Franck Camerel
email: franck.camerel@univ-rennes1.fr

Corinne Lagrost

Marc Fourmigué

Grégory Albert

Frédéric Barrière

Olivier Jeannin

Ambipolar discotic liquid crystals built around platinum diimine-dithiolene cores

come

Introduction

Discotic Liquid Crystals (DLSs) have attracted a lot of interest due to their charge transport properties, their ability to be easily aligned in thin films and their self-healing capability for applications in optoelectronic as active layers in OLED, OFET and solar cells. [1] Ambipolar DLCs are particularly appealing since they are able to simultaneously carry electrons and holes and new designs are developed to obtain novel ambipolar semiconducting soft materials. [2] A c c e p t e d

M a n u s c r i p t

Most examples of DLC semiconductors with ambipolar properties are purely organic compounds, such as triphenylenes or phthalocyanines, [3] while ambipolar charge transport has also been reported in triazine-based columnar liquid crystals. [4] In the latter, the triazine discotic core acts as an electron accepting unit whereas the peripheral thiophene units provide electrondonating properties. Another organic ambipolar DLC was obtained by covalently grafting a phtalocyanine as an electron-donor and a fullerene as an electron acceptor. [5] Muller and coworkers also reported an ambipolar DLC with n-type perylene monoimide (PMI) covalently linked around p-type hexabenzocoronene core. [6] Large ambipolar carrier mobility was also found in discotic liquid crystalline truxenes substituted with alkyl chains at bay-positions. [7] More recently, a DLC material, consisting of a planarized triphenylborane mesogen, was reported to form a hexagonal columnar LC phase exhibiting ambipolar carrier transport properties with electron and hole mobility. [8] Besides, the number of ambipolar DLC built around metal complexes remains scarce. The only examples involve gadolinium or zinc phthalocyanines [9,10] and very recently, ambipolar carrier mobility was mentioned for a series of liquid crystalline platinum (II) complexes with 2phenylpyridine derivatives as the main ligand and 5-substituted tetrazole as the auxiliary ligand. [11] In that respect, neutral platinum diimine-dithiolene complexes formulated as [Pt II (diimine)(dithiolato)] 0 are an interesting class of ambipolar complexes with heteroleptic ligands. Indeed, the diimine fragment is prone to undergo reduction at relatively accessible potentials whereas the electron-rich dithiolene fragment is easily oxidized. Several research groups [12] and in particular the group of R. Eisenberg [13] have developed the synthesis of platinum diimine-dithiolene complexes to understand and to modulate their photophysical and redox properties. Complexes have been prepared by using 2,2′-bipyridine or 1,10phenanthroline as diimine ligands and 1,2-benzenedithiolates, 1,1-dithiolates or 1,2-A c c e p t e d M a n u s c r i p t ethylenedithiolates as dithiolate ligands. These square planar [Pt II (diimine)(dithiolato)] 0 complexes also display solution luminescence and solvatochromic absorption bands which are attributed to common charge-transfer bands. Diimine-dithiolene complexes have also been proposed as light harvester in the visible region for light driven aqueous reduction to hydrogen [14] but also in solar cells. [15] Crown ethers have been introduced on the dithiolate ligand in the [Pt(NN)(SS)] system for developing optical and electrochemical sensors for alkali metal cations. [16] Surprisingly and to the best of our knowledge, only one liquid crystalline material build around a metal diimine-dithiolene core has been described up to now by Ho-Chol Chang and coworkers in 2011. [17] A platinum complex having an asymmetric molecular structure derived from 1,2-benzenedithiolato (bdt) and a bipyridine ligand carrying ramified C8 or C10 carbon chains forms a columnar mesophase of hexagonal symmetry over a large temperature range from -18 °C up to 194 °C. This complex undergoes quasi reversible one-electron reduction at -1.89 V vs Fc/Fc + that corresponds to bpy-based reduction processes. The dithiolate ligand can also be oxidized but according to a slow electrochemical process because the peak-to-peak separation of this oxidation process is found to be 0.17 V, far above the expected value for a nernstian one-electron transfer process (0.059 V). Thus, to obtain new ambipolar discotic liquid crystals, four diimine-dithiolene complexes, differently functionalized by long carbon chains or cyanobiphenyl fragments, have been developed herein by using a ligand metathesis between dichloroplatinum diimine derivatives and tin or nickel dithiolene complexes as dithiolate ligand precursors (Scheme 1).

The platinum complexes carry a 5,6-dihydro-1,4-dithiin-2,3-dithiolato (dddt) ligand (in 1a-c) or a 1,2-bis (3,4-bis(dodecyloxy)phenyl)ethene-1,2-bis(thiolato) (C12dt) ligand (in 2a, 2b and 2d) and as diimine ligand, a functional bipyridine carrying, either tris-dodecyloxyphenyl fragments connected through an amide linker and noted bpyC12 (in 1a and 2a) or cyanobiphenyl A c c e p t e d M a n u s c r i p t fragments connected through an ester linker carrying a C10 carbon chains and noted bpyCBP (in 1b and 2b). Compounds 1c and 2d have been synthesized as reference compounds. The electronic properties of these complexes and their precursors have been characterized by absorption and luminescence spectroscopies as well as by cyclic voltammetry and DFT calculations. The structural properties of these compounds were also investigated by a combination of optical microscopy under crossed polarizers, DSC analyses and small angle Xray diffraction. The results obtained confirmed that these compounds have indeed a strong ambipolar character with good reversibility and that some of them also display liquid crystalline properties over a large temperature range.

Results and discussion

Synthesis and characterization

Synthetic routes toward the functional diimine-dithiolene compounds are presented in Scheme 2. Full synthetic details are given in the experimental part. First, functional bipyridine carrying either tris-dodecyloxyphenyl fragments connected through an amide linker (bpyC12 3a), or cyanobiphenyl fragments connected through ester linker carrying a C10 carbon chains (bpyCBP 3b) were reacted with 1 eq. of PtCl2(DMSO)2 to afford the corresponding dichloroplatinum diimine complexes 4a and 4b in 76 and 52 % yield, respectively. The synthesis of these two functional bipyridine molecules 3a and 3b is fully described in the experimental part. For introducing the dddt dithiolene ligand, dichloroplatinum diimine complexes 4a-b were then reacted with one equivalent of 2,2-dibutyl -5,6-dihydro-1,3,2-dithiastannolo[4,5-b][1,4] complexes, the dichloroplatinum diimine complexes 4a-b were first reacted with silver triflate in order to exchange the chloride ligand by the more labile triflate anion. The triflate derivative was then refluxed with the neutral nickel bis(dithiolene) complex 6 in THF to afford after purification the expected compounds 2a and 2b. EDX analyses have also revealed that there is no trace of nickel in the isolated compounds.

The reference compounds 1c and 2d were prepared in a similar way. The dddt derivative 1c was readily obtained from the reaction of the dichloroplatinum diimine complex 4c with one equivalent of 5 in acetone, while 2d was also obtained in 28 % yield by first reacting [PtCl2(bpy)] 3d with silver triflate followed by reaction with 6.

The purity and the molecular structure of all the compounds were confirmed by elemental analyses, 1 H NMR and 13 C NMR spectroscopy, UV-vis, mass spectroscopy and IR spectroscopy. The introduction of Cl2Pt on the bipyridine fragments is characterized by a downfield shift of the 1 H signal of bipyridine protons. The introduction of the dddt fragment in place of the two chloride ligands results in a singlet between 2.61 and 3.51 ppm integrating for 4H corresponding to the hydrogen atoms of the S-CH2 groups. Despite several attempts in CDCl3, d6-DMSO and CD2Cl2 at room temperature but also at 60 °C, the two complexes 2a and 2b bearing long alkyl chains on both the dithiolene and the diimine ligands could not be properly characterized by NMR spectroscopy, likely due to strong aggregation effects in solution (vide infra). However, the optical, thermal and electronic properties as well as the mass spectroscopy and the elemental analysis unambiguously confirmed the formation of the expected complexes.

X-ray structure of 1c

Single-crystals suitable for X-ray diffraction of the model compound 1c with the dddt and (tBu)2bpy ligands were obtained in CHCl3 by slow diffusion of pentane. Crystallographic data S1-S4. This compound crystallizes as chloroform solvate in the triclinic system, space group 𝑃𝑃1 � (a = 7.2116(4) Å; b = 13.8530(9) Å; c = 15.3854 (10) Å; α = 69.100(2)°; β = 86.336(2)°; γ = 82.782(2)°; V= 1424.23(15) Å 3 , Z = 2). Figure 1 shows the atomic numbering scheme and a projection of the crystalline structure along a. The asymmetric unit contains one complex and one chloroform molecule, both in general position. The X-ray crystal structure confirms the chemical structure of the complex. The platinum atom is in a pseudo square planar environment (Pt-N1 = 2.053(4) Å; Pt-N2 = 2.056(3) Å; Pt-S4 = 2.2544 (11) Å;

Pt-S1 = 2.2574(12) Å; N1-Pt-N2 = 78.87( 14)°; N1-Pt-S4 = 96.26 (10)°; N2-Pt-S1 = 96.51 (10)°; S4-Pt-S1 = 89.13(4)°). The dithiolene fragment and the bipyridine fragment are not coplanar, bur slightly twisted by 16.89° around the platinum center. It can also be noticed that the ethylenic bridge of the dddt ligand is bended out of plane of the complex by 83°. The molecules are packed in a head-to-tail fashion along the a axe (Figure 1b), the best way to accommodate the bulky t Bu groups. Along the stack, bipyridine fragments exhibit a bond-overring overlap, preventing the formation of short platinum-platinum contacts. The shortest platinum-platinum distance along the stack is indeed 5.348 Å.

Spectroscopic properties in solution

Spectroscopic data for all the complexes and their precursors in diluted CH2Cl2 solutions are gathered in Table 1. The absorption spectra are presented in Figure 2a and in Figures S1-S5.

The absorption spectrum of the bpyC12 ligand 3a shows a main broad absorption band exhibiting a maximum at 298 nm (ε ~ 22450 M -1 cm -1 ) with a shoulder at 338 nm (Figure S1).

These absorption bands are assigned to π-π* and n-π* transitions localized on the bipyridine core and on the alkoxyphenyl fragments, respectively. [18] The absorption spectrum of the bpyCBP ligand 3b also displays an absorption band centred at 298 nm but the band is much sharper and the associated extinction coefficient is much higher compared with 3a (Figure 2a and S1). This absorption band is assigned to π-π* transitions localized on the bipyridine core but also to π-π* transitions localized on the cyanobiphenyl fragments. [19] Coordination of the PtCl2 fragment leads to a new absorption band at 412 nm for 4a and 429 nm for 4b (Figure S2 A c c e p t e d M a n u s c r i p t and 2a) with weak extinction coefficients. These absorption bands are readily associated to the charge transfer transition corresponding to excitations from a filled Pt (d) orbital to an unoccupied π* diimine orbital (MLCT). [20] Introduction of the dddt 2-in place of the chloride ligands is characterized in 1a by an additional absorption band on the spectrum at even lower energy, associated to mixed metal ligand-to-ligand charge transfer transition (MMLL'CT) corresponding to excitation from the electron donor dithiolate ligand having orbital contributions from the metal ion to the electron acceptor bipyridine ligand (Figure 2a andS3). [21] With the C12dt dithiolene ligand, the position of this MMLL'CT band in 1b is weakly affected by the nature of the bipyridine ligand and is located around 630-660 nm (Figure S4).

On the contrary, with the dddt ligand, the MMLL'CT band is located at 635 nm in 1c (Figure S5) whereas this band is red-shifted to 712 and 770 nm for 1a and 1b, respectively. An MLCT band is present for all the complexes and it can be noticed that with the bpyC12 ligand, the MLCT band of the complexes is slightly blue-shifted compare to the bpyCBP ligand. Solidstate absorption spectra of some complexes have been measured (Figure S6). The absorption maxima are close to those measured in solution and only a broadening of the absorption bands is observed. Solids-state absorption spectra of the platinum diimine-dithiolene complexes clearly display the LLCT at low energy, showing that the charge transfer is also effective in solid-state.

The luminescence properties of all the compounds were also investigated in CH2Cl2 solutions. The bpyC12 diimine 3a, its PtCl2 complex 4a and the dddt complex 1a are nonluminescent. On the other hand, spectrum of complex 1b with the other C12dt dithiolene ligand shows an emission band centered at 485 nm upon excitation in the MLCT band at 430 nm (Figure 2b). For all complexes carrying a bpyCBP ligand 3b, an emission band is observed around 370 nm upon excitation at 300 nm. This emission is attributed to the presence of cyanobiphenyl fragments (Figure S6). All the other complexes show a weak luminescence upon A c c e p t e d M a n u s c r i p t excitation in the MLCT band. Introduction of ester or amide functionalities on the bpy fragments (as in 3a or 3b) leads to a red-shift of the emission band, in line with the red-shift of the MLCT band. In fact, with the C12dt ligand, complex 2d absorbs at 348 nm and emits at 441 nm whereas 2a and 2b absorb at 430 and 443 nm and emit at 485 and 520 nm, respectively (Figure 2b). The same observation can be done with the dddt ligand between 1a, 1b and 1c.

Introduction of the ester or the amide groups leads to the red-shift of both the MLCT and the emission bands. Comparison of two bpyCBP complexes 1b and 2b with respectively the dddt and C12dt dithiolene ligands shows that the nature of the dithiolate ligand affects the emission properties much more strongly. Indeed, in 1b, the emission appears at 612 nm and is red-shifted by 92 nm when compared to 2b. This red-shift is likely attributed to the fact that the dddt ligand is more electron rich than the C12dt ligand. No emission has been detected at room temperature upon excitation in the low energy MMLL'CT band. Thus, it appears here that the emission observed at room temperature upon excitation around 450-500 nm is only due to a 3 MLCT state and not to the MMLL'CT state. [13] Quantum yields of emission of the various compounds upon excitation in the MLCT band were measured in CH2Cl2 solutions (Table 1). They are always very low, between 0.1 and 1.2 %. The highest quantum yields were found with the free bipyridine 3b. All complexes are luminescent in fluid solution at room temperature and their emission properties can be tuned through ligand variation. It can also be noticed that epifluorescence investigations on solids have revealed that the dichloroplatinum diimine complexes 4a and 4b show strong red and yellow luminescence at room temperature upon excitation in the range 350-380 nm, respectively, whereas all the diimine-dithiolene complexes (1a-c, 2a, 2b, 2d) are deprived of naked-eye luminescence properties in the solid state. For complexes 4a and 4b, a broad emission centered at 670 and 650 nm, respectively, is observed in solid-state upon excitation at 420 nm (Figure S8). [a] Determined in CH2Cl2 solution (c ∼ 10 -7 M) using [Ru(bpy)3]Cl2 as reference (ΦF = 0.059 in CH3CN, λexc = 450 nm). [22] All ΦF are corrected for changes in refractive index.

Compound

λabs (nm) ε (M -1 .cm -1 )
λex(nm) λF max (nm) ΦF [a] bpyC12 3a 298 ( 22450

Electrochemical investigations

The electrochemical behavior of complexes and their parent ligands was investigated by cyclic voltammetry in CH2Cl2 containing 0.2 M nBu4NPF6 as supporting salts at 293 K. Table 2 gathers the formal potentials E1/2 derived as the mid-sum of oxidation (Epa) and reduction (Epc) peak potentials (relative to the SCE reference electrode). Electrochemical measurements were run in the [-2V/+2V] potential range.

Cyclic voltammogram of the bipyridine 3b shows one irreversible reduction process at -1.80

V (Figure S9), probably due to the reduction of cyanobiphenyl groups [23,24] No reduction process has been detected for the bipyridine 3a but an almost irreversible oxidation at +1.15 V, followed by an ill-defined irreversible oxidation at +1.5 V are observed (Figure S10).

After metal complexation, the two bipyridine ligands undergo two successive reversible reductions at -0.95 V and -1.47 V for 4a (Figure S11) and at -0.85 and -1.46 V for 4b (Figure S12). Coulometric studies through comparison with ferrocene at 293 K confirm a one-electron reduction in each case. The two reversible reduction processes correspond to the formation of the monoanion and the dianion, respectively. The electron-withdrawing effect of the ester and amide groups stabilizes the di-reduced product sufficiently to allow bulk electrogeneration of the dianion at room temperature. [25] The ester functionality has a slightly stronger electronwithdrawing effect when compared with the amide function and the 4b complex is more easily reduced, at least in the first reduction process. The irreversible oxidation observed for 4a

(Figure S11) at +1.2 V could be attributed to the oxidation of the amide ligand.

The reference compound with the dddt ligand, 1c, exhibits one reversible reduction at -1.45 V, assigned to a bpy ligand-based reversible reduction (Figure S13). This compound also exhibits two reversible oxidation processes at +0.24 and +1.02 V, corresponding to the formation of a monocation and a dication, respectively. Both cationic species are stable at the cyclic voltammetry timescale. These oxidation processes are assigned to dddt ligand-based reversible oxidations. It can be noticed that with the known Pt(dddt)(bpy) complex (1d), only one irreversible oxidation system has been observed at +0.34 V. [26] The presence of both reversible reduction and oxidation potentials clearly highlights the ambipolar character of our model compound 1c. The cyclic voltamogramm of the C12dt complex with bipyridine, 2d also displays one reversible bpy ligand-based reduction system at -1.40 V, and two oxidation waves at +0.23 and +1.01 V, attributed to the C12dt ligand (Figure S14). The first oxidation system is reversible while the second one is only partially reversible, probably because of a possible degradation of the C12dt fragment. The oxidation potentials of the dddt and C12dt fragments are and+0.98 V (Figure 3). These values are very close to those observed with the dddt-containing complex 1c and these oxidation processes can be then confidently attributed to the oxidation of the common dddt ligand. 1b also exhibits two reversible reduction systems at -1.01V and -1.62 V, respectively (Figure 3).

These values are more negatively-shifted than those found for the PtCl2 precursor 4b. This can be explained by the charge transfer that occurs between the dddt and the bpyCBP ligands, as revealed by UV-visible measurements. Through charge transfer, the bpyCBP is more electron rich and thus this fragment becomes more difficult to reduce.

With both the bpyC12 and dddt ligands, complex 1a exhibits two reversible reduction processes located at -1.08 and -1.60 V (Figure S15), showing that the reduction processes are also negatively-shifted compared to Cl2Pt precursor 4a. However, only one irreversible oxidation at 1.10 V is observed, instead of having the expected two oxidations systems of dddt. We postulate that the bpyC12 ligand oxidation might overlap with the dddt oxidation systems since we observe that the current intensity of the irreversible oxidation at +1.1 V is much higher than the current intensity associated with the first or the second reduction process.

The electrochemical activity of the C12dt dithiolene complexes 2a and 2b with long alkyl chains on both ligands could not be measured due to solubility issues, despite attempts in different solvents, including DMF, CH2Cl2 and THF. However, in regard to the electrochemical activities of the reference compounds 2d, 4a and 4b, these two compounds should likely display similar electrochemical behaviours with two reversible reduction systems around -0.9 and -1.5 V as well as two quasi-reversible oxidation processes around +0.2 and +0.9 V. To summarize, these electrochemical investigations demonstrate that the diamine-dithiolene core is indeed a very Table 2. Electrochemical data [a] for all compounds (versus ECS).

[a] Determined in CH2Cl2 + 0.2 M nBu4NPF6 solution (c ∼ 10 -3 M) at room temperature; scan rate, 100 mVs -1 . E1/2 = (Epa+Epc)/2; Epa and Epc are the anodic peak and the cathodic peak potentials, respectively.

Compound

DFT calculations

In order to get more insight into the electronic properties of the newly developed diiminedithiolene complexes, DFT geometry optimization of models of the complexes were carried out in vacuo. To optimize the computing time, the long carbon chains have been systematically

replaced by methyl group, giving the corresponding 1a', 1b', 2a' and 2b' complexes. These calculations have also been conducted to estimate the energy levels and the nature of the redoxactive molecular orbitals of 2a and 2b since both these compounds are poorly soluble and not amenable to an electrochemical study. Figure 4 shows that all calculated compounds have a HOMO level comprised between -4.63 and -4.90 eV and a LUMO level between -3.17 and -3.48 eV. Specifically, the HOMO of 2a' (analog of insoluble 2a) is only 0.15 eV higher than that of 1a' while its LUMO lies 0.17 eV higher. Likewise the HOMO of 2b' (analog of the insoluble 2b) is also only 0.17 eV higher than that of 1b' while its LUMO lies 0.15 eV higher.

Taken together these results indicate that the oxidation potential of the C12dt-ligated insoluble compounds 2a and 2b should be slightly higher and their reduction redox potentials slightly diimine-dithiolene complexes is mainly centered on the bpy ligand with a metallic character while the LUMOs is mainly centered on the dithiolene ligand also with a metallic character.

Hence, from these calculations, the lowest-energy transition between the frontier orbitals is best described as a mixed metal-ligand to mixed metal-ligand charge transfer (MMLMML'CT). The HOMO-LUMO gaps were computed for all the complexes at ca.1.45 eV in vacuo which would correspond to a low energy transition in the UV-visible-NIR spectra around 855 nm. and the thermal behaviors of the liquid crystalline compounds are summarized in the Scheme 3.

Scheme 3. Summary of the thermal behaviour of the liquid crystalline compounds.

The bpyC12 ligand 3a is in a mesomorphic state between 30 and 146 °C (Figure S16).

On cooling from the isotropic state, a homogeneous and fluid texture develops between crosspolarizers (developable cylindrical domains) characteristic of a columnar phase (Figure S17).

X-ray diffraction patterns recorded between 30 and 146 °C exhibit a series of sharp peaks in the small angle region that can be indexed as the reflections of a rectangular lattice (a = 54.9 Å, b = 41.4 Å at 140 °C) (Figure S18). In the wide angle region, a broad halo centered at 4.5 Å, associated to the mean distance between the alkyl chains in a molten state, confirms the liquid crystalline nature of the phase. An additional peak (hstack) centered at 4.74 Å is also observed and is attributed to the stacking distance between the bpyC12 3a molecules along the column axis. Using a standard geometrical treatment, it is found that the rectangular unit cell hstack-thick ). [27] Based on X-ray data, the size of the molecule and the number of molecules inserted inside the unit cell, a packing model can be proposed in which the bpyC12 molecules are associated head to head to form a disc and the stacking of these dimeric discs leads to the formation of columns organized in the node of the rectangular lattice. FT-IR spectroscopic investigations performed on powder at room temperature show that the columnar organization is also stabilized by hydrogen bonding between the amide functionalities, as clearly evidenced by the νNH and νCO stretching vibrations observed respectively at 3246 and 1650 cm -1 (see experimental part). Note that corresponding values for the free amide are usually found at 3400 cm -1 for νNH and around 1680 cm -1 for νCO. [28] The presence of single νCO and νNH stretching vibrations on the FTIR spectra also indicate the formation of a hydrogen bonded network involving all amide functionalities.

Interestingly, PtCl2 complexation of the free bipyridine ligand 3a strongly increases the thermal domain of the mesophase, from -20 to +275°C (Figure S19). Above 275 °C, the dichloroplatinum complex 4a is in an isotropic state and upon cooling, a fluid and birefringent texture with pseudo-fans shapes characteristic of columnar phases readily forms (Figure S20).

Temperature-dependent XRD analyses confirm the existence of a columnar mesophase of hexagonal symmetry over the whole mesomorphic domain. The XRD patterns display in the small angle region four sharp peaks which can be unambiguously indexed as the 10, 21, 20 and 22 reflections of a 2D hexagonal lattice (Figure S21). The XRD pattern also displays a broad to Pt-Pt interactions has been observed in solid state (Figure S6 and Figure S8). [29] So, there is no evidence of the stabilization of the supramolecular arrangement through intermolecular Pt-Pt interactions. Room temperature FT-IR measurements also confirm here (νNH = 3372 cm -1 and νCO = 1672 cm -1 , see experimental part) that the columnar organization of 4a is stabilized by hydrogen bonding between the amide functions of the ligand 3a.

DSC and POM investigations have shown that the dddt/bpyC12 Pt complex 1a degrades above 200 °C. No phase transition could be detected between -25 °C and +200 °C (Figure S22).

Between room temperature and 200 °C, 1a appears as a birefringent and malleable soft material (Figure S23), which is a good indication that this compound is a liquid crystalline material. The SAXS patterns shows only one clear peak in the small angle region and no clear assignment can be done (Figure S24). However, in regard to the shape of the molecule and the previous results, it can be hypothesized that this compound is also likely organized into a columnar mesophase of hexagonal symmetry stabilized trough hydrogen bonding between the amide functionalities (νNH = 3326 cm -1 and νCO = 1676 cm -1 ). With this hypothesis, the single observed reflection can be tentatively assigned as the (10) reflection of a 2D hexagonal lattice.

It demonstrates however that the introduction of the dddt ligand strongly destabilizes the molecular organization inside the mesophase but the temperature range of existence of the mesophase is weakly affected. All these observations clearly highlight that this compound is also a liquid crystal.

Replacing the dddt ligand in 1a by the C12dt one gives 2a with long alkyl chains on both ligands. 2a is a birefringent soft material at room temperature. Upon heating, the viscosity of the compound decreases and the compound slowly become isotropic between 90 °C and 120 °C. The DSC traces display no thermal transition at 100 °C, in line with a slow isotropization process extended over a large temperature range (Figure S25). Only a broad transition, associated to the slow crystallization of the carbon chains, is observed around -15 °C.

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

Temperature-dependent XRD measurements confirm that the compound is isotropic above 100 °C with patterns displaying only broad halos in the whole 2θ range explored. Below 90°C, the obtained diffractions patterns, with several sharp peaks in the small angle region and a broad peak around 20° in 2θ, clearly indicates that this compound is a liquid crystalline material (Figure 5). The four sharp peaks observed at low angles can unambiguously be indexed as the ( 10), ( 11), ( 20) and ( 21) reflections of a 2D lattice of hexagonal symmetry. The broad peak (hch) In conclusion, all the compounds incorporating the bpyC12 ligand 3a, namely, 3a itself, 4a, 1a, and 2a were found to be liquid crystalline materials, highlighting that this novel ligand is a successful mesomorphic promotor of great interest to develop new metallomesogens.

DSC analyses, temperature-dependent XRD measurements and POM observations have revealed that the reference complex 2d, (C12dt)Pt(bpy) is a liquid crystalline material from 42

°C up to the decomposition temperature around 180 °C (Figure S26 andS27). All the recorded XRD diffractograms (between 60 to 180 °C) are identical, and five sharp and intense smallangle reflections with reciprocal spacings in the ratios 1:2:3:4:5 are observed (Figure S28).

These small-angle peaks are most readily assigned as the ( 001), ( 002), ( 003), ( 004) and ( 005) reflections of a lamellar phase with an interlayer spacing parameter d = 32.2 Å (at T = 150 °C, Table 3). In the wide angle region, a strong sharp peak is also observed at 3.46 Å and is to form columns with a periodicity of 3.46 Å and these columns are then organized at a distance of 9 Å into planes 32 Å thick. This complex is organized into a lamello-columnar mesophase from 42 °C to 180 °C. The proposed model in Figure S29 is in good agreement with the molecular dimensions but implies some interdigitations of the carbon chains (Figure S28).

Below 42 °C, the XRD patterns show several sharp peaks over the whole 2θ range and this confirms the crystallization of the compound at low temperatures.

Concerning the CBP series, the diimine ligand 3b is deprived of mesomorphic properties and this crystalline compound directly melts into an isotropic liquid around 140°C (Figure S30).

Coordination with PtCl2 to give 4b did not allow for the emergence of liquid crystalline properties and only crystalline phases have been detected by SAXS. The DSC obtained with 4b, displaying endothermic and endothermic peaks on the heating curves, is indicative of strongly hindered crystallization processes (Figure S31). DSC analyses, POM observations and X-ray analysis observations have revealed that the corresponding dddt complex 1b is a crystalline compound which decomposes above 180 °C (Figure S32). Finally, the introduction of the C12dt dithiolene ligand carrying long carbon chains confers liquid crystalline properties to the CBP series. The DSC traces of 2b, (C12dt)Pt(bpyCBP), obtained upon heating display two broad endothermic transitions extending from -10 to +40 °C and from +70 °C to +100 °C (Figure S33). Above 100 °C, POM observations confirm that the complex is in an isotropic state. The high temperature transition undergoes a strong supercooling effect and a fluid and birefringent film readily forms below 45 °C, indicative of a liquid crystalline state that remains likely associated with slow crystallization of the complex. In the mesomorphic domains, the SAXS patterns displays several sharp peaks in the small angle region which can tentatively be indexed as the ( 11), ( 02), ( 22), ( 31) and ( 24) reflections of a rectangular lattice corresponding to the plane group C2mm (h+k = 2n) (a = 42.8 Å, b = 42.5 Å at 30 °C) (Figure 7). Two broad peaks are also observed in the wide angle region at 5.6 and 4.4 and are attributed to the mean distance between the CBP fragments and the carbon chains, respectively. [19] A last broad peak is also observed at 3.4 Å and is attributed to the stacking distance between the disk molecules.

Applying the standard geometrical treatment, it is found that two molecules of 2b are contained inside a unit cell hstack thick, as expected for a rectangular cell. From the XRD data, an organization model can be proposed in which the molecules are stacked on top of each other to form columns and these columns are then organized on the two nodes of the 2D rectangular lattice (Figure 8). For a space filling, these dissymmetric disk-like molecules are certainly arranged head-to-tail with no obvious segregation between the cyanobiphenyl fragment and the carbon chains. To summarize, in the CBP series, only complex 2b forms a columnar mesophase of rectangular symmetry from 40 to 70 °C on heating and from 40 to 20 °C upon cooling. With the CBP ligand, it is mandatory to introduce long carbon chains on the other side of the molecule (as in 2b) to give it a disk-like shape able to organize into a mesophase. In the bpyC12 series, all the compounds were found to be liquid crystalline materials with columnar mesophase of hexagonal or rectangular symmetry, meaning that bpyC12 ligand is a very good mesogenic promotor. On the contrary, with the bpyCBP ligand, liquid crystalline properties could be obtained provided that numerous long carbon chains were introduced on the dithiolate ligand to make the molecule more disk-shape and to counter-balance the stacking/crystallization of the cyanobiphenyl fragments.

Conclusion

Highly functional platinum diimine-dithiolene complexes have been isolated through an original synthetic route based on ligand metathesis. For this purpose, novel functional bipyridines carrying either tris-dodecyloxyphenyl fragments connected through an amide linker (bpyC12) or cyanobiphenyl fragments connected through ester linker carrying a C10 carbon chain (bpyCBP) have been developed. After coordination to PtCl2, the chlorine ligands have been successfully exchanged by dddt or C12dt dithiolene ligands directly from preformed tin or nickel dithiolene complexes. Thermal and X-ray analyses have revealed that, with the bpyC12 diimine ligand, columnar mesophase can be obtained over a large temperature range, showing that this ligand is a good mesogenic promoter. On the contrary, with the bpyCBP diimine ligand, it was mandatory to introduce numerous long carbon chains on the dithiolene fragment to observe the emergence of liquid crystalline properties. Inside the mesophase, the platinum diimine-dithiolene complexes are stacked in a head-to-tail fashion to form columns and these columns are then organized on the nodes of the 2D lattices or into lamellas. Charge transfer occurs from the electron donor dithiolate ligand to the electron acceptor bipyridine, as revealed the additional absorption band on the spectrum at low energy around 600-800 nm, depending on the nature of the ligands. The ambipolar character of these compounds was unambiguously confirmed by electrochemical investigation coupled to DFT calculations. In fact, the liquid crystalline platinum diimine-dithiolene complexes can be oxidized and reduced at easily accessible potentials. In particular, the platinum compound 2d with the dddt and the bpyC12 ligands can clearly be reversibly oxidized or reduced and self-assembles into a lamellocolumnar phase over a large temperature range from 42 °C up to 180 °C. Such ambipolar and Optical microscopy investigations were performed on a Nikon H600L polarizing microscope equipped with a Linkam "liquid crystal pro system" hotstage LTS420. The microscope is also For the X-ray crystal structure of complex 1c, data were collected on an D8 VENTURE Bruker AXS diffractometer operating with graphite-monochromated Mo-Kα radiation (λ = 0.71073 Å).

The structures was solved by direct methods using the SIR92 program [30] and then refined with full-matrix least-square methods based on F2 (SHELXL-2014/7) [31] with the aid of the WINGX program. [32] All non-hydrogen atoms were refined with anisotropic atomic displacement parameters. All H atoms have been found in the electron density maps and refined in their idealized position using the AFIX instructions. Crystallographic data on X-ray data collection and structure refinements are given in Table S2-S6. Crystallographic data for structural analysis of the complex 1c has been deposited with the Cambridge Crystallographic Data Centre under CCDC 1867102. Copies of this information is available free of charge from the Web site (www.ccdc.cam.ac.uk).

Density Functional Theory [33] calculations were performed with the hybrid Becke-3 parameter exchange functional [34] and the Lee-Yang-Parr nonlocal correlation functional [35] (B3LYP) implemented in the Gaussian 09 (Revision B.01) program suite [START_REF] Frisch | Gaussian 09, Revision B.01[END_REF] using the pseudo-potentials LANL2DZ with the default convergence criteria implemented in the program. Calculations were carried out on the OCCIGEN calculator of the Centre Informatique National de l'Enseignement Supérieur (CINES (Montpellier) under project 2018-A0040805032). Figures were generated with GaussView 5.0.

Synthesis.

[2,2'-bipyridine]-4,4'-dicarboxylic acid [START_REF] Bai | [END_REF] , 3,4,5-tris(dodecyloxy)aniline [38] Bis [1,2bis(3',4'-di-n-dodecyloxyphenyl)ethane-1,2dithiolene]nickel (complex 6), [39] 4'-[(10bromodecyl)oxy]-4-carbonitrile-[1,1'-Biphenyl], [40] Dichloro(4,4'-di-ter/-butyl-2,2'bipyridine)platinum(II) ([PtCl2( t bu2bpy)]) (complex 4c), [41] Dichloro(2,2'bipyridine)platinum(II) ([PtCl2(bpy)]) (complex 4d), [41] 2,2-Dibutyl-5,6-dihydro-1,3,2dithiastannolo [4,5-b][1,4]dithiin (complex 5), [42] PtCl2(DMSO)2 [43] were synthesized as previously described. All the other reagents were purchased from commercial sources and used as received. All synthetic manipulations were performed under an inert and dry nitrogen atmosphere using standard techniques. The reactions were followed by Thin Layer Chromatography (TLC) plates, revealed with a UV-lamp at 254 nm or iodine. Silica gel used in chromatographic separations was obtained from Acros Organics (Silica Gel, ultra-pure, 40-60 µm). Aluminium oxide 90 standardized from Merck KGaA was also used for chromatographic separations.

Ligand 3a

[2,2'-bipyridine]-4,4'-dicarboxylic acid (0.1 g, 0.4 mmol) was first refluxed overnight in 10 mL freshly distilled SOCl2 at 90 °C under N2 with 1 drop of Et3N. After removal of the excess SOCl2 and drying, the residue was dissolved in 20 mL of dry CH2Cl2 with 3,4,5tris(dodecyloxy)aniline (0.58 g, 0.9 mmol) and Et3N (0.3 mL, 2.2 mmol) were added. The mixture was stirred at room temperature under N2 for 24h. The organic phase was washed with water (3x40 mL) and dried over MgSO4. The product was purified by column chromatography on alumina using a 50/50 petroleum ether/chloroform mixture as eluent. After recrystallization in a CH2Cl2/MeOH mixture, the product was isolated as a white powder in 40 % yield (0.25 g).

Ligand 3b

[2,2'-Bipyridine]-4,4'-dicarboxylic acid (0.12 g, 0.5 mmol) was first refluxed overnight in 10 mL freshly distilled SOCl2 at 90 °C under N2. After removal of the excess SOCl2 by distillation and drying, the residue was dissolved in 20 mL of dry CH2Cl2 together with 4'-[(10bromodecyl)oxy]-4-carbonitrile-[1,1'-Biphenyl] (0.3 g, 0.9 mmol). Et3N (0.3 mL, 2.2 mmol)

was added and the reaction mixture was stirred at room temperature for 3 days. After removal of the solvent, the residue was purified by column chromatography on alumina gel using a gradient of eluents for pure CH2Cl2 to CH2Cl2+1 %v/v MeOH. The product was isolated as a white powder in 56 % yield (0.25 g). 1394, 1366, 1314, 1289, 1270 , 1252, 1176, 1133, 1117, 1063, 1042, 1028, 1011, 997, 950, 920, 854, 823, 808, 768, 724, 693, 665, 616, 583, 563, 531, 510, 472, 424, 407. UV-vis [CH2Cl2, Ligand 3b (0.18 g, 0.2 mmol) was dissolved in 10 mL dry THF in a Schlenk flask with 1 eq. of PtCl2(DMSO)2 (0.08 g, 0.2 mmol) and the reaction mixture was then heated at 60 °C for 48h.

After removal of the solvent and purification by column chromatography on alumina gel using CH2Cl2 as eluent, the product was isolated as a yellow powder in 52 % yield (0.12 g). δCH2), 1289, 1248, 1180, 1142, 1116, 1062, 1031, 1013, 999, 959, 905, 874, 855, 821, 805, 762, 729, 708, 661, 564, 531, 421. UV-vis [CH2Cl2, λmax (nm), ε (M -1 .cm -1 )]: 429 (7020), 300

Complex 1a

Complex 4a (0.05 g, 0.03 mmol) and one equivalent of 2,2-Dibutyl-5,6-dihydro-1,3,2dithiastannolo [4,5-b][1,4]dithiin (0.012 g, 0.03 mmol) were dissolved in 5 mL acetone and 1 mL THF. The mixture was stirred at room temperature under air for 3 days. The green precipitate, which has formed, was filtered, washed with acetone and dried. The product was recrystallized by slow evaporation of CH2Cl2 from a CH2Cl2/CH3CN solvent mixture. After filtration and drying, the product was isolated as a green powder is 75 % yield (0.04 g). 1539, 1485 (νC=C), 1462 (δCH2), 1414, 1394 (δCH3), 1365 (vCH3), 1283, 1265, 1251, 1202, 1154, 1123, 1076, 1030, 973, 926, 903, 869, 850, 826, 772, 733, 688, 672, 593, 564, 532, 481, 442, 416. UV-vis [CH2Cl2, λmax (nm) (ε (M -1 .cm -1 ))]: 635

Complex 2d

First, [PtCl2(bpy)] (0.048 g, 0.11 mmol) was reacted with 2.2 eq. of silver triflate (0.064 g, 0.25 mmol) in 5 mL of dry CH3CN under N2 atmosphere for 4h. The suspension was filtered over celite to remove the formed silver chloride salt. After removal of the solvent, the residue was redissolved in 10 mL dry THF and 0.5 eq. of complex 6 were added (0.114 g, 0.055 mmol).

The mixture was heated at reflux under N2 for 3 days. After evaporation of the solvent, the product was purified by flash column chromatography on silica gel using a gradient of eluents for pure CH2Cl2 to CH2Cl2+ 5 %v/v MeOH. After removal of the solvents, the product was isolated as a blue powder in 28 % yield (43 mg). 7.42 -7.28 (m, 4H, CHbpy/CHph), 6.83 -6.65 (m, 4H, CHbpy/CHph), 4.40 -4.19 (m, 8H, OCH2), 2.11 -1.89 (m, 8H, CH2), 1.73 -1.12 (m, 72H, CH2), 1.05 -0.73 (m, 12H, CH3). 13 C NMR (75 MHz, Chloroform-d) δ 31.99, 29.84, 29.81, 29.79, 29.76, 29.70, 29.45, 29.37, 26.53, 26.35, 22.73, 14.09, 0.99. Only the peaks of the carbon chains are visible at high concentration on the 13 C NMR spectra. IR-ATR (cm -1 ): 3081 (νCH), 2955 (νCH), 2917 (νCH), 2850 (νCH), 1605 (νC=C), 1540, 1497 (νC=C), 1469 (δCH2), 1449 (δCH2), 1431 (δCH2), 1414, 1382 (δCH3), 1313, 1257, 1237, 1182, 1131, 1068, 1031, 995, 958, 905, 842, 809, 787, 746, 716, 654, 629, 607, 413. UV-vis [CH2Cl2, λmax (nm) (ε (M -1 .cm -1 ))]: 660 (11020), 348 (34500), 304 (91900), Complex 4a (0.055 g, 0.03 mmol) was reacted with 2.2 eq. of silver triflate (0.018 g, 0.07 mmol) in 10 mL of dry THF under N2 atmosphere for 24h. The suspension was filtered over celite to remove the formed silver chloride salt. 0.5 eq. of complex 6 (0.03 g, 0.015 mmol) were then added to the filtrate and the mixture was heated at reflux under N2 for 60 h. After evaporation of the solvent, the product was purified by flash column chromatography on silica gel using CH2Cl2+ 1 %v/v MeOH as eluent. After drying, the product was isolated as a green powder in 43 % yield (36 mg).

Despite several attempts (CDCl3, d6-DMSO, CD2Cl2), no clear 1 H and

Complex 2b

25 mg of complex 4b (0.02 mmol) were reacted with 2.2 eq. of silver triflate in 5 mL of CH3CN under N2 atmosphere for 17 h. The solution was filtered over celite and 0.5 eq. of complex 6 (0.021 g, 0.01 mmol) were then added to the filtrate and the mixture was heated at reflux under N2 for 48 h. After evaporation of the solvent, the product was purified by column chromatography on silica gel using a gradient of eluent from CH2Cl2+ 1%v/v THF to CH2Cl2+ 5%v/v THF. The product was isolated as a blue compound in 42 % yield (18.5 mg). Highly functional mesogens constructed around ambipolar platinum diimine-dithiolene cores have been isolated through an original ligand metathesis approach.

Scheme 1 .

 1 Scheme 1. Chemical structure and name of the functional diimine-dithiolene complexes

  Scheme 2. Synthetic routes used for the preparation of the functional diimine-dithiolene

  dithiin 5 in acetone to afford 1a (75 % yield) and 1b (63 % A c c e p t e d M a n u s c r i p t yield) as green powders. For introducing the C12dt dithiolene ligand to prepare in the 2a and 2b

Figure 1 .

 1 Figure 1. a) ORTEP diagram of 1c from the top and from the side with 50% thermal contours

Figure 2 .

 2 Figure 2. a) UV-Vis absorption spectra in CH2Cl2 (C ~ 10 -5 M) of 3b, 4b and 1b; b) Normalized emission spectra in CH2Cl2 (C ~ 10 -5 M) of all the compounds upon excitation in the MLCT

  s c r i p t very close but the dddt ligand is more stable toward oxidation. In conclusion, both model complexes 1c and 2d exhibit an ambipolar behavior. Turning now to the four complexes 1a,b and 2a,b, cyclic voltammogram of 1b shows two one-electron reversible oxidation processes located at +0.26

  s c r i p t attractive platform for preparing ambipolar compounds that can be easily and reversibly oxidized and reduced.

Figure 3 .

 3 Figure 3. Cyclic voltammogram of (dddt)Pt(bpyCBP) 1b (∼10 -3 M) in CH2Cl2 containing 0.2

  s c r i p t lower than their dddt-ligated congeners 1a and 1b. Examination of the nature of the frontier molecular orbitals of the calculated models (Figure4) shows that the HOMOs of the Pt(II)

Figure 4 .

 4 Figure 4. HOMO and LUMO frontier orbitals with energy levels (eV) of 1a', 2a', 1b' and 2b' obtained by DFT B3LYP/LANL2DZ.

  (N = Scell x hstack / Vm with Vm = (MW/0.6022

halo around 4 .

 4 85 Å, indicative of the molten state of the alkyl chains. The hexagonal unit cell hch-thick contains 2 molecules and this also indicates that two molecules are associated inside the columnar stratums. The observation of a broad halo around 8.5 Å (h'stack) corresponding to almost two times the hch distance and of a broad halo around 3.5 Å (hstack) accounts for a headto-tail organization of the molecules mainly driven by π-π stacking. No additional absorption or emission band associated to the presence of a metal-metal-to-ligand-charge-transfer state dueA c c e p t e d M a n u s c r i p t

at 4 . 5 Å

 45 indicates that the carbon chains are in a molten state. Thus, this compound is organized from -15 °C up to 90 °C into a columnar mesophase of hexagonal symmetry. The broad halo (hstack) observed at 3.4 Å is associated with short stacking along the column (π-π stacking). No evidence of Pt-Pt interactions has been detected by solid-state optical spectroscopy (FigureS6and S8). The hexagonal unit cell hstack-thick contains one molecule. So, here the columns are directly formed by a stacking of the disk-like molecules and the columns are then organized on the node of the 2D hexagonal cell with a parameter a of 41.2 Å. To compensate the dipole moment and for a better space-filling, the molecule should adopt a head-to-tail arrangement along the columnar stacks (Figure6).

Figure 5 .

 5 Figure 5. SAXS pattern of 2a recorded at 70 °C (2 nd heating).

Figure 6 .

 6 Figure 6. Proposed model for the organization of 2a in the Colh phase (Molecular diameter ~48

  s c r i p t associated to a strong regular stacking of the molecule into columns. The SAXS patterns also displaying two additional small reflections at 9.01 and 4.375 Å with reciprocal spacings in the ratio 1:2, which are associated to a lateral periodicity inside the plane. From the above XRD data, a model of organization can be proposed in which the molecules stack on top of each other

  s c r i p t down to room temperature. No clear textural defect could have been developed, so no proper assignment of the phase symmetry can be done by POM. The low temperature transition is

Figure 7 .

 7 Figure 7. XRD pattern of 2b, (C12dt)Pt(bpyCBP), recorded at 30 °C after cooling from the

Figure 8 .

 8 Figure 8. Proposed organization for 2b in the rectangular unit cell hstack thick (hstack = 3.6 Å)

  s c r i p t liquid crystalline platinum diimine-dithiolene complexes are good candidates to develop new semiconducting soft materials and this work paves the way to develop new active layers in optoelectronic devices.Experimental part.300 ( 1 H) and 75.5 MHz ( 13 C) NMR spectra were recorded on Bruker Avance 300 spectrometer at room temperature using perdeuterated solvents as internal standards. FT-IR spectra were recorded using a Bruker VERTEX 70 spectrometer equipped with an ATR apparatus. Elemental analyses were performed by the Service de Microanalyse, Institut de Chimie des Substances Naturelles, Gif sur Yvette, France. Mass spectra were recorded with a MALDI-TOF Microflex LT Bruker. UV-Vis spectra were recorded using a Cary 100 UV-Vis spectrophotometer (Varian). Photoluminescence spectra in solution were recorded with a Jobin-Yvon spectrofluorimeter. Quantum yields in solution (φsol) were calculated relative to Ru(bpy)3]Cl2 (φ = 0.059 in CH3CN). φsol was determined according to the following equation,φsol = φref × 100 × [(Ts × Ar)/(Tr × As)] × [(ns/nr) 2 ]where, subscripts s and r refer respectively to the sample and reference. The integrated area of the emission peak in arbitrary units is given as T, n is the refracting index of the solvent (n = 1.3404 for acetonitrile, n = 1.4242 for CH2Cl2 and n = 1.4305 for DMF) and A is the absorbance. Differential scanning calorimetry (DSC) was carried out by using NETZSCH DSC 200 F3 instrument equipped with an intracooler. DSC traces were measured at 10 °C/min down to -25 °C.

  s c r i p t equipped with a UV irradiation source (Hg Lamp, λ = 340-380 nm) and an ocean optic USB 2000+ UV-Vis-NIR spectrophotometer based on CCD detection technology. X-ray scattering experiments (SAXS) were performed using a FR591 Bruker AXS rotating anode X-ray generator operated at 40 kV and 40 mA with monochromatic Cu Kα radiation (λ = 1.541 Å) and point collimation. The patterns were collected with a Mar345 Image-Plate detector (Marresearch, Norderstedt, Germany). The samples were held in Lindeman glass capillaries (1 mm diameter). The capillaries were placed inside a Linkam HFX350-Capillary X-Ray stage which allow measurements from -196 °C up to 350 °C with an accuracy of 0.1 °C.Cyclic voltammetry measurements were performed with a SP-50 biologic or a PGSTAT 302N (Eco-Chemie B.V.) potentiostat in a three-electrode glass cell. The working electrode was a 1 mm diameter glassy carbon disk and the counter electrode was a platinum wire. All reported potentials are referred to KCl Saturated Calomel Electrode (SCE) (uncertainty ± 5 mV). Tetran-butylammonium hexafluorophosphate Bu4NPF6 was purchased from Fluka (puriss, electrochemical grade) and was used, as received, at 0.2 mol L -1 as supporting electrolyte in anhydrous CH2Cl2. All electrochemical measurements were carried out inside a Faraday cage, at room temperature (20 ± 2 °C) and under constant argon flow. Prior to electrochemical analyses, the working electrode was carefully polished with diamond paste (Struers) onto a 1µm paper cloth (Struers) and thoroughly rinsed.

(

  105200). MALDI-TOF-MS: m/z = 1140.8 (M + -Cl). Anal. Calc. for C58H62Cl2N4O6Pt, C7H8 (%): C 61.51,H 5.56, N 4.41. Found (%): C 61.75, H 5.91, N 4.23.

( 9 ,

 9 318 x 10 3 ), 380 (7510), 300 (65200). MALDI-TOF-MS: m/z = 643.3 (M + ) Anal. Calc. for C22H28N2PtS4 (%): C 41.04, H 4.38, N 4.35. Found (%): C 41.05, H 4.53, N 4.27

1 H

 1 NMR (300 MHz, Chloroform-d) δ 9.30 (s, 2H, CHbpy), 7.99 -7.84 (m, 4H, CHbpy/CHph),

  270 (117300), 254 (138800). MALDI-TOF-MS: m/z = 1329.4 (M + ). Anal. Calc. for

Table 1 .

 1 Optical data measured in CH2Cl2 solution at 298 K.

  13 C NMR spectra has been obtained for this compound. IR-ATR (cm -1 ): 3072 (νCH), 2956 (νCH), 2921 (νCH), 2852 (νCH), 1725 (νC=O), 1667 (νC=O), 1603 (νC=C), 1546 (δNH), 1505 (νC=C), 1466 (δCH2),1429, 1379 (δCH3), 1262, 1115, 1074, 1019, 802, 731. UV-vis [CH2Cl2, λmax (nm) (ε (M -1 .cm -1))]: 626 (6910), 430 (16830), 306 (72740). MALDI-TOF-MS: m/z = 2674.2 (M + ). Anal. Calc.

	for C158H268N4O12PtS2, 2CH2Cl2 (%): C 67.55, H 9.64, N 1.97, S 2.25. Found (%): C 67.62, H
	9.22, N 1.76, S 2.39.

Acknowledgements.

The CNRS, Rennes Metropole and the University of Rennes 1 are gratefully acknowledged for financial support. This work was granted access to the high performance computing resources of CINES (Montpellier, France) under allocation 2018-A0040805032 awarded by GENCI.

Antoine Vacher is gratefully acknowledged for his help in the solid-state absorption measurements.

λmax (nm) (ε (M -1 .cm -1 ))]: 298 (55900). MALDI-TOF-MS: m/z = 911.8 (M + ). Anal. Calc. for C58H62N4O6, CH3OH (%): C 75. 13, H 7.05, N 5.94. Found (%): C 75.68, H 6.83, N 5.72.

Complex 4a

Ligand 3a (0.1g, 0.07 mmol) was dissolved in 10 mL dry THF in a Schlenk flask with 1 eq. of PtCl2(DMSO)2 (0.028 g, 0.07 mmol) and the reaction mixture was then heated at 60 °C for 24h.

After removal of the solvent, the product was purified by column chromatography on alumina gel using chloroform as eluent. After recrystallization in a CH2Cl2/MeOH solvent mixture, the product was isolated as an orange powder in 76 % yield (0.09 g). 1467(δCH2), 1421(δCH2), 1383(δCH3), 1347(δCH3), 1307 (νC-N), 1259, 1231, 1174, 1113, 1017, 908, 835, 814, 754, 721, 702, 662, 626, 589, 415.UV-vis [CH2Cl2, λmax (nm) (ε (M -1 .cm - 1))]: 412 (9300), 320 (19100), 292 (28300). MALDI-TOF-MS: m/z = 1728.5 (M + -Cl). Anal.

Calc. for C96H162Cl2N4O8Pt, 0.5 CH2Cl2 (%): C 64.08, H 9.08, N 3.10. Found (%): C 63.79, H 8.83, N 2.90.

Complex 4b


Yusuf Yigit Pilavci

Nicolas Farrugia

SPECTRAL GRAPH WAVELET TRANSFORM AS FEATURE EXTRACTOR FOR MACHINE LEARNING IN NEUROIMAGING

Keywords: graph signal processing, wavelets, neuroimaging, regression

Graph Signal Processing has become a very useful framework for signal operations and representations defined on irregular domains. Exploiting transformations that are defined on graph models can be highly beneficial when the graph encodes relationships between signals. In this work, we present the benefits of using Spectral Graph Wavelet Transform (SGWT) as a feature extractor for machine learning on brain graphs. First, we consider a synthetic regression problem in which the smooth graph signals are generated as input with additive noise, and the target is derived from the input without noise. This enables us to optimize the spectrum coverage using different wavelet shapes. Finally, we present the benefits obtained by SGWT on a functional Magnetic Resonance Imaging (fMRI) open dataset on human subjects, with several graphs and wavelet shapes, by demonstrating significant performance improvements compared to the state of the art.

INTRODUCTION

The emergence of Graph Signal Processing (GSP) is mostly due to the elegant and powerful analogy between graph laplacian eigenvectors and classical Fourier analysis [START_REF] Shuman | The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains[END_REF]. As such, application domains involving graphs to model mutltivariate dependencies are naturally adapted to the GSP framework. In particular, recent studies in neuroimaging have leveraged the use of graph theory to study brain networks, giving rise to the field of network neuroscience [START_REF] Bassett | Network neuroscience[END_REF]. However, the majority of network neuroscience studies have focused on analyzing the properties of the graph itself (e.g. graph theoretical descriptors of white matter connectivity [START_REF] Bassett | Network neuroscience[END_REF]), rather than signals of brain activity on a brain graph. In turn, most studies analyzing brain signals relies on the use of massively univariate statistics, analyzing each brain region independently [START_REF] Friston | Statistical parametric mapping[END_REF]. Recent methodological efforts push towards the use of machine learning as multivariate methods able to capture whole brain dependencies of neural activity [START_REF] Varoquaux | How machine learning is shaping cognitive neuroimaging[END_REF].

Our aim with the present paper is to demonstrate the potential of simultaneously using brain connectivity and signals from neuroimaging data to boost performance of machine learning tasks, by leveraging the GSP framework. In particular, we aim at testing the benefits of using SGWT as a feature extractor for machine learning on neuroimaging data.

The remainder of the paper is organized as follows. In section 2 we will present previous studies related to SGWT and GSP applied to machine learning in neuroimaging. In section 3 we will present our experimental setup, the formulation of SGWT that will be used in this paper and the procedures used to build our graph models. In section 4 we present experiments and results on a synthetic regression problem and fMRI signals. Finally, we conclude in section 5.

RELATED WORK

With the development of GSP, frameworks based on wavelets on graphs have become promising, due to their over-complete analysis in both localization on graph nodes and different scales with respect to the spectrum of the graph. To obtain such analysis on irregular domains such as graphs, several formulations of graph wavelets have been proposed [START_REF] Sunil | Perfect reconstruction two-channel wavelet filter banks for graph structured data[END_REF][START_REF] Crovella | Graph wavelets for spatial traffic analysis[END_REF][START_REF] Hammond | Wavelets on graphs via spectral graph theory[END_REF]. For example, Narang reports a compact comparison of several formulations in terms of significant properties such as perfect reconstruction or orthogonality [START_REF] Sunil | Perfect reconstruction two-channel wavelet filter banks for graph structured data[END_REF]. In this paper, we use Spectral Graph Wavelet Transform (SGWT) introduced in [START_REF] Hammond | Wavelets on graphs via spectral graph theory[END_REF]. Basically, SGWT exploits the Fourier transform analogy that is defined on graphs [START_REF] Shuman | The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains[END_REF] and defines wavelet kernel functions in the spectral domain.

While there is a growing literature applying GSP to neuroscientific questions, (for a review, see [START_REF] Huang | A graph signal processing view on functional brain imaging[END_REF]), most studies use GSP to derive descriptors (such as alignement of functional signals to the underlying graph [START_REF] John D Medaglia | Functional alignment with anatomical networks is associated with cognitive flexibility[END_REF]) that are further analyzed using inference based statistics (e.g. [START_REF] Smith | Locating temporal functional dynamics of visual shortterm memory binding using graph modular dirichlet energy[END_REF]). For example, Leonardi [START_REF] Leonardi | Wavelet frames on graphs defined by fmri functional connectivity[END_REF] shows the statistical relevance of SGWT coefficients in different scales with varying experimental conditions in an fMRI paradigm.

However, studies applying GSP for machine learning in neuroimaging are relatively scarce. In [START_REF] Liu Rui | Simultaneous low-rank component and graph estimation for high-dimensional graph signals: Application to brain imaging[END_REF], the authors de-fined a low rank, dimensionality reduction approximation and recovers the underlying graph, showing performance improvements when using the learnt approximation as features for supervised classification. In [START_REF] Ménoret | Evaluating graph signal processing for neuroimaging through classification and dimensionality reduction[END_REF], the authors used GSP as dimensionality reduction and feature extraction in a supervised learning setting with fMRI. The authors show performance improvements in both simulated cases and real data. A recent contributions uses GSP to extract features for brain computer interfaces based of near-infrared spectroscopy brain signals [START_REF] Panagiotis | Single-trial nirs data classification for brain-computer interfaces using graph signal processing[END_REF], showing significant performance improvements compared to previous work on the same dataset. Nevertheless, to the best of our knowledge, there is no published study exploiting SGWT as feature extractor for machine learning in neuroimaging.

METHODS

Graph Wavelet Transform

Using graph wavelet transform enables multi-scale signal representations adapted to the underlying graphs, which in turn facilitate the detection of abnormal changes or discontinuities in the original domain, and ease the interpretation of signals in both localization and frequency. With these motivations, we adopt the formulation of SGWT [START_REF] Hammond | Wavelets on graphs via spectral graph theory[END_REF].

As in classical signal processing, wavelet functions are defined as ψ s,a (x) for different scales s, and translations a. Graph Wavelets can be also interpreted in the Fourier domain as:

ψ s,a (x) = 1 2π ∞ -∞ ψ(sω)e -jωa e jωx dω (1)
where ψ(sω) is the Fourier transform of the scaled wavelet, e -jωa is the Fourier transform of the spatial translation, (which can be seen as the Fourier Transform of a delta localized at a) and e jωx is the Fourier basis function. These terms will be addressed to corresponding terms in graph wavelet transform definition. Let an undirected, weighted graph G, with a vertex set V such as |V | = N , and weight matrix W ∈ R N . W is a symmetric matrix of weights w ij . The Laplacian operator of G is defined as follows:

L = D -W ( 2
)
where D is a diagonal matrix such as

D ii = j |w ij |.
Here, weights w ij are allowed to be negative, and we deal with issues related to semi-positiveness of the L by using the absolute diagonal degree matrix [START_REF] Leonardi | Wavelet frames on graphs defined by fmri functional connectivity[END_REF]. Also, the normalized Laplacian is defined as

L norm = D -1/2 LD -1/2
. Analogous to classical signal processing, eigenvectors U and eigenvalues of the Laplacian matrix L correspond to the Fourier basis and frequency values, respectively. A graph signal f is a vector in R N defined in the vertex domain [START_REF] Shuman | The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains[END_REF], and spectral filtering operations f are done through Graph Fourier Transform, defined by f = U T f .

By interpreting scaling and translation operations, as in equation 1, it is possible to define graph wavelets as follows:

ψ s,a = N n=1 g(sλ n ) δ(n)u n (3)
where g is a band-pass kernel defined in the spectral domain, corresponding to the Fourier transform of the wavelet at scale s in equation 1, and δ(n) is the Graph Fourier transform of δ localized at a, corresponding to the spatial translation component in equation 1. Finally, u n are the columns of U, eigenvectors of L. The complete frame for the wavelet transform is computed by adding a low-pass filter, h(λ), also called the scaling function. As a result, the obtained transform covers all parts of the graph spectrum. The final transformation for a graph signal f is the following inner product:

W f (s, a) =< ψ s,a , f > (4)

Graph Wavelet Kernel Design

The informative property of SGWT as signal representation is highly related to the selection of the scaling and wavelet functions, h(λ) and g(λ). Such a choice impacts the stability of reconstruction of the original graph signal. As reported in [START_REF] Hammond | Wavelets on graphs via spectral graph theory[END_REF] and [START_REF] Shuman | Spectrum-adapted tight graph wavelet and vertex-frequency frames[END_REF], a wavelet frame would be tight if the sum of squares of all kernels remains constant through the spectrum (Parseval identity), a necessary condition for perfect reconstruction of a signal. However, it is possible to relax this constraint by accepting some variation, resulting in more freedom of kernel selection (e.g. using cubic splines). Another aspect of kernel design is spectrum coverage. For a graph model, the spectrum is defined by the eigenvalues of L, and any continuous function that is defined in the spectral domain (as a function of λ) is only evaluated at those eigenvalues, λ n , [START_REF] Shuman | Spectrum-adapted tight graph wavelet and vertex-frequency frames[END_REF]. Therefore, one should examine the eigenvalue locations through the spectrum when designing kernel functions. Shuman et al.provides tight and spectrum adapted wavelet kernels, called Warped Translates. In [START_REF] Shuman | Spectrum-adapted tight graph wavelet and vertex-frequency frames[END_REF], a tight frame is generated with a special function:

q(λ) := K k=0 a k cos 2πk(ω(λ) - 1 2 ) 1 0≤λ<1 (5)
and its translated versions in the graph spectrum, q ω(λ) -m R where K k=1 (-1) k a k = 0, and ω is a non-decreasing warping function that modifies the kernels' behaviour on the spectrum. For example, choosing a warping function as the approximated cumulative distribution function of eigenvalues concentrates the kernels in ranges in which the eigenvalues are densely placed (see Fig. 1). In [START_REF] Shuman | Spectrum-adapted tight graph wavelet and vertex-frequency frames[END_REF], the superior discriminatory power of warped translates is clearly demonstrated, because different parts of the evaluated spectrum are perfectly covered and segmented by different kernels.

Synthetic Graph Signals and Regression Problem

In this work, synthetic signals are generated for getting more understanding on the behavior of SGWT in a regression problem, in the case where the signals are smooth on the graph. The workflow that generates the input and output starts with creating a Erdos Renyi graph (with a probability of edge presence of p = 0.1), G with N nodes and associated weight matrix W. A diffusion operator is computed using a lazy random walk, A = (I + D -1 W ). Secondly, we generate a random signal matrix R of size M × N , where M is number of samples and N is number of features, and the generated set of signals are diffused by multiplying it by the diffusion operator, A, such as the diffused signals are R = RA. The third step is to generate a random vector of regression weights β, and compute the nonlinear function output as y = log(β T R). Finally, zero-mean Gaussian noise is added on the graph signals, so the final observed signals are X = R + N (0, σ 2 ), with σ = 0.1. With this procedure, we are able to obtain graph signals, and also generate a problem that cannot be easily solved by linear regressors. Those signals are smooth on the graph likewise the FMRI signals on the brain nodes.

fMRI Datasets

We consider here an open dataset of fMRI data on human subjects who rated pictures with emotional content [START_REF] Chang | A sensitive and specific neural signature for picture-induced negative affect[END_REF]. We fetched statistical maps of whole brain activity during single trials for each subject, from neurovault [START_REF] Krzysztof | Neurovault. org: a web-based repository for collecting and sharing unthresholded statistical maps of the human brain[END_REF] (collection number 1964). The supervised learning task consists in predicting the rating given by the subject from brain maps. As this dataset didn't include connectivity data that could be used to compute subject-specific graphs, we estimated average brain graphs from resting state fMRI data (i.e. spontaneous fluctuations of the brain at rest) from 158 subjects of an open resting-state dataset [START_REF] Mendes | A functional connectome phenotyping dataset including cognitive state and personality measures[END_REF]. We used the preprocessed resting-state data, described here https: //neuroanatomyandconnectivity.github.io/ opendata/. As both datasets were spatially normalized in the standard MNI space, we defined regions of interest (ROI) to enable the correspondance between the graph, defined on the resting-state dataset, and the signals from the emotional rating dataset. Therefore, we parcellated all resting-state time-series and brain maps on 523 non-overlapping ROIs from the finest scale of BASC atlas (444 networks) [START_REF] Bellec | Multi-level bootstrap analysis of stable clusters in resting-state fMRI[END_REF].

Graph Construction

We explain here the different graph inference methods applied on the parcellated resting state time-series. The weight matrix, W formulations are as follows:

• Functional Connectivity with Covariance or Correlation Graph: We derive graphs from temporal covariance and correlation. As variant of these graphs, thresholded and binary versions of these adjacency matrices are also defined.

• KNN Covariance/Correlation Graph: Another variant to previous graphs is generated by limiting the numbers of neighbors per node. For each node, the K strongest edges are kept and rest are set to a weight of 0. For the symmetry, when W ij is set with nonzero edge, same value is kept in W ji . Binary versions are also generated by setting nonzero values to 1.

• Semi-Local Graph: Another strategy that exploits both the geometrical structure and functional connectivity is the semi-local graph, as tested in [START_REF] Ménoret | Evaluating graph signal processing for neuroimaging through classification and dimensionality reduction[END_REF]. The semi-local graph uses a threshold (set to keep the graph connected) on the euclidean distance between baricenters of nodes, and sets connection weights corresponding to long distances to 0.

• Kalofolias Graph: We used the method from Kalofolias [START_REF] Kalofolias | How to learn a graph from smooth signals[END_REF], which relies on defining a smoothness prior to infer the graph from the data.

Dimensionality Reduction and Regression

For the synthetic dataset, generated inputs X are first transformed using SGWT, followed by dimensionality reduction using 100-best feature selection. Performances of linear regression predicting y are compared with and without SGWT for different kernels. For the fMRI dataset, we reproduced the methods from the original paper [START_REF] Chang | A sensitive and specific neural signature for picture-induced negative affect[END_REF] to be able to compare results. A PCA with 121 components is used for dimensionality reduction, and regression is performed with Lasso. Careful cross-validation (CV) is performed over subjects and regularization parameter for LASSO, using leave-one-subject-out, enabling reliable generalization. We compared the original pipeline that uses no parcellation (original signal

RESULTS

For the evaluation of results on the synthetic dataset, R 2 -score and Mean Square Error (MSE) are used, whereas for the fMRI dataset, Root mean square error (RMSE) and Pearson correlation are employed , to be consistent with [START_REF] Chang | A sensitive and specific neural signature for picture-induced negative affect[END_REF]. Variability in generalization is reported using the average and the standard error of the mean (SE) over CV folds for each score. In addition, we report results on a generalization test set using a predefined, separate hold-out test dataset as explained in [START_REF] Chang | A sensitive and specific neural signature for picture-induced negative affect[END_REF]. Table 1 presents results obtained for the fMRI dataset. Result for SGWT are picked from the set of best results for different graphs and wavelet function. In Table 1, the best five results for SGWT are reported and these scores stands for the results of different graph and kernel selections. SGWT provides significant performance gains when compared to using only parcellated ROI signals, or original signals with no parcellation. In particular, warped translate have a better potential for generalization to the test dataset. We suggest that SGWT enables an efficient exploitation of underlying multivariate dependencies, using spectrum-adapted wavelet kernels on a brain graph. While the magnitude of performance gain is strongly dependent to underlying information inferred by the graph, warped translates are able to extract more informative features in terms of regression problems.

Comparisons for the synthetic dataset are reported in Table 2. The experiment for this analysis is repeated 500 times with randomly generated graphs with 500 nodes, and average scores are interpreted. As indicated by Table 2, SGWT, and in particular warped translate kernels are able to generate features that are significantly more informative to solve the regression problem. This indicates that the regression problem considerably benefits from using discriminative, spectrumadaptive coverage of kernels w.r.t. others.

We depict in Fig. 2 the different scale and spatial localization of the largest LASSO coefficients that solve the regression problem. Conceptually, this representation shows the most important graph scales for each localization in brain. Negative and positive weights are separately examined and the largest contribution for each node is denoted with its sign and scale in Fig. 2.

CONCLUSION

In this contribution, we have demonstrated the potential of combining SGWT and machine learning using synthetic data and fMRI data from open datasets. A key point of the proposed approach is to rely on Warped Translated kernels for wavelet definitions, which optimizes spectral coverage of SGWT. We showed that using features from SGWT can boost performance in a challenging regression task on neuroimaging data. In future work, we plan to better examine how the estimated features can be used to enhance interpretability of the trained models. Another perspective is to define new models based on dynamic graphs in order to fully exploit the temporal dimension of brain activity, instead of relying solely on spatial maps as graph signals.

Fig. 1 .

 1 Fig. 1. Warped Translate Wavelet Kernels on Spectral Domain, in the case of the KNN-Correlation Brain Graph. Vertical lines depict placement of eigenvalues.

Fig. 2 .

 2 Fig. 2. Significant Scale-Localization map on brain. Positive and negative weights are denoted with ± sign.

Table 1 .

 1 ), parcellated signals on BASC ROI, and SGWT representations. Results for the fMRI Dataset

	Data		CV Results			Test Results		Transform Properties
	Repr.	RMSE	R 2 -score	Pearson	RMSE R 2 -score Pearson	Graph	Kernel
	Original	1.080 ±0.028 0.204 ±0.073 0.810 ±0.018	1.036	0.451	0.693	NA	NA
	ROI	1.054 ±0.031 0.231 ±0.079 0.827±0.017	1.022	0.466	0.701	NA	NA
	SGWT-1 1.047 ±0.029 0.234±0.082 0.832 ±0.015	0.983	0.506	0.725	Corr.	Warped
	SGWT-2	1.067±0.030 0.205 ±0.085 0.840 ±0.014	0.987	0.502	0.737	KNN Corr.	Warped
	SGWT-3	1.056±0.034 0.205±0.085 0.839±0.014	0.988	0.500	0.722	KNN Cov	Meyer
	SGWT-4 1.033 ±0.030 0.245 ±0.082 0.828±0.016	0.990	0.498	0.720	Kalofolias Cubic Spline
	SGWT-5 1.062 ±0.031 0.196 ±0.107 0.843 ±0.014	0.991	0.487	0.730	KNN Corr.	Iter. Sinus
	Wavelet Kernels	MSE	R 2 -score
	Cubic Spline	1514.45e-05 0.392438
		Meyer	1518.24e-05 0.390937
	Iterated sinusoidal	1515.33e-05 0.392079
	Warped Translate 1507.40e-05 0.395246
	No Wavelet	1533.48e-05 0.384859

Table 2 .

 2 Results for the Synthetic dataset