Ivo Cacelli

Rinaldo Poli

B Elsje

Alessandra Quadrelli

Antonio Rizzo

Kevin M Smith

A Density Functional Study of Open-shell Cyclopentadienyl-molybdenum(II) Complexes. A Comparison of Stabilizing Factors: Spin-pairing, Mo-X π Bonding, and Release of Steric Pressure

The dissociation of PH 3 from the 18-electron system CpMoX(PH 3 ) 3 to afford the corresponding 16-electron CpMoX(PH 3 ) 2 fragment has been investigated theoretically by DFT for X = H, CH 3 , F, Cl, Br, I, OH, and PH 2 . The product is found to prefer a triplet spin state for all X ligands except PH 2 , the singlet-triplet gap varying between 1.7 kcal/mol for OH to 8.7 kcal/mol for F. The Mo-PH 3 bond dissociation energy to the 16-electron ground state varies dramatically across the series, from 4.5 kcal/mol for OH to 23.5 kcal/mol for H and correlates with experimental observations on trisubstituted phosphine derivatives. Geometry-optimized spin doublet CpMo(PH 3 ) 3 , on the other hand, has a Mo-PH 3 BDE of 24.3 kcal/mol. The modulation of the Mo-PH 3 BDE by the introduction of X is analyzed in terms of three effects which stabilize the 16-electron product relative to the 18electron starting complex: (i) adoption of the higher (triplet) spin state by release of pairing energy;

(ii) Mo-X π interactions; (iii) release of steric pressure. A computational model for the approximate separation and evaluation of these three stabilizing effects is presented. According to the results of these calculations, the relative importance of the three effects depends on various factors related to the nature of X. For double-sided π donor X ligands, the larger triplet-singlet gap is provided by the more electronegative atoms (F > Cl > Br > I), while single-sided π donors favor the singlet state. The π stabilization ability goes in the order PH 2 > OH > F > other halogens > H. Finally, the major steric interaction appears to be associated with the presence of inactive lone-pairs and by their orientation/proximity to the PH 3 ligands (Cl, Br > I, OH > F, PH 2 , H, CH 3 ). The 16-electron methyl system establishes a marked -agostic interaction in the singlet state, which remains nevertheless unfavored relative to an undistorted triplet configuration.

Introduction

The chemistry of organometallic compounds is dominated by the 18-electron rule and by diamagnetism. [START_REF] Collman | Principles and Applications of Organotransition Metal Chemistry[END_REF] This is the direct consequence of three factors: the high bond covalency in this realm of chemistry, the ability of the ligands to establish π back-bonding interactions with the central metallic element, and the relatively low electron-electron repulsion enabling the establishment of spin-paired configurations. Electronically unsaturated (open-shell) configurations are, however, frequently associated with reaction intermediates (this being the basis of Tolman's "16 and 18electron rule"), [START_REF] Tolman | [END_REF] and can lead to the isolation of stable compounds under favorable circumstances. A clear understanding of the factors at work in the stabilization of open-shell structures relative to saturated counterparts is therefore fundamental for the rationalization of reaction rates and catalytic activity.

Complexes having a 16-electron configuration may be accessed from closed-shell precursors in a number of ways, e.g. ligand dissociation, reductive elimination, migratory insertion, and so on. Four mechanisms may be distinguished for their energetic stabilization relative to the saturated precursor: (i) release of steric pressure associated with the decrease of interligand repulsive van der Waals interactions; 3 (ii) intervention of ligand lone pairs (π-donation); 4,5 (iii) release of pairing energy (this playing a role only when the open-shell and saturated species have different spin states); 6 (iv) interactions, including agostic ones, with other donor molecules (e.g. the solvent) or groups (e.g. dangling donor functions from ligands). The fourth mechanism effectively consists of the temporary saturation of the open coordination site (replacement of a ligand with a more labile one), rather than the relative stabilization of an unsaturated structure. It is responsible, for instance, for the acceleration of many reactions involving a rate-determining dissociative step when these are carried out in donor solvents. The present contribution focuses only on the analysis of the first three effects, although the intervention of intramolecular -agostic interactions will be highlighted in a particular case.

The relative importance of each of these effects cannot be easily determined or estimated. We will be concerned here with the formation of half-sandwich 16-electron Mo(II) complexes by ligand dissociation from 18-electron precursors, but the arguments may be extrapolated to any other reaction generating a 16-electron from an 18-electron compound or any (n-2)-electron from an n-electron compound. We shall take CpMoX(PH 3 ) 2 as a model for the bis-PMe 3 complexes previously used by us in a number of studies. [7][8][9][10][11] The relevance of a sterics-related stabilization is experimentally indicated by the equilibrium between Cp*MoCl(PMe 3 ) 3 and the mixture of Cp*MoCl(PMe 3 ) 2 and PMe 3 at room temperature, or between CpMoCl(PMe 2 Ph) 3 and the mixture of CpMoCl(PMe 2 Ph) 2 and PMe 2 Ph upon warming, whereas no phosphine loss was observed for CpMoCl(PMe 3 ) 3 under the same conditions. 8 The absence of any CpMo(OH)(PMe 3 ) 3 in equilibrium with a mixture of CpMo(OH)(PMe 3 ) 2 and PMe 3 , 10,11 on the other hand, demonstrates the intervention of additional stabilizing factors (OH occupies less space than Cl). Both Cl and OH have lone pairs and are thus capable of providing π stabilization. It is generally believed that a hydroxo ligand is a stronger π donor than the halogens but quantitative assessment, to our knowledge, are not available. On the other hand, since the stable 16-electron systems Cp*MoCl(PMe 3 ) 2 and CpMo(OH)(PMe 3 ) 2 exhibit a spin triplet ground state, a stabilizing factor associated to the release of pairing energy must also play a role.

The quantitative evaluation of π bond strengths is a difficult exercise. 4 It requires the separation of  and π bonding components, which is experimentally impossible and theoretically nonrigorous. 12- 14 From the experimental point of view, qualitative evaluations of trends in M-X π bond strengths, these relating in most cases to bonds between a metal and the halogens, have been deduced from the analysis of NMR chemical shifts, 15 EPR g values, 16 IR carbonyl stretching frequencies, 17,18 electrochemical data, 19,20 UV-visible spectra, [START_REF] Lever | Inorganic Electronic Spectroscopy[END_REF][START_REF] Bendix | [END_REF] valence photoelectron spectra, 23 X-ray crystal structures, 24,25 and rates of chemical and fluxional processes or even the simple observation that certain reactions take place whereas others do not. [26][27][28][29] The use of such a wide array of techniques, each necessitating a different set of assumptions and approximations, has led to controversy. For instance, no universal agreement seems to have been achieved as to the whether a lighter donor atom is a weaker or a stronger π donor than a heavier congener (e.g. Cl vs. I or SR vs. TeR); the relative donor power may well depend on the nature of the metal as well as on the chemical environment.

From the point of view of theory, different localization and partition schemes have been employed 14,[30][31][START_REF] Edmiston | Quantum Theory of Atoms, Molecules and Solid State[END_REF][START_REF] Pipek | [END_REF][34][35][36][37][38][39][40] but, to the best of our knowledge, these have not been applied to characterize the nature of the metal to ligand bonding in transition metal complexes of the kind studied here.

In a recent contribution, 11 we have presented a new computational model that has allowed us, within certain approximations, to tell apart the contributions of interligand repulsion, π donation, and electron pairing to the relative stabilization of the CpMoX(PH 3 ) 2 model systems. We have now refined this model and extended it to a wider range of X ligands. The results reported herein allow, among other things, a rough quantitative estimation of the Mo-X π bond strength.

Computational Details

All electronic structure and geometry optimization calculations were performed using Gaussian-94 41 on an SGI Origin 200 workstation at the Université de Bourgogne and on both a Alpha Digital and a SGI Indigo 2 in Pisa. The three-parameter form of the Becke, Lee, Yang and Parr functional (B3LYP), 42 was employed. The LanL2DZ basis set includes both Dunning and Hay's D95 sets for H, C, O and F [START_REF] Dunning | Modern Theoretical Chemistry[END_REF] and the relativistic Electron Core Potential (ECP) sets of Hay and Wadt for the 10 innner electrons of Cl and P, the 18 inner electrons of Br, and the 28 inner electron of Mo and I. [START_REF] Hay | [END_REF][45][46] Unless otherwise stated, calculations were carried out without spatial symmetry constraints.

The energies reported for the open shell systems correspond to unrestricted (UB3LYP) calculations.

In our [47][48][49] and other's 50-52 experience, this computational method correctly reproduces the experimentally observed spin state for open-shell systems. For open shell systems the mean value of the spin over the electronic density in an unrestricted calculations does not reproduce exactly the assigned spin multiplicity. In all our cases, though, it was considered to be suitable to identify unambiguously the spin state. Mean values of <S 2 > were in the narrow 2.012-2.015 range for triplets.

Results and Discussion

a. Geometries and Mo-PH3 bond dissociation energies. Singlet vs. triplet CpMoX(PH3). The considerations presented in this article are based on the energetics of the dissociation of one phosphine ligand on the model system CpMoX(PH 3 ) 3 (X = H, CH 3 , F, Cl, Br, I, OH, PH 2 ), see Scheme 1. The Mo-PH 3 bond dissociation energy (BDE) relates the 18-electron CpMoX(PH 3 ) 3 complex and the combination of 16-electron CpMoX(PH 3 ) 2 and free PH 3 , all geometry optimized. The BDE's relative to both singlet and triplet 16-electron products are collected in Table 1. While the 18-electron complex adopts a singlet ground state, the 16-electron complex has a lowest lying triplet configuration in all cases except for the phosphido derivative.

= E singlet -E triplet . b ∆E π = BET(Mo-X ) -BET(Mo-X ). c ∆E steric (singlet) = -∆E 1 +∆E 2 . d ∆E steric (triplet) = -∆E 1 +∆E 3 .
We have calculated the basis set superposition error (BSSE) 53 for the flouride system using the counterpoise technique, 54 and found a decrease of 2.9 kcal/mol for the Mo-PH 3 BDE. Since the BSSE depends largely on the bond distance and since the Mo-PH 3 bond length is essentially independent of X, we presume that all BDE's reported in Table 1 should be scaled down by the same amount. A reduction of all BDE's may in fact lead to a better agreement with available experimental data, as the lowest BDE for the OH system may be compared with the stability of triplet CpMo(OH)(PMe 3 ) 2 in the presence of excess PMe 3 . 10,11 The geometry optimized 18-electron and the triplet 16-electron systems correspond to essentially C s -symmetric structures which can be described, respectively, as four-and three-legged piano stools (see I and II). The singlet 16-electron systems, on the other hand, have optimized geometries exhibiting a certain degree of asymmetry. Two different minima were located for each X, the lowest one corresponding in all cases except for X = H to a C 1 geometry where the ligand X has more or The lowest energy n=2 (singlet) structure (see Figure 1a) has Mo- the Cp* analogue. 55 An estimate of the strength of this agostic interaction was obtained by imposing identical Mo-C-H angles for the Mo-CH 3 moiety during the optimization. This structure was found to be 3.7 kcal/mol less stable than that of Figure 1b. Geometrical distortions similar to those observed here for singlet CpMoX(PH 3 ) 2 have previously been analyzed computationally for related electronically unsaturated systems, for instance 16-electron d 6 and d 4 CpML n systems. 25,[56][57][58] In order to explain the geometries observed for the singlet d 4 CpMoX(PH3)2 systems, the Kohn and Sham orbitals of the highly

H = 1.700 Å, (Mo-X) = 1.2,  = 1.4° and  = 188.7°. b (Mo-X) = {[Mo-X (n=3) -Mo-X (n=2)]/[Mo-X (n=3)]} .
H P P P P C H (a) (b)
distorted hydride species were examined in detail. The use of these orbitals for both qualitative and quantitative assessments of chemical phenomena is well established. [START_REF] Baerends | Chemical Application of Density-Functional Theory[END_REF][START_REF] Baerends | [END_REF][61] The orbital energies and shapes of the frontier orbitals of singlet CpMoH(PH3)2 in various geometries are represented pictorially in Figure 2. In addition to the distorted optimized geometries (the higher energy local minimum, labeled III, and the global minimum IV), the orbitals of the undistorted, pseudo-octahedral (electronically speaking, when considering the Cp as occupying three mutually adjacent coordination positions) species were obtained via a single point calculation on an idealized three-legged piano stool geometry, labeled "Oh" in Figure 2. The "Oh" geometry has PH3 ligands that lie partially along the lobes of the HOMO. In both optimized structures III and IV, the distortion moves the PH3 ligands onto the nodal planes of this orbital, thereby lowering it in energy so that it becomes the SHOMO. The other doublyoccupied orbital, the HOMO for III and IV and the SHOMO for "Oh", has a nodal surface along the Mo-PH3 and Mo-H bonds in all three cases, and so it remains essentially constant in energy. The same geometry change that stabilizes one of the filled orbitals causes the PH3 groups to move onto the lobes of the LUMO, leading to the destabilization and rehybridization of this orbital in III and IV. This effect is accompanied by the stabilization of the corresponding metal-ligand bonding combination, which provides an additional, perhaps more important, stabilizing effect. The net result is that both distortions induce a significant stabilization of two filled orbitals and the increase of the HOMO-LUMO gap, thereby improving the relative stability of the spin-paired complexes. 62 This orbital splitting is not desirable for the triplet spin state and triplet CpMoH(PH3)2 does not exhibit these deformations. Parallels may be drawn to the studies of Eisenstein and co-workers, who have demonstrated that although triplet d 6 ML 5 compounds have undistorted trigonal bipyramidal structures, 63 two different deformation modes are observed for the singlet species, the relative energy of which are dependent on the -and -bonding properties of the ancillary ligands. 64,65 Although the geometric distortions are most pronounced for X = H and Me (see Table 2), large effectsare also displayed for the F, Cl and OH singlet complexes and the distortions are progressively smaller for Br, PH 2 and I systems. This variation with respect to the identity of the X ligand is presumably the result of competing -and -effects. For the hydride and methyl, no significant -donation interactions are possible, and so geometric distortions are the only available option to decrease the total energy. For X = π-donor ligand, the orbital energies are also influenced by -donation, 8,11 which is equally effective in a non-distorted geometry. Thus, although F and OH have stronger π donating properties (vide infra), they also provide a stronger  component leading to significant distortions.

All optimized parameters compare rather well with those experimentally observed for available related systems. The calculations correctly reproduce the observed ground state for all those 16-electron systems that have been isolated or observed in solution:

Cp*Mo(PR 2 )(PMe 3 ) 2 is diamagnetic, 66 while Cp*MoClL 2 (L = PMe 3 , PMe 2 Ph or L 2 = dppe) 7,8 and CpMo(OH)(PMe 3 ) 2 10,11 have two unpaired electrons. The calculated Mo-PH 3 BDE's (Table 1) are also consistent with the observed relative stability of the various 18electron systems: while no PMe 3 dissociation from CpMoH(PMe 3 ) 3 occurs under ambient conditions, 11 the same dissociation from CpMo(CH 3 )(PMe 3 ) 3 and Cp*Mo(CH 3 )(PMe 3 ) 3

readily takes place at 40∞C and room temperature, respectively, leading to metallation of the PMe 3 and Cp* ligand, respectively. 55 In addition, Cp*MoCl(PMe 3 ) 3 establishes an observable equilibrium with Cp*MoCl(PMe 3 ) 2 and PMe 3 , 8 and finally CpMo(OH)(PMe 3 ) 3 does not exist.

Steric effects are certainly involved in further stabilizing the unsaturated structure with respect to the computed PH 3 model system, see below. In addition, the use of the PH 3 model usually leads to weaker Mo-P bonds relative to PMe 3 . 67,68 b. Extent of the Mo-X π stabilization. As qualitatively discussed before, 7 an X ligand with two lone pairs (double-sided π donor) should interact with a 16-electron metal fragment by establishing one two-center two-electron π bond with the empty metal orbital in the singlet state and two two-center three-electron π interactions with the two singly-occupied metal orbitals in the triplet state. Thus, for both spin states, a double-sided π donor can transfer two π electrons overall to the metal center. In addition, a four-electron destabilizing interaction is present in both spin states. On the other hand, a single-sided π donor can donate both π electrons only in the singlet structure, while a one electron π-stabilization (one half bond order) occurs for the triplet structure. Finally, π neutral X ligands should establish only a pure  interaction in both singlet and triplet 16-electron systems like in the 18-electron system.

Breaking the Mo-X bond in I gives the radical pair CpMo(PH 3 ) 3 • and X • , both in the doublet state (Scheme 2). Energies for these systems are calculated in the frozen geometry derived from optimized CpMoX(PH 3 ) 3 , providing the so-called Bond Energy Terms (BET) 69 which are a measure of the Mo-X  bond strengths. The analogous process on II and III gives a BET which may be related to the strength of the (+π) interaction. The subtraction of the Mo-X BET (18-electron system) from the Mo-X BET (16-electron system) gives us an evaluation of the stabilization provided to the unsaturated system by the establishment of the π interaction (∆E π ).

The results obtained are listed in Table 1. These values are essentially unaffected by the BSSE, as the individual BET's are affected by BSSE by essentially the same amount. For instance, a counterpoise correction for the fluoride system has given BET decreases of 3.0, 2.6 and 2.6 kcal/mol for I, II and III, respectively, leading to correction of less than 0.5 kcal/mol for ∆E π .

Scheme 2

It is important to realize that the calculated ∆E π values for the triplet state are skewed by the influence of X on the electron pairing energies. In fact, removal of X • from triplet CpMoX(PH 3 ) 2 correlates with the spin quartet state, as shown in Scheme 3 (left). Therefore, there is a larger exchange interaction in this case relative to singlet system (Scheme 3, right). This is the reason for the much larger ∆E π values calculated for the triplet systems (Table 1).

Even without pairing energy problems (i.e. for the singlet state), the deduction of a "π-bond strength" from the ∆E π values requires a number of approximations: 2), weakening the  component of the bond, although the bond becomes stronger overall. This approximation leads to an underestimation of ∆E π . Single point calculations for I at the Mo-X distance of III show that this underestimation is 0.0 for H (as expected for a π neutral ligand) and up to 3.4 kcal/mol for the halides. The effect of the rehybridization of X is important only for PH 2 , again leading to an underestimation of the π bond strength for this ligand. The effect of a metal rehybridization is clearly illustrated by the structural distortions on going from I to II and III.

The other Mo-ligand bonds do not appear to vary greatly, but how these small variations reflect into energy changes cannot be evaluated easily. In the absence of all these effects, the ∆E π value for the π neutral H ligand should be exactly zero. The small negative value calculated for X = H (see Table 1) is an estimate of the limitations of these approximations. It should also be kept in mind that there is a nonzero (destabilizing) π interaction between the X and the metal lone pairs in CpMoX(PH 3 ) 3 . The calculated ∆E π values actually reflect the combination of this filled-filled repulsion 4 at the 18-electron level and the π stabilization at the 16-electron level.

The ∆E π results in Table 1 lend themselves to several considerations. Although a Mo-X πbond strength for the triplet state cannot be deduced from the data, the trend of the ∆E π values are approximately the same for the singlet and triplet species. In addition, while ∆E π (triplet) is greater than ∆E π (singlet) for all double-sided π donors, it is smaller for the phosphido ligand, confirming the qualitative considerations made above. This is probably the main reason for the adoption of a singlet ground state by the phosphido complexes. The action of the X ligands as π donors in the triplet complexes can also be judged by the percent of Mo-X bond shortening (, see Table 2), which is rather similar for triplet and singlet complexes containing doublesided π-donor ligands (i.e. the halogens). The PH 2 ligand, being able to provide only 1 π electron in the triplet state, leads to a significant increase of  on going from triplet II to singlet III. The OH case is interesting,  increasing by 50% on going from triplet to singlet. While the OH ligand acts as a double-sided π donor, 11 one orbital interaction is stronger than the other one leading to a weaker interaction in the triplet state. As a result, (F) > (OH) for triplet II whereas the reverse holds true for singlet III.

Scheme 3

The ∆E π value calculated for F is significantly greater than zero, in agreement with the notion that the fluoride ion is a good π donor ligand. The values calculated for the other halides are smaller but positive. Within the halogen group, however, the trend is not monotonic, iodide leading to a greater value than both chloride and bromide. Given the approximations alluded to above, we do not feel that too much emphasis should be placed on this trend. However, the results are in agreement with the halogens having a small but significant π donating capability.

The methyl ligand shows a 7.5% contraction for the agostic structure of Figure 1b. This shortening accompanies the high ∆E π value which is, obviously, a measure of the strength of the Mo-CH 3 agostic interaction rather than a π interaction. Finally, the much larger values calculated for OH and PH 2 agree well with the known strong π-donor power of hydroxide, alkoxides, aryloxides, and dialkyl-and diarylphosphido ligands.

Mo d Mo-X  (S = 1) (S = 0) CpMoX(PH 3 ) 2 -X • -X • CpMo(PH 3 ) 2 (S = 1/2) CpMo(PH 3 ) 2 (S = 3/2)
Somewhat surprisingly, the percent of Mo-X bond shortening (Mo-X) in Table 2 does not correlate with the ∆E π values. The smallest change is seen, as expected, for the π neutral H ligand. For the halogen series, the percent contraction increases in the order F < Cl < Br < I (in both spin states), while F has the greater ∆E π value. Also, OH has a ∆E π value similar to that of PH 2 (for the singlet) but a much smaller (Mo-X) value, similar to those of the halogens. These data illustrate that the percent bond contraction should not be used in general as a measure of relative π bond strengths.

An independent evaluation of the π bond strength has been obtained for those ligands, namely OH and PH 2 , for which the strength of the π interaction depends on the angular orientation. For singlet CpMoX(PH 3 ) 2 (X = OH, PH 2 ), single point calculations have been carried out on geometries derived from the optimized minimum by gradually rotating the X ligand around the Mo-X bond. The results are shown in Figure 3. Squares: E = P, n = 2; triangles: E = O, n = 1. For the phosphido system, the maximum π overlap is achieved at the optimized geometry with CNT-Mo-P-H = 0∞ or 180∞, while the orthogonal orientation gives a zero overlap (see V and VI in Scheme 4). The energy difference of 23.1 kcal/mole may be taken as an

CNT-Mo-E-H Torsion angle (degrees) Energy (Hartrees)

overestimation of the Mo-PH 2 π bond strength, because of the unrelaxed nature of the CpMo(PH 3 ) 2 moiety in the rotated geometry. The window between this overestimated value and the underestimated one of Table 1 is relatively narrow.

Scheme 4

For the hydroxide system, the two C s -symmetric structures (CNT-Mo-O-H angles of 0∞, endo, see VII, and 180∞, exo) are not identical, because of the greater filled-filled repulsion between the oxygen sp x lone pair and the Mo d z 2 lone pair in the exo conformation. In the 90∞ conformation (VIII), Mo-O π bonding is not quite zero, since OH is still able to overlap with the Mo d xy orbital (albeit not so as effectively) by using the sp x lone pair. At any rate, the energy difference between the most stable exo structure and the 90∞ maximum is 18 kcal/mol and is again slightly higher than the ∆E π values calculated for OH in Table 1.

c. Steric interactions. The bond dissociation energy of PH 3 from CpMoX(PH 3 ) 3 is modulated by π donation and by the release of pairing energy upon adoption of the triplet configuration, both being functions of the nature of X. However, differences in size and electronic environment for the various X ligands will also cause differences in the steric pressures exerted on the rest of the coordination sphere and provide an additional contribution to affect the Mo-PH 3 bond dissociation energy. These differences may be evaluated by comparing the relaxation energies of the fragments that are obtained from the Mo-X bond breaking process for each system. Thus, (-∆E 1 +∆E 2 ) = ∆E steric (triplet) is a measure of the release of steric pressure associated to the formation of the triplet 16-electron product, while (-∆E 1 +∆E 3 ) = ∆E steric (singlet) measures the same parameter for the formation of the singlet product. These values are again collected in Table 1. Positive values indicate greater pressure on the more saturated system, as is expected. In some cases small values are obtained by subtraction of individual large relaxation energies. For each X ligand, the singlet state gives rise to a greater ∆E steric value. This result correlates with the greater distortion that the CpMo(PH 3 ) 2 fragment has to withstand to lead to the triplet geometry upon binding X, thus more efficiently balancing out the greater relaxation experienced by the more saturated system.

We can immediately observe that the smallest X ligand, H, gives small steric contributions.

The optimized geometries of both CpMo(PH 3 ) 3 and CpMo(PH 3 ) 2 fragments are quite close to those of the same fragments in the corresponding optimized hydrides, and the individual relaxation energies ∆E 1 , ∆E 2 and ∆E 3 (3.2, 2.0, and 1.4 kcal/mol, respectively) are smaller than those of the other X ligands, indicating the H has a small steric influence in both 18-electron and 16-electron structures. It is notable that ∆E steric is relatively large for Cl and Br, while it is smaller for I and F. It is unexpectedly small for PH 2 , especially considering that the size of P is similar to that of Cl, and it is even smaller for CH 3 . These values suggest to us that the major steric repulsion derives from the interaction between the X lone pairs and the neighboring PH 3 ligands. The Cl and Br atoms have two p lone pairs oriented perpendicularly to the Mo-X bond, extending in the region of space occupied by the PH 3 ligands in the 18-electron complex (see Figure 4). On an energy scale, these two orbitals are placed immediately underneath the two filled metal orbitals. Correspondingly, OH has only one p lone pair (the second lone pair is a hybrid orbital pointing away from the PH 3 ligands, 11 as shown in VII), while PH 2 and CH 3 have none (the only P lone pair is a hybrid orbital with a large amount of s character, pointing away from the adjacent PH 3 ligands). This is a manifestation of an interligand filled-filled repulsion. The filled-filled repulsion between the X lone pairs and the filled metal orbitals, on the other hand, is accounted for in the ∆E π term.

It is interesting to observe the trend of ∆E steric values for the halogen series in the order (for both spin states) F < Cl ~ Br > I. This result is determined for the most part by the trend in the rearrangement factor ∆E 1 for the 18-electron compounds (7.11, 12.74, 13.35, and 8.7 kcal/mol for F, Cl, Br and I, respectively). The small value of ∆E steric observed for F may be attributed to the small size of the atom and of its orbitals, leading to a small interaction with the adjacent PH 3 ligands. The smaller value for I relative to Cl and Br, on the other hand, may be attributed to the longer distance and greater of the orbitals. These considerations appear consistent with the shape of the orbitals as shown in Figure 4.

These values are very close to each other because the optimized doublet and quartet CpMo(PH 3 ) 2 species have very similar energies, and can be taken as measures of the "intrinsic" Mo-PH 3 bond strength (for each spin state) in the absence of any stabilizing factor introduced by the presence of X. The introduction of X modulates these BDE's by stabilizing the less saturated and/or by destabilizing the more saturated structure by steric and π bonding effects.

The introduction of X also has a large effect on the electron pairing energy, as shown by the variable singlet-triplet gap (varying from 8.7 kcal/mol for F to -7.9 kcal/mol for PH 2 ) for the give interesting indications on the relative importance of spin-pairing effects, ligand π donation, and release of steric pressure for the relative stabilization of the 16-electron CpMoX(PH 3 ) 2 and therefore for the dependence of the Mo-PH 3 bond dissociation energy on the nature of X. The hydride system has a relatively unencumbering (∆E steric = 1.0 kcal/mol) and π neutral (∆E π = -2.0 kcal/mol) X group. Since the triplet state is only slightly stabilized relative to the singlet one (∆E S-T = 1.8 kcal/mol), the Mo-PH 3 BDE is quite close to the ìintrinsicî bond strength found in CpMo(PH 3 ) 3 and is the highest found for the series of X systems investigated in this work. For all other X systems, the Mo-PH 3 BDE drops dramatically, but for different reasons.

As discussed earlier, the steric stabilization is mostly related to the presence of inactive lone pairs. For the π neutral CH 3 system, there is essentially no sterics-related stabilization, while a significant ∆E π stabilization is related to the establishment of an agostic Mo-C-H interaction.

The change of spin state also contributes to a large extent to the stabilization of the 16-electron methyl system. We cannot rationalize the difference between ∆E S-T for H and CH 3 . The halogen systems are stabilized to a significant extent by each of the three effects, the ∆E S-T stabilization being nearly the same for all four (in the 8.7 -6.6 kcal/mol interval, predictably in the order F > Cl > Br > I), while the other two effects vary as a function of X in a way as to provide an approximately identical total contribution (in the 9-11 kcal/mol range; mostly ∆E π for F, mostly ∆E steric for Cl and Br, and about 50:50 for I). The OH system experiences an even greater overall stabilization, which is mostly due to O-M π donation, but ∆E S-T and ∆E steric also play a role, especially the latter one. Finally, the PH 2 system (which is the only one examined here to adopt a singlet ground state) is almost entirely stabilized by π effects, while the steric factor is nearly zero.

Conclusions

We have examined the relative importance of three difference factors

  Scheme 1

3 I

 3 less deviated from the P-Mo-P bisector plane, as schematically illustrated in III. The second minimum (lowest for X = H) is an essentially C S -symmetric structure where the P-Mo-P angle has more or less increased relative to the triplet II. The distortion from a regular (pseudo-octahedral) structure as found in the triplet can be assessed by two dihedral angles. The angle  is the angle formed by the CNT-Mo-X plane and the plane passing through CNT, Mo, and the bisector of the two Mo-PH 3 bonds, whereas the angle  is the dihedral P-Mo-CNT-P angle (CNT is the Cp ring centroid), see III. The values of the angles  and  for the lowest energy optimized CpMoX(PH 3 ) n (n = 2, 3) are collected in Table2together with the Mo-X distances. In most cases, the Mo-CNT and Mo-PH 3 distances for I have intermediate values between those of II (longer) and III (shorter), which differ from each other by less than 3%. (S = 0)

Figure 1 .

 1 Figure 1. MacMoMo 70 view of the optimized structures of singlet CpMoH(PH 3 ) 2 (a) and CpMo(CH 3 )(PH 3 ) 2 (b). The cyclopentadienyl H atoms are omitted for clarity.

Figure 2 .

 2 Figure 2. Frontier orbital evolution upon distortion of singlet CpMoH(PH 3 ) 2 from an idealized three-legged piano stool geometry.

  (i) considering the  bond as having the same strength in I and III; (ii) neglecting the rehybridization of X; (iii) neglecting the rehydrization of M; (iv) neglecting variations in the other M-L bonds. A π interaction compresses the Mo-X bond (lengths and shortening factors are shown in Table

Figure 3 .

 3 Figure 3. Plot of the energy of CpMo(EH n )(PH 3 ) 2 (S=0) vs. the CNT-Mo-E-H dihedral angle. All other geometrical parameters are those of the optimized geometry.

Figure 4 .

 4 Figure 4. MOLDEN views of the 3rd (left) and 4th (right) highest MO for CpMoX(PH 3 ) 3 .The orbital contour lines correspond to 4 % of the maximum electron density.

  (pairing energy associated to a spin state change, π donation from ligand lone pairs, and release of steric pressure) in the relative stabilization of the PH 3 dissociation product from CpMoX(PH 3 ) 3 as a function of X (X = H, CH 3 , F, Cl, Br, I, OH and PH 2 ). These are model systems for a class of phosphine-substituted half-sandwich Mo(II) compounds which exhibit richness in structure, magnetic properties, and chemical reactivity. The study has shown that the three effects can display all possible orders of relative importance depending on the nature of the donor atom, on the presence of inactive lone pairs, and on the number of π orbitals available (π neutral, single-or double-sided π donor). The spin state change plays a dominant role for the stabilization of the halide derivatives and the methyl derivative. The study has further shown a contribution to stabilization from the CH 3 group attributable to the establishment of an agostic interaction.

Table 1 .

 1 Relevant energetic parameters for the PH 3 dissociation from CpMoX(PH 3 ) 3 (see Schemes 1 and 2). All energies are in kcal/mol.

	X	BDE (Mo-PH 3 )	BDE (Mo-PH 3 )	∆E S-T	a	∆E π b	∆E π b	∆E steric c	∆E steric d
		(triplet)	(singlet)			(singlet)	(triplet)	(singlet)	(triplet)
	H	23.5	25.3	1.8		-2.0	1.3	1.0	-0.6
	Me	13.2	16.3	3.1		7.0	11.7	1.0	0.3
	F	6.3	14.9	8.7		7.7	19.3	1.7	-0.2
	Cl	5.9	13.4	7.5		2.8	14.3	8.1	5.2
	Br	6.5	13.6	7.0		1.8	13.1	9.0	5.7
	I	9.1	15.7	6.6		4.2	15.3	4.5	1.0
	OH	4.5	6.2	1.7		14.1	18.8	4.1	2.1
	PH 2	14.9	7.0	-7.9		16.0	10.2	1.3	0.3
	a ∆E S-T

Table 2 .

 2 Selected optimized bond angles (°) and lengths (Å) for CpMoX(PH 3 ) n (n = 3, 2)

		X	H a	CH 3	F	Cl	Br	I	OH	PH 2
	n = 3	Mo-X	1.722	2.299	2.085	2.633	2.805	3.002	2.095	2.696
		Mo-X	1.739	2.193	1.993	2.472	2.627	2.806	2.012	2.565
	n = 2	(Mo-X) b -0.99	4.6	4.4	6.1	6.3	6.5	4.0	4.9
	II (Triplet)	 c	0.0	0.1	0.0	0.0	0.0	0.0	0.0	6.7
		 c	159.0	130.7	123.4	120.0	119.0	117.2	123.6	129.0
		Mo-X	1.723	2.126	1.994	2.463	2.611	2.781	1.972	2.326
	n = 2	(Mo-X) b -0.06	7.5	4.4	6.5	6.9	7.4	5.9	13.7
	III (Singlet)	 c	43.9	26.0	25.5	13.1	6.4	0.3	10.5	1.2
		 c	105.7	102.0	102.2	102.4	102.3	101.9	102.7	102.6
	a

  The global singlet minimum for X = H is shown in Figure1a. One can imagine this structure as derived from structure I by removal of the PH 3 ligand trans to the H atom, whereas structure III may be imagined as derived by removal of a cis PH 3 ligand. All X ligands used in this study, except for H, have a weaker trans influence than PH 3 , thus the Mo-PH 3 bond trans to X is stronger than the Mo-PH 3 bond trans to PH 3 . A special word must be said about the methyl system, for which the ì16-electronî global singlet minimum corresponds to a distorted geometry similar to III with an additional agostic interaction involving one of the methyl group H atoms, see Figure1b. The agostic Mo … H distance in this optimized structure is 2.279 ≈ and the Mo-

100. c See drawing III. C-H angle is 82.7°. The agostic C-H bond is slightly longer (1.137 Å) than the other two C-H bonds (1.098 and 1.100 Å). The preference for this agostic structure is well in agreement with the C-H oxidative addition reactivity established for complexes CpMo(CH 3 )(PMe 3 ) 3 and for

  ). The correction of the Mo-PH 3 BDE (for either the singlet or the 16-electron product) by the ∆E π and the ∆E steric parameters (Table1) provides the BDE for the Mo-PH 3 bond in geometry optimized spin doublet CpMo(PH 3 ) 3 (relative to optimized doublet and quartet CpMo(PH 3 ) 2 , respectively). These values are independent on the nature of X and are calculated as 24.3 and 25.4 kcal/mol,

	respectively, see eqs. 1 and 2.
	BDE (singlet) + ∆E π (singlet) + ∆E steric (singlet) = 24.3 kcal/mol	(1)
	BDE (triplet) + ∆E

π (triplet) + ∆E steric (triplet) = 25.4 kcal/mol

  16-electron CpMoX(PH 3 ) 2 , as compared with the doublet-quartet gap of -1.10 kcal/mol for the 15-electron CpMo(PH 3 ) 2 .It is impossible to completely separate the effects caused by these stabilizing factors when one wishes to analyze the stabilization of triplet CpMoX(PH 3 ) 2 (i.e. the ground state in all cases except for X = PH 2 ) and free PH 3 relative to singlet CpMoX(PH 3 ) 3 , because these effects are linked to the structural changes associated with the change of spin state. We have already pointed out that pairing energy effects and π bonding effects are combined in the ∆E π term in equation 2. A convenient, though admittedly limited, approach is given in equation 3.This approach corresponds to the following stepwise process. The optimized CpMo(PH 3 ) 3 on one side and the combination of optimized doublet CpMo(PH 3 ) 2 and free PH 3 on the other side (relative energy 24.30 kcal/mol) are distorted to the geometries of the corresponding fragments in the adducts with X [∆E steric (singlet)]. Subsequently, X • is added to form the Mo-X bond, involving BET () for CpMoX(PH 3 ) 3 and BET (+π) for CpMoX(PH 3 ) 2 [∆E π (singlet)]. Finally, singlet CpMoX(PH 3 ) 2 is relaxed to the triplet ground state (∆E S-T ). While this scheme has limitations due to the interrelated nature of these effects, the same would hold true for possible alternative schemes.The comparison of the ∆E S-T , singlet ∆E π and singlet ∆E steric values in Table1for each X

	BDE (triplet) + ∆E S-T + ∆E π (singlet) + ∆E steric (singlet) = 24.30 kcal/mol (3)

Acknowledgement. We are grateful to the Conseil Régional de Bourgogne for support and to the European Commission for a Marie Curie postdoctoral fellowship to K.M.S. We also thank Odile Eisenstein for helpful discussion.


Christophe Milési

Anne Requirand

Aymeric Douillard

Julien Baleine

Erika Nogué

Stefan Matecki

Pascal Amedro

Marti Pons-Odena

Gilles Cambonie

Assessment of Peak Inspiratory Flow in Young Infants with Acute Viral Bronchiolitis: Physiological Basis for Initial Flow Setting in Patients Supported with High-Flow Nasal Cannula

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Karima Abidi
email: kabidi@loria.fr

Kamel Smaïli
email: ksmaili@loria.fr

Creating multi-scripts

Keywords: Maghrebi dialect, Word embedding, Semantic orientation

published or not. The documents may come

Introduction

To understand the requirements of users, clients or people in general, it is necessary to mine social media [START_REF] Abdul-Mageed | SAMAR: subjectivity and sentiment analysis for arabic social media[END_REF][START_REF] Abidi | A Fine-grained Multilingual Analysis Based on the Appraisal Theory: Application to Arabic and English Videos[END_REF][START_REF] Yimam | Exploring Amharic sentiment analysis from social media texts: Building annotation tools and classification models[END_REF] and to develop automatic tools allowing a systematic analysis of the contents. One can then extract useful information that could be used in marketing advising, political views, movies reviews, etc. Henceforth, proposing methods to understand opinions is necessary and it is considered as a challenging issue especially for under-resourced languages such as Maghrebi dialects. In this article, we will address the issue of developing a method allowing to analyse sentiments in the three following Maghrebi dialects: Algerian, Moroccan and Tunisian. The problem is that these dialects are under-resourced because they are not formal and not official languages. Basically, Arabic dialects are founded on Modern Standard Arabic (MSA), but not only. The originality of this work is to propose a sentiment analysis tackling two issues frequent in Algerian, Moroccan and Tunisian dialects: the code-switching nature of a document and its multi-script form. In order to explain the importance of this research work, let's give in the following the different particularities of the Maghrebi dialects.

The origin of Maghrebi dialects is mainly Standard Arabic, but not only. For practical reasons, several morpho-syntactic rules of MSA are not respected in Arabic dialects. This means that it is difficult to use the amount existing NLP resources developed for MSA to process Arabic dialects.

The vocabularies of the Arabic dialects evolve continuously by introducing new words, that could be considered as gibberish such as the word papicha that means beautiful girl in Algerian dialect. And as in any other language, Maghrebi dialects can borrow new words and adapt them phonologically to the local dialect such as:

(borrowed from the French word cuisine that means kitchen).

Another particularity of Maghrebi dialects is the fact that people can write Arabic by using multiple scripts: Arabic and Latin [START_REF] Abidi | An empirical study of the Algerian dialect of Social network[END_REF][START_REF] Abidi | An Automatic Learning of an Algerian Dialect Lexicon by using Multilingual Word Embeddings[END_REF]. In addition, in social media people can use digits when they write in Latin script to represent sounds that do not exist in French or English, such as which is replaced by the digit 3.

In addition to these phenomena, in north Africa, code-switching is common in conversations. One can mix in the same sentence local Arabic, MSA, and foreign languages, such as French or English. In the following, we give an example: merci pour la vidéo les boucles d'oreilles thanks.

Translation : "God bless you, thank you for this video, I really liked the earrings where did you buy them. Thank you."

In this sentence, one switched from Moroccan dialect written in Arabic script, to French, then to Arabic, then again to French then once again to Arabic and finally to English.

Only few works addressing the issue of sentiment analysis in Maghrebi dialects do exist. But most of them have ignored the problems already cited and have concentrated on sentiment analysis in Maghrebi texts written only in Arabic script. In this article, we propose a method that allows to create automatically sentiment lexicons for Arabic dialects taking into account all the phenomena aspects related to Maghrebi dialects. This approach could be adapted to any Arabic dialect and also to any other low-resourced languages.

The rest of the paper is organized as follows: Section 2 is dedicated to the related work, while Section 3 examines the corpus we harvested. In Section 4, we discuss the proposed method to analyse sentiment of Maghrebi dialect. In Section 5, we present the different used corpora and the experimental results and finally we conclude.

Related work

Many studies have been conducted to address the issue of sentiment analysis in Arabic documents [START_REF] Abdul-Mageed | Subjectivity and sentiment analysis of modern standard Arabic[END_REF][START_REF] Ibrahim | Sentiment analysis for modern standard arabic and colloquial[END_REF][START_REF] Abo | A review on arabic sentiment analysis: Stateof-the-art, taxonomy and open research challenges[END_REF]. Researchers proposed various interesting approaches, that we can classify into two categories: machine learning techniques [START_REF] Sallab | Deep learning models for sentiment analysis in Arabic[END_REF][START_REF] Heikal | Sentiment analysis of arabic tweets using deep learning[END_REF][START_REF] Ali | Measuring, understanding, and classifying news media sympathy on twitter after crisis events[END_REF][START_REF] Nejjari | Sahar-lstm: An enhanced model for sentiment analysis of hotels'arabic reviews based on lstm[END_REF][START_REF] Elfaik | Deep bidirectional lstm network learning-based sentiment analysis for arabic text[END_REF] and lexicon-based approaches [START_REF] Mohammad | Generating high-coverage semantic orientation lexicons from overtly marked words and a thesaurus[END_REF][START_REF] Badaro | A large scale arabic sentiment lexicon for arabic opinion mining[END_REF][START_REF] Abd-Elhamid | Feature-based sentiment analysis in online arabic reviews[END_REF][START_REF] Awwad | Performance comparison of different lexicons for sentiment analysis in arabic[END_REF][START_REF] Htait | Identification semi-automatique de mots-germes pour l'analyse de sentiments et son intensité[END_REF]. Unfortunately, most of these methods are not directly reusable for Arabic dialects for the reasons mentioned in the introduction. In this section, we discuss the research works proposed to analyse sentiments in Arabic dialects and we will focusing on those concerning the three Maghrebi ones studied in this article.

In the Arabic dialect sentiment analysis literature, several works have used machine learning techniques to address this issue. These methods require a significant amount of pre-annotated corpora to train a good classifier that is able to distinguish between positive and negative documents.

In [START_REF] Baly | Comparative evaluation of sentiment analysis methods across arabic dialects[END_REF], the authors proposed a deep learning model based on Long short-term memory (LSTM) architecture to identify the sentiments of documents written in Egyptian and Emirati dialects. To train this model, the authors collected and annotated a corpus of 470k tweets. This model achieved an accuracy of 70% and 63% for Egyptian and Emirati, respectively. The authors of [START_REF] Abu Kwaik | Lstm-cnn deep learning model for sentiment analysis of dialectal arabic[END_REF] proposed a model that combines LSTM with a convolutional neural network architectures. They used two existing annotated corpora extracted from Twitter to train the proposed model, which is composed of 10k and 2k of tweets written in Egyptian and Levantine, respectively. The method achieved an accuracy of more than 85%. Deep LSTM architecture has been also used by the authors of [START_REF] Jerbi | Sentiment analysis of code-switched tunisian dialect: Exploring rnn-based techniques[END_REF] to tackle the issue of sentiment analysis in Tunisian Dialects. The authors trained the model on a Tunisian corpus composed of 17k and the method achieved an accuracy of 90%.

Unlike the machine learning techniques, in the based-lexicon method, the global sentiment of a document is estimated by calculating the semantic orientation of the words appearing within the text. This approach requires the use of a lexicon of words with their polarities (positive and negative). In this approach, the need of sentiment lexicons is crucial for analysing documents in terms of opinions, that is why the authors in [START_REF] El-Beltagy | Nileulex: A phrase and word level sentiment lexicon for egyptian and modern standard arabic[END_REF] created semi-automatically a sentiment lexicon, where 45% of the entries are Egyptian while 55% are words of Modern Standard Arabic. A sentiment lexicon for the Khaliji dialect has been built manually by exploring and labelling the words of a Saudi dialect twitter corpus (SDTC) [START_REF] Al-Thubaity | Sentiment lexicon for sentiment analysis of saudi dialect tweets[END_REF]. The authors of [START_REF] Mataoui | A proposed lexicon-based sentiment analysis approach for the vernacular algerian arabic[END_REF] built a lexicon for Algerian dialect by translating manually an existing Egyptian polarity lexicon. In [START_REF] Ameur | Exploiting emoticons to generate emotional dictionaries from facebook pages[END_REF], the authors proposed an approach for emotion analysis of Tunisian comments posted in Facebook by using an emotion dictionary created automatically. Actually, only a limited number of researches have been carried out for sentiment analysis in the three Maghrebi dialects, while a majority of research in this scope are dedicated to texts written only in Arabic script.

The collected dataset

In this work, we are interested by the Algerian, Moroccan and Tunisian dialects. That is why, we extracted three large corpora from YouTube by using the approach proposed in [START_REF] Abidi | CALYOU: A Comparable Spoken Algerian Corpus Harvested from YouTube[END_REF]. This method crawls (by using the API2 ) the posts of videos using specific hashtags related to each country.

In Table 1, we give some figures about the collected data, where |C| indicates the number of comments, |W | the number of words and finally |V | the size of the vocabulary. We mention that these statistics concern the data obtained after the cleaning process.

The sentiment analysis method

In this work, we propose a lexicon-based approach to analyse the sentiments of Maghrebi comments extracted from social networks. In this approach, the polarity of a text can be obtained on the ground of the polarity of the words that compose it. To do this, a lexicon of words, where each entry is associated to its polarity is necessary. Because, in the Maghrebi dialects people use Latin and Arabic scripts and foreign languages to post their comments, we aim, in this work to handle this issue by building a multi-script and multilingual sentiment lexicon in order to analyze the sentiments of the collected corpus. A word and its polarity constitute an entry in the lexicon. Each word of this lexicon can be written in Arabic or Latin script and it can belong to one of the following languages: one of the three Maghrebi dialects, MSA, French or English as in the table 2. Concerning the polarity of each entry, we determined it automatically by using an approach similar to the one used in [START_REF] Turney | Measuring praise and criticism: Inference of semantic orientation from association[END_REF]. In this method, the authors proposed to tag the words by using the polarities of a small list of words called seed words for which the polarity is assigned by hand. A word is attached to the dominant polarity of the closest seed words. For example, a word is considered positive if it is closer, in terms of distance, to positive seed words than to negative words.

In the following, we will detail the two main steps of the method we used to assign a polarity to an entry of a sentiment lexicon.

Seed words identification

In [START_REF] Turney | Measuring praise and criticism: Inference of semantic orientation from association[END_REF], the authors used a list of seed words made up of seven positive words and seven negative words. In our case, for each dialect, we manually annotated a list of forty seed words for each of the polarities. The seed words have been selected, from a list of the most frequent not neutral words of the collected corpora. Then, we assigned manually to each of them its corresponding polarity. The number of seed words retained is relatively high compared to the experiment carried out by the authors of [START_REF] Turney | Measuring praise and criticism: Inference of semantic orientation from association[END_REF]. This is due to the fact that we want to cover as many words as possible since we deal with multi-script and multilingual words in our corpora. In the table 3 we give some examples of these retained seed words.

Estimation of the polarity of words

We propose to calculate the semantic orientation of a word w according to the difference between its closest positive seed words SW pos and its closest negative seed words SW neg . We estimate the degree of closeness between two words one of which is a seed word by using the cosine similarity as in the formula we propose in 1:

SO(w) = wp∈SWpos Cos(w, w p ) - wn∈SWneg Cos(w, w n ) (1)
w is considered as positive if SO(w) is positive, similarly w is considered as negative whether its orientation is negative. The similarity of the word w and a seed word is estimated by using the cosine measure between their corresponding embedding vectors. The embedding vectors are generated by using the Continuous Bag-of-Words (CBOW), one of the method of the Word2Vec approach proposed by Mikolov [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF]. The training has been achieved on the three large corpora presented in section 3. This led to the creation of a lexicon of sentiments for each of the dialects cited in this research. In the table 4, we detail each of them. In table 5, we give some examples extracted from our lexicons.

Experimentation

We used the created lexicons to evaluate the polarity of the four following labeled corpora.

-ElecMorocco: is a Moroccan corpus extracted from Facebook and annotated by the authors of [START_REF] Elouardighi | Analyse des sentiments à partir des commentaires facebook publiés en arabe standard ou dialectal marocain par une approche d'apprentissage automatique[END_REF]. The main topic of this corpus concerns the local elections. It is constituted by 6389 positive and 4367 negative comments. This corpus contains only comments written in Arabic script.

-TSAC: is a Tunisian corpus collected from comments posted on official Facebook pages of Tunisian radios and TV channels [START_REF] Medhaffar | Sentiment analysis of tunisian dialects: Linguistic ressources and experiments[END_REF]. It is composed of 5081 positive and 6514 negative comments written in Arabic and Latin scripts.

-CorpusAlg: is an Algerian corpus extracted from different Facebook pages, it contains 5079 posts, among them 3032 are positive comments [START_REF] Mataoui | A proposed lexicon-based sentiment analysis approach for the vernacular algerian arabic[END_REF]. The comments in this corpus are written in Latin and Arabic characters.

-SentAlg: The previous Algerian corpus (CorpusAlg) is small in comparison to the two others, that is why we decided to collect and annotate manually 10k of comments from Algerian YouTube comments. This achieved a corpus of positive and negative comments of 5562 and 4438 respectively. All of the comments are written in Arabic and Latin script.

Table 6 summarizes the figures of the different corpora used in our experimentation.

Results

As mentioned before, we used in this work a sentiment analysis method which is based on sentiment lexicons and annotated corpora. In this method, the aim is to identify in the sentence under analysis, the words that exist in the lexicon and to take into account the corresponding polarities in the opinion to assign to the sentence. Then the evaluation is estimated by using scores such as: accuracy, recall, precision, F-measure, etc. In table 7, we give the achieved results in terms of Recall and Precision on the corpora listed above. The results show that the weakest performance concerns the Moroccan corpus. An analysis of this corpus shown that this later contains a lot of sentences in Modern Standard Arabic, while our training was done on a corpus extracted from the comments of Youtube posted by Moroccan mostly in their dialect [START_REF] Abidi | An empirical study of the Algerian dialect of Social network[END_REF]. Another explanation of these results is due to the fact that ElectMoroccan contains only comments written in Arabic script which is not the case of the training corpus. Concerning the Tunisian and the Algerian test TSAC and Cor-pusAlg, respectively, thematically, they are far from the crawled corpora used for the training. That is why the performances are reasonable, but they are not as good as the results achieved on the corpus SentAlg. We recall, that we used a lexicon-based approach for sentiment analysis, but unfortunately we have not found any available sentiment lexicon for the three studied dialects, that is why we created them automatically. In the opposite, SentAlg is a corpus which is similar thematically to the training corpus, which explains why the performances are higher than those obtained for the others.

Conclusion

We proposed, in this article, a lexicon-based approach to analyse sentiments of three Maghrebi dialects, namely Algerian, Moroccan and Tunisian. The dialects lexicons used to classify the documents in terms of sentiments were created automatically. The approach, we proposed depends on a predefined list of 80 polarity seed words for each dialect, selected manually. Then, using a similarity measure, we estimated the proximity between an embedding word and the list of the embedding seed words.

One of the originality of this method is that it allowed to create multi-script and a multi-lingual sentiment lexicons for Algerian, Moroccan and Tunisian dialects which contain 11.2k, 23.4k and 10.8k entries, respectively. These sentiment lexicons were used to classify, in terms of polarities, three test datasets. This approach has been also tested on an Algerian corpus we collected and labelled manually. The performances we achieved depend on the quality of the corpora and they vary between 61.99 and 80.28 in terms of F-measure.

Table 1 :

 1 Statistics of the harvested corpora.

		Algerian (M) Moroccan (M) Tunisian(M)
	|C|	1.61	1.60	1.26
	|W |	23	22	17
	|V |	1.2	1.3	1

Table 2 :

 2 Few examples concerning the different forms of a word

	Script	language	Word Meaning
	Latin Algerian dialect Chaba Beautiful
	Arabic Algerian dialect		Beautiful
	Arabic	MSA		Liar
	Latin	MSA	Kadib	Liar
	Latin	English	Like	Like
	Arabic	English		Like

Table 3 :

 3 Some examples of positive and negative seed words for the three dialects.

		Algerian	Moroccan	Tunisian
	Positive	Negative	Positive	Negative	Positive	Negative
	chaba			Problème	To9tool
	(Pretty)	(Groveller)	(Wonderful) (Problem)	(so beautiful)	(Boring)
	Bravo	Mosakh	Hbiba		Ma7lek
		(Disgusting)	(Sweetie)	(Cursed) (How beautiful you are) (Ignorant )
		Na3ja	Tbarklah	Himar
	(Excellent) (A weak personality ) (Marvelous ) (Donkey)	(Wonderful )	(Beast )
		Roukhs
	(Health)	(Asshole )	(I love)	(Not good )	(Delicious )	(Snake )

Table 4 :

 4 Some figures about the lexicons of sentiments

		Algerian Moroccan Tunisian
	Number of entries	11243	23405	10810
	Positive words	8372	2326	19128
	Negative words	2871	8484	4277

Table 5 :

 5 Some examples of positive and negative words extracted from the three lexicon

	Word	Translation	Polarity Lexicon
		She makes me laughing Positive Moroccan
	Kanbghiwk	We like you	Positive Moroccan
		Stubborn	Negative Moroccan
	frahnalk	Happy for you	Positive Algerian
		Groveller	Negative Algerian
	wetek	It suits you very well Positive Tunisian
		Crafty	Negative Tunisian

Table 6 :

 6 Some figures about the different corpora.

		ElecMorocco TSAC CorpusAlg SentAlg
	Positive comments	3523	5081	3032	5562
	Negative comments	6431	6514	2047	4438

Table 7 :

 7 Experimental results on the three Maghrebi corpus.

		Recall (%) Precision(%) F-measure (%)
	ElecMorocco	59.29	63.23	61.19
	TSAC	64.03	63.78	63.90
	CorpusAlg	67.92	67.15	67.53
	SentAlg	79.78	80.79	80.28

https://smart.loria.fr/corpora

https://developers.google.com/YouTube