S N Mikhailenko

S Kassi

D Mondelain

A Campargue
email: alain.campargue@ujf-grenoble.fr

Water vapor absorption between 5690 and 8340 cm -1 : Accurate empirical line centers and validation tests of calculated line intensities

Keywords: water vapor, H2O, absorption spectroscopy, Cavity Ring Down Spectroscopy, HITRAN, GEISA, spectroscopic database

Water vapor absorption between 5690 and 8340 cm -1 : Accurate empirical line centers and validation tests of calculated line intensities

Introduction

In the two last decades, considerable progress has been achieved in the calculations of rovibrational spectra of small polyatomic molecules by ab initio and variational methods. Due to its importance for atmospheric applications, many works have been devoted to a better characterization of the water absorption spectrum (see for instance Refs. [START_REF] Partridge | The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data[END_REF][START_REF] Schwenke | Convergence testing of the analytic representation of an ab initio dipole moment function for water: Improved fitting yields improved intensities[END_REF][START_REF] Bubukina | Optimized semiempirical potential energy surface for H 2 16 O up to 26000 cm -1[END_REF][START_REF] Conway | A highly accurate ab initio dipole moment surface for the ground electronic state of water vapour for spectra extending into the ultraviolet[END_REF][START_REF] Mizus | High accuracy water potential energy surface for the calculation of infrared spectra[END_REF]). Completeness, reasonable line position accuracy and good line intensity accuracy give strong advantages to the variational line lists of small polyatomic molecules. The measurement of hundreds thousands line intensities with 1% accuracy is out of reach experimentally. In particular, the measurement of line intensities of water minor isotopologues is very challenging while theoretical intensity values have in general similar accuracy for the main and minor isotopologues. Nevertheless for line positions, theory cannot compete with experiment (except for H 2 and its isotopologues [START_REF] Campargue | The absorption spectrum of H 2 : CRDS measurements of the (2-0) band, review of the literature data and accurate ab initio line list up to 35 000 cm -1[END_REF]). As a result, the general strategy for the best line list for water (and CO 2 ) is to use variational line lists as basis and adjust line positions according to experimental values or to position values calculated from empirically determined energy levels. This method is that adopted for a large fraction of the water and carbon dioxide list in the last edition of the HITRAN [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] and GEISA [START_REF] Jacquinet-Husson | The 2015 edition of the GEISA spectroscopic database[END_REF] databases. Some years ago, under the project "A database of water transitions from experiment and theory", an IUPAC task group (IUPAC-TG) reported an exhaustive review and evaluation of rovibrational line positions, energy levels and assignments for all the main isotopologues of water. By using the procedure and code MARVEL (Measured Active Rotational-Vibrational Energy Levels) [START_REF] Furtenbacher | MARVEL: measured active rotational-vibrational energy levels[END_REF][START_REF] Furtenbacher | MARVEL: measured active rotational-vibrational energy levels. II. Algorithmic improvements[END_REF], all the high quality absorption or emission line positions available in the literature at that time were used to determine and validate the energy levels [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H 2 17 O and H 2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H 2 16 O[END_REF]. This cooperative effort led to recommended set of energy level values with their self-consistent uncertainties. Since then, some deficiencies were evidenced in the quality of the determined levels and error bars. In particular, the inclusion in the MARVEL procedure of a considerable number of transition frequencies reported with underestimated error bars from poorly resolved emission spectra degraded the quality of a fraction of the IUPAC-TG empirical levels. In addition, a few erroneous assignments in the original sources used by the IUPAC-TG could not be detected by the MARVEL procedure and affected the recommended levels.

Water vapor spectrum was the first high sensitivity spectrum that we recorded in 2004 with a newly built high sensitivity Cavity Ring Down Spectrometer. The use of a series of Distributed Feedback (DFB) laser diodes, each of them with 30 cm -1 tuning range, allowed a full coverage of the 1.6 µm transparency window (6132-6748 cm -1 ) [START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF]. Since then, the spectral coverage was extended over the wide 5690-8340 cm -1 range by using a collection of about one hundred DFB diodes [START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 μm transparency window (7408-7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Mikhailenko | New transitions and energy levels of water vapor by high sensitivity CRDS near 1.73 and 1.54 µm[END_REF] combined with an External Cavity Laser Diode (ECDL) in the 7920-8340 cm -1 region [START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 m atmospheric window (7911 -8337 cm -1 )[END_REF]. CRDS spectra of water vapor in natural isotopic abundance or enriched in D [START_REF] Liu | CW-Cavity Ring Down Spectroscopy of deuterated water in the 1.58 m atmospheric transparency window[END_REF], 18 O [START_REF] Liu | High sensitivity CW-CDRS of 18 O enriched water near 1.6 m[END_REF] or 17 O [START_REF] Mikhailenko | Cavity ring down spectroscopy of 17 O enriched water vapor near 1.73 µm[END_REF][START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H 2 17 O and HD 17 O newly determined[END_REF][START_REF] Mondelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF] were recorded with increasing sensitivity and accuracy, over the last fifteen years. These spectra revealed a considerable number of new observations. Those available at the date of the IUPAC-TG project were incorporated among the extensive sources of line positions used by the IUPAC-TG.

On the basis of these measurements [START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 μm transparency window (7408-7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 m atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Liu | CW-Cavity Ring Down Spectroscopy of deuterated water in the 1.58 m atmospheric transparency window[END_REF][START_REF] Liu | High sensitivity CW-CDRS of 18 O enriched water near 1.6 m[END_REF][START_REF] Mikhailenko | Cavity ring down spectroscopy of 17 O enriched water vapor near 1.73 µm[END_REF] and absorption data available in the literature mostly for the strongest lines [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF][START_REF] Toth | Line positions and strengths of HDO between 6000 and 7700 cm -1[END_REF][START_REF] Toth | Measurements of HDO between 4719 and 5843 cm -1[END_REF][START_REF] Naumenko | High resolution Fourier transform spectrum of HDO in the 7500-8200 cm -1 region: revisited[END_REF][START_REF] Tolchenov | Water line parameters for weak lines in the range 7400-9600 cm -1[END_REF][START_REF] Jenouvrier | Fourier transform measurements of water vapor line parameters in the 4200 -6600 cm 1 region[END_REF][START_REF] Mikhailenko | Critical evaluation of rotation-vibration transitions and an experimental dataset of energy levels of HD 18 O[END_REF][START_REF] Mikhailenko | Line positions and energy levels of the 18-O substitutions from the HDO/D 2 O spectra between 5600 and 8800 cm -1[END_REF][START_REF] Mikhailenko | Absorption spectrum of deuterated water vapor enriched by 18 O between 6000 and 9200 cm -1[END_REF][START_REF] Lisak | Spectroscopic line parameters of water vapor for rotationvibration transitions near 7180 cm -1[END_REF][START_REF] Sironneau | Line shapes, positions and intensities of water transitions near 1.28 µm[END_REF], in 2016, we released an empirical line list for the 5850-8340 cm -1 range [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]. This list corrected a number of deficiencies of the HITRAN2012 line list [START_REF] Rothman | The HITRAN2012 molecular spectroscopic database[END_REF], in particular the absence of many HDO lines of importance in the 1.6 µm window. Compared to the IUPAC-TG energy levels [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H 2 17 O and H 2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H 2 16 O[END_REF], new CRDS observations allowed extending the set of energy levels and correcting a number of inaccuracies. As a result, the GEISA database [START_REF] Jacquinet-Husson | The 2015 edition of the GEISA spectroscopic database[END_REF] reproduces our 2016 list in the considered region and the HITRAN2016 database used our list as main source of line positions of the main water isotopologue and reproduces part of the CRDS intensities. Let us underline the importance of the CRDS spectra at disposal for direct validation tests of the released water vapor lists. The available low pressure spectra of pure water vapor provide stringent tests to check the consistency of the empirical energy levels. This concerns in particular the large number of weak lines unobserved in atmospheric spectra or by Fourier Transform spectroscopy (FTS) associated with long absorption path (the weakest lines measured by CRDS have an intensity below 1×10 -29 cm/ molecule).

In the present updated list, new experimental results obtained during the last five years are considered to further improve the accuracy of the line positions, extend the 2016 list down to 5690 cm -1 [START_REF] Mikhailenko | New transitions and energy levels of water vapor by high sensitivity CRDS near 1.73 and 1.54 µm[END_REF][START_REF] Mikhailenko | Cavity ring down spectroscopy of 17 O enriched water vapor near 1.73 µm[END_REF] and lower the intensity cut-off from 1×10 -29 to 5×10 -30 cm/molecule at 296 K. Significant new information was retrieved from recordings performed with a sample highly enriched (~55 %) in 17 O:

(i) more than 1000 energy levels of H 2

17

O and HD 17 O were determined in the 1.6 µm transparency window (5850 and 6671 cm -1 ) [START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H 2 17 O and HD 17 O newly determined[END_REF],

(ii) between 6667 and 7921 cm -1 , the spectra were recorded with a CRD spectrometer newly coupled to a self-referenced frequency comb (SRFC) providing accurate frequency value for each ring down event. The comb assisted CRDS method (CA-CRDS) allowed improving the accuracy of the line centers determination which greatly improved the transitions of all water isotopologues contributing to the spectrum [START_REF] Mondelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF]. For instance, more than 5000 lines of the main isotopologue were used to decrease the uncertainties of the previously known H 2 16 O energy levels. Test comparisons of energy level values determined from different transitions sharing the same upper level agree within a few MHz (~10 -4 cm -1 ) [START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF], more than one order of magnitude better than the average accuracy claimed for the positions retrieved from standard CRDS recordings (~10 -3 cm -1 ). In addition, hundreds of new energy levels of H 2

17

O and HD 17 O were determined from these recordings [START_REF] Mondelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF].

(iii) Finally, the new set of energy levels benefited from additional recent sources [START_REF] Kassi | Lamb dip CRDS of highly saturated transitions of water near 1.4 m[END_REF][START_REF] Régalia | Line parameters of water vapour enriched by 18 O from 6525 to 8011 cm -1[END_REF][START_REF] Serdyukov | FTS absorption spectrum of 17 O enriched water vapour between 7900 and 9500 cm -1[END_REF][START_REF] Tan | CRDS absorption spectrum of 17 O enriched water vapor in the 12,277 -12,894 cm -1 range[END_REF] including very accurate Lamb dip measurements [START_REF] Kassi | Lamb dip CRDS of highly saturated transitions of water near 1.4 m[END_REF] and some recent analysis of FTS spectra of 18 O enriched water [START_REF] Régalia | Line parameters of water vapour enriched by 18 O from 6525 to 8011 cm -1[END_REF][START_REF] Serdyukov | FTS absorption spectrum of 17 O enriched water vapour between 7900 and 9500 cm -1[END_REF]. O [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF]. Several direct comparisons with the CRDS spectra at disposal will illustrate the advantages of our list. As concerned line intensities, a number of large deviations between measurements, HITRAN2016 and variational intensities will be discussed.

Line list construction

All transitions stronger than 5×10 -30 cm/molecule at 296 K of the variational line lists computed by S. Tashkun (IAO SB RAS, Tomsk, Russia) [45] on the basis of the results of Schwenke and Partridge (SP) [START_REF] Partridge | The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data[END_REF][START_REF] Schwenke | Convergence testing of the analytic representation of an ab initio dipole moment function for water: Improved fitting yields improved intensities[END_REF] were gathered in a list for water in natural isotopic abundance. These 20 years old variational line lists are probably not the best-to-date variational lists (in particular for line positions) but they still have the unique advantage to be consistent for the six required isotopologues, to include reasonable rovibrational assignments and to be publicly available at http://spectra.iao.ru/.

Fig. 1 Overview comparison between the list constructed in this work and the HITRAN2016 line list for water vapor between 5690 and 8340 cm -1 .

The resulting SP list for natural water at 296 K between 5690 and 8340 cm -1 includes 58,000 transitions with intensity larger than 5×10 -30 O, HD 16 O, HD 18 O, and HD 17 O). Contrary to the available calculated line lists and the HITRAN list, all the transitions are provided with unique rovibrational assignment. Note that SP assignments were modified in some cases of strongly interacting rovibrational levels. These corrections were made according to calculations based on the effective Hamiltonian method. Some details about these re-labelings can be found, for example, in Refs. [START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 m atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF][START_REF] Tan | CRDS absorption spectrum of 17 O enriched water vapor in the 12,277 -12,894 cm -1 range[END_REF]. As mentioned above, the variational line positions are replaced by corresponding values calculated from empirical rotationvibration energy levels. An overview of the resulting list is compared to the HITRAN list in Fig. 1.

Note that our intensity cut-off is twice lower than the HITRAN intensity cut-off (1×10 -29 cm/molecule) but HITRAN list includes D 2 16 O lines with intensities down to 1×10 -32 cm/molecule.

The experimental sources used to construct our set of upper empirical energies are absorption spectra summarized in Table 1. High sensitivity CRDS measurements [14-26, 36, 37, 40, 43] were complemented by the results of Fourier transform [27-35, 41, 42] and ICLAS [START_REF] Naumenko | High sensitivity absorption spectroscopy of HDO by ICLAS-VeCSEL between 9100 and 9640 cm -1[END_REF] measurements, in particular for the deuterated species. Note that more than half of the H 2

16

O transitions rely on the high precision line positions obtained by CA-CRDS [START_REF] Mondelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF][START_REF] Lisak | Spectroscopic line parameters of water vapor for rotationvibration transitions near 7180 cm -1[END_REF][START_REF] Sironneau | Line shapes, positions and intensities of water transitions near 1.28 µm[END_REF][START_REF] Kassi | Lamb dip CRDS of highly saturated transitions of water near 1.4 m[END_REF]. The considered experimental sources [14-37, 40-43, 46] did not provide upper energy empirical values for about 6000 weak transitions (~10 %). When available, we adopted the empirical energy levels recommended by the IUPAC-TG [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H 2 17 O and H 2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H 2 16 O[END_REF]. The energy levels adopted from IUPAC-TG concern mostly very weak hot band transitions with an upper energy level determined from experimental studies at higher energy, not included among our sources of line positions (the most excited upper level involved in the list is the (121) 15 2 14 level with an energy of about 12,902 cm -1 ).

About 1750 transitions are left without empirical determination of their upper energy levels. For about 530 transitions reaching an upper level not yet observed experimentally, the frequencies could be estimated by J, K extrapolation of the deviations between empirical and SP variational positions of observed transitions of the considered band. This procedure which was not implemented in the 2016 list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] is believed to improve significantly SP variational positions. About 1200 (very weak) transitions (0.2%) were left with their SP variational positions.

As concerned the lower energy levels, the IUPAC-TG values were adopted for H 2

16

O [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H 2 16 O[END_REF] and HD 16 O [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF]. For H 2 17 O and H 2 18 O isotopologues, we use rotational energies of the (000) and (010)

states derived from hot emission FTS spectra of water vapor enriched in 17 O and 18 O [START_REF] Gch | Rotational levels of five lowest states of H 2 18 O and H 2 17 O from hot emission spectra between 320 and 2500 cm -1[END_REF]. The lower energies for the HD 18 O and HD 17 O species were calculated in Refs. [START_REF] Liu | 000) and (010) energy levels of the HD 18 O and D 2 18 O molecules from analysis of their  2 bands[END_REF][START_REF] Gch | Hot water emission spectra: Rotational energy levels of the (000) and (010) states of HD 17 O[END_REF] using an effective

Hamiltonian approach [START_REF] Vlg | Calculation of high rotation energies of the water molecule using the generating function model[END_REF].

Table 1

Number of transition frequencies between 5690 and 8340 cm -1 calculated from different upper energy sources.

CA-CRDS [START_REF] Mondelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF][START_REF] Lisak | Spectroscopic line parameters of water vapor for rotationvibration transitions near 7180 cm -1[END_REF][START_REF] Sironneau | Line shapes, positions and intensities of water transitions near 1.28 µm[END_REF] Lamb dip [START_REF] Kassi | Lamb dip CRDS of highly saturated transitions of water near 1.4 m[END_REF] CRDS [START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 μm transparency window (7408-7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Mikhailenko | New transitions and energy levels of water vapor by high sensitivity CRDS near 1.73 and 1.54 µm[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 m atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Liu | CW-Cavity Ring Down Spectroscopy of deuterated water in the 1.58 m atmospheric transparency window[END_REF][START_REF] Liu | High sensitivity CW-CDRS of 18 O enriched water near 1.6 m[END_REF][START_REF] Mikhailenko | Cavity ring down spectroscopy of 17 O enriched water vapor near 1.73 µm[END_REF][START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H 2 17 O and HD 17 O newly determined[END_REF][START_REF] Tan | CRDS absorption spectrum of 17 O enriched water vapor in the 12,277 -12,894 cm -1 range[END_REF] FTS &ICLAS [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF][START_REF] Toth | Line positions and strengths of HDO between 6000 and 7700 cm -1[END_REF][START_REF] Toth | Measurements of HDO between 4719 and 5843 cm -1[END_REF][START_REF] Naumenko | High resolution Fourier transform spectrum of HDO in the 7500-8200 cm -1 region: revisited[END_REF][START_REF] Tolchenov | Water line parameters for weak lines in the range 7400-9600 cm -1[END_REF][START_REF] Jenouvrier | Fourier transform measurements of water vapor line parameters in the 4200 -6600 cm 1 region[END_REF][START_REF] Mikhailenko | Critical evaluation of rotation-vibration transitions and an experimental dataset of energy levels of HD 18 O[END_REF][START_REF] Mikhailenko | Line positions and energy levels of the 18-O substitutions from the HDO/D 2 O spectra between 5600 and 8800 cm -1[END_REF][START_REF] Mikhailenko | Absorption spectrum of deuterated water vapor enriched by 18 O between 6000 and 9200 cm -1[END_REF][START_REF] Régalia | Line parameters of water vapour enriched by 18 O from 6525 to 8011 cm -1[END_REF][START_REF] Serdyukov | FTS absorption spectrum of 17 O enriched water vapour between 7900 and 9500 cm -1[END_REF] IUPAC [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H 2 17 O and H 2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H 2 16 O[END_REF] Estimated O, HD 16 O and HD 17 O with SP intensities below our 5×10 -30 cm/molecule intensity cut-off are present in HITRAN2016 [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] (1×10 -29 cm/molecule intensity cut-off) or in the list of Conway et al. [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF] with an intensity larger than 5×10 -30 cm/molecule. For completeness, these transitions which are believed to have underestimated SP intensities were added to the list with empirical line positions.

Table 2

Comparison of the various determinations of upper energy levels determined from the line centers of transitions measured by CA-CRDS in refs. [START_REF] Mondelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF]. In the last column, the average value is given with the standard deviation in the unit of the last quoted digit.

ISO Line position (cm -1 )

Upper level (V1V2V3) J Ka Kc

Lower level J Ka Kc

Upper energy (cm -1 )

Average value (cm -1 ) H2 16 In terms of accuracy only average estimates can be provided for the considered large amount of line positions. Experimentally, the line center accuracy depends on (i) the accuracy of the calibration of the frequency axis and (ii) the precision of the line center determination depending on the signal-tonoise ratio of the spectra, the blending with nearby lines provided etc. Note that we consider here mainly absorption spectra of pure water vapor at room temperature, thus with a pressure value on the order of 20 Torr at most. Neither in the present study nor in the MARVEL treatment followed by the IUPAC-TG, the position values were corrected from the self-pressure shifts. Self-pressure shift coefficients vary typically in the ±10 -2 cm -1 atm -1 range which leads to shifts on the order of 10 -4 cm -1 (~ 3 MHz) which is small in general but might be significant for the line centers determined by CA-CRDS line centers. Additional biases related to the choice of the line shape used to fit the measured line profile are also expected to affect the line center determination but these effects are smaller. Most of the line centers were obtained using the standard Voigt profile. Significant residuals are generally obtained showing the typical W signature due to the Dicke narrowing effect [START_REF] Vasilchenko | Accurate absorption spectroscopy of water vapor near 1.64 mm in support of the MEthane Remote LIdar missioN (MERLIN)[END_REF]. Nevertheless, the obtained residuals are generally symmetric indicating that the line center determination is mostly unaffected.

We present in Table 2 some examples of determinations of the upper energy levels from line centers of different transitions measured by CA-CRDS. Similar accuracy tests included in Ref. [START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF] relative to the 6900-7400 cm -1 region, showed a consistency at the 10 -4 cm -1 level between the various determinations. Here, together with line positions of Ref. [START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF], we consider the transition frequencies reported in the 7400-7800 cm -1 region [START_REF] Mondelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF] which enlarges importantly the possibilities of redundant determinations of a given upper level. A similar agreement on the order of 10 -4 cm -1 is achieved, illustrating the consistency of the frequencies measured in Ref. [START_REF] Mondelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF] and Ref. [START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF]. As a result, the position accuracy for transitions frequencies derived from well isolated lines measured by CA-CRDS [START_REF] Mondelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF] is estimated to be 2×10 -4 cm -1 . For standard CRDS and FTS, an uncertainty of 10 -3 cm -1 as given in Ref. [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] is a reasonable average value. For ICLAS line positions [START_REF] Naumenko | High sensitivity absorption spectroscopy of HDO by ICLAS-VeCSEL between 9100 and 9640 cm -1[END_REF] and those estimated using an J, K empirical law correction of their SP positions, the uncertainty is on the order of 10 -2 cm -1 .

Finally, for the small fraction of purely SP variational positions [START_REF] Partridge | The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data[END_REF] included in our list, various comparisons with experimental values have shown that in our region, SP positions may deviate by a few tenth of wavenumber (see below). The most accurate line positions are those related to the ten Lamb dip measurements reported in Ref. [START_REF] Kassi | Lamb dip CRDS of highly saturated transitions of water near 1.4 m[END_REF] which allowed computing 84 line positions with an accuracy better than 10 -6 cm -1 (30 kHz). In the line list provided as Supplementary Material, the source of the upper energy level is provided for each transition. The number of decimal digits provided for each position has been adapted depending on the estimated uncertainties (for instance, five and six digits for the values relying on FC referenced CRDS and Lamb dips, respectively).

Fig. 2 shows a sample of the line list provided as Supplementary Material. Together with our recommended position and corresponding source, the list includes our rovibrational assignment, SP intensity, the lower state energy value and the corresponding HITRAN [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] and Conway et al. [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF] values for the positions and intensities. When a different rovibrational assignment was proposed by

Conway et al or in HITRAN2016 list, it is included for comparison. This global line list, gathering most of the information at disposal, was used for the systematic comparisons presented below.

In our region, the HITRAN list includes 48692 transitions for the six major water isotopologues.

Although the HITRAN intensity cut-off is 1×10 -29 cm/molecule, 40 transitions have an intensity below this value, down to 1.1×10 -37 cm/molecule for the 5 2 4 4 0 -4 1 3 transition of HD 17 O. In addition, many transitions of the D 2 16 O isotopologue with intensity below the cut-off are included in the HITRAN list (see Fig. 1). For the main isotopologue (about 21500 transitions), position and intensity values were taken from six and nine sources, respectively. Most of the line intensities (about 74%) have variational origin [START_REF] Barber | A high-accuracy computed line list[END_REF] while more than 80% of the positions are empirical values transferred from our 2016 list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]. The remaining H 2

16

O positions are empirical from the IUPAC-TG (9.7%) or measured by FTS values from Toth's database (6.4%) [START_REF] Toth | Line list of water vapor parameters from 500 to 8000 cm -1[END_REF], with a very small fraction of variational values and a few values with uncertain origin.

These H 2 16 O and H 2

18

O lists published by Conway et al. [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF] have intensities calculated using a semi-empirical potential energy surface [START_REF] Conway | A highly accurate ab initio dipole moment surface for the ground electronic state of water vapour for spectra extending into the ultraviolet[END_REF]. They were found to show a better agreement with experiment than the preceding 'POKAZATEL' line list [START_REF] Polyansky | ExoMol molecular line lists XXX: a complete high-accuracy line list for water[END_REF]. In the 5690-8340 cm -1 interval, Conway list includes 32553 H 2

16

O transitions above an intensity cut-off fixed to 1×10 -30 cm/molecule at 296 K.

Note that the maximum J value of the lower and upper levels is 20 while our list includes transitions with J values up to 22 and 23, respectively (the  1 + 3 21 1 21 -20 1 20 line at 7485.3914 cm -1 has for instance an intensity of about 5×10 -28 cm/molecule significantly above the intensity cut-off).

In our region, the H 2 18 O list of Conway includes 9191 transitions with intensity (including the abundance factor) larger than 5×10 -30 cm/molecule (to be compared to 8977 in our list). 263 of them are duplicate (same, position, same intensity, same assignment) and should be removed. In the whole Conway H 2 18 O line list (100% abundance for the line intensities) extending up to 20000 cm -1 , we could identify 5394 such duplicates. O transitions); Conway assignment -rovibrational assignment given only when it differs from ours; "HITRAN2016 Pos & Int" and "HITRAN2016 assignment" -same for the HITRAN database [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF].

The systematic comparison to HITRAN and Conway lists is not straightforward because these two references do not provide complete rovibrational assignments for part of the transitions. For instance, 1442 H 2

16

O transitions of the Conway list are provided with incomplete rovibrational assignment of the upper level. In those circumstances, the transitions in common with our list were identified by using as criteria identical lower state energy, identical upper J value and reasonable position and intensity matching (typically 0.5 cm -1 and a factor of 2, respectively). We have included in the Supplementary Material the position and intensity columns for the HITRAN and Conway transitions in coincidence (see Fig. 2). When a different or incomplete rovibrational assignment was attached to the considered transition, it is reproduced in the comparison list. HITRAN erroneous assignments include more than 160 ortho-para transitions between 6048 and 8233 cm -1 which are strictly forbidden by symmetry (all of them were erroneously referenced to our 2016 list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] in the HITRAN database).

As mentioned above less than 300 very weak lines (intensity smaller than 1.6×10 -27 cm/molecule) present in the list of Conway et al. or HITRAN with intensity larger than our 5×10 -30 cm/molecule intensity cut-off but with SP intensities below 5×10 -30 cm/molecule, were added to our list (these transitions with SP intensity smaller than 5×10 -30 cm/molecule are visible on the upper panel of Fig. 1).

Line position comparison

Fig. 5 presents an overview of the differences between position values and those provided in our 2016 list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF], in HITRAN2016 [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF], by Conway et al. [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF], and the SP variational values [45]

Fig. 5

Overview of the deviations between our position values and the values provided in different references (from to bottom): variational positions from Schwenke and Partridge (black) [START_REF] Partridge | The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data[END_REF][START_REF] Schwenke | Convergence testing of the analytic representation of an ab initio dipole moment function for water: Improved fitting yields improved intensities[END_REF]45], our 2016 list (blue) [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF], HITRAN2016 (red) [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] and Conway et al. (green) [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF]. Note the different scale used for the SP deviations. Fig. 5 illustrates the good agreement of the present and HITRAN positions of the main isotopologue. This simply reflects the fact that our 2016 list was adopted as HITRAN source for about 80% of the H 2 16 O positions in the region. For the H 2

18

O and H 2

17

O positions, a significant number of deviations are noted mostly due to variational position values used in HITRAN. Among the six sources used for HITRAN2016 positions in the region, most of the important deviations compared to the present position values are related to a variational value of the upper level, an erroneous determination of the IUPAC-TG energy level or some Toth's values. For instance; the maximum deviation ( = 4.898 cm -1 ) concerns the  1 +2 2 12 1 12 -12 2 11 transition observed at 6511.519 cm -1 [START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF] but reported by Toth [START_REF] Toth | Line list of water vapor parameters from 500 to 8000 cm -1[END_REF] at 6516.418 cm -1 . Note that this last line corresponds to the hot transition  1 +3 2 - 2 7 1 7 -8 0 8 . Transition frequencies reaching the (040) 14 8 6 upper level shows inconsistencies: while the HITRAN line positions of the 4 2 14 8 6 -13 5 9 (7781.700 cm -1 ) and 14 8 6 -13 77 (7441.155 cm -1 ) and 4 2 - 2 14 8 6 -13 1 13 (6977.101 cm -1 ) transitions coincide with our values, the 4 2 14 8 6 -15 1 15 (8010.110 cm -1 ) transitions deviates by 0.182 cm -1 . The line positions of the first three line centers were taken from our 2016 database [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] while the inaccurate position value is a variational value [START_REF] Liu | 000) and (010) energy levels of the HD 18 O and D 2 18 O molecules from analysis of their  2 bands[END_REF] provided without complete vibration-rotation assignment in HITRAN.

Unexpectedly, the H 2

16

O and H 2

18

O positions very recently reported by Conway et al. [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF] show -14 5 9 and 5 2 11 3 9 -12 0 12 transitions at 5736.5361 and 7986.2015 cm -1 , respectively. Their positions were computed using inaccurate empirical IUPAC-TG energy of the (110) 15 6 10 and (050) 11 3 9 upper levels, respectively [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H 2 16 O[END_REF]. Correct values of the considered frequencies were included in our 2016 list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF].

larger

Line intensity comparison

In Ref. [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF], we provided a line list in the 5850 -8340 cm -1 with empirical line positions and experimental values of the line intensities when available. FTS [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF][START_REF] Toth | Line list of water vapor parameters from 500 to 8000 cm -1[END_REF] and CRDS [14-18, 20, 37] intensity values were used for the strong lines and weaker lines, respectively (see Fig. 5 of Ref. [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]).

As in the present work, the list was made complete by including a number of weak transitions not yet measured, with empirical positions and SP variational intensities. Note that part of the same sets of FTS and CRDS intensity values are incorporated in the HITRAN2016 list. The discussion about the relative merit of experimental and variational line intensities was included in Ref. [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] and is not repeated here. Overall a set of more than 20000 line intensities were measured by CRDS in Refs. [START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 μm transparency window (7408-7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 m atmospheric window (7911 -8337 cm -1 )[END_REF] but no individual error bars were attached to this large set of measurements. In the case of wellisolated H 2

16

O lines of intermediate intensity, a 2-5% relative accuracy was uniformly estimated [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] but the lines in questions were not identified. In the present work, we examined in details the spectra and selected the isolated H 2 16 O lines for which the intensity determination is believed to be most reliable. Only lines with intensity larger than 1×10 -27 cm/molecule were considered. The following comparison is thus limited to these selected intensity values, about 5000 in total, which are listed in the Supplementary Material (see Fig. 2). Note that in the 7408 -7920 cm -1 strong absorption region [START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 μm transparency window (7408-7920 cm -1 )[END_REF], low pressure values (≈0.1 Torr) were used for the CRDS recordings and a systematic error due to the pressure gauge calibration was evidenced [START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 μm transparency window (7408-7920 cm -1 )[END_REF][START_REF] Sironneau | Line shapes, positions and intensities of water transitions near 1.28 µm[END_REF]. This systematic bias was corrected by applying a 1.044 multiplication factor to the intensities in the considered region (as done in the 2016 list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]). (from the BT2 [START_REF] Barber | A high-accuracy computed line list[END_REF] and Lodi et al. [START_REF] Lodi | A global, high accuracy ab initio dipole moment surface for the electronic ground state of the water molecule[END_REF] line lists) but part of the CRDS intensity values [START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 μm transparency window (7408-7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 m atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Lisak | Spectroscopic line parameters of water vapor for rotationvibration transitions near 7180 cm -1[END_REF][START_REF] Sironneau | Line shapes, positions and intensities of water transitions near 1.28 µm[END_REF] were adopted in the HITRAN list. An increasing dispersion of the ratios is observed for the lower intensities. A larger uncertainty on the experimental intensities of the weak lines is not believed to be the main reason of this observation. Indeed, the comparison between SP intensities and the semi empirical intensities by Conway et al. [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF] (right panel of Fig. 7) shows similar or even larger dispersion.

Several studies have shown that the line intensities of pure bending bands are difficult to be predicted by theory [START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF]. In Fig. 7, intensity ratios relative to the 4 [START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 m atmospheric window (7911 -8337 cm -1 )[END_REF]).

On average, SP variational values of the 4 2 band are closer to experiment than the recent semiempirical values of Conway et al. which appear to be underestimated on average. We present in Fig. 8 nine examples of comparisons between the various line lists and the CRDS spectra of Refs. [START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF] showing discrepancies of the line intensities. Six of the displayed examples are relative to the 4 2 band and three concern transitions of the  1 +2 2 band. Other clear examples were found for transitions of the 5 2 ,  1 +  and 6 2 bands.

Fig. 8

Examples of disagreement between calculated intensities and the observed spectrum of natural water vapor. Line lists of the H 2 16 O main isotopologue as provided by Schwenke and Partridge (full grey circles), by the HITRAN2016 database (full green circles), by Conway et al. [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF] (red stars) are compared to CRDS spectra. The blue hyphens correspond to the experimental CRDS intensities as reported in Refs. [START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF]. The problematic lines which belong to the 4 2 and  1 +2 2 bands are indicated.

Concluding remarks

In the recent years, a relatively high number of theoretical line lists have been computed for water vapor. Although often called "calculated" line lists, their line positions have an experimental origin and credits should be given to considerable experimental efforts performed over several decades and used to compute their accurate line positions. The direct confrontation of the available line lists produced by different approaches to high quality spectra is a laborious and necessary validation task.

Atmospheric validation provides tests in particular for the profile of air-broadened water lines but as concerned line centers, line intensities and completeness, high sensitivity recordings of pure water vapor at low pressure are necessary. In the present work, the CRDS spectra recorded in Grenoble over nearly two decades were used to test the HITRAN2016 list [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] which is the standard list used for atmospheric applications. In the transparency windows, the sensitivity of our CRDS spectrometers allows detecting lines with intensity as small as the 10 -29 cm/molecule HITRAN intensity cut-off [START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF]. This is significantly lower than the weakest lines which can be detected in atmospheric spectra. We have also considered in details the lists very recently released by Conway et al. [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF] O with intensities calculated from semi-empirical potential energy surfaces. According to the authors, their new dipole moment surface provides excellent calculated intensities and corrects some biases of their preceding POKAZATEL list [START_REF] Polyansky | ExoMol molecular line lists XXX: a complete high-accuracy line list for water[END_REF] and their lists will be used to update many transition intensities and line positions in the HITRAN2016 database [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF].

As concerned line positions, the IUPAC-TG approach consisting to collect and evaluate all the position measurements available in the literature in order to derive recommended values of the empirical energy levels by inversion of the transition frequencies using the MARVEL procedure, has proved to be efficient. Nevertheless, in absence of direct examination of the spectra, the weighting of frequency values according to their real accuracy is a major issue [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H 2 17 O and H 2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H 2 16 O[END_REF]. As said above the inclusion of a considerable number of transition frequencies reported with multiple assignments from highly congested emission spectra has degraded the quality of part of the IUPAC-TG empirical energy levels.

In the present updated version of the 2016 list of Ref. [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] covering the 5690 -8340 cm -1 range, the set of empirical energy levels used to compute the line centers has benefited from a large set of new measurements by CRDS referenced to a frequency comb. This CA-CRDS data [START_REF] Mondelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF] allowed achieving in routine an accuracy of the line center determination at the 10 -4 cm -1 level for well isolated lines. We believe that the line list provided as supplementary material gathers most of the high quality experimental information at disposal for line positions in the considered region. In contrast with the HITRAN2016 and calculated lists, each transition is provided with unique rovibrational labeling (see Fig. 2) and the ambiguities in the vibrational labeling have been resolved using effective Hamiltonian calculations.

HITRAN line positions [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] used six sources for the H 2 16 O line positions in the region (eleven sources for the first six isotopologues). Although, important improvements were incorporated in the 2016 HITRAN list, a number of issues remain to be fixed concerning erroneous rovibrational assignments (including a number of ortho-para transitions), a small number of missing lines and inaccurate line positions and line intensities. As concerned the recent list of Conway et al. [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF], it shows larger deficiencies in terms of line position accuracy. It seems that the set of empirical energy levels used for frequency calculations has to be significantly revised or updated using recent observations. In the considered region, our results clearly indicate that the line positions of the list of Conway et al. should not be used to update the HITRAN list (see Figs. O list (263 in our region) and it does not solve the intensity problem of the bending bands (e.g.  2 ,  2,  1 +3 2 ) -see Fig. 7.

The laborious evaluation of different theoretical line intensities on the basis of the CRDS recordings of Refs. [START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 μm transparency window (7408-7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Mikhailenko | New transitions and energy levels of water vapor by high sensitivity CRDS near 1.73 and 1.54 µm[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 m atmospheric window (7911 -8337 cm -1 )[END_REF], suggests that at present, none of the line lists at disposal predicts all the observations in the considered region at experimental accuracy (a few % for isolated lines). Some of the most recent line lists show deviations comparable of even worse than the twenty-year old results obtained by Schwenke and Partridge [START_REF] Partridge | The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data[END_REF][START_REF] Schwenke | Convergence testing of the analytic representation of an ab initio dipole moment function for water: Improved fitting yields improved intensities[END_REF]45]. To the best of our knowledge, no coherent set of line lists equivalent to the SP lists of the six required isotopologues is available in the literature. As demonstrated by Conway et al., their list represents important improvements compared to SP for the intensities at high energy [START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF], in particular in the visible but in the very important near-infrared region presently considered we did not find improvement concerning line intensities compared to the SP list of H 2 16 O (see Fig. 7).

The best intensity column for water vapor remains thus an open issue for the spectroscopic databases. Compared to measurements, calculations have unique advantages in particular in case of strong line overlapping, very weak lines or for the minor isotopologues and the determination of tens of thousands line intensities with 1% accuracy is out of reach experimentally. Nevertheless, for a more or less important fraction of the transitions, all the considered calculated lists show deviations larger than the experimental uncertainty. The best compromise is thus to use calculated intensities as default values and replace them by experimental values when clear deficiencies are evidenced. Taking into account the difficulties to estimate quantitatively the uncertainties on the calculated and measured (when available) intensity values, the criterion of preference between theoretical or experimental intensities remain to be defined.

Fig. 2

 2 Fig. 2 Sample of the line list provided as Supplementary Material. The different columns are: Int_obs -the measured value of the intensity measured from the CRDS spectrum of natural water (the listed values are limited to well isolated H 2 16 O lines with intensity larger than10 -27 cm/molecule); Pos(SP) -variational line center from Schwenke and Partridge results; Pos_empir -empirical value of the line center; Int(S) -SP variational line intensity [1,2,45]; ISO -isotopologue; Assignment -upper and lower level rovibrational assignment; Source -source of our empirical value of the upper energy level; Conway Pos & Int -line center and line intensity reported by Conway et al.[START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF] (for H 216 O and H 2 18

Fig. 3 18 O 16 O

 31816 Fig. 3 Overview of the transitions missing in the H 2 16 O lists provided by the HITRAN2016 [7] database (upper panel) and Conway et al. [44] (lower panel). Missing transitions are highlighted in light blue and green, respectively.

Fig. 4 16 O

 416 Fig. 4 Relatively strong H 2 16 O lines missing (red arrows) in the HITRAN2016 list. The present line list (open circles) is superimposed to the CRDS spectrum of natural water [16, 20] (blue solid line).

18 O while H 2 17 O

 1817 . The comparison is limited to the three first isotopologues and the position differences are plotted versus the line intensity in order to distinguish the weak lines for which experimental intensities are less accurate. Note that the comparison applies only to the lines for which an empirical value of the upper energy level was determined by CA-CRDS, CRDS or FTS (the line positions of our list with IUPAC-TG, estimated or variational position values are excluded from the comparison). As expected SP variational positions show relatively large deviations. It is worth noting that SP average deviations are close to zero for H 2 16 O and H 2 SP positions are systematically overestimated by about 0.25 cm -1 on average. Compared to our 2016 list, a significant number of deviations are noted for the two minor isotopologues (in particular H 2 17 O). This is due to the recent extension of the set of empirical energy levels of these two species [23-26, 41-43]. Most of the large deviations are related to newly determined energy levels for which SP variational values were used in the 2016 list (see for instance the set of large positive deviations around 0.25 cm -1 observed for H 2 17 O).

  deviations than the HITRAN positions. No information is given about the experimental sources used by Conway et al. to determine their MARVEL energy levels. This lack of knowledge (and recognition) of the experimental results considered in the "MARVELization" of the measured transition frequencies hinders to trace the origin of these erroneous line positions. Our analysis in the 5690-8340 cm -1 region, does not support the proposition of Conway et al. to use their H 2 16 O and H 2 18 O lists to update the water vapor line list in the next edition of the HITRAN database [44].

Fig. 6

 6 Fig. 6Inaccurate positions of H 216 O lines in the HITRAN2016 list and in the list by Conway et al.[START_REF] Conway | Calculated line lists for H 2 16 O and H 2 18 O with extensive comparisons to theoretical and experimental sources including the HITRAN2016 database[END_REF] (full green circles and red stars, respectively). The present line list (full grey circles) is superimposed to the CRDS spectrum of natural water[START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 μm transparency window (7408-7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Mikhailenko | New transitions and energy levels of water vapor by high sensitivity CRDS near 1.73 and 1.54 µm[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 m atmospheric window (7911 -8337 cm -1 )[END_REF].

Fig. 7

 7 Fig. 7 Intensity ratios for the H 2 16 O main isotopologue. The values relative to the 4 2 and  1 +3 2 transitions are highlighted (blue and red stars, respectively). The CRDS values are limited to lines of Refs. [] with intensity larger than 10 -27 cm/molecule not affected by strong blendings with nearby lines are considered (see Text).

Fig. 7

 7 Fig. 7 presents an overview of the ratios of SP, HITRAN and Conway et al. intensities to the CRDS values of the 5000 selected H 2 16 O lines. Most of the HITRAN intensities have variational origin

5

 5 and 6). Other minor issues concerning the list of Conway et al. are that it is limited to J values smaller than 21 and thus some transitions are missing, it includes a high number duplicate transitions in the H 2 18

  The rest of the paper is organized as follows. The line list construction is detailed in the next Section. In the sections 3 and 4, we present a systematic comparison of the positions and intensities to the corresponding values included in the HITRAN2016 database for natural water and to the very recent semi-empirical lists published byConway et al. for H 2

	16 O and H 2 18

  cm/molecule for the six most abundant isotopologues

	(H 2 16 O, H 2 18 O, H 2 17

  2 and  1 +3 2 bands are highlighted. Large differences are noted between SP and Conway intensities with a large dispersion for the 4 2 band and a systematic shift of about 25 % for the  1 +3 2 band. It is interesting to note that the experimental values of the  1 +3 2 transitions are on average intermediate between the two calculations: SP intensities are underestimated by 10 % while Conway intensities are overestimated by 15 %. We also note that the dispersion of the intensity ratios is smaller when compared to SP than to Conway et al. (HITRAN intensities of the  1 +3 2 transitions were taken from our CRDS study

Acknowledgements E.K. Conway (Center for Astrophysics, Cambridge and University College London) is acknowledged for providing us the submitted version of Ref. [44] together with the corresponding H 2

16

O and H 2 18 O lists, prior publication. The support of the CNRS (France) in the frame of International Research Project SAMIA is acknowledged. SNM activity was also partly supported in the frame of the Russian Science Foundation, grant no. 18-11-00024.


Keywords: solid state photodimerization, stilbazole, cyclobutane

[2 + 2]-Photodimerization of Stilbazoles Promoted by Oxalic Acid in Suspension

Thanh Binh Nguyen,* [a] Tuan Minh Nguyen, [b] and Pascal Retailleau [a] Abstract: In this study we reported on a very simple technique to perform efficiently photodimerization of some vinylpyridines. By irradiating a stirred mixture of several stilbazoles with solid oxalic acid dihydrate dispersed in a non-polar (e.g. cyclohexane) or moderately polar (benzene, dichloromethane, dioxane) solvent, the corresponding dimeric cyclobutane adducts were obtained in high yields with excellent of regio-and stereo-selectivities. The strategy could also be applied successfully to oily, waxy or even insoluble stilbazoles. Moreover, the oxalic acid loading could be lowered to substoichiometric amounts. When further optimizations were needed, our strategy was found to be highly flexible to identify other oligocarboxylic acids as alternative additive to improve or even overturn regioselectivity. Oxalic acid and other oligocarboxylic acids were found to be capable of orienting more than fifty stilbazoles toward photodimerization under these conditions.

Photodimerization of olefins to cyclobutane is one of the most studied photochemical transformation. Theoretically, an uncontrolled reaction in solution would lead to a multitude of possible stereoisomers due to the combination of two monomers in cis or trans configuration in different manners head-head vs head-tail and syn vs anti addition. [1] Since the seminal work of Schmidt et al on solid state [2 + 2] photocycloaddition reaction about 50 years ago, [2] different strategies [3] have been developed to achieve such a reaction with reasonable level of reactivity and high stereo-and regioselectivities, using small organic molecules, [4], [START_REF]Photoactive cocrystals between some stilbazoles and fumaric or maleic acid was described to be possible in methanol[END_REF] metal organic frameworks, [6] coordination with metal cations, [7] cation-π interactions via salt formation, [8] host-guest interactions, [9] and other. [10] All of them were based on the non-covalent rigidification of the relative conformation between two proximal molecules in confined media, especially in crystalline states, to achieve the favorable geometry for the photocycloaddition. Although some important achievements have been made, these strategies are not universal and not practical. Indeed, the screening step to determine the right components for the formation of photoactive complexes with appropriate geometry for subsequent dimerization reaction is time-consuming. This important step is strongly dependent on many factors such as the nature of such components and solvents as well as physical conditions of crystallization. The situation is further complicated for the olefins or additives that exhibit low solubility. Moreover, the structural determination of the obtained complexes and particularly their control of the purity are challenging. Additionally, due to limited molecular motion of starting materials in such rigidified media, full conversion for the [2+2] photodimerization step is not always achieved. All these difficulties explained the fact that most of the reports on photocycloaddition in confined media were performed in small scales with limited number of examples.

In this context, a versatile and flexible screening strategy to determine rapidly the right additives as well as for efficiently performing the photocycloaddition in a very simple manner would be highly desirable, especially for cost-effective and large-scale production of structurally and biologically relevant cycloadducts [START_REF] Beniddir | For selected reviews on cyclobutane natural products[END_REF] with well-defined regio-and stereo-chemistry.

In our previous work, we noticed that a mixture of different solid components of similar nature dispersed in an inert solvent could exhibit some degrees of homoselection, i.e. the molecules of exactly the same nature could recognize each other and combine together under irradiation conditions to give the expected correspondent homoadduct in excellent selectivities and yields as if all the homocycloaddition reactions were performed separately. [12] Scheme 1. Schematic description of our strategy

The cocrystallization between two different components was based on certain specific affinities. Crystalline arrangement of molecules upon exposure to UV irradiation should be considered as a dynamic system with certain degrees of free movement rather than a static structure. With these precedents in mind, we reasoned that such selective and dynamic interactions could take place even if the olefin and the additive even in powder states were simply mixed together in an inert solvent (Scheme 1).

Under irradiation conditions, if the resulting cocrystals could achieved the requirement for photodimerization, i.e. were photoactive, the [2+2] photodimerization would be realized under such technically simple one-pot conditions without isolation of photoactive species. Consequently, this strategy would reduce dramatically the necessary time and effort to identify the right additives.

The combination between high dynamicity of solution/suspension state and ordered arrangement of solid state would be an excellent solution to achieve reasonable conversion with excellent regio-and stereo selectivities. Herein, we describe a proof-of-concept demonstrating the feasibility of this idea. As initial point, we set up a model reaction of dimerization of stilbazole A1 in the presence of a solid additive under 365 nm irradiation. [START_REF]The reactions were performed in a 7-mL Pyrex tube containing 0.1 mmol olefin in 2 mL dispersing solvent. The reaction tubes were magnetically stirred and exposed to 365 nm UV light generated by 20[END_REF] A range of solid di-, tri-, tetra-and mono-carboxylic acids a-l was chosen as additives for the possible interaction of their carboxylic acid groups with the nitrogen atom of stilbazole A1 via hydrogen bond or salt formation (Table 1).

An inert solvent such as cyclohexane was used as a dispersing solvent due to its chemical inertness and very weak interaction with both stilbazole A1 and carboxylic acid additive. Indeed, all the investigated additives were shown to be practically insoluble in cyclohexane. [START_REF]The insolubility of these carboxylic acid additives were readily observed by gravimetric analysis or by 1 H NMR investigation on their saturated solution in cyclohexane-d12[END_REF] To our delight, while the reaction of A1 in the absence of additive led to a mixture of the starting materials in both cis and trans forms in 2:3 ratio (entry 1, Table 1), a relatively clean reaction mixture without any significant degradation of the starting stilbazole was observed when oxalic acid dihydrate was used as an additive in stoichiometric amount (entry 2, Table 1). Most strikingly, with this additive, the truxillic acid type adduct a1 was formed exclusively and could be isolated in high yield.

Other carboxylic acids such as higher analogues (malonic and succinic acids b-c, entries 3-4, Table 1), unsaturated acids (maleic and fumaric acids d-e, entries 5-6, Table 1), benzeneoligocarboxylic acids f-k (entries 7-12, Table 1) as well as simple monocarboxylic acid such as phenylacetic acid l (entry 13) displayed either lower efficiency (leading to lower yields but the reaction mixtures remained rather clean, entries 3, 6-7, 9-10, Table 1) or unsuitability as additive due to the formation of complex mixtures of other isomeric adducts and unidentified sideproducts (entries 4-5, 8, 11-13, Table 1).

Interestingly, we noticed that a slightly higher yield could be obtained with a slight excess of oxalic acid (entry 14, Table 1), whereas further increasing oxalic acid loading (4 equiv) had a detrimental effect on the yield. Gratifyingly, since a full and clean conversion was achieved in the first case (entry 14, Table 1), adduct a1 could be obtained by simply removal of oxalic acid with an aqueous NaHCO3 solution. This simplicity is particularly useful for large-scale production of this photoadduct as a single isomer in excellent yield and purity.

Notably, our conditions afforded adduct a1 in high yields even with catalytic amounts of oxalic acids (entries 16-18, Table 1) although longer reaction times were necessary.

It should be noted that it was possible that the molar ratios between stilbazole A1 and oxalic acid did not reflect the real stoichiometry of the photoactive complex since the interaction between stilbazole A1 (partially soluble in cyclohexane) and oxalic acid (totally insoluble in cyclohexane) is not as effective as Table 1. Screening of the reaction conditions for olefin A1 Entry [a] Additive (x equiv) Solvent Yield of a1 (%) [b] 1

- CyH 0 d 2 a (1) CyH 95 3 b (1) CyH 65 4 c (1

A1

α1

CO 2 H CO 2 H CO 2 H CO 2 H HO 2 C-CO 2 H•2H 2 O HO 2 C CO 2 H HO 2 C CO 2 H HO 2 C CO 2 H CO 2 H CO 2 H (CO 2 H) n a b c d e 2 3 4 1 5 f 1,2-(HO 2 C) 2 C 6 H 4 g 1,3-(HO 2 C) 2 C 6 H 4 h 1,4-(HO 2 C) 2 C 6 H 4 i 1,2,3-(HO 2 C) 3 C 6 H 3 j 1,3,5-(HO 2 C) 3 C 6 H 3 k 1,2,4,5-(HO 2 C) 3 C 6 H 2 l HO 2 CCH 2 C 6 H 5

carboxylic acid additives used for this study:

in case where both of these components were freely soluble. Compared to classical template strategy which requires inevitably the use of stoichiometric amount of the template molecules, this result showed clearly high dynamicity of the suspension conditions. This observation is a starting point for further development of catalytic system (similar to solution chemistry) taking advantage of highly ordered molecular arrangement of solid state chemistry.

The same efficiency (yield, regio-and stereo-selectivities) was maintained when using non-polar (hexane, heptane, cyclohexane) or moderately polar (PhH, PhMe, CH2Cl2, CHCl3, ethyl acetate, tetrahydrofuran or dioxane) solvents (some examples were shown in entries 19-23, Table 1). In all these cases, the complexes between A1 and oxalic acid were insoluble in dispersing solvents and both regio-and stereo-selectivities reaction could be considered to be governed by solid state arrangement of the two components.

As expected, when the reaction was performed in a protic solvent such as methanol which could break easily hydrogen bond interaction between A1 and oxalic acid, the required orientation for successful [2+2]-photodimerization could not be achieved and the corresponding adduct could not be formed (entry 24, Table 1).

With this set of optimized conditions in hand (entry 14, Table 1), we next evaluated the reactivity of a range of stilbazoles A2-A35 bearing a 4-pyridyl moiety listed in Table 2. In general, most of the tested olefins led to the desired products in excellent yields as a single regio-and stereo-isomers in the presence of an equimolar amount of oxalic acid additive.

It is important to note that for each olefin, a comparative background reaction was performed in the absence of oxalic acid and in the overwhelming majority of cases led to complex mixtures of cis and trans olefins, a-truxillic and b-truxinic type isomers and other stereo-isomers as well as degradation products in various proportion.

The configuration of [2+2] adducts was determined based on 1 H NMR signal of cyclobutane protons (J coupling constant and form of these signals). Interestingly, after UV irradiation, most of the tested stilbazoles A with different functional groups underwent [2+2] cycloaddition leading exclusively to either a-truxillic acid type adduct (anti HT) or b-truxinic type adduct (syn HH).

Monoalkylated stilbazoles A2-A5 reacted in the same manner as A1 and led to the corresponding a-truxinic acid type adducts a2-a5 (entries 1-4, Table 2). On the other hand, 4-isopropyl derivative A6 formed uniquely b6 adduct in high yield (entry 5, Table 2).

The photocycloaddition of sterically hindered (E)-4-(2,4,6trimethylstyryl)pyridine A7 could be achieved in excellent yield of a a7 adduct although longer reaction time was required (entry 6). Halogenated 4-stilbazoles A8-A16 could provide the corresponding [2+2] adducts also in excellent yields, even for polyhalogenated derivatives of the same or different halogen atoms (entries 7-15, Table 2). All tested halogeno stilbazoles led only to either a or b adduct.

For cyanated 4-stilbazoles, we noticed that the corresponding adduct of p-cyano-4-stilbazole A17 could be formed in excellent yield without any added additive (entry 16, Table 2). [15] Furthermore, the [2+2] photodimerization of o-cyano isomer A18 required oxalic acid additive with inversion of regiochemistry (entry, Table 2). Other 4-stilbazoles bearing a range of electron withdrawing group (NO2, CF3, CO2H, entries 18-20, Table 2) or electron donating group (MeO, AlkylCO2, entries 21-28, Table 2) in different positions of the phenyl ring could provide the expected adducts in excellent yield and selectivities. Amazingly, although stilbazole A21 bearing a free carboxylic group exhibits very low solubility in most common solvent for crystallization, its photocycloaddition performed with suspended oxalic acid could provide adduct b21 as the single product in good yield (entry 20, Table 2). The same product was previously obtained indirectly via saponification of the corresponding methyl ester. [4o] All three regiomeric monomethoxy stilbazoles (A22-A24) gave the same results in both reactivity and selectivities (entries 21-23, Table 2). The reaction of 2,4,6-trimethoxy stilbazole A25 proceeded slowly with reasonable yield obtained only after 72 h of irradiation (entry 24, Table 2). The behavior of all four p-acyloxy stilbazoles A26-A29 was found to be independent of the acyl chain length and ramification as all of them led efficiently to the expected single products of a-truxinic type stereochemistry irradiation (entries 25-28, Table 2).

The same stereochemistry outcome was obtained with both 1-and 2-naphthyl derivatives (A30, A31, entries 29-30, Table 2), both thienyl (A32-A33, entries 30-31, Table 2) and furyl analogues (A34-A35, entries 31-32, Table 2). We noticed that the reaction of 1-naphthyl derivative should be performed under an inert atmosphere to avoid a side reaction of oxidative cyclization leading to naphtho [1,2-H]isoquinoline (entry 29, Table 2). [16] Despite the apparent structural similarity between thienyl and furyl derivatives, the photodimerization of both sulfurated olefins (entries 31-32, Table 2) was found to proceed much efficiently with shorter reaction times and provided the corresponding adducts in higher yields than that of the corresponding oxygenated analogues (entries 33-34, Table 2).

Subsequently, the ability of oxalic acid in promoting selective photocycloaddition was evaluated with 2-stilbazole A36 and its derivatives (A37-A47), which were readily available by the condensation of the corresponding benzaldehydes with 2-picoline in the presence of acetic anhydride (Table 3). Such a systematic study on a range of 2-stilbazoles has never been carried out, possibly due to all the difficulties in obtaining well-defined and photoactive cocrystals between this kind of olefins and a suitable template molecule.

As in the previous cases with 4-stilbazoles (Table 2), excellent results were achieved for all 2-stilbazoles listed in Table 3. The reaction worked with a wide range of substituents, including alkyl (entry 2, Table 3), halogen (entries 3-8, Table 3), electron donating groups (methoxy and acyloxy, entry 9, Table 3), and electron withdrawing group (ester, carboxylic acid and nitro, entries 11-12, Table 3). As in the previous case with 4-stilbazole carboxylic acid A21 (Table 2, entry 20, Table 3), even though A46 was shown to be slightly soluble in most of the common solvents for cocrystallization and thus unsuitable for the template strategy, its good reactivity showcased an extremely useful complementary aspect of the present strategy.

In an interesting way, simply changing the free carboxylic acid of stilbazole A46 by its methyl ester A45 overturned the regiochemistry (entry 10 vs entry 11, Table 3).

Oxalic acid additive showed also its high performance in case of 2,4'-diazastilbene A48, leading to adduct b48 (entry 13, Table 3). Additionally, our strategy also enables the use of some selected stilbazoles A49-A51 bearing a methyl group in the pyridine ring (entries 1-3, Table 4). As in the two previous cases with 2,4-dichlorostilbazoles bearing 4-or 2-pyridyl substituents (A14 and A42) which led to b truxinic acid type adducts b14 and b42, we noticed the same tendency for stilbazole A51.

We emphasized that in some cases, the starting stilbazole exists as either an oily liquid, semi liquid, solid with near rt melting point or waxy/amorphous solid. Typically, a solid powder was formed when these stilbazoles were stirred with solid oxalic acid suspended in cyclohexane.

Although most of the above-mentioned results with oxalic acid as the additive were positive, we recognized quickly that some stilbazoles led to the products as a mixture of both a-truxinic and b-truxillic type adducts with low selectivity or were totally photoinactive with this additive. In such difficult cases, the versatility and flexibility of our strategy were demonstrated clearly by simply fine-tuning or reconsidering the choice of additive. For this purpose, we presented some troubleshooting examples. First, when the reaction of 3-pyridyl/2-pyridyl analogue using oxalic acid led to a mixture of both isomers a or b in low regioselectivity (b52:a52 2.5:1) despite high reactivity. An additional screening of other additives was therefore carried out to improve this low regioselectivity (Scheme 2). The result of such a rapid improvement led to the identification of fumaric acid as a more suitable additive with comparable activity and leading to better regioselectivity b52:a52 7:1. On the other hand, low reactivity was observed with malonic acid and maleic acid.

Scheme 2. [2+2] Photocycloaddition of A52

Second, when the condition using oxalic acid as an additive failed to provide the expected adduct as in the case of p-nitro-2stilbazole A53 or 2',4'-dinitro-2-stilbazole A54 wherein the starting material remained unchanged, a screening of new additives found again fumaric acid as an excellent additive to provide exclusively the adducts b53 and a54 in good yields (Table 5, entries 1-2). The structure of b53 was confirmed by X-ray crystallography (Figure 1). Third, our strategy could be applied successfully to both methyl and ethyl (E)-3-(pyridin-3-yl)acrylates A55-A56, which are semi solid (methyl ester) or liquid (ethyl ester) at rt (Table 5, entries 3-4). For both esters, 1,3,5-benzenetricarboxylic acid j was found to be the most suitable additive in terms of both reactivity and selectivities, providing the single adduct b55-b56 in reasonable yields. acids in Table 1 tested as an additive, only maleic acid was capable of promoting the [2+2]-photodimerization of b-(2quinolyl)acrylic acid A57, leading exclusively to adduct b57 (Scheme 3).

Fifth, the high specificity of our simple screening conditions was exemplified by the investigation of acid additives for [2+2]photodimerization of 4-aza-cinnamic acid A57 (Scheme 4). While most of the screened additives were found to be totally inactive to promote the photodimerization, we noticed that malonic acid led exclusively to 4,4'-diaza-b-truxinic acid b57 and fumaric acid resulted in only a-truxillic type dimer a57. Finally, our strategy could be applied to unprotected urocanic acid A59 (Scheme 5). This acid was found in animal sweat and epidermis. When absorbed ultraviolet light, trans-urocanic acid is converted in vivo to the cis isomer and acts as an endogenous sunscreen or photoprotectant against UV-induced DNA damage. [17] Similarly, UV irradiation in solution results in a mixture of cis and trans isomers whereas irradiation of crystalline urocanic acid produces no photochemical change. [START_REF]Urocanic acid as salts with hydrochloric acid or potassium hydroxide in aqueous solution was found to undergo [2+2] photodimerization[END_REF] While the direct [2+2]-photodimerization of urocanic acid itself has never been achieved, its derivatives were found to be capable of undergoing this transformation in solution [START_REF]Urocanic acid as salts with hydrochloric acid or potassium hydroxide in aqueous solution was found to undergo [2+2] photodimerization[END_REF],[19 or in solid state. [20] A rapid screening of some acid additives mentioned in Table 1 under our conditions of mixing/stirring irradiation led once again to the identification of oxalic as the unique suitable additive to provide exclusively b-truxinic type dimer b59 in 80% conversion after 7 d of irradiation (Scheme 5).

In all cases of b-substituted acrylic acids, no attempt has been made to isolate the diacid adducts. In order to understand the nature of this procedure, we first attempted to obtain and determine the structure of the expected photoactive cocrystals between 4-stilbazole A1 and oxalic acid by tentatively performing the cocrystallization in methanol, which is an excellent solvent for both constituting components. Although the desired cocrystals could be isolated, the structural determination of these cocrystals showed that they contained also methanol solvent. Furthermore, these ternary cocrystals were found to be unstable as the solvent residue escaped readily even during the structural determination by X-ray diffraction. We next turned our attention to a solvent-free approach to provide the cocrystals. For this purpose, we performed a sublimation of stilbazole A1 and oxalic acid under vacuum (0.01 mmHg) at 110-130 °C and allowed the two compounds to condense at lower temperatures. We were able to isolate two kinds of cocrystals CC1 and CC2 distinguishable by their different external aspects. Structural determination by X-ray diffraction showed that the first crystal CC1 with stoichiometric ratio 3:4 stilbazole:oxalic acid with head-to-head orientation of two neighboring stilbazole molecules was unsuitable for photocycloaddition due to large distance between two reactive C=C bond (5.30 Å) as well as largely non parallel orientation (4.49 Å and 3.38 Å) (Figure 2). Interestingly, the second cocrystal CC2 was a 1:1 complex stilbazole:oxalic acid with head-to-tail orientation between two neighboring stilbazole. The reactive carbon atoms of C=C bond are 4.03 Å and 4.22 Å (Figure 3).

80% conversion

Although these two crystals are not the only cocrystals that could be formed upon mixing two starting components, one of them are photoactive, leading to a1 adduct upon irradiation. Moreover, since A1 and oxalic acid could be moved freely under stirring conditions, the formation of at least one photoactive cocrystal is crucial to the success of our strategy. Indeed, as the [2+2] photodimerization proceeded for the photoactive cocrystals, new equilibria will be established to rearrange photoinactive cocrystals into inactive one and subsequently into photoadduct. By this way, the conditions for [2+2] photodimerization would be less strict, which requires only a tiny amount of photoinactive cocrystals.

In conclusion, we have reported here a simple and straightforward strategy for rapid screening of additive for selective [2+2] photodimerization of stilbazoles by implementation of irradiation on a mixture of stilbazoles and carboxylic acid additive suspended in a non-polar or moderately polar solvents. Having identified oxalic acid as an excellent additive for most cases, we applied this transformation to a wide range of structurally diverse stilbazoles. Particularly interesting was the ability of our strategy to apply to solid, waxy, amorphous, liquid or even insoluble stilbazoles, making it more powerful to traditional methods. In most cases, the purification of the expected adducts as single isomers in clean reaction mixtures relied principally on the removal of oxalic acid by simply washing with an aqueous solution of NaHCO3. The potential in application to polar olefins bearing many hydrogen bond forming sites has been demonstrated successfully with stilbazoles bearing a free carboxylic acid group as well as some b-hetarylacrylic acids such as 4-azacinnamic acid, b-(2-quinolyl)acrylic acid and urocanic acid. From a more general perspective, we envision that the operational simplicity, broad scope, low cost and scalability of this strategy make it undoubtedly suitable for application in both laboratory and industrial scales.

Experimental Section

A mixture of olefin A (0.2 mmol) and oxalic acid dihydrate (40 mg, 0.32 mmol) in cyclohexane (2 mL) in a 7-mL Pyrex tube was stirred in the photoreactor described in the Supporting Information for 16 h (unless otherwise noted). After removal of cyclohexane, the solid crude reaction mixture was stirred with CH2Cl2 (2 mL) and neutralized with an aqueous saturated NaHCO3 solution (2-4 mL). The CH2Cl2 layer was separated, the aqueous layer was extracted with CH2Cl2 (2 mL ´ 3). The combined organic layers were filtered through a short pad of solid NaHCO3 to afford the desired adduct. See Supporting information for more detail.

Entry for the

COMMUNICATION

In this study we reported on a very simple technique to perform efficiently photodimerization of some vinylpyridines. By irradiating a stirred mixture of several stilbazoles with solid oxalic acid dihydrate dispersed in a non-polar (e.g. cyclohexane) or moderately polar (benzene, dichloromethane, dioxane) solvent, the corresponding dimeric cyclobutane adducts were obtained in high yields with excellent of regio-and stereo-selectivities. The strategy could also be applied successfully to oily, waxy or even insoluble stilbazoles. Moreover, the oxalic acid loading could be lowered to sub-stoichiometric amounts. When further optimizations were needed, our strategy was found to be highly flexible to identify other oligocarboxylic acids as alternative additive to improve or even overturn regioselectivity. Oxalic acid and other oligocarboxylic acids were found to be capable of orienting more than fifty stilbazoles toward photodimerization under these conditions.

Thanh Binh Nguyen, Tuan Minh Nguyen, and

Figure 1 .Entry

 1 Figure 1. X-ray structure of b53, CDCC 1948883

Scheme 4 .

 4 Scheme 4. [2+2] Photocycloaddition of A58

Scheme 5 .

 5 Scheme 5. [2+2] Photocycloaddition of urocanic acid A59

Figure 2 .

 2 Figure 2. Packing arrangement of stilbazole A1-oxalic acid 3:4 cocrystal CC1 obtained by cocondensation

Figure 3 .

 3 Figure 3. Packing arrangement of stilbazole A1-oxalic acid 1:1 cocrystal CC2 obtained by cocondensation

  , Hetaryl, CO 2 Alk, CO 2 H

Table 2 .

 2 Reactions of b-(4-pyridyl)styrenes A2-A35

	N			N	Ar	N	N
			oxalic acid
				1.6 equiv		or
		Ar	cyclohexane 365 nm 35 °C, 16 h	Ar	N	Ar	Ar
	A2-A35			α		β
	Entry a	A		Ar		T (h)	yield (%)
	1	A2	4-MeC6H4			a2, 90
	2	A3	3-MeC6H4			a3, 92
	3	A4	2-MeC6H4			a4, 95
	4	A5	4-EtC6H4			a5, 96
	5	A6	4-iPrC6H4			b6, 72
	6	A7	2,4,6-Me3C6H2		a7, 90
	7	A8	4-FC6H4			a8, 90
	8	A9	2-FC6H4			a9, 95
	9	A10	4-ClC6H4			a10, 95
	10	A11	2-ClC6H4			b11, 70
	11	A12	4-BrC6H4			a12, 90
	12	A13	2-BrC6H4			b13, 94
	13	A14	2,4-Cl2C6H3			b14, 96
	14	A15	4-Br-3-FC6H3		a15, 95
	15	A16	2,4,6-F3C6H2		b16, 70
	16	A17	4-NCC6H4			a17, 100 b
	17	A18	2-NCC6H4			b18, 92
	18	A19	4-O2NC6H4			a19, 70
	19	A20	4-F3CC6H4			a21, 94
	20	A21	4-HO2CC6H4		b21, 87
	21	A22	4-MeOC6H4			a22, 73
	22	A23	3-MeOC6H4			a23, 50
	23	A24	2-MeOC6H4			a24, 95
	24	A25	2,4,6-(MeO)3C6H2		a25, 55
	25	A26	4-AcOC6H4			a26, 84
	26	A27	4-EtCO2C6H4		a27, 99
	27	A28	4-nPrCO2C6H4		a28, 94
	28	A29	4-iPrCO2C6H4		a29, 92
	29	A30	1-naphthyl			a30, 71
	30	A31	2-naphthyl			a31, 61
	31	A32	2-thienyl			a32, 64
	32	A33	3-thienyl			a33, 91
	33	A34	2-furyl			a34, 44
	34	A35	3-furyl			a35,58

[a] Reaction conditions: A (0.2 mmol), oxalic acid dihydrate (40 mg, 0.32 mmol), cyclohexane (2 mL), hn 365 nm, 16-72 h.

[b]

Yield of the background reaction.

Table 3 .

 3 Reactions of b-(2-pyridyl)styrenes A36-A47

	Entry [a]	A	Ar	T (h)	yield (%)
	1	A36	C6H5	16	a36, 94
	2	A37	4-MeC6H4	16	a37, 95
	3	A38	4-FC6H4	16	a38, 93
	4	A39	4-ClC6H4	16	a39, 93
	5	A40	3-ClC6H4	16	a40, 95
	6	A41	2-ClC6H4	16	a41, 88
	7	A42	2,4-Cl2C6H3	16	b42 [b] , 90
	8	A43	4-Br-3-FC6H3	16	b43, 94
	9	A44	4-AcO-3-MeOC6H3	16	a44, 80
	10	A45	4-MeO2CC6H4	16	a45, 90
	11	A46	4-HO2CC6H4	16	b46, 82
	12	A47	3-O2NC6H4	72	b47, 69
	13	A48	4-Pyridyl	16	b48, 72
	[a] Reaction conditions: A (0.2 mmol), oxalic acid dihydrate (40 mg, 0.32
	mmol), cyclohexane (2 mL), hn 365 nm, 16-72 h. [b] b42:a42 7:1.

Table 4 .

 4 Reactions of stilbazoles A49-A51

	Entry [a]	Stilbazole	T (h)	Product, %
	1		72	a49, 72
		A49
	2		72	a50, 62
		A50
	3		16	b51, 89
		A51

[a] Reaction conditions: A (0.2 mmol), oxalic acid dihydrate (40 mg, 0.32 mmol), cyclohexane (2 mL), hn 365 nm, 16-72 h.

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Acknowledgements

TB Nguyen thanks Engr. Nguyen Xuan Bong for all his support and encouragement throughout this work. We thank Dr. A. Marinetti (ICSN-CNRS) for her helpful support. Financial support from Merlion program of the Embassy of France in Singapore to initiate the collaboration between TB Nguyen and TM Nguyen is gratefully acknowledged.