Peter M Chapple

Marie Cordier

Vincent Dorcet

Thierry Roisnel

Jean-François Carpentier

Yann Sarazin
email: yann.sarazin@univ-rennes1.fr

A versatile nitrogen ligand for alkaline-earth chemistry †

The tridentate ligand 1,8-bis-(2,6-diisopropylphenyl)imino-3,6-di-tert-butyl-carbazolate, {Carb DiPP } -, has been used to prepare a variety of complexes of the large alkaline earths (Ae) calcium, strontium and barium.

A complex of their smaller congener, magnesium, has also been synthesised. The range of coligands that have been utilised include alkyls, amides, halides and tetrelides. All structurally characterised complexes presented herein are stable in solution and do not undergo ligand redistribution that is otherwise well-known to pollute the chemistry of the alkaline-earth metals. Detailed structural and spectroscopic data for these compounds are discussed. They provide compelling evidence that this nitrogen ligand allows for the kinetic stabilisation of Ae complexes through optimal steric encapsulation of the voluminous metal centres. Its ease of access combined to its evident versatility make {Carb DiPP }H stand out in the portfolio of proligands that have been devised for similar purposes in the past decade. Yet, it fell short in our attempts to synthesise heteroleptic Ae-hydrides upon action of PhSiH3 onto Ae-amides, as the crystallised products showed the imine groups were prone to hydride reduction and formal hydrosilylation.

Introduction

Although it has long been overlooked, the molecular chemistry of the large alkaline earths (Ae) calcium, strontium and barium is now blossoming into a vibrant area. Thanks to the development of their fundamental organometallic chemistry, it has now become evident that these metals display a rich and original chemistry, vastly different from that of their smaller and more well-known congener, magnesium. [1][2][3][4][5][START_REF] Barrett | Proc. R. Soc. A[END_REF][START_REF] Kobayashi | [END_REF][8][9][START_REF]Alkaline-Earth Metal Compounds: Oddities and Applications[END_REF][START_REF] Hill | [END_REF][12][13][14][START_REF]Early Main Group Metal Catalysis: Concepts and Reactions[END_REF][START_REF] Chapple | [END_REF] Hence, rather than mere derivatives of Grignard reagents, well-defined, soluble complexes of the heavier Ae metals constitute suitable precursors for MOCVD applications 1 and, perhaps more representatively, molecular catalysts and precatalysts for an array of metal-mediated organic reactions. [5][START_REF] Barrett | Proc. R. Soc. A[END_REF][START_REF] Kobayashi | [END_REF][START_REF]Alkaline-Earth Metal Compounds: Oddities and Applications[END_REF][START_REF] Hill | [END_REF][START_REF]Early Main Group Metal Catalysis: Concepts and Reactions[END_REF] Besides, they also display exciting sub-catalytic reactivity towards small molecules that was hitherto unsuspected. [START_REF]Alkaline-Earth Metal Compounds: Oddities and Applications[END_REF][17][18][19][20][21][22][23][24][25][26] These accomplishments have been made possible through a better understanding of the key principles that govern Ae chemistry. Calcium, strontium and barium are large, very electropositive metals that generate strongly ionic complexes, where weak bonding is primarily governed by electrostatic considerations (Fig. 1). These prominent features increase upon descending group 2, and to this day, the molecular coordination chemistry of barium has certainly proved difficult to assuage. One specific issue with Ae complexes is their propensity to undergo Schlenk equilibria in solution, a consequence of the ionic bonding in these divalent compounds. From a discrete heteroleptic complex [X-Ae-Y], this ligand-scrambling process forms homoleptic species [AeX2] and [AeY2]. Although it may be useful in specific cases, e.g. for the quantitative preparation of magnesium dialkyls from Grignard reagents, it often produces mixtures that are unsuitable for catalysis. Like electropositivity and bond polarity, this disposition augments with Mg < Ca < Sr < Ba. The design of kinetically stabilising bulky ligands has been instrumental in the developments of the molecular chemistry of Ca, Sr and, to a less successful extent, Ba. A number of monoanionic nitrogen-based ligands, e.g. amidinates and β-diketiminates, have been implemented. Amongst these, none has been more effective than the ubiquitous 2,6-bis-diisopropylphenyl-β-diketiminate (BDI DiPP , Fig. 2; DiPP = 2,6i Pr2C6H3). This easily accessed ligand has been tremendously useful for calcium as well as magnesium and A c c e p t e d M a n u s c r i p t also, to some level, strontium. 5,[START_REF] Barrett | Proc. R. Soc. A[END_REF][START_REF]Alkaline-Earth Metal Compounds: Oddities and Applications[END_REF][START_REF] Hill | [END_REF]14,[START_REF]Early Main Group Metal Catalysis: Concepts and Reactions[END_REF]27,28 . Since its introduction to alkaline-earth chemistry, 29 e.g. to devise heteroleptic catalysts for the ring-opening polymerisation of cyclic esters, 30 it has been the cornerstone for many of the breakthroughs in the field. Yet, for barium, it has not proved anywhere near as efficient, due to its inability to prevent ligand scrambling. For instance, [BDI DiPP BaN(SiMe3)2•(thf)] redistributes to [(BDI DiPP )2Ba] and [Ba{N(SiMe3)2}2•(thf)2]. 31 The stabilisation of heteroleptic barium complexes is a well-known issue. [START_REF]Alkaline-Earth Metal Compounds: Oddities and Applications[END_REF]14,32 Some other families of sterically congested multidentate ligands have been developed to address this specific problem (Fig. 2), such as the bulkier β-diketiminate BDI DiPeP , 33 iminoanilides, [34][35][36] dipyrromethene, 37 tris(pyrazolyl)borates, 38 or also non-nitrogen ligands, e.g. substituted cyclopentadienyls 39 and phenolates. [40][41] They have met some success but, owing either to their tedious syntheses or insufficient stabilising properties, they have seldom been generalised to all three Ae metals. In fact, to date, no ligand has been shown to be equally efficacious at stabilising calcium, strontium and barium complexes.

We have recently reported on an easily accessed and bulky bis(imino)carbazolate ligand, Carb DiPP (Fig. 2), that is particular effective at stabilising barium heteroleptic complexes. 42 It has enabled the first syntheses of unusual species, such as soluble Ba-fluorides and Ba-stannyls. As a follow-up on these initial results, we are now showing that beyond barium, the practicality of this ligand framework extends across group 2 to the synthesis of stable calcium and strontium complexes. Its suitability for magnesium chemistry is also demonstrated. The preparation and the characterisation of a number of heteroleptic carbazolate Ae-halides, amides and alkyls are presented.

Results and Discussion

The proligand 1,8-bis-(2,6-diisopropylphenyl)imino-3,6-di-tert-butyl-carbazole, designated as {Carb DiPP }H hereafter, is readily available (70% yield, 25 g scale) by condensation of 2,6-diisopropylaniline with 1,8diformyl-3,6-di-tert-butyl-carbazole. 42

Barium complexes 6-8

Beyond the reported complexes 1-5 that already illustrated its broad applicability in barium chemistry, 42 {Carb DiPP }H allows for the preparation of generally useful barium precursors. The thf-solvated Ba-amide [{Carb DiPP }BaN(SiMe3)2•thf] (6) was isolated in good yield (93%, 1.0 g scale) as a crop of bright yellow crystals following the treatment of the proligand with an equimolar amount of the convenient starting material [Ba{N(SiMe3)2}2•(thf)2], 43 or from the addition of thf to 1. The presence of one molecule of coordinated thf per metal was established by NMR spectroscopy. For instance, the 1 H NMR spectrum of 6 recorded in toluene-d8 at 25 °C features multiplets of expected intensities at 2.88 and 1.19 ppm for αand A c c e p t e d M a n u s c r i p t β-CH2(thf) groups; another diagnostic resonance is that assigned to the imino CH=N hydrogen atom, a singlet at 8.49 ppm. The 13 C{ 1 H} NMR spectrum of the complex is equally unequivocal. In a non-optimised process, crystals of the yellow Ba-alkyl complex [{Carb DiPP }BaCH(SiMe3)2•thf] (7) were obtained in 69% yield after the reaction in a J-Young NMR tube of {Carb DiPP }H with Hill's precursor, [Ba{CH(SiMe3)2}2•(thf)2]. [44][45] NMR spectroscopy of 7 confirms the presence of a single molecule of coordinated THF; diagnostic resonances in the 1 H NMR spectrum included a high-field resonance at -1.84 ppm assigned to CH(SiMe3)3, and the deshielded one at 8.47 ppm for CH=N. Complex 7 is one of the few discrete heteroleptic Ba-alkyls that have been structurally characterised to date (vide infra). Although 46 hits for compounds containing Ba-C bonds were identified in the CSD database, 46 48 The tetramethyldisilazide [{Carb DiPP }BaN(SiMe2H)2•thf] (8a) and[{Carb DiPP }BaN(SiMe2H)2•Et2O] (8b) were prepared from similar reactions between {Carb DiPP }H and a slight excess of [Ba{N(SiMe2H)2}2•(thf)4] for 8a and [Ba{N(SiMe2H)2}2]n for 8b. Alternatively, 8a can be easily prepared by simply dissolving 8b in thf. The thf adduct 8a is a pale orange solid in the solid state, while the ether adduct 8b is a bright yellow colour. The tetramethyldisilazide N(SiMe2H)2 -has on occasions been employed in alkaline-earth chemistry (and elsewhere [49][50] ) instead of the more routine hexamethyldisilazide N(SiMe3)2 - because it opens the possibility to set up favourable intramolecular β-Si-H anagostic interactions that help stabilise electrophilic metal centres. 40,51 All three complexes dissolve in ethers and toluene, but they are only sparingly to moderately soluble in aliphatic hydrocarbons and benzene.

XRD analysis of single-crystals of 6-8a shows that they generate five-coordinate monomers in the molecular solid state (Fig. 3, 4 and5). Complex 6 forms a C1-symmetric slightly distorted square pyramid (τ5 = 0.13), 52 with the Nsilazide atom (aka N4) occupying the apical position. At a distance of 1.1393(4) Å, the barium atom is located well above the mean plane and basis of the square pyramid delineated by the four coplanar atoms N1, N2, N3 and O60. The interatomic distances to the Nimine atoms N1 and N3 (2.798(3) and 2.809(3) Å) in 6 are substantially longer than in the four-coordinate congener [{Carb DiPP }BaN(SiMe3)2] (1) (2.741(3) and 2.739(3) Å). 42 The Ba-Nsilazide bond length is also somewhat longer in 6 (2.628(3) vs 2.585(4) Å). On the other hand, the Ba-Ncarbazolate distance in 6 (2.685(3) Å) is slightly shorter than in 1 (2.722(3) Å).

Unsurprisingly, the presence of the additional coordinated thf molecule in 6 (Ba1-O60 = 2.780(3) Å) overall results in a weakening and elongation of the other Ba-heteroatom bonds.

The barium-alkyl 7, with its distorted square pyramidal geometry (τ5 = 0.14), is isomorphous with the amido derivative 6. The alkyl group sits in apical position. The Ba-N and Ba-O interatomic distances are very similar in the two complexes. The Calkyl atom (aka C11) is located 2.821(4) Å away from the metal The tetramethyldisilazide congener 8a also forms a distorted square pyramid (Fig. 5), with the silazide in apical position (τ5 = 0.17). All Ba-heteroatom interatomic distances are commensurate with the equivalent ones in 6. At 2.614(2) Å, the Ba1-N71 distance to the Nsilazide atom is at the lowest end of the range for such bonds; 36,40,51 it is similar to that in the five-coordinate

[{2-(C=N-DiPP)-C6H4-N-Dipp}BaN(SiMe2H)2•(thf)2]
(2.601(4) Å). 53 The relatively small difference between the Ba1-N71-Si1A and Ba1-N71-Si2 angles (118.08(12)° and 108.58(12)°), together with the torsion angles Ba1-N71-Si1A-H1A and Ba1-N71-Si2-H2 (104.65(12)° and 17.46(15)°) both suggest that there is at best a single and mild Ba•••H-Si β-anagostic interaction involving the hydrogen atom H2. The 1 H NMR data displays a resonance for the Si-H hydrogen at 4.58 ppm, with a Si-H coupling constant of 161Hz, indicative of only mild Ba⋯H-Si interactions in solution. 28 The FTIR spectrum recorded in Nujol displays two characteristic broad Si-H stretching bands at 1998 and 1940 cm -1 . The ether adduct 8b (see SI, Fig. S31) exhibits similar structural features to 8a, although it forms a very distorted square pyramid (τ5 = 0.38). The Ba1-N1A distance of 2.587(4) Å is slightly shorter than that of 8a, as expected with a weaker donor solvent. The 1 H NMR spectrum displays a resonance for the CH=N carbon atom of the imino group appears at 173.7 ppm in the 13 C{ 1 H} NMR spectrum of this complex. For the thf-adduct derivative 10, the corresponding resonances are visible at 8.60 and -0.19 ppm and at 174.1 ppm in the 1 H and 13 C{ 1 H} NMR spectra in toluene-d8, respectively. Hence, the additional coordination of the thf molecule in 10 does not induce substantial variations of the chemicals shifts, consistent for complexes where bonding is essentially ionic. Both complexes 9 and 10 are stable in solution at room temperature, although they exhibit slightly different solubility; 9 dissolves well in benzene and moderately so in hexanes, while 10 is only slightly soluble in benzene (although it is soluble in toluene).

Note that complex 10 can be prepared upon dissolution of 9 in toluene containing a small amount of thf, followed by removal of the volatiles to constant weight.

The solvent-free 9 forms a monometallic four-coordinate complex with a slightly distorted trigonal pyramidal geometry in the molecular solid state (τ4 = 0.65; 54 Fig. 6). The metal centre Sr1 is only 0.1046 (3) Å above the plane defined by N1, N3 and N11. There is also considerable distortion in the ligand backbone, as the carbazolate core along with the imino fragments deviate clearly from the expected near planarity. 42 The various Sr-N interatomic distances in 9 are unremarkable; they are commensurate with those in related four-coordinate strontium complexes, e.g. [{BDI DiPP }SrN(SiMe3)2•thf], 55 [{BDI DiPeP }SrN(SiMe3)2•thf], 33 and [{2-(C=N-DiPP)-C6H4-N-Dipp}SrN(SiMe3)2•thf]. 48 A c c e p t e d M a n u s c r i p t Like its barium analogue 6, complex 10 forms an arrangement close to ideal square pyramidal (τ5 = 0.08) with the silazide in apical position (Fig. 7). The two complexes are isostructural. Compared to the non-solvated 9, the presence of metal-bound thf results in the elongation of the Sr-N bonds in 10. The strontium atom is 1.0032(4) Å above the best average plane defined by the four heteroatoms at the basis of the square pyramidal arrangement, O11-N21-N51-N81.

Calcium complexes 11-13

The bright yellow calcium iodide [{Carb DiPP }CaI•thf] (11) was prepared in 78% yield by reaction of 42 with CaI2 in thf. The reaction is slightly sluggish, requiring heating to 50 °C to drive it to completion overnight. This complex constitutes a useful starting material for the synthesis of other calcium compounds via salt metathesis (vide infra), related to the disolvated barium-iodide [{Carb DiPP }BaI•(thf)2] (3). It forms a five-coordinate monomer in the molecular solid-state (Fig. 8), where the iodide sits at the apex of a distorted square pyramidal geometry (τ5 = 0.17). It is one of the few fivecoordinate monomeric Ca-iodides (the lowest coordination number known for such species) that have been structurally authenticated; most form iodide-bridged di-or multimetallic species. 46 surprisingly, there is no available example of five-coordinate [Ca]-CH(SiMe3)2 in the CSD database. 46 The geometry about the calcium atom in the four-coordinate 13 approximates a trigonal pyramidal configuration (τ4 = 0.58), where Ca1 is actually located in the plane defined by N1, N11 and N31 (Fig. 10).

[{Carb DiPP }K•(thf)2]

Magnesium complex 14

Finally, the ability of the bis(imino)carbazolate ligand {Carb DiPP } -to stabilise magnesium complexes was confirmed upon reaction of the proligand with [Mg( n Bu)2]. The reaction, carried out in hexanes, readily afforded [{Carb DiPP }Mg n Bu] (14) as a yellow-orange powder in 91% yield. Diagnostic resonances in the 1 H NMR spectrum of 14 include a singlet at 8.36 ppm for the CH=N hydrogen atom, and a high-field multiplet at -0.36 ppm assigned to MgCH2 hydrogens. Its molecular solid-state structure (Fig. 11) shows the fourcoordinate complex to exist as a flattened trigonal pyramid (τ4 = 0.43), where Mg1 sits 0.6044(8) Å above the N1-N2-N3 plane while the angle C47A-Mg1-N2 is very wide (150.5(2)°). The Mg1-N2 and Mg-C47A bond lengths (2.029(2) and 2.086(12) Å) to the Ncarbazolate and Calkyl atoms in 14 are unexceptional. They compare well with to those in [{2,4,7,9-t Bu4-C12H4N}MgEt•(thf)2] (2.087(3) and 2.141(4) Å). 58 A c c e p t e d M a n u s c r i p t

Further reactivity

Alkaline-earth hydrides have proved extremely valuable as soluble catalysts for hydrogenation reactions, as well as suspected or established in-cycle catalytically active species in a wealth or organic reactions such as hydroelementations and dehydrocouplings. [START_REF]Early Main Group Metal Catalysis: Concepts and Reactions[END_REF] Whereas magnesium 59 and, to a lesser extent, calcium [60][61] hydrides have been known for some time, it is only recently that the first well-defined strontium [62][63] and barium 38,39,64 N,N,N',N'',) and [Ba7H7{N(SiMe3)2}7]. 60,62,64 Hence, in an attempt to generate a barium hydride supported by the {Carb DiPP } -framework, the barium amide 6 was reacted with a two-fold excess of PhSiH3. Yet, instead of the sought "[Carb DiPP }BaH•(thf)x]", a crop of bright yellow crystals of the bimetallic complex [Ba2{Carb DiPP, red }{Carb DiPP,silyl }•(thf)2] (15) was isolated in 30% yield, where {Carb DiPP,red } 3-and {Carb DiPP,silyl } -correspond respectively to formally reduced and hydrosilylated derivatives of the regular ligand (Scheme 2). The molecular structure of 15 features two inequivalent barium atoms (Fig. 12). Ba1 is five-coordinate, with a coordination sphere made of three Ba-N bonds in the range 2.706(4)-2.714(3) Å and completed by the presence of two thf molecules at distances of 2.731(3) and 2.761(4) Å. The atom Ba2 is four-coordinate, with interatomic distances to the nitrogen atoms N1, N2, N3 and N12 between 2.627(3) and 2.857(3) Å.

There are therefore considerable differences in the Ba-N interatomic distances in this bimetallic complex.

In addition, Ba2 is involved in two C(π)-interactions with C69 and C79, with short Ba2-C69 and Ba2-C79 distances of 3.042(4) and 2.969(4) Å, resulting in η 3 bonding with the carbazolate core. The N1-C13, N2-C34, N11-C63 and N13-C84 bond lengths, in the range 1.474(5)-1.483 (5), are all consistent with single C-N bond character and, thus, sp 3 -hybridised nitrogen and carbon atoms. Accordingly, the final refinement indicates that each of the atoms C13, C34, C63 and C84 are each bound to two H atoms, although their positions were idealised and not located from the Fourier difference map. Both 1 H and 13 C{ 1 H} NMR data confirmed the absence of imine groups in 15. This is seen as the result of imine reduction upon addition of a hydride at C13 and C34, or formal hydrosilylation in the case of the imine moieties corresponding N11-C63 and N13-C84. Note that the nitrogen atoms N11 and N13 of the (now) silazane functional groups do not interact with the metal centres.

A c c e p t e d M a n u s c r i p t

In a similar attempt to generate a putative "[Carb DiPP }CaH•(thf)x]" complex, with the hope that the pertaining Ca-H hydride would be less prone to unwanted reactivity due to the lower ionic nature of this bond with respect to the Ba-H equivalent, the calcium complex [{Carb DiPP }CaN(SiMe3)2] (13) was reacted with PhSiH3. Yet, instead of the sought complex, yellow crystals of the centro-symmetric tetranuclear dihydride [Ca4{Carb DiPP red }2H2•(thf)2] (16) were reproducibly isolated upon direct recrystallisation from the reaction mixture (Fig. 13). Although the quality of the data set and final refinement are insufficient to warrant a discussion of the metric parameters in this structure (Rint = 0.2440, R1 = 11.80), there is no ambiguity as to the atom connectivity.

There are two very distinct calcium environments, but where both Ca1 and Ca2 are five-coordinate.

Reduction from {Carb DiPP } -to {Carb DiPP,red } 3-is clear upon examination of the N1-C13 and N3-C34 fragments. Most importantly, the presence of bridging hydrides seems unequivocal; their positions correspond to electronic density in the Fourier difference map (although the inaccuracy of the data is high) and is required to ensure charge balance in the tetranuclear edifice. No silicon atom was detected in the structure of 16. Unfortunately, despite our repeated attempts, we were not able to record satisfactory NMR data for this complex. It is possible that a barium complex akin to of 16 is an intermediate en route towards the formation of 15. Several mechanistic scenarios are conceivable, but in the absence of further experimental data, we are refraining from making unsubstantiated claims about what are likely to be multi-A c c e p t e d M a n u s c r i p t step mechanisms. At this stage, the amalgamated data agree with the formation of Ae-hydrides supported by the {Carb} -ligand; yet, the imine groups in the ligand backbone appear to be exceedingly sensitive towards the high reactivity of these compounds and are further derivatised during so far uncontrollable processes.

Finally, the calcium-stannyl [{Carb DiPP }CaSn(SiMe3)3•thf] (17), that is, the direct analogue of the barium complex [{Carb DiPP }BaSn(SiMe3)3•thf] (5), 42 42 ). The molecular solid-state structure features the calcium atom Ca1 at the centre of a distorted square pyramidal arrangement (τ5 = 0.31), where the Nimine and tin atoms N1, N3 and Sn1 occupy the equatorial positions (Fig. 14). The Ca-Ncarbazolate and Ca-Nimines interatomic distances are similar to those measured in the other calcium complexes 11-13, although some small variations are observed (see Table 1). The Ca1-Sn1 bond length in 17, 3.2564(7) Å, is commensurate with those in [{BDI DiPP }Ca-μ2-H-(SnPh3)Ca{BDI DiPP }] and [{BDI DiPP }Ca(SnPh3)]2, 3.2137(4) and 3.3221 (5), although the Ca atoms are four-coordinate in these complexes. 67 It also compares well with that in the six-coordinate [Ca(SnMe3)2•(thf)4] (3.2721(3) Å). 66 Evidently, the coordination number around calcium influences little the Ca-Sn interatomic distances; this is thought to reflect the nature of the bond between the two metals, which DFT computations have shown to be highly ionic and polarised ( δ+ Ca•••Sn δ- ), with only a small covalent contribution. 42,67 The Sii-Sn-Sij angles around the tin atom range between 94.56(4)-100.51(4)°, as would be expected for a tin(II) centre with little hybridisation between s and p orbitals.

Concluding remarks

The bis(imino)carbazole {Carb DiPP }H appears to be a ligand suitable for the preparation of a very large range of alkaline-earth complexes. The new Mg-Ba complexes 6-17 disclosed herein are characterised by coordination numbers of four or five, with geometries that approximate trigonal pyramidal (i.e. highly distorted tetrahedral) and square pyramidal, respectively. A summary of the key structural features is collated in Table 1. Several trends emerge from examination of these data. The Nimine-Ncarbazolate-N'imine angle increases with the size of the Ae element, so that more room is created to accommodate increasingly large metals. Conversely, the bite angle Nimine-Ae-N'imine narrows substantially when the metal becomes bigger, because the hosting of the metal by the bis(imine) claw then gradually becomes more difficult. The further consequence of these distortions is a gradual increase of the distance between the metal and the best average N=Ciminie-C1-C9a-Ncarb-C8a-C8-C'imine=N' backbone plane, an additional adjustment of the geometrical pattern required to maintain the Ae-Ncarbazolate bond. The Ae-Ncarbazolate interatomic distances raise steadily from Mg to Ba, but these variations essentially match the increase of the ionic radii of the metals.

A c c e p t e d M a n u s c r i p t

Beyond its utility for barium, demonstrated in our earlier communication through the preparation of complexes 1-5, we have hence shown here that {Carb DiPP }H is a versatile platform that can be implemented to the other large alkaline earths, calcium and strontium, and also to their smaller congener, magnesium.

Overall, the preparation of stable Ae complexes has so far been successfully extended to various alkalineearth amides, alkyls, halides, silyls and stannyls. In this respect, and also because it is readily available on large scales within a matter of days, {Carb DiPP }H can be compared in efficiency to the ubiquitous βdiketimine {BDI DiPP }H that has proved so spectacularly successful with calcium and magnesium. Unlike {BDI DiPP }H, the new {Carb DiPP }H has failed so far to deliver isolable "simple" Ae-hydrides, even if the available experimental data (compounds 15 and 16) suggest that these species must be formed at least transiently. We are now modifying the ligand framework in order to take into account the observed fragility of the imine groups and make them less prone to hydride nucleophilic attack and formal hydrosilylation; the outcome of these alterations will be reported elsewhere in due course. On the other hand, {Carb DiPP }H allows for the synthesis of solution-stable barium complexes, something that {BDI DiPP }H could not achieve.

We therefore believe that the bis(imino)carbazole is a useful addition to the growing arsenal of tools available to the synthetic organic and organometallic chemists with an interest in alkaline-earth chemistry, and could contribute significantly to the further expansion of Ae-mediated reactivity and molecular catalysis.

Figure 1 .

 1 Figure 1. Trends in key physico-chemical features of the alkaline earths.

Figure 2 .

 2 Figure 2. Selected ligands used to stabilise heteroleptic barium complexes. (Mes = mesityl, Ad = 1-adamantyl).

Scheme 1 .

 1 Scheme 1. Synthesis of barium, strontium, calcium and magnesium bis(imino)carbazolates 6-14.

  the few relevant examples are confined to the triazenide [{Ar'N3Ar''}BaC6F5] where Ar' = 2,6-Mes2-C6H3 and Ar'' = 2-(2,4,6-i Pr3-C6H2)-C6H4, 47 the highly congested Ba-cyclopentadienyl [{C5Ar*5}BaCH(SiMe3)2•(thf)2] where Ar* = 3,5i Pr2-C6H3, 39 and the iminoanilide [{2-(C=N-DiPP)-C6H4-N-Dipp}BaCH(SiMe3)2•(thf)2].

A c c e

  p t e d M a n u s c r i p t centre, a distance matching that in [{2-(C=N-DiPP)-C6H4-N-Dipp}BaCH(SiMe3)2•(thf)2] (2.840(7) Å 48 ) and [{C5Ar*5}BaCH(SiMe3)2•(thf)2] (2.810(4) Å 39 ).

Figure 3 .

 3 Figure 3. Molecular solid-state structure of [{Carb DiPP }BaN(SiMe3)2•thf] (6). H atoms omitted for clarity. Only the main components of the disordered t Bu groups depicted. Selected interatomic distances (Å) and angles (°): Ba1-N1 = 2.798(3), Ba1-N2 = 2.685(3), Ba1-N3 = 2.809(3), Ba1-N4 = 2.628(3), Ba1-O60 = 2.780(3); N1-Ba1-N2 = 69.97(8), N1-Ba1-N3 = 124.93(8), N1-Ba1-N4 = 114.31(9), N2-Ba1-N3 = 68.98(7), N2-Ba1-N4 = 103.87(8), N3-Ba1-N4 = 109.96(8), N1-Ba1-O60 = 87.10(7), N2-Ba1-O60 = 132.02(8), N3-Ba1-O60 = 94.21(7), N4-Ba1-O60 = 124.07(8).

Figure 4 .

 4 Figure 4. Representation of the molecular solid-state structure of [{Carb DiPP }BaCH(SiMe3)2•thf] (7). H atoms omitted for clarity. Only the main components of the disordered t Bu groups depicted. Selected interatomic distances (Å) and angles (°): Ba1-C11 = 2.821(4), Ba1-N6 = 2.672(3), Ba1-N21 = 2.774(3), Ba1-N51 = 2.801(3), Ba1-O1 = 2.741(3); C11-Ba1-N6 = 103.69(10), C11-Ba1-N21 = 116.04(10), C11-Ba1-N51 = 106.56(10), C11-Ba1-O1 = 120.18(10), N6-Ba1-N21 = 69.63(8), N6-Ba1-N51 = 70.59(8), N6-Ba1-O1 = 135.31(8), N21-Ba1-N51 = 126.80(8), N21-Ba1-O1 = 96.24(9), N51-Ba1-O1 = 88.14(8).

Figure 5 .

 5 Figure 5. Representation of the molecular solid-state structure of [{Carb DiPP }BaN(SiMe2H)2•thf] (8a). H atoms other than SiH omitted for clarity. Only the main component of the disordered SiMe2H moiety at Si1A is depicted. Selected interatomic distances (Å) and angles (°): Ba1-N6 = 2.6951(17), Ba1-N11 = 2.7744(19), Ba1-N51 = 2.7801(18), Ba1-N71 = 2.614(2), Ba1-O1 = 2.7599(19); N6-Ba1-N11 = 70.37(5), N6-Ba1-N51 = 68.75(5), N6-Ba1-N71 = 104.70(7), N6-Ba1-O1 = 136.62(6), N11-Ba1-N51 = 126.60(5), N11-Ba1-N71 = 114.33(7), N11-Ba1-O1 = 90.44(6), N51-Ba1-N71 = 108.17(7), N51-Ba1-O1 = 96.43(6), N71-Ba1-O1 = 118.68(7); Ba1-N71-Si1A = 118.08(12), Ba1-N71-Si2 = 108.58(12). Torsion angles (°): Ba1-N71-Si1A-H1A = 104.65(12), Ba1-N71-Si2-H2 = 17.46(15).

  A c c e p t e d M a n u s c r i p t the Si-H hydrogen at 4.44 ppm, with almost identical Si-H coupling constant as 8a. The FTIR spectrum displays a broad band in at 2021 cm -1 attributed to the the Si-H stretching frequency.Strontium complexes 9-10The proligand {CarbDiPP }H allows for the formation of stable heteroleptic strontium amides. Reacting it in toluene with stoichiometric amounts of [Sr{N(SiMe3)2}2]2 or [Sr{N(SiMe3)2}2•(thf)2] affords [{Carb DiPP }SrN(SiMe3)2] (9) and [{Carb DiPP }SrN(SiMe3)2•thf] (10) as yellow solids in good isolated yields, typically around 60-65% without optimisation (see Scheme 1). The 1 H NMR spectrum of 9 recorded at 25 °C in benzene-d6 is characterised in particular by a singlet at 8.53 ppm assigned to CH=N, and a sharp, high-field singlet integrating for 18H at -0.15 ppm belonging to SiCH3 hydrogen atoms. The resonance for

Figure 6 .

 6 Figure 6. Representation of the molecular solid-state structure of [{Carb DiPP }SrN(SiMe3)2] (9). H atoms and noninteracting hydrocarbon molecule omitted for clarity. Only the main component of the disordered t Bu group depicted. Selected interatomic distances (Å) and angles (°): Sr1-N1 = 2.6201(17), Sr1-N2 = 2.4941(18), Sr1-N3 = 2.6194(18), Sr1-N11 = 2.423(2); N1-Sr1-N2 = 74.74(5), N1-Sr1-N3 = 138.75(6), N1-Sr1-N11 = 111.46(7), N2-Sr1-N3 = 74.67(6), N2-Sr1-N11 = 129.52(7), N3-Sr1-N11 = 109.27(7).

Figure 7 .

 7 Figure 7. Representation of the molecular solid-state structure of [{Carb DiPP }SrN(SiMe3)2•thf] (10). H atoms omitted for clarity. Only the main components of the disordered t Bu groups depicted. Selected interatomic distances (Å) and angles (°): Sr1-N1 = 2.4939(19), Sr1-N21 = 2.6943(18), Sr1-N51 = 2.6774(19), Sr1-N81 = 2.5116(17), Sr1-O11 = 2.6230(17); N1-Sr1-N21 = 110.64(6), N1-Sr1-N51 = 111.02(6), N1-Sr1-N81 = 102.44(6), N1-Sr1-O11 = 121.69(6), N21-Sr1-N51 = 130.69(5), N21-Sr1-N81 = 72.40(5), N21-Sr1-O11 = 93.74(6), N51-Sr1-N81 = 73.92(6), N51-Sr1-O11 = 86.06(6), N81-Sr1-O11 = 135.71(6).

A c c e

  p t e d M a n u s c r i p t

  Hence, the Ca1-I1 interatomic distance in 11 (2.9702(8) Å) is shorter than in the tris(imidazolin-2-ylidene-1-yl)borate [{HB(Im t Bu)3}CaI•thf] (3.0490(9) Å), 56 or in [{2,6-(4-tol)2C6H3}CaI•(thf)3] (3.0754(7) Å), 57 suggesting a stronger bond in the former.

Figure 8 .

 8 Figure 8. Representation of the molecular solid-state structure of [{Carb DiPP }CaI•thf] (11). H atoms and non-interacting benzene molecules omitted for clarity. Selected interatomic distances (Å) and angles (°): Ca1-I1 = 2.9702(8), Ca1-N1 = 2.479(3), Ca1-N2 = 2.317(3), Ca1-N3 = 2.471(3), Ca1-O1 = 2.365(3); I1-Ca1-N1 = 102.87(7), I1-Ca1-N2 = 100.72(7), I1-Ca1-N3 = 108.37(7), I1-Ca1-O1 = 104.33(8), N1-Ca1-N2 = 79.11(10), N1-Ca1-N3 = 144.44(10), N1-Ca1-O1 = 93.97(11), N2-Ca1-N3 = 78.80(10), N2-Ca1-O1 = 154.91(11), N3-Ca1-O1 = 94.36(10).

A c c e

  p t e d M a n u s c r i p t The alkyl complex [{Carb DiPP }CaCH(SiMe3)2•thf] (12) and the solvent-free [{Carb DiPP }CaN(SiMe3)2] amide (13) were obtained in 80-90% yields as yellow crystals following protonolysis between {Carb DiPP }H and [Ca{CH(SiMe3)2}2•(thf)2] or [Ca{N(SiMe3)2}2•(Et2O)2] (see Scheme 1). The resonance for SiCH3 hydrogen atoms appears at -0.22 ppm in the 1 H NMR spectrum of 13; that for CH(SiMe3)2 is located at -1.75 ppm in the spectrum of 12. While 13 is stable in solution, 12 decomposes slowly above 50 °C, via assumed alkylation of the imine by {CH(SiMe3)2} -(see Fig. S29) The molecular structure of the fivecoordinate calcium alkyl 12 is depicted in Fig. 9. It consists of a distorted square pyramid (τ5 = 0.13) that resembles very closely the structure of the barium derivative, 7. The metal atom Ca1 is situated 0.7988(5) Å above the best average plane defined by O1, N6, N21 and N51. The Ca1-C11 distance to the alkyl in 12

( 2 .

 2 539(3) Å) is appreciably longer than in [Ca{CH(SiMe3)2}2•(thf)2] (2.4930(18) Å 44 ) and in the tris(pyrazolyl)borate [{Tp Ad,iPr }CaCH(SiMe3)2] (2.4409(86) Å 38 ), both being four-coordinate compounds;

Figure 9 .

 9 Figure 9. Representation of the molecular solid-state structure of [{Carb DiPP }CaCH(SiMe3)2•thf] (12). H atoms omitted for clarity. Only the main components of the disordered t Bu groups depicted. Selected interatomic distances (Å) and angles (°): Ca1-C11 = 2.539(3), Ca1-N6 = 2.353(2), Ca1-N21 = 2.569(2), Ca1-N51 = 2.594(2), Ca1-O1 = 2.426(2); C11-Ca1-N6 = 107.26(9), C11-Ca1-N21 = 114.59(8), C11-Ca1-N51 = 105.49(9), C11-Ca1-O1 = 107.43(8), N6-Ca1-N21 = 76.38(7), N6-Ca1-N51 = 77.63(7), N6-Ca1-O1 = 144.85(8), N21-Ca1-N51 = 137.04(7), N21-Ca1-O1 = 94.17(7), N51-Ca1-O1 = 87.89(7).

Figure 10 .

 10 Figure 10. Representation of the molecular solid-state structure of [{Carb DiPP }CaN(SiMe3)2] (13). H atoms omitted for clarity. Only the main component of the disordered t Bu group depicted. Selected interatomic distances (Å) and angles (°): Ca1-N1 = 2.2808(14), Ca1-N8 = 2.3403(13), Ca1-N11 = 2.5128(13), Ca1-N31 = 2.5154(14); N1-Ca1-N8 = 132.49(5), N1-Ca1-N11 = 107.55(5), N1-Ca1-N31 = 106.89(5), N8-Ca1-N11 = 77.87(4), N8-Ca1-N31 = 79.86(4), N11-Ca1-N31 = 145.54(5).

Figure 11 .

 11 Figure 11. Representation of the molecular solid-state structure of [{Carb DiPP }Mg n Bu] (14). H atoms omitted for clarity. Only the main components of the disordered n-butyl (76% occupation site at C47A) and t-butyl (at C20) groups depicted. Selected interatomic distances (Å) and angles (°): Mg1-N1 = 2.256(2), Mg1-N2 = 2.029(2), Mg1-N3 = 2.249(2), Mg1-C47A = 2.086(12); N1-Mg1-N2 = 86.13(8), N1-Mg1-N3 = 148.87(8), N1-Mg1-C47A = 98.4(3), N2-Mg1-N3 = 85.09(8), N2-Mg1-C47A = 150.5(2), N3-Mg1-C47A = 103.9(3).

  hydrides were unveiled. An effective route to these compounds has consisted in reacting discrete [Ae]-N(SiMe3]2 silazides with hydrosilanes, typically PhSiH3. This has for instance delivered [{BDI DiPP }CaH•thf]2 as well as the clusters [Sr6H9{N(SiMe3)2}3•(pmdeta)3] (where pmdeta =

Figure 12 .

 12 Figure 12. Representation of the molecular solid-state structure of [Ba2{Carb DiPP,red }{Carb DiPP,silyl }•(thf)2] (15). H atoms, i Pr and t Bu groups omitted for clarity. Selected interatomic distances (Å): Ba1-N1 = 2.714(3), Ba1-N2 = 2.706(4), Ba1-N3 = 2.709(3), Ba1-O201 = 2.731(3), Ba1-O221 = 2.761(4), Ba2-N1 = 2.815(4), Ba2-N2 = 2.857(3), Ba2-N3 = 2.627(3), Ba2-N12 = 2.826(3), Ba2-C69 = 3.042(4), Ba2-C79 = 2.969(4), N1-C13 = 1.479(5), N2-C34 = 1.483(5), N11-C63 = 1.476(5), N13-C84 = 1.474(5).

Figure 13 .

 13 Figure 13. Representation of the molecular solid-state structure of [Ca4{Carb DiPP,red }2H2•(thf)2] (16). H atoms other than hydrides, i Pr and t Bu groups omitted for clarity. Metric parameters not given due to the limited quality of data set and refinement (Rint = 0.2440, R1 = 11.80).

  was successfully isolated in 39% yield from the reaction of 11 with in situ-prepared [KSn(SiMe3)3•thfn]. Examples of known Ca-stannyls are confined to the seminal [Ca(SnMe3)2•(thf)4] 66 and to the much more recent [{BDI DiPP }Ca-(μ2-H)-(SnPh3)Ca{BDI DiPP }] and [{BDI DiPP }Ca(SnPh3)]2. 67 The 1 H NMR spectrum of 17 is slightly different from the barium congener 5, in which the i Pr groups are fluxional at room temperature. Complex 17 shows 4 different i Pr environments, indicating a lack of free rotation of the two DiPP groups; this is unsurprising considering the more sterically saturated coordination sphere of Ca compared to Ba. In the 1 H NMR spectrum, the methyl resonance of the Sn(SiMe3)3 fragment at 0.30 ppm shows scalar H-Sn coupling constant ( 3 J1H-Sn = 10.7 Hz), similar to that of 5 ( 3 J1H-Sn = 10.6 Hz). The 29 Si{ 1 H} INEPT spectrum displays a sharp singlet at -12.5 ppm with clearly visible tin satellites and pertaining coupling constants ( 1 J29Si-119Sn = 27.1 Hz, 1 J29Si-117Sn = 26.0 Hz) much smaller than those in 5 ( 1 JSi-119Sn = 83.5 Hz, 1 JSi-117Sn = 73.1 Hz

Figure 14 .

 14 Figure 14. Representation of the molecular solid-state structure of [{Carb DiPP }CaSn(SiMe3)3•thf] (17). H atoms omitted for clarity. Only the main components of the disordered t Bu and i Pr groups depicted. Selected interatomic distances (Å) and angles (°): Ca1-N1 = 2.519(3), Ca1-N2 = 2.295(3), Ca1-N3 = 2.511(3), Ca1-O1 = 2.349(2), Ca1-Sn1 = 3.2564(7), Sn1-Si1 = 2.6092(12), Sn1-Si2 = 2.5781(11), Sn1-Si3 = 2.5923(12); N1-Ca1-N2 = 77.02(9), N1-Ca1-N3 = 134.39(9), N1-Ca1-O1 = 91.81(9), N1-Ca1-Sn1 = 114.79(6), N2-Ca1-N3 = 78.58(9), N2-Ca1-O1 = 152.79(9), N2-Ca1-Sn1 = 99.14(7), N3-Ca1-O1 = 92.72(9), N3-Ca1-Sn1 = 106.70(7), O1-Ca1-Sn1 = 108.06(6), Ca1-Sn1-Si1 = 121.97(3), Ca1-Sn1-Si2 = 126.11(3), Ca1-Sn1-Si3 = 108.07(3), Si1-Sn1-Si2 = 100.51(4), Si1-Sn1-Si3 = 94.56(4), Si2-Sn1-Si3 = 99.01(4).

  a sqp = square pyramid; trig. pyr. = trigonal pyramid. b Distance to the metal-bound Namide, Calkyl, halide, Si or Sn atom. c Nimine-Ncarbazolate-N'imine angle. d Nimine-Ae-N'imine angle. e Distance to the best N=Ciminie-C1-C9a-Ncarb-C8a-C8-C'imine=N' backbone plane. f Averaged over the two occupancy sites. A c c e p t e d M a n u s c r i p t

Table 1 .

 1 Summary of X-ray crystallographic structural data in Ae complexes 1-17 (Ae = Mg, Ca, Sr or Ba).

	Coord.	Geometry about	Ae-X	Ae-Ncarbazolate	Ni-Ncarb-N'i	Ni-Ae-N'i	Ae distance to
	number	Ae metal a	distance (Å) b	distance (Å)	angle (°) c	angle (°) d	best plane (Å) e

Acknowledgements

The authors thank the ANR for funding (ANR-17-CE07-0017-01) and for the provision of a PhD studentship to P. M. C.

The identity of 15 was unambiguously established by XRD analysis; on the other hand, the complicated NMR data subsequently recorded in toluene-d8 could not be matched with full certainty to the proposed formulation (see Fig. S30). Evidently, the imines in {Carb DiPP } -are prone to nucleophilic attack by a putative Ba-hydride species, and two of them have been reduced to amides in 15. On the other hand, it appears that the other two original imine groups have been subjected to a process akin to hydrosilylation, thus yielding two -CH2N(DiPP)SiH2Ph moieties. Although the sequence of elementary steps leading to the formation of 15 remains unclear, it seems reasonable to hypothesise that the complex results from self-promoted degradation of the initially targeted "[Carb DiPP }BaH•(thf)x]" through a succession of hydride-mediated reduction of imines and hydrosilylation. To support this latter assumption, we note that Ae-hydrides have recently been shown to act as excellent catalysts for imine hydrosilylation. 65 Although it is reproducible, the synthesis of 15 was not further investigated nor optimised.

A c c e p t e d M a n u s c r i p t

Conflicts of interest

There are no conflicts of interest to declare.


Florent Figon
email: florent.figon@univ-tours.fr

Jérôme Casas

Ilaria Ciofini
email: ilaria.ciofini@chimie-paristech.fr

Carlo Adamo

Electronic couplings in the reduced state lie at the origin of color changes of ommochromes

Keywords: Antiradical, Bathochromy, Insect pigment, Ommochrome, Phenoxazine, Time-Dependent Density Functional Theory

Highlights

1. Ommochrome pigments in insects uniquely display red shift upon reduction 2. Color changes were modelled at quantum level using TDDFT 3. Electron-withdrawing auxochromes affect optical properties only in reduced states 4. Electronic couplings that facilitate charge-transfer transitions drive red shifts 5. Larger red shifts are associated to higher antiradical behavior in reduced states Graphical

Introduction

Chemical colors in animals are mostly produced by π-conjugated organic molecules, which contain a chromophore with alternating single and double bonds. Extending the electronic conjugation of chromophores usually leads to bathochromic shifts (i.e. absorption at longer wavelengths), while breaking the π-system induces hypsochromic shifts (i.e. absorption at shorter wavelengths) [START_REF] Needham | The significance of zoochromes[END_REF][START_REF] Nassau | The fifteen causes of color: The physics and chemistry of color[END_REF]. Therefore, even limited chemical reduction of organic dyes and pigments can result in their bleaching due to the saturation of double bonds [START_REF] Needham | The significance of zoochromes[END_REF]. However, one class of biological pigments -the phenoxazinone-based ommochromes-has appeared to be an exception to this rule [START_REF] Figon | Ommochromes in invertebrates: biochemistry and cell biology[END_REF]. Xanthommatin, the best-known and most-widespread ommochrome, is yellow in its oxidized state (oxo-pyrido [3,2-a]phenoxazinone; absorption at 440 nm) but red when reduced to dihydroxanthommatin (oxo-pyrido [3,2-a]hydroxyphenoxazine; absorption at 480 nm) [START_REF] Figon | Ommochromes in invertebrates: biochemistry and cell biology[END_REF]. This unusual color-changing molecular property mediates important biological functions [START_REF] Linzen | The Tryptophan → Ommochrome Pathway in Insects[END_REF], such as nuptial colorations in dragonflies [START_REF] Futahashi | Redox alters yellow dragonflies into red[END_REF], light filtering in insect eyes [START_REF] Langer | Properties and functions of screening pigments in insect eyes[END_REF], as well as electron transfers in a marine worm [START_REF] Horowitz | Studies on the respiratory pigment of Urechis eggs[END_REF][START_REF] Linzen | Über Ommochrome, XV. Über die Identifizierung des "Urechochroms" als Xanthommatin[END_REF] and various insects [START_REF] Linzen | Biochemische und histologische Untersuchungen zur Umfärbung der Raupe von Cerura vinula L[END_REF][START_REF] Harano | A new diaphorase from Bombyx silkworm eggs-Cytochrome c reductase activity mediated with xanthommatin[END_REF][START_REF] Bellamy | The structure and metabolic properties of tissue preparations from Schistocerca gregaria (desert locust)[END_REF]. Besides, the bathochromic reduction of xanthommatin has shown biomimetic potential to craft colorchanging electrochromic devices [START_REF] Kumar | Xanthommatin-Based Electrochromic Displays Inspired by Nature[END_REF]. Thus, unraveling the chemical origin of this distinct bathochromic reduction may have implications for both biologists and material scientists.

In 1972, Schäfer and Geyer synthesized a series of bathochromic and hypsochromic phenoxazinone/phenoxazine pairs to mimic ommochromes, and analyzed them by UV-Vis spectroscopy [START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF]. They showed that only 1-acetyl-2-[amino/hydroxy]-phenoxazin-3-ones (see Figure 1 for the numbering of phenoxazinones) underwent bathochromic reduction. They concluded that this bathochromic shift was due to an increased resonance in the molecular reduced states, in relation to the dipolar structure of the 1-acetyl auxochrome [START_REF] Linzen | The Tryptophan → Ommochrome Pathway in Insects[END_REF][START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF].

Unfortunately, after this pioneering experimental study, the model proposed was never further validated, nor rationalized making use of quantum chemical approaches. Yet, understanding the correlation between geometrical and electronic molecular structures with chromatic shifts in phenoxazinonic dyes and pigments hold great promises to further unravel their natural functions and technological uses.

The recent advances in quantum chemical methods for the description of ground and excited electronic states has greatly helped to rationalize and to predict the optical properties of molecules, especially in the case of organic dyes [START_REF] Jacquemin | Accurate Simulation of Optical Properties in Dyes[END_REF][START_REF] Tommaso | Theoretical approaches for predicting the color of rigid dyes in solution[END_REF]. In particular, the advent of Density Functional Theory (DFT) and Time-Dependent DFT (TDDFT), together with an increased availability of computational resources, has enabled to successfully model a vast number of biochromes, pigments and dyes (see for instance references [START_REF] Adamo | A TDDFT study of the electronic spectrum of s-tetrazine in the gas-phase and in aqueous solution[END_REF][START_REF] Barone | A Multifrequency Virtual Spectrometer for Complex Bio-Organic Systems: Vibronic and Environmental Effects on the UV/Vis Spectrum of Chlorophyll a[END_REF][START_REF]Density-functional methods for excited states[END_REF]). Because of its favorable cost-to-accuracy ratio, we selected TDDFT to investigate the properties of phenoxazinone/phenoxazine pairs firstly to test the validity of Schäfer and Geyer's model and then to rationalize the link between the structure and photophysical properties of ommochromes. However, since TDDFT performances may quantitatively depend on the exchange correlation functional used [START_REF] Tommaso | Theoretical approaches for predicting the color of rigid dyes in solution[END_REF][START_REF] Laurent | TD-DFT benchmarks: A review[END_REF], a preliminary benchmark of commonly applied functionals has been performed on both phenoxazinones and phenoxazines. In particular, we tested a set of global hybrid functionals with various percentages of exact exchange, as well as range-separated hybrids (RSH), which usually perform better for excited states with a substantial amount of non-local charge transfer (CT). Once the computational approach set, several structural (e.g. planarity) and electronic properties (e.g. aromaticity indexes and CT character) were analyzed to establish the structure-property relationship of chromic shifts upon reduction. By applying the same techniques to ommochromes and resorufin, an important hypsochromic biotechnological dye, we rationalized their color-changing behavior upon reduction in terms of electronic and geometric couplings in the reduced phenoxazine state.

Finally, our electronic model of ommochromes provides a mechanistic understanding of their unique optical properties, which helps rationalizing their widespread and various uses in invertebrates, as well as in new biomimetic applications.

Computational Details

Computational Approaches and Benchmarks

All quantum chemical calculations were performed with the Gaussian program [START_REF] Frisch | Gaussian 16 Rev. C.01[END_REF] at the DFT level [START_REF] Kohn | Density functional theory of electronic structure[END_REF] while molecular orbitals were visualized using the Gabedit program [START_REF] Allouche | Gabedit-A graphical user interface for computational chemistry softwares[END_REF].

The B3LYP functional [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF] was used to locate minima since it generally provides reliable geometric parameters for organic compounds [START_REF] Jacquemin | Absorption spectra of azobenzenes simulated with time-dependent density functional theory[END_REF], while Grimme's dispersion correction using the D3(BJ) model [START_REF] Grimme | Effect of the damping function in dispersion corrected density functional theory[END_REF][START_REF] Becke | Exchange-hole dipole moment and the dispersion interaction revisited[END_REF] was also introduced to account for weak interactions.

Bulk solvent effects were considered using the COSMO approach to polarizable continuum models (CPCM) [START_REF] Cossi | Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model[END_REF]. Different solvents were considered depending on experimental conditions [START_REF] Linzen | The Tryptophan → Ommochrome Pathway in Insects[END_REF][START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF][START_REF] Song | Theoretical Study of Resorufin Reduction Mechanism by NaBH 4[END_REF], as specified in Supporting Information (SI). Each structural optimization was followed by a harmonic frequency calculation, ensuring that all computed vibrational frequencies were positive, as they should be for an energy minimum on the potential energy surface. The optimized coordinates of all investigated compounds investigated are listed in SI. The 6-311G(d,p) basis set was chosen for all structural optimizations, after a careful test (see SI for details).

Using these molecular structures optimized at the identified theoretical level (B3LYP-D3(BJ)/6-311G(d,p), vertical absorption energies (E vert ) were then computed within the linear response Time-Dependent DFT (TDDFT) framework [START_REF] Casida | Time-dependent density-functional theory for molecules and molecular solids[END_REF] using the non-equilibrium approximation of CPCM [START_REF] Cossi | Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model[END_REF]. It is well known that the computed electronic adsorption energies depend on the chosen DFT approach. While some general trends appear from previous detailed benchmarks [START_REF] Laurent | TD-DFT benchmarks: A review[END_REF][START_REF] Jacquemin | Extensive TD-DFT Benchmark: Singlet-Excited States of Organic Molecules[END_REF], it is a better practice to verify the performances on the systems under investigations. To this end, as functionals based on local-density (LDA) and generalized gradient approximation (GGA) are known to perform poorly for the calculation of vertical excited states [START_REF] Jacquemin | Extensive TD-DFT Benchmark: Singlet-Excited States of Organic Molecules[END_REF], TDDFT calculations were carried out only considering 12 functionals, chosen among the most representative (see SI for details) All 18 phenoxazinone/phenoxazine pairs depicted in Fig 1 were used for this TDDFT benchmark, while the experimental values were taken from reference [START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF]. If a compound in this dataset showed broad/unresolved absorbance peaks, the one with the highest wavelength was systematically used. The performance of the selected functionals was evaluated suing the following criteria: mean absolute errors (MAE) on ΔE vert (target to be below 0.2 eV), comparable errors for both phenoxazinones (ΔE vert ox) and phenoxazines (ΔE vert red), MAE on chromic shifts (defined as ΔE vert shift = ΔE vert red -ΔE vert ox; target to be below 0.2 eV), comparable errors for both bathochromic and hypsochromic redox pairs, high correlations with experimental values for both absorption energies and chromic shifts, and high number of wellpredicted chromic shifts.

Based on this benchmark, whose results are reported and commented in the SI, the M05 functional [START_REF] Zhao | Exchange-correlation functional with broad accuracy for metallic and nonmetallic compounds, kinetics, and noncovalent interactions[END_REF] results as the best compromise and the most reliable functional for predicting the chromic reduction of phenoxazinones to phenoxazines. Following previous experience [START_REF] Ciofini | Accurate Evaluation of Valence and Low-Lying Rydberg States with Standard Time-Dependent Density Functional Theory[END_REF] and the test carried out for the 2-amino-7-hydroxyphenoxazin-3-one molecule (see SI for details), all the vertical transition energies were computed using the 6-31+G(d) basis set.

Computation of Descriptors

Several descriptors were considered in order to assess the relationship between the structural and electronic parameters of the considered dyes and their optical behavior.

The Harmonic oscillator model of aromaticity for heterocycle electron delocalization (HOMHED) is a geometric index of aromaticity that evaluates bond conjugation by comparing bond lengths of a compound to those of an ideal aromatic compound [START_REF] Frizzo | Aromaticity in heterocycles: new HOMA index parametrization[END_REF]. The closer to 1 HOMHED is, the more conjugated, and thus aromatic, the compound is. The HOMED values were computed using the Gabedit program and the parameters described in reference [START_REF] Frizzo | Aromaticity in heterocycles: new HOMA index parametrization[END_REF].

Another commonly applied index is the so-called nucleus-independent chemical shifts (NICS) which is based on the deshielding induced at a center of an aromatic ring by the ring current [START_REF] Chen | Nucleus-Independent Chemical Shifts (NICS) as an Aromaticity Criterion[END_REF]. The more deshielded NICS is, the more aromatic the compound. The NICS indexes were computed at the center of each ring (NICS(0)) using the above mentioned level of theory and the gauge-including atomic orbital (GIAO) method [START_REF] Cheeseman | A comparison of models for calculating nuclear magnetic resonance shielding tensors[END_REF].

The third descriptor is the charge-transfer distance (DCT) that evaluates the hole-electron mean distance associated to an electronic excitation, thus unraveling its nature (local or charge transfer). It is easily computed measuring the distance between the barycenters of charge distributions corresponding to a density depletion and a density increase upon excitation [START_REF] Bahers | A Qualitative Index of Spatial Extent in Charge-Transfer Excitations[END_REF].

Finally, some descriptors, issued from the so-called conceptual DFT [START_REF] Proft | Conceptual and Computational DFT in the Study of Aromaticity[END_REF], were also considered, including electron affinity (EA), hardness (η) and electro-accepting power (ω + ).

The latter measures the local charge-acceptance of a compound and thus its capacity to accept fractions of electron during charge-transfer phenomena [START_REF] Gázquez | Electrodonating and Electroaccepting Powers[END_REF][START_REF] Pearson | The electronic chemical potential and chemical hardness[END_REF].

Results

A total of 15 molecular pairs from Schäfer and Geyer's series [START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF] were considered for a detailed analysis (see SI for the explanation on this choice). Electronic and geometric properties of the bathochromic ommochrome pair xanthommatin/dihydroxanthommatin and the hypsochromic dye pair resorufin/dihydroresorufin were also investigated for sake of completeness.

Experimental UV-Visible data for these molecules were taken from references [START_REF] Figon | Ommochromes in invertebrates: biochemistry and cell biology[END_REF] and [START_REF] Kitson | The Oxidative Addition Reaction between Compounds of Resorufin (7-Hydroxy-3Hphenoxazin-3-one) and 2-Mercaptoethanol[END_REF], respectively.

Schäfer and Geyer's Phenoxazine Series

Nearly 50 years ago, Schäfer and Geyer proposed that the bathochromic shifts of some substituted phenoxazinones upon reduction could be related to an increase of resonance forms [START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF], and thus to a greater conjugation of the phenoxazine chromophore. To test this hypothesis, we computed two indices that can be related to the degree of delocalization and aromaticity in a molecule, namely the HOMHED and NICS(0) indexes [START_REF] Proft | Conceptual and Computational DFT in the Study of Aromaticity[END_REF].

The HOMHED index basically considers computed structural parameters, namely related to bond length alternation between single and double bonds, to evaluate the degree of electron delocalization, as detailed in the computational section. This index has been evaluated for two possible delocalization patterns in the molecule as highlighted in Figure 2A In order to have a general picture of these behaviors and to propose a more general rationalization of the chromic reduction of phenoxazinones to phenoxazines, we analyzed the general trends arising from the mean values and dispersion of the set of structural and electronic parameters chosen, as reported in Table 1.

First, we note a significant structural difference between phenoxazines and phenoxazinones, the first being sizably less planar that the latter (+11.5°; Table 1), in agreement with the expected sp 3 configuration of the phenoxazine nitrogen. Consistently, in average, both the cHOMHED and the NICS(0) indicate an increased aromaticity in the reduced systems (Table 1). Nonetheless, no correlation between chromicity and structural parameters can be directly established.

At the ground electronic state (GS), reduction leads to the destabilization of both the highest occupied molecular orbital (HOMO, +1.47 eV) and the lowest unoccupied molecular orbital (LUMO, +1.7 eV; Table 1). The HOMO-LUMO gap is only slightly higher in phenoxazines (+0.23 eV) but the spreading of values for these systems is computed to be three times larger than for phenoxazinones (Table 1), thus indicating that phenoxazines present both significantly lower and higher HOMO-LUMO gaps than phenoxazinones. This pattern is mirrored by those of E vert and E exp , consistently with the presence of batho and hypsochromic pairs. Looking at properties involving excited states, reduction leads to oscillator strengths and transition dipole moments more than twice lower than in phenoxazinones (Table 1). These data are in agreement with the hypochromic shift (i.e. less intense absorption) observed upon reduction to phenoxazines [START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF]. Finally, dipole moments and, consistently, the charge-transfer distances (DCT) associated to excited states are computed to be higher in phenoxazines (+4.06 D and +0.9 Å, respectively; Table 1). This latter finding indicates a larger intramolecular charge transfer (ICT) character associated to electronic transitions in phenoxazines than in phenoxazinones.

More interestingly, we note that dispersion of the values associated to most of the electronic and structural parameters is greatly larger in phenoxazines (Table 1 andFig Furthermore, the range of HOMO-LUMO gap values in phenoxazines is primarily associated to a wider variation in LUMO than in HOMO energies (Table 1

and Fig S10).

All these data suggest that a simple correlation could link chromic shifts to LUMO energies of reduced phenoxazines, which are in fine directly related to their electron affinity (EA) and thus to their reactivity and antiradical properties [START_REF] Martínez | Donator Acceptor Map for Carotenoids, Melatonin and Vitamins[END_REF][START_REF] Romero | Antiradical capacity of ommochromes[END_REF]. Indeed, a clear correlation is found between computed chromic shift and electron affinity of phenoxazines (EAred, Fig 4A; Since LUMOs energies can be tuned by the presence of electron-withdrawing auxochromic groups (EWA) [START_REF] Mao | Unraveling substituent effects on frontier orbitals of conjugated molecules using an absolutely localized molecular orbital based analysis[END_REF], we computed the frontier orbital energies of the different EWA that can be placed in positions 1 and 8 (Fig 1). Consistently with our hypothesis, the two EWA (i.e. acetyl and γ-oxobutenyl) with the lowest LUMO energies and highest electroaccepting powers, ⍵ + , are associated to bathochromic shifts, while EWA with high LUMO energies (such as cyano or carboxy substituted) induce hypsochromic shifts (Table 2). Of note, the tert.butyl-carbonyl EWA shows a hypsochromic shift whereas its LUMO energy is close to that of acetyl. This result indicates that other parameters than the LUMO stabilization may play a role in the observed shifts. In particular, tert.butyl-carbonyl is a bulky EWA compared to acetyl and carbomethoxy. In this case, as already proposed by Schäfer and Geyer, steric hindrance can altered excitation energies by constraining the carbonyl out-of-plane [START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF]. Such an effect is observed in the case of compound 14r for which a large dihedral angle between ring C and carbonyl in position 1 is computed (59° in 14r vs 8° in 1r) (Fig S11). To test whether this torsion destabilized the LUMO and thereby induced the hypsochromic shift, we computed the E vert as a function of the torsional angle for compounds 1r, 14r and 15r (Fig 5A). The results show that for dihedral angles greater than 30° there is a significant hypsochromic effect, with the maximum hypsochromy obtained around 90° (from 0.30 eV for 1r to 0.83 eV for 15r; 2). However, 14r can never reach the bathochromicity of 1r, even at angles near 0° (Fig 5A). These results indicate that the steric hindrance of tert.butyl-carbonyl explains, partly at least, the hypsochromicity of 14r.

Next, we considered model systems obtained by functionalization of the 2-hydroxyphenoxazin-3-one/2,3-dimethoxy-phenoxazine pairs with EWA with either stabilized (nitro) or destabilized (carboxamide) LUMOs (Table S1 andFig S1).

Application to Ommochromes and Other Phenoxazinone Dyes

Chromic shifts of two other important pairs of natural and technological relevance were next considered, namely xanthommatin/dihydroxanthommatin (bathochromic invertebrate pigments) and resorufin/dihydroresorufin (hypsochromic biotechnological dyes; see Figure 6 and Table S2). (HOMO-LUMO) and 3.64 eV (HOMO-L+1), thus they lie within, and even beyond, the range of bathochromic transitions already investigated in this study (Table 1). In addition, dihydroxanthommatin hardness is the lowest we computed (Table S2 and Table 1). Excited state computations consistently predict two bathochromically shifted electronic transitions, which involve a HOMO-LUMO and a HOMO-L+1 transitions, respectively (Table S2). Both transitions are characterized by a significant ICT (Table S1 and Fig 6). The first excited state (S1) is less intense than the second (S2) and their ΔE vert bracket the experimental value (ΔES1 vert = 2.25 eV < ΔE exp = 2.58 eV < ΔES2 vert = 2.69 eV), which corresponds to the maximum of a broad absorption peak [START_REF] Linzen | The Tryptophan → Ommochrome Pathway in Insects[END_REF].

On the contrary, the resorufin/dihydroresorufin pair presents all the characteristics associated to hypsochromic shifts: the absence of EWA, a small HOMO-LUMO gap in the oxidized state, a highly destabilized LUMO and high chemical hardness (Fig 6 and Table S2).

Accordingly, TD-M05 calculations predict a highly hypsochromic shift upon reduction (1.05 eV; Table S2). To the best of our knowledge, the exact experimental absorbance of dihydroresorufin has never been reported in the literature, but resorufin is known to lose its color upon reduction [START_REF] Song | Theoretical Study of Resorufin Reduction Mechanism by NaBH 4[END_REF], which is in agreement with our calculations.

Discussion

The above reported results clearly show that the model originally proposed by Schäfer and Geyer to explain the experimentally observed chromic shifts in substituted phenoxazinone/phenoxazine pairs, which correlates bathochromic shifts to an increase in resonance structures [START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF], is unable to explain qualitatively why 1-acetyl-phenoxazines are bathochromic and why the closely-related 1-carbomethoxy-phenoxazines are hypsochromic.

Our analysis, based on modern descriptors of aromaticity, invalidates the general applicability of this model, showing that there is no clear correlation between descriptors of aromaticity and bond conjugation with color changes upon reduction. On the other hand, it appears that bathochromic and hypsochromic shifts correlate well with electronic properties of reduced forms, in particular with all descriptors containing information on the strength and nature of the EWA present in the molecule, such as LUMO energy, electro-accepting power and EA. proposed by Schäfer and Geyer [START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF]. Overall, we propose that electronic and geometric interactions of EWA with the phenoxazine UMOs produce a wide range of ICT energies, which ultimately leads to a continuous hypso-to-bathochromic scale (Fig 7B ).

Note that this model can be refined in several ways. For example, we could take into account the effect of electron-donating auxochromes (EDA) on the phenoxazine HOMO. This would explain why HOMO-LUMO gaps, rather than LUMO alone, better predicted chromic shifts in the complete set of investigated compounds (in which EDA in position 2 varies). We could also add the effect of EWA in other positions than 1. From the investigated compounds, it appears that EWA at position 5, 6, 7 and 8 have an effect on the phenoxazinone LUMO too, which (slightly) modifies the threshold for bathochromy. Most interestingly, EWA in position 8 could interact with the EWA in position 1 either synergistically (both EWA are similar and stabilize the same ICT, see 8r), additively (different bathochromic EWA stabilize two different ICT, see dihydroxanthommatin) or antagonistically (hypsochromic and bathochromic EWA lead to ICT not stabilized enough, see 9r). Note that for pair 9 TD-M05 calculations could not predict the correct color-changing behavior upon reduction. This indicates that other parameters not modelled in this study, such as direct solvent interactions [START_REF] Adamo | A TDDFT study of the electronic spectrum of s-tetrazine in the gas-phase and in aqueous solution[END_REF], could also finely tune the color-changing effect of reduction.

Of note, the structure-to-property relation found here has also implication for the reactivity of these compounds. Indeed, HOMO-LUMO gap and LUMO energy are known to be directly related to hardness and electron affinity, respectively, which define some aspects of the chemical reactivity of a compound [START_REF] Pearson | The electronic chemical potential and chemical hardness[END_REF]. Our calculations showed that those two chemical parameters were highly correlated with the direction of chromic shift. We conclude that the softer and the more electrophilic a phenoxazine is, the more bathochromic and antiradical it becomes.

Conclusions

In this study, we unraveled the electronic mechanisms behind the atypical bathochromic (i.e. red shift) reduction of ommochrome pigments in invertebrates, particularly at play in the ecologically important nuptial coloration of dragonflies [START_REF] Futahashi | Redox alters yellow dragonflies into red[END_REF]. We established the relation between the nature and strength of electron-withdrawing auxochromes (EWA) that rules the magnitude of the phenoxazine intramolecular charge-transfer and the observed chromic shift.

Other parameters, such as the angle formed by EWA with the attached phenoxazine ring, tune the direction of the chromic shift upon reduction.

From a technological viewpoint, crafting phenoxazines with new EWAs that allow a wider range of chromic shifts than currently available [START_REF] Kumar | Xanthommatin-Based Electrochromic Displays Inspired by Nature[END_REF] might foster the field of ommochrome-based electro-chromic devices. The influence of EWA conjugation on chromic shifts suggests that these devices could be made even more flexible by dynamically altering the torsion angle of EWAs, for example through tunable interactions with the coated surface.

From a biological viewpoint, it is well established that optical properties and chemical behaviors are both important functions of pigments [START_REF] Needham | The significance of zoochromes[END_REF][START_REF] Mcgraw | The antioxidant function of many animal pigments: are there consistent health benefits of sexually selected colourants?[END_REF][START_REF] Gandía-Herrero | Biological Activities of Plant Pigments Betalains[END_REF][START_REF] Ostrovsky | Vertebrate Eye Melanosomes and Invertebrate Eye Ommochromes as Antioxidant Cell Organelles: Part 2[END_REF]. By linking together those two functions through EWA properties, our study suggests that invertebrates may have favored bathochromic ommochromes because of both their better capacity to protect cells against reactive species in the reduced state, as previously suggested [START_REF] Romero | Antiradical capacity of ommochromes[END_REF], and their tunable red shift, which we discuss in two biological situations. First, the occurrence of a decarboxylated form of xanthommatin can be explained by its decarboxylated EWA producing a less bathochromic reduced state. It could therefore allow a wider range of colorations than with xanthommatin alone, as seen in cephalopods [START_REF] Williams | Contributions of Phenoxazone-Based Pigments to the Structure and Function of Nanostructured Granules in Squid Chromatophores[END_REF]. Second, it has long been known that absorbance spectra of ommochromes are red-shifted in insects eyes compared to in vitro ([6,48,49]). We propose that properties of the matrix in which ommochromes are deposited and that alter their absorbance, such as proteins [START_REF] Langer | Über die Pigmentgranula im Facettenauge von Calliphora erythrocephala[END_REF][START_REF] Williams | Dynamic pigmentary and structural coloration within cephalopod chromatophore organs[END_REF] and metals [START_REF] Liao | Ditopic Complexation of Selenite Anions or Calcium Cations by Pirenoxine: An Implication for Anti-Cataractogenesis[END_REF][START_REF] White | Calcium is a component of ommochrome pigment granules in insect eyes[END_REF], do so by modulating the electrophilicity and the conjugation of ommochrome EWAs, leading ultimately to their bathochromic behaviors uniquely observed in vivo.

In conclusion, our study reinforces the idea that the unique electronic properties of ommochromes make them a powerful technological and biological framework to tune rapidly and efficiently color-changing materials.

Tables

  and Figure S7 namely: i) the pattern involving delocalization along ring C (cHOMHED, Fig 2A) and ii) the delocalization pattern along all bonds involved in the resonant forms produced by substituents in position 1, 2 and the phenoxazine nitrogen (sHOMHED, Fig S7). In contrast with the experimental hypothesis, no clear correlation with chromic shifts can be drawn in the case of the sHOMHED pathway Fig S7) while, in the case of the cHOMHED index, a partial positive correlation (R 2 = 0.77) can be found (Fig 2B). According to this index, hypsochromicity is associated with an increase in aromaticity of ring C. This partial correlation is nonetheless lost when considering the NICS(0) index, an index based on electronic properties. While considering only bathochromic pairs (Fig 2C), a positive correlation between aromaticity and bathochromicity can be found (R 2 batho = 0.79), in agreement with the experimental hypothesis, no correlation can be found if both batho and hypsochromic pairs are considered. Indeed three hypsochromic phenoxazines show the lowest NICS(0) and thus the highest aromaticity. In short, these two measures of the aromaticity, which are different in nature (electronic and structural origin), do not support the hypothesis of Schäfer and Geyer on the observed color change of ommochromes and, particularly on the different batho and hypsochromic behavior.

  3A).Therefore, we can formulate the hypothesis that different chromic shifts are essentially driven by differences in the reduced systems independently of the corresponding oxidized ones. Consistently to this hypothesis, chromic shifts show a relatively strong linear correlation (R 2 = 0.84) with E vert red (Fig 3B) but no correlation at all with E vert ox (Fig S8). In line with these results, there is a clear distinction between E vert red of bathochromic and hypsochromic compounds, while E vert ox do no significantly differ (Fig 3A).To further validate the hypothesis that chromicity is mainly linked to properties of the reduced forms, the electronic properties of four representative pairs, including two bathochromic (1 and 2) and two hypsochromic phenoxazines (14 and 15), were considered (FigS9). In all cases, since the π-π* excited states of interest have a dominant HOMO-LUMO character for both oxidized and reduced compounds, energies of the HOMO and LUMO were firstly analyzed. Consistently with the results presented in Table1, only the molecular orbital energies of the reduced compounds vary consistently with chromic shifts (FigS10).

R 2 =

 2 0.61). This correlation is further improved by considering chemical hardness in the reduced states (ηred, Fig 4B; R 2 = 0.82), which implicitly takes into account also the variation of the energy of the HOMO level.

Fig

  Fig 5A). Below 60°, 14r becomes less hypochromic than 15r in its optimized geometry (Fig 5A), in agreement with the lower LUMO energy of tert.butyl-carbonyl compared to carbomethoxy (Table2). However, 14r can never reach the bathochromicity of 1r, even at

  5B-C). All substituents were placed in position 1 and forced to lie within ring C plane after geometrical optimization to avoid torsion of molecular orbitals due to steric hindrance. The results show that LUMO energies of substituents explain 95 % of the variation in chromic shifts upon reduction (Fig 5B). They also confirme that increasing the electro-accepting power of substituents in position 1 leads to more bathochromic phenoxazines (Fig 5B-C and Table

The 8 -

 8 substituted-oxo-pyrido[3,2-a]phenoxazin-3-one xanthommatin presents HOMO (-6.89 eV) and LUMO (-3.35 eV) energies very close to the mean HOMO and LUMO energies of the phenoxazinones investigated above (compare Fig 6 with Table 1 and Fig S9). The corresponding reduced 8-substituted-oxo-pyrido[3,2-a]-3-hydroxy-phenoxazine dihydroxanthommatin possesses not only a highly stabilized LUMO (-2.02 eV), but also a relatively stabilized LUMO+1 (-1.59 eV). Overall, the molecular orbitals of xanthommatin and dihydroxanthommatin resemble those of the phenoxazinones and phenoxazines described above both qualitatively and quantitatively (Fig 6 and Fig S9), which indicates that the effect of EWA on the reduced state should also control their chromic shifts. The substituent in position 8 if ommochromes is closely related to acetyl, while the oxo-pyrido ring attached on positions 1 and 2 resembles γ-oxo-butenyl. The two corresponding carbonyl functions lie within ring A and C planes, respectively. All these characteristics predicted a bathochromic shift upon reduction. Accordingly, the molecular orbital gaps of dihydroxanthommatin are 3.21 eV

  On this basis, to explain the color-changing behavior of substituted phenoxazinones upon reduction, we propose the following structure-property model. (Fig 7). The bright excited state of phenoxazinones (i.e. oxidized forms) that is responsible for the yellow-orange color of this chromophore is of Locally Excited (LE) character stemming from a π-π* transition. This transition is not particularity affected by EWA in position 1, explaining why excitation energies of substituted phenoxazinones do not vary significantly as a function of the EWA. Therefore, the energy of this LE state in phenoxazinones defines a common reference for bathochromy and hypsochromy of substituted phenoxazines (Fig 7B). The 3-hydroxy-phenoxazine chromophore (i.e the reduced form of the pair) is on the other hand characterized by a bright excited state displaying a partial intramolecular CT (ICT) character (Fig 7A). When 3-hydroxyphenoxazine is substituted in position 1 with a EWA, the EWA LUMO hybridizes with the phenoxazine UMOs and stabilizes them, thus lowering the energy of ICT. The strength of stabilization depends primarily on two factors (Fig 7A): (1) an electronic one that is the energy of EWA LUMO and (2) a structural one that is the magnitude of the dihedral angle formed by the EWA with the corresponding phenoxazine ring ruling its conjugation. First, EWAs with high (low) electro-accepting powers stabilize (destabilize) the corresponding substituted phenoxazine UMOs, which decreases (increases) their excitation energies and leads to bathochromic (hypsochromic) shifts upon reduction (Fig 7B). This translates into ICT associated to lower (higher) energies, hence into red (yellow)-shifted colors (Fig 7B). This mechanism explains why acetyl and carbomethoxy induced bathochromic and hypsochromic shifts, respectively.Second, from a structural viewpoint, when a substituent in position 1 is coplanar with the phenoxazine ring, the (L)UMOs are fully conjugated and thus highly stabilized. Structural decoupling decreases this effect (Fig 7B)explaining why sterically hindered EWA, despite having a high electro-accepting power can indeed induce hypsochromic shifts, as in the case of the tert.butyl-carbonyl. The same applies for the methylated phenoxazine nitrogen that induced a hypsochromic shift because of steric hindrance with the acetyl in position 1, as already

Figure captions Figure 1 .

 captions1 Figure captionsFigure 1. Set of substituted phenoxazin-3-ones and 3-methoxy-phenoxazines investigated in this study.

Figure 2 .

 2 Figure 2. Computed vertical chromic shifts (E vert shift) of phenoxazinone/phenoxazine pairs as a function of two aromaticity indexes (A), cHOMHED (B) and NICS(0) (C), of phenoxazines. Batho, bathochromy. Hypso, hypsochromy. Red, reduced state (i.e. phenoxazine).

Figure 3 .

 3 Figure 3. Relationship between computed vertical excitation energies (E vert ) chromic shifts of phenoxazinone/phenoxazine pairs. Batho, bathochromy. Hypso, hypsochromy. Red, reduced state (i.e. phenoxazine).

Figure 4 .

 4 Figure 4. Comparison of chromic shifts (E vert shift) of phenoxazinone/phenoxazine pairs with electron affinity (EA, A) and chemical hardness (η, B) of phenoxazines. Batho, bathochromy. Hypso, hypsochromy. Red, reduced state (i.e. phenoxazine).

Figure 5 .

 5 Figure 5. Comparison of computed chromic shifts (E vert shift) of phenoxazinone/phenoxazine pairs with geometric (A) and electronic (B-C) properties of electron-withdrawing auxochromes (EWA) in position 1. Batho, bathochromy. Hypso, hypsochromy. Arrow, angle at the optimized geometry.

Figure 6

 6 Figure 6. Orbital diagrams of the bathochromic ommochrome pair xanthommatin/dihydroxanthommatin and the hypsochromic pair resorufin/dihydroresorufin. ICTs, intramolecular charge-transfers; LE, local excitation.

Figure 7 .

 7 Figure 7. Model of the effect of geometric and electronic couplings on chromic shifts and chemical behaviors of phenoxazinone/phenoxazine pairs upon reduction. EWA, electronwithdrawing auxochrome. EDA, electron-donating auxochrome. ICT, intramolecular charge-transfer. e -(*) , (excited) electron.

Figures Figure 1

 1 Figures

Figure

  Figure 7

7

 7 Figure 7

Table 1 .

 1 Average values and dispersion of electronic and structural parameters computed for oxidized phenoxazinones and reduced phenoxazines.

		Phenoxazinone	Phenoxazine
		(mean ± SD)	(mean ± SD)
	ΔE exp (eV) a	2,80 ± 0,10	2,91 ± 0,20
	ΔE vert (eV)	2,71 ± 0,09	2,75 ± 0,23
	Phenoxazinone/Phenoxazine	0,6	12,0
	dihedral angle (°)	± 0,3	± 5,9
	HOMO energy	-6,84	-5,37
	(eV)	± 0,14	± 0,10
	LUMO energy	-3,34	-1,64
	(eV)	± 0,13	± 0,25
	HOMO-LUMO	3,50	3,73
	gap (eV)	± 0,08	± 0,26
	Oscillator	0,83	0,40
	strength	± 0,21	± 0,15
	Transition dipole	12,45	5,85
	moment (D)	± 3,41	± 2,58
	Dipole moment	6,34	6,52
	of GS (D)	± 1,98	± 2,56
	Dipole moment	8,29	12,35
	of ES (D)	± 2,70	± 4,19
	NICS(0) of ring C	-0,87	-8,77
	(ppm)	± 0,64	± 0,54
	cHOMHED of ring C	0,65 ± 0,05	0,97 ± 0,01
	DCT (Å)	1,71 ± 0,30	2,61 ± 0,60

a Experimental values are taken from reference

[START_REF] Schäfer | Über das redoxverhalten der ommochrome UV/S-spektren von 3hphenoxazinonen-(3) und phenoxazinen[END_REF]

Table 2 .

 2 Computed chemical descriptors (in eV) of electron-withdrawing auxochromes (EWA) in relation with the chromic shifts they induce experimentally in phenoxazinone/phenoxazine pairs.

	EWA	HOMO LUMO	H-L gap	⍵ +
		bathochromic shifts
	Acetyl	-7.64	-0.59	7.06	1.01
	γ-oxo-butenyl	-7.56	-1.59	5.97	2.05
		hypsochromic shifts
	Carbomethoxy	-8.59	0.01	8.60	0.72
	Cyano	-10.61	0.32	10.93	0.74
	tert.butyl-carbonyl	-7.42	-0.57	6.85	0.98

Acknowledgments

We are grateful to Alistar Ottochian, Michele Turelli and Bernardino Tirri for their technical support. F.F. thanks the ENS de Lyon for financial support. I.C. gratefully acknowledges support from the European Research Council (ERC) for funding under the European Union's Horizon 2020 research and innovation program (grant agreement No 648558, STRIGES CoG grant). This works formed part of the doctoral dissertation of F.F. under the supervision of J.C.


Molka Tounsi Dhouib

Catherine Faron

Andrea G B Tettamanzi

Injection of Knowledge in a Sourcing Recommender System

Recommender systems provide suggestions to users for items that best meet their needs. In this work, we study the benefits of using knowledge and, more specifically, a 'bag of concepts' representation to enhance a recommender system in the sourcing domain. We tested our approach in a real-world case study provided by the Silex company. The experimental results show that injecting knowledge in the recommendation process outperforms word embedding approaches.

I. INTRODUCTION

Nowadays, Recommender systems (RS) are primarily used in commercial applications to provide a personalized experience and suggest relevant items to users such as music, movies, books, trips, products. In the context of the Silex company, our goal is to propose a RS that can predict relevant providers (items) that are likely to be of interest for a service request (user). Silex simplifies the sourcing process by allowing companies to provide a description of their professional activities, their offers and/or the services they are looking for in natural language, in French.

In this paper, we propose to combine a conceptual representation of texts to their representation based on word embedding to enhance the recommendation in the sourcing domain. Our main research question is: Can the integration of domain knowledge enhance the performance of a recommender system in our use case? We focus on the following sub-questions: (i) What is the best way to integrate domain knowledge into the representation of service requests and providers in order to enhance the quality of recommendations? (ii) To what extent does the injection of domain knowledge improve the performance of the system?

The remainder of this paper is organized as follows. Section II gives an overview of state of the art recommendation approaches. Section III presents the recommendation approach we propose. Section IV reports and discusses the results of our experiments in the sourcing domain. Section V concludes and provides an outline of future work.

II. RELATED WORK

There are four main approaches to RS:

• Content-based recommendation [START_REF] Lang | Newsweeder: Learning to filter netnews[END_REF]: This approach consists in analyzing the content (i.e., set of attributes or metadata) of items liked by users in the past and suggests items with similar content [START_REF] Yu | Data mining and personalization technologies[END_REF]. • Collaborative filtering [START_REF] Shardanand | Social information filtering: algorithms for automating "word of mouth[END_REF]: It is based on the feedback (rating) on items provided by similar users. • Knowledge-based recommendation [START_REF] Ameen | Knowledge based recommendation system in semantic web -a survey[END_REF]: This approach consists in using ontologies to model knowledge about the user context, the item context and the domain. • Hybrid recommendation [START_REF] Adomavicius | Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions[END_REF]: This approach combines the three above ones, to take advantage of the benefits of each of them. Our method is at the intersection of the content-based and knowledge-based approaches. The idea behind our approach is to take advantage of the power of word embedding, which approximates a general semantic relation, and the power of domain knowledge, which models a more specific semantic relation, to provide high quality recommendations.

III. PROPOSED APPROACH

Our proposal relies on the use of domain knowledge that can be captured into a thesaurus or an ontology. In the following we will refer to vocabulary indistinctly as a thesaurus or an ontology. In the experiments reported in this paper and conducted to answer the Silex use case, we are using a sourcing domain vocabulary, as we exploit different types of relationship between concepts and their labels (and not intentional definitions).

Our approach comprises five steps: (i) construction of a vocabulary for the sourcing domain, (ii) entity recognition from the textual descriptions of service requests and providers, (iii) entity management, (iv) vector representation of service requests and providers, and (v) recommendation algorithm.

A. Vocabulary for the Sourcing Domain

The preliminary step of our approach is the construction of a vocabulary to capture the sourcing knowledge [START_REF] Dhouib | Construction d'ontologie pour le domaine du sourcing[END_REF] by identifying and combining several relevant standard metadata repositories such as ESCO,1 ROME,2 NAF, 3 UNSPSC, 4 and CPF, 5 . Our sourcing vocabulary gathers 124040 concepts. We proposed an alignment method and applied it to automatically align the above-mentioned vocabularies, which where partially overlapping [START_REF] Dhouib | An ontology alignment approach combining word embedding and the radius measure[END_REF].

B. Sourcing Named Entity Recognizer

The second step of our approach consists in extracting the relevant entities (i.e., services, products, occupations, skills, and business sectors) from the textual descriptions (i.e. service requests and company descriptions), based on our sourcing vocabulary. To handle this type of textual data, our approach [START_REF] Daoud | A hybrid bi-lstm-crf model for sequence labeling applied tothe sourcing domain," 6ème conférence sur les Applications Pratiques de l'Intelligence Artificielle APIA[END_REF] is based on a Bidirectional Long-term and Short-term Mermory (Bi-LSTM) encodes an input textual description and a Conditional Random Fields model (CRF) labels every word to detect entities. In addition to word embedding, we extract three other kinds of embedding for each word in the textual description: (i) a character-level embedding to represent rare words or words with spelling errors; (ii) a syntax embedding to locate the user's need in a description: and (iii) a position embedding to push the model to understand it is highly likely that the words at the beginning of the text are relevant information.

C. Entity Linking with the Sourcing Vocabulary

In order to link the named entities extracted from the descriptions of service requests and providers with the closest concepts in the sourcing vocabulary, we defined a similarity measure between an entity and a concept.

We first represent each extracted entity and each concept of the sourcing vocabulary by an embedding vector which is computed as the average of the word embedding vectors of all the words participating in the entity or label of concept and occurring in the dictionary. In the absence of a large corpus available to train a word embedding model for our use case, we use fastText pre-trained word vectors for French.

The embedding vector for an entity or a (label of) concept x is thus computed as

V (x) = 1 n n i=1 w i , (1)
where n is the number of words of the dictionary occurring in x and w i ∈ R 300 denotes the word embedding vector of the ith word of x occurring in the dictionary. If a word of x does not belong to the dictionary, it is just ignored.

Then we define the similarity between an entity e extracted form a request or provider description and a concept c in the sourcing vocabulary as the cosine similarity between their embedding vectors V (e) and V (c):

sim(e, c) = V (e) • V (c) ||V (e)|| • ||V (c|| . (2)
Finally, we link each entity with the most similar concept in the vocabulary O: linked 0 (e, c) ⇐⇒ sim(e, c) = max ci∈O sim(e, c i ). (3) 5 https://www.insee.fr/fr/metadonnees/cpfr21/section/A?champRecherche= true

D. Vector Representation of Service Requests and Providers

We aim to represent each service request or provider by a vector that summarizes the semantics of the entities extracted from its description. For each description of a service request or provider, we consider three alternative vector representations: (i) the average of the embedding vectors of the entities in the textual description, (ii) a bag of concepts representation, and (iii) a vector representation combining the two former ones.

1) Word Embedding of Entities: The base vector representation V Emb (x) of a service request or provider x is the average of the embedding vectors of all the entities e i , i = 1, ..., n extracted from its description:

V Emb (x) = 1 n n i=1 V (e i ), (4)
where V (e i ) is the vector representation of entity e i as defined in "(1)".

2) Bag of Concepts: Using the result of the above described entity linking process, we consider an alternative representation V BoC (x) of a service request or provider x based on the sourcing vocabulary S: the bag of the concepts (BoC) in S which the entities e i extracted from x are linked to according to "(3)":

V BoC (x) = BoC S (x) = (b 1 , ..., b m ) (5)
where m is the size of the sourcing vocabulary S and b i = 1 if ∃e ∈ x, linked S (e, c i ), and b i = 0 otherwise. Additionally, we considered enriching the BoC representation of a service request or provider, by considering not only the concepts linked to the entities it contains but also some neighbors in the vocabulary to the linked concepts. More precisely, we considered the parents of the concepts linked to the entities (skos:narrower relation) or those semantically close (skos:closeMatch relation). Formally, we define three alternative BoC representations:

V
where m is the size of the sourcing vocabulary S and b i = 1 if ∃e ∈ x, linked S (e, c i ) or linked S (e, c j ) with c j skos:narrower c i or c j skos:closeMatch c i ; and b i = 0 otherwise.

  BoC (x) = BoC S (x) = (b 1 , ..., b m ) (6)where m is the size of the sourcing vocabulary S and b i = 1 if ∃e ∈ x, linked S (e, c i ) or linked S (e, c j ) with c j skos:narrower c i ; and b i = 0 otherwise.V BoC (x) = BoC S (x) = (b 1 , ..., b m ) (7)where m is the size of the sourcing vocabulary S and b i = 1 if ∃e ∈ x, linked S (e, c i ) or linked S (e, c j ) with c j skos:closeMatch c i ; and b i = 0 otherwise.V BoC (x) = BoC S (x) = (b 1 , ..., b m )

https://ec.europa.eu/esco/portal/home

http://www.pole-emploi.org/accueil/mot-cle.html?tagId= 94b2eaf6-d7bd-4244-bddc-01415605563b

https://www.insee.fr/fr/information/2406147

https://www.unspsc.org/

V. CONCLUSION

In this paper, we presented a sourcing recommender system based on domain knowledge. We focus especially on the vector representation of the descriptions by evaluating the performance of the system using word embedding or injecting domain knowledge into the representation. Our experiments show that recommendation accuracy can be greatly improved through the injection of domain knowledge in the recommendation process. As future work, we aim firstly to use BERT or Camembert for French texts as models to generate word embedding representations.

3) Combination of Vector Representations: We define a third type of vector representation of a description of service request or provider as the concatenation of the vector representations defined in "(4)" and one of the BoC representations defined in "(5)", "(6)", "(7)", and "(8)", respectively:

E. Recommendation Algorithm

We define two metrics to measure the similarity between a service provider p and a service request r. The first one is the cosine similarity between the vector representations of p and r:

sim

where V stands for one of the representations defined in "(4)" to "(12)". The second metrics is

where sim 1 is then computed with the base vector representation V 1 .

A service provider p is recommended for a service request r if sim 1 (p, r) or sim 2 (p, r) is greater than a given threshold, depending on the chosen similarity measure.

IV. EXPERIMENTS AND RESULTS

A. Dataset and Protocol

We evaluate the performance of our recommendation approach on a dataset provided by sales experts at Silex. This dataset comprises 109 descriptions of service requests and the 649 providers in various areas which were manually selected and recommended for these requests. We consider two sets of annotations of this dataset: A is the set of annotations automatically performed by our NER approach; A is the result of a manual cleaning of A that we performed.

To decide on the optimal vector representation and algorithm to recommend service providers, we conducted eleven experiments whose settings are depicted in Table I, the baseline being experiment Emb.

TABLE I: Experimental settings

Experiment

Vector representation Similarity measure

In order to evaluate the performance of the proposed settings, and therefore the interest of injecting domain knowledge into vector representations, we used the precision, recall, F1 score metrics and the precision score considering the N top ranking providers (up to the tenth) according to the usual formula for "precision at N ": .

We conducted the parameter learning (i.e threshold) through 5-fold cross validation.

B. Results and Discussion

Table II and III present the performance of our system for each tested setting in terms of precision, recall and F1 score with datasets A and A respectively. In order to evaluate to what extent the performance of our proposed approach depends on the method adopted to automatically annotate the descriptions of the service requests and providers, we conducted some additional experiments in which we used DBpedia spotlight 6 for NER. Table IV presents the results on dataset A when named entities are extracted with DBpedia spotlight [START_REF] Mendes | Dbpedia spotlight: Shedding light on the web of documents[END_REF], [START_REF] Daiber | Improving efficiency and accuracy in multilingual entity extraction[END_REF].

Figures 1a and1b present the performance of our system for each tested setting in terms of P@N on dataset A and dataset A respectively. 6 All methods, where a word embedding representation is enriched with domain knowledge, obtain a better precision measure than the baseline method using word embedding alone. Focusing on the precision@N results, with both datasets, we can conclude that injecting domain knowledge is highly beneficial to our RS. Although a BoC representation performs very well from the 2 top-ranking items on dataset A, we can observe that its performance keeps steady on both datasets up to the tenth item. Using this cleaned dataset, the performance of all methods are increased. This emphasizes the fact that all methods are very sensitive to the quality of entity linking.

All in all, it appears that injecting domain knowledge into the vector representations is all the more beneficial the greater the quality of the annotations. Also, enriching the conceptual representations by considering the subsumption relation and skos:closeMatch relation clearly gives a better results. Finally, the comparison with the experiments using DBpedia spotlight for NER confirms that the introduction of domain knowledge in the recommendation process is beneficial and helps enhance the performance of the system even when one cannot rely on a high-quality NER method.