Abdelhakim Laachir

Ferdaousse Rhoufal

Salaheddine Guesmi

Mostafa El

Laurent Ketatni

El-Kebir Jouffret

Nicolas Hlil

Saïd Sergent

Fouad Obbade

Bentiss
email: fbentiss@gmail.com

Ketatni

Laurent Jouffret

El Kebir Hlil

Nicolas Sergent

Saïd Obbade

Fouad Bentiss

Cobalt(II) coordination complex with 2,5-bis(pyridine-2-yl)-1,3,4-thiadiazole and thiocyanate as co-ligand: Synthesis, crystal structure, Hirshfeld surface analysis, spectroscopic and magnetic properties

Keywords: 2,5-Bis(pyridin-2-yl)-1,3,4-thiadiazole, Thiocyanate, Mononuclear Co(II) complex, Crystal structure, Hydrogen bonds, Antiferromagnetic interaction

    Cobalt(II) coordination complex with 2,5-bis(pyridine-2-yl)-1,3,4-thiadiazole and thiocyanate as co-ligand: Synthesis, crystal structure, Hirshfeld surface analysis, spectroscopic, thermal and magnetic properties

Introduction

Over the last few decades several research studies have shown the importance of transition metal complexes in various fields such as biology for their antibacterial [1,2], antifungal [1,3] or antitumor [4,5] activities; pharmacology for the treatment of certain diseases [6,7] and catalysis for the selectivity of reactions [8,9]. Since the nitrogen atom is present in many natural molecules or in those of pharmacological interest [6,10], research has been devoted to the synthesis of transition metal complexes with hetero-atom and chelating ligands [11][12][13]. It is also well established that some of these organic molecules (drugs) are much more effective when administered linked to a metal [14][15][16]. The 1,3,4-thiadiazole derivatives such as 2,5-bis(pyridin-2-yl)-1,3,4-thiadiazole (L) have been studied and have allowed access essentially to mono and bimetallic complexes [17][18][19][20][21][22].

The biological activity of some of these complexes was examined: It confirms the growth of the efficiency of the ligand according to its environment in the coordination sphere of the metal. For example, in phytopathology, we have shown that this efficiency varies according to the following sequence: NiL 2 (N 3 ) 2 > Ni 2 L 2 (H 2 O) 4 Cl 4 3H 2 O > L [23,24]. Recently, we have reported the synthesis of mono and binuclear compounds of transition metals (M = Cu, Ni and Co) with pseudo halide anions (N 3 and SCN -) as co-ligands [23][24][25][26][27][28]. The magnetic study of  2 -1,1-azido double-bridged [Cu 2 L 2 (-N 3 ) 2 (N 3 ) 2 ] complex revealed that the latter is weakly antiferromagnetic [27].

The pseudo halide complexes so exhibit interesting properties in many areas, this prompted us to continue this study by trying to isolate other complexes with Co(II) metal, 2,5-bis(pyridin-2yl)-1,3,4-thiadiazole ligand (L) and thiocyanate ions. Recently, the new complex of formula (C 26 H 16 CoN 10 S 4 ) noted CoL 2 (SCN) 2 has been synthesized under heating for 3 days and its crystallographic structure was briefly described by Wang [29]. In parallel and independently of this work, we synthetized the same complex but in mild thermal conditions (without heating) and herein we report a detailed structural study and Hirshfeld surface analysis of CoL 2 (SCN) 2 complex as well as its spectroscopic characterisations (IR, UV-Visible and Raman). The magnetic properties of the title complex were also performed and discussed.

Experimental

Materials

The ligand, namely 2,5-bis(pyridin-2-yl)-1,3,4-thiadiazole (L) was synthesized according to the literature procedure [30]. All solvents and reagents for synthesis were purchased from Aldrich and Merck and used as received without further recrystallization or distillation.

Synthesis of the title compound Co(C 12 H 8 N 4 S) 2 (NCS) 2 : CoL 2 (NCS) 2

A mixture of ligand L (24 mg, 0.1 mmol) and CH 3 CN (10 mL) was carefully layered onto a solution of CoCl 2 6H 2 O (24 mg, 0.1 mmol,) and KSCN (20 mg, 0.2 mmol) in CH 3 CN/H 2 O (1:1 v/v, 10 mL). The test tube was sealed with parafilm and left to stand at room temperature. Slow diffusion between the metal salt solution and the 1,3,4-thiadiazole ligand (L) produced red blockshaped crystals of CoL 2 (NCS) 2. They were separated, washed with cold ethanol and dried under vacuum. Yield: 55% (based on Co). Anal. Calcd. (%) for C 26 H 16 CoN 1636 (m), 1600 (w), 1564 (w), 642 (w); UV-Vis (λ max , nm (ε max , M -1 cm -1 )) in DMSO solvent: 796 (860), 642 (180), 431 (2620), 317 (33720), 272 (27300).

Crystal X-ray data collection

Single crystal selected for the X-ray diffraction (XRD) data collection (0.082 × 0.084 × 0.218 mm) was mounted on cryoloop and tested on a Bruker APEX II diffractometer with a MoK α graphite-monochromated radiation ( = 0.71073 Å). The diffractometer is equipped with a CCD bidimensional detector and an OXFORD CRYOSTREAM 700 system to cool the sample to 173 K [31]. SAINT + 6.02 program was used for extraction and integration of diffraction intensities [32] and SADABS program was carried out for correction of absorption effect [33]. The structures were solved by direct methods using SHELXL [34] and refined (by weighted full matrix least-square on F 2 techniques) to convergence using the SHELXL program. All non-hydrogen atoms were refined anisotropically. All hydrogen atoms were positioned geometrically and refined using a riding model.

Routine powder X-ray diffraction (PXRD) data of pure phase for CoL 2 (SCN) 2 complex have been collected at room temperature in the angular range 5 to 70 of 2θ with a scan step width 0.016° using a X'pert Pro PANalytical θ/2θ diffractometer (CuK α radiation,  = 1.5405 Å) in Bragg-Brentano geometry. Cell parameters have been refined using the pattern matching option of Fullprof suite [START_REF] Rodriguez-Carvajal | A graphic tool for powder diffraction[END_REF]36], by means of PXRD profile patterns adjustment.

Hirshfeld surface analysis

The Hirshfeld surfaces calculated for CoL 2 (NCS) 2 complex provide additional information on the distinctive contributions made to the molecular packing by the independent molecules. Thus, a Hirshfeld surface analysis 37 and the associated two-dimensional fingerprint plots 38 were performed using CrystalExplorer17.5 39 to figure out the normalized contact distance (d norm ),which depends on contact distances to the closest atoms outside (d e ) and inside (d i ) the surface. The 3D d norm surfaces are mapped over a fixed colour scale of -0.185 to 1.334 and -0.222 to 1.337 a.u for Co(1)L 2 (NCS) 2 and Co(2)L 2 (NCS) 2 molecules respectively, and shape index mapped in the colour range of -1.0 to 1.0 a.u.

physical measurements

UV-Visible absorption spectra in dimethyl sulfoxide (DMSO) solvent were recorded in the range 200-900 nm using a SHIMADZU 2450 spectrophotometer. Element analyses (C, H, N and S) were performed on a VARIO-ELEMENTAR analyzer.

FTIR spectra were recorded on a SHIMADZU FT-IR 8400S spectrometer with samples dispersed in KBr pellets in the range 500-3000 cm -1 .

Raman spectra have been acquired with a Renishaw InVia spectrometer in micro-Raman configuration (objective  50) equipped with a Peltier cooled CCD detector. The 785 nm excitation line of a LASER diode have been used at a power less than 3 mW onto the sample in order to avoid local heating.

The 1 H and 13 C NMR spectra of complex were recorded with the Bruker AVANCE 300 at 25 °C. All chemical shifts 1 H and 13 C are given in ppm using dimethyl sulfoxide-d 6 (DMSO-d 6 ) DMSO as solvent.

Thermal gravimetric analysis (TGA) has been performed under air flow (20 ml/min), using a SETARAM TAG24-16 thermal analyzer and platinum crucibles, in the range of room temperature to 700°C under air with 5 °C min -1 fixed heating rate. The TGA curve has been normalized with respect to the sample weight.

Magnetic measurements were carried out using the commercial Physical Properties Measurements System device (Quantum Design, PPMS), and magnetization M(T) was measured versus temperature ranging from 2 to 300 K, under an external magnetic field of 0.05 T. The magnetic field dependence of the magnetization M(H) was also measured at 2 K by varying the applied magnetic field between -6 and 6 T.

Results and discussion

Crystal structure determination and description

The mononuclear title Co(II) complex, namely bis(2,5-di(pyridin-2-yl)-1,3,4-thiadiazole-

κ 2 N,N′)-bis(thiocyanato-κ 1 N)cobalt(II), Co(C 12 H 8 N 4 S) 2 (NCS) 2 ,
was obtained by reaction between the thiadiazole ligand (L), CoCl 2 ,H 2 O and KSCN in H 2 O/CH 3 CN solution. The obtained complex CoL 2 (NCS) 2 , crystallizes in monoclinic symmetry and P 2 1 /c space group with two independent cobalt crystallographic sites, Co1 and Co2, and four CoL 2 (SCN) 2 molecules by unit cell as shown in Fig. 1. The details for the crystal data collection and the processing, together with the measurement parameters of the title complex are given in Table 1. Final atomic coordinates and isotropic or equivalent isotropic displacement parameters are given in Table 2. The selected interatomic distances are listed in Table 3. Hydrogen bonds are reported in Table 4. CCDC 1878437 (CSD, Cambridge) contains the supplementary crystallographic information for the CoL 2 (NCS) 2 complex.

Crystal structure was solved in the centrosymmetric P 2 1 /c space group by means of a direct methods strategy that localizes the heavy atoms Co and S, followed by a Fourier-difference maps examination to localize non-hydrogen light atoms N and C. All non-hydrogen atoms were refined with anisotropic displacement factors. Hydrogen atoms were included in idealized position and refined with fixed isotropic displacement factors U eq in the final cycles of refinement. The final refinement by using geometrical restraints with C-H = 0.95 Å (aromatic ring). At the end of the crystal structure refinement a last Fourier-difference examination reveals no significant peak, with acceptable remaining maximum and minimum electron densities. [43].

N1-C1 1.342(3) N1-C5 1.358(2) N2-C6 1.318(2) N2-N3 1.373(2) N3-C7 1.308(2) N4-C12 1.339(3) N4-C8 1.344(2) N5-C13 1.166(3) N6-C17 1.340(2) N6-C16 1.356(2) N7-C15 1.315(2) N7-N8 1.374(2) N8-C14 1.309(2) N9-C22 1.336(2) N9-C21 1.345(2) N10-C26 1.168(3) C1-C2 1.390(3) C7-C8 1.473(3) C2-C3 1.386(3) C8-C9 1.388(3) C3-C4 1.392(3) C9-C10 1.394(3) C4-C5 1.384(3) C10-C11 1.378(3) C5-C6 1.473(3) C11-C12 1.393(3) C14-C21 1.468(3) C19-C20 1.387 (3)
In this crystal structure each independent centrosymmetric cationic entity [CoL 2 ] 2+ is connected apically to two axial thiocyanate anions SCN -to build CoL 2 (SCN) 2 complex, as indicated in the Fig. 1, where the both 2,5-bis(pyridin-2-yl)-1,3,4-thiadiazole ligands (L) adopt a trans configuration. The same configuration was previously observed in other cobalt complexes with the thiocyanate ion as coligand [17,26,[40][41][42]. Indeed, the 2,5-bis(pyridine-3-yl)-1,3,4-oxadiazole ligand (L 3 ) adopts a trans conformation in [Co(L 3 ) 2 (NCS) 2 ] n complex and bridges two Co 2+ centers to give a bi-dimensional layer, featuring [Co 4 (L 3 ) 4 ] macrocycles as subunits [40]. In the case of [Co(bpox) 2 (SCN) 2 ]H 2 O complex, the 2,5-bis(pyridin-2-yl)-1,3,4-oxadiazole ligand bpox adopts a trans conformation, and forms hydrogen bonds with the water molecule localized in the intermolecular space [41]. The trans behaviour was also found in the case of Co(II) coordination complex with the same investigated ligand (L) without thiocyanate ion as coligand [17,26,42].

Thus, the crystallographically independent unit of the title compound is comprised of two different CoL 2 (NCS) 2 molecules, linked together by different weak interactions, like - stacking interactions as well as the various intermolecular hydrogen interactions to form a three-dimensional structure, Tables 4-5 and Fig. 2 (for the clarity of the Fig. 2, the latter is presented in the ac plan).

Thus, the crystal cohesion is ensured by Co-N, C-H⋯N, C-H⋯, C-H⋯S interactions and - stacking interactions between pyridyl rings of neighbouring molecules. As indicated in the Fig. 3 In addition, three different intermolecular C-H⋯π interactions are also observed between the centroids of pyridyl rings and aromatic H atoms H4 and H9 with distances of 3.370(2), 3.440(2) and 3.736(2) Å, as indicated in Table 5. These interactions also contribute to the cohesion of the structure as shown in Fig. 7. They are often observed between arenes, alkenes or alkynes in hydrocarbons and play an important role in chemistry and biology [START_REF] Nishio | The CH/ Interaction. Evidence, Nature and Consequences[END_REF]. There are also three different π-π stacking interactions existing in crystal structure of CoL 2 (NCS) 2 complex, observed between the pyridyl ring centroids of neighbouring molecules with distances range from 4.036 to 4.480 Å, as indicated in Fig. 8. Indeed, these stacking interactions connect the molecules together and participated to the cohesion of the structure to form a 3D supramolecular structure. These interactions are often observed in the molecules containing aromatic rings and generally depend upon charge distribution and also the shape of molecule; and require geometrical requisites [START_REF] Jennings | [END_REF][46][47]. It should be also noted that these interactions are of utmost importance in drug chemistry, as most drugs are aromatic. The purity of prepared powder of CoL 2 (NCS) 2 was also verified by powder X-ray diffraction (PXRD). The diffractogramme profile refinement, in monoclinic symmetry with P 2 1 /c space group, was carried out according the Le Bail method [START_REF] Bail | Ab-initio structure determination of LiSbWO 6 by X-ray powder diffraction[END_REF] using the pattern matching option of Fullprof program [START_REF] Rodriguez-Carvajal | A graphic tool for powder diffraction[END_REF], where only the profile parameters (cell dimensions, symmetry, peak shapes, and zero-point correction) have been refined. Pseudo-Voigt function with an asymmetry correction at low angles was used to describe the peak shape. The final observed, calculated, and difference PXRD patterns resulting from the profile-matching procedure are plotted in Fig. 9.

Refined cell parameters with their profile reliability factors (R p and R wp ) are also listed in Table 6.

The obtained structure refinement parameters showed that PXRD and crystal diffraction findings are in good agreement for CoL 2 (NCS) 2 .

Fig. 9. Profile-matching result of CoL 2 (NCS) 2 complex using powder X-ray diffraction. The observed, calculated, and difference patterns are in red, black and blue, respectively. The small marks in green correspond to the Bragg peaks positions.

Hirshfeld surface analysis

The Hirshfeld surface was calculated for the individual Co(1)L 2 (NCS) 2 and Co(2)L 2 (NCS) 2 molecules in the title complex (Fig. 1), and for overall (CoL 2 (NCS) 2 ). In order to compare with an isostructural complex, the Hirshfeld surface was also performed for overall FeL 2 (NCS) 2 [43] . The contact analysis for the investigated complex suggests that the C⋯H/H⋯C contacts (Fig. 12b) are the driving force in molecular arrangement and crystal packing formation, the largest contribution with 27.4% of the surface is from C⋯H contacts in C-H⋯ interactions between the centroids of pyridyl rings and aromatic H-atoms H4 and H9 (Table 5), in the crystal (Fig. 11b). In the fingerprint plot delineated into S⋯H/H⋯S contacts in Fig. 12c, the pair of spikes 2) molecules (Figs. 8 and11c), as can be inferred from inspection of the adjacent red and blue triangles (highlighted by red circles) on the shape-index surface (Fig. 10). The C⋯C contacts have an arrow-shaped distribution of points with the tip at d e  d i  1.6 Å (Fig. 12f). When the two molecules in the asymmetric unit of CoL 2 (NCS) 2 are compared with each other (Table 7), there is little difference between them. The small contributions from other remaining interatomic contacts have negligible effect on the packing. A comparison of the molecular surfaces of Hirshfeld in two complex CoL 2 (NCS) 2 and FeL 2 (NCS) 2 [43] clearly shows that the Hirshfeld surface have similar shapes and fingerprint plots (Fig. 12), reflecting the same packaging and intermolecular patterns solid state arrangements.

Spectroscopy studies 3.3.1. Ultraviolet-visible spectroscopy

The electronic spectra of the ligand (L) and its complex (CoL 2 (NCS) 2 ), are shown in Fig. 13.

The absorption maxima (λ max ) are also shown in Table 8. If the cobalt(II) d 7 ion is in an octahedral environment, it has three transitions d-d in UV-Visible spectroscopy:  1 : 4 T 1g (F) → 4 T 1g (P),  2 : 4 T 1g (F) → 4 A 2g (F) and  3 : 4 T 1g (F) → 4 T 2g (F) [49,50]. The complex CoL 2 (NCS) 2 in DMSO, its electron spectrum in the visible range, effectively displays three low-intensity bands at 431( 1 ), 642( 2 ) and 796 nm ( 3 ) successively attributable to the transitions mentioned above. This seems to indicate that the metal is probably hexa-coordinated. In the UV domain two more intense bands at 272 and 317 nm are assignable to the intra-ligand transitions → * and n → * of L linked to the metal. These transitions should be compared with those of the free ligand L, in the same solvent, who appear at 245 and 305 nm successively [24].

Table 8

Assignments of the main UV bands of the ligand (L) and of the title complex CoL 2 (NCS) 2 in DMSO (10 -4 M).

Compound

λ max (nm) (ε max , M -1 cm -1 ) * n * d-d
Ligand 245 (11810) 305 (15700) -Co(L) 2 (SCN) 2 272 (27300) 317 (33720) 431 (2620) 4 T 1g (F)→ 4 T 1g (P) 642 (180) 4 T 1g (F)→ 4 A 2g (F) 796 (860) 4 T 1g (F)→ 4 T 2g (F)

FTIR spectroscopy

The FTIR spectra of ligand and its complex are shown in Fig. 14. In infrared spectroscopy, the presence of the thiocyanate is revealed mainly by a fine and intense peak around 2100 cm -1 which corresponds to the  as (CN) stretching of the SCN -group. If this value is less than 2100 cm -1 , it is generally attributed to a terminal ligand bound by the nitrogen atom [51][52][53]. The IR spectrum of the complex seems to indicate, by the value of this frequency (2079 cm -1 ) that the two thiocyanates are bound by nitrogen atom. The non-duplication of the signal suggests that the two co-ligands are equivalent to each other in the coordination sphere of the metal. The spectrum of the studied complex also shows several absorption bands, which correspond to the different modes of vibration of the ligand L (Table 9). We note in particular those of 1636 and 642 cm -1 successively attributable to the C=N and C-S-C bonds.

Fig.14.

Infrared spectra of ligand (L) and its complex CoL 2 (NCS) 2 in the 500-3000 cm -1 range.

Raman spectroscopy

Fig. 15 shows the Raman spectra of the ligand L and title complex "CoL 2 (NCS) 2 ". Only the main differences between the two spectra will be discussed in the following. Compared to the ligand spectrum, a new feature appears at 2072 cm -1 for the cobalt complex (Fig. 16). This band can be attributed to NCS -anions [START_REF] Nakamoto | Infrared and raman spectra of inorganic and coordination compounds: Part B: Applications in coordination[END_REF]. In the 1520-1650 cm -1 range, two bands at 1585 and 1567 cm -1 are observed for the ligand while three bands at 1601, 1585 and 1568 are obtained for the complex (Fig. 17). According to da Mota et al. [START_REF] Da Mota | [END_REF], the presence of three bands for the complex instead of two for the free ligand suggests the coordination of only one pyridine group to the metal. The 1400-1500 cm -1 range is characteristic of C=N bonds in the thiadiazole ring as illustrated in Fig. 18 [56]. Additional bands together with slight Raman shifts are observed for the complex compared to the free ligand in this region. This can be explained by the coordination of the thiadiazole ring to the metal via N atom.

Fig. 17.

Raman spectra of the ligand and its complex in the 1520-1650 cm -1 range.

Fig. 18.

Raman spectra of the ligand and its complex in the 1350-1550 cm -1 range.

1 H and 13 C NMR analysis

The 1 H and 13 C NMR spectrum were recorded in DMSO-d6 for complex and compared with the corresponding spectrum of free ligand (L), as described in the literature [30]. The 1 H and 13 C NMR chemical shifts ( ppm) of the 1,3,4-thiadiazole ligand (L) and its complex "CoL 2 (NCS) 2 " are listed in Table 10. Compared to the free ligand, some changes were observed in the proton chemical shift values of the cobalt complex. This behaviour may be due to the formation of the various intermolecular hydrogen interactions and the coordination of the thiadiazole ring to the cobalt via N atom [57]. The 13 C NMR signals of the ligand (L) are also slightly downfield shifted upon coordination to the cobalt metal (Table 10) [57], supporting therefore the conclusions drawn on the basis of 1 H NMR measurements. On the other hand, one more signal observed at 132.12 ppm in the case of the investigated complex was assigned to carbon atom of the isothiocyanate coordinated in CoL 2 (NCS) 2 [58].

Thermal decomposition study

In order to ascertain its thermal stability, CoL 2 (NCS) 2 was subjected to thermogravimetric analysis (TGA) under air in the temperature range of 20-700°C and the obtained thermogram is given in Fig. 19. The TGA plot can be analyzed as having three stages of decomposition. Indeed, the cobalt complex shows a weight loss in the 200-500°C range, complying with the decomposition of the thiocyanates part and the organic ligands from the cobalt complex. The obtained experimental value is 64% which is in agreement with the theoretical value of 63.3% and complying with the possible removal of the two thiocyanate co-ligands and two thiadiazole ligands (L). The first weight loss (17.98 %) occurs between 200 and 262 °C; the second and third is an overlapping stage, with a weight loss of 46.02 % of the initial weight, take place approximately between 307 and 436°C. On the basis of the experimental mass losses, the first decomposition step can be ascribed to the loss of the two thiocyanate co-ligands (calc. 17.7%) [59]. In the highertemperature stage, the overlapping decomposition steps can be attributed to the successive loss of two 1,3,4-thiadiazole ligands (L) to form a metallic oxide Co3O4 as a residual mass (calcd. 45.7%). The formation of the cobalt oxide was confirmed by Energy Dispersive X-Ray analysis (EDX). The good thermal stability of the CoL 2 (NCS) 2 complex is supported by the thermal decomposition data showing that the investigated cobalt complex is thermally stable up to 200°C.

Magnetic properties

The bivalent transition metals (Mn II , Fe II and Co II ) based coordination compounds have attracted considerable attention due to their magnetism preliminary magnetic study of our complex has been also performed under an applied magnetic field of 500 Oe in temperature range 2-300 K. Before measurement, the crystallographic phase purity of crushed crystalline samples was confirmed Powder X-Ray Diffraction analysis. The temperature dependence of the magnetic susceptibility of CoL 2 (NCS) 2 complex in the form of χ and χ*T is shown in Fig. 20. As observed in the structure determination section above, the crystal structure of CoL 2 (NCS) 2 complex consists of a 3D network arrangement, in which two Co II ions are separated by large distances and no plausible exchange interactions are possible. The experimental χ*T value at room temperature is 5.99 emu K mol -1 , which is much higher than the expected spin-only value of 3.76 emu K mol -1 for two free high-spin Co II ions (with for S = 3/2 and g = 2) in an octahedral coordination environment, indicating the spin-orbit coupling. This is due to orbital contribution typical for the 4 T 1g ground state of octahedral high-spin Co II ions [65,[67][68][69][70]. In addition, as the temperature decreases, the value of *T decreases down to 0.24 emu K mol -1 at 2K, which indicates an antiferromagnetic coupling between the Co II ions. It is also interesting to compare the thermal-magnetic behaviours between our compound

Co II (L) 2 (NCS) 2 and the iron isostructural complex Fe II (L) 2 (NCS) 2 , prepared by reaction under protective atmosphere of argon, using Fe(NCS) 2 in MeOH with a 2 : 1 ligand-to-metal molar ratio [43]. As shown in thermal-magnetic behaviours of both compounds in Fig. 232, two different magnetic evolutions were observed: in the case of cobalt complex Co II (L) 2 (NCS) 2 only a paraferrimagnetic transition has been observed at low temperature (Figs. 22 and23a), whereas in the case of Fe II (L) 2 (NCS) 2 , Klingele et al. have highlighted two step spin crossover, corresponding to two magnetic transitions, as presented in Fig. 23b and confirmed by Mössbauer measurements [43].

These both magnetic transitions correspond exactely to a switch from a high-spin (HS at at 167 K) to a low-spin (LS at 112 K), through an intermediate magnetic phase between the two transition temperatures. It should also be noted that this ferrimagnetic behavior with a strong antiferromatic interaction at low temperature, has already been observed in some transition metal complexes previously described [70][71][72][73].

The occurrence of such weak ferrimagnetic ordering has been additionally characterized by the magnetic field-dependent isothermal magnetization M(H) at 2.0 K, with magnetic field up to 6 T (Fig. 24a). It is noticeable that a typical hysteresis curve for the ferrimagnetic behaviour is well observed at 2.0 K, as frequently observed in ferrimagnetic molecular systems; with a negligible coercive field (H c ) and remanent magnetization (Mr). Thus, the M(H) hysteresis curve shows a quick increase with increasing magnetic field, reaching a value of 4.0 emu g -1 at 15 T, then slowly increasing, attaining 5.7 emu g -1 for 6 T. As indicated in Fig. 24b, the coercivity field (H c ) is found to be equal to 7.5 Oe and, while remanent magnetization (Mr) is estimated to 0.008 emu g -1 .

Fig. 1 .

 1 Fig. 1. Coordination environment cobalt sites in the crystal of CoL 2 (NCS) 2 complex.

Fig. 2 .

 2 Fig. 2. Three-dimensional crystal structure view along b axis of CoL 2 (NCS) 2 complex.

Fig. 3 .Fig. 4 .Fig. 4 .

 344 Fig. 3. Formation of infinite chain involving C23-H23⋯N4 hydrogen bonds in crystal structures of CoL 2 (NCS) 2 .

Fig. 5 .

 5 Fig. 5. Partial packing diagram of the complex showing the network of sulfur-hydrogen bonds linking of CoL 2 (NCS) 2 into layers parallel to the ac plane.

Fig. 6 .

 6 Fig. 6. Carbon Hydrogen C-H⋯C interactions in crystal structure of CoL 2 (NCS) 2 .

Fig. 7 .

 7 Fig. 7. C-H⋯π stacking interactions in crystal structures of CoL 2 (NCS) 2 .

Fig. 8 .

 8 Fig. 8. π-π stacking interactions in crystal structure of CoL 2 (NCS) 2 .

Fig. 10 .

 10 Fig. 10. Views of the Hirshfeld surfaces mapped over d norm and shape-index for components of CoL 2 (NCS) 2 : (a) Co(1) molecule and (b) Co(2) molecule.

at d e + d i  2 . 6 Å

 26 and 2.7 Å for the Co(1) and Co(2) molecules respectively, represent the presence of the C-H⋯S hydrogen bonds between them. The H⋯H (d e + d i  2.5 Å) and H⋯N/N⋯H (d e + d i  2.6 Å) contacts (Figs. 12d and 12e) makes similar contributions to the total Hirshfeld surface of 15.6 and 15.0%, respectively. H⋯H contacts represent van der waals interactions and H⋯N/N⋯H correspond to hydrogen bonds.

Fig. 11 .

 11 Fig. 11. Hirshfeld surfaces mapped over (a) d norm to visualize the intermolecular C-H⋯S and C-H⋯C and shape-indexed property for Co(1) and Co(2) molecules highlighting intermolecular (b) C-H⋯ and (c) - interactions through black dashed lines.

Fig. 12 .

 12 Fig. 12. (a) The full two-dimensional fingerprint plots for Co(1)L 2 (NCS) 2 and Co(2)L 2 (NCS) 2 molecules, overall of CoL 2 (NCS) 2 and FeL 2 (NCS) 2 complexes and (b)-(f) those delineated into C⋯H/H⋯C, S⋯H/H⋯S, N⋯H/H⋯N, H⋯H and C⋯C contacts in Co(1)L 2 (NCS) 2 and Co(2)L 2 (NCS) 2 molecules and in CoL 2 (NCS) 2 and FeL 2 (NCS) 2 complexes.

Fig. 13 .

 13 Fig. 13. Electronic spectra of the ligand L and the title complex CoL 2 (NCS) 2 in DMSO (10 -4 M).

Fig. 15 .Fig. 16 .

 1516 Fig. 15. Raman spectra of the ligand and its complex in the 500-2200 cm -1 range.

Fig. 19 .

 19 Fig. 19. TGA analysis of CoL 2 (NCS) 2 in air with a heating rate of 5 K/min.

Fig. 20 .

 20 Fig. 20. Magnetic susceptibility *T and  versus temperature for CoL 2 (NCS) 2 complex.

Fig. 21 .

 21 Fig. 21. Magnetic susceptibility  and inverse  -1 versus temperature from 2 to 300K for CoL 2 (NCS) 2 complex.

Fig. 22 .

 22 Fig. 22. Magnetic susceptibility  and inverse  -1 versus temperature from 2 to 50 K for CoL 2 (NCS) 2 .

Fig. 23 .Fig. 24 .

 2324 Fig. 23. T vs. T plot for (a) Co II (L) 2 (NCS) 2 and (b) Fe II (L) 2 (NCS) 2 [41]. The inset in (b) shows the first temperature derivative of the T.

  di(pyridin-2-yl)-1,3,4-thiadiazole-κ 2 N,N′)-bis(thiocyanato-κ 1 N)cobalt(II) complex has been synthesized and its crystal structure has been characterised by single-crystal X-ray diffraction and different spectroscopic techniques (UV-Visible, FTIR, Raman, and NMR). The obtained structure presents two independent Co(II) atoms in octahedral environment, with two thiadiazole molecules acting as bidentate ligands (L) with a trans coordination mode and two axially coordinated thiocyanate SCN -ions to form neutral coordination complexes (CoL 2 (SCN) 2 ).The crystal structure is mainly stabilized by intermolecular hydrogen bonding, C-H⋯π and - stacking; in addition to the N-Co coordination bonds. Indeed, the stabilization of the structure is supported by C-H⋯N hydrogen bond interactions between pyridyl rings with alternate cobalt sequences ''CoL 2 (NCS) 2 '' to form an infinite chain [(CoL 2 (NCS) 2 ) 2 ]  . Threedimensional Hirshfeld surface analysis and two-dimensional fingerprint maps revealed that the C⋯H/H⋯C and S⋯H/H⋯S contacts represent an important contribution of the Hirshfeld surface result of hydrogen-bonding interactions in CoL 2 (SCN) 2 . Thermal decomposition study reveals that the investigated complex is thermally stable up to 200 °C. Magnetic measurements showed an

  10 S 4 : C, 47.63; H, 2.46; N,

	21.36; S, 19.56. Found (%): C, 47.69; H, 2.52; N, 21.29; S, 19.51; IR (KBr pellet, cm -1 ): 2079 (vs),

Table 1

 1 Single crystal and structure refinement data for CoL 2 (NCS) 2 complex.

	Chemical formula	C 26 H 16 CoN 10 S 4
	Formula weight	655.66 g/mol
	Temperature	173(2) K
	Wavelength	0.71073 Å
	Crystal size	0.082 × 0.084 × 0.218 mm
	Crystal system	monoclinic
	Space group	P 2 1 /c
	Unit cell dimensions	a = 22.876(4) Å	α = 90°
		b = 7.9167(12) Å	β = 110.204(5)°
		c = 16.403(3) Å	γ = 90°
	Volume	2787.8(8) Å 3
	Z	4
	Density (calculated)	1.562 g/cm 3
	Absorption coefficient	0.953 mm -1
	F(000)	1332
	Theta range for data collection	3.20 to 31.50°
	Index ranges	-33 < = h < =33, -11 < = k < = 11, -24 < = l < = 23
	Reflections collected	105365
	Independent reflections	9198 [R (int) = 0.0909]
	Coverage of independent reflections	99.0%
	Absorption correction	Numerical Mu From Formula
	Refinement method	Full-matrix least-squares on F 2
	Refinement program	SHELXL-2014/7 (Sheldrick, 2014)
	Function minimized	Σ w(F o 2 -F c	2 ) 2
	Data / restraints / parameters	9198 / 0 / 373
	Goodness-of-fit on F 2	1.005
	Δ/σ max	0.002
	Final R indices	6184 data; I > 2σ(I)	R 1 = 0.0386, wR 2 = 0.0719
		all data		R 1 = 0.0808, wR 2 = 0.0868
	Weighting scheme	W = 1/[σ 2 (F o 2 )+(0.0234 P) 2 + 2.2054 P] where P = (F o 2 + 2F c 2 )/3
	Largest diff. peak and hole	0.445 and -0.628 eÅ -3
	R.M.S. deviation from mean	0.088 eÅ -3

Table 2

 2 Fractional non hydrogen atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å 2 ).

		x/a	y/b	z/c	U eq
	Co1	0.0	0.5	0.0	0.01601(8)
	Co2	0.5	0.0	0.0	0.01652(8)
	S1	0.14339(2)	0.41758(6)	0.86879(3)	0.01936(10)
	S2	0.16790(2)	0.82432(7)	0.19507(4)	0.02654(12)
	S3	0.64515(2)	0.59909(6)	0.01490(3)	0.01983(10)
	S4	0.33729(2)	0.79479(7)	0.74160(3)	0.02543(12)
	N1	0.01138(7)	0.6963(2)	0.91514(10)	0.0178(3)
	N2	0.06959(7)	0.3986(2)	0.95458(10)	0.0171(3)
	N3	0.10123(7)	0.2480(2)	0.97058(10)	0.0176(3)
	N4	0.21513(9)	0.1095(2)	0.87984(12)	0.0271(4)
	N5	0.06951(8)	0.6134(2)	0.10116(11)	0.0228(4)
	N6	0.49964(7)	0.7743(2)	0.07308(10)	0.0180(3)
	N7	0.43210(7)	0.1561(2)	0.02660(10)	0.0181(3)
	N8	0.39598(8)	0.1348(2)	0.07761(11)	0.0192(3)
	N9	0.26665(7)	0.3951(2)	0.07693(11)	0.0200(3)
	N10	0.42991(8)	0.9111(2)	0.89237(11)	0.0224(4)
	C1	0.98090(9)	0.8441(3)	0.89676(13)	0.0209(4)
	C2	0.99353(9)	0.9660(3)	0.84419(13)	0.0228(4)
	C3	0.03935(9)	0.9342(3)	0.80875(13)	0.0209(4)
	C4	0.07156(9)	0.7817(3)	0.82737(12)	0.0192(4)
	C5	0.05611(8)	0.6663(2)	0.88000(12)	0.0165(4)
	C6	0.08649(8)	0.5004(3)	0.90309(12)	0.0170(4)
	C7	0.14161(9)	0.2409(2)	0.93041(12)	0.0167(4)
	C8	0.18451(9)	0.0989(2)	0.93638(12)	0.0182(4)
	C9	0.19257(9)	0.9699(3)	0.99661(13)	0.0227(4)
	C10	0.23529(10)	0.8431(3)	0.99847(15)	0.0277(5)
	C11	0.26679(11)	0.8506(3)	0.94057(15)	0.0321(5)
	C12	0.25539(11)	0.9851(3)	0.88241(15)	0.0346(6)
	C13	0.11056(9)	0.7013(3)	0.14001(12)	0.0184(4)
	C14	0.35376(9)	0.2535(2)	0.06306(12)	0.0179(4)
	C15	0.58300(9)	0.7099(2)	0.02373(12)	0.0178(4)
	C16	0.54630(9)	0.6646(2)	0.07828(12)	0.0178(4)
	C17	0.46242(9)	0.7377(3)	0.11827(13)	0.0210(4)
	C18	0.46988(10)	0.5934(3)	0.16928(13)	0.0241(4)
	C19	0.51813(10)	0.4839(3)	0.17473(14)	0.0261(5)
	C20	0.55707(10)	0.5198(3)	0.12824(13)	0.0230(4)
	C21	0.30817(9)	0.2697(2)	0.10731(13)	0.0186(4)
	C22	0.22408(9)	0.4142(3)	0.11511(14)	0.0237(4)
	C23	0.22112(10)	0.3133(3)	0.18268(14)	0.0263(5)
	C24	0.26460(10)	0.1859(3)	0.21319(14)	0.0274(5)
	C25	0.30960(10)	0.1624(3)	0.17502(13)	0.0239(4)
	C26	0.39105(9)	0.8657(2)	0.82887(13)	0.0178(4)

Table 3

 3 Selected bond distances (Å) for the CoL 2 (NCS) 2 complex.

	Co1-N5	2.0654(17)	Co2-N10	2.0563(17)
	Co1-N2	2.1337(15)	Co2-N7	2.1442(16)
	Co1-N1	2.1615(16)	Co2-N6	2.1529(16)
	S1-C6	1.7164(18)	S1-C7	1.735(2)
	S2-C13	1.633(2)	S3-C15	1.7188(19)
	S3-C14	1.738(2)	S4-C26	1.631(2)

Table 3 .

 3 Therefore, the CoN 6 octahedra are slightly axially compressed. This structural feature is typical for related compounds[17,26,[40][41][42], and isostructural to iron complex FeL 2 (NCS) 2 described by Klingele el al.[43]. The iso-thiocyanate coligands bound through the nitrogen atoms

	C15-C16	1.467(3)	C21-C25	1.390(3)
	C16-C20	1.381(3)	C22-C23	1.387(3)
	C17-C18	1.391(3)	C23-C24	1.384(3)
	C18-C19	1.382(3)	C24-C25	1.390(3)
	2.065(2)-2.161(2) Å and 2.056(2)-2.153(2) Å for Co1 and Co2 atoms, respectively, as indicated in
	Fig. 1. The Co-N bond lengths involving the nitrogen atoms of the SCN -thiocyanate ions in the
	axial direction of the CoN 6 polyhedra, are much shorter (2.056(2)-2.065(2) A˚) than those
	containing the nitrogen of the thiadiazole ligand (L) in the basal plane [2.134(2)-2.161(2) A˚],

In this structure each transition metal atom Co is linked by six nitrogen atoms with two thiadiazole ligands (L) in the equatorial plan and with two thiocyanate coligand ions SCN -in apical direction, to form a distorted octahedral environment CoN 6 , with Co-N bond lengths in the range of

Table 4 C

 4

	D-H⋯A	D-H (Å)	H⋯A (Å)	D⋯A (Å)	D-H⋯A (°)
	C23-H23⋯N4	0.95(1)	2.722(2)	3.340(3)	123.4(1)
	C13-H2⋯C2	0.95(1)	2.750(2)	3.619(3)	152.5(1)
	C13-H4⋯C4	0.95(1)	2.776(2)	3.486(3)	132.2(1)
	C13-H22⋯C22	0.95(1)	2.771(2)	3.579(3)	143.4(1)
	C26-H12⋯C12	0.95(1)	2.860(2)	3.630(4)	138.8(1)
	C26-H18⋯C18	0.95(1)	2.796(2	3.670(4)	153.4(1)
	C26-H20⋯C20	0.95(1)	2.771(2)	3.262(3)	131.5(1)
	C4-H4⋯S2	0.95(2)	2.762(2)	3.684(3)	163.8(1)
	C9-H9⋯S2	0.95(2)	2.872(1)	3.676(3	143.1(1)
	C24-H24⋯S2	0.95(2)	3.103(1)	3.567(3)	111.8(1)
	C12-H12⋯S4	0.95(3)	2.926(1)	3.756(3)	113.1(1)
	C18-H18⋯S4	0.95(3)	2.917(1)	3.725(3)	143.7(1)
	C25-H25⋯S4	0.95(2)	3.043(1)	3.771(3)	134.4(1)

-H⋯A hydrogen-bond geometry of CoL 2 (NCS) 2 (A = N, C and S).

  and Table4, the stabilization of the structure is supported by

C-H⋯N hydrogen bond interactions (C23-H23⋯N4 = 2.722(2) Å) between pyridyl rings with alternate sequences of ⋯Co(1)L 2 (NCS) 2 ⋯Co(2)L 2 (NCS) 2 ⋯Co(1)L 2 (NCS) 2 ⋯Co(2)L 2 (NCS) 2 ⋯, to form an infinite chain [(CoL 2 (NCS) 2 ) 2 ]  .

Table 5 C

 5 -H⋯ Hydrogen-bond geometry for CoL 2 (NCS) 2 .

Table 6

 6 Lattice parameters and reliability factors of of CoL 2 (NCS) 2 .

	Complex	a (Ǻ)	b (Ǻ)	c (Ǻ)	 (°)	R p (%)	R wp (%)
	CoL 2 (NCS) 2	22.866 (4)	7.920 (1)	16.395 (4) 110.17 (1)	2.36	3.48

Table 7

 7

	. For both molecules, the

Table 7

 7 Percentage contributions of interatomic contacts to the Hirshfeld surface for the Co(1)L 2 (NCS) 2 and Co(1)L 2 (NCS) 2 molecules and for overall CoL 2 (NCS) 2 complex.

	Contact		Percentage contribution
		Co(1)L 2 (NCS) 2	Co(2)L 2 (NCS) 2	CoL 2 (NCS) 2 complex	FeL 2 (NCS) 2 complex [43]
	C⋯H/H⋯C	29.9	24.3	27.4	26.6
	S⋯H/H⋯S	26.1	24.8	24.5	25.8
	H⋯H	12.5	18.2	15.6	15.6
	H⋯N/N⋯H	15.3	14.3	15.0	15.1
	C⋯C	5.4	6.8	6.2	5.9
	C⋯N/N⋯C	4.1	4.0	4.1	4.0
	S⋯C/C⋯S	2.6	3.8	3.2	3.1
	S⋯S	2.6	1.0	1.8	1.8
	N⋯S/S⋯N	1.2	2.6	1.9	2.0
	N⋯N	0.2	0.2	0.2	0.2

Table 9

 9 FTIR data (cm -1 ) of the ligand and its complex CoL 2 (NCS) 2 .

	Ligand	637	1560 -1580	-	-
	Complex	642	1564 -1600	1636	2079

Compound ν (C-S-C) ν (C=C) ν (C=N) ν (NCS -)

Table 10

 10 NMR data (cm -1 ) of the ligand and its complex CoL 2 (NCS) 2 in DMSO-d 6 .

	Position	Data free ligand	Data complex
		1 H NMR chemical shift ( ppm)
	H b	7.59	7.61
	H d	8.03	8.07
	H c	8.31	8.33
	H a	8.73	8.75
		13 C NMR chemical shift ( ppm)
	C b	120.56	121.05
	C d	126.22	126.73
	C c	138.02	138.52
	C -NCS		132.12
	C a	148.17	148.62
	C e	150.30	150.81
	C f	171.14	171.64

Acknowledgements

The authors are greatly thankful to the CUR CA2D of Chouaib Doukkali University for its support and UCA-PARTNER for the use of the Bruker SC diffractometer.

antiferromagnetic exchange between the two non-equivalent cobalt(II) ions in CoL 2 (SCN) 2 complex with a ferrimagnetic behavior at low temperature.

Supplementary material


Morgane Tidière
email: mtidiere@gmail.com

Patrick Duncan

Jean-François Lemaître

Jean-Michel Gaillard

Laurie Bingaman Lackey

Dennis W H Müller

Marcus Clauss

Do equids live longer than grazing bovids?

Keywords: actuarial senescence, biological times, demography, pace of life, slow-fast continuum Equids vs bovids' actuarial senescence

A large part of the diversity of longevity and actuarial senescence (i.e. the progressive decline of survival probabilities with age) across vertebrates can be related to body size, phylogeny and the species' position on the slow-fast continuum of life histories. However, differences in mortality patterns between ecologically similar species, such as bovids and equids, remain poorly understood. Equids are commonly understood to outlive bovid species relative to their body mass, despite very similar feeding niches. Comparing survival patterns of 13 bovid and 10 equid sub-species, our findings confirm that equids outlive bovid species, with a higher adult survival rate and a delayed onset of senescence for equids, but no difference of rate of actuarial senescence. These differences are associated with a slower generation time and longer inter-birth interval, due to a longer gestation period, for equids compared to bovids.

Finally, our results suggest that all biological times (i.e. all life history traits expressed in time units) have evolved synchronously in bovids, whereas in equids gestation time and inter-birth interval either were never in synchrony with, or have slowed down relative to other biological times. Our findings suggest the existence of different selection pressures, or different constraints, on specific time-related traits between these two mammalian orders.

INTRODUCTION

Actuarial senescence, defined as the progressive decrease of survival with increasing age, is a ubiquitous process across the tree of life [START_REF] Nussey | Senescence in natural populations of animals: widespread evidence and its implications for bio-gerontology[END_REF][START_REF] Jones | Diversity of ageing across the tree of life[END_REF]. Striking differences in actuarial senescence and lifespan have been found in related species, such as the naked mole rat (Heterocephalus glaber) which lives nine times longer than similar-sized rodents [START_REF] Buffenstein | Negligible senescence in the longest living rodent, the naked mole-rat: insights from a successfully aging species[END_REF][START_REF] Ruby | Naked mole-rat mortality rates defy Gompertzian laws by not increasing with age[END_REF]). Such differences across phylogenetically related species or across species sharing the same lifestyle remain poorly understood and are currently attracting much interest [START_REF] Gorbunova | Comparative genetics of longevity and cancer: insights from long-lived rodents[END_REF][START_REF] Healy | Ecology and mode-of-life explain lifespan variation in birds and mammals[END_REF]. However, little work has been done, so far, to understand variation in senescence between distantly related species that have converged into closely similar niches.

Here we compare patterns of actuarial senescence (hereafter 'senescence') between taxa from two orders of mammals, equids (Perissodactyl) and grazing bovids (Artiodactyl), which are large herbivores whose evolution separated 55 million years ago [START_REF] Janis | The evolutionary strategy of the Equidae and the origins of rumen and cecal digestion[END_REF]).

Many of the grazing species, among the equids and bovids, have evolved in parallel in similar environments since the Miocene [START_REF] Janis | The evolutionary strategy of the Equidae and the origins of rumen and cecal digestion[END_REF]). These two groups of herbivores display evolutionary convergence in key morphological characters, such as elongated limbs and hypsodonty (i.e. the height of the molar teeth), and occupy similar feeding niches despite having different digestive systems [START_REF] Janis | The evolutionary strategy of the Equidae and the origins of rumen and cecal digestion[END_REF]). Moreover, it is commonly assumed that horses live longer than cattle. For instance, in the AnAge database [START_REF] Tacutu | Human Ageing Genomic Resources: integrated databases and tools for the biology and genetics of ageing[END_REF], the maximum lifespan recorded for the seven species of extant equids ranges from 30.1 years for kiang (Equus kiang) to 57 years for domestic horse (E. caballus), while for grazing bovids the maximum longevity recorded is 36.1 years for the lowland anoa (Bubalus depressicornis).

Among bovids, grazers live longer and senesce later and more slowly than do browsers, both in the wild [START_REF] Gaillard | Managing large herbivores in theory and practice: is the game the same for browsing and grazing species[END_REF] and in captive populations [START_REF] Lemaître | Comparing free-ranging and captive populations reveals intra-specific variation in aging rates in large herbivores[END_REF][START_REF] Tidière | Does sexual selection shape sex differences in longevity and senescence patterns across vertebrates? A review and new insights from captive ruminants[END_REF]. This difference is even more marked in captivity, probably because the food provided in zoos is more suitable for grazers than for browsers [START_REF] Müller | Relevance of management and feeding regimens on life expectancy in captive deer[END_REF][START_REF] Müller | Mating system, feeding type and ex situ conservation effort determine life expectancy in captive ruminants[END_REF][START_REF] Lemaître | Comparing free-ranging and captive populations reveals intra-specific variation in aging rates in large herbivores[END_REF][START_REF] Tidière | Does sexual selection shape sex differences in longevity and senescence patterns across vertebrates? A review and new insights from captive ruminants[END_REF]. The extant equids are typically grazers [START_REF] Schulz | Historical distribution, habitat requirements and feeding ecology of the genus Equus (Perissodactyla)[END_REF], while bovids comprise species ranging over a continuum of dietary niches from grazers to browsers [START_REF] Hofmann | Evolutionary steps of ecophysiological adaptation and diversification of ruminants: a comparative view of their digestive system[END_REF][START_REF] Gordon | The Ecology of Browsing and Grazing[END_REF]; therefore, we only used data from grazers among the bovids to perform a valid comparison of longevity and senescence patterns across these groups. The use of captive populations allows patterns of longevity and senescence of the two orders to be studied independently of environmental variation, which is likely to be a key driver of mortality patterns [START_REF] Gaillard | Roe deer survival patterns: a comparative analysis of contrasting populations[END_REF]. In captivity, animals are protected against starvation and predation, and competition for resources is minimal or absent.

Using a dataset of 15 species (comprising 23 species or subspecies; 13 bovids and 10 equids) living in captivity, we found strong support for longer longevity in equids than in bovids after taking into account allometric relationships. This difference is associated with higher adult survival and delayed onsets of senescence for equids, but there is no difference between the two orders in the rate of actuarial senescence.

A major axis of variation in longevity and senescence across species is included in the slow-fast continuum of the life histories [START_REF] Stearns | The influence of size and phylogeny on patterns of covariation among lifehistory traits in the mammals[END_REF]. Indeed, variation in life history traits among species is structured along a continuum of biological times that contrasts species with short longevity, early reproduction, high annual fecundity, and early onset and/or fast rates of senescence (at the continuum's fast end), with species with long longevity, delayed reproduction, low annual fecundity, and late onset and/or slow rates of senescence (at its slow end, e.g. [START_REF] Gaillard | An analysis of demographic tactics in birds and mammals[END_REF][START_REF] Ricklefs | Evolutionary theories of aging: confirmation of a fundamental prediction, with implications for the genetic basis and evolution of life span[END_REF][START_REF] Ricklefs | Life-history connections to rates of aging in terrestrial vertebrates[END_REF][START_REF] Jones | Senescence rates are determined by ranking on the fastslow life-history continuum[END_REF][START_REF] Bronikowski | Metabolism, body size and life span: a case study in evolutionarily divergent populations of the garter snake (Thamnophis elegans)[END_REF].

We, therefore, assessed whether observed differences of longevity between bovids and equids simply correspond to a different ranking over the slow-fast continuum as measured by the generation time [START_REF] Gaillard | Generation time: a reliable metric to measure life-history variation among mammalian populations[END_REF]. Two plausible, but different, demographic scenarios were tested: (1) all biological times or (2) only certain biological times are slower in equids than in bovids, leading to a difference in the pace of life (as represented by longer generation times in equids). Causes of the differences could be selection pressures for a slower pace of life in equids, or for a faster pace of life in bovids, with potentially different selection pressures and constraints acting on the different components of generation time. Evolutionary processes behind the differences in extant equids and bovids are discussed.

METHODS

Datasets

The life tables of the zoo populations were compiled from the Species360 database, which contains data since 1817 from more than 1,000 member institutions in over 90 countries worldwide. Information on sex, dates of birth and death is available for each individual.

Assuming that the total number of individuals living in zoos for a given species corresponds to a worldwide meta-population, we computed population parameters for species living in captivity. We constructed life tables available for females of equid and grazing bovid species for which the exact dates of birth and death are known. We considered all dead and living females but, to avoid any overestimation of the species' longevity due to some individuals never being recorded as dead, we removed individuals still alive in January 2014 with an age more than 125% older than the maximum age at death reported in AnAge, as longevity can be longer in zoos today than 20 years ago due to the improvement of captive conditions (e.g. [START_REF] Wich | Captive and wild orangutan (Pongo sp.) survivorship: a comparison and the influence of management[END_REF] for orang-utan, Pongo sp.). To ensure that the inclusion of all cohorts did not bias the results, the same analyses were done with cohorts for which all individuals are dead, defined as cohorts for which all females were already dead in January 2014. For some species, wild-type and domestic populations are kept in zoos (e.g. Bos javanicus). For these species, only the wild-type taxa were retained in the analyses. We obtained a final dataset of 23 taxa including 13 grazing bovids and 10 equids (Fig. S1).

Survival and actuarial senescence metrics

For each species, five different, and complementary, metrics were used to assess senescence patterns: maximum age at death, longevity, average adult survival rate, age at the onset of senescence and rate of senescence. The maximum age at death was determined as the maximum age at death observed in the database (Table S1). For the four other metrics, we built the capture history of each female and obtained age-specific survival estimates using the CMR (capture-mark-recapture) software E-SURGE [START_REF] Choquet | Program E-SURGE: a software application for fitting multievent models[END_REF]) (see appendix S1 for more details). From these age-specific survival estimates, we calculated the proportion of individuals alive at each age (lx, with l0=1) and longevity was measured as the age at which 90% of individuals from the initial cohort were dead (age x at which lx=0.1) (Table S1). This avoids spurious estimates due to different sample sizes or exceptionally long lives of a few individuals [START_REF] Moorad | A comparative assessment of univariate longevity measures using zoological animal records[END_REF].

To assess actuarial senescence, we fitted different age-dependent models from birth onwards: constant survival, two age-classes, full age-dependence, and several Gompertz models with different onsets of actuarial senescence (see appendix S1 for more details). To select the best survival model, we used a model selection procedure based on the Akaike Information Criterion (AIC, [START_REF] Burnham | Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach[END_REF]. For each species, we retained the model with the lowest AIC (Table S2). For 10 of the 13 bovids and 9 of the 10 equids, a Gompertz model provided a better fit than either the constant or the two-age class model, and was more parsimonious than the full age-dependent model (Table S2). The age at which survival begins to decline, corresponding to the age at the onset of senescence [START_REF] Péron | Age at the onset of senescence in birds and mammals is predicted by early-life performance[END_REF], varied among taxa (Table S1). In addition, from the selected Gompertz model, we measured both adult survival rate as the mean annual survival estimated between 1 year of age and the onset of senescence (Table S1) and rate of senescence as the exponential rate of mortality increase with age (Table S1). On a logit scale, age variation in survival was, therefore, constrained to be linear from the age at the onset of senescence onwards [START_REF] Gaillard | Assessing senescence patterns in populations of large mammals[END_REF]). For four species (Connochaetes taurinus albojubatus, Kobus kob leche, Syncerus caffer and Equus quagga boehmi), the full age-dependent model had a lower AIC than any Gompertz model. For these four taxa, only the maximal age at death and longevity were analyzed.

Mean values for the traits of adult females in each taxon

Mean body mass (BMa, in kg) for adult females was extracted from the literature (Table S3) to correct for allometric constraints. When available, body mass measures from wild populations were preferred.

The pace of life of a given taxon was measured as the generation time using the method described in [START_REF] Gaillard | Generation time: a reliable metric to measure life-history variation among mammalian populations[END_REF] (see appendix S1 for more details). As life history traits with a currency of time, we considered gestation length (GL, in days), age at first parturition (AFP, in days), and the inter-birth interval (IBI, in days) to test the potential difference of life history strategy between equids and bovids (Table S3). Values for GL, AFP, and IBI were extracted from the literature (Table S3).

Analyses

We first tested the differences in survival and actuarial senescence metrics between bovids and equids, accounting for body mass, because large species live longer and senesce later and more slowly than small species (e.g. [START_REF] Jones | Senescence rates are determined by ranking on the fastslow life-history continuum[END_REF][START_REF] Ricklefs | Life-history connections to rates of aging in terrestrial vertebrates[END_REF][START_REF] Lemaître | A test of the metabolic theory of ecology with two longevity data sets reveals no common cause of scaling in biological times: longevity scaling in mammals[END_REF][START_REF] Tidière | Does sexual selection shape sex differences in longevity and senescence patterns across vertebrates? A review and new insights from captive ruminants[END_REF]. Dependent variables included maximum age at death, longevity, adult survival rate, onset of senescence and rate of senescence. The full models included body mass and order (as factor) as independent variables.

In a second step, we tested whether the differences in survival and actuarial senescence metrics between bovids and equids parallel a difference in life history strategy. For each trait corresponding to a biological time included in the study (i.e. generation time, gestation length, inter-birth interval and age at first parturition), the full models included body mass and order (as factor) as independent variables.

In a third step, we ran a normed Principal Component Analysis (PCA, package 'ade4', [START_REF] Dray | The ade4 package: implementing the duality diagram for ecologists[END_REF] for bovids (N=5 taxa) and equids (N=7 taxa) separately, with generation time, longevity, age at first parturition, gestation length and inter-birth interval as biological times. Under scenario 1, all biological times in both equids and bovids should contribute equally to the overall time scale (i.e. equi-correlation sensu [START_REF] Morrison | Multivariate Statistical Methods[END_REF], which corresponds to the slow-fast continuum [START_REF] Gaillard | Life history axes of variation[END_REF]. In contrast, under scenario 2, equi-correlation should not be observed, meaning that the overall time scale is driven more strongly by some specific biological times and less by others.

Analyses were not corrected for phylogenetic relatedness beyond the inclusion of order as a factor because the number of species was rather small and did not allow estimating reliably the phylogenetic inertia. All traits were log-transformed to improve the normality of the distributions, except order (entered as a factor) and adult survival rate that was logittransformed. Analyses were performed using the linear model (lm) in R version 2.14.0 (R Development Core Team 2016) and parameter estimates are given ± SE and/or 95% confidence intervals.

The datasets generated during and/or analysed during the current study are available in the supplementary data. However, the raw longevity dataset used to compute the survival and senescence metrics are available upon request and with permission of Species360.

RESULTS

Differences in survival and actuarial senescence parameters

As expected, all survival metrics (i.e. maximum age at death, longevity and adult survival rate) increased with adult body mass (Tables 1 andS4, Fig. 1). Moreover, for a given body mass, equids had a maximum age at death 6.9 years (95%CI [3.9; 10.0], Table 1, Fig. 1A) longer and a longevity 5.5 years (95%CI [2.4; 8.6], Table 1, Fig. 1B) longer than bovids.

Equids also had a higher adult survival (+ 0.018, 95%CI [0.002; 0.035], Table 1, Fig. 1C) than bovids. Order was the only factor included in the selected model to explain variation observed in the onset of actuarial senescence (Table S4): equids began to senesce 5.89 years (95%CI [2.33; 9.44], Table 1) later than bovids, irrespective of body mass (Fig. S2). Finally, observed variation in the rate of senescence was explained only by the age at the onset of senescence (Table S4), with the rate of senescence increasing when the onset was late (Table 1, Fig. S3).

However, the model also including body mass was competitive (D AIC = -1.31, Table S4) that for a given onset of senescence, the rate of senescence tended to decrease with increasing body mass (β=-0.342±0.196). There was no detectable difference between bovids and equids in the rates of senescence in any of the models.

Using only extinct cohorts in the dataset results were similar to those obtained with all individuals (Tables S5-S7): the order factor was included in the selected models for all survival metrics, which indicates that equids outlived bovids and had higher adult survival.

For senescence metrics, the selected models did not include body mass or the order factor.

However, for the onset of senescence, the AIC of the model with order as a factor was only 0.51 AIC units lower than the selected model with equids senescing 4.21±1.57 years later than bovids. Finally, the rate of senescence was only influenced by the onset of senescence.

Differences in life history traits

As expected, irrespective of the order, the four biological times were positively correlated to adult body mass (Table 2 andS8, Fig. S4). Bovids had shorter generation times (by 2.31 years, Fig. S4A), shorter gestation lengths (by 89.2 days, Fig. S4B) and shorter inter-birth intervals (by 157.3 days, Fig. S4C) than equids. On the other hand, no detectable difference of age at first parturition was found between equids and bovids (Fig. S4D, Tables 2 andS8).

Evolutionary pathways

In absence of species-specific selection pressure on a particular trait, generation time is expected to be isometrically related to other biological times such as longevity, age at first reproduction, inter-birth interval and gestation length. The generation time thus constitutes an integrative measure of the time scale at which the life cycle of a given species is completed [START_REF] Gaillard | Generation time: a reliable metric to measure life-history variation among mammalian populations[END_REF][START_REF] Staerk | Performance of generation time approxiamtions for extinction risk assessments[END_REF]. Here, we assessed whether equids displayed longer generation times either, as a part of a generally slower pace of life compared to bovids, in which case all biological times should be isometrically associated, or whether the two groups differed in only one particular biological time such as gestation length, which would lead to longer generation times in equids than bovids. We found that all five of the biological times contributed almost equally to the bovids' pace of life, although the gestation length was slightly less tightly associated with other time-related traits (Table S9, Fig. 2A). Moreover, the generation time was equivalent to the PC1 (Fig. 2A), which means that generation time provides an overall measure of the pace of life in bovids. On the other hand, the picture was markedly different for equids. Age at first parturition, instead of generation time (Fig. 2B), was the closest to PC1 and was independent of inter-birth interval and gestation length (Table S9). Longevity was negatively associated with the overall time scale (Table S9, Fig. 2B).

These findings demonstrate that, while bovids closely match the biological time syndrome hypothesis, the variation among biological times was uncoupled in equids. This suggests the existence of different selection pressures, or different constraints, on specific time-related traits between the families.

DISCUSSION

Our findings confirm that, for a given body mass, equids live longer than bovids, whatever the metric used (maximum age at death or longevity). This difference in longevity between bovids and equids is associated with both higher survival and a delay in the onset of actuarial senescence in equids, but there is no difference in the rates of actuarial senescence. This is consistent with several recent studies highlighting that the onset of senescence has to be considered when analyzing senescence, and is more responsive than the rate of senescence [START_REF] Péron | Age at the onset of senescence in birds and mammals is predicted by early-life performance[END_REF][START_REF] Hammers | The impact of reproductive investment and early-life environmental conditions on senescence: support for the disposable soma hypothesis[END_REF][START_REF] Gamelon | Do age-specific survival patterns of wild boar fit current evolutionary theories of senescence?[END_REF][START_REF] Tidière | Does sexual selection shape sex differences in longevity and senescence patterns across vertebrates? A review and new insights from captive ruminants[END_REF], although the latter is still preferentially used in comparative analyses (e.g. [START_REF] Jones | Senescence rates are determined by ranking on the fastslow life-history continuum[END_REF][START_REF] Ricklefs | Life-history connections to rates of aging in terrestrial vertebrates[END_REF]. Moreover, the analyses of covariation among biological times in bovid and equid taxa indicate that a synchronization of all biological times evolved in bovids, whereas biological times were uncoupled in equids. This could be the result of a specific selection for longer gestation lengths in equids, a physiological constraint that prevents the evolution of shorter gestation lengths in equids, a stronger selection for a faster pace of life in bovids, or a combination of any of these factors.

Tooth wear is an essential process in mammalian ageing [START_REF] Skogland | Tooth wear by food limitation and its life history consequences in wild reindeer[END_REF][START_REF] King | Dental senescence in a long-lived primate links infant survival to rainfall[END_REF], and there is evidence that tooth height is related to longevity within species [START_REF] Veiberg | Bigger teeth for longer life? Longevity and molar height in two roe deer populations[END_REF]. The difference in longevity we reported may be explained by a difference in a key morphological adaptation of grazers, hypsodonty. Comparison of estimates of hypsodonty index for six bovid and seven equid taxa (see Table S3) showed that equids have hypsodonty about 50% higher than bovids (difference = 2.49; t = 4.69; df = 10.678; p-value < 0.001, Fig. S5). Dental anatomy could, therefore, provide a mechanical explanation for the greater longevity of equids relative to similar-sized bovids, through a longer functional duration of the chewing tooth-row. It has been suggested that wear rates should be less in ruminants, because much of the chewing occurs during rumination, on material that has already been washed of grit in the forestomach [START_REF] Hatt | The rumen washes off abrasives before heavy-duty chewing in ruminants[END_REF]. However, the limited information available has not yet demonstrated different rates of tooth wear between equids and bovids [START_REF] Damuth | A comparison of observed molar wear rates in extant herbivorous mammals[END_REF]. More data like that measured in red deer (Cervus elaphus) by Péres-Barberia and [START_REF] Pérez-Barberia | The influence of molar occlusal surface area on the assimilation efficiency, chewing behaviour and diet selection of red deer[END_REF] are needed on tooth wear in free-ranging equids and grazing bovids to conclude firmly whether the greater hypsodonty in equids plays a key role in explaining their greater longevity.

The longer generation time of equids demonstrates that they have a slower pace of life than similar-sized grazing bovids. This difference of pace of life is partly due to a difference of inter-birth interval, itself caused in part by the longer gestation length of equids, and partly to their higher adult survival, which also contributes to their slow pace of life. Two different concepts exist for the occurrence of a slow pace of life. It could be the result of specific selection pressures that facilitate its evolution as a specific adaptation to resource-limited niches. Alternatively, species characterized by a slower pace of life might be displaced by species with a faster pace of life except in resource-poor niches [START_REF] Vermeij | The evolutionary interaction among species: selection, escalation, and coevolution[END_REF]. There are differences in susceptibility to resource constraints between bovids and equids: the abundance of wildebeest (i.e. a grazing bovid) is much more affected by food resources than zebras (a similar-sized equid) [START_REF] Grange | Bottom-up and top-down processes in African ungulate communities: resources and predation acting on the relative abundance of zebra and grazing bovids[END_REF]. Whether longer gestation periods evolved in equids from a common ancestor of the two groups, perhaps a Condylarth (Rose 1996), which had shorter gestation periods, or whether a generally slower pace of life is a characteristic of the equid lineage, cannot be determined from our study, since the common ancestor's life history is of course unknown.

Most bovid species have an inter-birth interval of less than one year (mean of 334.00 days, 95%CI [286.54;381.46]), which allows them to produce one litter per year. On the other hand, equids display mean inter-birth intervals of about 1 year and 4 months (491.29 days, 95%CI [440.34;542.23]). The bovid life history strategy thus allows breeding seasonally to match plant phenology, which is clearly an advantage in many grassland systems. Decreasing the gestation length may have been part of the bovid evolution towards seasonal breeding [START_REF] Zerbe | Reproductive seasonality in captive wild ruminants: implications for biogeographical adaptation, photoperiodic control, and life history[END_REF], and the shorter generation times may have allowed bovids to increase their demographic rates and abundances. This may give them an advantage in resource rich environments where predation pressure is higher than in poor environments [START_REF] Melis | Roe deer face competing risks between predators along a gradient in abundance[END_REF]. Indeed, the faster pace of life allows higher population growth rates, leading to a better demographic response to predation pressure [START_REF] Grange | What limits the Serengeti zebra population?[END_REF]. A shorter generation time allows faster evolution and this may also have facilitated their species diversity. For instance, the shorter gestation length in bovids compared to giraffids has been invoked to explain the replacement of a diverse giraffid community with a diverse bovid one over evolutionary time [START_REF] Clauss | Old world ruminant morphophysiology, life history, and fossil record: exploring key innovations of a diversification sequence[END_REF].

To conclude, equids live longer than grazing bovids of similar size. This is because equids have higher survival, and their actuarial senescence begins at a later age. Equids also have greater hypsodonty, which could be a key morphological adaptation allowing greater longevity in equids, though more data are needed on wear rates in the wild to reach a firm conclusion. Grazing bovids have a faster pace of life, with shorter gestation periods. The shorter gestation periods of bovids may be associated with accelerated rates of intrauterine growth [START_REF] Baur | Morphometry of the Placental Exchange Area[END_REF], although the morphological and physiological mechanisms involved remain to be discovered. This scenario considers equids to be constrained by slower intrauterine growth and a slower pace of life, which makes them mainly competitive in environments with limited resources. Alternatively, a longer gestation length for equids may be a specifically evolved adaptation to increased survival in these environments. The fast pace of life in bovids may be a key to the rapid evolution of the bovids since the Miocene; today they dominate communities of grazing animals, in species diversity and in abundance.

Figure legends Figure 1 .

 legends1 Figure legends

Figure 2 .

 2 Figure 2. Normed Principal Component Analyses performed on 5 biological times for 5 bovid

ACKNOWLEDGMENTS

We are very grateful to the many people who generously provided data on live weights and on the animals' life histories so that we could carry out the analyses with confidence, in particular Kristin Brabender (Hortobagy National Park, Hungary), Frédéric Joly (Takh, France), Jim Kao (Taipei Zoo), Klaus Mueller-Schilling (Hannover Zoo), Peter Novellie (Nelson Mandela Metropolitan University, South Africa), Kate Schoenecker (US Geological Survey, USA), Juan Soy (Al Wabra Wildlife Preservation, Qatar), Beatrice Steck (Basel Zoo, Switzerland), Tim Thier and Martha Fischer (St. Louis Zoo, USA), and Tim Woodfine, Tanya Langenhorst and Danielle Free (Marwell Wildlife, UK) who provided data on liveweights, and/or on the animals' life histories; and Patricia Moehlman and Sarah King (IUCN Equid Specialist Group), Ulrike Rademacher (Stuttgart Zoo, Germany), Belinda Low Mackey (Grevy's Zebra Trust, USA) and Laurent Tatin (Conservatoire des Espaces Naturels, Provence-Alpes-Côte d'Azur, France) who kindly linked us to sources of knowledge. We are grateful to one anonymous referee for helpful comments on a previous draft.