C Gunnar Werncke

Mohammed-Amine Bouammali

Julie Baumard

Nicolas Suaud

Cyril Martins

Nathalie Guihéry
email: nathalie.guihery@irsamc.ups-tlse.fr

Laure Vendier

Jianxia Zheng

Jean-Baptiste Sortais

Christophe Darcel

Sylviane Sabo-Etienne

Jean-Pascal Sutter

Sébastien Bontemps
email: sebastien.bontemps@lcc-toulouse.fr

Céline Pichon
email: celine.pichon@lcc-toulouse.fr

Ising-type Magnetic Anisotropy and Slow Relaxation of the Magnetization in Four-Coordinate Amido-Pyridine FeII Complexes

come

Abstract. A family of four-coordinate Fe II complexes formed with N,N'-chelating amidopyridine ligands has been synthesized and their magnetic properties investigated. These distorted tetrahedral complexes exhibit significant magnetic anisotropy with Zero-Field Splitting parameter D ranging between -17 and -12 cm -1 . Ab initio calculations enabled to identify the structural factors which control the nature of the magnetic anisotropy in these complexes and to rationalize the variation of D between the three complexes. It is shown that a reduced N-Fe-N angle involving the chelating nitrogen atoms of the ligands is at the origin of the negative D value and that the torsion between the two N-Fe-N planes imposed by steric hindrances further increases the |D| value. Field-induced slow relaxation of magnetization was observed for the three compounds and a SMM behavior with an energy barrier for magnetization flipping (Ueff) of 27 cm -1 could be evidenced for one of them.

INTRODUCTION.

Slow relaxation of magnetization at the molecular scale was initially discovered in the complex [Mn12O12(OAc)16(H2O)4]. [START_REF] Sessoli | Magnetic bistability in a metal-ion cluster[END_REF] This seminal work initiated active research on coordination complexes displaying such a unique magnetic phenomenon. In these so-called Single-Molecule Magnets (SMMs), each individual nano-magnet exhibits a magnetic hysteresis in the magnetization versus field curve and displays slow relaxation of the magnetization when removing the external field at low temperatures. This molecular magnetic bistability arises from a splitting of the Ms components of the ground spin state S due to both relativistic effects and a lowering of the ligand-field-induced symmetry. In the absence of magnetic field, the low energy spectrum presents an energy barrier between the various Ms components with a degenerate ground state corresponding to the +Ms and -Ms components, i.e. with two different magnetization orientations. This phenomenon is therefore called Zero- Field Splitting (ZFS) and is characterized with two parameters: the axial parameter D which by convention is negative when the largest |Ms| components are the lowest in energy and the rhombic parameter E which mixes the various Ms components and is therefore responsible for tunneling. The height of the energy barrier  is given by  = D•S² for systems with integer spin ground states (S) and  = D•(S²-1/4) for systems with half-integer spin ground states.

In 2010, the first report of slow relaxation of the magnetization in a mononuclear trigonal pyramidal Fe II complex 2 fueled the interest for single-ion transition metal complexes. These are indeed the simplest systems to exhibit SMM behaviors provided they possess substantial magnetic anisotropy and, ideally, uni-axial (i.e. Ising-type) anisotropy characterized by a negative D value. Interestingly, control of the coordination sphere (geometry, symmetry, ligand field) and relevant electronic configuration for the metal ion allows reaching significant magnetic anisotropy. [START_REF] Bar | Magnetic anisotropy in two-to eight-coordinated transition-metal complexes: Recent developments in molecular magnetism[END_REF] For instance, weak ligand fields resulting from low coordination numbers are favorable parameters for large magnetic anisotropy in 3d ions because i) orbital angular momentum is stronger and ii) second-order contribution of Spin-Orbit Coupling (SOC) is enhanced when the energetic splitting between the ground state and first excited states is reduced.

Following the report by Freedman et al., several tetracoordinated Fe II complexes have been reported to exhibit magnetic anisotropy with D parameters spanning from positive to strongly negative values (Table 1). 2.4 Although the most negative D has been found for Fe II in trigonal pyramid surrounding, the variety of geometries and nature of ligand systems preclude easy comparison and thus convincing rationalization for the D values (Table SI1).

To provide further insights into the role of geometrical parameters on the anisotropy of four-coordinate Fe II compounds, we synthesized a new family of complexes formed with chelating amido-pyridine ligands (Scheme 1). [START_REF] Lu | Neutral Bis(αiminopyridine)metal Complexes of the First-Row Transition Ions (Cr, Mn, Fe, Co, Ni, Zn) and Their Monocationic Analogues: Mixed Valency Involving a Redox Noninnocent Ligand System[END_REF] In these complexes, the metal center has similar coordination surrounding but exhibit distinct distorted tetrahedral coordination (1,1,1,3,3,3-hexafluropropan-2-ol); tpa DFP = tris (5-2,6-difluorophenyl-pyrrol-2-yl)methyl)amine; tpa Mes = tris(5-mesityl-pyrrol-2-yl)methyl)amine; tpa Ph = tris(5-phenyl-pyrrol-2-yl)methyl)amine; tpa t-Bu = tris (5tert-butyl-pyrrol-2-yl)methyl)amine.

Experimental Section.

General Considerations. All manipulations were carried out in a glove-box or using Schlenk-type techniques under a dry argon atmosphere. Solvents were dried using a MBraun solvent purification system and stored over 4 Å molecular sieves. The 1 H NMR spectra were recorded on a Bruker AV400 NMR spectrometer. Chemical shifts are reported in ppm relative to the residual proton of C6D6 (7.15 ppm). IR measurements were conducted on a Bruker Alpha ATR-IR spectrometer. Elemental analyses were performed by the internal service of the Laboratoire de Chimie de Coordination, Toulouse. It is worth mentioning that several A c c e p t e d m a n u s c r i p t attempts have been conducted in elemental analyses but the extreme sensitivity of the compounds precluded better results. NBu4PF6 for cyclovoltammetry was dried overnight in vacuo at 100 °C. Solution magnetic susceptibilities were determined by the Evans method. [START_REF] Evans | The determination of the paramagnetic susceptibility of substances in solution by nuclear magnetic resonance[END_REF] Fe(N(SiMe3)2)2, HN2mes, HN2Dipp and H2N3Dipp were prepared according to literature procedures. [START_REF] Andersen | Synthesis of bis[bis(trimethylsilyl)amido]iron(II). Structure and bonding in M[N(SiMe3)2]2 (M = manganese, iron, cobalt): two-coordinate transition-metal amides[END_REF] Syntheses of complexes 1-3.

Fe(N2mes)2, 1. To a solution of 2-[(mesitylamino)methyl]pyridine (HN2mes, 155 mg, 0.68 mmol, 1 equiv.) in pentane (5 mL) was added Fe(N(SiMe3)2)2, (125 mg, 0.34 mmol, 0.5 equiv.) dissolved in 2 mL of pentane at room temperature, resulting in an immediate color change to red and precipitation after 1 minute. After 15 min. of stirring stirring at the same temperature, the solution was removed by filtration and the residue dried in vacuo to yield 130 mg of 1 (0.26 mmol, 76%) as a bright red solid. [START_REF] Sessoli | Magnetic bistability in a metal-ion cluster[END_REF] H NMR (400.1 MHz, C7D8, 298K)  = 77. 6, 44.38, 42.80, 40.40, 39.96, 22. (C30H34FeN4, 506.47 g/mol) C 71. 14 H 6.77 N 11.03, exp. C 70.52 H 6.64 N 10.84. Single crystals, suitable for X-ray diffraction analysis, were obtained from a saturated pentane solution placed at -38 °C. µeff = 4.80 µB (Evans, C6D6 + 1%TMS, 400.1 MHz, r.t.). Fe(N2Dipp)2, 2. To a solution of 2-[(diisopropylphenylamino)methyl]pyridine (HN2Dipp, 268 mg, 1.0 mmol, 1 equiv.) in Et2O (5 mL) was added Fe(N(SiMe3)2)2 (188 mg, 0.5 mmol, 0.5 equiv.) dissolved in 2 mL of pentane at room temperature, resulting in an immediate color change to red. After 1 h of stirring at the same temperature, the solution was filtered, the solvent evaporated under reduced pressure and the red residue washed with 5 mL of pentane 125, 79.8, 45.01, 38.75, 37.85, 11.80, -32.1, -34.94; IR (ATR, cm -1 ) = 2953 (m), 2859 (w), 2749 (w), 1477 (w), 1456 (w), 1429 (s), 1357 (w), 1343 (w), 1307 (m), 1247 (s), 1209 (w), 1200 (w), 1151 (m), 1110 (m), 1073 (s), 1045 (s), 1012 (w), 904 (m), 799 (m), 752 (vs), 719 (m), 620 (w), 586 (w), 554 (w), 416 (vs); elemental analysis calc. (C36H46FeN4, 590.64 g/mol) C 73.21 H 7.85 N 9.49, exp. C 72.73 H 8.22 N 9.40. Single crystals, suitable for X-ray diffraction analysis, were obtained by slow diffusion of pentane into a saturated Et2O solution at -38 °C. µeff = 4.85 µB (Evans, C6D6 + 1%TMS, 400.1 MHz, r.t.). Fe(HN3Dipp)2•C5H12, 3. 2,6-bis[(mesitylamino)methyl]pyridine (H2N3Dipp, 305 mg, 0.67 mmol, 1 equiv.) was dissolved in 5 mL of Et2O and filtered. By addition of a solution of Fe(N(SiMe3)2)2 (125 mg, 0.34 mmol, 0.5 equiv.) in 2 mL of Et2O an immediate color change to reddish violet was observed. After stirring for 2 h at room temperature, the solution was filtered and all volatiles were removed in vacuo. Washing the residue with 3 mL of cold Et2O (-38 °C) and 3 mL of cold pentane (-38°C) with subsequent drying in vacuo yields 200 mg of Fe(HN3Dipp)2 (0.20 mmol, 61%). [START_REF] Sessoli | Magnetic bistability in a metal-ion cluster[END_REF] H NMR (400.1 MHz, C6D6, 298K)  = 72 .11, 44.93, 44.25, 40.43, 34.95, 17.35, 7.58, -3.71, -13.56, -19.53, -31.56, -34.94; IR (ATR, cm -1 ) = 3052 (vw), 2953 (s), 2927 (w), 2862 (m), 2724 (vw), 1599 (w), 1565 (w), 1459 (vs), 1427 (vs), 1382 (m), 1358 (m), 1310 (s), 1253 (vs), 1194 (m), 1156 (w), 1112 (m), 1076 (m), 931 (w), 888 (w), 873 (w), 800 (s), 770 (vs), 760 (vs), 713 (vs), 548 (w), 438 (w), 414 (vs); elemental analysis calc. (C67H96FeN6, 1041.35 g/mol ) C 77. 27 H 9.29 N 8.07, exp. C 76.32 H 9.56 N 8.23. µeff = 4.98 µB (Evans, C6D6+1%TMS, 400.1 MHz, r.t.). Single crystals, suitable for X-ray diffraction analysis, were obtained from slow evaporation of a saturated pentane solution at r.t. µeff = 4.80 µB (Evans, C6D6 + 1%TMS, 400.1 MHz, r.t.). Crystallography. Data for 1 and 3 were collected at low temperature (180 K and 100 K respectively) on a Gemini Agilent diffractometer using a graphite-monochromated Mo-K radiation and equipped with an Oxford Instrument Cooler Device. Data for 2 were collected at 100 K on a Bruker Kappa Apex II diffractometer using a graphite-monochromated Mo-K radiation ( = 0.71073Å) and equipped with an Oxford Cryosystems Cryostream Cooler Device. The structures have been solved using SUPERFLIP [START_REF] Palatinus | SUPERFLIP -a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions[END_REF] or SHELXS-97 [START_REF] Sheldrick | A short history of SHELX[END_REF] and refined by means of least-squares procedures using the software package CRYSTALS. [START_REF] Betteridge | CRYSTALS version 12: software for guided crystal structure analysis[END_REF] The atomic scattering factors were taken from International Tables for X-Ray Crystallography. [START_REF] Schmitz | Herausgegeben von der International Union of Crystallography[END_REF] All nonhydrogen atoms were refined anisotropically. All hydrogens atoms were refined by using a riding model. [START_REF] Cooper | CRYSTALS enhancements: dealing with hydrogen atoms in refinement[END_REF] Absorption corrections were introduced by using the MULTISCAN program. [START_REF] Sheldrick | University of Göttingen, Germany Program for Empirical Absorption Correction of Area Detector Data[END_REF] Drawings of molecules were performed with the programs DIAMOND and POV-Ray. H atoms are omitted for clarity. Full crystallographic data and structure refinement for compounds 1-3 are gathered in Table SI2.

Magnetic measurements.

The samples for magnetic measurements were prepared in a glovebox under argon atmosphere and were introduced as polycrystalline powders into quartz tubes with solid eicosane. The tube was then gently warmed to melt the eicosane, ensuring a good mixing to avoid torqueing of the crystallites and provide good thermal contact between the samples and the cryogenic bath. The quartz tubes were closed with a plastic cork which was immediately melted after exiting the tube from the glovebox. Magnetic susceptibility measurements were carried out with a Quantum Design MPMS-5S SQUID susceptometer.

The absence of ferromagnetic impurities was checked by measurement of M vs. H at 100 K. dc measurements were conducted from 300 to 2 K at 1 kOe and the data were corrected for the diamagnetic contribution of the sample holder, grease and sample by using Pascal's tables. [START_REF] Kahn | [END_REF] The field dependences of the magnetization were measured at several temperatures between 2 and 10 K with dc magnetic field up to 5 T. ac susceptibility experiments were SI3.

All matrix elements can be numerically determined. In a first step, the Complete Active Space Self Consistent Field (CASSCF) method has been used to determine the wave functions and energies of the lowest quintet and triplet states. Then a correlated electronic spectrum has been computed adding a second-order perturbative evaluation of electron dynamic correlation corrections to the CASSCF energies. Finally the various states have been coupled through the spin-orbit interaction.

The second step consists in extracting the matrix elements from the effective Hamiltonian theory. For this purpose, a numerical effective Hamiltonian (Heff) is built from the wave functions and energies of the five components of the quintet ground state. This method is extensively described in one of our publication [START_REF] Maurice | Universal Theoretical Approach to Extract Anisotropic Spin Hamiltonians[END_REF] and is only shortly reviewed here. A model space based on the five {|2, -2⟩, |2, -1⟩, |2,0⟩, |2, +1⟩, |2, +2⟩} configurations is defined.

Then, the Heff matrix is determined so that its eigenvalues coincide exactly with those of the five Ms components of the quintet ground state and its eigenvectors are the projections of the Electronic energies of the lowest states have been calculated at the CAS-PT2 20 and NEVPT2 21 levels of correlation while the spin-orbit interactions have been introduced via the Spin-Orbit State Interaction (SO-SI) method [START_REF] Heß | A mean-field spin-orbit method applicable to correlated wavefunctions[END_REF] . X-Ray geometrical structures of complexes 1, 2 and 3 were used in the calculations. The CAS(6,5) contains 6 electrons in 5 active d orbitals essentially located on the iron ion while in CAS(6/10) an additional set of diffuse d orbitals has also been included in the active space, as such a procedure has shown to provide better results [START_REF] Maurice | Universal Theoretical Approach to Extract Anisotropic Spin Hamiltonians[END_REF] .

In Molcas calculations, ANO-RCC 23 atomic basis sets are used: 6s5p3d2f for Fe, 3s2p for C and N and 1s for H. Orca calculations were performed using cc-(p)VDZ Dunning [START_REF] Woon | Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties[END_REF] atomic basis sets: 6s5p3d1f for Fe, 3s2p1d for C and N and 2s for H.

The impact of the computational parameters (atomic basis set quality, size of the active space, methods to calculate dynamic correlation corrections and the number of states included in the SO-SI matrix) on D and E has been studied for complex 1 and is discussed in Supplementary Information.

RESULTS AND DISCUSSION.

Synthesis.

Fe(N(SiMe3)2)2 is a reactive complex, 8a.25 notably toward compounds featuring amine moiety. The coordination of such compounds generate amido ligand and release the volatile bis(silyl)amine HN(SiMe)3)2. 5b-d.26 Following a similar synthetic strategy, Fe(N(SiMe3)2)2 was reacted with 2 equivalents of the respective amido-pyridine ligand (HN2mes for 1; HN2Dipp for 2; H2N3Dipp for 3, see Scheme 1), resulting in a rapid color change to red. Workup afforded the respective compounds 1-3 in good yields (50-76%). All compounds are highly oxygen

Solid state characterization.

Single-crystals suitable for X-Ray diffraction analysis were obtained for the three compounds. Complexes 1-3 crystallized in the monoclinic P21, C2/c and triclinic P-1 space groups, respectively. Their crystal structures are shown in Figure 1. In each complex, the Fe II center is tetracoordinated, surrounded by two amido-pyridine ligands, coordinated in a bidentate fashion. The bond distances are similar in the three complexes: for example, the Fe-N distances vary by only 2 and 0.5% in the Fe-NPy and Fe-Nam fragments, respectively (see Table 2). In addition, these parameters are in the same range as the one observed by Westerhausen et al. in analogous high-spin tetrahedral Fe II complexes. 5b In 1, the Fe II center resides along a 2-fold screw axis leading to two crystallographically equivalent ligands. In the case of 3, the additional amine groups remain pendants. Yet, some N-Fe-N angles and the dihedral angle defined by the two NFeN planes of each ligand varies significantly: 89.8° for 1, 69.0° for 2 and 75.3° for 3 (see Table 2). 5a

Finally, the iron centers are well separated within the crystal lattice, with Fe•••Fe distances of at least 8.3 Å (Table 2). The 3-D crystal packing is promoted by short contact interactions between aromatic rings for 1 (Figure SI11) and neighboring isopropyl groups for 2 and 3 (Figures SI12 andSI13). The description of the overall geometry is not straightforward since the metal center lies between tetrahedron and seesaw coordination arrangement. We thus sought for additional information by carrying out Continuous Shape Measurement 27 (CShM) calculations. CShM values provide a quantitative measurement about the deviation of a given coordination sphere from the ideal geometry for which shape values equal to zero. Table SI1 gathers the results of the calculations performed considering all the possible geometries for a four coordinate complex. Every complex exhibits a polyhedral shape deviating markedly from an ideal geometry and best described as distorted tetrahedral or see-saw coordination arrangement.

Figure SI1 provides further visual information about their relative distortion. These complexes are located outside the distortion path expected between tetrahedral and see-saw due to bond length distortions. A minimal distortion path analysis was also carried out with SHAPE for 1-3 along the distortion pathway from tetrahedral (T-4) to see-saw (SS-4). The results are summarized in Table 3. The deviation path parameter equals to 0 % for ideal Td

Magnetic properties.

The temperature dependence of the molar magnetic susceptibility (M defined as M/H per mole of Fe II complex) for 1-3 are shown as T vs. T plots in Figure 2. The room temperature values of 3.10, 3.16 and 3.21 cm 3 K mol -1 (5.03, 4.97, and 5.05 B mol -1 ) are consistent with the values determined by the Evans method (Table 4). Upon cooling, the MT product of 1-3 remains constant until ca. 50 K below which a quick drop can be observed. This susceptibility decrease can be attributed to the ZFS effect (magnetic anisotropy) because the magnetic centers are quite well separated in the solid (see structure description above). In transition-metal complexes, the effect of ZFS on the magnetic properties is usually observed at low temperatures. Thus, the most sensitive and accurate evaluation of the magnetic anisotropy of polycrystalline samples from SQUID data relies on the field and values of respectively 12.3(1) cm -1 (1), 16.9(7) cm -1 (2), and 16.5( 5) cm -1 (3). In the case of complexes 1 and 2, fits of analogous quality could be reached with or without taking into account the E parameter. For complex 3, it was necessary to add the contribution of the rhombic anisotropy E to reach good reproduction of the data. However, the experimental errors on this parameter is high keeping in mind that the intermolecular interactions (zJ') were neglected to avoid overparametrization. The set of parameters determined from the best fits shown in Figures 3 andSI13 are gathered in Tables 5 and6. These parameters were systematically validated by at least two investigations on different batches. Fitting the data with positive D values were also attempted but this only led to unsatisfactory E/D ratios (higher than 0.33). The effect of the geometry distortion on D for these complexes will be discussed below. but upon application of an external field, a response was observed with visible maxima in M'' curves above 2 K for 1 and 2 (Figure SI17). The relaxation times () were determined at each temperature fitting the M" = f() curves with a generalized Debye model. 29 For 2, M'' = f() is only slightly frequency-dependent (Figure SI19) revealing an almost temperature independent relaxation regime likely stemming from multiple spin-lattice vibrational relaxation mechanisms with a main contribution from quantum tunneling of the magnetization (QTM).

For 1, a linear dependence of the relaxation time was found above 3 K (Figure 4a), suggesting a thermally activated regime characteristic of a SMM behavior. For lower temperatures, the  = f(1/T) curve deviates from linearity highlighting contributions from additional relaxation modes shortcutting the thermal relaxation pathway. In mononuclear complexes, QTM, Raman and direct spin-phonon processes are often playing an important role in the magnetization dynamics when a dc field is applied. [START_REF] Marriott | Pushing the limits of magnetic anisotropy in trigonal bipyramidal Ni(ii)[END_REF] The coexistence of multirelaxation processes is also suggested by the relatively large distribution of relaxation times obtained from the analysis of the Cole-Cole plots ( parameter in Table SI4 corresponding to the fits shown Figure SI20). [START_REF] Cole | Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics[END_REF] Quantum tunneling contributions were neglected to avoid overparametrization as QTM is usually minimized under external magnetic field. This is also supported by the temperature dependence of the out-of-phase susceptibility ''M maximum even at the lowest temperatures. Direct spin-lattice process is known to operate in the low temperature regime under applied dc field [START_REF] Novikov | A Trigonal Prismatic Mononuclear Cobalt(II) Complex Showing Single-Molecule Magnet Behavior[END_REF] and to be field dependent (equation 1). As the position of the ac maximum of 1 is field dependent (Figure SI17a) and Ising-type magnetic anisotropy promotes Orbach relaxation, the temperature dependence of  was fitted taking into account direct and Orbach relaxation mechanisms (equation 1).

A c c e p t e d

m a n u s c r i p t

             T k U T AH B eff exp 1 0 2 1   (1)
A good fit was obtained from this model with A = 2.18 10 -4 s -1 Oe -2 K -1 (A is a coefficient and H is the external dc field), 0 = 3.3 10 -9 s and Ueff = 26.7 cm -1 (Figure 4b). Raman and Orbach mechanisms were also considered but this other model was excluded because the Raman values are not coherent for integer spin ground state (see Supporting Information, Figure SI21). 30d. [START_REF] Abragam | Electron paramagnetic resonance of transition ions[END_REF] The effective energy barrier for 1 is of the same order of magnitude and compares with the anticipated Orbach barrier 3*|D| = 37 cm -1 . Slow relaxation of the magnetization is also present in 3 but at lower temperatures (Figure SI17c), preventing further studies to estimate the energy barrier for spin reversal. It can be noticed that the magnetization blocking characteristics found for 1-3 do not parallel the magnetic anisotropy exhibited by the complexes. Indeed, compound 1 with smallest magnetic anisotropy is the only compound for which an energy barrier for spin reversal could be evaluated. Such a behavior is not unusual and was observed for the [Fe(tpa X )] -complexes 2 or in a family of four-coordinated Co II complexes (Table 5). [START_REF] Ziegenbalg | Cobalt(II)-Based Single-Ion Magnets with Distorted Pseudotetrahedral [N2O2] Coordination: Experimental and Theoretical Investigations[END_REF] It must be kept in mind that different mechanisms regulate the relaxation of the magnetization and their relative contributions are strongly dependent of the lattice vibrations. 30d. 33.35 Table 5. Magnetic parameters of 1-3 compared with similar four-coordinate Fe II complexes.

Compound D (cm -1 ) E (cm - 1 )
g Slow relaxation

Hdc (Oe) 0 (s) Ueff (cm - 1 )
Ref.

[ 6. They were obtained at CAS(6/10)PT2 level using basis set 1 and considering 5 quintet and 35 triplet states. They are compared to those obtained at the NEVPT2 level for CAS(6/5) for an equivalent atomic basis set. A good agreement of both calculations with experimental values is achieved. The magnetic axes extracted from the ab initio calculations are very similar in the three complexes (see Figure 5). For the three complexes, the energetic order of the orbitals located on the Fe II ions and their occupation in the two first states are reported in Figure 6. The MOs are represented in Figure SI22. The spectra of the lowest quintet states and a perturbative evaluation of the contribution . One can note that the Ms = ±2 components of the quintet states are essentially single reference (a single determinant is enough to describe each of the two quintet state components). Hence the coupling is larger for these components than for the others for which several determinants weighted by coefficients lower than 1 are required. As a consequence, the lowering of the Ms = ±2 components through the spin-orbit interaction is larger than that of the other components and the contribution to D is therefore negative. It is interesting to note that the energy difference between the ground and first excited state are 2346 cm -1 , 1445 cm -1 , and 1581 cm -1 for complexes 1, 2 and 3 respectively at the CAS(6/10)PT2 level. As the energetic stabilization due to spin-orbit coupling is inversely proportional to the energy difference between the ground and excited states (at the second order of perturbation), the similar values of D in complexes 2 and 3 and the smaller value of |D| in complex 1 can be correlated with the energy of the first excited quintet state. One may also conclude that to increase the |D| value one must decrease the energy difference between the dx2-y2 and dxy orbitals. Indeed, this difference is 1840 cm -1 for 1, 1340 cm -1 for 2, and 1450 cm -1 for 3, in complete agreement with the evolution of the D value. We firstly wanted to understand which distortion from the tetrahedron is responsible for the negative D value. The first deviation from an ideal Td geometry comes from the N-Fe-N angle  (see Figure 5) involving two chelating nitrogen atoms, which is close to 80° in all studied complexes instead of 109° in a tetrahedron. The second difference comes from the distances between the iron and the nitrogen atoms. In all the complexes, the Fe-N bond distances between the amide nitrogen atoms (Fe-N2 and Fe-N3) are shorter than the ones to the pyridine N atoms (see Table 2). However, the respective Fe-N bond lengths vary only negligibly between the complexes. We secondly wanted to understand how small structural differences in the first coordination sphere between the three complexes affect the D value. The main difference between the complexes comes from the torsion angle which induces a loss of the C2 axes present in the tetrahedron. Figure 5 shows a view of the complexes in which the angle of distortion (is represented. In our definition, an undistorted complex would have an angle between the ligand planes of 90° (). As the distortion closes this angle which varies from 90° to 67° in the complexes, varies from 0 to 23°. The values are and 16°for 1, In order to understand the effect of these distortions (the angular , the distances d and the torsion  distortions), calculations on three model complexes have been performed: the pyridine group was replaced by NCH while the N2 and N3 atoms were modeled by NC - anions as the formal charge of the ligand is carried by these N atoms. In order to check that there is no large bias introduced by the change of chemical groups, we have first calculated the D values in model complexes where the position of the nitrogen atoms is exactly the same as in the real complex and the model ligands are aligned with the metal ion. CAS(6/5)NEVPT2 calculations were then performed. The values of D (11.7 cm -1 , 14.1 cm - 1 , and 15.1 cm -1 for models of complexes 1, 2 and 3 respectively) are in qualitative agreement with the values obtained for the real complexes. Then, starting from the tetrahedron angular, distance, and  torsion distortions were applied. The curves of D as function of the three distortions d and are represented in Figure SI24. Theangular distortion is responsible for the negative D value observed in the three complexes as larger negative D values are found when the bite angle decreases. This result can also be correlated with the energetic order of the orbitals. Indeed, all the orbitals which have XY components are stabilized in comparison to the perfect tetrahedron by the decrease of the angles in the Z direction. The resulting energetic order of the orbitals is given in Figure 6. In contrast, the deformations (simultaneous elongation of the Fe-NCH bonds and contraction of the Fe-NC - bonds) have no important effect on the D values. Finally the distortion introduced by  is responsible for the differences observed between the three complexes. It induces a significant increase of the absolute value of the negative D parameter. This last result can also be easily rationalized from a ligand field point of view. Indeed, when the system is not distorted the dx2- Conclusions. This family of four-coordinate bis-(amido-pyridine) Fe II complexes provided insights on the distortion effects at the origin of the modulation of the magnetic anisotropy for such tetrahedron-shaped d 6 centers. The main conclusions are: i) the negative D value arises from the decrease of the N-Fe-N bite angles. This distortion stabilizes the dxy and dx2-y2 orbitals involved in the excitation at the origin of the sign of the magnetic anisotropy of all studied complexes; ii) a further analysis of the structural parameters revealed that the torsion between the planes of the two ligands in the first coordination sphere strongly contributes to the negative D value and is responsible for the difference of D for these complexes. These For the reported complexes, D parameters ranging from 17 to 12 cm -1 have been obtained. Interestingly, field-induced slow magnetic relaxation was detected in all cases despite moderate magnetic anisotropy. A thermally activated relaxation process characterized by an effective energy barrier of 27 cm -1 was observed for complex 1. Associated content. The Supporting Information is available free of charge on the ACS The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

  , their D parameter was found to range from -17 to -12 cm -1 . In-depth theoretical investigations were decisive in identifying the geometrical distortions involved in the observed variation of D values.

  05; IR (ATR, cm -1 ) = 3306 (vw), 2982 (w), 2938 (vw), 2906 (vw), 2744 (m), 2668 (vw), 1599 (w), 1560 (w), 1476 (s), 1435 (s), 1364 (vw), 1343 (m), 1297 (m), 1235 (vs), 1146 (s), 1102 (w), 1073 (s), 1043 (s), 949 (m), 886 (m), 846 (s), 801 (m), 750 (vs), 719 (s), 619 (m), 532 (s), 469 (m), 406 (m); elemental analysis calc.

  mg of 2 (0.25 mmol, 50%).[START_REF] Sessoli | Magnetic bistability in a metal-ion cluster[END_REF] H NMR (400.1 MHz, C6D6, 298K)  =

  s c r i p t performed at various frequencies ranging from 1 to 1500 Hz with an ac field amplitude of 3 Oe. Computations. The method proposed in 2009 16 to extract the D and E parameters from the computed spectrum and wavefunctions of low energy and the effective Hamiltonian theory 17 has been adapted to an S = 2 pseudo-spin. The analytical derivation of the model Hamiltonian 𝐻 ̂𝑚𝑜𝑑 = 𝑆 ⃗ ̂. 𝐷 ̿ . 𝑆 ⃗ ̂ in the {|2, -2⟩, |2, -1⟩, |2,0⟩, |2, +1⟩, |2, +2⟩} basis set of the five Ms components of the quintet ground state gives the representative matrix shown Table

  quintet component wave functions onto the model space. Comparison between the numerical values of Heff and the expression of the ZFS tensor in the same basis provides a direct evaluation of Dxx, Dyy, Dyy, Dxy, Dxy, and Dyz. Finally, the diagonalization of the 𝐷 ̿ tensor gives the D and E values and allows the determination of the magnetic axes.

  s c r i p tCalculations have been performed using both Molcas 8.0 18 and ORCA 3.0.3[START_REF] Neese | The ORCA program system[END_REF] packages.

  Scheme 1. Syntheses of compounds 1-3.

Figure 1 .

 1 Figure 1. Molecular crystal structure of 1-3 (ellipsoids of the N and Fe atoms at 30%

  for see-saw one. The values range between 53.6 % for 1 to 80.2 % for 2 with an intermediate value of 65.1 % for 3.

Figure 2 .

 2 Figure 2. Temperature dependence of T for 1-3 with the best fits in solid lines (see

  temperature-dependent measurements of their magnetization. The field-dependence of the magnetization (M) measured for 1-3 are plotted in Figures 3 and SI13 under the form of M vs. H. The magnetization obtained at 2 K under a field of 5 T are 2.70 (1), 2.23 (2) and 2.38 (3)B, values lower than expected for a spin-only S = 2 system (i.e. 4 B). Interestingly, the magnetization curves are not matching on a single master curve (FigureSI15), a characteristic indicative for significant magnetic anisotropy in these complexes. This anisotropy was estimated considering the ZFS axial and rhombic magnetic anisotropy parameters D and E by A c c e p t e d m a n u s c r i p t concomitant fits of M vs. H and MT vs. T curves with the program PHI 28 yielding negative D

Figure 3 .

 3 Figure 3. Field dependence of the magnetization (M) for [Fe(N2mes)2] (1) with the best fits in

Figure 4 .

 4 Figure 4. (a) Frequency dependence of the out-of-phase ac magnetic susceptibility (M") of

  Theoretical calculations. Calculations have been performed in order to determine the structural factors which control the magnetic anisotropy in this family of complexes. For a series of pseudo-tetrahedral Co II complexes, ab initio calculations revealed the influence of the first and second coordination sphere on the ZFS parameters[START_REF] Suturina | Magneto-Structural Correlations in a Series of Pseudotetrahedral [CoII(XR)4]2-Single Molecule Magnets: An ab Initio Ligand Field Study[END_REF] depending on the heteroatom coordinated to the metal center. Complexes 1-3 feature similar coordinated amido-pyridine ligands to the Fe II ions, hence variation in D can be related to mostly geometrical considerations. The computation methodology described in the experimental section lead to the D and E values reported in Table

  on the D value are given in FigureSI23. The main contribution to D is brought by the first excited state that is obtained from the ground state by a single excitation from the dx2-y2 to the dxy orbitals. As these two orbitals are linear combinations of the d2+ and d2spherical harmonics, the two states are coupled through the

Figure 5 .

 5 Figure 5. Complexes 1 (left), 2 (center) and 3 (right) represented with their magnetic axes

3

 3 respectively and are a consequence of steric and crystal packing hindrances due to the different chemical groups bound to the pyridine and/or to the phenyl group bound to N2/N3.

  s c r i p t y2 and dxy orbitals are far apart in energy as the dxy points towards the ligands while the dx2-y2 does not. When the distortion takes place the energy difference between the two orbitals decreases. As a consequence the energy difference between the two quintet states differing by the occupation of these orbitals decreases and the absolute value of D increases. As complex 1 does not show any angular distortion while complexes 2 and 3 have a non-negligible and similar distortion, one may rationalize why complexes 2 and 3 have large and similar values of D in comparison to complex 1.

Figure 6 .

 6 Figure 6. Energetic order and physical content in the magnetic axes frame shown Figure 5 of

  s c r i p t results suggest that larger magnetic anisotropy (i.e. more negative D values) might be anticipated for similar nitrogen-based bidentate ligands with a smaller bite angle and inducing larger torsion between the two chelate planes. The magneto-structural correlation discussed in this work is valid for Fe II complexes with intermediate geometry between Td and D4h. A different coordination environment and distortion would modify the orbital splitting and thus the relative contribution of SOC to D.

  Acknowledgements. C. P. and J.-P. S. acknowledge CEFIPRA/IFCPAR (Indo-French Center for the Promotion of Advanced Research) for support. J-B. S., C. D., C. G. W., S.S. E. and S. B. thank the ANR (programme blanc "IRONHYC" ANR-12), the DFG (WE 5627/1-1 personal grant for C. G. W.) This work was granted access to the HPC resources of CALMIP supercomputing center under the allocation 2012-P1517, 2011-P1144 and 2015-P0059.

  Table of Contents Graphic and SynopsisThree new distorted tetrahedral Fe II complexes formed with N,N'-chelating amido-pyridine ligands are shown to exhibit significant magnetic anisotropy and field-induced slow relaxation of magnetization. Ab initio calculations rationalize the impact of structural distortions on both the nature and the magnitude of the magnetic anisotropy D: reduced N-Fe-N bidentate angles are responsible for its negative sign while the torsion angle controls its value.

Table 1 .

 1 Selected examples of magnetic anisotropy parameter (D) in distorted four-coordinate Fe II complexes reported in the literature.

	Compound a			Geometry	D (cm -1 ) Ref.
	[Fe(CF3-ONO)Cl]	Square	17.4	6
					planar
	[Fe(Bc tBu )2]			Tetrahedral -10.74	4c
	[Fe(N(SiMe3)2)2		Tetrahedral +4.1	4d
	(depe)]
	[Fe(C3S5)2](NBu4)2	Tetrahedral +5.61(9) 4a
	Na[(tpa t-Bu )Fe]•		Trigonal	-48	2
	THF			pyramidal
	K[(tpa Mes )Fe]•2 DME Trigonal	-44(4)	2
					pyramidal
	K[(tpa Trip )Fe]•3 DME Trigonal	-30(2)	2
					pyramidal
	Na[(tpa Ph )Fe]•3 DME Trigonal	-26(2)	2
					pyramidal
	K[(tpa DFP )Fe]•2 DME Trigonal	-6.2	2
					pyramidal
	a	Bc tBu	=	bis(3-tert-butylimidazol-2-ylidene)borate;	[CF3-ONO]H3	=	2,2'-(azanediylbis(2,1-
	phenylene))bis

Table 2 .

 2 Selected structural parameters of compounds 1-3 in the solid state.

	Compound	1	2	3
	Distances /Å
	Fe1-N1	2.1238(9)	2.1257(12)	2.1690(16)
	Fe1-N2	1.9397(8)	1.9313(9)	1.9304(19)
	Fe1-N3(N2')	1.9397(8)	1.9307(10)	1.935(2)
	Fe1-N4(N1')	2.1238(9)	2.1522(11)	2.1623(12)
	Fe•••Fe	8.3442(4)	9.5481(4)	8.8056(9)
	Angles /°
	N1-Fe1-N2	81.28(4)	81.13(4)	81.76(8)
	N1-Fe1-N3	117.72(4)	126.54(4)	121.44(8)
	N1-Fe1-N4	104.70(4)	92.11(4)	99.11(7)
	N2-Fe1-N3	150.25(3)	141.70(5)	136.65(8)
	N2-Fe1-N4	117.72(4)	129.42(5)	134.19(6)
	N3-Fe1-N4	81.28(4)	80.39(5)	81.68(7)
	Dihedral
	angle /°
	N1-Fe-N2/N3-	89.8	69.0	75.3
	Fe-N4

Table 3 .

 3 Minimal

	distortion path (DevPath) analysis using SHAPE for compounds 1-3 from
	T-4 (0 %) to SS-4 (100 %).
	Compound	T-4 a SS-4 b DevPath
	[Fe(N2mes)2] (1)	6.206 5.514 53.6
	[Fe(N2Dipp)2] (2)	7.778 8.222 80.2
	[Fe(HN3Dipp)2]•C5H12 (3) 6.598 6.892 65.1
	a T-4 stands for Td (Tetrahedron)

b SS-4 stands for C2v (Seesaw)

Table 4 .

 4 Magnetic moments of 1-3 in solid state and solution.

	Compound	eff (B mol -1 )	eff (B mol -1 )	M at 2 K and 5 T (B)
		solid state	solution
	[Fe(N2mes)2] (1)	5.03	4.80	2.70
	[Fe(N2Dipp)2] (2)	4.97	4.85	2.23
	[Fe(HN3Dipp)2]•C5H12 (3) 5.05	4.80	2.38

Table 6 .

 6 Evaluation of D and E from Wave Functions Theory (WFT) calculations compared with the experimental values.

		1		2		3
		D (cm -1 ) E (cm -1 ) D (cm -1 ) E (cm -1 ) D (cm -1 ) E (cm -1 )
	CAS(6/10)PT2	10.7	0.02	16.6	1.16	15.8	0.59
	CAS(6/5)NEVPT2 13.7	0.09	19.3	1.15	18.2	0.66
	Experimental	12.3(1) ± 0.01(2) 16.9(7) ± 0.05(2) 16.5(5) ± 2.13(3)

Author Contributions


Friardi Ismed

Françoise Lohézic-Le Dévéhat

Isabelle Rouaud

Solenn Ferron

Amri Bakhtiar

Joël Boustie

NMR reassignment of stictic acid isolated from a Sumatran lichen Stereocaulon montagneanum (Stereocaulaceae) with superoxide anion scavenging activities

Keywords: antioxidant, cytotoxic, lichen, Stereocaulon, stictic acid chemosyndrome

The phytochemical study of Stereocaulon montagneanum harvested in Sumatra (Indonesia) led to the isolation of 11 known compounds including two metabolites not previously described in the genus Stereocaulon, peristictic acid (8) and menegazziaic acid (10). The complete 1 H and 13 C NMR spectral assignments of stictic acid derivatives are reported with some revisions. Five depsidones belonging to the stictic acid chemosyndrome were superoxide anion scavengers as potent as ascorbic acid and with no toxicity on two human cell lines.

Stereocaulon represents a cosmopolitan lichen genus of over 130 species occurring from temperate to tropical regions. The main Stereocaulon metabolites have been initially studied by Duvigneaud [START_REF] Duvigneaud | Contribution à l′étude systématique du genre Stereocaulon[END_REF] using microchemical studies, and they were also compiled by Lamb in the conspectus about the lichen genus Stereocaulon [START_REF] Lamb | A conspectus of the lichen genus Stereocaulon (SCHREB.) HOFFM[END_REF]. The depside atranorin was a constant marker for the genus, while lobaric, stictic and norstictic acids are the most common depsidones. In a previous study, we investigated the phytochemical content of Stereocaulon halei, harvested in Indonesia. Indeed, we isolated lobaric acid and a related metabolite, the diphenyl ether lobariol carboxylic acid, as a new natural product [START_REF] Ismed | Lobarin from the Sumatran lichen, Stereocaulon halei[END_REF]. To implement the chemical knowledge of this tricky genus and find new photoprotective compounds, we focused our phytochemical investigation on another Indonesian species, Stereocaulon montagneanum, collected on rocks exposed to the sun. Like plants, lichens use various strategies to protect themselves against UV radiations and to inactivate the radical oxygen species generated. Mineral crystals of calcium oxalate and pigments such as melanins, phenols and carotenoids [START_REF] Solhaug | UV-induction of sun-screening pigments in lichens[END_REF] are present in lichens and are supposed to block UV radiations. An increase in secondary metabolite content such as dibenzofurans, depsides and depsidones was also reported for lichens collected in sun-exposed conditions and at high altitude [START_REF] Nguyen | UV-protectant metabolites from lichens and their symbiotic partners[END_REF]. So, the current work aimed at investigating the chemical content of this Indonesian lichen and at exploring the photoprotective properties (antioxidant, sunscreen) and cytotoxicity of its main metabolites, highlighting their role in the lichen defense against UV.

Methods

General experimental

Melting points were measured on a hot-stage Kofler apparatus. Optical rotation was determined with a Perkin-Elmer model 341 polarimeter. UV spectra were performed on an Uvikon 931 spectrophotometer. FT-IR spectra were run on a Perkin-Elmer 16 PC IR spectrometer. 1 H and 13 C NMR spectra were recorded at 500 and 125 MHz, respectively, on a Bruker DMX 500 WB NMR spectrometer or at 300 and 67. Bruker 300 NMR spectrometer, using CDCl 3 , DMSO-d6, acetone-d6 and MeOH-d4 as solvents. HRMS measurements for exact mass determination were performed on a Varian MAT 311 mass spectrometer for electron spray and a Micromass ZabspecTOF mass spectrometer for chemical ionization at the Centre Régional de Mesures Physiques de l′Ouest. Chromatographic separation was performed using vacuum liquid chromatography on silica gel (Merck 35-70 μm) and C18 Chromabond (45 mL/10 g). Medium pressure chromatography was conducted on a SPOT Flash Liquid Chromatography (Armen Instrument) using silica or C18 pre-packed columns (Super Vario Flash D26 cartridge SI60 40-63 µm, 30 g Merck, normal phase; SVF D26-RP18 25-40 µm, 31 g, Merck, reversed phase) or manually packed silica columns (40-63 µm, Kieselgel 60, Merck, 7667). Semi-preparative high-performance liquid chromatography (HPLC) was performed on Smartline pump 1000 Knauer equipped with a diode array detector (HPLC 540 DAD, Kontron Instruments), using Kromasil ® C18 (5 µm, 250 × 10 mm, CIL Cluzeau, detector set at 254 and 310 nm) at a flow rate of 3.0 mL/min. Thinlayer chromatography (TLC) analytic and preparative plates (Merck silica gel 60F254) were eluted using three standard solvent systems: n-hexane/diethylether/formic acid (130 : 80 : 20 v/v/v) (B); toluene/acetic acid (85 : 15 v/v) (C); toluene/EtOAc/formic acid (139 : 83 : 8 v/v/v) (G); n-hexane/EtOAc (95 : 5 v/v) (K); CHCl 3 /MeOH/H 2 O (6 : 4 : 1 v/v/v) (L). Visualization of plates was carried out under UV light (254 and 365 nm) using anisaldehyde-H 2 SO 4 reagent and then heating.

Lichen material

S. montagneanum Lamb was collected on rocks exposed to the sun of Plateau Simanau (1500 m), Solok, West Sumatra, Indonesia. After identification by Harrie Sipman (Berlin Museum) and Martin Grube (Karl-Franzens University, Graz, Austria), the voucher specimens were deposited at the herbarium of Pharmacognosy and Mycology, Rennes and Biota Sumatran Laboratory, Andalas University, West Sumatra (Indonesia) with the reference codes JB/09/119 and SmV 3, respectively.

Extraction and isolation

The air-dried whole thalli of S. montagneanum (1.3 kg) were macerated with n-hexane, acetone and methanol successively. Each extract was concentrated in vacuo and precipitates formed after evaporation at room temperature in the n-hexane and acetone extracts afforded compound 1 (0.2 g) and compound 7 (11 g), respectively. The n-hexane filtrate (2 g) was chromatographed on vacuum liquid chromatography silica gel (150 g, 4 × 30 cm) with a solvent gradient consisting of n-hexane/EtOAc v/v (100 : 0 → 0 : 100) as the mobile phase. Six sub-fractions (SH1-SH6) were obtained. Subfraction SH3 (594 mg) was selected for further chromatography using a silica gel column (15 g, 3.5 × 60 cm) and was eluted employing n-hexane/CHCl 3 v/v (60 : 40). From this, four fractions were obtained and compound 2 (13 mg) was purified by recrystallization in n-hexane. Sub-fraction SH2 was further purified by flash chromatography over a silica gel 60 with petroleum ether/EtOAc v/v (90 : 10) as the mobile phase and then subjected to preparative TLC with eluent n-hexane/ethyl acetate v/v (95 : 5). Compounds 3 (2 mg), 4 (10 mg) and 5 (2 mg) were obtained as crystalline residues. Flash chromatography on the C 18 column of the acetone filtrate (4 g) with an increasing gradient solvent system of H 2 O/ACN v/v (100 : 0 → 0 : 100) yielded eight sub-fractions (A1-A8). Compound 8 (20 mg) was purified from sub-fraction A3 by recrystallization in diethyl ether. Sub-fraction A4 (905 mg) yielded compound 9 (38 mg) and compound 10 (4 mg) after separation on C 18 flash chromatography (solvent system of H 2 O/ACN v/v, 60 : 40), and further purification by semi-preparative HPLC with the Kromasil ® C 18 column using H 2 O/MeOH v/v (60% for 20 min) and H 2 O/methanol-TFA v/v 0.2% with a non-linear gradient (50% for 20 min). Compound 11 (8 mg) was also obtained by flash chromatography on the C 18 column with eluent H 2 O/ACN v/v (40 : 60) and recrystallization in ethyl acetate. The methanol extract (4 g) was purified using flash chromatography on the RP C 18 column with eluent H 2 O/CAN v/v (100 : 0 → 0 : 100) to afford nine sub-fractions (M1-M9). The sub-fraction M1 gave compound 6 (20 mg) by liquidliquid purification with isopropanol/water v/v (1 : 1).

Antioxidant assays

Two antioxidant assays were performed on compounds 1, 2, 7-9 and 11, one using the 1,1′-diphenyl-2-picrylhydrazyl free radical (DPPH) and the other based on the measurement of superoxide anion scavenging activity described previously [START_REF] Dévéhat | Lichenic extracts and metabolites as UV filters[END_REF]. Ascorbic acid was used as positive control.

The percentage inhibition at a steady state for each dilution was used to calculate the IC 50 values. This gave the amount of antioxidant required (measured as the concentration of the stock solution added to the reaction mixture) to scavenge 50% of O 2 . All tests were performed in triplicate and the results averaged.

v/v/v) (G); n-hexane/ EtOAc (95:5 v/v) (K); CHCl3/MeOH/ H2O (6:4:1 v/v/v) (L)'.

Cytotoxic assays

Cytotoxic activities of compounds 1, 2, 7-9 and 11 were evaluated against B16-F10 (melanoma; ATCC CRL-6475) and HaCaT cells (Human Epidermal Keratinocytes, ATCC). In brief, the cells were maintained in RPMI medium culture with 5% FBS at 37 °C in an atmosphere of 10% CO 2 . Test compounds (100 mM) were prepared in dimethyl sulfoxide and added to each well 1 day after seeding. The amount of DMSO was adjusted to give a final concentration lower than 0.1%. Cytotoxic activity was determined on B16 and HaCaT cells seeded at 20,000 cells/mL at day 0. Compounds were serially diluted in RMPI 1640 at day 1 in a 96-well plate, with a concentration ranging from 1 to 100 µm. After a new incubation period, cell growth and viability were measured at day 5, using an MTT (3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide) assay, as previously described [START_REF] Bézivin | Cytotoxic activity of some lichen extracts on murine and human cancer cell lines[END_REF][START_REF] Millot | Metabolites from the lichen Ochrolechia parella growing under two different heliotropic conditions[END_REF]. Doxorubicin was used as positive control. All tests were performed in triplicate and the results were subsequently averaged.

Photoprotective index calculation

The most used absolute indexes are UV-PF and UVA-PF. Relative indexes -UVA-PF/UV-PF ratio, critical wavelength λ c -are indicators that reflect a ratio of the UV absorbing efficacy of the sunscreen in given UV regions. So, UV-PF, UVA-PF, critical wavelength (λ c ) calculation was assessed by an in vitro screening method [START_REF] Dévéhat | Evaluation of a new UV-filter screening method. In 4èmes journées de l'AFERP[END_REF]. Briefly, indexes were calculated from absorbances of the tested compounds in ethanolic solution at 10% through Diffey's formulae taking into account the spectral irradiation of terrestrial sunlight and the erythemal action spectrum. Tinosorb M was used as positive control.

Results and discussion

The lichen was sequentially extracted with solvents of increasing polarity (n-hexane, acetone and methanol) to afford 11 compounds including known compounds, atranorin (1), methyl orcinol carboxylate (2), methyl hematommate (3), ethyl hematommate (4), atranol (5), mannitol [START_REF] Dévéhat | Lichenic extracts and metabolites as UV filters[END_REF], stictic acid (7) (Figures S1-S4) and norstictic acid [START_REF] Ewing | 13 C substituent effects in monosubstituted benzenes[END_REF] (Figures S13 andS14). All of them were determined by comparing their spectroscopic data with the reported literature values [START_REF] Huneck | Identification of lichen substances[END_REF], leading to some necessary re-evaluation of their stictic acid datasets (Figure 1).

The complete assignments of 13 C NMR signals for stictic acid [START_REF] Bézivin | Cytotoxic activity of some lichen extracts on murine and human cancer cell lines[END_REF] are given in Table 1. Directly bonded CH carbons were assigned by the heteronuclear single-quantum coherence (HSQC) experiment and the long-range couplings were established by a heteronuclear multiplebond correlation (HMBC) spectrum (Figures S1-S4). A noticeable delta (δ 4.4 ppm) between δ 13 C of C5 for compound 7 and other stictic derivatives is a characteristic downfield shift indicating the ortho phenol substitution at C4 [START_REF] Ewing | 13 C substituent effects in monosubstituted benzenes[END_REF][START_REF] Stothers | Carbon-13 NMR Spectroscopy[END_REF] as observed for subnorstictic and substictic acids [START_REF] Elix | A further three new lichen depsidones[END_REF]. Four of the 13 C NMR signals exhibited close signals in the 160-167 ppm range, and the HMBC spectrum was useful to clarify the carbon attributions. The assignment of C-4 (δ 162.6) was suggested by the high correlation with OCH 3 -4 (δ 3.91) (Figure S4b), and C-7′ was assigned to δ 166.5 ppm because no HMBC correlation was observed with H-5 (δ 7.08) or H-9 (δ 2.50) in opposition to δ 160.8 and δ 163.0, which were both correlated with H-9 (δ 2.50). The strong correlation ( 4 J) between H-5 (δ 7.08) and δ 160.8 suggested a W-coupling and was assigned to C-7. C-2 correlated only with H-9 (δ 2.50) corresponded to the signal at δ 163.0. The assignments of C-2 and C-7′ differed from the first attributions [START_REF] Ewing | 13 C substituent effects in monosubstituted benzenes[END_REF] and were in agreement with the revised assignments reported for salazinic acid [START_REF] Eifler-Lima | NMR spectral data of salazinic acid isolated from some species of Parmotrema[END_REF].

COOCH 3 OH CH 3 HO CH 3 OH O O CHO CH 3 1 R 2 CH 3 HO R 1 OH 2 R 1 = CH 3 , R 2 = COOCH 3 3 R 1 = CHO, R 2 = COOCH 3 4 R 1 = CHO, R 2 = COOC 2 H 5 5 R 1 = CHO, R 2 = H OH H 3 C R 2 O O O O O HO R 1 CH 3 1 2 3 4 5 6 7 1' 2' 3' 4' 5' 6' 7' 8' 9' 8 9 7 R 1 = CHO, R 2 = OCH 3 8 R 1 = COOH, R 2 = OCH 3 9 R 1 = CH 2 OH, R 2 = OCH 3 10 R 1 = OH, R 2 = OCH 3 11 R 1 = CHO, R 2 = OH
Compound 8 was obtained as a white amorphous powder. Its molecular formula was assigned as C 19 H 13 O 10 on the basis of the ESIMS m/z 401.05087 [M-H] -(calcd. for C 19 H 13 O 10 = 401.0511). The UV spectrum and the number of unsaturations were the same as for stictic acid. The IR bands were close to stictic acid (3419, 2951, 1735, 1731 and 1609 cm -1 ) except the signal at 1609 cm -1 . No aldehyde signal was detected on the 13 C NMR spectrum, but the presence of an additional carbonyl signal was confirmed around 160 ppm (Spectra S5-S6). The assignment of C-4 was confirmed by the HMBC correlation with OCH 3 -4 (δ 3.98); the deshielded signal (δ 169.3) was attributed to C-7′, which was correlated with H-9′ (δ 6.98) (Figure S7), suggesting a stabilizing hydrogen bond. C-7 (δ 158.4) and C-8 (δ 165.5) were both correlated with H-5 (δ 7.05), but an upfield shift is usually observed for an ester group. Compound 8, which differed from stictic acid by having a carboxylic group in C-3, was identified for peristictic acid (8) [START_REF] Elix | Lusitanic acid, peristictic acid and verrucigeric acid. Three new β-orcinol depsidones from the lichens Relicina sydneyensis and Xanthoparmelia verrucigera[END_REF]. Compounds 9 and 10 were allocated to cryptostictic acid and menegazziaic acid, respectively, as suggested by their molecular formula with negative HRESIMS of C 19 H 15 O 9 (m/z 387.0716 [M-H] -) and C 18 H 13 O 9 (m/z 373.0566 [M-H] -). The UV spectra had the same profile as compounds 7 and 8, but one peak was missing on the IR absorption spectra (around 1690-1600 cm -1 ) and the number of unsaturations was calculated to be 12, suggesting a lack of a carbonyl group. The 1 H NMR, 13 C NMR along with the HSQC experiment and HMBC spectra (Figures S1-S12) and distortionless enhancement by polarization transfer spectra (Spectra S8-S12) confirmed this and showed as a difference a methylic alcohol at C-8 with a broad signal (δ H 4.68) (Figure S10a) coupled with the methylenic carbon δ C 53.1 ppm for compound 9 and the presence of a broad phenolic proton (δ H 10.14) in replacement of the formyl proton for compound 10. The spectra were acquired first in acetone-d 6 for compound 9 to report the major assignments, but one experiment was carried out in DMSO-d 6 and confirmed a correlation between C-7′ (δ 169.3) and H-9′ (δ 7.28) (Figure S10b) and attribution of the assignments for C-2 and C-4 as for stictic acid. This complete attribution for 13 C NMR signals was first assigned for peristictic, cryptostictic and menegazziaic acids and then for norstictic acid (Table 1). Therefore, five β-orcinol depsidones related to the stictic acid chemosyndrome [START_REF] Elix | Lusitanic acid, peristictic acid and verrucigeric acid. Three new β-orcinol depsidones from the lichens Relicina sydneyensis and Xanthoparmelia verrucigera[END_REF] were isolated. Structures of stictic acid [START_REF] Bézivin | Cytotoxic activity of some lichen extracts on murine and human cancer cell lines[END_REF], peristictic acid (8), cryptostictic acid (9), menegazziaic acid [START_REF] Huneck | Identification of lichen substances[END_REF] and norstictic acid [START_REF] Ewing | 13 C substituent effects in monosubstituted benzenes[END_REF] showed some variation in the degree of oxidation of the C-8 side group R 1 (i.e. CHO, COOH, CH 2 OH or OH) and the methylation of phenolic groups (i.e. R 2 = OCH 3 , OH) (Figure 1). Stictic acid derivatives have been found in S2). many lichen families (Figure 2), in particular in the Parmeliaceae [START_REF] Kosanić | Biological activities and chemical composition of lichens from Serbia[END_REF], Pertusariaceae and Usneaceae families. Concerning the Stereocaulaceae, peristictic acid and menegazziaic acid were isolated for the first time in the Stereocaulon genus, while cryptostictic acid was isolated in Stereocaulon azoreum [START_REF] González | Chemical constituents of the lichen Stereocaulon azoreum[END_REF]. S. montagneanum belongs to the Stereocaulon massartianum complex [START_REF] Lamb | The Stereocaulon massartianum assemblage in East Asia[END_REF], which also has been found in Indonesia (Java, Sumatra, Borneo and Celebes), Malaya and New Guinea even if it is mainly distinguished from S. massartianum senso stricto by the larger size of its pseudopodetia. Four chemosyndromes are reported for S. massartianum correlated with phenotypic morphological differences, different distribution patterns and different ecological preferences [START_REF] Lamb | A conspectus of the lichen genus Stereocaulon (SCHREB.) HOFFM[END_REF][START_REF] Huang | Noteworthy species of Stereocaulon from China[END_REF]. The typical strain I contains the depside atranorin and the depsidones stictic acid, norstictic acid and possibly constictic acid; the strain II contains atranorin, norstictic and connorstictic acids; the strain III contains atranorin and lobaric acid; and the strain IV contains atranorin and lobaric acid with additional stictic and norstictic acids. Interestingly, the strain I of S. massartianum from which S. montagneanum is chemically close was encountered in the same geographical places. A phylogenetic study has to be conducted to clarify the relative position of these two Stereocaulon species. Compounds 1, 2, 7-9 and 11 were tested for radicalscavenging activity against 2,2-diphenyl-1-picrylhydrazyl (DPPH) radicals and superoxide anion (O 2 -• ). The radicalscavenging effect of antioxidants on DPPH is a simple and reliable method to quantify the hydrogen-donating potency of chemicals. Lichen compounds did not seem Compounds 3-5, and 10 were not in sufficient amounts to be tested, compound 6 has no activity and so was not reported here. Data are means ± SD of triplicate experiment and values were calculated according to negative control.

to have labile hydrogen atoms even at 3000 µM for which the most active were compounds 7 and 8 with an activity of about 10% (Figure 3). This was in accordance with the literature; most of lichen compounds showed a weak reducing activity in electron transfer assays such as the DPPH test [START_REF] Dévéhat | Oxidative stress regulation in lichens and its relevance for survival in coastal habitats[END_REF]. Interestingly, atranorin and all stictic acid derivatives exhibited an activity against superoxide anion equivalent to that of ascorbic acid (7, 9) as for the depside atranorin (1) or twofold better (8, 11) (Figure 3). Atranorin was already reported as a superoxide anion scavenger, but this activity was revealed for the first time for the stictic acid derivatives. As a preliminary assay to evaluate their safety in a possible cosmetic use, the cytotoxic activities of 1, 2, 7-9 and 11 were tested on HaCaT human keratinocyte cell lines (Figure 4). Additionally, cytotoxic activities on B16 murine melanoma were recorded (Figure S15). The dose-response curves showed that compounds 8, 9, 11 were safe for both cell lines with IC 50 higher than 100 µM. So, compounds 8, 9 and 11 are valuable compounds with superoxide anion scavenging without toxicity on both cell lines. As sunscreen properties were previously reported for atranorin and methyl orcinol carboxylate [START_REF] Dévéhat | Lichenic extracts and metabolites as UV filters[END_REF][START_REF] Fernandez | Photoprotector capacity of lichen metabolites assessed through the inhibition of the 8-methoxypsoralen photobinding to protein[END_REF][START_REF] Fernandez | Lichen metabolites as UVB filters[END_REF][START_REF] Hidalgo | Spectroscopic and photochemical properties of the lichen compound lobaric acid[END_REF], their absorbances in the UVB and UVA regions and calculation of their UV-PF and UVA-PF indexes were compared with the broad spectrum UV-filter Tinosorb M (Table S1). None of the tested lichen compounds was found to pass the preliminary threshold to go on for a sunscreen development.

Conclusions

Phytochemical studies of S. montagneanum harvested in Sumatra Island (Indonesia) at high altitude and exposed to the sun not only led to the isolation of the common atranorin and its derivatives but also to five stictic acid derivatives. The structural NMR data for stictic acid were re-examined and partially modified from originally published datasets. Stictic acid derivatives could be more involved in the protection of the lichen against the deleterious effects of UV via reactive oxygen species (ROS) formation than by filtering the UV. Lichens could be a valuable source of new active molecules by limiting ROS damages without a marked cytotoxicity on human keratinocytes.

Supplementary material

Experimental details relating to this article are available online alongside the structure NMR spectra of compounds 7-11 (Spectra S1-S14), tables where NMR shifts and attributions of stictic acid derivatives (Table S1) are reported, photoprotective activities and references used to build Figure 2.

2

  Ismed et al.: NMR reassignment of stictic acid

  Ismed et al.: NMR reassignment of stictic acid 3 effective scavenging of O 2 -•

6 Figure 1 :

 61 Figure 1: Compounds isolated from Stereocaulon montagneanum lichen thalli.

4

  Ismed et al.: NMR reassignment of stictic acid

  Ismed et al.: NMR reassignment of stictic acid 5

Figure 2 :

 2 Figure 2: Correlation profile of the stictic acid derivatives and the lichen families (based on the literature, 1970-2013). G, Graphidaceae; H, Hymeneliaceae; L, Lobariaceae; N, Nephromataceae; P, Parmeliaceae; PT, Pertusariaceae; S, Stereocaulaceae; T, Thelotremataceae; U, Usneaceae; 1, stictic acid; 2, deoxystictic acid; 3, 8′-methyl stictic acid; 4, substictic acid; 5, α-acetylconstictic acid; 6, 8′-ethyl stictic acid (vesuvianic acid); 7, 8′-methyl constictic acid; 8, constictic acid; 9, norstictic acid; 10, subnorstictic acid; 11, connorstictic acid; 12, peristictic acid; 13, lusitanic acid; 14, neotricone; 15, norperistictic acid; 16, cryptostictic acid; 17, cryptostictinolide; 18, menegazziaic acid; 19, 8′-methyl menegazziaic acid; 20, hypoconstictic acid; 21, hypostictic acid; 22, α-acetyl hypoconstictic acid; 23, isidiophorin; 24, verrucigeric acid; 25, 2′-O-methyl hypostictic acid; 26, 2′-O-isidiophorin; 27, 2′-O-methylcryptostictic acid. (Complete references in TableS2).

6

  Ismed et al.: NMR reassignment of stictic acid

Figure 4 :

 4 Figure4: Dose-response curves determined with the MTT assays on murine melanocytes B16. Compounds 3-5, and 10 were not in sufficient amounts to be tested, compound 6 has no activity and so was not reported here. Data are means ± SD of triplicate experiment and values were calculated according to negative control.

  Ismed et al.: NMR reassignment of stictic acid 7

Solenn Ferron and Joël Boustie

	Q1:
	Editorial
	assistance
	has been
	given to
	improve the
	clarity of
	this article -
	please check
	to ensure
	that none
	of your
	meaning has
	been lost or
	misconstrued
	*Corresponding author: Françoise Lohézic-Le Dévéhat, UMR-CNRS
	6226 ISCR, Equipe PNSCM, Faculté des Sciences Pharmaceutiques
	et Biologiques, Université de Rennes 1, 35043 Rennes Cedex,
	France, E-mail: francoise.le-devehat@univ-rennes1.fr
	Friardi Ismed and Amri Bakhtiar: The Laboratory of Natural Resource
	of Sumatra (LBS) and Faculty of Pharmacy, Andalas University,
	26163 Padang, Indonesia
	Isabelle Rouaud,
	5 MHz, respectively, on a

: UMR-CNRS 6226 ISCR, Equipe PNSCM, Faculté des Sciences Pharmaceutiques et Biologiques, Université de Rennes 1, 35043 Rennes Cedex, France

Table 1 :

 1 1 H and 13 C NMR (500/125 MHz) data for stictic derivatives (δ in ppm, J in Hz).

	Position Stictic acid (7) Peristictic acid (8) Cryptostictic acid (9) Menegazziaic acid (10) Norstictic acid (11)	(DMSO-d 6 ) (acetone-d 6 ) (acetone-d 6 ) (DMSO-d 6 ) (DMSO-d 6 )	δ C δ H HMBC δ C δ H HMBC δ C δ H HMBC δ C δ H HMBC δ C δ H HMBC	1 113.3 -114.2 --114.1 --113.1 --111.6 --	2 163.0 -161.3 --162.1 --161.4 --160.3 --	3 114.6 -116.3 --119.4 --151.3 --110.6 --	4 162.6 -160.3 --162.8 --162.4 --163.9 --	5 112.9 7.08 (1H, s) 1, 3, 4, 6, 7, 8, 9 112.7 7.05 (1H, s) 1, 3, 4, 7, 8, 9 112.1 6.94 (1H, s) 1, 3, 9 111.6 6.80 (1H, s) 1, 3 117.3 6.88 (1H, s) 1, 3, 4, 7, 9	6 150.8 -147.4 --145.6 --148.2 --152.2 --	7 160.8 -158.4 --160.0 --160.7 --163.5 --	8 186.7 10.47 (1H, s) 1, 3, 4, 5 165.5 --53.1 4.96 (2H, s) --10.14 (1H, s) -192.6 10.50 (1H, s) 4	9 21.5 2.50 (3H, s) 1, 2, 5, 6, 7, 8 21.4 2.54 (3H, s) 1, 5, 6 21.2 2.49 (3H, s) 1, 5, 6 19.7 2.36 (3H, s) 1, 5 21.3 2.48 (3H, s) 1, 5, 6	1′ 109.3 -109.1 --109.1 --108.0 --109.1 --	2′ 152.0 -152.5 --152.5 --152.3 --151.9 --	3′ 120.8 -121.0 --120.7 --120.3 --120.9 --	4′ 148.1 -149.6 --150.1 --148.9 --147.8 --	5′ 137.6 -139.4 --139.6 --139.1 --137.3 --	6′ 135.9 -135.6 --135.9 --134.9 --135.8 --	7′ 166.5 -169.3 --169.3 --163.0 --166.6 --	8′ 9.6 2.19 (3H, s) 1′, 2′, 3′, 4′, 5′, 6′ 9.2 2.25 (3H, s) 2′, 3′, 4′ 9.1 2.22 (3H, s) 2′,3′, 4′, 6′ 9.8 2.20 (3H, s) 2′, 3′, 4′, 5′, 6′ 9.4 2.15 (3H, s) 2′, 3′, 4′	9′ 95.4 6.62 (1H, s) 98.5 6.98 (1H, s) 7′ 98.0 7.28 (1H, s) --94.6 6.79 (1H, s) 7′ 95.4 6.65 (1H, s)	OCH 3 -4 56.8 3.91 (3H, s) 1, 4 56.9 3.98 (3H, s) 4 56.6 3.94 (3H, s) 4 56.7 3.85 (3H, s)

  and 10 were not in sufficient amounts to be tested, compound 6 has no activity and so was not reported here. Data are means ± SD of triplicate experiment and values were calculated according to negative control.

	Superoxide
	scavenging
	assay (IC50 -
	µM)
	DPPH assay (%
	activity at
	9 Figure 3: Antioxidant assays of compounds isolated from Stereo-1 1 Ascorbic acid 3000 µM) caulon montagneanum extract: scavenging ability on DPPH radicals and superoxide anion radicals. Compounds 3-5, Q13: Please check and clarify the sentence "Compounds 3-5, and 10...… according to negative con-
	trol" given in
	the caption
	of Figures 3
	and 4

Acknowledgements: We gratefully acknowledge the French Ministry of Research and Education [Bio-Asie Program, DREIC [International Relations and Cooperation

Department)] and the French Embassy in Indonesia for a PhD grant to Friardi Ismed. We also thank Thi Hang Dao for contributing to the phytochemical work, Nova Syafni and the Sumatran Biota Laboratory team for their help to collect the lichens. We are grateful to P. Jéhan, F. Lambert and N. Le Yondre, CRMPO, Rennes, France, for the mass spectrometer measurements, B. Gargadennec for her help in the sun indexes calculation and P. Uriac. We also thank Arnaud Bondon (PRISM platform) for accurately recording stictic acid spectra as well as Stephane La Barre for critical comments on the text and proofreading service.


Saurabh Kataria

Clément Gaultier

Antoine Deleforge

HEARING IN A SHOE-BOX : BINAURAL SOURCE POSITION AND WALL ABSORPTION ESTIMATION USING VIRTUALLY SUPERVISED LEARNING

Keywords: Sound source localization, Acoustic Modeling, Machine Learning

This paper introduces a new framework for supervised sound source localization referred to as virtually-supervised learning. An acoustic shoe-box room simulator is used to generate a large number of binaural single-source audio scenes. These scenes are used to build a dataset of spatial binaural features annotated with acoustic properties such as the 3D source position and the walls' absorption coefficients. A probabilistic high-to low-dimensional regression framework is used to learn a mapping from these features to the acoustic properties. Results indicate that this mapping successfully estimates the azimuth and elevation of new sources, but also their range and even the walls' absorption coefficients solely based on binaural signals. Results also reveal that incorporating randomdiffusion effects in the data significantly improves the estimation of all parameters.

INTRODUCTION

Most existing methods in multichannel audio signal processing, including speech enhancement, denoising or source separation, rely on a good knowledge of the geometry of the audio scene. In other words, what are the positions of the sources, sensors, and how does the sound propagate between them. Since this knowledge is most of the time unavailable, it is usually estimated from measured signals. A typical assumption is the free-field model in which the sound propagates in a straight line from each source to each sensor. Then, if sensor positions are known, sound source directions may be determined based on estimated time-differences of arrival. However, typical real-world audio scenes include reflecting and diffusive walls, floor, ceiling or filtering effects due, e.g., to the head of a binaural (2 microphones) receiver. Accurate audio scene geometry estimation is much more challenging in this context.

Two orthogonal research directions have recently emerged to tackle this challenge. The first one is physics-driven, and consists in using more advanced acoustical models of the audio scenes. Such models may range from the image source model that incorporates specular reflections [START_REF] Antonacci | Inference of room geometry from acoustic impulse responses[END_REF][START_REF] Dokmanić | Acoustic echoes reveal room shape[END_REF], to the full wave propagation equation within boundaries of arbitrary shape and impedance [START_REF] Bertin | Joint estimation of sound source location and boundary impedance with physics-driven cosparse regularization[END_REF][START_REF] Sr Dan Kitić | Physics-driven inverse problems made tractable with cosparse regularization[END_REF]. These methods are computationally intensive but yield encouraging results in simulated settings. The second direction is data-driven, and consists in learning a mapping from measured high-dimensional acoustic features to source postions. Such mappings are learned from carefully recorded datasets in a supervised [START_REF] Deleforge | Variational EM for binaural sound-source separation and localization[END_REF][START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF] or semi-supervised [START_REF] Laufer-Goldshtein | Semi-supervised sound source localization based on manifold regularization[END_REF] way. Since obtaining these datasets is time consuming, the methods are usually working well for one specific room and setup, and are hard to generalize in practice.

We now propose a third direction that somehow makes use of both worlds, namely, virtually supervised learning. The idea is to use a physics-based room-acoustic simulator to generate arbitrary large datasets of audio-features in various geometrical settings. These data are then used to learn an efficient mapping from audio features to geometrical parameters. In this study, we make a first proof-of-concept by focusing on the scenario of a binaural receiver in a shoebox room of specific size. Over 80, 000 audio scenes with varying source direction, source distance, wall absorption, and random diffusion are generated using the ROOMSIM software of Shimmel and et al. [START_REF] Steven | A fast and accurate "shoebox" room acoustics simulator[END_REF]. We then extend the supervised sound-source localization method of [START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF] to not only estimate 2D directions (azimuth, elevation) but also source ranges and mean wall absorption coefficients, solely based on binaural signals. Our experiments show promising results, and reveal that in the considered setting, the addition of diffusion effects significantly improve estimation of all parameters. While diffusion effects are most often neglected in the sound source localization literature, this suggests that they carry rich spatial information which may be helpful for binaural hearing.

DESCRIPTION OF EXPERIMENTAL SETUP

The problem of single-source localization in a reverberant room using a binaural receiver is considered. It is well-known from both psychophysical [START_REF] William M Hartmann | Localization of sound in rooms[END_REF][START_REF] Rakerd | Localization of sound in rooms, ii: The effects of a single reflecting surface[END_REF] and machine hearing [START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF] studies that perceived binaural features do not only depend on the source's azimuth, but also on its elevation, its range, the position of the receiver in the room, and the room acoustic properties. The aim of this study is to investigate whether some of these additional parameters can be learned and estimated based on perceived spatial binaural features. The number and range of such parameters can be extremely vast con- sidering the variety of real-world rooms, from anechoic chambers to cathedrals. Therefore, we choose to make a trade-off between realism and the number of parameters considered. The room size, receiver position and absorption profiles of the floor and ceiling are assumed fixed in all experiments. However, the azimuth, elevation and range of the source as well as the absorption profile of the walls (assumed identical for all walls), are varied. In addition, random-diffusion effects are added to account for the presence of sound scattering due to objects in the room. Finally, a white-noise emitter is used to avoid biases due to the specific spectral shapes of, e.g., speech signals. Details of the room simulation parameters are showed in Table 1).

The efficient C++/MATLAB "shoebox" 3D acoustic room simulator ROOMSIM developed by Schimmel et al. is selected for simulations [START_REF] Steven | A fast and accurate "shoebox" room acoustics simulator[END_REF]. This software takes as input a room dimension (width, depth and height), a source and receiver position, a receiver's head-related-transfer function (HRTF) model, and frequency-dependent absorption and diffusion coefficients for each surface. It outputs a corresponding pair of room impulse responses (RIR) at each ear of the binaural receiver. Specular reflections are modeled using the imagesource method [START_REF] Jont | Image method for efficiently simulating small-room acoustics[END_REF], while diffusion is modeled using the socalled rain-diffusion algorithm. In the latter, sound rays uniformly sampled on the sphere are sent from the emitter and bounced on the walls according to specular laws, taking into (b) Legend for the plot above Fig. 2. Pictorial view of the dataset constructed account surface absorption. At each impact, each ray is also randomly bounced towards the receiver with a specified probability (the frequency-dependent diffusion coefficient of the surface). The total received energy at each frequency is then aggregated using histograms. This model was notably showed to realistically account for sound scattering due to the presence of objects, by comparing simulated RIRs with measured ones [START_REF] Wabnitz | Room acoustics simulation for multichannel microphone arrays[END_REF].

The source positions considered are distributed on six spherical grids centered on the receiver, with radii vary from 1 meter to 2.5 meters. Each grid consists of 651 training positions and 150 distinct testing positions with uniformly distributed azimuths and elevations. The angular separation between consecutive positions is 3 • for training and 6 • for testing. Fig. 1 shows the receiver and the different source positions within the room.

Since the absorption profile of a surface depends on frequency, the number of parameters required to fully model an absorption profile is too high, making its estimation unrealistic. A database of 18 measured absorption profiles of real materials was collected from [START_REF] Vorländer | Auralization: fundamentals of acoustics, modelling, simulation, algorithms and acoustic virtual reality[END_REF] and [START_REF]Acoustic project company , Ukraine[END_REF], and is listed in Fig. 2b. As illustrated in Fig. 2a, these materials show a strong absorption variability below 500 Hz. Then, the absorption slowly decreases or increases with frequency to reach a nearly constant value. These profiles were selected because the standard deviation (std) of their absorption is always below 0.07 between 500 Hz and 4 kHz. This allows to summarize the absorption profile of the four walls with a single parameter: the mean absorption coefficient above 500 Hz. Consequently, observations in frequencies under 500 Hz will be ignored in all experiments. Note that there is a second reason for ignoring these frequencies. The 60 dB reverberation times (RT60) measured in our experiments ranged from 0.09 to 1 second. This gives an upper-bound for the Schroeder frequency of 200 Hz. The Schroeder frequency is given by f sch = 2000 RT60/V where V is the room volume in m 3 , and provides the frequency limit above which sound intensity is approximately homogeneous and isotropic [START_REF] Bruneau | Fundamentals of acoustics[END_REF][START_REF] Kuttruff | Room acoustics[END_REF]. Above that limit, the modal theory does not hold and is replaced by statistical models of diffuse fields. The simulator, which relies on such models, is thus more likely to give realistic results above that bound. The diffusion profile used in all experiments corresponds to the diffusion field added by three chairs, one table and one computer, as measured in [START_REF] Faiz | Measurement of sound diffusion coefficients of scattering furnishing volumes present in workplaces[END_REF]. As in, e.g., [START_REF] Wabnitz | Room acoustics simulation for multichannel microphone arrays[END_REF], the same profile is used for all surfaces. Overall, each pair of generated RIR depends on four parameters: the source's azimuth, elevation and range, and the mean absorption coefficient of walls. The complete dataset is available online at http://theVASTproject.inria.fr (see also [START_REF] Gaultier | VAST: The virtual acoustic space traveler dataset[END_REF]).

MAPPING BINAURAL FEATURES TO GEOMETRICAL PROPERTIES

Computing Binaural features

Let u ∈ R 4 be a parameter vector containing the source's azimuth, elevation and range, and the mean wall absorption. We denote the associated generated left and right RIR by (h L (u), h R (u)). Each of these pairs is convolved with a 1 second random white Gaussian noise signal, and the result is resampled at 8kHz. The short-time Fourier transform is then applied to both signals, using a 64ms sliding time window with 50% overlap. This results in a left-microphone spectrogram {L(f, t)} F,T f =1,t=1 and a right-microphone spectrogram {R(f, t)} F,T f =1,t=1 , where F = 256 and T = 32. If {S(f, t)} F,T f =1,t=1 denotes the emitted white-noise spectrogram, under the assumption that most of the RIR energy is concentrated on the first 64ms, we have the following approximate multiplicative model

L(f, t) ≈ ĥL (f, u)S(f, t) R(f, t) ≈ ĥR (f, u)S(f, t) (1)
where• denotes the discrete Fourier transform. The interaural level difference (ILD) and interaural phase difference (IPD) spectrograms are defined by

ILD(f, t) = 20 * log(|L(f, t)|/|R(f, t)|) ∈ R IPD(f, t) = L(f,t)/|L(f,t)| R(f,t)/|R(f,t)| ∈ C ≡ R 2 .
(

) 2
Using the approximation (1), it is easily seen that both ILD and IPD solely depend on the parameter vector u and do not depend on the emitted signal. Similarly to [START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF], the ILD and IPD spectrograms are vertically concatenated and averaged over time to form a high-dimensional feature vector y ∈ R D associated to the low-dimensional parameter vector u ∈ R L (L = 4). As explained in Section 2, only the F = 481 bins corresponding to frequencies above 500 Hz are used in y, resulting in a dimension D = 3F = 1443 in practice.

Gaussian Locally-Linear Mapping

The training dataset is composed of

N pairs {(y n , u n )} N n=1 ⊂ R D × R L .
A mapping needs to be learned from this dataset such that given a new test observation y t ∈ R D , an associated parameter vector u t can be estimated. To achieve this, we use the high-to low-dimensional regression method Gaussian locally-linear mapping (GLLiM) proposed in [START_REF] Deleforge | Highdimensional regression with gaussian mixtures and partiallylatent response variables[END_REF]. GLLiM is a probabilistic method that estimates K local affine transformation from the space of u to the space of y using a Gaussian mixture model. This mapping is then reversed through Bayes' inversion, yielding an efficient estimator of u given y. GLLiM was successfully applied to supervised 2D sound source localization on a real dataset in [START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF]. In practice, a fixed value K = 25 is used in all experiments, as this showed to be a good trade-off between accuracy and computational time using preliminary validation sets.

EXPERIMENTATION AND RESULTS

We first conduct an experiment to reproduce the supervised binaural 2D localization results of [START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF] in our setting. The GLLiM model is trained on 651 individual white noise (WN) recordings obtained from sources lying on a grid at a range of 1 m (the closest grid in Fig. 1). The chosen wall absorption profile is "Rockwool backing behind plaster" (Fig. 2b) with mean absorption value 0.16. Random diffusion effects are added on both training and testing data. Two test cases are compared. First, testing in the same configuration, i.e. , absorption and range are the same between training and testing. Second, testing with the different wall absorption profile "Rockwool core fabric panel (8pcf)" (Fig. 2b, mean absorption value 0.96) and a grid range of 2.5 m. As expected, table 2 illustrates that the localization error is higher when testing in a configuration different from the training configuration, in particular in elevation. The same phenomenon was observed in [START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF] with real data. As in [START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF], it can be noted that estimating elevation is harder than azimuth, which is expected because of head symmetry. This difficulty seems further increased here by the use of a cutoff frequency at 500 Hz. This fundamental experiment motivates the idea of a robust training using multiple configurations of absorption values and grid ranges. We then trained the GLLiM model using all 651 training directions, 6 ranges (Fig. 1 Results are presented in the first column of Table 3. As can be seen, training with the entire dataset improves localization results compared to training using a single room and range (Table 2). Moreover, our method is able to estimate the mean wall absorption between 0 and 1 with an accuracy of 0.18, as well as the range of the source between 1 and 2.5m with an accuracy of 54cm. To the best of the authors' knowledge, the only other binaural range estimation method in the literature is [START_REF] Lu | Binaural estimation of sound source distance via the direct-to-reverberant energy ratio for static and moving sources[END_REF], which showed an accuracy of about 1m using direct-to-reverberant ratios. Figure 3a shows mean source direction errors as a function of wall absorption. Note that too large or too little absorption hinders elevation estimation, the optimal results being obtained in the range [0.3, 0.8]. This is probably because a high-level of reverberation implies that model (1) is more approximate, while too little reverberation means less spatial richness, and less symmetry breaking. Similarly, Fig. 3b shows errors as a function of source distance. As commonly observed, farther sources are slightly harder to localize, although the method seems to be particularly robust to range variations.

Comparing now the first and second column of Table 3, we observe an interesting result. When removing diffusion in both training and test data, the estimation of all variables is degraded. It was consistently observed that adding diffusion in simulations improved results, even when using a number of other diffusion profiles and different room dimensions. This is particularly striking for elevation and absorption. We suspect diffusion to increase the spectral richness of binaural cues, making them more discriminative by breaking inherent symmetries of the problem. The authors are not aware of previous work specifically studying this effect in the literature.

We finally test the influence of removing absorption or 3).

As expected, removing this information increases errors, but overall, the GLLiM probabilistic framework seems to be relatively robust to additional non-annotated effects such as absorption and range. This is promising for future experiments on larger datasets with larger parameter variability, where full annotation of all effects may not necessarily be possible.

CONCLUSION

In this paper, we presented a proof-of-concept for the novel framework of virtually-supervised learning for audio-scene geometry estimation. Obtained results are encouraging, revealing that estimating the 2D direction and range of a source as well as some of the wall acoustic properties is possible using binaural recordings only. Moreover, we observed that incorporating random diffusion effects in simulations significantly increased the spatial richness of binaural features, improving estimation of all parameters. In a simultaneous companion paper [START_REF] Gaultier | VAST: The virtual acoustic space traveler dataset[END_REF], we validated the virtually-supervised learning framework by successfully localizing sources from real-room signals and showed the superiority of the approach over a traditional time-delay-based method. Extensions to speech [START_REF] Deleforge | Co-localization of audio sources in images using binaural features and locally-linear regression[END_REF], multiple sources [START_REF] Deleforge | Variational EM for binaural sound-source separation and localization[END_REF] and additional partially-latent variables in GLLiM [START_REF] Deleforge | Highdimensional regression with gaussian mixtures and partiallylatent response variables[END_REF] will also be considered.

  Fig. 1. Illustration of room setup

  ), and 21 constant wall absorption values in {0, 0.05, ..., 1}. This results in a dataset of N = 651 × 6 × 21 = 82, 026 binaural feature vectors associated toL = 4-dimensional parameter vectors {(y n , u n )} N n=1 ⊂ R D × R L .The 21 absorption values used here correspond to ideal materials with perfectly constant absorption coefficient in the frequency range [0.5, 4] KHz. Testing is done on the 108 test directions (Fig.1), 6 grid ranges, and the 18 real material absorption profiles of Fig.2band six grid ranges. By choosing ideal materials for training and real materials for testing, it is ensured that the training and testing sets are significantly different.

Fig. 3 .

 3 Fig. 3. Mean localization error (in degrees) as a function of absorption (a) and range (b). range annotation during training (Columns 3 to 5 in Table3). As expected, removing this information increases errors, but overall, the GLLiM probabilistic framework seems to be relatively robust to additional non-annotated effects such as absorption and range. This is promising for future experiments on larger datasets with larger parameter variability, where full annotation of all effects may not necessarily be possible.

Table 1 .

 1 General information about room setup.

	Illustration of room setup
	Room dimensions (in m)	6 x 5 x 3.3
	Receiver coordinates (in m)	(2, 2.5, 1.6)
	Receiver HRTF model	MIT Kemar [11]
	Sensor type	Omnidirectional
	Six grid ranges (in m)	{1, 1.3, 1.6, 1.9, 2.2, 2.5}
	Angular range for sources (azimuth)	[-45 • , 45 • ]
	Angular range for sources (elevation)	[-30 • , 30 • ]
	Frequency bins from which
	absorption and diffusion profiles are	{0.125, 0.25, 0.5, 1, 2, 4}
	linearly interpolated (in KHz)
	Frequency-dependent absorption values for ceiling (gypsum board)	(0.45, 0.55, 0.60, 0.90, 0.86, 0.75)
	Frequency-dependent absorption values for floor (thin carpet)	(0.02, 0.04, 0.08, 0.20, 0.35, 0.40)
	Frequency-dependent diffusion values for all surfaces	(0.003, 0.004, 0.045, 0.077, 0.210, 0.431)

Table 2 .

 2 Comparing the mean and std of absolute localization errors when training with a single room and source range.

		Testing in the same	Testing in a different
		configuration	configuration
	Azimuthal error ( • )	1.67 ± 1.22	1.99 ± 1.42
	Elevation error ( • )	8.78 ± 7.08	15.79 ± 12.39

Table 3 .

 3 Mean±std localization errors for various training sets. The second column is the same as first one but without diffusion. Vertical labels denote variables to be estimated. Horizontal labels denote parameters supplied during training (vector u).