PhD Abdelkrim Mannioui

MS Quentin Vauzanges

PhD Jean Baptiste Fini

MS Esther Henriet

PhD Somya Sekizar

MS Loris Azoyan

PhD Jean Léon Thomas

PhD David Du Pasquier

PhD Carine Giovannangeli

PhD Barbara Demeneix

MD Catherine Lubetzki

MD, PhD Bernard Zalc
email: bernard.zalc@upmc.fr

The Xenopus tadpole: an in vivo model to screen drugs favoring remyelination

Keywords: Multiple sclerosis, Xenopus laevis, transgenic, demyelination, remyelination, Crispr/Cas9, oligodendrocyte, gene editing 5, Color figures: 4, Table: 1 (Supplementary files: 2 figures: 1 B&W and 1

Background:

In MS development of screening tools for remyelination-promoting molecules is timely.

Objective: A Xenopus transgenic line allowing conditional ablation of myelinating oligodendrocytes has been adapted for in vivo screening of remyelination-favoring molecules.

Methods:

In this transgenic, the green fluorescent protein reporter is fused to E. coli nitroreductase and expressed specifically in myelinating oligodendrocytes. Nitroreductase converts the innocuous pro-drug metronidazole to a cytotoxin. Spontaneous remyelination occurs after metronidazole-induced demyelinating responses. As tadpoles are transparent, these events can be monitored in vivo and quantified. At the end of metronidazole-induced demyelination, tadpoles were screened in water containing the compounds tested. After 72h remyelination was assayed by counting numbers of oligodendrocytes per optic nerve.

Results: Among a battery of molecules tested, siponimod, a dual agonist of sphingosine-1phosphate receptor 1 and 5, was among the most efficient favoring remyelination. Crispr/cas9 gene editing showed that the promyelinating effect of siponimod involves the sphingosine-1phosphate receptor 5.

Conclusion:

This Xenopus transgenic line constitutes a simple in vivo screening platform for myelin repair therapeutics. We validated several known pro-myelinating compounds, and demonstrated that the strong remyelinating efficacy of siponimod implicates the sphingosine-1phosphate receptor 5.

Introduction

Oligodendrocytes are the myelin-forming cells of the CNS. During embryonic development, cells of the oligodendrocyte lineage emerge from the ventricular zone. Successive developmental stages transform the neural stem cells into proliferating oligodendrocyte progenitors, which migrate into the parenchyma as oligodendrocyte precursor cells (OPCs) before differentiating, successively into a pre-oligodendrocyte, then a mature postmitotic oligodendrocyte and finally a myelin-forming oligodendrocyte. These developmental stages, which are associated with different capacities of proliferation, migration, differentiation, survival, maturation, and finally myelin deposition, are cell autonomous, but also depend on a variety of extrinsic factors.

In multiple sclerosis (MS) remyelination often fails despite OPC presence around demyelinating areas. [START_REF] Franklin | Why does remyelination fail in multiple sclerosis?[END_REF] Repair of demyelinated lesions could enhance successful re-ensheathing of naked axons by oligodendrocyte processes. Existing MS models (mostly rodent and primates) are not ideal for monitoring in vivo demyelination and remyelination, hence the need to develop simpler strategies for larger scale screening of compounds favoring myelin repair. [START_REF] Miller | Restoring the balance between disease and repair in multiple sclerosis: insights from mouse models[END_REF] We developed a transgenic Xenopus laevis permitting live imaging of demyelination and remyelination by conditionally triggering apoptotic ablation of myelin forming oligodendrocytes. [START_REF] Kaya | Live imaging of targeted cell ablation in Xenopus: a new model to study demyelination and repair[END_REF] This line, MBP-GFP-NTR, expresses green fluorescent protein (GFP) fused to E. coli nitroreductase (NTR) under control of the mouse 1.9kb myelin basic protein (MBP) regulatory sequence. In the mouse, this portion of the proximal upstream region of MBP gene drives reporter expression specifically in myelinating oligodendrocytes. [START_REF] Stankoff | Transcription of myelin basic protein promoted by regulatory elements in the proximal 5' sequence requires myelinogenesis[END_REF] Like the mouse, the transgenic MBP-GFP-NTR X. laevis expresses the GFP-NTR transgene specifically in myelin-forming oligodendrocytes.

The NTR enzyme converts the nitro radical of prodrugs, including metronidazole, to a highly cytotoxic hydroxylamine derivative. In metronidazole-exposed transgenic MBP-GFP-NTR tadpoles demyelination is restricted to the CNS, without axonal damage. [START_REF] Kaya | Live imaging of targeted cell ablation in Xenopus: a new model to study demyelination and repair[END_REF] The extent of demyelination depends on the concentration and duration of metronidazole exposure.

Spontaneous remyelination occurs and is nearly complete 8 days after cessation of metronidazole.

As embryos are transparent, demyelination and remyelination can be monitored and quantified in vivo under a fluorescent macroscope. [START_REF] Kaya | Live imaging of targeted cell ablation in Xenopus: a new model to study demyelination and repair[END_REF] We used this model to screen molecules favoring remyelination. Among the battery of molecules tested, one of the most potent to accelerate remyelination was siponimod, which was recently evaluated in a Phase III trial in secondaryprogressive MS. [START_REF] Kappos | Efficacy and safety of siponimod in secondary progressive multiple sclerosis-Results of the placebo controlled, double-blind, Phase III EXPAND study[END_REF] Siponimod is a dual agonist of sphingosine-1-phosphate receptors, S1PR1 and S1PR5.

Sphingosine-1-phosphate (S1P) has been identified as the endogenous ligand of the five known S1P receptors (S1PR1, S1PR2, S1PR3, S1PR4 and S1PR5) a family of G-protein coupled receptors. [START_REF] Lee | Sphingosine-1-phosphate as a ligand for the G protein-coupled receptor EDG-1[END_REF] In the rodent CNS, the S1PR5 receptor is expressed only by cells of the oligodendroglial lineage and its activation is important in the oligodendrocyte maturation. It was therefore suggested that S1PR5 may play a key role in myelin sheath repair. [START_REF] Jaillard | Edg8/S1P5: an oligodendroglial receptor with dual function on process retraction and cell survival[END_REF] Here we questioned whether the remyelinating effect of siponimod implicated S1PR5. We show that, in tadpoles with Crispr/Cas 9 gene deleted S1PR5, siponimod no longer promotes remyelination. Another S1PR5 agonist (UC-42-WP04) also favored remyelination, while an S1PR1 agonist (AUY954) had no effect. The data provide strong evidence that siponimod-stimulated remyelination implicates S1PR5 activation and illustrate that MBP-GFP-NTR Xenopus is an efficient and simple experimental model to screen molecules favoring remyelination.

Materials and methods

Animals

Xenopus tadpoles were staged according to Nieuwkoop and Faber. 8 X. laevis is an allotretraploid composed of two separate diploid genomes (2n=36). X. laevis has nine pairs of chromosomes named Xla1S and Xla1L through Xla9S and Xla9L where S (short) and L (long) refer to their relative lengths.

Antibodies

Mouse anti-MBP (directed against Xenopus MBP, 1:1000, kindly provided by Dr. Saburo Nagata), chick anti GFP (1:1000, Aves Lab, USA), rabbit anti-S1PR5 antibody (1:100 Imgenex, USA), goat anti-human Sox10 (1:50 R&D systems). Corresponding secondary antibodies conjugated Alexa 350, Alexa 488, Alexa 594 and Alexa 647 (1: 1000, Invitrogen). For CLARITY we used chicken anti-GFP, Avès Labs, 1:400 as primary antibody and goat anti-chicken Alexa Fluor 488, Invitrogen, 1:600 as secondary one.

CLARITY and Imaging using a high refractive index solution are detailed in the supplementary materials.

Immunostaining of clarified samples CLARITY-processed brains were incubated in blocking solution overnight at 4°C. Samples were further incubated in staining solution with primary antibodies (anti-GFP) for 7d at room temperature with under gentle agitation. After 2 washes with PBT, samples were incubated in a staining solution with secondary antibody for 7d at room temperature. Samples were subsequently washed for 48h in PBT.

Immunolabeling on tissue sections

Tadpoles were fixed by immersion in 4% paraformaldehyde and treated for immunostaining as described. [START_REF] Kaya | Live imaging of targeted cell ablation in Xenopus: a new model to study demyelination and repair[END_REF] Electron microscopy and morphometry are detailed in the supplementary materials.

Metronidazole preparation and use

Metronidazole (10mM, Fluka) was dissolved in filtered tap water containing 0.1% DMSO (Sigma Aldrich) and added to aquaria water for 10 days. Tadpoles were maintained in 600 ml of metronidazole solution (maximum 10 tadpoles/600 ml) at 23.5˚C in complete darkness (metronidazole is light-sensitive) and changed every 72h throughout treatment. For regeneration experiments, metronidazole-treated animals were allowed to recover for up to 8 days in either normal water or containing compounds to be tested at different concentration in ambient laboratory lighting (12h light 12h dark).

Quantification of GFP + cells

GFP was detected directly by fluorescence in live embryos using an AZ100 Nikon Zoom Macroscope. In the optic nerve, the total number of GFP + cells was counted, from the emergence of the nerve (i.e., after the chiasm) to the retinal end before and after metronidazole treatment and after treatment with the compound to be tested on the same embryos. Doubleblind counts were performed independently by two researchers. Data were compared to control untreated animals of the same developmental stage. Data presented are the mean ± SEM of number of GFP+ cells counted on at least 6 tadpoles per condition.

Preparation of sgRNAs, generation of S1P5 null mutant and PCR primers are described in the supplementary materials.

Statistical Analysis

Prism v5 software was used for statistical analyses. Results are expressed as means ± SEM. To assess differences between more than two groups when comparing efficiency of remyelinating drugs, parametric two way ANOVA was used (after normality test passed using Shapiro Wilk

Results

Oligodendrocyte visualization in MBP-GFP-NTR transgenic Xenopus

In the brain stem, GFP positive cells are detected from stage 43 onward. This corresponds to the developmental stage when myelination markers such as proteolipid protein and MBP are first immunodetected in the hindbrain (stage 42/43) before spreading throughout the brain and spinal cord by stages 46/47. [START_REF] Yoshida | Oligodendrocyte maturation in Xenopus laevis[END_REF] Electron microscope studies on optic nerve [START_REF] Cima | Development of the optic nerve in Xenopus laevis. II. Gliogenesis, myelination and metamorphic remodelling[END_REF] showed myelination to begin in the middle portion at stage 48/49, with numbers of myelinated axons increasing sevenfold between stage 50 and 57. Distribution of myelin forming oligodendrocytes at stage 48 and 52 is shown (Figure 1A-C). Oligodendrocytes populate the ventral half of the hindbrain and spinal cord on each side of the mid-line. At this early developmental stage oligodendrocytes have not yet migrated long distances from their origin and are myelinating the major descending fibre tracts. This is well illustrated by the 3D-reconstruction of whole-mount CNS preparations performed after tissue clarification, i.e. replacement of light-scattering lipids of the brain and spinal cord by a transparent hydrogel matrix (Supplementary file Movie 1).

Conditional ablation and spontaneous repair in the MBP-GFP-NTR Xenopus tadpole

Stage NF52-53 MBP-GFP-NTR transgenic X. laevis were treated with metronidazole (10mM) introduced in the aquarium water to induce conditional demyelination. Screening experiments focused on the embryonic optic nerve, easily monitored by live imaging. The number of GFP + oligodendrocytes is moreover small and very reproducible at each developmental stage, facilitating quantification. After 10 days metronidazole, the number of GFP+ cells per optic nerve significantly decreased from 13.9 + 1.0 to 2.3 + 2 (p<0.01) (Figure 1D upper panel). The extent of demyelination was further investigated using electron microscopy (EM) showing the depletion of myelin around axons, and the presence of myelin debris (Supplementary Figure S2 A, B). After 10 days metronidazole exposure, tadpoles were returned to normal water and recovery occurred rapidly: oligodendrocytes per optic nerve reached 8.3 + 0.9 and 13.3 + 1. 5

Transgenic MBP-GFP-NTR Xenopus tadpoles as a screening platform for molecules enhancing remyelination

We reasoned that our model could serve for screening potential remyelination-favoring molecules by quantifying remyelination rates as a function of increases in GFP+ cell numbers following demyelination. Since spontaneous repair was often complete at R8, we chose to evaluate repair efficiency only at R3, i.e., 3 days after metronidazole removal. We compared the promyelinating effect of 20 compounds for which an effect on myelination (or remyelination) has been described

(Table 1). Among the molecules tested, the three most efficient were, by increasing order: siponimod (3nM), UC-42-WP04 (10nM) and clemastine (100nM)(Figure 2). It is noteworthy that UC-42-WP04, a selective S1PR5 agonist, [START_REF] Mattes | Design and synthesis of selective and potent orally active S1P5 agonists[END_REF] was amongst the most efficient remyelinating drugs, while AUY954, a selective S1PR1 agonist, [START_REF] Pan | A monoselective sphingosine-1-phosphate receptor-1 agonist prevents allograft rejection in a stringent rat heart transplantation model[END_REF] had no effect. Since siponimod is a dual S1P1 and S1P5 receptor agonist, we investigated further siponimod's remyelinating potential.

Xenopus oligodendrocytes express S1P5 receptor

As oligodendrocytes in the mouse brain selectively express S1PR5, [START_REF] Jaillard | Edg8/S1P5: an oligodendroglial receptor with dual function on process retraction and cell survival[END_REF] we questioned whether S1PR5 expression was also restricted to oligodendrocytes in X. laevis. We investigated oligodendroglial expression of S1PR5 in X. laevis by triple immunolabeling of brainstem tissue sections of MBP-GFP-NTR tadpoles (stage 52-53) using a rabbit anti-S1PR5 antibody, a chicken anti-GFP to label mature oligodendrocyte and a goat anti-Sox-10 to label all cells from the oligodendroglial lineage. We observed a perfect cellular co-localisation of Sox10 and S1PR5 (21.5 + 6.5 cells/mm 2 ) and all the GFP+ cells were S1P5+ (14.5 + 5.3 GFP + /S1PR5 + cells/mm 2 ).

Since, in the CNS, Sox10 is an established marker of the oligodendroglial lineage, we concluded that the S1P5+/Sox10+/GFP-cells are most likely OPCs. Altogether our data suggest that in the Xenopus CNS, as in the mouse, S1P5 expression is restricted to the oligodendrocyte lineage and that all myelin-forming oligodendrocytes (GFP+ cells) express S1PR5 (Figure 3).

Detection of myelinated fibers following siponimod treatment

To verify that increased numbers of myelinating oligodendrocytes translated into increased myelination, brain stem tissue sections were immunolabeled with anti-MBP, an established myelin marker. Transgenic MBP-GFP-NTR X. laevis (n=18)(stage 52-53) were treated for 10 days with metronidazole (n=15), then returned to normal water (n=3) or water containing siponimod (3nM) for either 3 days (n=3) or 8 days (n=3) prior to MBP immunostaining (Figure 4). After 10 days of metronidazole treatment a nearly complete demyelination was achieved (compare D0 and D10 in Figure 4). After metronidazole removal, exposure to siponimod for 3 days (Figure 4 Siponimod

The promyelinating effect of siponimod is mediated through S1PR5

Siponimod is a potent and selective agonist of S1P receptors with an EC50 of 0.39nM for S1P1 and 0.98nM for S1P5 receptors, respectively. [START_REF] Gergely | The selective sphingosine 1-phosphate receptor modulator BAF312 redirects lymphocyte distribution and has species-specific effects on heart rate[END_REF] We questioned which receptor implicated the promyelinating effect of siponimod. As remyelination was observed with the selective S1PR5 agonist (UC-42-WP04), but not with the selective S1PR1 agonist (AUY954) we favored the possibility that siponimod induced remyelination through S1PR5. If this were the case, siponimod should lose efficiency after S1P5 receptor deletion. We took advantage of the clustered regularly interspaced short palindromic repeats (CRISPR)-Cas system (Crispr/Cas9) to test this hypothesis. [START_REF] Jinek | A programmable dual-RNA-guided DNA endonuclease in adaptive bacterial immunity[END_REF] To determine the exact mutations of s1pr5-S and s1pr5-L the genomic DNA from 6 F0 embryos, identified after the T7 endonuclease-based mutation detection, was extracted and sequenced. Each embryo presented different degrees of deletion (between 2 to 169 bp) leading to shift of the reading frame and premature STOP codon, for both s1pr5-L and s1pr5-S genes (Figure 5A). Each of these embryos at stage 55 was submitted to metronidazole demyelination and treated with siponimod. The pro-remyelinating effect of siponimod was no longer observed in the S1PR5 -/-embryos (Figure 5B).

To confirm oligodendroglial S1P5 receptor loss, mutated tadpoles were euthanized after the demyelination-remyelination experiments, and immunolabeled with anti-S1PR5 antibodies on brain stem sections. As illustrated, (Figure 5C), S1PR5 protein was not immuno-detectable in GFP+ cells in any of the six MBP-GFP-NTR; s1pr5 -/-tadpoles examined.

Discussion

For the past 15-20 years significant therapeutic progress has resulted from developing antiinflammatory strategies in MS. These treatments are efficient in diminishing numbers of relapses, but their influence on long-term disability is unclear. Loss of the myelin sheath perturbs normal axon functioning and persistent demyelination renders them vulnerable to irreversible damage leading to axonal transection, with consequent disability accumulation. Spontaneous remyelination can occur, but most often endogenous repair mechanisms are insufficient, notably during aging. The experimental demonstration that environmental clues can restore remyelination potential of aging OPCs indicates that pharmacological approaches may be developed to restore, increase or accelerate remyelination. [START_REF] Ruckh | Rejuvenation of regeneration in the aging central nervous system[END_REF] Several groups have recently developed in vitro screening approaches for small molecules that drive OPC differentiation. [START_REF] Deshmukh | A regenerative approach to the treatment of multiple sclerosis[END_REF][START_REF] Mei | Micropillar arrays as a high-throughput screening platform for therapeutics in multiple sclerosis[END_REF][START_REF] Najm | Drug-based modulation of endogenous stem cells promotes functional remyelination in vivo[END_REF] These in vitro high throughput screens can identify hit molecule candidates to be further validated in in vivo experimental models of demyelination.

Rodents are the preferred animal models, with primary demyelination induced either by detergents to disorganize the myelin sheath (e.g. lysolecithin) or by killing oligodendrocytes with toxins (such as cuprizone or ethidium bromide). In other models demyelination is secondary to an auto-immune attack as in MOG-induced EAE. [START_REF] Linington | Augmentation of demyelination in rat acute allergic encephalomyelitis by circulating mouse monoclonal antibodies directed against a myelin/oligodendrocyte glycoprotein[END_REF] Toxin-induced models of demyelination do not mimick MS, but they allow the fundamental biology of remyelination to be explored without the confounding and complicating involvement of an autoimmune process. [START_REF] Franklin | Regenerative Medicines for Remyelination: From Aspiration to Reality[END_REF] Although rodents may be considered as the "standard" experimental model to investigate demyelination and remyelination, they are costly, time consuming and not ideal for longitudinal investigation in the same animal. Although the last decade has seen considerable progress for in vivo imaging of live cells in the normal and demyelinated CNS, [START_REF] Fenrich | Long-term in vivo imaging of normal and pathological mouse spinal cord with subcellular resolution using implanted glass windows[END_REF] technical issues strongly limit imaging in deep layers of mouse brain, such as myelinated axonal tracts. Tadpole transparency allowed us to overcome these limitations by using transgenic Xenopus expressing fluorescent reporter and a suicide protein in oligodendrocytes.

We present results on 20 molecules previously described, usually in vitro, as candidates to promote remyelination. The Xenopus results are in good agreement with reports on pro-myelinating efficacy of clemastine, 17 benztropine [START_REF] Deshmukh | A regenerative approach to the treatment of multiple sclerosis[END_REF] and retinoic acid [START_REF] Huang | Retinoid X receptor gamma signaling accelerates CNS remyelination[END_REF] in mammalian cells. A recent small size phase 2 study of clemastine in chronic optic neuritis showed some positive results. Concerning siponimod no data on remyelination is reported, but a recently completed phase 3 study showed some positive results in secondary progressive MS. [START_REF] Kappos | Efficacy and safety of siponimod in secondary progressive multiple sclerosis-Results of the placebo controlled, double-blind, Phase III EXPAND study[END_REF] Fingolimod, (acting on S1PR1, S1PR2, S1PR3 and S1PR5, and which is used in the clinic) also promoted remyelination, a finding in agreement with previous data in culture. [START_REF] Miron | Fingolimod (FTY720) enhances remyelination following demyelination of organotypic cerebellar slices[END_REF] In contrast, clobetasol and miconasole, known to be efficient remyelinating candidates in vitro as well as in vivo in the mouse [START_REF] Najm | Drug-based modulation of endogenous stem cells promotes functional remyelination in vivo[END_REF] were without effect in the Xenopus model. One possible explanation is that these molecules were screened for their ability to generate new oligodendrocytes, while in the MBP-GFP-NTR Xenopus model there is no need to generate new OPCs since remyelination results from maturing OPCs (Sox10+ cells) already present in the optic nerve prior to demyelination, without requiring additional production of OPCs. [START_REF] Sekizar | Remyelination by Resident Oligodendrocyte Precursor Cells in a Xenopus laevis Inducible Model of Demyelination[END_REF] Generation of new oligodendrocytes is only one possible mechanism to favor remyelination. It has been described

that OPCs are present in some chronic lesions of MS, so remyelination is not only limited by an absence of precursors or their failure to generate oligodendrocytes, but by the defective maturation of OPCs. [START_REF] Chang | Premyelinating oligodendrocytes in chronic lesions of multiple sclerosis[END_REF] However, an advantage of Xenopus as opposed to other aquatic models, lies in myelin biology and the fundamental difference in the molecular composition of myelin between teleosts and tetrapods. Teleosts, and zebrafish in particular, use P0 as major myelin protein both in the CNS and the peripheral nervous system (PNS). In contrast, starting with amphibians (including Xenopus), a dramatic evolutionary change in myelin composition between PNS and CNS occurred. In tetrapods (including amphibians and mammals) the major myelin protein in the PNS remains P0, while in the CNS it is PLP and MBP. This event occurred in amphibians and has been maintained throughout evolution up to mammals, including humans.

An advantage of the Xenopus model is read-out rapidity: after 10 days of demyelination, remyelination effects were seen by 3 days recovery (hence a total of 13 days), while the cuprizone model in rodent requires at least 6 weeks for demyelination and an additional 3 weeks for recovery. A final advantage of the Xenopus model is that assessing demyelination and remyelination is performed on the same animals and does not require immunohistochemistry.

Although the Xenopus model, as described, is more indicated as a medium throughput screen, it has the potential to be automatized for high-throughput screens. Live imaging of remyelination (automated counting of GFP+ cells) is theoretically possible through the modification of existing automated devices such as the VAST (Vertebrate Automated Screening Technology, Union Biometrica, MA, USA). This device allows the automated pumping from multiwell plates and automated imaging at cellular level of whole zebrafish embryos. This system is limited by the valve and motor pin diameter, which has a maximum of 700 micron diameter. To be transposable to Xenopus tadpoles would require adapting the technology by using larger size capillaries. Overall, the procedure is far more efficient when compared with the efforts, time and cost necessary to perform the same type of experiment in mice. However, whilst ideal for screening small molecules, a limit of the MBP-GFP-NTR Xenopus model is that it is not designed to test antibodies, such as anti-Lingo, which would require to be injected into the tadpole and not simply added to the swimming water. Another limitation is that the Xenopus tadpole model may not be adapted to screen drugs aimed at overcoming the decline in remyelination that occurs with advancing age particularly for long-term demyelinating diseases such as MS.

In addition to the rapidity with which the test can be performed, another appreciable advantage of the Xenopus model is using Crispr/Cas9 technology so the molecular mechanism of a given compound can be dissected, with ease and precision. [START_REF] Jinek | A programmable dual-RNA-guided DNA endonuclease in adaptive bacterial immunity[END_REF] In the case of siponimod, not only S1P5

receptor was directly deleted in the MBP-GFP-NTRlineage, but the effect of the deletion was tested on 6 different KO animals. Three arguments strongly support that the remyelinating potency of siponimod is mediated through the S1P5 receptor, first, another S1PR5 agonist improved remyelination; second, in the absence of S1PR5 siponimod was no longer active and, third, a S1PR1 agonist was inefficient. We did not attempt to delete S1P1 because it is established that within endothelial cells this receptor is required for the coverage of vessels by vascular smooth muscle cells [START_REF] Obinata | Individual variation of human S1P₁ coding sequence leads to heterogeneity in receptor function and drug interactions[END_REF] and lethality occurs in embryos of S1P1 receptor-deficient mice, due to rupture of the unreinforced vessels. [START_REF] Liu | Edg-1, the G protein-coupled receptor for sphingosine-1phosphate, is essential for vascular maturation[END_REF] However, although unlikely, we cannot definitively exclude that some of the benefit from siponimod could be from its potential to act through a different mechanism than a S1PR5 agonist.

A recently completed Phase III randomized, controlled study of siponimod in secondary progressive MS has met its primary endpoint, compared with placebo. [START_REF] Kappos | Efficacy and safety of siponimod in secondary progressive multiple sclerosis-Results of the placebo controlled, double-blind, Phase III EXPAND study[END_REF] Obinata and co-workers have reported the genetic variations of the s1pr1 coding region from exon sequencing of about 12,000 individuals and their functional consequences, suggesting that individual genetic variations of s1pr1 can influence receptor function and, therefore, infer differential interaction with S1PR1targeted therapeutics. [START_REF] Obinata | Individual variation of human S1P₁ coding sequence leads to heterogeneity in receptor function and drug interactions[END_REF] Concerning s1pr5, deletion of s1pr5 has no apparent evident clinical phenotype in either mouse or Xenopus. Whether patients with s1pr5 mutation or deletions may differ in their remyelination capacity, disease severity and/or response to siponimod is an as yet unexplored hypothesis.

  normality test) followed by an uncorrected Fisher's LSD test. Other P-values for comparison of means are from Student's two-tailed t-tests. Analysis of covariance was used to analyze regression lines. Statistical significance was set at p < 0.05. Significant differences are indicated by asterisks: *p<0.05, ** p<0.01, and *** p<0.001.

  R3) resulted in a dramatic increase in myelinated internodes by comparison with spontaneous remyelination (Figure 4 Control R3). At R8 the extent of myelinated fibers was back to the level prior to demyelination (Figure 4 D0, Siponimod R8, and control R8. EM examination of tadpoles following 6 days of recovery confirmed a partial remyelination of MTZ-induced demyelinated axons (Supplementary Figure S2 C), in agreement with the return to nearly normal level of the number of GFP + cells. Evaluation of the g-ratios representing myelin thickness with respect to axon diameter revealed a reduction in myelin thickness, suggestive of remyelination, in siponimod remyelinated animals (g= 0.85 + 0.04) versus controls not subjected to demyelination (g= 0.82 + 0.04, p<0.001) (Supplementary Figure S2 D).

  Tadpoles of either sex were anesthetized in 0.05% MS-222 (Ethyl-3aminobenzoate methanesulfonate; Sigma-Aldrich) before quantification of GFP+ cells, and returned to normal water to recover. Before brain and spinal cord dissection, tadpoles were

	euthanized in 0.5% MS-222. Animal care was in accordance with institutional and national
	guidelines. All animal procedures conformed to the European Community Council 1986 directive
	(86/609/EEC) as modified in 2010 (2010/603/UE) and have been approved by the ethical
	committee of the French Ministry of Higher Education and Research. Transgenic tadpoles were
	treated between stages NF 50 and 55, corresponding to pre-metamorphosis, a stage of ongoing
	myelination.

Table 1 :

 1 List of compounds tested. (a) Concentrations used in vivo (when available) are shown

	in italics
	Compound tested	Known mode of action	Concentration used (a) Reference
	AUY954	Sphingosine 1 phosphate	1.2nM//1-10mg/kg/d	(12) Pan et al., 2006
		receptor 1
	Benztropine	Anticholinergic	2µM//2.5mg/kg	(16) Deshmukh et al., 2013
	BD 1008	Sigma receptor	5µM	(29) Demerens et al., 1999
				& unpublished data
	Biotin	Vitamin B8	300mg/d	(30) Sedel et al., 2015
	Clemastine	Anti-histaminic anti-	1µM /10mg/kg	(17) Mei et al., 2014
		muscarinic
	Clobetasol	Glucocorticoid anti-fungal 5µM//10mg/kg	(18) Najm et al., 2015
	Creatine	Peptide derived from	Ratio NAA/Cr P<0.16	(31) Fayed et al., 2006
		arginine, glycine &
		methionine
	Fingolimod	Sphingosine 1 phosphate	10nM/ 0.5mg/d	(23) Miron et al., 2010
		receptor 1, 2, 3 and 5
	Lithium	Alcalin bipolar disorder	50mg/kg/d	(32) Makoukji et al., 2012
	MDL29951	NMDA antagonist	100nM	(33) Hennen et al., 2013
	Metformin	Biguanide Type2 diabetes	200µM	(34) Paintlia et al., 2013
	Miconasole	Imidazole anti-fungal	1µM//1mg/kg	(18) Najm et al., 2015
	Rapamycin	Inhibitor of mTOR	15nM	(35) Tyler et al., 2014
	9-cis-Retinoic acid	Retinoic receptor	50nM	(22) Huang et al., 2011
	Sildenafil	Phosphodiesterase inhibitor 25mg/kg/d	(36) Raposo et al., 2014
	Siponimod	Sphingosine 1 phosphate	1-1000nM//0.25-10mg/d (37) O'Sullivan et al., 2016
		receptor 1 and 5
	Siramesine	Sigma receptor	1µM	(29) Demerens et al., 1999
				& unpublished data
	TFA-12	Tocopherol derivative	0.39mg/kg	(38) Blanchard et al., 2013
	TRO 19622 (Olesoxime) Cholesterol derivative	5ml/kg or 60-600µg/g	(39) Magalon et al., 2012
	UC-42-WP04	Sphingosine 1 phosphate	3nM//3mg/kg	(11) Mattes et al., 2010
		receptor 5

Acknowledgments

We thank Pierre Affaticati and TEFOR Infrastructure for CLARITY and 3D imaging of tadpoles. AM and BZ are thankful to the Marine Biological Laboratory, National Xenopus Resource for helpful introduction to gene editing technologies in the Xenopus.

Funding

This work was supported by Inserm, CNRS, UPMC, the program "Investissements d'Avenir" ANR-10-IAIHU-06, NeurATRIS, and ANR grant OLGA to B.D. and B.Z. The study was partially funded by grants from Novartis-France and Novartis-Pharma to BZ.

Using this site for GGTTCGGATGAAACACTACAG sgRNA we can find 5 off-targets sites with 3 and 4 mismatches and no mismatches in the 12 bp adjacent to the PAM. However, all these potential off targets are present in introns. We did not confirm these potential sites by sequencing.

In addition, to facilitate detection of embryos KO for s1pr5, we co-injected sgRNA for slc45a2, a gene required for pigmentation, assuming that albinos embryos would also be KO for s1pr5 (not shown). sgRNA for slc45a2 were designed by M. Salanga, (National Xenopus Ressource, Woods Hole, MA). Oocytes from MBP-GFP-NTR were fertilized with spermatozoids from wild type male Xenopus laevis and immediately microinjected with a mixture of slc45a2 and s1pr5 sgRNA and

PCR primers

The regions targeted by the complex Cas9 protein-sgRNA were PCR amplified with genomic primers. We used specific forward primers to amplify the s1p5L (Fn1)

CTTCTGGCTGGTGTGGCATA and s1p5S (Fn2) CTTCACCGGGAAGCTCAACA, respectively. Reverse primer (Rd1) GGTCAACAGCCAGAGACTTGGC was common to s1p5L and s1p5S. PCR parameters were: 5 min at 95 °C followed by 35 Images were analyzed using Image J (NIH) for g-ratio measurements by manually drawing 2 lines across the long and short axis of each axon and axon plus myelin (myelinated fiber). Lengths of the lines (in pixels) as generated by ImageJ were averaged across the 2 perpendicular measurements and converted to micrometer (μm) using the image scale bars. The g-ratio was determined by dividing the mean diameter (long and short axis) of an axon by the mean diameter of the same myelinated fiber.


P Asselin

Y Belkhodja

A Jabri

A Potapov

J Loreau

A Van Der Avoird

Rovibrational laser jet-cooled spectroscopy of the NH3-Ar complex in the ν2 umbrella region of NH3 : comparison between new infrared data and an ab initio calculated spectrum

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Introduction

The interaction of ammonia with rare gases has been the subject of a large number of studies motivated mainly by the interest in weak interactions 1 and, in particular, in the effect of the van der Waals (vdW) interaction on the NH3 inversion tunneling. The inversion-tunneling splitting in NH3 is extremely sensitive to intermolecular interactions and thus represents a valuable probe of asymmetry in the intermolecular potential energy surface (PES) and the vibration-rotation-tunneling (VRT) states of NH3 complexes along the inversion coordinate. Upon complexation, NH3 generally acts as a hydrogen acceptor and binds (near) axially to its binding partner. 2 This leads to a large asymmetry in the NH3 inversion potential which quenches the tunneling, but NH3-Ar has been considered as an exception to this case. The NH3-Ar vdW complex has been the subject of extensive microwave and far infrared spectroscopic studies. The first measurements were performed in the microwave region. 3,4 They determined the expectation value of the intermolecular separation, the dipole moment and the nuclear quadrupole coupling constant. In addition to the assigned pure rotational transitions, many other transitions due to the non-rigidity of the complex were observed and attributed to inversion-tunneling transitions 5,6,7,8,9 , which showed that ammonia behaves almost as a free rotor in the complex. This large collection of results provided further evidence for the free-rotor picture from the precise knowledge of the bound states of the complex, that correlate to the jk = 00,10 and 11 levels of free NH3, including states with vibrational excitations in the vdW stretching coordinate.

Early ab initio studies combined with these in-depth far-infrared measurements led to a semi-empirical intermolecular PES obtained by fitting the experimental data. 10 Structures with various possible orientations of ammonia relative to the vdW bond axis were found, depending on whether the internal angular momentum of the almost freely rotating NH3 unit, is roughly directed along (Π) or perpendicular (Σ) to this axis.7 ,8 Several more and more sophisticated PESs have been developed over the years to improve the understanding of spectroscopic data. More recently, good agreement was obtained between geometry optimizations performed by Bistoni et al. 11 using the coupled cluster method, and molecular beam experiments probing the isotropic part of the PES. In 2014, a four-dimensional (4D) PES was computed by Loreau et al. 12 that includes explicitly the ν2 umbrella motion of NH3 and ND3. Further insight into the internal-rotation dynamics of the complex could be obtained from a direct comparison between the bound states of both NH3-Ar and ND3-Ar calculated on this PES for total angular momentum values up to J = 10 with the inclusion of Coriolis interactions, and spectroscopic data accumulated over 30 years in the microwave and far-infrared regions for both complexes.

Mid- 13,14 and near-infrared 15 data on NH3-Ar remain scarce due to the lack of broadband laser sources in both regions. Using a microwave-sideband CO2 laser optothermal spectrometer, Fraser et al. 13 observed a Π←Σ type infrared transition in the ν2 umbrella excited state and derived spectroscopic constants containing information about the ν2 dependence of the NH3-Ar interaction. From the microwaveinfrared double-resonance technique, Fraser et al. 13 and Bizzari et al. 14 also found in the same region three CO2 laser coincidences, respectively at 938.6893, 970.5498 and 974.6248 cm -1 . The observation of two high frequency rovibrational lines, located 32 and 36 cm -1 above the transition of Fraser et al. 13 was taken as further evidence that the NH3 inversion frequency is essentially unchanged upon complexation, since the tunneling splitting in v2=1 for free NH3 is about 36 cm -1 .

In the present paper, we describe high resolution infrared laser jet-cooled measurements in the ν2 umbrella mode region of NH3-Ar. The main objective is to provide new reliable infrared data to be compared with VRT levels of the ground and v2=1 excited state calculated on the 4D PES of Loreau et al. 12 , the most advanced one computed so far, and thereby to further test the accuracy of this PES. In a first step, band assignments guided by the calculated VRT states, and rovibrational analyses of five v2=10 transitions observed in ortho-NH3-Ar and para-NH3-Ar enabled us to derive precise spectroscopic parameters. Four of these excited states were not previously observed. Band centers of both the lower and upper states of the inversion doublet are exploited to determine the tunneling splitting of the ν2 umbrella state. In a second step, these new infrared data are compared to the VRT levels and transitions calculated on the ab initio 4D PES in order to evaluate the accuracy of the ab initio results in predicting band origins, rovibrational states, inversion tunneling splittings and a manifold of Coriolis couplings in both ground and ν2 states.

Theory

Potential energy surface

In order to assign the experimental bands, we have performed bound state calculations for the ground vibrational state of NH3-Ar and for the first excited v2 = 1 state of the umbrella vibration. These calculations are based on the potential energy surface (PES) presented in Refs. [12, 16]. The PES depends on four coordinates: the distance 𝑅𝑅 between the argon atom and the center of mass of the ammonia molecule, two angles Θ and 𝜑𝜑 that define the orientation of NH3 in the complex, and the coordinate 𝜌𝜌 that describes the umbrella vibrational motion. In the ground state of free NH3, the equilibrium value is 𝜌𝜌 = 112.15°, while 𝜌𝜌 = 90° corresponds to planar NH3. The PES was constructed by computing the interaction energy at 6820 geometries by means of the coupled-cluster method with single, double, and perturbative triple excitations [CCSD(T)] with the AVQZ-DK basis set supplemented by midbond functions using the MOLPRO package. At the global minimum of the PES, the depth of the potential is 147.6 cm -1 . The accuracy of the PES has been assessed in several ways. In its application to NH3-Ar scattering experiments, good agreement was found between calculated and measured differential and integral cross sections. 17,18 Applying it in bound state calculations on the NH3-Ar complex in the ground vibrational state of NH3, the computed rovibrational energy levels and rotational constants were found to be in excellent agreement with the available experimental spectra. 12

Bound states

Our bound state calculations of NH3-Ar are based on the following Hamiltonian

𝐻𝐻 = 𝐻𝐻 int - ℏ 2 2µ𝑅𝑅 𝜕𝜕 𝜕𝜕𝑅𝑅 2 𝑅𝑅 + 1 2µ𝑅𝑅 2 (𝐽𝐽 2 + 𝑗𝑗 2 -2𝒋𝒋. 𝑱𝑱) + 𝑉𝑉(𝑅𝑅, 𝜃𝜃, 𝜑𝜑, 𝜌𝜌) , ( 1
)
where 𝜇𝜇 is the reduced mass of the system, 𝒋𝒋 is the angular momentum operator describing the rotation of NH3 in the complex, and 𝑱𝑱 is the total angular momentum operator. This is a special form of the Hamiltonian for molecule-molecule complexes in body-fixed coordinates derived in Refs. [19,20]. The Hamiltonian 𝐻𝐻 int of the NH3 monomer is given by

𝐻𝐻 int = � 𝑗𝑗 𝑖𝑖 2 2𝐼𝐼 𝑖𝑖𝑖𝑖 (𝜌𝜌) + 𝑇𝑇(𝜌𝜌) + 𝑉𝑉 umb (𝜌𝜌) 𝑖𝑖 (2)
Where 𝑖𝑖 = 𝑥𝑥, 𝑦𝑦, 𝑧𝑧 and the 𝐼𝐼 𝑖𝑖𝑖𝑖 are the corresponding principal moments of inertia. The operator ) (ρ T is the kinetic operator for the curvilinear umbrella motion 21 , while

V umb (𝜌𝜌) is an analytical function describing the double well potential of NH3 in the 𝜌𝜌 coordinate 22 𝑉𝑉 umb (𝜌𝜌

) = 𝑘𝑘 𝜌𝜌 2 �𝜌𝜌 - 𝜋𝜋 2 � 2 + 𝑎𝑎 𝜌𝜌 𝑒𝑒𝑥𝑥𝑒𝑒 �-𝑏𝑏 𝜌𝜌 �𝜌𝜌 - 𝜋𝜋 2 � 2 � (3)
The parameters in this function are 𝑘𝑘 𝜌𝜌 = 92026 cm -1 rad -2 , 𝑎𝑎 𝜌𝜌 = 23383 cm -1 , and 𝑏𝑏 𝜌𝜌 = 3.205 rad -2 . With these parameters, the Hamiltonian of Eq. ( 2) with the potential of Eq. ( 3) accurately reproduces the experimental tunneling frequencies in the ground (v 2 = 0) and first excited (v 2 = 1) umbrella vibrational states (0.79 cm -1 and 35.2 cm -1 , respectively), as well as the v 2 = 0 → 1 excitation frequency of 949.9 cm -1 .

The Hamiltonian is diagonal in the quantum numbers 𝐽𝐽 (total angular momentum) and 𝑀𝑀 (its projection on the space-fixed z axis). The states are also labeled by the quantum number 𝐾𝐾, the projection of 𝐽𝐽 on the van der Waals bond axis 𝑹𝑹, although this is not an exact quantum number due to the Coriolis couplings that mix states with ∆𝐾𝐾 = ±1. States with 𝐾𝐾 = 0 are called Σ states, states with 𝐾𝐾 = 1 are called Π states.

The eigenstates of the Hamiltonian in Eq. (1) were obtained by a variational approach 23,24,25,26,27 with the basis of functions

|𝑗𝑗, 𝑘𝑘, 𝐾𝐾, 𝐽𝐽, 𝑀𝑀, 𝑛𝑛, 𝑣𝑣〉 = � (2𝑗𝑗 + 1)(2𝐽𝐽 + 1) 32𝜋𝜋 3 � 1 2 𝐷𝐷 𝐾𝐾𝐾𝐾 (𝑗𝑗) (0, 𝜃𝜃, 𝜑𝜑) * 𝐷𝐷 𝑀𝑀𝐾𝐾 (𝐽𝐽) (𝛼𝛼, 𝛽𝛽, 𝛾𝛾) * 𝜒𝜒 𝑛𝑛 (𝑅𝑅) 𝑅𝑅 𝛷𝛷 𝑣𝑣 ± (𝜌𝜌) (4)
where 𝑗𝑗 and 𝑘𝑘 are the rotational quantum numbers of NH3, and 𝐷𝐷 denotes the Wigner functions. The angles (𝛼𝛼, 𝛽𝛽, 𝛾𝛾) are the overall rotation angles of the complex: 𝛽𝛽 and 𝛼𝛼 are the polar angles of the vector 𝑹𝑹 with respect to the space-fixed frame and γ describes the rotation of the complex about 𝑹𝑹. The subscript v in 𝛷𝛷 𝑣𝑣 ± (𝜌𝜌) denotes the umbrella vibrational quantum number and the superscript ± labels the symmetric and antisymmetric umbrella tunneling components of each 𝑣𝑣, while 𝜒𝜒 𝑛𝑛 (𝑅𝑅)/𝑅𝑅 is a set of radial basis functions. Experimentalists often use the labels s and a to denote the symmetric and antisymmetric inversion tunneling states of the complex, and we follow this convention elsewhere in this paper.

In a first step, the four functions 𝛷𝛷 𝑣𝑣 ± (𝜌𝜌) corresponding to v 2 = 0 and v 2 = 1, were obtained by solving the one-dimensional Schrödinger equation with the Hamiltonian of Eq. ( 2) in a sinc function discrete variable representation. 28,29 The first two functions 𝑣𝑣 = 0 ± were employed in the basis (4) for the bound state calculations for v 2 = 0, while the next two functions v= 1 ± were selected to construct the basis for v 2 = 1. The calculation of the bound states for v 2 = 0 thus differs slightly from that of Ref. [12] in which all four 𝛷𝛷 𝑣𝑣 ± (𝜌𝜌) functions were included in the basis set; the resulting difference in the rovibrational energies is negligible.

In a second step, the functions 𝜒𝜒 𝑛𝑛 (𝑅𝑅) were obtained using an effective radial potential of the form 25 𝑉𝑉 𝑒𝑒𝑒𝑒𝑒𝑒 = 𝛼𝛼[𝑉𝑉 0 (𝑅𝑅) -𝜁𝜁𝑅𝑅], where 𝑉𝑉 0 (𝑅𝑅) is a radial cut through the minimum of the 4D PES. The parameters 𝛼𝛼 and 𝜁𝜁 were optimized by minimizing the energy of the lowest rovibrational state of the NH3-Ar complex with five eigenfunctions 𝜒𝜒 𝑛𝑛 (𝑅𝑅). The optimized values are 𝛼𝛼 = 1 and 𝜁𝜁 = 1 × 10 -3 𝐸𝐸 ℎ /𝑎𝑎 0 .

Finally, the rovibrational bound states of NH3-Ar were calculated with a basis with 𝑗𝑗 𝑚𝑚𝑚𝑚𝑚𝑚 = 10 and 20 functions 𝜒𝜒 𝑛𝑛 (𝑅𝑅) calculated on an equidistant grid of 110 points from 4.5 to 20 𝑎𝑎 0 . For each irreducible representation (irrep) of the full molecular symmetry group 𝐷𝐷 3ℎ (𝑀𝑀), we calculated the lowest 20 eigenvalues of the Hamiltonian for each 𝐽𝐽 ranging from 0 to 10 by means of the iterative algorithm of Davidson. 30 The irreps are 𝐴𝐴 1 ′ , 𝐴𝐴 1 ′′ , 𝐴𝐴 2 ′ , 𝐴𝐴 2 ′′ , 𝐸𝐸 ′ , 𝐸𝐸 ′′ . Eigenstates carrying irreps 𝐴𝐴 2 ′ , 𝐴𝐴 2 ′′ belong to ortho-NH3-Ar, with nuclear spin statistical weight 12, states carrying irreps 𝐸𝐸 ′ , 𝐸𝐸 ′′ belong to para-NH3-Ar, with nuclear spin weight 6, while states carrying irreps 𝐴𝐴 1 ′ , 𝐴𝐴 1 ′′ are Pauliforbidden. In the calculations of the one-dimensional irreps 𝐴𝐴 1 ′ , 𝐴𝐴 1 ′′ , 𝐴𝐴 2 ′ , 𝐴𝐴 2 ′′ the basis in Eq. ( 4) could be restricted to functions with the NH3 quantum number k = 0 (modulo 3). For the 𝐸𝐸 ′ , 𝐸𝐸 ′′ irreps only basis functions with k = 1(modulo 3) are needed; the basis functions with k = -1(modulo 3) correspond to the other component of these two-dimensional irreps and yield the same energy levels. The 𝐴𝐴 1 ′ , 𝐴𝐴 2 ′ , 𝐸𝐸 ′ states have + parity under inversion, the 𝐴𝐴 1 ′′ , 𝐴𝐴 2 ′′ , 𝐸𝐸 ′′ states have -parity.

Intensities

In order to obtain a complete ab initio prediction of the spectra, we use the wave functions from the bound state calculations to compute line strengths of all allowed ∆𝐽𝐽 = 0, ±1 transitions between the VRT states of the NH3-Ar complex for total 𝐽𝐽 = 0 -10 that accompany the v 2 = 0 → 1 transition of the NH3 monomer. The formulas used to compute the line strengths are taken from Ref. [31], where they have been explicitly derived. Ab initio absorption spectra are then computed from the line strengths by assuming a Boltzmann distribution (at some rotational temperature) of the lower states, and summing over all allowed transitions to the upper states.

The v 2 = 0 → 1 transition is a parallel vibration-tunneling transition of NH3, which obeys the selection rules 𝐴𝐴 2 ′ ↔ 𝐴𝐴 2 ′′ and 𝐸𝐸 ′ ↔ 𝐸𝐸 ′′ . That is, it is allowed between the symmetric (lower) umbrella-inversion tunneling state of the vibrational ground state and the antisymmetric (upper) inversion state of the v 2 = 1 state, and vice versa. Since the tunneling splitting is 0.79 cm -1 in the v 2 = 0 state and as large as 35.2 cm -1 in the v 2 = 1 state this gives rise to two series of lines centered around 968 and 932 cm -1 , respectively. However, the ortho-NH3-Ar complex is bound by 94 cm -1 and the para-NH 3 -Ar complex by 98 cm -1 and the inversion-tunneling splittings are in some cases altered with respect to free NH3. 12 Moreover, the states of even parity of the complex, 𝐴𝐴 2 ′ and 𝐸𝐸 ′ , contain both the even and odd parity states of the NH3 monomer, and so do the states of odd parity, 𝐴𝐴 2 ′′ and 𝐸𝐸 ′′ . Hence, the rovibrational transitions of the complex that accompany the vibration-tunneling transitions on the NH3 monomer cover a large range of frequencies. Since we are only interested in the relative line strengths, the two (nearly equal) transition dipole moments of the parallel vibration-tunneling transitions in NH3 were set equal to 1. Absolute line strengths can be obtained by multiplication with the square of the actual transition dipole moment.

2-Experimental

The rovibrational spectra in the region of the ν2 umbrella mode of NH3-Ar were recorded using a jet-cooled laser spectrometer recently developed at the MONARIS laboratory. This set-up couples an external-cavity quantum cascade laser (EC-QCL) with a pulsed supersonic jet to realize direct absorption in the jet and has already been described in detail in recent papers. 32,33 Only the main characteristics will be presented hereafter.

As clearly demonstrated in many previous jet-cooled studies, the combined use of very diluted molecular samples seeded in high backing pressures of carrier gas enabled to obtain an efficient rovibrational cooling and to stabilize weakly bound complexes. NH3-Ar complexes are produced in a planar supersonic expansion using ternary He/Ar/NH3 mixtures with typically 2% NH3 and Ar/He =2/1 and optimal backing pressures of 3 bar. The light source is a continuous-wave room-temperature mode hop-free EC-QCL with a spectral width of 10 MHz, which covers the 930-990 cm -1 range (Daylight Solutions). About 8% of the total light is sent through two additional laser channels for relative and absolute frequency calibrations. Relative frequencies are monitored by measuring the intensity transmitted through a solid germanium etalon with a free spectral range of 490 MHz, to provide a relative frequency scale. Absolute laser frequencies are obtained by measuring the transmission through a 15 cm-length reference cell containing a known reference gas at a pressure of about 5 mbar (ethene in the present work). The main part of the light is sent through a multipass optical cavity mounted in the jet chamber, which is evacuated by a 2000 l s -1 oil diffusion pump backed by a combination of a 350 m 3 h -1 Roots blower and a 40 m 3 h -1 rotary pump. The optical configuration used for the present study is an astigmatic cavity composed of two 1.5" astigmatic mirrors (R = 99.2%, AMAC-36, Aerodyne Research) aligned according to a 182-pass configuration. Three liquid-nitrogen cooled HgCdTe detectors (Judson J15D12) are used to measure the powers transmitted through the multipass cavity, the etalon and the reference gas cell. The molecular jet is produced by a pulsed nozzle (General Valve Series 9) by fitting a 0.9 mm diameter pin hole nozzle with two modified industrial blades, forming a 30 mm length x 50 µm width slit opening, and serving as the molecular expansion source. Rovibrationally cooled complexes were probed by the infrared laser light at short distances, not larger than 3 mm from the nozzle exit to keep a sufficient density of van der Waals complexes to be probed in the slit jet expansion. Our rapid scan scheme described in detail elsewhere is close to the original designs used for high resolution molecular spectroscopy. 34 Fine tuning of the laser frequency over about 0.8 cm -1 at a repetition rate of 100 Hz is obtained by a sine wave generated by a Labview code and delivered to a piezoelectric transducer attached to the diffraction grating that ends the external cavity. The intensities transmitted through the supersonic jet, the etalon and the reference gas cell are digitized and recorded simultaneously as a function of time. A baseline-free transmittance through the multipass cavity is then obtained by taking the ratio of the corresponding signals recorded with and without the jet. The procedure for absolute frequency calibration is achieved in real time by measuring the deviation between experimental and HITRAN12 35 database C2H4 frequencies after each laser sweep to correct the free spectral range value of the etalon fixed at the beginning of each experiment. The accuracy of the frequency calibration is around 0.0005 cm -1 . While the line width of the QCL source is typically 20 MHz, the resolution (full-width-at-halfmaximum, FWHM) of isolated rovibrational lines achieved with the jet-cooled QCL spectrum is about 75 (10) MHz, limited by both residual Doppler broadening at the temperature of the expansion and a small contribution (dependent on mass of carrier gas) from non orthogonal laser and planar jet crossings in the multi pass optical cavity.

3-Results

3-1 Energy level scheme of the ν2 transition of NH3-Ar

Our high resolution infrared jet-cooled measurements in the ν2 umbrella region of NH3-Ar are guided by many theoretical and experimental studies realized over thirty years. The pioneering microwave study of Fraser et al. 3 evidenced a series of ground state transitions interpreted with a model of the NH3 molecule almost freely rotating due to a nearly isotropic interaction potential. In the ν2 region the observation of several laser coincidences with rovibrational lines of NH3-Ar was interpreted as a proof that the NH3 inversion frequency is practically unchanged upon complexation. 13,14 Here, we further investigate this assumption and provide a precise determination of the inversion splitting in the ν2 state.

Figure 1 displays the internal rotor energy levels of NH3-Ar for the v2=10 transition with their two distinct nuclear-spin modifications noted ortho and para.

Only the ground vibrational state energy levels thermally populated in a pulsed supersonic expansion are shown in the scheme, i.e., the lowest ortho state labeled by Σa(j,k=0) and three para states labeled by Σs(j,k=1), Σa(j,k=1) and Πs(j,k=1), located 12.45, 13.2069 and 13.9603 cm -1 above Σa(j,k=0), respectively. The notations Σ (K=0) and Π (K=1) indicate the projection K of the total rotational angular momentum J on the vdW bond axis, the subscripts s and a designate a symmetric or antisymmetric NH3 inversion wave function, and the state labels j and k are only approximate quantum numbers in the complex that indicate the correlation between the internal rotor state of the complex and the j, k rotational state of the free NH3 monomer.

Accurate energy values for the ground states of ortho and para NH3-Ar were obtained from microwave and submillimeter-wave measurements.5 , 6 , 7 , 8 , 9 Five v2=10 transitions of NH3-Ar were observed with our jet-cooled infrared laser spectrometer: the two ortho transitions are easily assignable due to the presence of a single initial state and the absence of Coriolis couplings in both ground and excited states. They correspond to Πs(j=1,k=0) Σa(j,k=0) and Σs(j=1,k=0) Σa(j,k=0) transitions with the final states shown in Figure 1. Table 1 lists the observed transitions for the two bands of ortho-NH3-Ar. Three additional transitions were also observed in the 938, 970 and 974 cm -1 regions, More challenging assignments to the Πs/a,lower(j,k=1)Σa(j,k=1) and both Πs/a,upper(j,k=1)Σs(j,k=1) transitions in para-NH3-Ar will be justified in detail hereafter. Table 2 lists the observed transitions for the three bands of para-NH3-Ar. The energies of ortho transitions observed correspond to band centers derived from the rovibrational analysis while those of the para transitions correspond to Q(0) line frequencies extrapolated from the Q branch (very close to the band centers). The relative energies of the para and ortho NH3-Ar stacks shown in Figure 1 are extracted from the ground state VRT levels presented by Loreau et al. 12

3-2 Jet-cooled laser spectra results

In the following, we present the five rovibrational bands observed in the region of the v2=10 NH3 monomer band. The two most intense bands characterized by the absence of rotational perturbation are ascribed to NH3-Ar ortho complexes. The three weaker ones are strongly perturbed and unambiguous transition assignments require the use of our ab initio calculated VRT levels and v 2 = 0 → 1 transition frequencies and intensities.

3-2-1 Ortho NH3-Ar complexes

Figure 2a displays the jet-cooled spectrum of the Πs(j=1,k=0)← Σa(j,k=0) transition. This spectrum resembles that of a Π ← Σ type vibrational band of a linear molecule, confirmed by the presence of an R(0) transition and a strong Q branch and the absence of a P(1) transition. As seen in Fig. 2a, the Q branch degrades to the low frequency side but we were unable to resolve the individual Q branch lines. This band was already observed by Fraser et al. 13, but only partially due to the lack of side-band coverage of the lamb-dip stabilized CO2 laser in this region. Thanks to its much higher resolution attainable (∼1 MHz) Fraser et al. could determine the l-type doubling constant q which is involved in the expression of the energy of P, Q and R transitions for the ground and excited states:

𝐸𝐸(±, 𝐽𝐽, 𝑙𝑙) = ν 0 + 𝐵𝐵[𝐽𝐽(𝐽𝐽 + 1) -𝑙𝑙 2 ] ± (𝑞𝑞 2)(𝐽𝐽(𝐽𝐽 + 1) ± 𝑞𝑞 𝐽𝐽 (𝐽𝐽(𝐽𝐽 + 1) 2 ⁄ (5)
where for the ground state, ν 0 , 𝑙𝑙, 𝑞𝑞 and 𝑞𝑞 𝐽𝐽 = 0. 𝑞𝑞 is the 𝑙𝑙-type doubling constant, the + sign is taken for the upper state in the Q-branch transition and the -sign is taken for the upper state in the P-and R-branch transitions of the l-doubled pair in the excited state.

The positive value of q (90.928 MHz) derived from the least squares fit of Fraser et al 13 provided information about the location of neighboring Σ-type states that are Coriolis coupled to the observed Π state and confirmed that the dominant Σ perturbing state is above the Π state, by about 12 cm -1 using a pure precession model.13 Figure 2b displays our global fit of the Πs(j=1,k=0) state parameters using the PGOPHER software 36 with 25 rotational lines,18 R(J) and P(J) lines from the present study and 7 Q(J) lines determined at sub MHz precision by Fraser et al. 13 Figure 3a displays the jet-cooled spectrum of the Σs(j=1,k=0)← Σa(j,k=0) transition never observed previously. The absence of a Q branch confirms the assignment of a Σ ← Σ type vibrational band. The spectrum is slightly blurred by intense NH3 monomer lines but the simulation (Fig. 3b) well matches the observed one with a rms error of about 5 MHz for 23 rovibrational lines and a rotational temperature of about 3 K. Table 3 lists the molecular parameters derived from the simulation of both rovibrational band contours, as well as the values extracted from a fit to the VRT levels that we calculated for total angular momentum J values up to 10.

3-2-2 Para NH3-Ar complexes

Figure 4a displays the jet-cooled spectrum observed in the 936.8-939.4 cm -1 region where we expected to observe the lower component of the inversion doublet. The spectrum is quite puzzling due to the presence of several overlapping series of rotational lines with strongly unequal spacings, characteristic of Coriolis couplings. Another difficulty is related to the weakness of the observed para transitions. There are three reasons why these transitions are weaker than the ortho transitions: i) the relative population of ortho and para states is determined by the nuclear spin weights, which are 12 and 6, respectively, ii) the population of the para states is shared by three low-lying states and iii) the line strengths of the para lines are generally smaller in NH3-Ar.

Taking advantage of microwave transitions assigned for the NH3-Ar states correlating with Ar+NH3 (j=1,|k|=1) by Zwart et al.8, we are able to provide combination differences in the ground state allowing us to check the initial state of the observed transitions. We found a remarkable agreement between the energy difference measured by submillimeter spectroscopy between the J=2 and J=4 levels of the Σa(j=1,k=1) state and that between two rotational lines observed at 938.4191 and 937.2592 cm -1 , both equal to 1.1598 cm -1 . This allowed us to assign these lines to R(2) and P(4), respectively. Moreover, our attributions are confirmed by the microwave-infrared double resonance measurements of Fraser 13 who tentatively assigned two CO2 laser coincidences at 937.1656 and 938.6893 cm -1 to P(5) and R(3) lines of the Πs/a,lower(j=1,k=1)← Σa(j=1,k=1) transition, very close to the lines observed in the present study at 937.1658 and 938.6896 cm -1 . Finally our calculated VRT levels, transition frequencies, and line strengths are used to provide a definite proof of this assignment: on the basis of energy and relative line strengths only one v2=1←0 transition of NH3-Ar is compatible with our observations in the investigated region, namely the Πs/a,lower(j=1,k=1)← Σa(j=1,k=1) transition. According to the selection rules of l-doubling in a Π←Σ transition, P and R branch lines terminate on rotational levels of the same parity (a↔a) as opposed to the Q branch lines that terminate on rotational levels of the opposite parity (a↔s). [START_REF] Bernath | Spectra of atoms and molecules[END_REF] Figure 4b displays the theoretical spectrum of the Πs/a,lower(j=1,k=1)← Σa(j=1,k=1) transition weighted by a rotational population at 3 K. Q branch lines were slightly shifted in frequency, as well as P and R branch lines to obtain a correct absolute frequency agreement with the jet-cooled spectrum.

In the same manner, Figure 5a displays the jet-cooled spectrum observed in the 973.2-976.6 cm -1 region where we expected to observe the upper component of the inversion doublet. Spectral assignments are not straightforward either except for the Q branch pattern clearly observed around 974.5 cm -1 . Following the same approach as for the lower component region, an excellent match is found between the energy difference of 1.1988 cm -1 separating the J=2 and J=4 levels of the Σs(j=1,k=1) state and that between two rotational lines observed at 975.0561 and 973.8573 cm -1 , which enabled us to assign these lines to R(2) and P(4), respectively. Again our ab initio calculated results nicely confirm this preliminary assignment as proved by the very good agreement between the jet-cooled and the theoretical spectrum of the Πs/a,upper(j=1,k=1)← Σs(j=1,k=1) transition (Fig. 5b) shifted in frequency by the same value for all branches.

Lastly, Figure 6 displays the jet-cooled spectrum observed in the 969.3-972.5 cm -1 region. Our calculation of the VRT levels of the ν2 state predicts a second Πs/a,upper (j=1,k=1) state of the same symmetry and with the same approximate quantum numbers as the first Πs/a,upper(j=1,k=1) state, but lower in energy by -3.536 cm -1 (see Figure 1). A second Πs/a,upper(j=1,k=1)← Σs(j=1,k=1) transition is indeed observed in this region, but it is less intense, in agreement with the smaller line strengths calculated. Only the Q and R branches are clearly observed and assigned [as for example the Q(2) line corresponding to the CO2 laser coincidence observed by Bizzari et al. 14 at 970.5498 cm -1 ], while the P branch displays a confused pattern of weak lines that makes a reliable assignment difficult. Actually, the calculated VRT levels predict two transitions likely to be observed in this region, terminating in the nearby states Πs/a,upper(j=1,k=1) and Δs/a(j=2,k=2) with an intensity ratio of 4/1. The calculated Q branch pattern of the Δs/a(j=2,k=2)←Σs(j=1,k=1) transition nicely reproduces the asymmetry on the high frequency side observed in the jet-cooled spectrum, while the Πs/a,upper(j=1,k=1)←Σs(j=1,k=1) transition does not. It fails to reproduce the rovibrational spacings, however, so we essentially assign the band in this region to the Πs/a,upper(j=1,k=1)← Σs(j=1,k=1) transition. As discussed in Section 4, the nearby states Πs/a,upper(j=1,k=1) and Δs/a(j=2,k=2) are very strongly mixed by Coriolis coupling.

From the assignment of the observed para-NH3-Ar transitions, we could determine two different inversion splittings in the ν2 state. Due to probable Coriolis couplings within these transitions it is not possible to correctly reproduce the observed spectra to extract precise band centers. According to the diagram energy level in Figure 1, the splittings between the Πs/a,lower(j=1,k=1)←Σa(j=1,k=1) transition and each of the two Πs/a,upper(j=1,k=1)← Σs(j=1,k=1) transitions in para-NH3-Ar observed and analyzed in the present study correspond to the sum of the Σa-Σs splitting of 22.691 GHz determined precisely in the ground state and two different inversion splittings in the ν2 state. Using extrapolated Q(0) frequency values of 937.6621 cm -1 for the lower band, and 970.4215 and 974.4268 cm -1 for the two higher bands, we derived inversion splittings of 32.003(1) and 36.008(1) cm -1 . These values are of roughly the same size as the corresponding inversion splitting in free NH3.

These findings imply that the inversion splitting pattern in the v2=1 excited state is qualitatively different from that in the ground state. Loreau et al. 12 found for the ground state that the inversion splitting of the Σ levels is nearly unchanged with respect to free NH3, while in the Π states inversion tunneling is nearly quenched and the level splitting is very small. All v2=1 excited states involved in the transitions observed here are Π states, but we still find inversion splittings nearly as large as in free NH3. A detailed picture of the inversion tunneling in both the v2=0 and v2=1 states can be obtained by careful inspection of our ab initio calculated VRT levels and wave functions. Also the Coriolis couplings that are important in the observed para NH3-Ar spectra can be understood from the analysis of the wave functions, because we explicitly take this type of perturbation into account in our calculations. These points will be examined below.

4-Discussion

New reliable infrared data are derived from the band contour analysis of rovibrational jet-cooled spectra of two ortho and three para v2=10 transitions. For the Πs(j=1,k=0)← Σa(j,k=0) band, the molecular parameters for the Πs(j=1,k=0) state determined by Fraser 13 using Lamb dip spectroscopy are more accurate than ours by about a factor 20. We note, however, a difference of about 0.004 cm -1 between the respective band origins. Our accuracy in the absolute frequency from calibration based on the correction of the free spectral range of the etalon after measuring the deviation between about fifty experimental and HITRAN 35 C2H4 frequencies over the 949-951.5 cm -1 range, is about 10 times less than the difference reported between both measurements. Therefore, we are confident that the band origin value determined in the present study is correct.

More generally, we could determine with a very good precision the band origins of five ν2 states. The energy difference between the ortho states Σs(j=1,k=0) and Πs(j=1,k=0), equal to 10.34974 cm -1 , is now corrected with respect to the estimated value (12.1 cm -1 ) of Fraser 13 and can be used to refine predictive models. Even though we could not determine the band origin of the para bands with the same precision as for the ortho ones, the extrapolated Q(0) line frequencies reported in Figure 1 are sufficiently reliable to determine whether our new infrared data related to the ν2 mode of NH3-Ar agree with our ab initio calculated frequencies. From the energies and wave functions of the VRT states of the complex we computed transition frequencies and line strengths, from which we generated theoretical spectra at the experimental rotational temperature for the five bands observed. For the ortho bands, the experimental band origins are reproduced to within 0.04 and 0.74 cm -1 for the Πs(j=1,k=0) and Σs(j=1,k=0) states, respectively, and the rotational constants B differ by at most 0.4% from the experimental values. For the para bands, the maximum deviation is 0.38 cm -1 for the band origins. Table 4 displays a comparison between band centers (or Q(0) line positions) of the five ν2=10 transitions of NH3-Ar observed and calculated ab initio. Our experimentally determined tunneling splittings of the ν2 state of 32.003 and 36.008 cm -1 agree well with the values of 32.09 and 35.51 cm -1 predicted by the extrapolated Q(0) lines from the ab initio calculated VRT levels.

The inversion tunneling pattern in the v2=1 excited states, which is qualitatively different from that in the ground state, 12 can be understood by analysis of the ab initio calculated wave functions. In the lower component of the inversion doublet in para NH3-Ar excited in the band at 937.6621 cm -1 the umbrella wave function of the NH3 monomer in the complex is a pure symmetric inversion state. This implies that inversion is nearly unhindered, as in free NH3, even though this state is a Π state. The upper component of the inversion doublet is actually split into two Π levels. In the lower one of these levels, accessed by the band at 970.4220 cm -1 , the NH3 umbrella wave function contains 65% of the symmetric inversion state and 35% of the antisymmetric one. In the higher one, accessed by the band at 974.4268 cm -1 , the umbrella wave function has 43% of symmetric and 57% of antisymmetric inversion character. This implies that the NH3 inversion tunneling is hindered by the interaction with Ar and that the umbrella wave functions are more or less localized in one or the other of the wells of the double-well inversion potential. In such a complicated case, the question is how to define the inversion splittings. Adopting the conventional picture from the literature, we chose to identify the two inversion splittings of 32.003 and 36.008 cm -1 with the frequency differences between the origins of the bands at 970.4215 and 974.4268 cm - 1 and the band at 937.6621 cm -1 . However, since the character of the upper states accessed by the bands at 970.4220 and 974.4268 cm -1 indicates that inversion tunneling is nearly quenched in these states, it would perhaps be better to consider the frequency difference of 4.005 cm -1 between the origins of these upper states as the inversion splitting.

The very good reproduction of rovibrational band patterns of three para bands terminating on the lower and upper components of the inversion doublet (Figures 4, 5 and6) nicely proves that the Coriolis couplings included in our calculations of the VRT levels give a realistic picture of the internal dynamics in the ν2 mode. More information can be now be extracted about the relative contribution of these couplings for the five ν2 para states involved in this study, namely Σa(j=1,k=1), Σs(j=1,k=1), Πs/a,lower(j=1,k=1) and Πs/a,upper(j=1,k=1), where the latter state has two components separated by about 4 cm -1 .

We illustrate the importance of Coriolis coupling in the excited para states Πs/a,upper and Πs/a,lower with nearby states by comparing the relative weights of the final states. For the Πs/a,lower (j=1,k=1) state, the relative weight of the Π state is higher than 99.3% for all J. This state is weakly coupled with the Σa,s(j=1,k=1) state, 4.95 cm -1 lower in energy. For the highest Πs/a,upper (j=1,k=1) state, the relative weight of the Π component decreases from 99.9 to 89.5% as J increases from 1 to 8. It is therefore more strongly coupled than the lower Π state, with three closer states, namely Σa (j=1,k=1) (not shown in Fig. 1) and Δs/a(j=2,k=2), which are 4.05 and 3.194 cm -1 lower in energy, respectively and Δs/a(j=2,k=1), which is 2.247 cm -1 higher (Figure 1). The contribution of Σ and Δ states coupled to Πs/a,upper(j=1,k=1) is almost equal. It is not surprising that Coriolis coupling is stronger in this Πs/a,upper(j=1,k=1) state, due to the presence of three states closer in energy. The lowest Πs/a,upper (j=1,k=1) state lies even closer to the Δs/a(j=2,k=2) state, which implies that Coriolis coupling is still stronger. The weight of the Π component decreases from 99.7 to 63.4% when J increases from 1 to 8 and the nearby Δs/a(j=2,k=2)←Σs(j=1,k=1) transition clearly affects the band contour of the lowest Πs/a,upper (j=1,k=1) ←Σs(j=1,k=1) transition. Accordingly, the Δs/a(j=2,k=2) state contains a substantial amount of Πs/a,upper (j=1,k=1) character, up to 35% for J = 8. Such a mixing of states is confirmed by the good match of the Q(J) ∆←Σ band contour with our observations. Coriolis coupling is expected to be very strong also in the ground states of para NH3-Ar, since the coupled state Πs/a(j=1,k=1) is close in energy to the perturbing states: it is only 1.51 and 0.76 cm -1 higher than Σs(j=1,k=1) and Σa(j=1,k=1), respectively. Figure 7 displays the evolution of the relative weight of Πs/a(j=1,k=1) of the lower states Σs(j=1,k=1) and Σa(j=1,k=1) as a function of the rotational quantum number J, extracted from our calculations of the VRT wave functions. A nearly linear increase of the coupling from 0 (J = 0) to 15.11% (J = 8) for Σs(j=1,k=1), and from 0 to 19.71% for Σa(j=1,k=1) is observed, directly correlated with a decrease of the relative weight of Πs/a,upper(j=1,k=1). Hence, the accurate reproduction of the band contour pattern of most of observed transitions by our ab initio calculations allows us to claim that the unequal rovibrational spacings observed are mainly due to strong Coriolis coupling in the ground states for the Πs/a,lower(j=1,k=1)← Σa(j=1,k=1) transition, and in both ground and excited states for the Πs/a,upper(j=1,k=1)← Σs(j=1,k=1) transition.

Finally, Coriolis coupling contributes to the complexity of the assignment of rovibrational lines in both regions 969.5-972.5 cm -1 and 973.2-976.6 cm -1 since the transitions Δs/a(j=2,k=2)←Σs(j=1,k=1) and Δs/a(j=2,k=1)← Σs(j=1,k=1), are allowed by mixing of the Δs/a(j=2,k=2) and Δs/a(j=2,k=1) states with the two Πs/a,upper(j=1,k=1) states. Our ab initio calculations predict that the Q branch of the weak Δs/a(j=2,k=1)←Σs(j=1,k=1) transition is expected to lie at about 975 cm -1 .

Conclusion

The tunable infrared laser spectrometer recently developed at MONARIS has been exploited to probe the rarely investigated ν2 umbrella mode region of the NH3-Ar van der Waals complex in a pulsed supersonic jet expansion. Our rovibrational study was guided by sub-MHz microwave-infrared double resonance experiments 13 and by calculations of the VRT levels based on a 4D potential energy surface from ab initio calculations that includes explicitly the umbrella inversion motion 12 .

Two bands in ortho-NH3-Ar and three bands in para-NH3-Ar were unambiguously assigned in the 936-975 cm -1 region on the basis of a rovibrational analysis for the ortho ones, and by comparison with our ab initio calculated VRT levels and transitions for the para bands. The ab initio results for both the ortho and para species turn out to be very predictive in terms of band centers, upper state rotational constants, and relative weight of Coriolis couplings in the ground and excited ν2 states. Moreover, the values of the tunneling frequencies derived from the calculated VRT states agree with the experimental values measured in the ν2 state within an error not larger than 1.4 %.

As already highlighted in recent studies combining spectroscopy with high level ab initio calculations [START_REF] Ziemkiewicz | [END_REF]39 , the present study demonstrates once again the interest to compare spectroscopic measurements and theoretical predictions based on ab initio calculated PESs in order to improve the understanding of weak interactions: the computation of multi-dimensional PESs and VRT spectra based on these potentials helps to unravel the rovibrational spectra of VdW complexes showing a rich internal dynamics, while a wealth of reliable spectroscopic data is needed to check and possibly improve the accuracy of a PES and to make it fully predictive. In the near future, other NH3-containing complexes could be investigated in the ν2 umbrella mode region with the same set-up to probe the asymmetry of the intermolecular PES with respect to the umbrella inversion motion. The energies reported for ortho transitions correspond to band centers derived from the fitting of rovibrational band contours. The energies reported for para transitions correspond to frequencies of Q(0) lines extrapolated from the rovibrationally resolved distribution of the Q branch. The NH3-Ar states involved in this study are labeled by Σ(j,k), Π(j,k), ∆(j,k) where Σ, Π, ∆ …denote the projection of the total rotational angular momentum J on the vdW bond axis, while j and k give the correlation between the internal-rotor state of the complex and the j,k rotational states of the free NH3 monomer. Other NH3-Ar states which are Coriolis coupled to the initial and final states of the observed transitions are written in italics. The energy difference of 12.45 cm -1 between the lowest ortho and para states corresponds to the difference between the calculated zero-point levels of ortho NH3-Ar (-94.22 cm -1 ) and para NH3-Ar (-81.77 cm -1 ). 12 Ground state para energies are given by Zwart et al. 8 The relative energies of the para ν2 levels are derived from our ab initio calculated VRT levels. In the 938 cm -1 region, they are defined with respect to the Πs/a,lower(j=1,k=1) state. In the 970-974 cm -1 region, they are defined with respect to the highest Πs/a,upper(j=1,k=1) state. As discussed in the text, there are two Πs/a,upper(j=1,k=1) states with the same symmetry and the same approximate quantum numbers, but different in energy and with different umbrella inversion wave functions. For the sake of comparison between the spectra, the Q branch has been shifted by -0.12 cm -1 , the P and R branches by +0.02 cm -1 in the theoretical spectrum. The final state of the Q branch transition is Πs (opposite parity with respect to Σa), while that of the P and R branches is Πa (the same parity as Σa). 4 For the Πs(j=1,k=0) state, the molecular parameters reported in the column "this work" are obtained from a line list composed of 18 P(J) and R(J) rotational lines observed by direct absorption spectroscopy (this work) supplemented with 7 Q(J) lines observed using saturated absorption spectroscopy by Fraser et al. 13 This set of parameters is compared to that obtained by Fraser et al. 13 with a resolution twenty times better. The parameters "calculated" are from fits to the VRT levels calculated for J values up to 10.

Transition ν0 (cm -1 ) exp ν0 (cm -1 ) calc Πs(j=1,k=0)←Σa(j=0,k=0) Σs(j=1,k=0)←Σa(j,k=0) Πs/a,lower(j=1,k=1)←Σa(j=1,k=1) Π s/a,upper(j=1,k=1)←Σs(j=1,k=1) Π s/a,upper(j=1,k=1)←Σs(j=1,k=1) 950.38396 (7)

  Rovibrational laser jet-cooled spectroscopy of the NH 3 -Ar complex in the ν 2 umbrella region of NH 3 : comparison between new infrared data and an ab initio calculated spectrum Pierre Asselin, Yacine Belkhodja, Atef Jabri, Alexey Potapov, Jérôme Loreau, Ad van Der Avoird To cite this version: Pierre Asselin, Yacine Belkhodja, Atef Jabri, Alexey Potapov, Jérôme Loreau, et al.. Rovibrational laser jet-cooled spectroscopy of the NH 3 -Ar complex in the ν 2 umbrella region of NH 3 : comparison between new infrared data and an ab initio calculated spectrum. Molecular Physics, 2018, 116 (23-24), pp.3642 -3655. 10.1080/00268976.2018.1471533. hal-01912258

Figure 1 :

 1 Figure1: Lowest internal rotor energy levels in both v2=0 and v2=1 states of the ν2 umbrella mode of NH3-Ar. The five mid-infrared transitions observed are represented by bold type arrows. The energies reported for ortho transitions correspond to band centers derived from the fitting of rovibrational band contours. The energies reported for para transitions correspond to frequencies of Q(0) lines extrapolated from the rovibrationally resolved distribution of the Q branch. The NH3-Ar states involved in this study are labeled by Σ(j,k), Π(j,k), ∆(j,k) where Σ, Π, ∆ …denote the projection of the total rotational angular momentum J on the vdW bond axis, while j and k give the correlation between the internal-rotor state of the complex and the j,k rotational states of the free NH3 monomer. Other NH3-Ar states which are Coriolis coupled to the initial and final states of the observed transitions are written in italics. The energy difference of 12.45 cm -1 between the lowest ortho and para states corresponds to the difference between the calculated zero-point levels of ortho NH3-Ar (-94.22 cm -1 ) and para NH3-Ar (-81.77 cm -1 ).12 Ground state para energies are given by Zwart et al.8 The relative energies of the para ν2 levels are derived from our ab initio calculated

Figure 2 :

 2 Figure 2: Jet-cooled laser spectrum of the transition Πs(j=1,k=0)← Σa(j=0,k=0) in ortho NH3-Ar (a) compared to the PGOPHER fit of 25 rotational lines, 18 P(J) and R(J) lines from the present study and 7 Q(J) lines from Fraser et al. 13 (b). The lines marked by an asterisk are from the NH3 monomer.

Figure 3 :

 3 Figure 3: Jet-cooled laser spectrum of the transition Σs(j=1,k=0)← Σa(j,k=0) in ortho NH3-Ar (a) compared to the PGOPHER fit of 23 rotational lines observed in the present study (b). The lines marked by an asterisk are from NH3 monomer.

Figure 4 :

 4 Figure4: Jet-cooled laser spectrum of the transition Πs/a,lower(j=1,k=1)← Σa(j=1,k=1) in para NH3-Ar (a) compared to the theoretical spectrum of the same transition at a rotational temperature of 3K generated with our VRT levels and transition line strengths. (b) For the sake of comparison between the spectra, the Q branch has been shifted by -0.12 cm -1 , the P and R branches by +0.02 cm -1 in the theoretical spectrum. The final state of the Q branch transition is Πs (opposite parity with respect to Σa), while that of the P and R branches is Πa (the same parity as Σa).

Figure 5 :

 5 Figure 5: Jet-cooled laser spectrum of the highest transition Πs/a,upper(j=1,k=1)← Σs(j=1,k=1) in para NH3-Ar (a) compared to the theoretical spectrum of the same transition at a rotational temperature of 3 K generated with our VRT levels and transition line strengths. (b) For the sake of comparison between the spectra, the theoretical spectrum has been shifted by +0.38 cm -1 . The final state of the Q branch transition is Πa (opposite parity with respect to Σs), while that one of the P and R branches is Πs (the same parity as Σs).

Figure 6 :

 6 Figure 6: Jet-cooled laser spectrum of the lowest Πs/a,upper(j=1,k=1)← Σs(j=1,k=1) transition in para NH3-Ar.The final state of the Q branch transition is Πa (opposite parity with respect to Σs), while that of the P and R branches is Πs (the same parity as Σs). The very intense band at 971.88203 cm -1 is the R(1,1) line of NH3 monomer.

Figure 7 :

 7 Figure 7: Relative weights of the Σs(j=1,k=1) (*) and Σa(j=1,k=1) (o) components in the Πs/a(j=1,k=1) ground state of para NH3-Ar.

Table 1

 1 Experimental and ab initio calculated frequencies of observed transitions (in cm -1 ) for the Πs(j=1,k=0)←Σa(j=0,k=0) and Σs(j=1,k=0)←Σa(j,k=0) bands of ortho NH3-Ar complexes.Transition Πs/a,lower(j=1,k=1)← Σa(j=1,k=1) Πs/a,upper(j=1,k=1)← Σs(j=1,k=1) Πs/a,upper(j=1,k=1)← Σs(j=1,k=1)

	Transition Πs(j=1,k=0)← Σa(j=0,k=0)	Σs(j=1,k=0)← Σa(j,k=0)
		Experimental Calculated Experimental Calculated
	P(1)	-	-	960.5416	961.285
	P(2)	949.9938	949.956	960.3530	961.096
	P(3)	949.7896	949.754	960.1673	960.910
	P(4)	949.5789	949.547	959.9850	960.726
	P(5)	949.3624	949.335	959.8056	960.545
	P(6)	949.1404	949.117	959.6296	960.364
	P(7)	948.9121	948.894	959.4570	960.187
	P(8)	-	-	959.2873	960.012
	P(9)	-	-	959.1212	959.840
	P(10)	-	-	958.9574	959.668
	R(0)	950.5697	950.528	960.9287	961.668
	R(1)	950.7489	950.707	961.1267	961.863
	R(2)	950.9216	950.880	961.3273	962.059
	R(3)	951.0876	951.048	961.5310	962.258
	R(4)	951.2475	951.210	961.7369	962.457
	R(5)	951.4007	951.366	961.9456	962.659
	R(6)	951.5476	951.516	962.1562	962.861
	R(7)	951.6878	951.660	962.3689	963.065
	R(8)	-	-	962.5831	963.269
	R(9)	-	-	962.7992	963.475

Table 2 :

 2 Experimental and ab initio calculated frequencies of observed transitions (in cm -1 ) for the Πs/a,lower(j=1,k=1)←Σa(j=1,k=1) and for both Πs/a,upper(j=1,k=1)←Σs(j=1,k=1) bands of para NH3-Ar complexes.

		Σa(j=0,k=0)	Πs (j=1,k=0)	Σs (j=1,k=0)
			This work	Fraser et al.	This work
			Calculated		Calculated
	ν0 (cm -1 )		950.38396(7)	950.38769(3)	960.73361(5)
			950.342(3)		961.475(3)
	B''(B') (MHz)	2876.84901(79)	2826.06(43)	2826.9116(93)	2922.83(5)
			2837.6(84)		2913.0(80)
	DJ''(DJ') (MHz)	0.088695(98)	0.07276(52)	0.07815(19)	0.11470(33)
			0.18(11)		0.22(12)
	q'(MHz)		88.46(81)	90.928(12)
			81.5(88)
	Number of lines		19	18	23
	RMS error (MHz)		4.3	0.25	5.0

Table 3 :

 3 Molecular parameters for the transitions v2=1←0 Πs(j=1,k=0)← Σa(j,k=0) and Σs(j=1,k=0)← Σa(j,k=0) of ortho NH3-Ar. The molecular parameters of the Σa(j,k=0) state are given by Nelson et al.

Table 4 :

 4 Experimental and calculated band origins of the observed bands. The asterisk * marks the band origins of para bands corresponding to the extrapolated Q(0) rotational line.

		950.342(5)
	960.73361(3)	961.475(3)
	937.6621*	937.7821*
	970.4220*	970.6340*
	974.4268*	974.0468*

Acknowlegments

This work was supported by the MICHEM Labex at Sorbonne Université. AP acknowledges COST Action CM1401 "Our Astro-Chemical History".