R A Motiyenko
email: roman.motiyenko@univ-lille.fr

V V Ilyushin

J Demaison

N Vogt

L Margulès

H Møllendal F

J.-C Guillemin

Dr Jon T Hougen

The Rotational Spectrum of Methylarsine $

Keywords: Investigation V. V. Ilyushin : Formal analysis, Validation J. Demaison : Conceptualization, Formal analysis N. Vogt: Formal analysis, L. Margulès: Investigation, H. Møllendal: Investigation, J.-C. Guillemin : Conceptualization, Investigation Methylarsine, torsional large amplitude motion, microwave spectrum, quadrupole hyperfine structure

Accurate quantum chemical calculations of the equilibrium structure of CH 3 AsH 2 A case study of a molecule with torsional LAM and relatively strong quadrupole coupling Analysis of the ground, first, and second excited torsional states of CH 3 AsH 2 1

Introduction

Methylarsine, CH 3 AsH 2 , is an extremely poisonous gas (b.p. 2 • C) with an intense garlic odour. Its pyrolysis at 300 • C generates As, CH 4 , and H 2 . It is found in some lakes because of arsenic methylation by bacterial cultures and by lake sediments [START_REF] Braman | Methylated forms of arsenic in the environment[END_REF]. Methylarsine was also identified as a decomposition product of arsine in the presence of trimethylgallium in the studies of metal-organic chemical vapour deposition growth processes [START_REF] Armstrong | The pyrolysis of precursors for GaAs MOCVD studied by in-situ and ex-situ Fourier transform infrared spectroscopy[END_REF].

From a spectroscopic point of view, methylarsine is an interesting case for studying the methyl top internal rotation in a molecule with a relatively strong nuclear quadrupole coupling. Due to nonzero quadrupole moment of 75 As, the quadrupole hyperfine splittings in methylarsine may be of the order of several tens of MHz. Furthermore, this molecule is a near-symmetric top (A = 65 GHz, B -C = 40.4 MHz, κ = -0.9986) and, for this reason, the asymmetry splittings for many low K energy levels may have the same order of magnitude as the quadrupole splittings. In addition, we have torsional splittings due to hindered internal rotation of the methyl top in CH 3 AsH 2 . Despite a rather heavy AsH 2 frame, in this molecule, the internal rotation is characterized by a rather large coupling between internal and overall rotations. The coupling is usually defined by the absolute value of the so-called ρ vector. The components of the ρ vector are calculated using the following expression: ρ g = (λ g I α /I g ), (g = a, b, c), where λ g are the direction cosines of the internal rotation axis of the top in the principal axis system, I g are the principal inertia moments and I α is the inertia moment of the methyl top. In methylarsine, the internal rotation axis of the methyl top practically coincides with the principal axis a thus λ a ≈ 1.0, λ c ≈ 0.0 (λ b = 0.0 by symmetry). In addition, despite the presence of a rather heavy 75 As atom, I a is relatively small since 75 As atom almost lies at the principal axis a and contributes only slightly to the I a moment of inertia. The combination of these two factors gives a rather large value of ρ = 0.413. Thus, we have an interesting case of interplay of different splittings in a molecule with a rather large coupling between internal and overall rotations.

Very few spectroscopic studies have been devoted to methylarsine. There is a dissertation submitted in August 1973 by D. M. Levine at the Pennsylvania State University which is devoted to the methylarsine microwave spectrum measured with a Stark spectrometer in the range 17 -40 GHz [START_REF] Levine | The microwave spectra of methylarsine and dimethylarsine[END_REF]. The rotational constants, the nuclear quadrupole coupling constants due to 75 As and an approximate value for the barrier height for internal rotation of the methyl group were determined. Also, the a-component of the dipole moment was determined by Stark measurements, µ a = 0.84(5) D. To the best of our knowledge this work has not been published in any peer-reviewed journal. The infrared spectrum of methylarsine has been studied at low resolution by Harvey and Wilson [START_REF] Harvey | Vibrational spectrum of methyl arsine[END_REF] who managed to determine a force field and measure the torsional vibration frequency.

In this paper, we present the results of our study of the torsion-rotational spectrum of methylarsine. The new measurements of the methylarsine spectrum were done up to 652 GHz and transitions belonging to the ground, first, and second excited torsional states were involved in the analysis. The analysis was done using the rho-axis-method (RAM) Hamiltonian, which takes into account quadrupole coupling in the first order of perturbation treatment as realized in the RAM36hf code (see Section 3.2). Previously, the RAM36hf code was successfully applied to the analysis of the rotational spectra of N-methylformamide [START_REF] Belloche | Rotational spectroscopy, tentative interstellar detection, and chemical modeling of N-methylformamide[END_REF] and nitromethane [START_REF] Ilyushin | Millimeter wave spectrum of nitromethane[END_REF], molecules with correspondingly 3-and 6-fold barriers to internal rotation. In these two studies, the hyperfine interaction due to the non-zero nuclear electric quadrupole moment Q of the nitrogen atom was treated but it is much weaker than the corresponding electric quadrupole moment Q in methylarsine. Thus, methylarsine may be considered as a more interesting benchmark molecule for testing the RAM36hf code.

Experiment

Synthesis

Caution. Methylarsine is a pyrophoric and toxic compound; all preparations and handling must be carried out in a well ventilated hood. Dichloromethylarsine (3.2 g, 20 mmol) was slowly introduced under nitrogen in a 250 mL flask partially immersed in a bath cooled at -35 • C and containing LAH (0.76 g, 20 mmol) in tetraglyme (50 mL). At the end of the addition, the mixture was stirred for 15 min at -35 • C and the flask was fitted to a vacuum line equipped with two traps. The first trap was immersed in a bath cooled at -50 • C to remove high boiling impurities and the second one at -196 • C to trap methylarsine. Methylarsine was obtained in pure form in a 45% yield (0.83 g).

Spectroscopy

The measurements of the rotational spectrum of methylarsine in the frequency range 10 to 80 GHz were performed using the Stark-modulated spectrometer of the University of Oslo [START_REF] Samdal | Microwave Spectrum and Conformational Properties of 4-Isocyano-1-butene (H 2 CCHCH 2 CH 2 NC)[END_REF]. The spectrum was In the frequency range 150 to 660 GHz, the spectrum of methylarsine was recorded using the Lille spectrometer [START_REF] Zakharenko | Terahertz spectroscopy of deuterated formaldehyde using a frequency multiplication chain[END_REF], equipped with a fast-scan mode [START_REF] Motiyenko | Rotational spectroscopy of malononitrile and its corresponding monoisocyanide isomer, isocyanoacetonitrile[END_REF]. The measurements were performed in a static mode, in which the absorption cell was filled with the sample every 4 hours at typical pressure of 25 -30 µbar. In the case of the Lille measurements, the measurement accuracy for a strong isolated line was estimated to be 0.05 MHz. This value is somewhat worse compared with the typical measurement accuracy of 0.03 MHz and is chosen to take into account the partially resolved or unresolved hyperfine and internal rotation splittings that may lead to a broadening or a deformation of the lineshape even for a strong isolated line.

Analysis

Quantum chemical calculations

The structure calculations were carried out at the correlated levels of second-order Møller-Plesset perturbation theory (MP2) [START_REF] Møller | Note on an approximation treatment for many-electron systems[END_REF] and coupled-cluster theory with single and double excitations [START_REF] Purvis | A full coupled-cluster singles and doubles model: The inclusion of disconnected triples[END_REF] augmented by a perturbational estimate of the effects of connected triple excitations (CCSD(T)) [START_REF] Raghavachari | A fifth-order perturbation comparison of electron correlation theories[END_REF]. The cc-pwCnZ-PP (n = T, Q, 5) basis sets were used [START_REF] Peterson | Systematically convergent basis sets with relativistic pseudopotentials. I. Correlation consistent basis sets for the post-d group 13-15 elements[END_REF] all electrons being correlated (AE). The CCSD(T) calculations were performed with the MOLPRO program [START_REF] Werner | Molpro: a general-purpose quantum chemistry program package[END_REF][START_REF] Werner | version 2019.2, a package of ab initio programs[END_REF] and the MP2 calculations with Gaussian 09, Revision D.01 [START_REF] Frisch | Gaussian 09 Revision D.01[END_REF].

Table 1 shows the equilibrium geometries computed at different levels of theory. Improvement of the basis from cc-pwCVTZ-PP to cc-pwCVQZ-PP leads to very small changes of the structural parameters except for the C-As bond length which is shortened by as much as 0.004 Å. Therefore, the question arises whether the computed geometrical parameters of CH 3 AsH 2 are already converged when using the cc-pwCVQZ-PP. For this reason, the structural effects of further basis set improvement (cc-pwCVQZ-PP → cc-pwCV5Z-PP) were also investigated. As the changes are expected to be small, the corrections were estimated at the MP2 level. The decrease for the C-As bond length is small, 0.0007 Å whereas the other parameters are not significantly affected. However, it is known that at the CCSD(T) AE level of theory with a quadruple zeta basis set, the cancellation of errors is optimum. This is no longer true for a larger basis set. To check this point, we have compared the rotational constants computed with the ab initio structure with the semiexperimental equilibrium ones. For this goal, the cubic force field has been calculated at two different levels of theory: the B3LYP method [START_REF] Lee | Development of the Colle-Salvetti conelation energy formula into a functional of the electron density[END_REF] with the pc3 basis set [START_REF] Jensen ; Ca | Polarization consistent basis sets. VII. The elements K[END_REF] and the MP2 FC method with the SDB-cc-pVTZ basis set [START_REF] Martin | Correlation consistent valence basis sets for use with the Stuttgart-Dresden-Bonn relativistic effective core potentials: The atoms Ga-Kr and In-Xe[END_REF]. FC meaning that the frozen core approximation is used. The choice of this second method is justified by the fact that it delivers structures close to equilibrium values [START_REF] Császár | Anharmonic molecular force fields[END_REF]. The derived rovibrational corrections are (in MHz): B e -B 0 = 83.08 , C e -C 0 = 82.82 at the MP2 FC/SDB-cc-pVTZ level and B e -B 0 = 83.81 , C e -C 0 = 83.19 at the B3LYP/pc3 level, respectively. As the A rotational constant is much larger, its rovibrational correction is proportionally larger, and the agreement between different levels of theory is worse: A e -A 0 = 618.9 MHz at the MP2 FC/SDB-cc-pVTZ level and A e -A 0 = 524.4 MHz at the B3LYP/pc3 level (the A/B ratio is about 7.4 in CH 3 AsH 2 ). The two force fields give compatible values for B e -B 0 and C e -C 0 giving us confidence that they are reliable. It allows us to estimate the semiexperimental equilibrium rotational constants B e and C e . Assuming that the CCSD(T) AE/wCVQZ-PP structure is accurate except for the C-As bond length, it is possible to estimate this bond length by comparing the semiexperimental equilibrium rotational constants with the computed ones. Both B e and C e yield exactly the same value for r e (C-As) = 1.9686 Å. It is still possible to improve this value by applying an offset correction for the As-H bond length which may be obtained by comparing the ab initio and experimentally determined equilibrium values for r(As-H) in AsH 3 [START_REF] Ulenikov | High-resolution infrared study of the ν 1 and ν 3 bands, and the equilibrium structure of AsD 3[END_REF]. The structure of AsH 3 computed at the CCSD(T) AE/pwCVQZ-PP level gives r(As-H) = 1.5092 Å whereas the experimental equilibrium value is 1.51130( 16) Å [START_REF] Ulenikov | High-resolution infrared study of the ν 1 and ν 3 bands, and the equilibrium structure of AsD 3[END_REF]. In other words, the CCSD(T) AE/pwCVQZ-PP value for As-H is too short by 0.0021 Å. In this particular case, the "offset" method gives reliable results because the As-H bond length in both molecules (AsH 3 and CH 3 AsH 2 ) is quite similar as confirmed by using the Atom In Molecule (AIM) theory [START_REF] Bader | Atoms in molecules: A quantum theory[END_REF], see Appendix. Taking this small offset into account, it gives for CH 3 AsH 2 r(As-H) = 1.5136 Å. Using this improved value of r(As-H), both B e and C e give 1.967 Å, confirming the hypothesis that it is better not to take into account the correction cc-pwCVQZ-PP → cc-pwCV5Z-PP.

For the prediction of the ground state rotational constants and torsional parameters, we retained the MP2/SDB-cc-pVTZ as well as DFT M06-2X/pc-4 method/basis set combinations. The M06-2X method [START_REF] Zhao | The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals[END_REF] has previously been shown to provide relatively highly accurate results when compared with the experimental values [START_REF] Motiyenko | Laboratory spectroscopy of methoxymethanol in the millimeterwave range[END_REF] while demanding much less computational effort. In terms of rotational constants, the M06-2X/pc-4 calculation is the most satisfactory but only the MP2/SDB-cc-pVTZ [START_REF] Demaison | Equilibrium CAs and CSb bond lengths[END_REF] method in the frozen core approximation gives a geometry very close to the equilibrium structure. This behavior was previously noticed [START_REF] Demaison | Equilibrium CAs and CSb bond lengths[END_REF] and might be useful to calculate reliable structures of arsenic derivatives.

Theoretical model

The Hamiltonian used in the present work is the so-called RAM torsion-rotation Hamiltonian based on the works [START_REF] Kirtman | Interactions between ordinary vibrations and hindered internal rotation. I. Rotational energies[END_REF], [START_REF] Lees | Torsion-vibration-rotation interactions in methanol. I. Millimeter wave spectrum[END_REF], and [START_REF] Herbst | A new analysis and additional measurements of the millimeter and submillimeter spectrum of methanol[END_REF], which has proved its effectiveness for a number of molecules containing the C 3v rotor and C s , C 2v , or C 1 molecular frames. In the current study we employ the RAM36 (rhoaxis-method for 3 and 6-fold barriers) code that realizes the RAM approach for molecules with a C 3v top attached to a molecular frame of C s or C 2v symmetry and having a 3-or 6-fold barrier to internal rotation, respectively [START_REF] Ilyushin | A new torsion-rotation fitting program for molecules with a sixfold barrier: Application to the microwave spectrum of toluene[END_REF][START_REF] Ilyushin | Submillimeter wave spectrum of acetic acid[END_REF]. This code was successfully applied to molecules such as acetaldehyde [START_REF] Smirnov | Spectroscopy of the ground, first and second excited torsional states of acetaldehyde from 0[END_REF] and methyl mercaptan [START_REF] Zakharenko | Rotational spectroscopy of methyl mercaptan CH 32 3 SH at millimeter and submillimeter wavelengths[END_REF] which like methylarsine are characterized by a rather large coupling between internal and overall rotations (ρ = 0.329 for CH 3 CHO, ρ = 0.652 for CH 3 SH). A general expression for the RAM Hamiltonian implemented in the RAM36 code takes the following form:

H = 1 2 knpqrs B knpqrs0 J 2k J n z J p x J q y p r α cos(3sα) + cos(3sα)p r α J q y J p x J n z J 2k + 1 2 knpqrt B knpqr0t J 2k J n z J p x J q y p r α sin(3tα) + sin(3tα)p r α J q y J p x J n z J 2k (1)
where the B knpqrst are fitting parameters. In the case of a C 3v top and C s frame (as is appropriate for methylarsine), the allowed terms in the torsion-rotation Hamiltonian must be totally symmetric in the group G 6 (and also must be Hermitian and invariant to the time reversal operation).

To take the quadrupole hyperfine structure into account, we use a modified version of RAM36, which we call here RAM36hf, that allows us to fit together individual hyperfine components as well as torsion-rotation transitions with an unresolved hyperfine structure. Previously, the RAM36hf code was successfully applied to the analysis of the rotational spectrum of N-methylformamide [START_REF] Belloche | Rotational spectroscopy, tentative interstellar detection, and chemical modeling of N-methylformamide[END_REF] and nitromethane [START_REF] Ilyushin | Millimeter wave spectrum of nitromethane[END_REF]. In the RAM36hf code the standard hyperfine energy expression is used:

E hf = χ aa J 2 a + χ cc J 2 c -(χ aa + χ cc ) J 2 b + χ ac J a J c + J c J a 2f (I, J, F ) J(J + 1)
where f (I, J, F ) is the Casimir function. In RAM36hf, the hyperfine structure and the fine torsion-rotation structure of the spectrum are treated simultaneously, in contrast to the approach applied in some other studies where hyperfine shifts are removed and hypothetical hyperfine free transition frequencies are fit using theoretical models that only take large amplitude motions in the molecule into account (as for example acetamide [START_REF] Suenram | Reinvestigation of the microwave spectrum of acetamide[END_REF][START_REF] Ilyushin | Ground and first excited torsional states of acetamide[END_REF] or methylamine [START_REF] Ilyushin | The rotational spectrum of the ground state of methylamine[END_REF][START_REF] Motiyenko | Rotational spectroscopy of methylamine up to 2.6 THz[END_REF]).

Assignment and fit

Methylarsine is a prolate asymmetric top molecule close to the symmetric top limit. For a C s symmetry molecule, the RAM36hf code defines the symmetry plane as the zx plane (molecule fixed-axis system). In the case of methylarsine, the symmetry plane is defined as the ac plane (principal axis system). Therefore, in this study the molecular Hamiltonian was established in a rather unusual I l coordinate representation: z = a, x = c, and y = b.

We started the assignment with the cm-wave spectra where the transition 1 0,1 ← 0 0,0 in the ground vibrational state was easily located around 17.6 GHz on the basis of the predictions obtained from quantum chemical calculations. In the vicinity of the ground state transition, we also assigned the transition of the first excited torsional state which is characterized by a larger torsional A -E splitting and a lower intensity owing to the lower Boltzmann factor. In the next step, we assigned a series of a-type transitions with J = 2 ← 1, 3 ← 2, and 4 ← 3. The initial fit of these transitions allowed us to make predictions which were good enough to continue the assignment. The assignment was continued in the classical bootstrap manner, where newly assigned transitions were used to improve the frequency predictions and search for new ones.

In total, we assigned 2473 distinct frequency lines corresponding to 4158 transitions of the ground, first, and second excited torsional states with the J quantum number up to 50. In addition to a-type transitions, we also assigned c-type transitions owing to non-zero µ c dipole moment component. In general, the calculation of the dipole moment using different methods (MP2, B3LYP, MO62X) and different basis sets (wCV5Z-PP, pc3, pc4) gives consistent results with 0.84 ≤ µ a ≤ 0.88 D (in agreement with ref. [START_REF] Levine | The microwave spectra of methylarsine and dimethylarsine[END_REF]) and 0.22 ≤ µ c ≤ 0.32 D. The µ b dipole moment component is set to zero due to molecular symmetry. The assigned transitions were fitted using the RAM36hf code to the RAM Hamiltonian model containing 45 parameters plus 3 quadrupole hyperfine parameters χ aa , χ cc and off-diagonal χ ac . A fit achieving a unitless rms deviation of 0.92 was obtained. The final set of molecular parameters is presented in Table 2. The numbers of terms in the model distributed between the n op = 2, 4, 6, 8 orders of the operators are equal to or less than the total numbers of determinable parameters for those orders, as calculated according the ordering scheme of [START_REF] Nakagawa | Effective torsion-rotation hamiltonian for methanol-type molecules[END_REF]. We note in passing that the ordering scheme of [START_REF] Nakagawa | Effective torsion-rotation hamiltonian for methanol-type molecules[END_REF] assumes that cos(3nα) and sin(3nα) are regarded as 2n th -order terms, whereas (p α ) n and (J i ) n (i = x, y, z) are regarded as n th -order terms. There were no problems with convergence observed for the final fit. The full dataset of the assigned rotational transitions of methylarsine is available as a Supplementary material. The table provided in Supplementary material includes for each transition: assignment, measured (observed) frequency and its uncertainty, calculated frequency and its uncertainty, as well as 'obs-calc' difference obtained in the final fit.

A portion of the rotational spectrum of methylarsine predicted using the final set of molecular parameters is shown on Fig. 1 where it is compared with the experimental spectrum. The overall correspondence between the experimental and theoretical spectra is good. The strongest lines are well predicted by our current model, although one can also find several relatively strong unassigned lines around 245 GHz. These lines correspond to rotational transitions of the third excited torsional state that are predicted by our model sufficiently well to be assigned. However they are not included in the current fit, as we suppose that the v t = 3 state may be subjected to a downward propagation of a perturbation of the ν 9 mode, which is located in vicinity of a n = t + r, where n is the total order of the operator, t is the order of the torsional part and r is the order of the rotational part, respectively. b Parameter nomenclature based on the subscript procedures of Ref. [START_REF] Xu | Torsion-rotation global analysis of the first three torsional states (vt= 0, 1, 2) and terahertz database for methanol[END_REF]. c {A, B} = AB + BA. The product of the operator in the third column of a given row and the parameter in the second column of that row gives the term actually used in the torsion-rotation Hamiltonian of the program, except for F , ρ and ARAM , which occur in the Hamiltonian in the form F (pα -ρJz) 2 + ARAM J 2 z . d All values are in cm -1 (except ρ which is unitless). Statistical uncertainties are shown as one standard uncertainty in the units of the last two digits. the v t = 4 torsional excited state. Such type of perturbation propagation was previously observed in the case of methyl mercaptan [START_REF] Zakharenko | Rotational spectroscopy of methyl mercaptan CH 32 3 SH at millimeter and submillimeter wavelengths[END_REF]. An example of comparison of the observed and predicted spectra at a finer scale is shown on Fig. 2. Owing to the hyperfine structure and internal rotation, the spectrum contains a set of multiple components many of which are not resolved in the Doppler resolution mode of the spectrometer. A combination of resolved and unresolved components may form rather complex multiplets that depend on the interplay of quadrupole, asymmetry and torsional splittings in the spectrum. As was already mentioned above, the asymmetry splittings for some energy levels in methylarsine may have the same order of magnitude as the quadrupole splittings, that could affect the first order perturbation treatment of the hyperfine energies.

Nevertheless, there were no 'anomalous' hyperfine splittings (i.e. deviating from the current model) observed in this study. It is seen that the final set of molecular parameters predicts well the experimental spectrum reported on Fig. 2.

Discussion

Internal rotation and centrifugal distortion parameters

Table 3 presents a comparison of rotational, quartic centrifugal distortion, torsion, and quadrupole coupling parameters of methylarsine obtained from the RAM36hf fit and from quantum chemical calculations. Frequency (MHz) As one can see, a good agreement is observed for all parameters except for two centrifugal distortion constants D JK and D K . Initially we thought that this discrepancy is the consequence of the way the coupling of internal and overall rotations is treated in the RAM36 code. According footnote 'c' of Table 2 the second order parameters F , ρ and A RAM occur in the Hamiltonian in the form

F (p α -ρJ z ) 2 + A RAM J 2 z . The F (p α -ρJ z ) 2 +A RAM J 2
z part of the Hamiltonian may be regrouped (as it was done for example in Ref. [START_REF] Ilyushin | A new torsion-rotation fitting program for molecules with a sixfold barrier: Application to the microwave spectrum of toluene[END_REF] to reduce a correlation between main parameters) as

F (p α ) 2 -2F ρp α J z +A ef f J 2
z , where A ef f = A RAM +F (ρ) 2 and F (ρ) 2 is a modification of the rotational constant A due to internal rotation. The F (ρ) 2 modification is negligible when the ρ value is small, but is very significant (1.52 cm -1 ) in methylarsine where the ρ value is rather large (0.413). In the RAM36 code, the mixed internal angular momentum expression p α -ρJ z which brings together the coupling between internal and overall rotation is used only in the second order of the RAM Hamiltonian. This gives an unbiased A rotational constant which can be compared to the ab initio value after transforming from RAM to PAM axis system (and we see in Table 3 a rather good agreement for this constant). For the higher orders of the RAM Hamiltonian (fourth, six etc.), RAM36 does not allow at the moment a mixed angular momentum expression p α -ρJ z and all corresponding terms only contain powers of the internal rotation angular momentum p α . Thus, we expected some modifications of the values of centrifugal distortion parameters caused by the fact that the coupling between internal and overall rotations is not represented explicitly in the 4th, 6th etc. orders of torsion-rotation RAM Hamiltonian terms.

One may think that a way to estimate these modifications of the centrifugal distortion parameters due to the non-explicit way of representing the coupling between internal and overall rotations at higher orders of the RAM Hamiltonian would be to replace p α by the mixed internal angular momentum expression p α -ρJ z in the RAM Hamiltonian of Table 2, and after raising to corresponding powers and opening brackets collect those terms which will contribute to D K , D JK etc. as it was done above for the A rotational constant.

In our case, this would mean that from the available Hamiltonian terms of Table 2 we need to take the contributions due to ρ K , ρ m , F K into account in the case of D K , and F J , ρ J in the case of D JK . In practice, this procedure does not work because the replacement of p α by the mixed internal angular momentum expression p α -ρJ z led to a significant change in the values of all parameters of corresponding order. If we consider for example the F m term (not present in the model of Table 2), and replace (p α ) 4 by (p α -ρJ z ) 4 with further expanding the obtained expression we will see that the transformed F m term in addition to (p α ) 4 term itself also contains p 3 α J z , p 2 α J 2 z , p α J 3 z , and J 4 z terms which are related to the ρ m , F K , ρ K , and D K parameters of the original model of Table 2:

H (m) TR,mixed = F * m p 4 α -4ρp 3 α J z + 6ρ 2 p 2 α J 2 z -4ρ 3 p α J 3 z + ρ 4 J 4 z (2)
Similarly, if we perform the same procedure of replacing p a by p a -ρJ z for F J , F K terms we will see that after the transformation they will contain terms not only related to the D JK , D K parameters but also to the ρ J , and ρ K parameters:

H (J) TR,mixed = F * J p 2 α J 2 -2ρp α J z J 2 + ρ 2 J 2 z J 2 (3)
H (K) TR,mixed = F * K p 2 α J 2 z -2ρp α J 3 z + ρ 2 J 4 z (4)
Because of this interconnection between different terms, the calculation of the modifications of centrifugal distortion parameters due to the coupling of internal and overall rotations based on the parameter values of Table 2 is not that straightforward.

A way to get an estimate of the centrifugal distortion constants unbiased by the torsion-rotation coupling would be to perform a fit with p α replaced by the mixed internal angular momentum expression p α -ρJ z in all 4th order terms containing p α . Unfortunately, at the moment the RAM36 code does allow such fit. What we can try to do is to represent the terms with mixed internal angular momentum expressions by a linear combination of terms allowed by RAM36, i.e. implement equations Eqs. 3-4 as a linear combination of terms with fixed ratio coefficients calculated from the current ρ value. The coefficients in front of these linear combinations i.e. F * J , F * K , etc. will be varied by RAM36 whereas the ratios inside these combinations (which depend on different powers of ρ) will be fixed. The star symbol is used here to distinguish between the parameters of the operators in Table 2, and the parameters of the linear combination terms of Eqs. 3-4. When trying to determine the D JK and D K constants without torsional contribution, we performed a new least-squares fit in which we replaced all 4th order parameters containing p α namely F J , F K , F bc , ρ J , ρ K , ρ bc , and ρ m , from the Hamiltonian model of Table 2 by a group of terms F * J , F * K , etc. representing expressions analogous to Eqs. 3-4. In this case we got practically the same rms deviation of the fit, but the values of 4th order torsion-rotation centrifugal distortion parameters are changed, redistributing contributions to energy levels between new versions of the terms. As a result of such a redistribution we got a much better agreement for the D JK parameter (transformed value 39.6708(24) kHz) but for the D K parameter the deviation from the quantum chemical calculations value became much larger (the transformed value of 72082.(34) kHz instead of 1269.9 kHz of Table 2 with quantum chemical calculations value being 202.49 kHz). Such a large discrepancy cannot be explained by the rotation from the RAM to PAM axis systems since the angle between those two systems is only 0.17 degree and even for the A rotation constant the correction due to rotation from RAM to PAM is only 0.5 MHz or 7.7 × 10 -4 %.

Two possible explanations may be considered. The first one is connected to some strong intervibrational interaction with a low lying nontorsional mode. This perturbation may propagate through intertorsional interactions down to the torsional states considered in this study and may be absorbed in part by the F K , ρ K , and D K parameters (namely replacing p α by p α -ρJ z in the F K , ρ K terms causes this huge increase in the D K value when we try to take explicitly into account the contribution from the torsion-rotation coupling). The second possible explanation is connected to the reduction scheme of the Hamiltonian, which we effectively adopt by keeping one set or the other one of the RAM Hamiltonian parameters. According to the ordering scheme of [START_REF] Nakagawa | Effective torsion-rotation hamiltonian for methanol-type molecules[END_REF] we can have 22 parameters for the 4th order RAM Hamiltonian as calculated from the difference between the total number of symmetry-allowed Hamiltonian terms of 4th order [START_REF] Suenram | Reinvestigation of the microwave spectrum of acetamide[END_REF] and the number of symmetry-allowed contact transformation terms of 3rd order [START_REF] Purvis | A full coupled-cluster singles and doubles model: The inclusion of disconnected triples[END_REF]. The problems may appear if one tries to eliminate one term with a relatively large magnitude (as calculated from the molecular force field), keeping another term of relatively small magnitude. Then, a contribution to the energy from the eliminated 'large' term should be somehow redistributed among other terms. If by misfortune, at the beginning of our fitting process for the methylarsine spectrum, we don't include some important term whose contribution is then effectively redistributed between other terms of 4th and higher orders, we may believe that this term is insignificant (since we have a compensation of its contribution from other terms) but the values of some other parameters appear to be biased. Considerable work should be done before we will be able to check both these explanations of the discrepancy of D K value.

Tunneling barriers

Using the V 3 , V 6 , and V 9 terms of the potential energy function from Table 2, the estimated value of the barrier to internal rotation in methylarsine is 513.84 cm -1 . It is somewhat higher compared to the value obtained from the M06-2X/pc-4 calculations in Table 3 indicating that while this method/basis set combination gives excellent consistency for the experimental rotational constants, it is less suited for torsional barrier height estimation in the case of methylarsine. At the same time, the obtained experimental value of the barrier height is in excellent agreement with the theoretical value of 518.3 cm -1 obtained by Kim et al. [START_REF] Kim | Infrared spectra prediction and potential energy surface studies of methylarsine and methylstibine[END_REF] using a fitted potential energy surface generated from the optimized geometries of methylarsine. Moreover, in the present study, the estimated energies of the 0 0,0 rotational levels of A and E symmetry of the v t = 1 state are respectively 181.1 cm -1 and 179.4 cm -1 . These values are also in agreement with the frequency of the torsional mode of 185 cm -1 measured in the low-resolution IR spectrum of methylarsine by Harvey and Wilson [START_REF] Harvey | Vibrational spectrum of methyl arsine[END_REF], and determined by the theoretical calculations by Kim et al. [START_REF] Kim | Infrared spectra prediction and potential energy surface studies of methylarsine and methylstibine[END_REF]. In ref. [START_REF] Kim | Infrared spectra prediction and potential energy surface studies of methylarsine and methylstibine[END_REF], torsion barrier and inversion barrier of the first and second-order for the CH 3 XH 2 (X = N, P, As, Sb) molecules are compared. In particular, in ref. [START_REF] Kim | Infrared spectra prediction and potential energy surface studies of methylarsine and methylstibine[END_REF] it is shown that the first and second-order inversion barriers exhibit a rapid increase from CH 3 NH 2 (22.8 and 22.41 kJ/mol respectively) to CH 3 PH 2 (149.88 and 149.65 kJ/mol respectively), CH 3 AsH 2 (170.93 kJ/mol and 170.70 kJ/mol), and CH 3 SbH 2 (204.44 and 204.24 kJ/mol respectively). In contrast, the torsional barriers show only a slight decline from 8.73 for CH 3 NH 2 to 5.53 kJ/mol for CH 3 AsH 2 , and to 3.06 kJ/mol for CH 3 SbH 2 . Therefore, both torsional and inversion splittings were observed in the rotational spectrum of methylamine [START_REF] Motiyenko | Rotational spectroscopy of methylamine up to 2.6 THz[END_REF] but only torsional splittings were observed in the rotational spectra of methylphosphine [START_REF] Halfen | Millimeter/submillimiter spectroscopy of PH 2 CN ( X 1 a ) and CH 3 PH 2 ( X 1 a ): probing the complexity of interstellar phosphorous chemistry[END_REF], and methylarsine (this study). In the latter two cases, owing to high barriers, the inversion splittings are so small that they were not resolved under the Doppler-limited spectral resolution of conventional absorption spectrometers used to record the spectra.

Conclusion

We performed a new study of the methylarsine spectrum in a broad frequency range, from 15 to 660 GHz. The new data for the v t = 0, 1, 2 torsional states involving rotational transitions with J up to 50 were analyzed using the rho-axis-method and a fit within experimental error has been achieved. There were no 'anomalous' hyperfine splittings (i.e. deviating from the current model) observed in this study of methylarsine spectrum, although the asymmetry and quadrupole splittings for some energy levels have the same order of magnitude, that in principle could affect the first order perturbation treatment of the hyperfine energies employed in this study. A comparison of the obtained results with high level ab initio calculations of the quartic centrifugal distortion parameters reveals a significant discrepancy in the value of the D K parameter, which we are not able to explain at the current stage of methylarsine spectrum investigation.

Figure 1 :

 1 Figure 1: Predicted and calculated spectra of CH 3 AsH 2 in the vicinity of the J = 14 ← 13 series of a R 0,1 transitions of vt =0, 1, and 2 states.

Figure 2 :

 2 Figure 2: A portion of a simulated stick spectrum of CH 3 AsH 2 around 228930 MHz with assignments of rotational transitions that contribute to this stick spectrum. Each stick corresponds to a hyperfine component of a torsion-rotation transition. In blue: line profile spectrum simulated using the stick spectrum. In red: experimental spectrum of CH 3 AsH 2 . For interpretation of the references to color in this figure legend the reader is referred to the web version of this article.

Table 1 :

 1 Structure of methylarsine (distances in Å and angles in degrees)

	Method	CCSD(T) AE CCSD(T) AE MP2 AE	MP2 AE	r e	a
	Basis set	pwCVTZ-PP	pwCVQZ-PP pwCVQZ-PP pwCV5Z-PP
	C-As	1.9713	1.9671	1.9548	1.9541	1.9664
	C-H s	1.0856	1.0849	1.0817	1.0814	1.0846
	C-H a	1.0880	1.0873	1.0841	1.0838	1.0870
	As-H	1.5119	1.5115	1.4993	1.4997	1.5119
	H s -C-As	112.294	112.296	112.493	112.459	112.263
	H-As-C	95.657	95.721	95.721	95.725	95.726
	H a -C-As	108.367	108.345	108.248	108.218	108.315
	H s -C-As-H	-46.310	-46.293	-46.296	-46.291	-46.288
	H a -C-As-H s 121.192	121.206	121.294	121.290	121.202
	a CCSD(T) AE/pwCVQZ-PP + MP2 AE/pwCV5Z-PP -MP2 AE/pwCVQZ-PP
	recorded at room temperature, and at a pressure of a few tens of µbar. The measurement accuracy for a
	strong isolated line was estimated to be 0.15 MHz.

Table 2 :

 2 Molecular parameters of methylarsine obtained with the RAM36HF program. ntr a Parameter b Operator c

	Value d

Table 3 :

 3 Comparison of the main rotation, torsion and hyperfine parameters of methylarsine with ab initio results

	Parameter	RAM36HF fit M06-2X/pc-4
	A (MHz)	65221.4	65641.6
	B (MHz)	8840.8	8840.2
	C (MHz)	8800.4	8793.0
	D J (kHz)	8.477	8.151
	D JK (kHz)	134.97	36.29
	D K (kHz)	1269.9	202.6
	d 1 (kHz)	0.05911	0.05591
	d 2 (kHz)	-0.01197	-0.01118
	F (cm -1 )	8.958	9.051
	V 3 (cm -1 )	517.5	482.5
	ρ	0.413	0.409
	χ aa (MHz)	35.4	34.7
	χ cc (MHz)	-117.2	-122.8
	χ ac (MHz)	115.7	119.8

Acknowledgements

Financial support by the Dr. Barbara Mez-Starck Foundation (Germany) is gratefully acknowledged. J.-C.G. thanks the Centre National d'Etudes Spatiales (CNES) for a grant.

Appendix A.

The Atom in Molecules (AIM) theory [START_REF] Bader | Atoms in molecules: A quantum theory[END_REF][START_REF] Gillespie | Chemical bonding and molecular geometry[END_REF] with its implementation in Gaussian by Cioslowski et al. [START_REF] Cioslowski | Rapid evaluation of atomic properties with mixed analytical/numerical integration[END_REF][START_REF] Cioslowski | An observable-based interpretation of electronic wavefunctions: application to "hypervalent" molecules[END_REF][START_REF] Cioslowski | Covalent bond orders in the topological theory of atoms in molecules[END_REF][START_REF] Stefanov | An efficient approach to calculation of zero-flux atomic surfaces and generation of atomic integration data[END_REF][START_REF] Cioslowski | Variational determination of the zero-flux surfaces of atoms in molecules[END_REF][START_REF] Cioslowski | A new robust algorithm for fully automated determination of attractor interaction lines in molecules[END_REF][START_REF] Cioslowski | An efficient evaluation of atomic properties using a vectorized numerical integration with dynamic thresholding[END_REF] was used. The calculations were performed at the B3LYP/6-311+G(2d,2p) level of theory with the equilibrium structure. The following parameters were compared:

The bond critical point density, ρ b , which is a measure of the amount of electron density shared between the two bonded atoms.

The bond ellipticity, . It provides a measure of the extent to which the charge is preferentially accumulated at a given angle in a plane perpendicular to the bond path.

The charges, q, on the atoms.

The strength of a bond increases and its length decreases as the bond critical point density ρ b increases. The increasing charges on the bonded atoms have the same effect.


N Lemire

M Costet

P Lucas

Ayotte

Dr Sylvaine Cordier
email: sylvaine.cordier@inserm.fr

M Lemire

N Costet

Michel Lucas

Pierre Ayotte

Association between exposure to persistent organic pollutants and mercury, and glucose metabolism in two Canadian Indigenous populations

Keywords: Conceptualization, Methodology, Writing -original persistent organic pollutants, mercury, diabetes, glucose, insulin, First Nations, Inuit

Association between exposure to persistent organic pollutants and mercury, and glucose metabolism in two

Canadian Indigenous populations

Introduction

The prevalence of type 2 diabetes mellitus (T2DM) is increasing among Indigenous populations of Canada with a projection of 214% overall increase between 2000 and 2030 [START_REF] Leung | Diabetes mellitus and the Aboriginal diabetic initiative in Canada: An update review[END_REF]. However there are large disparities among Indigenous populations: age-adjusted T2DM prevalence is much higher in First Nations peoples (17.2% when living on reserve; 10.3% off reserve) than in Metis (7.3%) or Inuit (5.0%) (similar to the general Canadian population) (PHAC, 2011). Specific genetic polymorphisms conferring susceptibility to T2DM have been identified among some First Nations populations [START_REF] Hegele | Genes, environment and Oji-Cree type 2 diabetes[END_REF] and Inuit [START_REF] Manousaki | Toward Precision Medicine: TBC1D4 Disruption Is Common Among the Inuit and Leads to Underdiagnosis of Type 2 Diabetes[END_REF]. These genotypes, in combination with lifestyle changes and dietary transition, may partly explain the differences in T2DM prevalence between Indigenous populations. At different periods of time in their history, these populations have faced profound societal changes, as a result of residential schools and other legacies of colonization, resulting in a shift away from traditional lifestyles and diet. Initially composed of local and highly nutritious fish, seafood, marine and terrestrial mammals, wild birds and plants, these are now increasingly replaced by imported nutrient-poor, energy-dense processed foods. Concomitantly, a reduction of the daily level of physical activity has occurred. Both are major risk factors of obesity, which is a major driver of T2DM. Conversely, despite their modest contribution to total energy intake, traditional foods are still an integral part of Indigenous cultures, and continue to largely contribute to diet quality and nutrient intakes [START_REF] Willows | Modelling optimal diets for quality and cost: examples from Inuit and First Nations communities in Canada[END_REF][START_REF] Willows | Modelling optimal diets for quality and cost: examples from Inuit and First Nations communities in Canada[END_REF][START_REF] Batal | A Scoping Review of Obesity among Indigenous Peoples in Canada[END_REF].

Unfortunately, worldwide increase of industrial activity has brought chemical contamination of the environment, bioaccumulation and biomagnification of metals and persistent organic pollutants (POPs) including polychlorinated biphenyls (PCBs) in some freshwater fish and marine species, and ultimately, to an increased body burden of these contaminants in populations that rely on these species for sustenance (AMAP, 2015). Thus, despite the many benefits of traditional foods, some of them can also be a source of exposure to environmental contaminants, especially predatory fish and marine mammals that are at the top of the food chain. Whereas several fish species are often consumed by different Indigenous communities, marine mammals are almost uniquely consumed by Inuit communities [START_REF] Noreen | Factors associated with the intake of traditional foods in the Eeyou Istchee (Cree) of northern Quebec include age, speaking the Cree language and food sovereignty indicators[END_REF][START_REF] Lemire | Local country food sources of methylmercury, selenium and omega-3 fatty acids in Nunavik, Northern Quebec[END_REF]. This translates into a high exposure to mercury and PCBs, but also to elevated intakes of marine food nutrients, such as omega-3 polyunsaturated fatty acids, iron, selenium, iodine and lipophilic vitamins, in Inuit communities (AMAP, 2015;[START_REF] Lemire | Local country food sources of methylmercury, selenium and omega-3 fatty acids in Nunavik, Northern Quebec[END_REF][START_REF] Laird | Dietary advice on Inuit traditional food use needs to balance benefits and risks of mercury, selenium, and n3 fatty acids[END_REF].

Recent reviews have concluded that body burden of several of these contaminants has been associated with an increased risk of T2DM [START_REF] Lee | Chlorinated persistent organic pollutants. obesity. and type 2 diabetes[END_REF][START_REF] Thayer | Role of environmental chemicals in diabetes and obesity: a National Toxicology Program workshop review[END_REF][START_REF] Taylor | Evaluation of the association between persistent organic pollutants (POPs) and diabetes in epidemiological studies: a national toxicology program workshop review[END_REF][START_REF] Roy | Is mercury exposure causing diabetes, metabolic syndrome and insulin resistance? A systematic review of the literature[END_REF]. This contamination could therefore contribute to the rising epidemics of diabetes in several Indigenous populations of Canada. High exposure levels to these contaminants have been reported in several of these communities [START_REF] Liberda | Plasma concentrations of persistent organic pollutants in the Cree of northern Quebec. Canada: results from the multicommunity environment-and-health study[END_REF][START_REF] Donaldson | Environmental contaminants and human health in the Canadian Arctic[END_REF]. The role of this exposure in T2DM onset has been studied, with conflicting results, among Inuit populations in Greenland (Jorgensen et al., 2008;[START_REF] Jeppesen | Association between whole blood mercury and glucose intolerance among adult Inuit in Greenland[END_REF] and Canada (Inuvialuit Settlement Region, Nunavut and Nunatsiavut) [START_REF] Singh | Persistent organic pollutants and diabetes among Inuit in the Canadian Arctic[END_REF], and among First Nations in Manitoba and Ontario [START_REF] Marushka | Association between fish consumption, dietary omega-3 fatty acids and persistent organic pollutants intake, and type 2 diabetes in 18 First Nations in Ontario, Canada[END_REF]. Possible reasons for these discrepancies include different population characteristics such as exposure levels or prevalence of other T2DM risk factors, and different methods used to assess glucose metabolism, environmental exposures and dose-response relationships.

In the present study, we evaluated the associations between POPs and mercury exposure with altered glucose metabolism in two Indigenous populations of Northern Quebec, Canada that exhibit different exposure levels and different genetic backgrounds. Similar methods were used in both populations for assessing exposure to these contaminants and health outcomes.

Methods

Population and data collection

Comprehensive environmental health surveys were conducted between 2004 and 2009 in two Indigenous populations living in Northern Quebec (Inuit of Nunavik, Cree of Eeyou Istchee) using similar protocols. The Qanuippitaa? Nunavik Health Survey was conducted during the summer of 2004 among Inuit adults (aged 18years and over) from 14 Nunavik villages. A clinical and paraclinical exam was organized onboard the Canadian Coast Guard Icebreaker Amundsen. Each individual who agreed to participate in the survey signed a consent form. The study protocol was approved by the ethics committee of Laval University; more details are available in Rochette and Blanchet (2007). The Community consent was obtained through formal resolutions, and all individual participants provided informed written consent. More details about this second study is available in [START_REF] Nieboer | Public Health Report Series 4 on the Health of the Population[END_REF].

The enrolled individuals answered a series of questionnaires documenting lifestyle and dietary habits, and diagnosed health conditions including diabetes. Subsequently, a series of tests and anthropometric measurements (height, weight, waist circumference) were conducted during a clinical session and blood samples were collected for measures of glucose metabolism and biomarkers of exposure to environmental contaminants. Medical records were also reviewed for several health outcomes including diabetes and medication use.

Among the 914 Inuit participants who participated in the clinical session in 2004, 37 were excluded because of missing values on essential variables (disease, glucose), 62 (7.1%) were identified with a diagnosis of diabetes and 815 were considered non-diabetic. Among these 815 a priori non-diabetic participants, 144 were in a non-fasting state and were excluded, leaving 671 participants for which biological measures were performed; 161 of them also underwent an oral glucose tolerance test (OGTT). Out of 881 Cree participants, 101 could not be assessed for diabetic status and 158 had diagnosed diabetes (20.3%). Biological measures were performed for the remaining 599 subjects a priori non-diabetic, in fasting state, with full data on main covariates (only 59 were also submitted to OGTT and data will not be reported).

Diagnosis of T2DM and laboratory analyses

Prevalent T2DM among participants was assessed from previous diagnosis confirmed by medical chart review, or from consumption of antidiabetic drugs as indicated in medical records (more details are given in supplemental file 1).

Fasting plasma insulin (pmol/L) was measured with the chemiluminescent detection immunoassay system (ADVIA Centaur CP Immunoassay system; Bayer HealthCare, Toronto, ON. Canada). Blood glucose (mmol/L) was quantified by a spectrophotometric assay (Vitros 950; Ortho-Clinical Diagnostics) [START_REF] Chateau-Degat | Diabetes and related metabolic conditions in an aboriginal Cree community of Quebec, Canada[END_REF]. All analyses were performed by the Clinical Biochemistry Laboratory of the Centre Hospitalier de l'Université Laval (CHUL), Québec. We used the homeostasis model assessment (HOMA) to assess insulin resistance (HOMA-IR) and pancreatic β-cell function (HOMA-B) [START_REF] Matthews | Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man[END_REF][START_REF] Song | Insulin sensitivity and insulin secretion determined by homeostasis model assessment and risk of diabetes in a multiethnic cohort of women: the Women's Health Initiative Observational Study[END_REF]. The HOMA-IR score was calculated for each

Exposure assessment

We analyzed plasma samples of participants to determine their body burden of the following POPs: 7 polychlorinated biphenyls (PCBs) congeners (IUPAC nos.105, 118, 138, 153, 156, 170 and 180) (NIOSH, 1977;[START_REF] Patterson | Determination of specific polychlorinated dibenzo-p-dioxins and dibenzofurans in blood and adipose tissue by isotope dilution-high-resolution mass spectrometry[END_REF]; 13 organochlorine (OC) pesticides or metabolites (aldrin, ß- and omega-3 polyunsaturated fatty acids (omega-3 PUFAs) were quantified in whole blood and plasma phospholipids, respectively [START_REF] Liberda | Plasma concentrations of persistent organic pollutants in the Cree of northern Quebec. Canada: results from the multicommunity environment-and-health study[END_REF]Rochette and Blanchet, 2007). Data for PBDE 47, PBDE 153, and toxaphene congeners were not available for some Cree participants, leaving 519 subjects for analysis relative to these compounds.

hexachlorocyclohexane [HCH], α-chlordane, γ-chlordane, oxychlordane, trans-nonachlor, cis- nonachlor, p,p'-dichlorodiphenyltrichloroethane, p,p'-dichlorodiphenyldichloroethylene [DDE],
Organohalogenated compounds were extracted from plasma using solid-phase extraction. The precision (typically <3%), inter-day precision (mostly ≤ 10%, but 25-35% for the brominated compounds) and recoveries (mostly ≥ 70%) were all in the acceptable range. The measurement of whole blood total mercury (Hg) concentration was performed by ICP-MS at the Centre de Toxicologie du Québec and the complete analytic method was detailed elsewhere [START_REF] Valera | Environmental mercury exposure and blood pressure among Nunavik Inuit adults[END_REF]. LOD for the determination of Hg was 0.12 µg/L.

Cholesterol and triglycerides were analyzed using a Hitachi 917 Chemistry Analyzer. Total plasma lipids (as an adjustment variable for lipophilic contaminants) were then estimated from cholesterol and triglyceride levels. Plasma phospholipids were isolated from the lipid extract by chromatography, and the fatty acid profile, including DHA and EPA (omega-3 PUFAs), was determined by capillary gasliquid chromatography as described by [START_REF] Jacobson | Beneficial effects of a polyunsaturated fatty acid on infant development: evidence from the inuit of arctic Quebec[END_REF].

Statistical analysis

Because glucose, insulin, HOMA-IR and HOMA-B values were substantially skewed, we used a logarithmic transformation of these variables for the analysis. Two extreme values were also winsorized to reduce the impact of outliers. Imputations were performed for missing values on main covariates and the results were bootstrapped in order to take into account the complex survey design (Inuit study).

Ten contaminant categories were created: ∑PCBs (105,118,138,153,156,170,180), dioxin-like PCBs (105+118+156), DDE, HCB, mirex, oxychlordane+trans-nonachlor, PBDE (47+153), toxaphene (26+50), ∑OC pesticides (HCB, mirex, oxychlordane, trans-nonachlor, DDE), and Hg. Contaminant concentrations were grouped in tertiles (µg/L) in each study population. Omega-3 PUFAs concentration was considered as a continuous variable.

All multivariate models were adjusted for age (years), sex, waist circumference (cm), smoking (never smoker, ex-smoker, occasionally, daily -for Cree; current non-smoker, occasional smoker, daily smoker -for Inuit), omega-3 PUFAs (% of total fatty acids by weight in plasma phospholipids) and total lipids (g/L) (when appropriate).

Odds ratio of T2DM for each group of contaminants was estimated by logistic regression in each population separately. Linear trend tests for odds ratios and percent changes were obtained using orthogonal polynomial contrast on risk factor levels. Accordingly, the median values for each tertile were used to create polynomial coefficients, using the SAS proc IML. The latter coefficients were then applied in the contrast statement to achieve a dose response trend. Likewise, within each population, an interaction term between the risk factor components (∑PCBs, DDE) and waist circumference (above and below the median) was also tested.

The shape of dose-response associations for the main contaminants (∑PCBs and DDE), was also explored using spline regression modeling in order to detect non-linear relationship between the exposure (ng/g plasma lipids) and the outcome that would not otherwise be captured with the exposure categorization (tertiles). Restricted cubic spline was selected to insure stability at tails. A Regressions models were also used in order to evaluate the relationship between environmental contaminants and biomarkers of glucose metabolism among non-diabetic participants. Percent of change coefficients ((exp(β)-1)x100) were calculated (as the dependent variables were logtransformed) to provide a measure of change for the selected glucose metabolism marker that occurs for any tertile of exposure compared to the reference (lower tertile).

Statistical analyzes were performed by SAS software, version 9.4 (SAS Institute. Cary. NC).

Results

The prevalence of T2DM was 20.3% among Cree and 7.1% among Inuit. PUFAs (Table 2) were higher in the Inuit compared to the Cree population. When grouped into tertiles, the second tertile of environmental contaminants and nutrients distributions in the Inuit population was approximately equivalent to the third tertile in the Cree population. Due to low percentage of detection of toxaphene 26+50 in the Cree population, results relative to these compounds are not reported. Concentrations of several of these contaminants were highly correlated (r>0.9 between ∑PCBs, DDE, mirex, and oxychlordane+transnonachlor) (Supplemental File 2).

All contaminant concentrations, except PBDE and Hg, were associated with an increased risk of prevalent T2DM in the Cree population (Table 3). In the Inuit population, significant trends were observed for ΣPCBs, mirex, and ΣOC pesticides. When modelling non-linear dose-response curves of log(Odds) in association with ΣPCBs and DDE, including Cree and Inuit populations with the same reference value, the interaction was not statistically significant (Figures 12). Within the range of exposure common to the two populations (<1200 ng/g lipids for DDE, <2300 ng/g lipids for ∑PCBs), the risk of T2DM increased in a similar fashion among Cree and Inuit but kept increasing beyond this range only among Inuit. Interaction between plasma ΣPCBs or DDE levels and waist circumference did not reach statistical significance. However among Inuit, linear trends of risk of T2DM with contaminant levels are observed only among subjects with waist circumference above median, whereas in the Cree population, linear trends of risk of T2DM are observed in both strata. (Supplemental File 3)

In the Inuit population free of previously diagnosed diabetes, higher plasma concentrations of ∑PCBs, dioxin-like PCBs and some OCs (HCB, mirex, toxaphene) were associated with decreasing levels of fasting insulin (up to a 13% decrease), but not with increasing fasting glucose levels (Table 4).

However, the decrease in insulin was not linearly related to exposure, as it was more pronounced in the second tertile of exposure. Similar patterns of associations were observed for HOMA-IR or HOMA-B levels, with decreased levels occurring in the intermediate range of concentrations. In the subsample of Inuit participants submitted to the OGTT test (n=161), a linear decrease in glucose level was observed in association with higher concentrations of mirex. A notable exception in the direction of these associations was the positive association between DDE concentration and an increase in insulin and in HOMA-IR levels (up to 9%) (Figure 3). Increased blood Hg concentration was associated with a linear increase in fasting glucose (+3% in the third tertile of exposure) and this association was more pronounced in the subsample submitted to the OGTT test (+26% in the third tertile).

In the Cree population free of previously diagnosed diabetes, fewer changes in markers of glucose metabolism were observed in association with exposure to POPs (Table 5). An increase in fasting glucose was observed in association with PBDE plasma level, and a decrease in HOMA-B with increasing concentrations of ∑PCBs, dioxin-like PCBs, DDE, PBDE and ∑OC pesticides, although the shape of the relationship was not always linear (Figure 4).

Discussion

Our results obtained in two different Northern Quebec Indigenous population indicate similar doseresponse associations between POPs exposure and T2DM risk, despite markedly different exposure levels, glucose metabolism measures and diabetes prevalence. However, the patterns of association between exposure and biomarkers of glucose metabolism differed between the two groups of nondiabetic adults, suggesting different processes linking environmental contaminants to diabetes onset in these populations, perhaps linked to abdominal obesity.

The two populations studied present contrasted characteristics at baseline, both in terms of T2DM prevalence (20% among Cree, 7% among Inuit) and markers of glucose metabolism (altered among Cree), and in terms of exposure to environmental contaminants (higher among Inuit). In the Cree study population, the median fasting plasma glucose level (5.32 mmol/l) and waist circumference (108.9 cm) were at the cutoff points for definition of metabolic syndrome [START_REF] Goldenberg | Definition, Classification and Diagnosis of Diabetes, Prediabetes and Metabolic Syndrome[END_REF]. Conversely, blood levels of total PCBs and ∑OC pesticides were 2 to 3 times, and mercury level up to 7 times higher among Inuit compared to Cree.

Previous studies pertaining to POPs exposure and risk of diabetes in different Inuit populations have reported contrasted results. Among Inuit from Greenland, a previous cross-sectional study conducted between 1999study conducted between and 2002study conducted between (Jorgensen et al., 2008) ) reported plasma concentrations of total PCBs and OCs at least 4 times higher than in the present study in Nunavik. However, contrary to our findings, no association was observed between exposure to POPs and diabetes prevalence. As suggested by the authors, because very high levels of exposure are present in their population, the range of exposures may not have been large enough to reveal associations with metabolic dysfunctions (see Figure 2).

Nevertheless, both in Inuit populations from Greenland and Nunavik (present study), an inverse association with insulin levels is observed: in Greenland, Jorgensen et al. (2008) reported inverse associations between stimulated insulin level and total PCBs or several OC pesticides, whereas in Nunavik we also found inverse associations between fasting insulin and these contaminants (stimulated insulin was not measured in our study). In the Adult Inuit Health Survey conducted in Nunavut, Inuvialuit Settlements and Nunatsiavut in the Canadian Arctic (Nunavik not included) in 2007-2009, POPs blood plasma levels were similar to those observed in our Nunavik Inuit population [START_REF] Singh | Persistent organic pollutants and diabetes among Inuit in the Canadian Arctic[END_REF]. In this cross-sectional survey, they reported an association between POPs exposure and (self-reported) diabetes as well as fasting glucose. The latter finding is hard to interpret however, since the authors apparently did not exclude prevalent cases of diabetes when performing these statistical analyses. The potential impact of mercury exposure on glucose metabolism was studied previously in the Inuit population of Greenland [START_REF] Jeppesen | Association between whole blood mercury and glucose intolerance among adult Inuit in Greenland[END_REF]. The authors reported a positive association between mercury exposure and T2DM prevalence and with fasting glucose and 2h-glucose; the relationship appeared linear in their range of exposure levels (median 17.3 µg/L; range: 0.05-490 µg/L). Whereas we do not find an association between mercury exposure and T2DM prevalence in the Nunavik Inuit population, similar associations with 2h-glucose are observed, but statistical significance was reached only in the higher exposure range (our third tertile > 16 µg/L) for fasting glucose.

In summary, our results combined to those obtained in similar studies conducted in other Inuit populations suggest an association between POPs exposure and diabetes prevalence. Moreover, our results obtained in non-diabetic individuals suggest that reduced insulin secretion, rather than early signs of insulin resistance, is associated with increasing contaminant concentrations, but mostly at intermediate levels of exposure. The existence of non-monotonic dose-response curves in these associations has already been suggested [START_REF] Lee | Chlorinated persistent organic pollutants. obesity. and type 2 diabetes[END_REF]. Although we did not find an association between mercury exposure and T2DM prevalence, our results suggest that an increase in glucose levels may occur at blood mercury levels above 16 µg/L, which is coherent with the data from a previous study among Greenlandic Inuit [START_REF] Jeppesen | Association between whole blood mercury and glucose intolerance among adult Inuit in Greenland[END_REF].

The risk of diabetes in relation with POPs exposure was previously studied in the Mohawk population of Akwesasne, a First Nations community located along the St Lawrence River in New York State, USA [START_REF] Codru | Diabetes in relation to serum levels of polychlorinated biphenyls and chlorinated pesticides in adult Native Americans[END_REF]. In this cross-sectional study, blood concentrations of total PCBs, DDE, HCB and mirex were 2 to 3 times higher than those observed in the Cree participants in our study. The authors reported positive associations between elevated serum concentrations of PCBs, DDE and HCB and diabetes prevalence, but a negative association with mirex. An update of this analysis has subsequently been published [START_REF] Aminov | Akwesasne Task Force on the Environment.Diabetes Prevalence in Relation to Serum Concentrations of Polychlorinated Biphenyl (PCB) Congener Groups and Three Chlorinated Pesticides in a Native American Population[END_REF] with an extended sample of the same Mohawk population. Serum concentrations of 101 PCB congeners and 3 pesticides (DDE, HCB, mirex) were measured and statistical analyses included mutual adjustment for concentrations of other POPs.

Significant associations were reported between diabetes prevalence and serum levels of lowchlorinated non-dioxin-like PCBs congeners and HCB. Another large study conducted among First Nations adults in Ontario, Canada focused on risks and benefits of fish consumption in relation with T2DM risk [START_REF] Marushka | Association between fish consumption, dietary omega-3 fatty acids and persistent organic pollutants intake, and type 2 diabetes in 18 First Nations in Ontario, Canada[END_REF]. Globally, a frequent consumption of fish (>= once a week), and the estimated DDE and PCBs intakes from fish, were associated with increased risk of T2DM. Our study is the first to report an association between PBDE exposure and impairment of glucose metabolism in a First Nations population, and these results add to the growing knowledge on the potential health effects of brominated flame retardants [START_REF] Kim | Health consequences of exposure to brominated flame retardants: a systematic review[END_REF].

In summary, in coherence with results of other studies conducted in First Nations populations, we observed an association of POPs exposure with diabetes prevalence. In addition, among non-diabetic participants, we observed a decrease in HOMA-B, indicative of reduced β-cell function, in association with ∑PCBs, DDE, PBDE and ∑OC pesticides exposures.

With regard to the effect of POPs on insulin levels, there is in-vitro evidence indicating that POPs can directly reduce insulin secretion of beta cells at very low doses, following a non-linear relationship [START_REF] Lee | Low-dose persistent organic pollutants impair insulin secretory function of pancreatic beta-cells: human and in vitro evidence[END_REF]. Results from the latter study also suggest the possibility that a compensatory oversecretion of insulin among individuals exhibiting insulin resistance may mask a direct effect of POPs on pancreatic beta-cell function. Accordingly, a recent review article on POPs and T2D concluded that the role of POPs would be more prominent in the development of beta-cell dysfunction-dominant T2D rather than insulin resistance-dominant T2D [START_REF] Lee | Persistent Organic Pollutants and Type 2 Diabetes: A Critical Review of Review Articles[END_REF].

Assuming that a similar linear dose-response relationship exists between the main POPs exposures and T2DM risk among Cree and Nunavik Inuit populations, in their common range of exposure (<1200 ng/g lipids for DDE, <2300 ng/g lipids for ∑PCBs -that concern the majority of the two populations), the population fraction of T2DM attributable to POPs exposure is likely to be higher among Inuit compared to Cree, because exposure levels are higher among Inuit. This potential impact is likely to decline over the next decades, because of decreasing environmental levels and human body burden of most POPs in the Arctic (AMAP 2015), except for PBDE.

A number of limitations are present in our study. Although we had the opportunity to study a large number of POPs, several of them are highly correlated. Some combinations of contaminants are driven by one main compound: for example, ∑OC pesticides concentrations are largely explained by DDE, especially among Cree where DDE represents 82% of ∑OC pesticide concentration. The large number of tests performed has increased the likelihood of positive findings. However, due to high correlations among several POPs, significant associations found with some specific compound (such as DDE or mirex) may be attributed to the mixture rather than to the compound itself. Diagnosis of diabetes was based on medical records, an improvement over studies relying only on self-reported diabetes, but we cannot exclude that some cases may have been missed. Some potential confounders such as alcohol consumption, physical activity or family history of diabetes were difficult to assess with precision in these two populations and could not be taken into account. Most of the contaminants measured in our study persist for many years in the body; however simultaneous crosssectional assessment of blood contaminant levels and disease status may also have introduced measurement error or even reverse causation, due to the lipophilic properties of several POPs [START_REF] Zong | Persistent organic pollutants and risk of type 2 diabetes: A prospective investigation among middle-aged women in Nurses' Health Study II[END_REF]. In addition, the duration of disease (median 5.5 years among Cree, 3.3 years among Inuit) may also have introduced behavior changes (including dietary) that modified their current circulating levels of pollutants. Despite these potential limitations, common to most cross-sectional studies on this issue, our study relied on a detailed assessment of contaminants and nutrients biomarkers in two large population samples. The originality of our analysis lies in parallel observations of disturbances of glucose metabolism and diagnosed T2DM in two Indigenous populations of Canada with contrasted characteristics.

Conclusion

The observed link between POPs exposure and T2DM risk in the two populations studied should be confirmed using preferably a prospective design. Our results also suggest the need for additional research on the physiopathological process through which POP exposure may induce type 2 diabetes in these Indigenous populations.

  Multi-community Environment-and-Health Study is a cross-sectional investigation that was carried out in nine Cree communities located in theEeyou Istchee territory between 2005 and 2009 collecting similar clinical and personal information. All of the study's components were reviewed and approved by the ethics committees of the participating institutions: McMaster, Laval and McGill universities.

  participant using the following formula: HOMA-IR = [fasting glucose (mmol/L)] × [fasting insulin (mIU/L) /22.5]. The HOMA-B (or HOMA β-cell) was calculated as follows: HOMA-B = [20 x fasting insulin (mIU/L)] / [fasting glucose (mmol/L) -3.5].

  hexachlorobenzene [HCB], mirex, toxaphene congeners Parlar no. 26 and Parlar no. 50 [toxaphene 26+50]), and 5 brominated organic compounds (polybrominated biphenyl [PBB] congener no. 153, polybrominated diphenyl ethers [PBDEs] congeners nos. 47, 99, 100, and 153). Total mercury (Hg)

  resulting extract was cleaned on florisil columns and analysed by high resolution gas chromatography-mass spectrometry (HRGC-MS) at the Centre de Toxicologie du Québec. Limits of detection (LODs) were based on a signal-to-noise ratio of 3:1 for all compounds. LODs changed over the course of the projects, due to instrument optimization; the most conservative (highest) LOD values were assigned to each compound: 0.005 µg/L: toxaphene congeners; 0.02 µg/L: all PCBs congeners, aldrin, α-chlordane, γ-chlordane, oxychlordane, mirex, trans-nonachlor, PBB 153, PBDE nos. 99, 100 and 153; 0.03 µg/L: PBDE 47; 0.04 µg/L: HCB; 0.05 µg/L: ß-HCH, DDT; 0.09 µg/L: DDE. Intra-day

  th percentiles) allowed an adequate fit of the data. Graphs are represented as the log(odds) of T2DM by contaminant levels. Log(Odds) were derived at minimum value (reference value) of the exposure. To test whether the shape of the outcome-exposure relationship is different between the two populations (Inuit and Cree), an interaction term (population by exposure components) was used. An overall model was first assessed; the model estimates were then contrasted at specific range of data points for each population to derive the log(Odds) function.

Table 1

 1

	contains descriptive

population. Conversely, plasma concentrations of all POPs (except PBDE), of Hg and omega-3

Table 2 :

 2 Blood levels of POP (ng/g lipids), mercury (Hg) and omega-3 polyunsaturated fatty acids in Inuit and Cree adult populations (non-diabetic, fasting state)

		N	%>LOD	P10	P25	P50	P75	P90	Max
	Inuit
	∑PCB (ng/g)	671	100	78	175	366	850	2000	8342
	dioxin-like PCB (ng/g)	671	99.42	6.5	14	30	66	149	689
	p,p'-DDE (ng/g)	671	100	129	233	421	818	1672	8307
	HCB (ng/g)	671	99.59	14	25	52	116	228	1246
	Mirex (ng/g)	671	91.05	1.6	4.3	9.6	24	55	293
	Oxychlordane + trans-	671	100	38	74	159	429	974	6395
	nonachlor (ng/g)
	PBDE (47 +153)	669	85.5	<LD	2.7	8.3	15	35	402
	(ng/g)
	Toxaphene 26 + 50	671	98.14	7.6	14	32	80	177	968
	(ng/g)
	∑OC pest (ng/g)	671	100	207	375	698	1471	3131	14688
	Hg (µg/L)	671	100	2.46	5.32	10.3	20.7	38.2	152
	Omega-3 (% total FA)	671	100	5.19	6.78	9.03	11.7	14.3	19.5
	Cree
	∑PCB (ng/g)	599	99.3	17	45	169	542	1548	13200
	dioxin-like PCB (ng/g)	599	88.1	<LD	4.6	16	51	160	1978
	p,p'-DDE (ng/g)	599	99.8	38	64	143	355	823	7144
	HCB (ng/g)	599	99.8	3.3	3.8	8.0	16	32	240
	Mirex (ng/g)	599	78.8	<LD	1.8	7.7	30	94	645
	Oxychlordane + trans-	599	92.8	1.1	4.0	11	28	67	483
	nonachlor (ng/g)
	PBDE 47 +153 (ng/g)	479	82.5	<LD	5.1	9.8	18	33	219
	Toxaphene 26 + 50	479	39.9	<LD	<LD	<LD	2.4	5.6	53
	(ng/g)
	∑OC pest (ng/g)	599	100	46	73	175	442	1088	8212
	Hg (µg/L)	599	100	0.41	0.98	3.00	7.99	16.5	82.2
	Omega-3 (% total FA)	598	100	4.92	5.35	5.95	6.77	7.74	17.4

Σ PCB = sum (105+118+153+156+170+180); dioxin-like PCB = sum (105+118+156); Σ OC pest = sum (HCB+mirex+oxychlordane+trans-nonachlor+p,p'-DDE); FA: fatty acids

∑OC pest d <2.92 (ref) (µg/L) 1 ∑OC pest c <0.73 (ref) (µg/L) 1 2.92-8.13

			0.58	[0.15 -2.30]	0.73-2.73	2.78	[1.38 -5.61]
		>8.13	2.54	[0.79 -8.16]	>2.73	3.93	[1.73 -8.92]
	P Trend		0.018	P Trend		0.003
	PBDE 47+153 <0.02 (ref)	1	PBDE 47+153	<0.04 (ref)	1
	(µg/L)			(µg/L)
		0.02-0.08	1.16	[0.55 -2.45]	0.04-0.09	1.40	[0.78 -2.53]
		>0.08	0.90	[0.40 -2.04]	>0.09	0.99	[0.54 -1.81]
	P Trend		0.716	P Trend		0.773
	Toxa 26+50	<0.13 (ref)	1
	(µg/L)
		0.13-0.43	0.71	[0.20 -2.55]
		>0.43	1.82	[0.54 -6.13]
	P Trend		0.159
	Mercury	<7.21 (ref)	1	Mercury	<1.84 (ref)	1
	(µg/L)			(µg/L)

Acknowledgments

The authors would like to thank Nunavimmiut and Cree of Eeyou Istchee who participated to the health surveys. We are also grateful to the Nunavik Nutrition and Health Committee and the

Funding for the Qanuippitaa? 2004 Nunavik Inuit Health Survey was provided by the Northern Contaminants Program (Indigenous Affairs and Northern Development Canada), the Nunavik Regional Board of Health and Social Services, Quebec's Ministry of Health and Social Services, and ArcticNet Network of Centres of Excellence of Canada. This scientific communication is a report from the Nituuchischaayihtitaau Aschii: Multi-Community Environment-and-Health Longitudinal Study in Iiyiyiu Aschii supported by the Cree people of northern Québec, the Cree First Nations and the Cree Board of Health and Social Services of James Bay through financial contributions from Niskamoon Corporation. Nituuchischaayihtitaau Aschii Data Access Committee for their collaboration and input. We thank Myrto Mondor (CHU de Québec Research Centre Québec, QC, Canada) for her assistance in statistical analysis. Human subjects research review All study components were reviewed and approved by the ethics committees of the participating institutions (McMaster, Laval and McGill universities). Community consent was obtained through formal resolutions, and

Inuit

Cree Variable a Total Population (n=671)

Subsample OGTT (n=161)

Total Population (n=599) Age (years) 32.9 [24.4-43.6] 38.8 [27.2-50.1] 33. 8 [25.1-43.9 [-17.8 --1.75] -10.1 [-18.9 --0.30] -15.4 [-25.6 --3.69] -8.39 [-20.4 -5.45] >4.08 0.81 [-2.51 -4.24] -2.97 [-13.6 -8.93] -2.18 [-14.2 -11.49] -11.0 [-24.2 -4.60] -9.24 [-28.4 -14.97 -10.9 [-18.9 --2.20] 0.59 [-10.7 -13.30] 0.40 [-11.7 -14.13] >0.59 -1.44 [-4.76 -2.00] -5.52 [-16.7 -7.18] -7.05 [-19.2 -6.94] 3.83 [-14.6 -26.23 [-10.3 -7.36] -1.94 [-11.6 -8.77] -3.72 [-15.0 -9.05] 6.73 [-7.70 -23.42] >1.98 0.02 [-3.03 -3.17] 2.61 [-8.04 -14.50] 2.45 [-9.47 -15.94] -0.84 [-15.0 -15.69] 11.57 [-12.5 -42.23 [-13.3 -6.10] -6.28 [-16.9 -5.75] 3.05 [-9.96 -17.92] >7.27 1.29 [-1.63 -4.30] 7.30 [-3.60 -19.43] 8.53 [-3.91 -22.57] -3.96 [-17.3 -11.50] 12.83 [-9.88 -41.26 (µg/L) 0 0 0 0 0.5-1.5 0.95 [-2.46 -4.48] -6.17 [-14.6 -3.14] -4.99 [-14.7 -5. (µg/L) 0 0 0 0 0.02-0.12 2.11 [-1.34 -5.67] 0.84 [-8.27 -10.9] 3.38 [-7.20 -15.2] -5.73 [-14.9 -4.48] >0.12 0.17 [-4.02 -4.54] -4.14 [-14.8 -7.85] -3.49 [-15.6 -10.4] -6.24 [-17.5 -6.57 . Several Indigenous people of Canada are exposed to mercury and mixtures of POPs . Levels of exposure are much higher in Inuit compared to Cree . In both populations, risk of diabetes increased with exposure to several POPs . In diabetes-free Inuit, reduced insulin secretion was associated with several POPs

Declaration of interests

x The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: