements by Ruscic et al. [51]. Highly sensitive laser techniques are required to probe states approaching D0 [53][54][55][56][57][58][59][60][61][62][63][64]. In a series of previous works by cavity-ring-down spectroscopy (CRDS), we investigated systematically the 5850-7920 cm - 1 spectral region [54][55][56][57][58][59][60][61][62][63][64]. More than thirty vibrational bands of 16 O3 were rovibrationally assigned and modelled using the effective Hamiltonian approach. The analyses of the corresponding bands provided a set of more than 5000 rovibrational levels. Their comparison with ab initio potential energy surfaces (PES) [26] gave new experimental insight [52] into the long-standing "reef structure" issue [19,[25][26][27][34][35][36] of the PES shape in the transition state.

In the present work, improved performances of the used CRDS setup (routine noise equivalent absorption, αmin, on the order of a few 10 -11 cm -1 ) allowed for extending the measurements above 7920 cm -1 and for the detection the most excited absorption bands of ozone reported so far. In particular, the highest energy level determined from the analysis is only 3% below the dissociation threshold. The rest of the paper is structured as follows. The experimental work, including spectrometer and measurement of line parameters, is described in Section II. Section III is devoted to the assignment of the observed lines, band analyses, determination of rovibrational energies and effective dipole moments. The discussion (Section IV) includes a comparison with ab initio predictions.

II. EXPERIMENT

Compared to our previous CRDS studies of ozone below 7920 cm -1 [54][55][56][57][58][59][60][61][62][63][64][65], the present use of an external cavity diode laser (ECDL) instead of a series of fibered distributed feedback (DFB) allows for a more efficient light injection into the CRDS cell and thus for an improved sensitivity. These improved performances are necessary to detect the extremely weak ozone bands located around 8000 cm -1 . The same setup was recently used to characterize the high energy part of the O2 band at 1.27 µm [65] and extremely weak transitions in the 1.18 µm window of CO2 [66]. From recordings with noise equivalent absorption, αmin, on the order of a few 10 -12 cm -1 , lines among the weakest ever reported (intensity as low as 5×10 -31 cm/molecule) could be measured [65,66]. In the following we recall the different parts of the setup and the procedure adopted for the recording of the ozone spectra.

A. The CW-CRDS spectrometer

The heart of the spectrometer is a high-finesse optical resonator made of a stainless tube fitted with two highly reflective mirrors on its extremities, one of them being mounted on a piezo electric element (PEE) PEEC, that allows the cavity length to be slightly length-modulated. To limit the gas temperature gradients, this sample cell was covered with a tube of insulation foam and placed inside a plexiglas enclosure in order. The stainless tube temperature was continuously monitored with an analogue temperature sensor (TSic 501, IST-AG, ±0.1 K accuracy). The sample pressure, in the cell, was continuously monitored with a 1000 Torr capacitance gauge (MKS Baratron, 0.15% accuracy of the reading). During the various days of the measurement campain the temperature varied between 293.8 and 294.1 K.

The reader is referred to Konefal et al. (in particular its Fig. 2) [65] for a detailed description of the CRDS set-up, except that, in sake of a faster scan rate, we did not implement the optical frequency comb referencing or disciplining. Briefly, the ECDL light is first sent into a polarization maintained fiber coupler (PFC, 90/10), which directs about 10% of the emitted light to a Fizeau wavemeter (High Finesse WS-U-30 IR, 5 MHz resolution, 20 MHz accuracy) and the remaining 90% into a fibered acousto-optic modulator (AOM) inserted before the 1.4-meter-long high-finesse cavity (HFC) (F≈ 200,000). The AOM, used on its order +1, interrupts the excitation once resonance with one of its longitudinal modes is achieved, leading to a ring down (RD) event. Each RD is detected with an InGaAs photodiode. The resonance is sought by adjusting the length of the cavity over λ/2 with PEEC, hosting the output mirror.

The cavity losses at each laser wavelength were obtained by averaging the results of exponential fits to some tens of ring-down events, thus giving one data point in the spectrum. The absorption coefficient, α (cm -1 ), was then directly calculated from the decrease of the cavity ring-down time τ (in s) induced by the molecular absorption:

, ( 1
)
where c is the light velocity and t0 is the ring-down time of the empty cell depending of the mirror transitivity, diffraction losses, volume scattering etc… The frequency emission of the ECDL (DL pro 1200 from Toptica) was tuned by acting on its internal grating angular position and the laser chip current, in an electronically-controlled lasercurrent-feed-forward scheme. The grating angular position can be roughly set with an external step motor and finely adjusted with an internal PEEL. The ECDL has a mode-hop-free tuning range limited to 0.8 cm -1 obtained with a linear scan of the PEE voltage over about 80% of its full range capability. Broadband spectra were therefore obtained by concatenation of series of slightly overlapping individual narrow spectra. During automatic broadband acquisition, the laser frequency was iteratively stepped by about 0.5 cm -1 , by acting on the grating with the step motor. A mode-hop-free scanning situation was then automatically sought by adjusting the PEE ramp offset over successive fast (1s) test scans. The instantaneous laser frequency and the Fizeau wavemeter raw signals were used as mode hop free and monomode emission criterion, respectively. Once the optimal PEEL voltage offset was determined, a 10 minutes long, ~60 MHz step by step scan was started. After each frequency jump, 80 RDs were acquired before a new frequency step. In all the recordings, the sampling step was chosen to be about 2×10 -3 cm -1 to be compared to a HWHM Doppler line width of about 7×10 -3 cm -1 (220 MHz) and an ECDL emission linewidth of 150 kHz at 1 ms integration. Typically, the recording of a 5 cm -1 wide spectral interval required about one hour. Overall, the presently analysed spectrum covers the 7925-8070 cm -1 interval located just above the 5850-7920 cm -1 wide range previously studied with DFB lasers [54][55][56][57][58][59][60][61][62][63][64]. The most excited band of 16 O3 previously analysed is centred at 7860 cm -1 [63].

The absolute calibration of the frequency axis as provided by the wavemeter was refined using accurate line centres of O2 lines that we recently reported with an accuracy better than 10 -4 cm -1 [65].

B. Ozone preparation

The ozone sample was prepared using a silent electric discharge (12 kV, 400 Hz) at liquid nitrogen temperature (LNT= 77 K). This system described in Ref. [67] allows obtaining a quasicomplete conversion of oxygen to ozone after a few minutes. First, the CRDS stainless steel cell and the glass ozoniser connected with a glass tube were filled with oxygen (AlphaGaz2 from Air Liquide, purity≥ 99.9995 %) at a typical pressure of P0= 40 Torr at room temperature. Then the ozonizer was immersed into a Dewar filled with liquid nitrogen and the discharged was switched on during a few minutes. The total pressure was observed to decrease with time during a few minutes as a result of the 3O2→2O3 conversion of oxygen to ozone, the latter being trapped in the ozonizer. At a residual pressure of 0.05 Torr, the discharge was interrupted and the Dewar was removed. Ozone was then evaporating leading to an initial pressure very close to (2/3)P0≈26 Torr of pure ozone.

The long duration required for the spectra recordings made the slow decomposition of ozone in oxygen a major issue. In order to slow down the decomposition, EPDM O-rings were used instead of Viton and their number was minimized. Vacuum grease was also avoided. The quantitative estimation of the ozone decomposition is generally obtained from the increase of the total pressure. As a result of the 2O3→ 3O2 reaction, a 1 Torr increase of the total pressure is expected to correspond to a 2 Torr decrease of the ozone partial pressure and the ozone partial pressure is deduced from the total pressure, P, measured at each spectral point P O 3 = 2(P 0 -P). The dependence of 𝑃 𝑂 3 versus the wavenumber i.e. versus time as the scanning speed of the laser frequency was constant, is presented on Fig. 1. During the 26 hours duration of the recordings of the displayed 7920-8012 cm -1 region, the ozone partial pressure is observed to decrease mostly linearly with time from 26 Torr to 17.6 Torr, with a decomposition rate of 0.2 Torr/hour. The plot includes the corresponding oxygen partial pressure obtained from P O 2 = 3P-2P 0 . Interestingly, the range of the present recordings makes possible an independent determination of the oxygen partial pressure and thus to check the above pressure values. Indeed, the studied spectral interval covers part of the R branch of the 𝑎 ∆ 1 𝑔 -𝑋 Σ g -3 (0 -0) band of O2 centered at 1.27 µm. The corresponding oxygen lines can be used to determine the oxygen concentration. The resulting oxygen partial pressures deduced from the O2 lines are plotted in Fig. 1 together with the corresponding ozone partial pressures obtained by difference from the measured total pressure. (Note that we derived the O2 concentration using the line intensity values recently reported in Ref. [65] which correct HITRAN values by 2-4%).

FIG. 1.

Pressure variation due to the ozone decomposition in oxygen, during the CRDS recordings between 7920 and 8012 cm -1 . The ozone and oxygen partial pressures were determined by two independent ways: from the total pressure (dashed and solid red lines, respectively) and from the oxygen concentration derived from R branch of the 𝑎 ∆ The two pressure determinations lead to similar wavenumber (e.g. time) dependences and an overall satisfactory agreement except for a mostly constant difference of about 1.2 Torr on 𝑃 𝑂 3 . The origin of this difference is unclear. It could be due to an incomplete ozone conversion or thermal effects. For the ozone line intensity retrieval presented below, the ozone partial pressure calculated from the total pressure was adopted. The evidenced 1.2 Torr difference between the two 𝑃 𝑂 3 determinations represents a fraction of 𝑃 𝑂 3 increasing from 4.5 to 7% over the 7920-8012 cm -1 region. This uncertainty on 𝑃 𝑂 3 is thus a major source of the overall error bar on the intensity values.

In the following, for the convenience of the data treatment, the obtained absorption coefficients were normalized to an arbitrary constant ozone pressure (e.g. 10. Torr).

C. Impurities and line parameters retrieval

An important difficulty of the spectrum treatment is related to the superposition of many impurity lines to the targeted ozone spectrum. In fact, as illustrated in Fig. 2, the spectrum is largely dominated by lines due to oxygen, water, CO2 and HF. During the recordings, the relative concentration of these species vary according to the ozone decomposition, to desorption or chemical reaction with the walls of the setup . The strongest ozone lines observed in the region have an intensity on the order of 10 -27 cm/molecule, which is to be compared to maximum intensity values on the order 5×10 -26 , 5×10 -25 , 2×10 -26 and 3×10 -20 cm/molecule for oxygen, water, CO2 and HF, respectively. The relative concentrations of water, CO2 and HF, are roughly estimated to be on the order of 10 -3 , 2×10 -3 and 10 -4 for respectively while, due to ozone decomposition, oxygen partial pressure can be on the same order as the ozone partial pressure at the end of the spectra recording (see Fig. 1). Due to the extension and congestion of the spectrum, an accurate and systematic removal of the impurity lines from the spectrum after a careful line-by-line fit of all the absorption features was not systematically undertaken. This laborious work was limited to small spectral intervals around ozone lines which were rovibrationally assigned (see below). Nevertheless, an automatic program using as starting point a spectrum simulation using the HITRAN line lists [48] of the various impurity species with concentration dynamically adjusted according to the wavenumber, was elaborated in order to highlight the ozone contribution to the recorded spectra. The results of the procedure are presented on the right panel of Fig. 2. After subtraction of the impurities contribution, two ozone A-type bands showing a band head near 7973 and 7998 cm -1 are clearly apparent. The corresponding rovibrational assignments will be described in the following sections. It is interesting to note that the strongest absorption feature observed on the "cleaned" spectrum at about 7997.6 cm -1 is an ozone line belonging to the 3 A2(0 0 0)-X(0 2 0) hot band of the Wulf electronic system. This rovibronic band center at about 8154 cm -1 is predissociated but show a series of narrow absorption lines which extends down to 8000 cm -1 and will be the subject of a separate study (see Refs. [68,69] for an analysis of a similar hot band in 18 O3).

Line parameters were determined for most of the ozone lines which could be rovibrationally assigned. The line centers and line intensities were obtained by using a homemade interactive least squares multi-lines fitting program written in LabVIEW. As the ECDL line width is much smaller than the Doppler broadening, the contribution of the apparatus function to the observed profiles was neglected. The fits were done over narrow spectral intervals including the assigned ozone lines and overlapping lines (unassigned ozone lines or impurities) which could be fitted independently. For each spectral interval, the line center, integrated absorption coefficient and Lorentzian width of each line as well as the baseline (assumed to be a linear function of the wavenumber) were provided by the fitting procedure. The Doppler broadening was fixed according to the mass of the species and the temperature of the gas. The Lorentzian width was fitted when possible or fixed to a value calculated from the default value of 0.09 cm -1 /atm provided by the HITRAN database for self-broadening coefficient of ozone. Note that in our pressure conditions (about 25 Torr), the Lorentzian width (~3×10 -3 cm -1 HWHM) is about half the Doppler line width (7×10 -3 cm -1 ).

The difficulty of the line parameter derivation due to the considerable spectral congestion is illustrated in Fig. 3 in a spectral interval near 7948 cm -1 . The simulation based on the retrieved line parameters (middle panel) is compared to the experimental spectrum. The contribution of impurity lines (water and CO2) are accounted for, and the (exp.-sim.) residuals (lower panel) correspond to a root mean square deviation of about 10 -11 cm -1 . The rovibrational lines of ozone which could be assigned in the displayed region are indicated.

The line intensity, 𝑆 𝜈 0 (𝑇) of a rovibrational transition centered at 0, was obtained from the integrated absorption coefficient, 𝐴 𝜈 0 (cm -2 /molecule):

𝐴 𝜈 0 = ∫ 𝛼 𝜈 𝑑𝜈 = 𝑆 𝜈 0 (𝑇)𝑁 𝑙𝑖𝑛𝑒

(2) Where ν is the wavenumber in cm -1 , αν is the absorption coefficient in cm -1 obtained from the cavity ring down time (Eq. 1) and N is the volume number density in molecule/cm 3 obtained from the measured pressure and temperature values: P = NkT. In the favourable cases of well isolated and relatively strong lines (we are speaking about line intensities on the order of only a few 10 -28 cm/molecule!), the accuracy of the line positions is estimated to be about 10 -3 cm -1 . Because of the moderate signal-to-noise-ratio, the statistical error of the fit leads to error bars on the integrated absorption coefficient of about 3 to 5 %. Nevertheless, taking into account frequent line overlapping and the above discussed uncertainty of the ozone partial pressure, we estimate to 10-15% the average value of the reported obtained intensity values. This is comparable or even a better precision compared to what was previously achieved in some lower wavenumber ranges for this unstable molecule.

III. ANALYSES AND RESULTS

Two types of vibration-rotation absorption bands exist in the ozone molecule [40,42,50]. The strongest ones are activated due to the component of the dipole moment which is parallel to the aaxis of the principal inertia moment. Such bands, usually called "parallel" bands or A-type band, follow the selection rules ʋ3 = odd and Ka = even. The second type of bands are the "perpendicular" bands or B-type bands which follow the selection rules ʋ3 = even and Ka = odd. Within the same frequency interval, these latter bands are usually weaker and have quite irregular line intensity patterns making more difficult their rovibrational assignment. Due to their weakness and irregular structure, perpendicular bands have not been assigned in wavenumber ranges above 6770 cm -1 [42,63]. However, the corresponding upper states play the role of "dark" states which may perturb observed "bright" states via accidental resonance interactions [42].

Many previous studies have made it clear that vibrational extrapolation using standard Dunhamtype expansion [70] in terms of quantum numbers ʋ1,ʋ2,ʋ3 does not give reliable results for the ozone band centres near the dissociation threshold. In this work, the identification of new bands in the recorded CRDS spectrum relied on the variational predictions from the ab initio PES reported in Ref.

[26] where the "global" vibrational assignment (, N) was given by the irreducible representation  of C2V point group and the ranking number N, increasing with energy.

In the 7920-8000 cm -1 range of the present recordings, eight vibrational levels of A1 and B1 types in C2V point group are predicted [26]. Four of them -(B1, N=87-90) at 7928.76, 7944.73, 7971.69 and 7991.66 cm -1 , respectively, -belong to the B1 irreducible representation (anti-symmetric with respect to the C2 axis). Note that for B1 vibrational levels, J= 0 states are not spin-allowed [40,42] because all 16 O nuclei of the main ozone isotopologue, 16 O3, are bosons. However, the calculation of such states, via the diagonalization of ab initio based vibrational Hamiltonian, is meaningful because they correspond to observable band centres obtained as J0 limit of experimental rotational line series. The J > 0 rovibrational states of B1 vibrational levels do exist, and the transitions to these states correspond to parallel (A1 vib B1 vib ) bands, which are determined experimentally. Another four vibration levels belonging to totally symmetric A1 irreducible representation are predicted: (A1, N=117-120) at 7943.77, 7949.65, 7957.13 and 7973.76 cm -1 , respectively. They could give rise to very weak perpendicular (A1 vib A1 vib ) bands with hardly assignable tiny and irregular patterns, which do not exhibit characteristic band heads [add refs].

As in previous studies [52,71], to help the assignment, the rovibrational J= 1 and J= 2 levels were computed from the ab initio PES [26] and used to determine theoretical values of AV, BV and CV rotational constants of the different predicted vibrational states. Their comparison with observations will be discussed in section IV.

A. Spectra assignment

The effective Hamiltonian (EH) and effective dipole moment (EDM) models were used for the assignments. The basic definitions and technical details can be found in Refs. [39,40,42,50]. The iterative fits of observed transitions and elaboration of calculated line lists used the GIP program [72]. At the initial iteration, ab initio values [26] were adopted for the band centers and rotational constants involved in the EH model as the adjustable parameters. This allows us for following series of lines with increasing total rotational quantum number J for various values of Ka. In general, the (obs-calc) position difference versus rotational quantum numbers showed a smooth dependence until a resonance perturbation appears. A comparison of the corresponding deviation curves as a function of Ka permits assigning few lines for low values of rotational quantum numbers. A second way, particularly relevant for A-type bands in the CRDS spectral range, was to look at the sharp observed band head in the R-branch, trying various assignments and seeking the same (obs-calc) residuals in the P-branch. Successive fits of EH parameters allowed us to assign more and more lines by iterations.

The most complicated issue was the modeling of irregular deviations from a single-vibrationstate model, which appears to be due to perturbations caused by resonance interactions with "dark" states. This problem becomes very difficult to solve at high energy range where the density of rovibrational states drastically increases towards the dissociation threshold. In these conditions, EH models suffer from lack of experimental information for numerous closely lying "perturber states". For this reason the rms (obs-calc) deviations of the EH fits systematically increase with vibration energies (see Fig. 7 of Ref. [26]). Another difficulty is that many observed lines are blended or hidden by impurities or unidentified ozone lines, including hot band vibronic transitions. To overcome the shortcomings of incomplete EH models, we have determined effective parameters specific for different J, Ka series by separating the data according to the parity of J for Ka = 1, 2 and 3. This permitted extending assignments with smaller partial rms deviations for separate series of lines.

As far as possible, ground state combination differences (GSCD) relations from transitions belonging to P-, R-or Q-branches, were checked to insure the assignments. In we also verified that relative intensities calculated with an approximate value of the fitted effective dipole moment were qualitatively consistent with the observations, thanks to synthetic spectra computed by MULTIFIT program [73].

The ν1+6ν2+3ν3 band in the 7930-7973 cm -1 range

The position of the band head observed at 7973 cm -1 (see Fig. 2) points the (B1, N=89) upper state at 7971.69 cm -1 as most probable candidate for the upper state of the corresponding parallel band. This is consistent with simulations using tab initio values of the corresponding rotational constants which indicate that the centre of the observed band should lie about 2-3 cm -1 below the sharp absorption feature of the band head. The (B1, 89) upper vibration level is assigned as (ʋ1,ʋ2,ʋ3) = (1,6,3). This vibrational assignment relies on the decomposition of the corresponding ab initio wavefunction in the normal mode basis set using the contact transformation (CT) method. To this end, we used MOL_CT program suite [74,75]; the technical aspects of calculations were described in [71,74,75].

(a) Line positions and energy levels. The first series of assignments concerned the Ka = 4 upper state levels abd was validated by GSCD relations involving the P-, Q-and R-branches. Then, a similar procedure was applied to other Ka values leading to the assignment of 243 transitions of the ν1+6ν2+3ν3 band reaching a total of 130 upper state energy levels. The experimentally determined energy levels are listed in Table I with their corresponding statistical error bars when they could be derived from different transitions.

A fit of the experimental line positions using an isolated state EH model leads to an rms deviation of 0.148 cm -1 , largely above the experimental uncertainty. Deviations between measured and calculated position values were found to be either positive or negative, depending on the parity of J, without smooth dependence on rotational quantum numbers. Particular large perturbations were detected for Ka = 1 and 2 series. The introduction of a Coriolis interaction with the (A1,118) dark state predicted at 7949.65 cm -1 [26] allowed for a reduction of the rms deviation by a factor of two (0.078 cm -1 ). The set of derived parameters is given in Table II. Note that the mixing coefficient between J, Ka, Kc =14, 2, 13 state of the (B1, 89) state and J, Ka, Kc =14, 3, 11 of the (A1,118) state is about 50-50 % making an assignment of this particular rovibrational level ambiguous. Notes: Nb is the number of observed transitions used to determine the upper energy level E (cm -1 ). ΔE is the rms error of the experimental energy determination (in 10 -3 cm -1 unit).

Notes

a Two transitions to the upper state level J, Ka, Kc =21, 2, 19 were excluded from the fit. b Sum of intensities in the combined line list (366 lines).

[f] -fixed to the values predicted from the PES of Ref. [26]. All higher order centrifugal distortion parameters [77] quoted in [78] were held fixed to their ground state values. Grey background corresponds to the (=A1, N=118) dark state.

(b) Line intensities and effective dipole transition moment. The empirical determination of weak band transition moments from crowded spectra is quite sensitive to uncertainties of experimental intensities and to the completeness of underlying theoretical model. Among the assigned transitions of the ν1+6ν2+3ν3 band, a subset of 182 relatively isolated lines sampling the P-, Q-and R-branches was selected. Depending on the proximity with other lines, realistic error bars were evaluated and associated to the corresponding line intensities. The intensity values were used as input data of a weighted fit of the EDM parameters. The standard EDM model [79,80] for A-type bands of C2V molecules were adopted [79,80]:

        () ( )( ) 2 2 1 2 3 4 1 , , , , 2 ul A V V A A A A z z z z x y y x Z d d d J d iJ i J         J               5 6 1 1 , ,i( , , ... 2 2 A A x x z z x y y z z y x y y x d J J J J i J J J J d iJ i J                   , (3)
where the notation   X, Y XY YX stands for an anti-commutator,  are direction cosines for the Eckart molecular fixed frame, Jα are the molecular fixed component of the total angular momentum, and () A i d are band-specific transition moment parameters empirically retrieved from the line intensities of the observed band. Five parameters of the effective dipole transition moment could be well determined with a weighted standard deviation 1.061 and an rms deviation of 12 %. The results of the fit are provided as a Supplementary Material while the derived EDM parameters are listed in Table II together with corresponding fit statistics. The comparison of the measured and calculated line intensities for the 182 lines included in the fit is presented in Fig. 4. (c) Line list and comparison with observations. A list of 366 transitions of the ν1+6ν2+3ν3 band allowed by Ka = 0 selection rule was generated using the EH and EDM parameters of Table II. The list was limited to transitions reaching experimentally determined upper state levels and line positions were empirically corrected according to the experimental value of the upper energy levels listed in Table I. Line intensities were computed using the fitted EDM parameters and wavefunctions corresponding to the EH of Table I. Note that the resulting list includes a number of lines unobserved in the spectrum (e.g. hidden by impurity lines) which have experimental accuracy on their line centers because they reach an upper level empirically determined from different transitions. The obtained line list leads to the overview comparison presented in Fig. 5.

FIG. 5.

Overview of the ν1+6ν2+3ν3 absorption band of 16 O3. Upper panel: CRDS spectrum with impurity lines (partly) removed at a pressure normalized to 10 Torr (the grey trace corresponds to the original CRDS spectrum with impurity lines). Lower panel: simulation limited to transitions reaching experimentally determined upper levels with intensities computed from EH and EDM (Table II) and line positions empirically corrected.

More detailed blown-up comparisons in the P and R-branches are shown in Figs. 6 and7. These figures provide extended qualitative validation of the assignments and of intensities computed from the fitted effective dipole transition moments of Table II. They contain supplementary information with respect to Fig. 4 concerning absorption features composed of doublet, triplet and other overlapping lines, which were not possible to include in the dipole moment fit. The account for new computed transitions (beyond 182 intensities included in the fit -Fig. 4) are particularly important for the R-branch (Fig. 7) because they contribute to overlapping lines near the compressed band head, which correspond to the strongest absorption features of the band. 2. The 6ν1+ν2+ν3 band in the range 7951-8000 cm -1 A head of a weak vibration-rotation band is observed near 7998 cm -1 , (Fig. 2) but it is superimposed with H2O impurity lines, other ozone lines in particular some strong absorption features due to vibronic transitions of the 3 A2(0 0 0)-X(0 2 0) hot band of the Wulf electronic, making the assignment more challenging. According to the ab initio predictions, the (B1, 90) vibrational level predicted at 7991.66 cm -1 [26] is the most plausible candidate for the upper state of this A-type band. This is confirmed by calculations using theoretical values of rotational constants which predict a band head agreeing with the observations within about 1 cm -1 . The decomposition of the (B1,90) ab initio wavefunction in the normal mode basis gives a major contribution to the (ʋ1,ʋ2,ʋ3) = (6,1,1) normal mode vibration. Consequently, the corresponding parallel absorption band was assigned as 6ν1+ν2+ν3. Note that the low energy neighbor of the (B1, 90) level -(B1, 89)-is the upper level of the ν1+6ν2+3ν3 parallel band assigned above, whereas the next parallel band (B1, 91) is predicted 52 cm - 1 [26] above the observed band head.

(a) Line positions and energy levels. Following the above described techniques, 189 transitions of the 6ν1+ν2+ν3 band corresponding to 110 upper state energy levels could be assigned. It appeared that the Ka = 3 series was strongly perturbed. Thanks to ab initio predictions [26], this perturbation was identified as a strong Coriolis resonance with the Ka = 4 levels of the (A1,119) vibrational state predicted at 7957.13 cm -1 and confirmed by next assignments. The introduction of this dark state in the EH model permitted reducing the final rms deviation in line positions from 0.12 to 0.016 cm -1 . The fitted values of the spectroscopic parameters are given in Table III. The experimentally determined values of the (611) rovibrational levels are included in Table I (b) Line intensities and effective dipole transition moment. As for the previous band, a restricted set of relatively isolated lines were used for the determination of the EDM parameters. Note that the weakness of the band (line intensities between 10 -29 and 10 -28 cm/molecule) results in larger uncertainties on the intensity values. Only the principal transition moment parameter could be determined from the weighted fit of 67 line intensities belonging to P-, Q-and R-branches (weighted standard deviation of 1.009 and the rms deviation of 15.5% -see Table III and Supplementary Materials). The general agreement between the measured and fitted intensity values is illustrated in Fig. 8. (c) Line list and comparison with observations. In the same way as for the ν1+6ν2+3ν3 band, a line list reaching the experimentally determined energy level of the (611) state was generated. Line positions were adjusted according to the experimental energy values (Table I) while line intensities were computed using the EDM parameters and EH eigenfunctions (Table III). The list provided as Supplementary Material includes 306 transitions up to Jmax = 25, Ka max = 6. The sum of their calculated intensities is SV = 1.3×10 -26 cm/molecule, a factor of three smaller than for the ν1+6ν2+3ν3 band.

Fig. 9 and 10 show an overview comparison of the simulated absorption coefficient using this combined line list of the 6ν1+ν2+ν3 band (lower panel) to the CRDS spectrum (upper panel) in the Pand R-branch region, respectively. Let us note that the CRDS spectrum is formed by narrow rovibrational lines superposed to broad diffuse structures. Based on the previous works of Bouvier et al. and Abel et al.[add refs!] on the 3 A2(0 0 0)-X(0 0 0) rovibronic band of 16 O3 near 10080 cm -1 and on previous observations of similar broad structures assigned to the 3 A2(0 0 0)-X(1 1 0) hot band of the heavy 18 O3 isotopologue near 7880 cm -1 band [16,17], these diffuse absorption patterns are believed to be due to rovibronic transitions reaching the metastable levels of excited electronic 3 A2 triplet state from the (0 2 0) bending state at 1399 cm -1 (the center of the 3 A2(0 0 0)-X(0 2 0) hot band is predicted near 8154 cm -1 ). In addition, to these rovibronic structures (two narrow ones are marked on Fig. 10), the very weak lines of the 6ν1+ν2+ν3 band are superimposed to strong lines of impurities (in particular water and CO2) and other narrow lines which are believed to belong to ozone but remain to be identified. To make the comparison clearer, we have extracted in the middle panel of Fig. 9, the lines of the 6ν1+ν2+ν3 band for which line parameters were derived from a fit of their line profile. A care has to be taken for interpretation of fine details in such comparison because of the presence of overlapping multiplets, some of them not belonging to the assigned band. However, the general agreement of the intensity patterns in the measured (middle panel) and calculated (lower panel) spectra validates the assignments of the 6ν1+ν2+ν3 band. I) and line positions empirically corrected. FIG. 10. Same as Fig. 9 in the region R branch of the 6ν1+ν2+ν3 band of 16 O3. The original spectrum including impurity lines is also displayed on the upper panel (dashed grey) Relatively broad features marked with asterisks correspond to electronic 3 A2(0 0 0) -X 1 A1(020) hot band transitions In order to illustrate the difficulty of the analysis of the 6ν1+ν2+ν3 band, we present in Fig. 11 a direct comparison between the CRDS spectrum in a section of the P-branch and a simulation based on our combined list. Note the presence of a high number of unassigned narrow lines in the displayed interval which are believed to be belong to ozone rovibrational bands which remain to be identified. I) and line positions empirically corrected.

IV. SUMMARY AND DISCUSSION

The exceptional sensitivity of the CRDS experimental setup used in the present work has allowed for the detection and analysis of two extremely weak combinations bands of 16 O3 above 7900 cm -1 , with upper states involving up to ten vibrational quanta. In Fig. 12, their line lists have been gathered with the HITRAN2016 list and previous CRDS data, below and above 5850 cm -1 , respectively. The two newly reported bands are the highest energy bands reported so far. Their intensity is smaller by nine orders of magnitude compared to the fundamentals bands [41,81]. The line lists provided in Supplementary Materials contains Einstein coefficients of these transitions involving large changes in vibrational quantum numbers that can have implications for modelling the ozone dynamics including non-LTE processes [17].

The assignment of 432 transitions of the ν1+6ν2+3ν3 and 6ν1+ν2+ν3 bands allowed us to determine 240 upper state vibration-rotation levels between 7969 and 8277 cm -1 (see Fig. 13). This represents the highest so far obtained experimental set of rotationally resolved data up to Jmax = 25 in the range 93.1-96.6 % of the dissociation threshold, D0 (The highest energy level is [J, Ka, Kc]= [25,3,22] with an energy of 8277.3 cm -1 ). As anticipated from previous studies [], the conventional effective Hamiltonians fits based on semi-rigid rotor approximation, including centrifugal distortion and empirical resonance coupling terms, do not reach experimental accuracy in this range. This is consistent with the general trend of rms deviations of EH fits plotted in Fig. 7 of Ref. [42]. However, most of our assignments are supported by GSCD relations involving transitions from P-, Q-and Rbranches providing thus reliable information independently of a shortcoming of EH models. The consistence of the energy level values determined from different lines (see Table I) indicates that the average uncertainty of our energy set is better than 10 -3 cm -1 which is better than achieved in some lower energy ranges. The effects of the interactions among the three potential wells should be confirmed by further observations above 8000 cm -1 . Besides the experimental challenge, an extension of the analyses towards D0 will require accurate theoretical predictions both for hot bands in electronic transitions 3 A2(000)-X(V1V2V3) and ab initio intensities of rovibrational bands with large variation of vibration quantum numbers, which up to now were limited by Vmax =6 [71]. A study of qualitative changes of vibrational modes [85] on global ab initio PESs will be helpful for band assignments as well as for the account of non-adiabatic interactions of electronic states [20][21][22]29] near the dissociation asymptote.

  band of O2 (grey and open squares, respectively)

FIG. 2 .

 2 FIG. 2.Overview of the CRDS ozone recordings between 7925 and 8010 cm -1 . Left panels: Due to the weakness of the ozone spectrum, the recorded spectrum (lower panel) is dominated by impurity lines. The contributions of oxygen, water, CO2 and HF are simulated using the HITRAN database with rough estimated relative concentration. CRDS spectrum of ozone was normalized at the ozone pressure of 10 Torr. Right panel: Enlargement of the ordinate scale by a factor of about 20 showing ozone bands after subtraction of the sum of the simulated contributions of the impurity species.

FIG. 3 .

 3 FIG. 3. Example of line parameters retrieval near 7948 cm -1 . Upper panel: CRDS spectrum normalized at the ozone pressure of 10 Torr. Middle panel: Absorption simulation based on the retrieved line parameters and the corresponding stick spectrum. The contribution of the ozone and impurity lines (water and CO2) are shown in different colors (red and blue, respectively). The rovibrational lines of 16 O3 assigned in this work are marked by asterisks. Lower panel: (exp.-sim.) residuals. The corresponding rms deviation is about 10 -11 cm -1 .

FIG. 4 .

 4 FIG. 4. Comparison for the measured and calculated line intensities for the selected set of 182 lines used to fit of effective dipole moment of the ν1+6ν2+3ν3 band. Error bars correspond to estimated experimental uncertainties.

FIG. 6 .

 6 FIG. 6.Example of comparison of CRDS and simulated spectra in the P-branch region in the ν1+6ν2+3ν3 band. Upper panel: CRDS spectrum with impurity lines (partly) removed (black). The original spectrum including impurity lines is also displayed (dashed grey) Lower panel: simulation limited to transitions reaching experimentally determined upper levels with intensities computed from EH and EDM (TableII) and line positions empirically corrected.

FIG. 8 .

 8 FIG. 8. Comparison for the measured and calculated intensities for the selected set of 67 lines band used to fit of effective dipole moment of the 6ν1+ν2+ν3 band. Error bars correspond to estimated experimental uncertainties.

FIG. 9 .

 9 FIG. 9. Spectrum overview in the region of P-branch of the 6ν1+ν2+ν3 band of 16 O3. Upper panel: CRDS spectrum including the 6ν1+ν2+ν3 band, impurity lines (water and CO2), broad structures due to the 3 A2(0 0 0)-X(0 2 0) hot band of 16 O3 and additional unidentified lines of ozone. Middle panel: lines of the 6ν1+ν2+ν3 band of 16 O3 which were reproduced with a Voigt profile fit. The plotted lines are simulations based on the retrieved line profile parameters Lower panel: simulation limited to transitions reaching experimentally determined upper levels with intensities computed from EH and EDM (TableI) and line positions empirically corrected.

FIG. 11 .

 11 FIG. 11. Example of spectrum comparison in the region of P branch of the 6ν1+ν2+ν3 band of 16 O3. Upper panel: CRDS spectrum including the 6ν1+ν2+ν3 band, impurity lines (water and CO2) and additional unidentified lines probably due to ozone. Lower panel: simulation limited to transitions reaching experimentally determined upper levels with intensities computed from EH and EDM (TableI) and line positions empirically corrected.

FIG. 12 .

 12 FIG.12. Overview of the line lists of the analyzed rovibrational bands of 16 O3. Up to 5850 cm -1 , line list provided by the HITRAN2016 database (black circles) is reproduced. The CRDS data of Refs. [] cover the 5850-7900 cm -1 region (blue circles) while the most excited bands above 7900 cm -1 are the ν1+6ν2+3ν3 band (green) and 6ν1+ν2+ν3 (red) bands studied in this work. The dissociation threshold (8520 cm -1 [51]) is indicated.

Table I .

 I Rovibrational energy levels derived from observed transitions for the (1,6,3) and (6,1,1) vibration states of 16 O3.

										continued
	(ʋ1,ʋ2,ʋ3) :	(1,6,3)		(6,1,1)					(1,6,3)		(6,1,1)
	J	Ka	Kc	E (cm -1 )	Nb ΔE	E (cm -1 )	Nb ΔE	J	Ka	Kc	E (cm -1 )	Nb ΔE	E (cm -1 )	Nb ΔE
	1	0	1	7969.5294	1		7993.6164	1		13	2	11	8049.7297	2	0.1	8077.0688	1
	1	1	0				7996.6583	2	0.0	13	3	10	8064.2333	2	0.2	8091.8783	2	0.8
	2	1	2	7974.0368	1		7998.1394	2	1.2	13	4	9	8085.6814	3	0.3	8112.4860	1
	2	2	1	7983.3140	1		8007.2677	1		13	5	8	8113.2495	3	0.2	8139.6000	2	0.9
	3	0	3	7973.2411	1		7997.5429	2	0.7	13	6	7	8146.9147	2	0.7	8172.5748	2	0.5
	3	1	2				8000.7153	1		13	7	6	8186.7142	2	0.1
	3	2	1	7985.5595	2	0.3	8009.6269	2	0.1	14	1	14	8046.6396	2	0.2	8075.5942	1
	3	3	0	8000.9057	1		8024.7016	2	0.2	14	2	13				8087.2677	2	0.2
	4	1	4	7979.1191	2	0.1	8003.4646	1		14	3	12	8074.6230	1		8102.8590	1
	4	2	3	7988.5467	1		8012.7694	3	0.3	14	4	11	8096.1139	2	0.2	8123.4674	2	0.6
	4	3	2	8003.8791	3	0.3	8027.7930	1		14	5	10	8123.6803	3	0.7	8150.5991	2	0.1
	4	4	1	8025.3594	1		8048.9209	1		14	6	9	8157.3485	2	0.5	8183.5544	2	0.5
	5	0	5	7979.9085	2	0.0	8004.6010	2	0.6	14	7	8	8197.1597	2	0.1
	5	1	4	7983.4015	2	0.1	8008.0042	1		15	0	15	8056.4647	2	0.0	8085.8301	2	0.2
	5	2	3	7992.3147	2	0.3	8016.7197	3	0.5	15	1	14	8063.7405	2	0.0	8092.6683	2	0.4
	5	3	2	8007.5955	1		8031.6599	2	0.1	15	2	13	8071.8674	2	0.1	8100.2682	1
	5	4	1	8029.0788	1		8052.8445	2	0.2	15	3	12	8085.9023	2	0.1	8114.7291	1
	5	5	0	8056.6525	2	0.4	8079.8977	1		15	4	11	8107.3017	3	1.0	8135.2315	1
	6	1	6	7987.1440	2	0.6	8011.8310	2	0.5	15	5	10	8134.8562	3	1.5	8162.3864	2	0.8
	6	2	5	7996.7518	3	0.1	8021.4119	2	1.0	15	6	9	8168.5267	2	0.7	8195.2969	3	0.9
	6	3	4	8012.0628	1		8036.2627	1		15	7	8	8208.3566	2	0.6
	6	4	3	8033.5441	3	0.7	8057.5532	2	0.5	16	1	16	8069.2015	2	0.2	8099.0372	1
	6	5	2	8061.1204	2	0.2	8084.6104	1		16	2	15				8111.5025	2	0.6
	6	6	1	8094.7657	1		8117.5858	1		16	3	14	8097.7524	2	0.6	8127.2479	2	0.0
	7	0	7	7989.5056	1		8014.7591	1		16	4	13	8119.2302	2	0.0
	7	1	6	7993.3939	2	0.2	8018.5229	2	0.1	16	5	12	8146.7797	3	0.8	8174.9631	2	0.1
	7	2	5	8002.0477	2	0.6	8026.9860	2	0.5	16	6	11	8180.4505	2	0.9
	7	3	4	8017.2666	2	0.4				16	7	10	8220.3162	2	1.6
	7	4	3	8038.7549	2	0.0	8063.0481	2	0.1	17	0	17	8080.2014	2	0.0	8111.0405	1
	7	5	2	8066.3336	1		8090.1066	3	0.2	17	1	16	8088.8058	2	0.2	8119.1313	1
	7	6	1	8099.9823	2	0.3	8123.0871	1		17	2	15	8097.1639	2	0.5	8126.7428	1
	7	7	0	8139.7261	1					17	3	14	8110.6071	2	0.3	8140.7770	2	0.3
	8	1	8	7997.8048	1		8023.2820	2	0.0	17	4	3	8131.9187	1
	8	2	7	8007.9584	1		8033.1941	2	0.4	17	5	12	8159.4508	2	0.2	8188.3177	1
	8	3	6	8023.1759	2	0.1	8048.6488	1		17	6	1	8193.1237	2	0.4
	8	4	5	8044.7091	1		8069.3261	3	0.3	17	7	0	8232.9711	1
	8	5	4	8072.2890	2	0.3	8096.3904	2	0.3	18	1	18	8093.4451	1		8125.4869	1
	8	6	3	8105.9426	2	0.2	8129.3746	2	0.8	18	2	17				8138.8183	1
	8	7	2	8145.6921	3	0.7				18	3	16	8123.8834	2	0.4	8154.7910	1
	9	0	9	8001.9979	1		8027.9996	2	0.3	18	4	15	8145.3442	2	0.6
	9	1	8	8006.4413	2	0.3	8032.2651	2	0.4	18	5	14	8172.8712	1		8202.4610	2	0.5
	9	2	7	8014.8527	2	0.4	8040.4497	1		18	6	13	8206.5448	2	0.4
	9	3	6	8029.9235	2	0.4	8055.7098	3	0.6	18	7	12	8246.4216	1
	9	4	5	8051.4112	2	0.4	8076.3875	2	0.0	19	0	19	8106.7415	2	0.5	8139.1848	1
	9	5	4	8078.9957	1		8103.4616	3	0.4	19	1	18	8116.7904	1
	9	6	3	8112.6463	2	0.5	8136.4454	3	0.5	19	2	17	8125.6173	2	0.0	8156.4829	1
	9	7	2	8152.4021	3	0.4				19	3	16	8138.3634	2	0.1	8170.0370	1
	10	1	10	8010.7210	1		8037.6875	2	0.7	19	4	15	8159.5516	1
	10	2	9	8022.1628	2	0.0	8048.1028	2	0.7	19	5	14	8187.0380	2	0.4	8217.3867	1
	10	3	8	8037.3507	2	0.1	8063.5567	2	0.5	19	6	13	8220.7143	2	0.1
	10	4	7	8058.8605	1		8084.2362	2	0.3	20	1	20	8121.3250	1
	10	5	6	8086.4358	3	0.1	8111.3170	3	0.2	20	2	19				8169.1989	2	0.5
	10	6	5	8120.0957	2	0.7	8144.3052	1		20	3	18	8153.0237	2	0.1	8185.4851	1
	10	7	4	8159.8598	2	0.0				20	4	17	8174.4616	2	0.0
	11	0	11	8017.3447	2	0.2	8044.2821	2	0.4	20	5	16	8201.9579	2	0.5	8233.0670	1
	11	1	10	8022.5294	2	0.2	8049.2157	2	0.3	20	6	15	8235.6359	2	0.1
	11	2	9	8030.7350	2	0.4	8057.1341	2	1.1	20	7	14	8275.5665	2	0.5
	11	3	8	8045.5758	2	0.2	8072.2030	1		21	0	21	8136.3201	2	0.3	8170.2547	2	0.2
	11	4	7	8067.0537	2	0.5	8092.8695	3	0.7	21	1	20	8147.6594	2	0.3
	11	5	6	8094.6283	3	0.3	8119.9577	3	0.3	21	2	19	8157.2112	2	0.0
	11	6	5	8128.2870	1		8152.9438	2	0.0	21	3	18	8169.1961	2	0.4	8202.5291	1
	11	7	4	8168.0643	1					21	5	16	8217.6239	3	1.2
	12	1	12	8027.2777	2	0.0	8055.1341	1		21	6	15	8251.3031	1
	12	2	11	8039.4034	2	0.0	8066.1303	2	0.2	22	2	21				8202.6317	2	1.3
	12	3	10	8054.4907	2	0.4	8081.6279	2	0.0	22	3	20	8185.1884	2	0.2	8219.3199	2	0.2
	12	4	9	8075.9933	3	0.2	8102.2870	2	0.7	22	5	18	8233.9755	1
	12	5	8	8103.5671	3	0.9	8129.3868	3	0.2	23	0	23				8204.2476	2	0.5
	12	6	7	8137.2301	3	0.6	8162.3699	1		23	3	20				8238.2803	1
	12	7	6	8177.0147	2	0.9				24	3	22				8256.2835	1
	13	0	13	8035.5106	2	0.3	8063.5688	2	0.3	25	3	22				8277.2962	2	0.7
	13	1	12	8041.6376	2	0.0	8069.3585	2	0.4

Table II .

 II Spectroscopic parameters and fit statistics for the ν1+6ν2+3ν3 band of 16 O3 band centred at 7968.8 cm -1 .

						(i) Spectroscopic parameters (cm -1 )		(iii) Statistics for line positions
	Upper states	(1,6,3) ≡ (B1,89)	(A1,118) dark state	J max	22
	E VV			7968.7826 (18)		7949.761 (34)	Ka max	7
	A-(B+C)/2	3.07698 (15)		3.1646 (33)	Number of transitions	243
	(B+C)/2		0.371387 (18)		0.385644 (95)	Number of levels	130
	(B-C)/2		0.030444 (45)		0.0255 [f]	rms (cm -1 ) a	0.078
	ΔK			10 3	0.3009 (30)					(iv) Statistics for line intensities
	ΔJK		10 4	-0.2296 (39)					J max	22
	ΔJ			10 5	-0.1523 (71)					Ka max	7
	δJ			10 5	0.6036 (52)					Number of transitions	182
	δK			10 3	-0.2033 (91)					rms (%) a	12.0
	Coriolis coupling between (A1,118) and (1,6,3) states 011 C 0.01725 (16)		Sv = 4.18×10 -26 cm/molecule at 296 K b
					(ii) Dipole transition moment parameters (Debye)
	d	( 1	A	)	10 5	0.60284 (62)	d	() 4 A	10 7	-0.1189 (16)
	d	() 2 A	10 8	-0.15684 (81)	d	() 6 A	10 7	0.3903 (50)
	d	() 3 A	10 8	-0.3974 (83)

Table III .

 III . Spectroscopic parameters and fit statistics for the 6ν1+ν2+ν3 band of 16 O3centred at 7992.6 cm -1 .

					(i) Spectroscopic parameters (cm -1 )	(iii) Statistics for line positions
	Upper states	(A1,119) state	(611)	J max	25
	E VV			7962.6235 (56)	7992.83075 (35)	Ka max	6
	A-(B+C)/2	3.6674 [f]	3.020654 (42)	Number of transitions	189
	(B+C)/2		0.370599 (77)	0.3929895 (31)	Number of levels	110
	(B-C)/2		0.0263 [f]	0.0242569 (24)	rms ( cm -1 )	0.016
	ΔK			10 3		0.4003 (12)	(iv) Statistics for line intensities
	ΔJK		10 5		-0.327 (15)	J max	18
	ΔJ			10 6		0.8277 (50)	Ka max	6
	Coriolis coupling term between (611) and (A1,119) (cm -1 ): Number of transitions	67
	011 C		-0.019545 (24)	rms (%)	15.5
					(ii) Dipole transition moment (Debye)	Sv = 1.36×10 -26 cm/molecule at 296 K a
	d	( 1	A	)	10 5	0.31870 (26)
	Notes
	a Sum of intensities in the combined list (306 lines).
	[f] -fixed to the values predicted from the PES of Ref. [26]. All higher order centrifugal distortion parameters
	[77] quoted in [78] were held fixed to their ground state values. Grey background corresponds to the (=A1,
	N= 119) dark state.

Acknowledgements

The supports from CNRS (France) in the frame of the International Research Project SAMIA with IAO-Tomsk and from the Russian Science Foundation (project RNF-19-12-00171) are acknowledged. We are grateful to S. Tashkun (IAO Tomsk, Russia) for collaboration in software development.

Detection and assignment of ozone bands near 95% of the dissociation threshold

Semen Vasilchenko, 1,3 Alain Barbe, 2 Evgeniya Starikova, 1,3 Samir Kassi, 4 Didier Mondelain, 4 Alain Campargue, 4,* and Vladimir Tyuterev 3,2 The derived experimental band centres and AV, BV, CV rotational constants provide valuable information for comparison with ab initio calculations. Predicted values of AV, BV, CV were critical for the rovibrational assignments, as they essentially determine the distance between the band centres and the band heads. The overall agreement (Table IV) is almost as good as for bands at lower energy [42,52,63,64] confirming the validity of the ab initio PES of Ref. [26] in this very high energy range. It is instructive to examine in more details the comparison for the band centres EV with ab initio predictions using two types of recent variational calculations. It is well-known that the equilibrium geometry of ozone molecule corresponds to (r (e) 13 = 4.1a0) > (r (e) 12 = r (e) 23 = 2.4 a0), where low case indices stand for O(1) and O(3) edge oxygen atoms and O(2) for the central oxygen atom making ozone an asymmetric top molecule of C2V point group (a0 is the Bohr radius). The first variational method [26] was constrained to bound levels calculations within one potential well of the "open-state" configuration belonging to C2V point group, which corresponds to the geometrical sector (r12 <r13> r23). The other variational method [30,31] is based on a full account of the permutation symmetry among three identical oxygen nuclei, corresponding to D3h(M) group using symmetry adapted hyperspherical coordinates [82][83][84]. The used PES was the same in both calculations with the same shape in the transition state range and towards the dissociation limit, just symmetrised in three sectors of nuclear geometries (r12<r13>r23; r13<r12>r23; and r12<r23>r13). This gives rise to three identical potential wells separated by barriers. For all bound states of ozone experimentally measured up to now [42,50,[54][55][56][57][58][59][60][61][62][63] both theoretical approaches produced identical energy values (differences less than 0.01 cm -1 ) [26,30]. The first notable difference of 0.57 cm -1 is predicted for the (B1,89) vibration level assigned to (ʋ1,ʋ2,ʋ3) = (1,6,3), observed in this work. The discrepancies between the 1-well and 3-wells calculations, increasing towards D0, can be explained by interactions among the three potential wells, which had not been experimentally evidenced yet. Though at this stage of the study it is too early to claim for an experimental proof of such coupling effects, the comparison (Table IV) with our experimental value for the level (1,6,3) gives a hint that the 3-wells predictions go to the right direction slightly diminishing the ab initio error by more than 20%. A particular sensitivity of the (1,6,3) state to this interaction is supported by vibrational dynamics considerations: a simultaneous excitation of the high bending 62 and asymmetric stretching 33 modes points in the direction towards another potential well making the molecule more floppy. Such effect is not expected in the (6,1,1) state where mostly quite rigid symmetric stretch vibrations 61 are activated (The 1well and 3-wells ab initio values are identicalsee Table IV).