Adina Ceausu -Velcescu

Petr Pracna

Roman A Motiyenko

Laurent Margules

Dr Adina Ceausu-Velcescu

Rotational spectroscopy in the v3=v6=1 and v6=2 vibrational states of CH 35 Cl3

Keywords: chloroform, high-resolution MMW spectroscopy, excited vibrational states

 sublevels. As a consequence, several resonant q12 (∆k=±1, ∆l=m2) crossings occur, which enabled the precise determination of the q12 interaction parameter for this state. Altogether, 1182 rotational transitions in the v3=v6=1 combination level have been measured and fitted, with a standard deviation of 41.2 kHz.

For the v6=2 (A1+E) overtone level, the combined effects of the q22 and q12 l-type interactions induce resonant crossings between the (k, l6=0)/(k+1, l6=-2) pairs of levels, for a large variety of k values. Altogether, 1463 rotational transitions in the (l6=0) A1 sublevel and 2924 rotational transitions in the (l6=±2) E sublevels, together with nine perturbation-allowed transitions induced by the q12 (∆k=±1, ∆l=m2) interaction, have been measured and fitted, with a global standard deviation of 41.4 kHz. This resulted in the first accurate determination of the molecular constants of this overtone level.

Introduction

CHCl3 (chloroform, trichloromethane) is a clear, colorless, highly volatile, nonflammable liquid at room temperature. It is widely used as an extraction solvent for fats, oils, greases, rubber, resins, lacquers, artificial silk manufacture, gums and adhesives. Chloroform is also employed as an industrial solvent in the extraction and purification of some antibiotics, alkaloids, vitamins and flavors [1]. This explains why most of the oldest investigations of its vibrational spectrum were done in the liquid phase.

Chloroform may be hazardous to the environment, as it can be transported in air as vapor and dissolved in water. In the air, chloroform eventually breaks down to other toxic chemicals, such as phosgene and hydrogen chloride.

Gas-phase spectroscopy is an invaluable tool for monitoring atmospheric pollutants [START_REF] Cossel | Gas-phase broadband spectroscopy using active sources: progress, status, and applications[END_REF]. Unfortunately, with several low-lying excited states, small rotational constants, and four isotopologues simultaneously present, the gas-phase high-resolution infrared spectra of natural chloroform are almost impossible to interpret. The use of (expensive) isotopically pure samples seems thus to be the only possibility.

Rotational spectra of the symmetric species, in the ground vibrational state and the low-lying vibrational states v2=1 (676 cm -1 ), v3=1 (367 cm -1 ), and v6=1 (260 cm -1 ), were studied by Carpenter et al. [START_REF] Carpenter | The rotational spectrum of chloroform in its ground and excited vibrational states[END_REF]. The ground vibrational state was also studied using millimeter and submillimeter-wave spectroscopy by Cazzoli et al. [START_REF] Cazzoli | Millimeter and submillimeter-wave spectrum of CHCl3. Determination of the h3 splitting constant[END_REF], who obtained very accurate centrifugal distortion constants. For the main isotopologue CH 35 Cl3, these authors also resolved the splitting of the K=3 transitions, for J≥45, and obtained thus a value of the h3 (∆k=±6) interaction parameter in the ground state. Colmont et al. [START_REF] Colmont | Rotational spectra of the isotopic species of chloroform: experimental and ab initio structures[END_REF] analyzed the ground state rotational spectra of various isotopic species of chloroform and obtained empirical experimental and ab initio structures. Later, Demaison [START_REF] Demaison | Equilibrium structure of chloroform[END_REF] recalculated the ab initio equilibrium structure and derived also, as a check, a semi-experimental equilibrium structure.

Rovibrational studies were performed for all fundamental bands of CH 35 Cl3 [START_REF] Pietilä | High-Resolution Infrared Studies of ν1, 2ν1, and 2ν4 Bands of CH 35 Cl3[END_REF][START_REF] Paso | High-resolution study of the infrared band ν2 of CH 35 Cl3[END_REF][START_REF] Pietilä | High-resolution infrared study of the parallel band ν3 of chloroform CH 35 Cl3[END_REF][START_REF] Anttila | The C-H bending vibration ν4 of chloroform CH 35 Cl3[END_REF][START_REF] Pietilä | The perpendicular fundamental ν5 of chloroform 12 CH 35 Cl3: high resolution infrared study of the ν5 band together with the millimetre-wave rotational spectrum[END_REF] including recently the ν6 fundamental vibration, located near 260 cm -1 [START_REF] Pracna | The ground and v6=1 vibrational levels of HC 35 Cl3: The first high-resolution analysis of the ν6 fundamental band[END_REF]. The latter study, which merged rovibrational wavenumbers of the ν6 band and rotational data from a previous work of Margulès et al. [START_REF] Margulès | Rotational spectrum in the v6=1 and v3=1 levels of chloroform[END_REF] in a global least-squares fit, comprises also a first accurate determination of the axial ground state constants C0, , and . Unfortunately, the infrared study of the 2ν6 lowest overtone levels was not possible so far due to very low intensities of both the overtone and hot bands reaching this level.

The aim of the present study is thus to provide a first accurate parameter set for the v6=2 overtone levels of CH 35 Cl3, near 520 cm -1 , through the analysis of the rotational spectrum, which has been recorded on a natural sample. In fact, contrarily to the infrared vibration-rotation spectra, where the high congestion imposes the use of rather expensive isotopically pure samples, the rotational (millimeter-wave) spectrum of a natural sample may present several distinct regions where the contributions of the different isotopologues and vibrational levels of a given isotopologue occur.

The present study includes also a detailed analysis of the rotational spectrum of CH 35 Cl3 in the v3=v6=1 combination level, near 627 cm -1 . This combination vibration has been already analyzed through a high-resolution study of the IR ν3+ν6-ν6 hot band, in the ν3 region, near 367 cm -1 [START_REF] Pietilä | High-resolution infrared study of the parallel band ν3 of chloroform CH 35 Cl3[END_REF]. In this study, Pietilä et al. assigned 199 peaks of the above mentioned hot band, the wavenumbers of which were fitted using a fourth-order polynomial in m 1 . However, the two components (l6=-1 and l6=+1) of this bi-parallel band were treated separately, the strong l(2,2) interaction, present both in the lower and the upper levels, being absorbed into effective B(±l) constants. The authors further remarked that the resonance was almost exact, since the difference B(-l)-B(+l)=237(3)×10 -6 cm -1 almost equals 4|q22|=243.87(4)×10 -6 cm -1 . Thus, the aim of the present study is to provide a more accurate treatment of this combination level with explicit inclusion of the l-type interactions, resulting in accurate molecular parameters, necessary to further studies of merged IR and rotational data.

Experimental details

The measurements in the frequency range under investigation (150-660 GHz) were performed on a chloroform sample with natural abundance, using the Lille spectrometer [START_REF] Zakharenko | Terahertz Spectroscopy of Deuterated Formaldehyde Using a Frequency Multiplication Chain[END_REF]. The absorption cell was a stainless-steel tube (6 cm diameter, 220 cm long). Measurements were conducted at room temperature and at a sample pressure of about 30 Pa. The frequency ranges 150-330 and 360-660 GHz were covered with various active and passive frequency multipliers from VDI Inc. and an Agilent synthesizer (12.5-18.25 GHz) was used as the source of radiation. In order to improve the signal sensitivity, the sources were frequency modulated at 30.5 kHz and lock-in detection with the second harmonic was used. Typical estimated uncertainties for measured line frequencies are 30 to 50 kHz, depending on the observed S/N ratio and the frequency range.

1 Where, as usual, m= -J for a P transition (∆J=-1) and J+1 for a R transition (∆J= +1).

Despite the rather low pressure used in the experiment, we could not achieve Doppler-limited linewidths, for at least two reasons: (i) The hyperfine structure (HFS), which is still apparent for rotational lines with intermediate J/high K values. Many of the observed lines are thus partially or completely unresolved hyperfine structure components, even at Doppler linewidth. (ii) The increase of the frequency modulation depth during the experiment, which was necessary for improving the S/N ratio, for a better observation of transitions pertaining to the excited vibrational states. This increase resulted in additional broadening, giving for instance linewidths of the order of 1 MHz in the intermediate J-values region (compared to an estimated Doppler linewidth of the order of 0.3 MHz). Consequently, broader intermediate-J/low-K lines, with no apparent HFS, were included in the least-squares fit with higher uncertainties, whereas weaker, intermediate-J/high-K lines, showing partly resolved HFS, were excluded from the fit (as explained later).

The rotational spectrum

The degenerate fundamental vibration v6=1 (CCl3 asymmetric bending vibration), located at 260.6 cm -1 , is well separated from other vibrational levels and could be therefore treated as isolated [START_REF] Pracna | The ground and v6=1 vibrational levels of HC 35 Cl3: The first high-resolution analysis of the ν6 fundamental band[END_REF][START_REF] Margulès | Rotational spectrum in the v6=1 and v3=1 levels of chloroform[END_REF]. This is also the case of the v6=2 (A1+E symmetry) and v3=v6=1 (E) levels, which are separated by more than 100 cm -1 .

We started assignments with the rotational transitions in the v3=v6=1 level. Like the v6=1 fundamental vibration, the v3=v6=1 combination level is characterized by an accidentally small value of | --| ≈ 88 . This combination of constants determines the separation of unperturbed (K-1, l6=-1)/(K+1, l6=+1) levels coupled by the q22 l-type resonance [START_REF] Margulès | Rotational spectrum in the v6=1 and v3=1 levels of chloroform[END_REF], which is roughly given by Δ ≈ 4 --≈ -0.012 (in cm -1 units). This separation increases only slowly with K, whereas the l(2,2) coupling matrix elements rapidly increase with J. This confers to the q22 interaction a globally resonant character, which is for vibrational levels with --≈ 'reserved' to the kl=+1 sublevels only. The q22 resonance produces an effective contribution to the B rotational constant Δ ≈ ±2| |, with the upper sign corresponding to the higher level in the (K+1, l6=+1) / (K-1, l6= -1) pairs of levels in resonance. Thus, the K-clusters become wide separated, with the l6=+1 lines pushed down to lower frequencies and those of l6=-1 up to higher frequencies. For a given J, the l(2,2) resonance term decreases with k, whereas the unperturbed energies difference increases only slightly with k. Hence, the absolute magnitude of the energy shift decreases with k, for a given J. The, otherwise degenerate, |kl=+1, J+1> ← |kl=+1, J> transitions are symmetrically split by about ±4| | + 1 , with the A-component at lower frequencies. For kl≠+1, due to the negative sign of --, the l6=+1 lines are pushed down to lower frequencies, whereas the l6=-1 lines are pushed up to higher frequencies. The displacement decreases with k, for a given J cluster. The combined effects of DJK < 0 and of the q22 resonance make thus the lower l6=+1 cluster degraded towards higher frequencies, for all the values of J. The l6=-1 clusters are degraded towards lower frequencies for J ≤ 35; a bandhead is observed for moderate J values (Fig. 1), whereas, for higher J values, these clusters become also degraded towards higher frequencies (Fig. 2).

Assignment of the v3=v6=1, l6= -1 and +1, clusters of rotational lines, which much resemble those of v6=1, was thus straightforward, despite their weakness as shown in Fig. 1.

A total of 1182 lines of the l6=±1 components have been assigned and fitted.

The pattern of rotational transitions in the v6=2 overtone level is quite different from that of the fundamental level v6=1. The l(2, 2) resonance connects the triplets of levels (K+2, l6=+2)/(K, l6=0)/(K-2, l6= -2), the relative positions of which are mainly determined by the g66 anharmonicity parameter and the combination of the Cζ and (C-B) parameters, as follows:

± 2, = ±2 - , = 0 ≈ ±4 -- ± 1 + 4 ! - = ∓0.012 ± 1 + 0.550 (in cm -1 units).
This puts the (K, l6=0) levels below their (K-2, l6= -2) resonance partners for all values of K.

Also, the (K, l6=0) levels lie below the (K+2, l6=+2) ones for K < 45.

The appearance of the K-clusters of rotational lines, for a given J value, in the v6=2 level, can be easily understood again by considering the case of exact resonance, which concerns the |0 〉 and |±2 ± 〉 levels, the latter being degenerate. The Wang transformation yields an A+ block of interacting levels, symmetrically displaced with respect to the mean value of their unperturbed energies, and a |2 , % & 〉 unperturbed level. Hence, the (2 2 , A-, J+1)← (2 2 , A-, J) transition is unperturbed. Three clusters can thus be observed, for each value of J (Fig. 1): a lower-frequency one, which corresponds to l=0, a middle one, composed of l=+2 transitions, which 'follows' the (2 2 , A-, J+1)← (2 2 , A-, J) transition, and a higherfrequency one, composed of l= -2 transitions and 'following' the (2 2 , A+, J+1)← (2 2 , A+, J)

transition. This latter cluster contains also the (1 2 ) and (0 2 ) transitions. The effect of the l(2,2)

resonance on the appearance and behavior of the l=0, +2, and -2 J-clusters of lines is by the way nicely depicted in Fig. 5 of Ref. [START_REF] Carpenter | The Millimeter-Wave Rotational Spectrum of CF3CCH in the Excited Vibrational State v10=2[END_REF], for the v10=2 rotational spectrum of CF3CCH.

The lower frequency clusters, corresponding to l6=0 and composed of regularly spaced lines, degraded to higher frequencies, were clearly observed in the spectrum, distinct from the much stronger rotational transitions of the vibrational ground state and the fundamental v6=1 level, not being obscured by them (Figs. 1 and2). Assignment of the l6=0 transitions at moderate J-values (Fig. 1), facilitated by the intensity alternation due to nuclear spin statistics, was the starting point of the analysis, yielding more reasonable values of the B (0) and B (2) rotational constants, which were used for further assignments. At this stage, the AABS package, designed by Kisiel et al. for broadband rotational spectroscopy [START_REF] Kisiel | Spectroscopy from Space[END_REF], has been extensively used. Finally, the middle and the upper clusters, corresponding to l6=+2 and l6= -2, respectively, were also assigned. Like before, intensity alternation due to nuclear spin statistics and the Loomis-Wood representation of the spectrum in the AABS package were extremely helpful in progressive extension to higher J values. A total of 1463 lines of the l6=0 component and 2924 lines of the l6=±2 components (22≤J"≤49 and 55≤J"≤99) have been thus assigned and fitted.

With the energies of the l6=0 levels being pushed down by the q22 resonance, these fall into local resonances with both l6=+2 and l6=-2 levels due to other vibration-rotation interactions, such as q12 (∆k=±1, ∆l=m2), but also higher-order f42 (∆k=±4, ∆l=m2) and f52 (∆k=±5, ∆l=±2) interactions. In addition to this, resonant crossings between the l6=+2 and l6= -2 levels due to the f14 interaction occur for several low K values, as shown in Figure 3 with the reduced energy plot of the whole system of rotational levels of v6=2. Nine perturbation-allowed transitions, induced by the q12 interaction, were also included in the fit.

Results and discussion

For fitting the experimental frequencies, a conventional Hamiltonian of a symmetrictop molecule has been used, the matrix elements of which are given in Appendix A. For the least-squares fitting, using the SIMFIT program [START_REF] Pracna | High-resolution study of the v5=1 level of CDF3[END_REF], the data were given statistical weights proportional to the inverse square of their estimated uncertainties.

The present work is based on a huge set of rotational data. Part of the observed transitions would be further split by the hyperfine quadrupole interactions due to the three chlorine nuclei with nuclear spin 3/2. The detailed description of the tensorial coupling techniques allowing to construct the nuclear quadrupole part of the Hamiltonian, for any number of nuclei of spin ≥1, can be found for instance in Refs. [START_REF] Wolf | Hyperfine structure in the microwave spectra of CFCl3 and CHCl3[END_REF][START_REF] Wollrab | Rotational Spectra and Molecular Structure: Physical Chemistry[END_REF]. This tensorial coupling mechanism is implemented in the SPFIT/SPCAT program package [START_REF] Pickett | The fitting and prediction of vibration-rotation spectra with spin interactions[END_REF], which was already used for studying the HFS of the J=1←0 and J=2←1 transitions in the ground vibrational state of CHCl3 [START_REF] Białkowska-Jaworska | Nuclear quadrupole coupling in chloroform and calibration of ab initio calculations[END_REF]. This structure is quite complex, extending over more than 50

MHz and consisting of a great number of measurable components. The analysis performed by the authors of Ref. [START_REF] Białkowska-Jaworska | Nuclear quadrupole coupling in chloroform and calibration of ab initio calculations[END_REF] allowed fitting all determinable components of the inertial nuclear splitting tensors for the chlorine nuclei. On the contrary, there are only few studies dealing with HFS of rotational transitions in degenerate excited states of symmetric top molecules [START_REF] Carpenter | The rotational spectrum of chloroform in its ground and excited vibrational states[END_REF][START_REF] Müller | Rotational spectroscopy as a tool to investigate interactions between vibrational polyads in symmetric top molecules: low-lying states v8≤2 of methyl cyanide, CH3CN[END_REF]. For the v6=1 state of CHCl3, Carpenter et al. [START_REF] Carpenter | The rotational spectrum of chloroform in its ground and excited vibrational states[END_REF] constrained the '( )) and * + parameters to the corresponding ground state values.

In our current analysis we could in principle attempt either at assigning the resolved HFS and fit them explicitly with the SPFIT program, or reducing the resolved HFS to ´hyperfine-free´ rotational frequencies, using e.g. the HFS parameters constrained to their ground vibrational state values, and fit them with the use of SIMFIT program [START_REF] Pracna | High-resolution study of the v5=1 level of CDF3[END_REF]. Our moderate J-values (22≤J"≤35) spectrum clearly shows hyperfine quartets in the vibrational ground, v3=1, and v6=1 states, for high K values, as, for a given J, the quadrupole splitting of lines increases with K. At the same time, intensities are decreasing with increasing K; this makes the quartets of the, much weaker, v6=2 band, more difficult to distinguish, as they are often overlapped by other, stronger, transitions. For such J-values, HFS structure is already partly collapsing, even though still visible. This means, however, that the reliable assignments of the hyperfine components for using them in either of the mentioned fitting approaches, remains somewhat problematic. Therefore we decided to exclude from the data set the lines corresponding to these intermediate J / high K-values, showing partly resolved hyperfine structure, and those only broadened due to hyperfine interaction give lower weights (i.e.

higher uncertainties of 100-200 kHz) and fit them with the SIMFIT program.

Despite this reduction of the data set, frequent overlaps with much stronger transitions in the lower lying levels and of course vanishing intensities for growing J values, we were still able to collect over 1000 transitions in the two l-sublevels of the v3=v6=1 vibrational state and over 4000 transitions in the three l-sublevels of the v6=2 vibrational state, which we believe to be a sound basis for determination of parameters of the centrifugal distortion expansion and all relevant off-diagonal interaction terms of the effective rotational Hamiltonian of a symmetric top molecule.

The v3=v6=1 level

In the v3=v6=1 vibrational level, situation is almost the same as that described for v6=1 [START_REF] Margulès | Rotational spectrum in the v6=1 and v3=1 levels of chloroform[END_REF]: the q22 resonance pushes the pairs of interacting levels (k, l6=-1)/(k+2, l6=+1) apart so that they are brought into local resonances due to the q12 l-type interaction. We were able to detect and assign transitions on both sides of the crossings for the pairs of levels 1 +1 /2 -1 (at J=43/44) and 3 +1 /4 -1 (at J=67/68) only: the 2 +1 /3 -1 crossing, occurring at J=56/57, is in a spectral range not recorded by our spectrometer, whereas the crossings 4 +1 /5 -1 , 5 +1 /6 -1 , and so on, occur at J values which are too high for detecting the corresponding transitions.

The fits were performed with two reduced forms of the effective rotational Hamiltonian, the Q and D reductions [START_REF] Watson | Indeterminacies in the vt(E)=1 Levels of C3v Symmetric-Top Molecules[END_REF]. With 14 refined parameters (out of 22), these reduction schemes provided an identical reproduction of the data, with a standard deviation of 41.2 kHz (Table 1). We have to notice that the C, DK, and ηK coefficients of the K-dependent part of the rotational energies were kept fixed, in order to avoid too high correlation between these parameters and Cζ, the latter parameter being refined.

The unitary equivalence checking of the Q and D reductions, up to 3 rd order is shown in Table 2. The results of this Table can be compared to those presented for the v6=1 level, given in Table 3 of Ref. [START_REF] Pracna | The ground and v6=1 vibrational levels of HC 35 Cl3: The first high-resolution analysis of the ν6 fundamental band[END_REF]. Surprisingly, the discrepancies noticed for v6=1, for instance that between -2 , -// and , 0 1 + / , seem to be less important for the v3=v6=1 level: for the latter level, the above mentioned quantities agree within 2σ. The 3 rd order combinations also show quite good agreement, except the Δ +,-* 2 difference, which is statistically not defined.

The v6=2 level

For each value of the rotational quantum number J, rotational levels are grouped into three-level-systems with the same value of G=|k-l|. Several kinds of level crossings take place, but only two of them result into resonances due either to Δ 3 -= 3 or to Δ 3 -= 6 interactions, which have strong, local effects on energy levels with a large variety of G values.

First, the q22 resonance pushes the pairs of levels (k, l6=0)/(k-2, l6=-2) apart, so that local resonances due to the q12 interaction (∆G=±3) occur (Fig. 3). We have observed such crossings between (k, l6=0)/(k+1, l6=-2) levels for a large variety of k values and were thus able to refine not only the main interaction parameter, q12, but also the parameter of the ldependent term, , 6 , which is of the same order of magnitude as q12 [START_REF] Sarka | The reduced effective vibration-rotational Hamiltonian for the vt=2 levels of C3v symmetric-top molecules[END_REF]. Second, the (k, l6=0)/(k+4, l6=-2) levels are interacting through a f42 l-type interaction (∆k=±4, ∆l=m2). Level crossings occur for J=60 in the 0 0 /4 -2 pair, 71 in the 1 0 /5 -2 pair, 81 in the 2 0 /6 -2 pair and so on. Unfortunately, only the first crossing occurs at a J-value which is low enough for observing transitions with a reasonable intensity.

Another interesting phenomenon, due to the strong l(2,2) resonance and the resulting mixing of states, occurs: for each G value, G≥45, the two lower levels in the three-levelsystem (i.e. (k, l6=0) and (k+2, l6=+2) change their relative positions, though they do not cross in a conventional sense. This phenomenon has been already described for the v10=2 state of 1,1,1-trifluoropropyne by Wötzel et al. [START_REF] Wötzel | The direct l-type resonance spectrum of CF3CCH in the vibrational state v10=2[END_REF]. Thus, for a certain value of J, the mixing of the |3, = 0〉/|3 + 2, = +2〉 wavefunctions is so strong that an unambiguous labeling of the levels is not possible. For higher values of J, the labeling becomes again unambiguous, but with reversed ordering of the levels.

The approach employed in the present work for fitting the frequencies of the assigned transitions is that proposed by Sarka and Harder [START_REF] Sarka | The reduced effective vibration-rotational Hamiltonian for the vt=2 levels of C3v symmetric-top molecules[END_REF], who developed, for an isolated vt=2 level of a C3v symmetric-top molecule, five reduced forms of the effective Hamiltonian. The common feature of these reduced forms is that from the four lower order ∆(k-l)=3

interactions, two have to be constrained and the other two refined, but the simultaneous constraint of the k-and l-dependent terms of the (2,-1) interaction is not allowed. Therefore, the following constraints have been suggested up to fifth order [START_REF] Sarka | The reduced effective vibration-rotational Hamiltonian for the vt=2 levels of C3v symmetric-top molecules[END_REF]: all parameters of the Kdependent terms of off-diagonal interactions (7 , 7 , , 7 , 6 , 7 6 , 8 , 0 1 ) and the parameter f14 of the (4,1) interaction should be fixed to zero. In the present case, all these constraints have been applied except for 7 (see below). Indeed, it has been shown by Watson et al. [START_REF] Watson | Indeterminacies in the vt(E)=1 Levels of C3v Symmetric-Top Molecules[END_REF] that the constraint 7 9 = 0 should be avoided if | --| is accidentally too small. This is the case for the 2ν6 vibration of CHCl3 (and situation was of course the same for ν6 [START_REF] Pracna | The ground and v6=1 vibrational levels of HC 35 Cl3: The first high-resolution analysis of the ν6 fundamental band[END_REF]), where --≈ -92 . For accidentally small values of --, one can alternatively use one of the following constraints: ;̃2 = 0, or ;̃2 = 0, or ;̃ = 0.

The reduction schemes employed in the present work correspond to the Q, D, and L reductions described in Ref. [START_REF] Sarka | The reduced effective vibration-rotational Hamiltonian for the vt=2 levels of C3v symmetric-top molecules[END_REF]. As pointed out in this Reference, the parameters 7 9 ,= , 7 9 , 62 , 7 9 , 6 , 7 9 6 depend on the transformation parameters o, p, r and therefore three of them should be constrained. The constraints suggested in the above mentioned Reference are thus 7 9 ,= = 0; 7 9 , 6 = 0; 7 9 6 = 0, the 7 9 , 62 parameter being refined. In the present case, the f24 interaction parameter (∆k=±2, ∆l=m4) was not refined in the final stage of the calculations but kept fixed to a value obtained in a preliminary stage (see footnote b of Table 3).

With the final choice of 28 refined parameters, the data could be reproduced within error limits comparable to the estimated experimental accuracy, of 50 kHz. The global standard deviation is thus of 41.4 kHz for the three reductions D, Q, and L (Table 3).

The unitary equivalence of the three parameter sets, up to third order, was also checked and the results are presented in Table 4. For this purpose, the following relations, derived for the lowest order parameters of the ∆(k-l)=3 interactions, have been employed [26] -

> ?@ A B = C D E > @@ C D F > @@ = > ?@ G,A H , 6,-= , 6,+ + HC D E => @@ , I = , -+ B> ?@ G,A H
As shown in Table 4, the above equalities are satisfactorily, though not perfectly, fulfilled.

Good fulfillment of the unitary equivalence of parameters occurs also for the third-order constants * 2 and * , for which the following equalities can be established [26]:

Δ +,-* 2 = -Δ J,K * = - 8 , - / = - L0 M + N / 2 Δ +,I * 2 = -Δ +,I * = - 8 , I / = - 8L , 6,+ N / O Δ I,-* 2 = -Δ I,-* = 8P , I -, - Q /
In these relations, the symbol ∆ X,Y implies the difference between the values of a parameter in the X and Y reductions (X,Y = Q, D, or L). By the way, the refinement of the 7 6 parameter has a noticeable effect on the third-order parameters * 2 and * , thus improving the fulfillment of the above mentioned equalities.

We have not shown the unitary equivalence relations for the fourth-order parameters 7 2 and 7 = , as suggested for instance in Ref. [26], because the corresponding differences are only poorly defined. It would be however interesting to check, even only partly, the fourth order contributions to the rotational constants B and C. The dependence of these rotational constants on the transformation parameter s writes ([26], corrected in [START_REF] Ceausu-Velcescu | The v4=1 and v4=2 rovibrational levels of PF3 revisited: New solutions for old topics[END_REF]):

R,6 S = R,6 + 4 T 1 2 U - + UV W , S + 1 4 /S X -4 U + 2U -3 W , 6 S - 1 4 OS X R,6 S = R,6 -8 T 1 2 U - + UV W , S + 1 4 /S X
From these relations, one can derive for a vt=2 state the following equalities:

Δ +,- = -16 Z , - / + 2 L , 6,-N -L , 6,+ N O [ Δ +,- = -8 Z , - / -2 L , 6,-N -L , 6,+ N O [
as well as

1 2 Δ +,- = Δ +,- = 16
, -

/

For the C constants, checking of the above equalities is meaningless, the uncertainties being larger than the experimental differences. For the ∆B values however, good fulfillment is observed, even though uncertainties of the experimental differences are of the same order of magnitude as the differences themselves. We obtain for instance for the l6=0 sublevel, LΔ +,- N \]^= 5.27 188 × 10 &a cm -1 and LΔ +,- N 1b = 4.701 62 × 10 &a cm -1 . For the l6=±2 sublevels, we obtain LΔ +,- N \]^= -1.97 116 × 10 &a cm -1 and LΔ +,- N 1b = -1.740 31 × 10 &a cm -1 .

As said previously, the experimental frequencies could be reproduced with a global standard deviation of 41.4 kHz. It should be mentioned, however, that we have not succeeded in reproducing in such a quantitative manner the (k=±1, l6=m2) and (k=±5, l6=±2) series, as well as the low-J (k=±3, l6=0) transitions, which were excluded from the final fits.

These series connect levels pertaining to the nine-level system (0 0 , A+), (3 0 , A+/A-), (1 -2 , A+/A-), (2 2 , A+/A-) and (5 2 , A+/A-) in which the higher-order diagonal splitting terms f24 and h3 compete with the, much stronger, q22 and q12 resonances. These latter resonances act globally all over the system of rotational levels of v6=2, the q12 term producing a series of resonant level crossings. This is illustrated in Fig. 3 and also in a broader J/K span in the reduced energy diagram included in the Supplementary material.

The interplay of all these interactions produces strongly irregular patterns of the A+/Asplittings of the above mentioned series. The independent determination of the parameters of the three Δ 3 -= 6 interactions (i.e. f42, f24, and h3) would be probably enabled by the observation and inclusion in the fit of transitions with different selection rules, e.g. direct ltype resonance transitions, like achieved in analogous studies of the vibrational state v10=2 of CF3CCH [START_REF] Wötzel | The direct l-type resonance spectrum of CF3CCH in the vibrational state v10=2[END_REF] or the vibrational state v6=2 of SiHF3 [26]. This was unfortunately not the case in the present work as such measurements would have required a completely different experimental setup, which we did not have at our disposal. As a consequence, the f42 and h3 parameters could be determined, but may still remain correlated. The f24 parameter could not be determined and was kept fixed in the final stage of the calculations (as described earlier on page 10).

Nevertheless, the exclusion of the above mentioned low-K series from the final fits did not deteriorate the consistency of the diagonal and off-diagonal parameters of the v6=2 level with those of v6=1. This is shown in Table 5, for the reduction Q, by comparing the q22, 7 2 , dt, and f42 off-diagonal parameters of the two levels. Inspection of this Table shows an excellent agreement for q22, 7 2 , and dt (within less than 2%), whereas the f42 values differ by about 5%. The same difference is obtained for the f42 values in the reduction D. Situation is somewhat worse for the off-diagonal parameters of v3=v6=1, some of which present larger differences with the corresponding v6=1 values (Table 5). In this case, excellent agreement is observed for q22 and f42 (within less than 2%), whereas the 7 2 values differ by about 5%, and the dt values by about 14%.

Supplementary data associated with this article can be found in the online version, at doi: …

Conclusions

The present work reports on the first high-resolution study of the v6=2 (A1+E) and v3=v6=1 (E) vibrational states of the CH 35 Cl3 molecule through the analysis of the corresponding rotational spectra. The reproduction of the rotational data pertaining to v3=v6=1 level is fully quantitative. This is also the case for the majority of the data pertaining to the v6=2 overtone level, except the (±3,0), (±1,m2) and (±5,±2) series, where unusually large splittings occur.

( , , )

( 1)

v v v vr t v v v v J JK K v v v v J JK KJ K v v v v v J JJK JK JKK K E J k l E B J J C B k D J J D J J k D k H J J H J J k H J J k H k L J J L J J k L J J k L J J k L k = + + + - - + - + - + + + + + + + + + + + + + + + + + ( ) 2 2 2 2 4 3 3 2 2 2 4 6 2 ( 1) ( 1) ( 1) ( 1)
( 1) ( 1)

t tJ tK tJ v tJK tK tJ tJK tKJ tK t C J J k J J J J k k J J J J k J J k k kl ζ η η τ τ τ σ σ σ σ - + + + + +  + + + + +  + + + + +  (A1)
The following off-diagonal matrix elements were considered a) l-type operators ( ; ,

t t l l t t J K t t t t JJ JK KK v J k v J k v l v l q f J J f k k f J J f J J k k f k k F J k ± ± ± + +   = ± + + + + + ±           + + + + + ± + + ±     H H H m (A2) ( )( ) ( ) ( ) 2 ; , 2 ( 1) 2 ( 1) ( 1) 2 2 ( , )
{ } ; , 1 ; ,

2

( 1) 2 1 1 ( , )

t t l l t t J K t t t t v J k v J k v l v l q f J J k f k k F J k ± +     = ± + + + + +         H H m m m m m (A3) ( )( ) ( ) { } ( )
v J k v J k v l v l q f J J f k k l F J k ± +   = ± + + + + + ±       H H m m m m (A4) ( )( ) { ( ) } 1/
v J k v J k v l v l f f J J f k k F J k ± + = ± + + +       + +   H H m m m m (A5) ( )( )( )( ) 1/
f v J k v J k v l v l v l v l F J k ± = - ± + ± +     H m m m m (A6) ( ) ( )( ) ( )( ) 4
f v J k v J k k v l v l v l v l F J k ± ± ± = ± -   × ± + ± +   H m m (A7) b) ∆k=±3 operators ( ) { } 2 2 23 25 3
; , 3 ; , ( 1) 3 ( , )

t t l l J K t t t t t t v J k v J k d d J J d k k l F J k ±   ± + = + + + + ±   H H (A8) [ ]( ) ( ) { } 2 2 04 06 3 ; , 3 ; , ( 1) 2 3 3 ( , ) t t l l t t J K v J k v J k J J k k k F J k ε ε ε ±   ± + = + + ± + + ±   H H (A9) c) ∆k=±6 operator ( ) { } 2 2 06 08 3 3 3 6
; , 6 ; , ( 1) 6 ( , )

t t l l J K t t v J k v J k h h J J h k k F J k ±   ± + = + + + + ±   H H (A10)
The notation of the matrix elements of the rotational shifting operators was taken as

( )( ) 1/2 1 ( , ) ( 1)
1 a Constrained to a value obtained from the GS, v3=1, and v6=1 values (Refs. [START_REF] Pietilä | High-resolution infrared study of the parallel band ν3 of chloroform CH 35 Cl3[END_REF] and [START_REF] Pracna | The ground and v6=1 vibrational levels of HC 35 Cl3: The first high-resolution analysis of the ν6 fundamental band[END_REF]). b Constrained to the corresponding v6=1 value quoted in [START_REF] Pracna | The ground and v6=1 vibrational levels of HC 35 Cl3: The first high-resolution analysis of the ν6 fundamental band[END_REF]. Numbers in parentheses are standard deviations in units of the last digit quoted. 10 -10 cm -1 3.880 ( 16)

n n i F J k J J k i k i ± = = + -± ±     ∏ m (A11)
( ) Q D J J - η η 10 -10 cm -1 5.1 (94) ( ) Q D K K - - η η 10 -10 cm -1 0.89 b a F = C-B + 2Cζ.
b Constrained to the value obtained in Ref. [START_REF] Pracna | The ground and v6=1 vibrational levels of HC 35 Cl3: The first high-resolution analysis of the ν6 fundamental band[END_REF] for the v6=1 level. 4.861 [START_REF] Białkowska-Jaworska | Nuclear quadrupole coupling in chloroform and calibration of ab initio calculations[END_REF] , 12 l D q 10 -6 cm -1 3.052 [START_REF] Margulès | Rotational spectrum in the v6=1 and v3=1 levels of chloroform[END_REF] 12 L q 10 -6 cm -1 -6.164 [START_REF] Kisiel | Spectroscopy from Space[END_REF] , 12 [START_REF] Müller | Rotational spectroscopy as a tool to investigate interactions between vibrational polyads in symmetric top molecules: low-lying states v8≤2 of methyl cyanide, CH3CN[END_REF] 4 Q l Q t Gd q q = + 10 -6 cm -1 3.069 [START_REF] Margulès | Rotational spectrum in the v6=1 and v3=1 levels of chloroform[END_REF] , [START_REF] Pracna | The ground and v6=1 vibrational levels of HC 35 Cl3: The first high-resolution analysis of the ν6 fundamental band[END_REF] 12

D l D F q q G = +
10 -6 cm -1 -6.180 (16) a Parameters taken from [START_REF] Pracna | The ground and v6=1 vibrational levels of HC 35 Cl3: The first high-resolution analysis of the ν6 fundamental band[END_REF].

10

 10

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. The rotational spectrum of chloroform in the region of J=61←62 transitions. Upper panel: experimental spectrum (natural sample). Lower panel: simulated spectrum, showing several J-clusters of the CH 35 Cl3 isotopologue, with the same color code as for Figure 1. The lines marked with an asterisk are ground state rotational transitions of the CH 35 Cl2 37 Cl isotopologue.

Figure 3 .

 3 Figure 3. Reduced energies (pure J-dependent terms not included) against J, for the v6=2 levels. Positions of resonant crossings due to q12, f42, and f14 interactions are indicated. Dashed arrows indicate interaction between only one of either the A+ or A-sublevels.

Figure 4 .

 4 Figure 4. Hyperfine splittings of the rotational transitions in the v6=1 level. The J=34, l6=-1 cluster is shown; the simulated spectrum (lower panel) does not account for these splittings. Several, much weaker, v6=2 transitions, are indicated by an asterisk.

  C-B + 2Cζ; G = Cζ + 2gll.

Table captions Table 1 .

 captions1 Molecular parameters of the v3=v6=1 level of CH 35 Cl3.

Table 2 .

 2 Demonstration of unitary equivalence between the D and Q reductions, for the v3=v6=1 level.

Table 3 .

 3 Molecular parameters of the v6=2 level of CH 35 Cl3.

Table 4 .

 4 Demonstration of unitary equivalence of the different parameter sets for the v6=2 level (2 nd and 3 rd order).

	Table 5. Parameters of the (2,2), (3,0) and (4,-2) interactions (in MHz units) in the vibrational
	states v6=1, v3=v6=1, and v6=2 of CH 35 Cl3 (reduction Q).

Table 1 . Molecular parameters of the v3=v6=1 level of CH 35 Cl3

 1

	Parameter	Reduction D	Reduction Q
	B (MHz)	3301.228 336 (55)	3301.228 335 (55)
	C (MHz)	1711.524 214 a	1711.524 214 a
	DJ (kHz)	1.514 619 (13)	1.514 618 (13)
	DJK (kHz)	-2.527 72 (22)	-2.527 71 (21)
	DK (kHz)	0.834 58 b	0.834 58 b
	HJ (mHz)	1.256 7 (11)	1.256 6 (11)
	HJK (mHz)	-5.092 (22)	-5.089 (22)
	HKJ (mHz)	6.96 (22)	6.94 (22)
	HK (mHz)	-2.435 b	-2.435 b
	LJ (nHz)	-2.538 b	-2.538 b
	Cζ (MHz)	-1502.060 8 (84)	-1502.062 4 (84)
	ηJ (kHz)	-4.407 (20)	-4.392 (20)
	ηK (kHz)	3.267 5 b	3.264 9 b
	22 q (MHz)	-1.813 161 (18)	-1.813 154 (18)
	22 J f (Hz)	4.051 4 (21)	4.052 9 (21)
	22 K f (Hz)	-2.981 (19)	-2.975 (19)
	f	22 JJ	(µHz)	-8.677 b	-8.677 b
	f	22 JK	(µHz)	23.058 b	23.058 b
	12 q (kHz)	-82.07 (17)	0.
	t d (kHz)	0.	0.129 03 (27)
	42 f (Hz)	0.490 0 (59)	0.493 5 (59)
	3 h (mHz)	0.155 5 (10)	0.155 6 (10)
	σ (kHz)	41.2	41.2

Table 2 . Demonstration of the unitary equivalence between the D and Q reductions, for the v3=v6=1 level

 2

		Equation a	Unit	Verification
			-	2	12 D q F /	10 -5	-3.573 2 (75)
			1 2	d	Q t	/	q	22	10 -5	-3.558 0 (75)
		-	2 8( ) / 12 D q	F	10 -10 cm -1	3.913 (16)
	-	1 2 ( F d	Q t	2 ) /	2 22 q

Table 3 . Molecular parameters of the v6=2 states of CH 35 Cl3

 3 Constrained to the v6=1 values obtained in Ref.[START_REF] Pracna | The ground and v6=1 vibrational levels of HC 35 Cl3: The first high-resolution analysis of the ν6 fundamental band[END_REF]. b Constrained to a value obtained in a preliminary fit, which still included the (k=1, l6=-2) lines. These lines were excluded from the final fit (see text). Numbers in parentheses are standard deviations in units of the last digit quoted.

			Parameter	Reduction D	Reduction Q	Reduction L
			B	MHz	3305.138 203 (80)	3305.138 361 (80)	3305.138 006 (80)
		C	MHz	1710.636 4 (37)	1710.636 3 (37)	1710.636 4 (37)
		DJ	kHz	1.520 418 (16)	1.520 426 (16)	1.520 405 (16)
		DJK	kHz	-2.545 53 (14)	-2.545 54 (14)	-2.545 54 (14)
		DK	kHz	0.834 58 a	0.834 58 a	0.834 58 a
	l6=0
		HJ	mHz	1.284 09 (96)	1.284 16 (96)	1.284 00 (96)
		HJK	mHz	-5.172 8 (71)	-5.172 9 (71)	-5.173 5 (71)
		HKJ	mHz	6.902 (20)	6.903 (20)	6.901 (20)
		HK	mHz	-2.434 67 a	-2.434 67 a	-2.434 67 a
		LJ	nHz	-2.538 a	-2.538 a	-2.538 a
		4gll	MHz	10468.65 (17)	10468.64 (17)	10468.67 (17)
		C	MHz	1710.665 5 (33)	1710.665 5 (33)	1710.665 5 (33)
		DJ	kHz	1.520 277 (10)	1.520 273 (10)	1.520 283 (10)
	l6=±2	DJK	kHz	-2.545 540 (79)	-2.545 535 (79)	-2.545 541 (79)
		DK	kHz	0.835 04 (20)	0.835 03 (20)	0.835 06 (20)
		HJ	mHz	1.293 13 (60)	1.293 09 (60)	1.293 17 (60)
		HJK	mHz	-5.163 6 (41)	-5.163 4 (41)	-5.163 5 (41)
		HKJ	mHz	6.774 0 (87)	6.773 4 (87)	6.775 2 (87)
		HK	mHz	-2.434 67 a	-2.434 67 a	-2.434 67 a
		LJ	nHz	-2.538 a	-2.538 a	-2.538 a
		Cζ	MHz	-1502.373 4 (31)	-1502.373 0 (31)	-1502.374 2 (31)
		ηJ	kHz	-4.951 4 (18)	-4.942 4 (18)	-5.001 7 (18)
		ηK	kHz	3.238 3 (23)	3.229 3 (23)	3.288 3 (23)
		q12	kHz	-72.507 (70)	0.	-184.78 (49)
	Off-	12 l q	kHz	91.50 (40)	150.58 (40)	0.
	diagonal	, 12 l J q	Hz	-6.541 (88)	-6.602 (88)	-6.445 (87)
	parameters	q22	MHz	-1.829 779 5 (77)	-1.829 780 3 (76)	-1.829 778 7 (77)
		f	22 J	Hz	3.861 4 (14)	3.863 3 (14)	3.865 5 (14)

a

Table 4 Demonstration of unitary equivalence of the different parameter sets for the v6=2 level (2 nd and 3 rd order) Equation a Unit Verification Equation a Unit Verification

 4

Table 5 . Parameters of the (2,2), (3,0) and (4,-2) interactions (in MHz units) in the vibrational states v6=1, v3=v6=1, and v6=2 of CH 35 Cl3 (reduction Q)

 5

	Parameter	v6=1 a	v3=v6=1	v6=2
	q22	-1.827 752 (19)	-1.813 154 (18)	-1.829 780 3 (76)
	× 10	3.855 2 (43)	4.052 9 (21)	3.863 3 (14)
	dt × 10 4	1.127 14 (15)	1.290 3 (27)	1.148 89 (111)
	f42 × 10 7	4.873 6 (60)	4.935 (59)	5.095 1 (44)

Acknowledgements

One of the authors (A. C-V) wishes to thank Drs. Z. Kisiel (Warsaw) and J. Demaison (Lille) for fruitful discussions.

Appendix A. Definition of the matrix elements of the effective vibration-rotational

Hamiltonian

The diagonal matrix elements were defined conventionally as


Jacques Slembrouck
email: jacques.slembrouck@ird.fr

Zenal Otong

Arifin

Simon Pouil

Jojo Subagja

Akhmad Yani

Asependi Asependi

Anang Hari Kristanto

Marc Legendre

Seasonal variation of giant gourami (Osphronemus goramy) spawning activity and egg production in aquaculture ponds

Keywords: Reproduction control, Breeding cycle, Natural spawning, Freshwater aquaculture, Indonesia

The giant gourami Osphronemus goramy Lacépède, 1801, spontaneously spawns in captivity, making nests for egg deposition when suitable nest supports and nesting material are made available in rearing facilities. The seasonal variation in reproductive performance of the giant gourami was characterized during a 20-month experiment in two compartmentalized ponds (about 550 m 2 each) at a fry production center in West Java, Indonesia. A total of 208 giant gourami broodfish were introduced in the two experimental ponds, with a sex-ratio of one male to three females in each of the 52 spawning compartments delimited by vertical nets. Nesting supports in each spawning compartment were examined every two days for the presence of eggs resulting from natural reproduction. Three performance indicators were quantified from the collected nests: spawning frequency (monthly number of spawns per female), effective fecundity (number of eggs per spawn) and egg quality (estimated from the proportion of clear living eggs in each spawn). The seasonality of giant gourami reproduction was analyzed as a function of seasonal variation in rainfall, rearing water temperature and day length. Based on a total of 413 collected spawns, the multiple linear regression models did not show any significant relationship between giant gourami spawning frequency and the three environmental variables studied. In contrast, the number of eggs per spawn was highly and positively related to rainfall (p < 0.0001), moderately and negatively related to water temperature (p < 0.001), and weakly and negatively related to day length (p < 0.01). The proportion of clear eggs was a positively related to day length (p < 0.01). Overall, this study represents one of the first comprehensive datasets on the reproductive phenology of giant gourami, and as such will be helpful in formulating broodfish management strategies for the species.

Introduction

Native to Southeast Asia, notably from Indonesia, the Malay Peninsula, Thailand and the Mekong basin, the giant gourami Osphronemus goramy Lacépède, 1801, has been introduced to several other countries for aquaculture purposes (Welcomme, 1988). This fish is omnivorous, with a strong vegetarian tendency, and shows relative robustness and adaptability to unfavorable environmental conditions (aerial respiration), which make it a very attractive candidate for low-input aquaculture [START_REF] Caruso | Osphronemus goramy[END_REF]. In Indonesia, the giant gourami is one of the main freshwater commodities of economic importance owing to its high price and local demand [START_REF] Rimmer | A review and SWOT analysis of aquaculture development in Indonesia[END_REF]. Since 2000, giant gourami aquaculture production has grown by a factor of 10 in Indonesia, the main country farming this species (145,000 tons in 2017; [START_REF] Fao | FishStatJ: software for fishery statistical time series[END_REF]. The Indonesian national production is ensured by approximately 100,000 small-scale fish farmers mainly located on Java Island (79%; [START_REF] Bps | Number of non-ornamental fish farms by region and fish species[END_REF]. Although the giant gourami has been reared for decades and has now reached a significant production level, there are still important gaps in our knowledge on several aspects of its biology.

The production of giant gourami fry relies on the natural spawning of captive broodfish held in ponds, but the commercial-scale propagation of the species still needs to be standardized (Amornsakun et al., 2014a;[START_REF] Arifin | Effect of stocking density on growth, food intake and survival of giant gourami (Osphronemus goramy, Lacepède) larvae[END_REF][START_REF] Prakoso | Effects of temperature on the zootechnical performances and physiology of giant gourami (Osphronemus goramy) larvae[END_REF]. The overall recruitment of this multiple spawning species (i.e. number of fry produced per broodfish and per spawn) in the breeding ponds remains generally low, resulting from variable spawning frequency or success, and variable egg number and quality [START_REF] Azrita | Morphological character among five strains of giant gourami, Osphronemus goramy Lacepède, 1801 (Actinopterygii: Perciformes: Osphronemidae) using a truss morphometric system[END_REF]. Therefore, ensuring a regular and sufficient supply of fry through reliable production methods remains a major challenge for the expansion of gourami aquaculture (Amornsakun et al., 2014a, b;[START_REF] Slembrouck | Gender identification in farmed giant gourami (Osphronemus goramy): A methodology for better broodstock management[END_REF].

Among the various biotic and abiotic factors influencing the reproductive performance of broodfish, the effects of pond management strategies, sex-ratio and duration of egg production periods were specifically investigated in a recent study [START_REF] Arifin | New insights into giant gourami (Osphronemus goramy) reproductive biology and egg production control[END_REF]. Nevertheless, the seasonality of reproduction has also been mentioned as an important limitation to a regular supply of giant gourami fry (e.g. [START_REF] Arfah | Induced spawning of giant gourami Osphronemus gouramy Lac. by Ovaprim[END_REF][START_REF] Kristanto | Egg and fry production of giant gourami (Osphronemus goramy): Rearing practices and recommendations for future research[END_REF][START_REF] Wijayanti | Reproductive hormone profiles and gametogenegis in female giant gourami (Osphronemus gouramy) (in Indonesian)[END_REF]. In some instances, this seasonality has prompted studies to test hormonal treatments that induce oocyte maturation and ovulation of giant gourami broodfish [START_REF] Arfah | Induced spawning of giant gourami Osphronemus gouramy Lac. by Ovaprim[END_REF].

Nevertheless, to our knowledge, an accurate description of the seasonal variation in reproductive performance of captive giant gourami broodfish is still lacking in the scientific literature. Such information would help to rationalize and optimize hatchery operations, as in many intensively farmed finfish species [START_REF] Migaud | Gamete quality and broodstock management in temperate fish[END_REF]. Because there are considerable interspecific variations in the patterns of reproductive seasonality [START_REF] Wootton | Reproductive Biology of Teleost Fishes[END_REF][START_REF] Paugy | Reproduction[END_REF], such investigation would also be useful to further document the influence of the environment on the reproductive phenology of freshwater tropical fishes for which, with the exception of some families (mostly cichlids and clariids), availability of accurate datasets remains limited.

The objective of the present study was to assess seasonal fluctuations in the reproduction of giant gourami (spawning frequency, number of eggs in a spawn and egg quality), based on nearly two years of follow-up in ponds at the Tasikmalaya Center for the Development of Giant Gourami Culture (BPPSIGN), the largest giant gourami fry production center in the West Java Province, Indonesia. The seasonality of giant gourami reproduction was analyzed in function of seasonal variation in rainfall, rearing water temperature and day length, three environmental parameters considered as major cues for the reproductive phenology of most tropical fishes [START_REF] Lowe-Mcconnell | Ecological aspects of seasonality in fishes of tropical waters[END_REF][START_REF] Legendre | Physiology of reproduction[END_REF][START_REF] Paugy | Reproduction[END_REF].

Materials and Methods

Experimental facilities and pond water quality

This study was carried out at the BPPSIGN Tasikmalaya Center (7°19′37.992″N, 108°6′101.155″E; altitude 489 m). The experiment was performed over a period of 20 months from May 2016 to December 2017. Experimental structures were two earthen-bottom ponds of 527 and 563 m 2 in surface area with vertical concrete banks and an average water depth of 0.6 m. The two ponds were divided into spawning compartments of about 20 m 2 each (52 compartments in total), delimited with nets embedded in the sediment and held vertically on bamboo poles. Ponds were supplied from a conduit carrying spring water from the Galunggung Mountain located less than 10 km from the BPPSIGN Center.

Before starting the experiment, the spawning ponds were dried, cleaned, rid of all other species and limed before being refilled. Pond water pH, dissolved oxygen, conductivity, and turbidity were measured at quarterly intervals between 07:00 and 08:00 AM with direct measurements using a multi-parameter probe (HI 9829 Hanna). Water concentration in ammonia (NH3), nitrite (NO2 -) and nitrate (NO3 -) was measured at the same time using spectrophotometry analysis (Hanna HI83399). The average and range of variation of these parameters are provided in Table 1 and indicate that the pond water quality remained stable during the experiment and within appropriate standards for tropical freshwater fish [START_REF] Colt | Water quality requirements for reuse systems[END_REF].

Fish maintenance and assessment of reproductive performance

The mature broodfish (n = 208) used in this study were descendants of giant gourami belonging to the "Galunggung" strain [START_REF] Arifin | Intraspecific hybridization between two populations of Galunggung giant gourami (Osphronemus goramy, Lacepède, 1801)[END_REF]. The females were 3-5 years old and weighed ~3 kg, whereas males were 5-7 years old and weighed ~4 kg. Identification of fish sex and assessment of their sexual maturity were done on the basis of morphological criteria, milt emission following gentle abdominal massage or examination of oocytes obtained by intraovarian biopsies as described by [START_REF] Slembrouck | Gender identification in farmed giant gourami (Osphronemus goramy): A methodology for better broodstock management[END_REF]. One sexually mature male and three sexually mature females were placed in each of the 52 spawning compartments of the two experimental ponds.

The giant gourami is a nest builder; therefore, nest supports and nesting material were provided in each compartment for spawning. Nest supports were baskets made of braided bamboo strips (total length: 25 cm, including an opening of about 30 cm in diameter), attached to bamboo stakes, and placed about 15 cm below the water surface with the opening positioned slightly downward (angle of about 30°). Plant fibers from palm trees (Arenga sp.) were piled on a bamboo table positioned at the surface of the water in the middle of every compartment, so that the broodfish could easily grasp the fibers with their mouths and build their nests (see [START_REF] Arifin | New insights into giant gourami (Osphronemus goramy) reproductive biology and egg production control[END_REF], for picture of the nest supports).

Every two days, all nest supports were examined and closed nests containing eggs were collected, transferred to the hatchery, then immersed in a water tank to release the eggs by carefully opening the palm fiber material as detailed in [START_REF] Arifin | New insights into giant gourami (Osphronemus goramy) reproductive biology and egg production control[END_REF]. All the eggs from each nest were manually counted, separating live (transparent/clear) eggs from dead (opaque/white) eggs. During the experiment, reproductive performance was assessed by monitoring spawning frequency (the number of spawns per female per month), the number of eggs in a spawn (i.e., numbers of eggs in a nest) and egg quality (estimated by the proportion of clear eggs in each spawn). In some instances, the eggs were newly hatched at the moment of nest collection; however, this had no or little incidence on the evaluation of progeny number and spawn quality because white (dead) eggs take more than one day to break up and newly hatched larvae, unable to swim, remain inside the nest.

During the egg production periods, the broodfish were fed with leaves of elephant ear plants (Alocasia macrorrhizos) and commercial floating pellets (32% proteins, 5% lipids) distributed at a daily feeding rate of 2% and 1% of fish biomass, respectively. The egg production periods lasted for 3 or 7 months depending on spawning compartments, two durations that lead to equivalent results in terms of egg production over the long term [START_REF] Arifin | New insights into giant gourami (Osphronemus goramy) reproductive biology and egg production control[END_REF]. Between two successive egg production periods, the broodfish were reconditioned for 1 month (separating males and females in different ponds and using reverse daily feeding rates of elephant ear leaves and floating pellets). The broodfish fish were examined every three months and weighed with a digital scale for adjustment of feeding rations.

Monitoring of environmental conditions

Throughout the 20-month experiment, fluctuations of three environmental parameters were considered: rainfall, pond water temperature and day length. Pond water temperature was monitored continuously using a data logger (Onset HOBO) placed in the center of the ponds at 20 cm depth. A rain gauge was installed in the immediate vicinity of the ponds to record the daily rainfall and the information related to day length was collected from Time and Date (2019).

Data treatment and statistical analysis

Prior to statistical analysis, fish reproduction and environmental data were compiled and, for each pond and each variable, monthly means of the recorded values were calculated. Statistical analyses were then performed on these average monthly values.

The non-significance of the variable "pond", initially included in general linear models (GLM) with quantitative environmental variables was confirmed. Then, stepwise multiple linear regression models (MLR) were used to test for relationships between female spawning frequency, egg numbers or clear egg proportion in spawns and environmental variables (rainfall, water temperature and day length). The assumptions underlying the MLR were checked by visual observation of the model residuals and by statistical analysis (Goldfeld-Quandt test, Rainbow test and Shapiro-Wilk test). Variance inflation factors (VIF) were used to estimate collinearity of the explanatory variables, with VIF values close to 1 indicating the absence of strong multi-collinearity [START_REF] Hair | Multivariate data analysis[END_REF]. Statistical analyses were performed using R freeware version 3.5.2 using the packages "car", "lmtest" and "stats" (R Development Core Team, 2019).

Results

At the BPPSIGN Tasikmalaya Center, day length varied annually between 11 h 41 min and 12 h 33 min, and pond water temperature ranged from 22.6°C to 32.7°C. The cumulative monthly rainfall ranged from 5 to 528 mm during the experiment, from May 2016 to December 2017.

Overall, the monthly mean of the pond water temperature showed limited variation (between 25.4°C and 28.0°C), whereas the monthly rainfall was much lower during the second than during the first half of the experimental period (from 331 to 528 mm vs. 0.5 to 288 mm, respectively; Figure 1A).

During this 20-month period, as determined from the 413 spawns collected in the two experimental ponds (206 and 207 spawns per pond), the reproduction of giant gourami occurred continuously. Because no effect of the duration of egg production periods (successive periods of 3 or 7 months) was detected for any variable (spawning frequency, egg number and quality), the data were pooled for analyses. The mean monthly spawning frequency of giant gourami varied between 0.07 and 0.26 spawn female -1 month -1 without a clear seasonal rhythm in the intensity of spawning activity (Figure 1B). The mean monthly number of eggs per spawn collected from the nests varied between 2020 and 5920 eggs spawn -1 and peaked (more than 4000 eggs spawn -1 ) during the period between July and November 2016 (Figure 1B). The mean monthly proportion of clear (live) eggs in the spawns varied between 79 and 96% (Figure 1B).

The MLR did not reveal any significant relationship between giant gourami spawning frequency and any of the environmental variables (Table 2). Observed monthly variation in spawning frequency had no clear seasonal rhythm; it was not related to simultaneous variations in rainfall, water temperature or day length. In contrast, variation in the number of eggs produced per spawn was clearly related to variation in environmental variables (multiple R 2 = 0.71; p < 0.0001). Egg number was highly and positively related to rainfall (t-value = 7.777, p < 0.0001), moderately and negatively related to water temperature (t-value = -4.387, p = 0.001), and weaklier and negatively related to day length (t-value = -2.983, p < 0.01) (Table 2). For egg quality, as evaluated through the proportion of clear eggs, there was a positive but relatively weak relationship with day length (t-value = 3.126, p < 0.01), but not with rainfall or water temperature.

Discussion

In the present study, giant gourami clearly reproduced all year round in the ponds at the BPPSIGN Tasikmalaya Center. No clear seasonal rhythm was revealed in the spawning frequency of broodfish, which was not related to concurrent variations in rainfall, water temperature or day length. Although the spawning activity of the giant gourami is often considered as continuous all year round [START_REF] Bhimachar | Observations on the acclimatization, nesting habits and early development of Osphronemus gorami (Lacepède)[END_REF], seasonal variations in the spawning frequency have been noted, depending on the region or authors [START_REF] Arfah | Induced spawning of giant gourami Osphronemus gouramy Lac. by Ovaprim[END_REF][START_REF] Bhimachar | Observations on the acclimatization, nesting habits and early development of Osphronemus gorami (Lacepède)[END_REF][START_REF] Wijayanti | Reproductive hormone profiles and gametogenegis in female giant gourami (Osphronemus gouramy) (in Indonesian)[END_REF], but relationships between these variations and environmental variables were not documented. In a recent study performed in the West Java Province, targeted questionnaires and interviews also highlighted that fish farmers from Bogor districts report seasonal variation in the reproductive intensity of their giant gourami broodfish, with rain events (possibly together with associated variation in water temperature) leading to a reduction in spawning frequency [START_REF] Kristanto | Egg and fry production of giant gourami (Osphronemus goramy): Rearing practices and recommendations for future research[END_REF]. In the same study, farmers from the Tasikmalaya district observed no clear seasonality in giant gourami spawning activity, which the present investigation confirms. In contrast to spawning frequency, the number of eggs collected from the nests were strongly related to environmental factors; it was positively related to rainfall, intermediately and negatively related to water temperature and weakly, and negatively related to day length. To our knowledge, such temporal variation in egg number and their strong relationship with rainfall and water temperature has not been reported previously in the giant gourami. However, seasonal variation in fecundity is known to occur in several tropical species reproducing all year round. In the African catfish Heterobranchus longifilis, maximal egg production is observed during the rainy season, whereas in the lagoon tilapias Sarotherodon melanotheron and Tilapia guineensis, fecundity is highest during the hot, dry season [START_REF] Legendre | Aquaculture potentialities of cichlids (Sarotherodon melanotheron, Tilapia guineensis) and clariids (Heterobranchus longifilis) autochthonous from lagoons of Ivory Coast (in French)[END_REF]. In Oreochromis niloticus, the peak of fecundity corresponds with maximum resource availability and flooding imminence [START_REF] Duponchelle | Variations in fecundity and egg size of female Nile tilapia, Oreochromis niloticus, populations from man-made lakes of Côte d'Ivoire[END_REF]. Tropical fish species are generally very plastic and can allocate resources to reproduction according to rainfall regimes [START_REF] Chellappa | Reproductive seasonality of the fish fauna and limnoecology of semi-arid Brazilian reservoirs[END_REF]. In the present study, the giant gourami egg quality was positively, although weakly, related to day length. [START_REF] Prayogo | Identification and expression of vitellogenin gene in the gouramy (Osphronemous gouramy) under photoperiod manipulation[END_REF] claimed that experimentally controlled long photoperiods (18L-6D) have a positive effect on the expression levels of vitellogenin genes. It is well known that fish vitellogenins are critical for providing an adequate nutritional reserve for embryonic development and are also involved in other complex functions that influence egg quality [START_REF] Reading | Oogenesis and egg quality in finfish: Yolk formation and other factors influencing female fertility[END_REF]. Nevertheless, further studies are needed to better understand the mechanisms underlying the positive influence of day length observed here on giant gourami egg quality.

As a whole, the present study provides the first detailed long-term investigation on the seasonal variation of the spawning performance of captive giant gourami. We found no clear spawning rhythms in this species in the environmental conditions of the Tasikmalaya area. On the same location and using identical rearing procedures, it was observed that a same female spawns in average every 5 months and that spawning frequency was strongly influenced by broodfish sexratio [START_REF] Arifin | New insights into giant gourami (Osphronemus goramy) reproductive biology and egg production control[END_REF]. In Tasikmalaya ponds, fluctuations of environmental parameters were limited (particularly temperature) and, as a matter of fact, remained during the whole study in a range favorable to giant gourami gametogenesis and spawning. Nevertheless, in other areas, several studies (op. cit.) reported the occurrence of seasonal variation in giant gourami reproduction, probably as a consequence of a locally less stable environment. Further investigation conducted in such area with the same methodology as in the present study would provide complementary view on the environmental control of giant gourami reproductive phenology. By contrast to spawning frequency, the number of eggs per spawn showed greater sensitivity to environmental changes and was strongly related to variations of environmental variables (particularly rainfall and, to a lesser extent, water temperature and day length). Egg quality was also affected by day length. These findings should be taken into consideration when establishing egg production plans in commercial hatcheries. For instance, egg production periods of 6-7 months separated by resting/reconditioning periods of 1 month are recommended in the management of giant gourami spawning ponds [START_REF] Arifin | New insights into giant gourami (Osphronemus goramy) reproductive biology and egg production control[END_REF]. As far as possible, it is therefore recommended for optimizing egg production to synchronize the broodfish resting/reconditioning periods with the periods of the year during which rainfall and broodfish fecundity are at their lowest.

Captions to figure

Figure 1 .

 1 Figure 1. Mean monthly variation in environmental variables (A) and egg production

Figure 1

 1 Figure 1 364

Acknowledgements

The authors acknowledge Maman Sudirman and the technicians of the West Java Center for the Development of Giant Gourami Culture (BPPSIGN) for sharing their experience and for their assistance throughout this study. This is a publication ISEM no. XXX-XXX.