Keywords: acceptor-donor-acceptor (A-D-A) materials, π-conjugation, electron mobility, perovskite solar cells

Organic semiconductor (OSC) materials with a high electron affinity are required for many optoelectronic applications. In this work a series of twelve novel acceptor-donor-acceptor (A-D-A) materials with low-lying LUMO energy levels are designed, synthesized, and characterized. In this strategy, two acceptor dyes, isatin and its dicyanovinyl derivatives are connected by various π-bridges. We have varied the π-conjugation length of the central core and altered the linkage position of the acceptor core (4-position vs. 6-position of the phenyl ring of the isatin moiety) to study the effect of extended π-conjugation and point of linkage of the acceptor on optical and electrochemical properties of the new dyes. Density functional theory (DFT) and time-dependent DFT (TD-DFT) studies have been performed to gain an insight into their electronic properties by determining the energy levels and maps of the HOMO, LUMO as well as HOMO-LUMO gap (energy differences between the highest occupied and lowest unoccupied molecular orbitals). Our findings demonstrate that with increasing the acceptor strength and π-conjugation length of the core, the wavelength of the longest absorption maximum as well as their respective extinction coefficients are enhanced, which resulted in band-gap reduction either by lowering the LUMO and or raising the HOMO energy level of the molecules.

Space-charge-limited current measurements (SCLC) were investigated to probe the electron mobility of these molecules. Electron only devices were fabricated by the spin-coating and the trap-limited electron mobility was calculated using Mott-Gurney law. 10a exhibited an intrinsic moderate electron mobility of 8.94×10 -4 cm 2 V -1 s -1 .

The potential practical utility of these materials as an electron-transport material for perovskite solar cells (PSCs) has been demonstrated.

Tuning

Introduction

OSC materials with low-lying LUMO energy levels are particularly interesting for many optoelectronic applications, in particular for n-channel organic field-effect transistors (OFET), as non-fullerene acceptors and electron transporting materials for perovskite solar cells [START_REF] Braga | High-Performance Organic Field-Effect Transistors[END_REF]. To date, tremendous efforts have been devoted to explore new building blocks for the fabrication of novel n-type OSC. One key requirement for developing n-type OSC is the high electron affinity, which facilitates electron injection and stabilizes injected electrons. This is usually expressed in terms of the energy level of the LUMO, which should be sufficiently low-lying (≤ -3.5 eV) to facilitate electron injection from the cathode. The chemical structure and the nature of the electron-withdrawing building block are used mainly to settle the LUMO energy level.

Various building blocks have been employed to construct new n-type OSC. Among them, bis-lactam are of particular interest owing to their strong electron-withdrawing ability and dipolar carbonyl groups which facilitate strong intermolecular interactions [START_REF] Rumer | Bis-lactam-based donor polymers for organic solar cells: Evolution by design[END_REF][START_REF] Alsufyani | The effect of aromatic ring size in electron deficient semiconducting polymers for n-type organic thermoelectrics[END_REF]. Based on the bis-lactam design strategies, various novel electron-deficient building blocks for high-performance OSC have been reported [START_REF] Kim | Novel Organic Semiconductors Based on 1,5-Naphthyridine-2,6-Dione Unit for Blue-Selective Organic Phototransistor[END_REF][START_REF] Takagi | Synthesis and Field-Effect Transistor Application of pi-Extended Lactam-Fused Conjugated Oligomers obtained by Tandem Direct Arylation[END_REF]Isatin and its dicyanovinyl derivatives belong to this family, and they are good synthetic precursors of many natural products and also promising n-type acceptor-donor-acceptor (A-D-A)-type OSC due to their planar framework with two electron-withdrawing carbonyl groups [START_REF] Gomaa | Synthesis, characterization, and antimicrobial activity of some new N-aryl-N'-(2-oxoindolin-3-ylidene)-benzohydrazonamides[END_REF][START_REF] Yousaf | Isatin-derived non-fullerene acceptors for efficient organic solar cells[END_REF][START_REF] Liu | Recent Advances in Diversity Oriented Synthesis through Isatin-based Multicomponent Reactions[END_REF]. In the past, various D-A type dyad and triad architectures have been designed and synthesized, their photophysical properties are largely influenced by the way in which the dyad and triad systems is constructed (AD, DAD, ADA, etc.).

Through appropriate chemical modification of isatin core, a significant number of n-type OSC with a low LUMO energy level have been reported. Kuo and co-workers reported molecular design strategies of three di-2-(2-oxindolin-3-ylidene) malononitrile derivatives (I-1a, 1b, and 1c in Figure 1) with various numbers of nitrogen substituents on the phenyl rings for use as n-type OFET-materials [START_REF] Dhondge | Di-2-(2-oxindolin-3-ylidene)malononitrile Derivatives for N-Type Air-Stable Organic Field-Effect Transistors[END_REF]. They demonstrated by selectively controlling the number of nitrogen atoms introduced on the phenyl group, that the LUMO energy level could be fine-tuned from -4.02 eV for the unsubstituted to -4.16 eV for the disubstituted derivative. The introduction of the amine functionality not only lowers the LUMO level but also enhances the molecule's coplanarity, which results in a moderate electron mobility of 0.059 cm 2 V -1 s -1 .

However, the replacement of a phenyl ring with a pyridine had a slight effect on the absorption spectra. The same group later reported the synthesis and characterization of two derivatives of fused angular-shaped naphthalene bis-isatin (I-2) core [START_REF] Dhondge | Angular-Shaped Naphthalene Bis(1,5-diamide-2,6-diylidene)malononitrile for High-Performance, Air-Stable N-Type Organic Field-Effect Transistors[END_REF].

These new derivatives showed a low-lying LUMO energy level of -4.25 eV, lower than that of previously reported, making them suitable materials for air-stable n-type OSC. These naphthalene derivatives, I-2 displayed a broad absorption with two main absorption bands at 300-450 and 550-800 nm, assigned as the π-π* and intramolecular charge transfer (ICT) transitions, respectively.

Benzodipyrrole-2,6-dione-3,7-diylidenedimalononitrile, I-3, which was a structural analogue to I-2 by replacing naphthalene core with a phenyl moiety, was recently reported and its electrochemical behavior was investigated by cyclic voltammetry (CV) [START_REF] Dhondge | Benzodipyrrole-2,6-dione-3,7-diylidenedimalononitrile Derivatives for Air-Stable n-Type Organic Field-Effect Transistors: Critical Role of N-Alkyl Substituent on Device Performance[END_REF]. The CV results showed reversible reduction-oxidation processes and the LUMO levels were estimated at -4.42 eV. To analyse the effect of acceptor strength on the optoelectronic properties, Mori et al. synthesized I-4a in which the phenyl ring of the isatin core is replaced by a thiophene ring [START_REF] Yoo | n-Type Organic Field-Effect Transistors Based on Bisthienoisatin Derivatives[END_REF]. I-4b exhibited a considerably stronger electron deficiency properties than that found in I-4a parent, with a deep LUMO level of -4.28 eV. Compared with I-4a, the absorption spectra of thienoisatin derivatives displayed a broader and red-shifted features with a λ max of 650 nm. The red-shift was due to an increased D-A character of I-4b compared to I-4a. All these features make these materials promising for use as n-type OFET materials, with electron mobility of 0.10 cm 2 V -1 s -1 . pyrrolo [4,5-b]pyridin-2,3-dione (I-5b) [START_REF] Zhang | Fused Heptacyclic-Based Acceptor-Donor-Acceptor Small Molecules: N-Substitution toward High-Performance Solution-Processable Field-Effect Transistors[END_REF]. The replacement of the benzene ring with a pyridine moiety enhances the planarity and improves the structural ordering through non-covalent interactions, due to the lower steric requirements of nitrogen atom compared to the C-H unit, which results in a remarkable enhancement of hole mobility. In a separate study, the same authors showed that changing the end group from the I-5c to the thienyl methylene-oxindole unit, I-5d, while keeping the same π-bridge, indacenodithieno[3,2-b]-thiophene, enables high hole OFET-mobility of over 0.27 cm 2 V -1 s -1 [START_REF] Zhang | Improved charge transport in fused-ring bridged hemi-isoindigo-based small molecules by incorporating a thiophene unit for solution-processed organic field-effect transistors[END_REF]. A series of A-D-A-type OSC based on indacenodithiophene as a bridging group were synthesized and their opto-electrical properties were investigated by Zhao [START_REF] Zhao | Isatylidene malononitrile derived acceptors for fullerene free organic solar cells[END_REF][START_REF] Zhao | Isatin-derived non-fullerene acceptors towards high open circuit voltage solar cells[END_REF]. Compound I-6a in chloroform solution showed a major absorption peak at 540 nm, which underwent a considerable red-shift for I-6b (675 nm) and I-7 (730 nm) because of the gradual increase in the electron-withdrawing ability of the acceptor moieties of these molecules. This red-shift was accompanied by reducing the corresponding optical band-gap values from 1.95 eV for I-6a to 1.48 eV for I-6b and 1.43 eV for I-7. The LUMO energy level of these A-D-A-type OSC was found to vary significantly with the strength of the acceptor fraction. The LUMO energy of I-6b was significantly reduced to -4.02 eV. On the other hand, the LUMO energy of I-7 was close to that of I-6b. and to analyze how these modifications affect the photophysical, and electrochemical properties of these new dyes. DFT and TD-DFT studies have been performed to gain an insight into their electronic properties by determining the energy levels and maps of HOMO and LUMO as well as the HOMO-LUMO gap. To demonstrate their ability to act as n-type OSC, we performed SCLC measurements to probe their electron mobility. Electron only devices were fabricated by the spin-coating and the trap-limited electron mobility was calculated using Mott-Gurney law. 10a exhibited an intrinsic moderate electron mobility of 8.94×10 -4 cm 2 V -1 s -1 . The potential practical utility of these materials is demonstrated as an electron-transport materials (ETMs) for PSCs, with maximum power conversion efficiencies of 6.24% and 6.94%

for 10a and 4/10a respectively.

Experimental section

Materials and methods

Detailed synthetic procedures and characterization, NMR, UV-visible spectroscopy and high-resolution mass spectroscopy of new molecules, their intermediates, device fabrication and current-voltage characteristics, are available in the supplementary information (SI).

Theoretical and computational details

Geometries of all the molecules were fully optimized with B3LYP functional and Cadogan cyclisation, would be the optimal strategy to prepare five rings fused systems Y6 analog. The dinitro derivatives 7b and 8b were obtained using Stille coupling reaction followed by a Knoevenagel condensation with malononitrile. To extend the conjugation length between the two isatin moieties, terthiophene was appended to the isatin. Reaction of 2-tributylstannylthiophene with 17a or 17b under Stille coupling condition, produced the asymmetrical dye 18a (or 18b) in 80% yield.

Selective bromination at the 5-position of thiophene using the N-bromosuccinimide, afforded the intermediate 19a (or 19b). The obtained bromo thienyl-isatin was then coupled to the 2,5-di-tributylstannylthiophene to form 9a. To improve the solubility, the analogue 9b with a branched alkyl chain was obtained in a similar yield.

Optical characterization

The photophysical properties of A-D-A-type OSC based on bis-isatin and di-2-(2-oxindolin-3-ylidene) malononitrile derivatives were investigated by UV-vis spectroscopy, and the corresponding absorption data were listed in Table 1. For comparison purposes between malononitrile derivatives and bis-isatin derivatives, the absorption spectra of 1, 3, 5, 7a, 7b, 9a and their derivatives, 2, 4, 6, 8a, 8b, 10, were normalized to enable direct comparison of substituent effects, Figure 4. We note that we encountered difficulties in reproducibility of the molar extinction coefficients, because these molecules exhibit a strong tendency to aggregate in dilute solution.

Their spectra shared a common feature with two absorption bands: a low energy band in the visible region attributed to the ICT transition arising from the acceptor moieties and a high energy band in the range of 300-450 nm attributed to the π-π* bridge. The position of these bands were strongly influenced by the molecular structure of compounds, conjugation length of π-bridge, and the nature of acceptor moiety. The effect of the acceptor end group was demonstrated by comparing the absorption maxima of 7a and 8a, the solution spectrum of 8a exhibits bands for the π→π* transition (457 nm) and ICT (550 nm), while those of 7a are at 393 nm and 440 nm, demonstrating that the introduction of the dicyanovinylene groups resulted in a 100 nm bathochromic shift in absorption, (Table 1, entries 7 and 8).

A comparison of the absorption spectra of 3 (λ max = 349 nm) with 7a (λ max = 393 nm) revealed that the replacement of phenyl with thienyl ring caused a red-shift of the high energy band. This observation clearly indicated that the incorporation of thiophene moiety in A-D-A-type OSC enhanced their ICT-properties, as previously reported in the literature [START_REF] Azeem | Tuning of a A-A-D-A-A-Type Small Molecule with Benzodithiophene as a Central Core with Efficient Photovoltaic Properties for Organic Solar Cells[END_REF][START_REF] Raynor | Significant Improvement of Optoelectronic and Photovoltaic Properties by Incorporating Thiophene in a Solution-Processable D-A-D Modular Chromophore[END_REF]. This trend was also observed for the malononitrile derivatives, where a bathochromic shift of 43 nm was seen for the high energy band.

As shown in

Electrochemical study

The electrochemical behavior of the A-D-A type OSC based on bis-isatin and malononitrile derivatives were evaluated by means of CV using tetrabutylammonium perchlorate as supporting electrolyte in dichloromethane and the electrochemical data were listed in Table 2. The energy levels of HOMO (E HOMO ) and LUMO (E LUMO )

were respectively estimated from the onset potential of the first oxidation and reduction peak vs. Fc/Fc + , assuming an ionization energy of 4.80 eV for ferrocene.

The CVs of the bis-isatin derivatives showed one oxidation wave and two well-reversible reduction waves. The reduction potentials were found to be dependent on the bis-isatin structure. The CV of di-2-(2-oxindolin-3-ylidene) malononitrile derivatives under the same condition also showed two sets of reduction, but shifted to more positive values than that of the parent compound, bis-isatin, Figure 5. For example, compound 2 exhibited E red1 = -0.61 V (vs Ag/AgCl) compared to 1 (-1.11

V), thus leading to a shift of 0.50 V. This suggests that the LUMO energy levels were predominantly controlled by the nature of the acceptor units. Regardless of the nature of the end-group substituents, both reduction potentials followed the trend Ph < BTD < Th. For instance, in the first reduction process of the A-D-A-type malononitrile family, the BTD and thiophene were easier to reduce than the phenyl, corresponding to peaks of -0.52 V, -0.46 V, and -0.58 V respectively. Nevertheless, the difference in the reduction potential was less than 0.15 V, this small change was indicative of a minor contribution of the flanking aryl groups to the LUMO (Figure 5). On the other hand, compounds 7a and 9a, b (or compounds 8a and 10a, b) with one thiophene and terthiophene unit as a π-bridge group presented pretty close LUMO energy levels.

Changing the conjugate length of the π-bridge had a more significant effect on the HOMO energy level. 8b functionalized with -NO 2 and -CN group exhibited a low-lying LUMO energy level. The LUMO energy level could be tuned from -3.54 eV (7a) to -4.23 eV (8b), due to the fact that nitro was one of the strong electron-accepting groups. Changing the linkage pattern of the malononitrile derivatives (4-position to 6-position) had a small effect on the HOMO and LUMO energy levels, with a slightly higher HOMO energy level of 0.05 eV and a slightly lower LUMO energy level of approximately 0.02 eV for 4 compared to that of 2. The HOMO energy level of 8a was 0.07 eV higher than that of 4, which was caused by the stronger electron-donating ability of thiophene. In addition, the HOMO energy level of 7a was significantly higher than that of 5 (- The HOMOs mainly occupy the double bonds along the long-axis direction of the molecules while the LUMOs mostly distribute on single bonds perpendicular to the long-axis direction. For bis-isatin compounds, the distribution of HOMO and LUMO decreases from center π-bridge to terminal A segments. On the contrary, the HOMO and LUMO of malononitrile derivatives appear to distribute more on acceptor than π-bridge. Table 3 summarized the calculated HOMO and LUMO energy levels. For bis-isatin compounds, the HOMO energies have the order of 4 ≈ 6 < 8a < 10a while the LUMO energies show the trend of 6 < 8a < 4 ≈ 10a (Table 3). The resulted HOMO-LUMO gaps decrease in the order of 4 > 6 > 8a > 10a. It is a common rule that both HOMO and LUMO increase with polymer/oligomer length and the relatively higher HOMO and LUMO energy of 10a than 8a are easily understandable.

Electronic transitions

The computed energy levels are close to those obtained experimentally in the THF solution, indicating that M06L provides a good estimate of the HOMO-LUMO gap.

The aforementioned changes in the orbitals' shapes and energies can be related to the differences in the electronic transitions involved in the lowest-energy and highest-energy excited states of these molecules. The calculated optical gap (excitation energy of the first excited state) has the same trend as the HOMO-LUMO gaps, but the optical gaps have larger values due to orbital coupling energy. The lowest energy bands are due to the electronic transition from HOMO to LUMO and could be assigned to ICT transition between the π-conjugated bridge and end-group acceptor. ICT type transitions generally have a weak intensity, however, when the π-conjugation length increases, the intensity of the lowest energy band increases due to the contribution from π-π* transition of the donor. The comparison between the calculated and experimental HOMO and LUMO energies and HOMO-LUMO gap of all the molecules is depicted in Figure 7. The calculated energy values of HOMO and LUMO agree with experimental data within less than 0.15 eV for the entire series of molecules, which is not the case for the optical band gap energy. The underestimation is more severe for the larger molecules 9 and 10. The error, however, is not dramatic considering the size of the molecules. The high energy band is attributed to the π-π* transition for both π-bridge and acceptor groups. DFT simulated UV-vis data, Figure 8 supports the above observations that these lower energy transitions which are assigned as ICT have the maximum contribution in the visible region. In short summary, TD-DFT calculations were carried out to investigate the electronic effects of conjugation length and the substitution position of the end-group on molecular orbitals and electronic absorption spectra. The calculated molecular orbital energies and gap correspond well with the corresponding experimental data. The deviation between calculated and experimental orbital energies are less than 0.15 eV for most cases. In addition, the calculated trends for orbital energies among different compounds are the same as the experimental ones, as shown in Figure 7. with a clear slope variation from 4-10 V. From these J-V curves, the charge carrier mobility can be extracted using the Mott-Gurney equation:

. Therein ε 0 , is the permittivity of vacuum, ε r is the relative permittivity of the organic compound, μ is the charge carrier mobility, V is the voltage, and L is the thickness of the tested layer. As plotted in Figure 9, the current density-voltage characteristic curves and SCLC fittings for both films reveal the SCLC region (> 6V). This allows us to extract an average electron mobility of µ e = 3.51×10 -4 cm 2 V -1 s -1 and µ e = 3.61×10 -5 cm 2 V -1 s -1 for 10a and 4 respectively. The highest electron mobility of 10a is 8.94×10 -4 cm 2 V -1 s -1 . When compared to other A-D-A-type OSC small molecules from the literature, the mobility of 10a and 4 are in the same order of magnitude, where bis-lactam-based materials had an OFET mobility of 2.30×10 -4 cm 2 V -1 s -1 . [START_REF] Zhang | Acceptor-donor-acceptor small molecules based on fuse ring and 2-(2-oxindolin-3-ylidene)malononitrile derivatives for solution-processed n-type organic field-effect transistors[END_REF] Figure 9 SCLC measurements of the electron-only devices for 10a and 4 semiconductors with ohmic and trap-free space charge limited current regions.

Based on these results, several observations can be drawn. First, the finding that the higher mobility observed in films of 10a (A-D-A) cannot be explained only by the downshifted LUMO energy level, from -3.93 eV for 4 to -4.03 eV for 10a, which could, in fact facilitate electron injection, but also by a better planarity of 10a compared to 4. In fact, a better coplanarity of the π-system due to the introduction of

Ohmic region SCLC region

Ohmic n=1

Trap limited n>2 The 10a solutions were optimized to a concentration of 5 mg/ml and tested for different spin coating deposition speeds. Figure 12 shows the J-V curve of champion devices with 10a, 4/10a, and PCBM as an ETM, respectively. Table 4 summarizes the corresponding PV parameters. The surface morphology of perovskite layer was examined by SEM and AFM (top-view SEM in Figure 13 and AFM images in Figure S3 in SI). The distribution of grain sizes seems more homogeneous for the perovskite film cast on ITO/PEDOT:PSS and exhibits large grains size of between 400-500 nm range (Figure 13a). Figure 13b , and an FF of 73%, which is inferior to that reported in other literatures. [START_REF] Sharma | Inverted perovskite solar cells with air stable diketopyrrolopyrrole-based electron transport layer[END_REF][START_REF] Mamun | New PCBM/carbon based electron transport layer for perovskite solar cells[END_REF] The 10a based device showed a PCE of 6.24% with a J SC of 16.30 mA cm -2 , a V OC of 0.82 V, and an FF of 47%. 10a showed low performance with low FF compared to the PCBM one, which could be related to several reasons, such as a higher mobility of PCBM (µ PCBM = 1.22×10 -3 cm 2 V -1 s -1 ) compared to that of 10a (µ 10a =1.09×10 -4 cm 2 V -1 s -1 ). One of the reasons for the low value of Voc and FF for both devices could be related to the non-radiative recombination. Generally, it has been agreed that the non-radiative recombination losses arise from defects (charge-carrier traps) either in the bulk perovskite or at the interfaces. [START_REF] Yang | Stable and low-photovoltage-loss perovskite solar cells by multifunctional passivation[END_REF] Therefore, an optimization effort to passivate the defects on the perovskite surfaces and at the grain boundaries is necessary to enhance efficiency. Previous work has demonstrated that suitable small molecules, such as D-A-D with malononitrile as acceptor moiety, can effectively passivate the perovskite via Pb-N interactions. [START_REF] Daskeviciute-Geguziene | Passivating Defects of Perovskite Solar Cells with Functional Donor-Acceptor-Donor Type Hole Transporting Materials[END_REF][START_REF] Byranvand | Defect Passivation of Perovskite Films for Highly Efficient and Stable Solar Cells[END_REF] To verify the passivation effect, we prepared samples: pristine perovskite film and perovskite complexed with 4 via solvent annealing process, respectively. Compared with a control cell, the devices incorporating the derivative 4 exhibited improved performance with PCE = 6.94%, Voc = 0.79 V, Jsc = 17.11 mA cm -2 , FF = 51%. Thus, passivation treatment improved the Jsc and FF and confirming the less nonradiative recombination in the perovskite films. The overall improvement of the PCE should be ascribed to the ability of derivative 4 to passivate various trap sites on the crystal surface and at the grain boundaries of perovskite to minimize the non-radiative charge recombination. In summary this un-optimised device was operational with a PCE around 7%. Albeit displaying lower PCE compared with a reference device using PCBM (PCE of 9%), this initial device work highlights the potential of these materials to perform as ETL in solar cells.

Conclusion

We provide a wide range of systematic structure-property relationships that offer new perspectives on the design of electron-acceptor materials. Appropriate chemical modifications of both π-bridge and end capped group can effectively manipulate the optical, electrochemical, and energy levels of these molecules. When the isatin ring was replaced by the isatylidene malononitrile ring, a bathochromic shift of 80-110 nm at the longest wavelength was observed, which reduced the optical band-gap. The

  : A Joint Experimental and Theoretical Study Shiwei Ren, a Amirhossein Habibi, b Pingping Ni, b Yuexing Zhang* c and Abderrahim Yassar* b

Figure 1

 1 Figure 1 Chemical structures of bis-lactam-based organic materials reported in the literature. Besides their use as OFET materials, A-D-A-type OSC with deep LUMO levels

Figure 2

 2 Figure 2 Chemical structures of bis-isatin and di-2-(2-oxindolin-3-ylidene) malononitrile derivatives.

3. Results and discussion 3 . 1

 31 Design, synthesis and characterization of A-D-A-type OSCThe synthetic route to the target A-D-A-type OSC based on isatin derivatives, is shown in Scheme 1. The detailed synthesis and characterization are shown in the Experimental Section of SI. The desired bromoisatins[START_REF] Zhang | Fused Heptacyclic-Based Acceptor-Donor-Acceptor Small Molecules: N-Substitution toward High-Performance Solution-Processable Field-Effect Transistors[END_REF][START_REF] Zhang | Improved charge transport in fused-ring bridged hemi-isoindigo-based small molecules by incorporating a thiophene unit for solution-processed organic field-effect transistors[END_REF] were synthesized through a two-step procedure followed by intermediate 12, using the corresponding commercial 3-bromoaniline, 11, as a starting material. To overcome the solubility issue, alkyl solubilizing side chains, hexyl or long branched alkyl were introduced to 13 or 14 at the nitrogen atom to produce 16 or 17a-c in excellent yields. 16 and 17a were further reacted with 1,4-benzenediboronic acid bis(pinacol) ester, in the presence of [Pd 2 (dba) 3 ] as a catalyst, and K 3 PO 4 as a base to afford 1 and 3 in 60% and 70% yield, respectively. Subsequently, the bis-isatin compounds 1 and 3 were treated with malononitrile via a Knoevenagel condensation reaction to generate the target products 2 and 4, respectively. Replacement of phenyl with electron-withdrawing benzo[c][1,2,5]thiadiazole (BTD) was targeted to analyze the effect of π-bridge. The Suzuki-Miyaura reaction of 17a with BTD afforded 5 with 55% yield and subsequent Knoevenagel condensation with malononitrile provided 6 with 80% yield. Introducing a thiophene ring between the acceptor units was realized under Stille coupling reaction between 17a and 2,5-di-tributylstannylthiophene in the presence of [Pd(dppf)Cl 2 ] as a catalyst and afforded 7a in 64% yield. With the aid of a catalytic amount of the pyridine, the Knoevenagel condensation reaction could occur at room temperature, and afforded 8a in 89% of yield. It was envisaged that introduction of a nitro group, which could be subsequently employed in a late-stage in a double

Scheme 1 2 , 4 , 6 , 8 , 10 .

 1246810 Scheme 1 Synthetic route to bis-isatin compounds 1, 3, 5, 7, 9 and di-2-(2-oxindolin-3-ylidene) malononitrile derivatives 2, 4, 6, 8, 10. Reagents and conditions: (i) chloral hydrate, Na 2 SO 4 , H 2 NOH . HCl, 65 °C, 2 h; (ii) H 2 SO 4 , 75 °C, 15 mins, 35% over two steps; (iii) K 2 CO 3 , Br-R, R = -C 6 H 13 or -C 20 H 41 , DMF, 90 °C, 24 h, 80%-90%; (iv) NaNO 3 , H 2 SO 4 , 0 °C, 1 h, 87%; (v) 2-tributylstannylthiophene, [Pd(dppf)Cl 2 ], DMF, 90 °C, 80%; (vi) AcOH, NBS, THF, 0 °C, 5 h, 82%; (vii) 4,4,5,5-tetramethyl-2-(4-(4,4,5,5-tetramethyl-1,3-dioxolan-2-yl)phenyl)-1,3,2-dioxaborolane, P(o-tyl) 3 , [Pd 2 (dba) 3 ], K 3 PO 4 , Toluene, H 2 O, 90 °C, 24 h, 60%-70%; (viii) [Pd 2 (dba) 3 ], 4-(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)-7-(4,4,5,5-tetramethyl-1,3-dioxolan-2-yl) benzo[c][1,2,5]thiadiazole, P(o-tyl)3 , K 3 PO 4 , toluene, H 2 O, 90 °C, 24 h, 55%; (ix) 2,5-di-tributylstannylthiophene, [Pd(dppf)Cl 2 ], DMF, 90 °C, 64%-75%; (x) malononitrile, EtOH, reflux, 80%-90%; (xi) malononitrile, pyridine, EtOH, rt, 85-90%.

Figure 3 1 H

 1 Figure 3 1 H NMR spectra of compounds 6 (a); and 5 (b) in CDCl 3 (*: solvent peak).

  Figure S1 b, both absorption spectra of 1 and 3 exhibit two peaks assigned to π→π* transition (350 nm) and ICT (450 nm). A Comparison of the spectra of compounds 1 and 3 shows an increase of ICT band intensity for compound 1. The enhancement of the ICT band intensity could be attributed to a better planarity of the structure induced by an electrostatic interaction between the carbonyl of isatin and the phenyl ring forming a hydrogen bond. However, there was no much variation between the main absorption peaks of the phenyl ring units at the 4-and 6-positions (compound 2 and 4), FigureS1 c, probably because they are both linearly conjugated. This is supported by geometry optimizations where the molecule 1 exhibits a more coplanar molecular conformation with a dihedral angle of 46 ° (FigureS2), while the dicyanovinyl analog 2 exhibits a 68° dihedral angle between the phenyl and isatin planes in its most stable conformation. The H-bond H•••O distance of 2.60 A which is significantly shorter than the sum of van der Waals radii of O and H atoms (2.72Å)[START_REF] Bondi | van der Waals Volumes and Radii[END_REF].Additionally, the possible steric hindrance of the chemical structure has always limited the introduction of a large aromatic ring at 4-position of isatin. The absorption spectra of 10a and 10b (FigureS1 d) showed almost identical absorptions in the visible range, indicating that changes in the alkyl group on the nitrogen atom hardly influenced the electronic structure of the malononitrile derivatives. For both series of bis-isatin and malononitrile derivatives, the absorption spectra revealed that the absorption peaks rising from the aromatic bridges were gradually red-shifted to longer wavelengths with increasing the conjugation length. For instance, 10a exhibited a broad and strong absorption spectrum with a λ max of 605 nm. Obviously, this red-shift could be attributed to the extended π-conjugation length compared with that of 8a.Variation of the π-conjugated bridge units had a notable impact on the absorption profiles of the new bis-isatin and malononitrile derivatives. An intriguing feature observed was that 8b displayed a blue-shift of the maximum of the absorption compared to 8a (Figure4bpurple line vs. green line). This blue-shift could be attributed to the steric hindrance of the two nitro groups (-NO 2 ). This is consistent with studies by Jean at al. who reported the decrease intensities and hypsochromic shifts in the absorption spectra of non-coplanar conjugated molecules sterically 4,4'-tetra-nitro-5,5'-dimethyl-3,3'-bithienyl; 3,3'-dinitro-5,5'-diacetyl-2,2'-bithienyl; and 3,3'-Dinitro-5,5'-dicarbometh-oxy-2,2'-bithienyl, are a result of the steric hinderance on the part of the ortho substituted groups [27]. A similar trend in the absorption features is observed when comparing the absorption bands,  max of 7a and 7b. The optical gaps of the bis-isatin derivatives were approximately 2.25 eV, while the optical gaps of the di-2-(2-oxindolin-3-ylidene) malononitrile series were lowered to around 1.90 eV, with the lowest optical gap of 1.63 eV for compound 10.

Figure 4

 4 Figure 4 Normalized UV-vis absorption spectra of bis-isatin derivatives 1, 3, 5, 7a, 9a,b (a) ; and di-2-(2-oxindolin-3-ylidene) malononitrile derivatives 2, 4, 6, 8a, 8b, 10a,b (b) in THF (concentration range 0.05-0.10 mg/ml). Compounds λ max sol (nm) a λ onset sol (nm) a E g opt (eV) b

Figure 5

 5 Figure 5 Cyclic voltammograms of bis-isatin compounds 1, 3, 5, 7a, 9a, b (a); and malononitrile derivatives 2, 4, 6, 8a, 8b, 10a, b (b) in dichloromethane (concentration range of 10 -4 to 10 -3 M).As shown in Table2, the LUMO energy levels of A-D-A type OSC based on

3. 4

 4 FigureS3in SI shows the molecular orbital maps of all the molecules. Both

Figure 6

 6 Figure 6 reports a survey of the calculated orbital energy levels and maps of the

Figure 6

 6 Figure 6 The evolution of energy levels of frontier molecular orbitals of five bis-isatin derivatives (top); and six di-2-(2-oxindolin-3-ylidene) malononitrile derivatives (bottom). Lines connecting the dots (different compounds) to better visualise the trends.

Figure 7

 7 Figure 7 Comparison between calculated and experimental LUMO, HOMO, HOMO-LUMO energy gap and optical band gap of eleven bis-isatin and di-2-(2-oxindolin-3-ylidene) malononitrile derivatives.

Figure 8

 8 Figure 8 TD-DFT simulated UV/vis absorption spectra with half-width at half height of 2000 nm of the bis-isatin and di-2-(2-oxindolin-3-ylidene) malononitrile derivatives.3.5 Electrical characterization

  8.94×10 -4 cm 2 .V -1 .s -1 µ e = 3.61×10 -5 cm 2 .V -1 .s -1 thiophene units, may induce a strong π-π stacking interactions in the solid state, leading to improved charge transport and higher electron mobility value. Second, the finding that the electron mobility of 4 is only one order of magnitude lower than the electron mobility of 10a means that the molecular design, extending π-conjugation core, does not affect too much the electrical properties. As reported in literature charge transport, morphology and molecular aggregation in thin film are intimately related. Surface morphologies of 10a and 4 films were examined by atomic force microscopy (AFM). As shown in Figure10both films exhibited a relatively smooth surface with root mean square of 0.96 nm for molecule 4, and 1.15 nm for molecule 10a, indicating their good film forming ability and more uniform thin film microstructures.

Figure 10

 10 Figure 10 AFM topographic images of a) 4 and b) 10a thin film on silicon wafer.

Figure 11

 11 Figure 11 Energy band diagram of malononitrile derivative 10a material used as an ETM in the perovskite solar cell.

Figure 13

 13 Figure 13 Top-view SEM images of the perovskite thin film deposited on the PEDOT:PSS (a); and cross sectional image of the perovskite solar cell device (b).

  photovoltaic characterization. Pingping Ni: PhD student performed the organic

Table 1

 1 Optical properties analysis data of synthesized bis-isatin and di-2-(2-oxindolin-3-ylidene) malononitrile derivatives 1-10. a λ max in THF solution, b the optical energy gap is estimated from the absorption onset in THF solution E g opt = 1240 / λ onset .

	1	430, 347	530	2.34
	2	514, 415	628	1.97
	3	434, 349	532	2.33
	4	515, 414	630	1.97
	5	440, 380	546	2.27
	6	533, 423	651	1.90
	7a	440, 393	553	2.24
	8a	550, 457	670	1.85
	8b	432, 520	642	1.93

Table 2

 2 5.35 vs. -5.53 eV, Table2) in bis-isatin series, which also indicated the strong electron donor characteristics of the thiophene. The HOMO level

		E red1	E red	onset	E LUMO	E HOMO	E g	CV
		(eV)	(eV)	(eV) c	(eV) c	(eV) d
	1	-1.11	-0.87	-3.40	-5.46	2.06
	2	-0.61	-0.36	-3.91	-5.92	2.01
	3	-1.03	-0.81	-3.46	-5.52	2.06
	4	-0.58	-0.34	-3.93	-5.87	1.94
	5	-0.93	-0.74	-3.53	-5.53	2.00
	6	-0.52	-0.29	-3.98	-5.82	1.84
	7a	-0.94	-0.73	-3.54	-5.35	1.81
	8a	-0.46	-0.19	-4.08	-5.80	1.88
	8b	-0.30	-0.04	-4.23	-5.96	1.73
	9a,b	-0.95	-0.71	-3.56	-5.11	1.55
	10a,b	-0.47	-0.24	-4.03	-5.23	1.20

of compound 10 bearing either linear or branched alkyl side chains (10a or 10b) was much higher than one thiophene or one phenyl unit bridge compound, due to the nature of the long conjugation donor chain. The resulted HOMO-LUMO gaps decreased to 1.20 eV. Finally, a change in the alkyl chain length does not affect the UV-visible and the electrochemical properties, both series, 10a, 10b exhibit identical HOMO/LUMO energy levels, suggesting that the influence of the alkyl chains on the HOMO/LUMO energy level is negligible. Cyclic voltammetry results of bis-isatin and di-2-(2-oxindolin-3-ylidene) malononitrile derivatives 1-10. c HOMO/LUMO energy levels were calculated from the onset of oxidation and reduction waves using an offset of -4.80 eV for saturated Ag/AgCl, E LUMO = -4.80 eV -[(Eredonset) -E 1/2 (ferrocene)] and E HOMO = -4.80 eV -[(E ox onset ) -E 1/2 (ferrocene)], d E g cv = electrochemical gap.

Table 3

 3 The higher HOMO and LUMO energy of 8a than 6 indicates that thiophene moiety has larger electron-donating ability than BTD group. Calculated energies of the HOMO and the LUMO (E HOMODFT and E LUMO solvent model in THF on the basis of the optimized geometries at B3LYP/6-31G(d) level with IEFPCM solvent model in THF. All energies are in eV.

		E g-opt	DFT	E LUMO	DFT	E HOMO	DFT	E g	DFT
	1	2.30	-3.37	-5.60	2.23
	2	1.83	-4.01	-5.78	1.77
	3	2.35	-3.48	-5.68	2.20
	4	1.78	-4.13	-5.76	1.63
	5	2.17	-3.67	-5.69	2.02
	6	1.72	-4.20	-5.76	1.56
	7a	2.17	-3.60	-5.54	1.94
	8a	1.62	-4.21	-5.62	1.41
	8b	1.78	-4.46	-6.06	1.60
	9a,b	1.68	-3.48	-5.00	1.52

Table 4 PV

 4

parameters of PSCs using PCBM or 10a, 4 (passive tretment)/10a and PCBM as ETMs.

Data in parenthesis are the average over 8 for PCBM, 6 for 10a and 5 for 4 /10a.

Acknowledgements

This work benefited from the support of EDF in the framework of the research and teaching Chair «Sustainable energies » at Ecole polytechnique. Y. Z. gratefully thanks the financial support from the Science and Technology Research Project of Hubei Province Department of Education (D20191001), Hubei and Dezhou University. A.Y. thanks ANR-16-CE07-0024(GATE), S.R. thanks the China Scholarship Council for a PhD fellowship (No.201808070090) and the fellowship of China Postdoctoral Science Foundation No.2022TQ0399.

Data availability

No data was used for the research described in the article.

synthesis of dyes. Yuexing Zhang: carried out the theoretical calculations.

Abderrahim Yassar: Supervised the whole project and, Funding acquisition, written the original draft. Yuexing Zhang: Supervised the whole project and, Funding acquisition, written the original draft. All authors have contributed in correcting, enhancing the quality of the discussion and editing the manuscript.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https:


Corentin Gay

Pauline Spaeter

Nassima Chenikha

Lionel Aranda

Patrice Berthod

Dependence on their Mn and Cr contents of the microstructures, melting range and high temperature creep behaviors of Cantor's alloy and versions strengthened by MC carbides

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

Introduction

Chemical compositions & as-cast microstructures of the alloys [2-4]

• The corresponding supplemental proceeding TMS is available; see pp.659-668.

Decreasing

  Mn and increasing Cr in the cast Cantor's alloys and their MC-strengthened versions induce significant improvements for their oxidation behaviors at high temperature [1]. But these changes in the chemical composition may have also consequences on the microstructures, the refractoriness and the high temperature mechanical properties. The aim of this work is first to perform differential thermal analyses (DTA) for specifying the temperatures of starts and stops of melting and solidification. Second, it is also to characterize the creep resistances of these alloys by the mean of 3 points flexural creep tests, carried out at several temperatures in the [1,000 -1,200°C] range for several values of the induced maximal tensile stress varying ranging from 10 to 20 MPa.

•

  "Mn1Cr1" is the original Cantor's alloy (equimolar in Co, Ni, Fe, Cr and Mn) in a conventionally cast version; "Mn0.5Cr1.5" is a modified version resulting from a decrease in Mn (× 0.5 → 10 at.%) and an increase in Cr (× 1.5 → 30 at.%) ; both of them are single-phased • "Mn1Cr1TaC" and "Mn0.5Cr1.5TaC" are developed from the quinary "Mn1Cr1" and "Mn0.5Cr1.5" alloys respectively; they additionally contain 4 wt.% Ta and 0.25 wt.% C; their matrixes are similar to the two quinary alloys (except the additional presence of about 1 wt.%Ta in solid solution); eutectic TaC carbides, located in the interdendritic spaces, are present in their microstructures • "Mn1Cr1HfC" and "Mn0.5Cr1.5HfC" are the "Mn1Cr1" and "Mn0.5Cr1.5" alloys modified by the addition of 4 wt.% Hf and 0.25 wt.% C; their matrixes are similar to the two quinary alloys described above (notably: no Hf in solid solution); eutectic HfC carbides are present in the interdendritic spaces; some blocky HfC carbides -probably of a pre-eutectic nature -also formed, forming clusters. Dependence on their Mn and Cr contents of the microstructures, melting range and high temperature creep behaviors of Cantor's alloy and versions strengthened by MC carbides Corentin Gay 1 , Pauline Spaeter 1 , Nassima Chenikha 1 , Lionel Aranda 2 , Patrice Berthod 1,2 1 Faculté des Sciences et Technologies, Campus Victor Grignard, F-54500 VANDOEUVRE-LES-NANCY (France) 2 Institut Jean Lamour, CNRS (UMR 7198), 2 allée André Guinier, Campus Artem, F-54000 NANCY (France) patrice.berthod@univ-lorraine.fr DTA results Decreasing the Mn content and increasing the Cr one induced refractoriness improvement • The presence of the TaC or HfC eutectic carbides shifts downwards the melting or solidification temperature ranges 3 points bending creep results at 1000°C • "Mn1Cr1" and "Mn0.5Cr1.5" deformed rather slowly under 10 MPa; the most resistant among the two is clearly "Mn0.5Cr1.5"; unfortunately, for 20MPa the behavior of "Mn0.5Cr1.5" is considerably worse • The influence of the presence of carbides is contrasted: TaC allows the Mn1Cr1 base behaving much better while this is more to be discussed in the case of the Mn0.5Cr1.5 base • Adding HfC seems less efficient than adding TaC for reinforcing the Mn1Cr1 base (due to the presence of some HfC clusters which tends, at constant Hf and C contents, to lower the script HfC presence between dendrites?) Conclusion Clearly, the contents in Mn (the less refractory element in the Cantor's composition) and in Cr (the most refractory one), have both an influence of the melting range of the three types of alloys: the carbide-free ones, the TaCcontaining ones and the HfC-containing ones. Decreasing the Mn content and increasing the Cr one at the same time induce an increase in solidus temperature, with possible favorable consequence on the creep resistance. An increase in liquidus temperature can be also noted and this may influence the castability of the alloys. Concerning the creep resistance, no certain effect of these refractoriness differences was proven with the creep tests which were performed. This is much more the presence or not of TaC or HfC carbides which plays an important role for the creep resistance.

Acknowledgements:

Nassima Chenikha, Corentin Gay and Pauline Spaeter for their help for synthesizing some of the alloys.


Evelyne Benoit

Michel De Waard

Rémy Béroud

Michel Partiseti

Denis Servent

Multi-scale evaluation of spider toxins as potential anti-nociceptive agents: example of cyriotoxin-1a

Venom collection Purification

Fractions Sub-fractions Primary (Na V 1.7) Secondary (Na V 1.7 vs1.5)

Screening

Selected pure peptides

Sequencing Synthesis Structure

In vitro In vivo

Testings SAR optimisation

In vivo

Validation

Multi-scale evaluation of spider toxins as potential anti-nociceptive agents: Example of Cyriotoxin-1a Na V 1.7 channel subtype is highly expressed in dorsal root ganglia (DRG) and plays a key role in pain signaling. We performed high-throughput screening of an original animal venom library, using automated patchclamp experiments on human Na V channel subtypes, to find new selective inhibitors of this target ①, and then in vitro and in vivo electrophysiological experiments to characterize the active peptides that have been purified, sequenced and chemically synthesized ②. We identified a novel peptide, , isolated from Cyriopagopus schioedtei spider venom ①. This 33 amino acids toxin inhibits hNa V 1.1-1.3 and 1.6-1.7 in the low nanomolar range, compared to the micromolar range for hNa V 1.4-1.5 and 1.8. CyrTx-1a is 920 times more efficient at inhibiting tetrodotoxin (TTX)-sensitive than TTX-resistant Na currents of adult mouse DRG neurons in vitro, and approximately 170 times less efficient than huwentoxin-IV at altering mouse skeletal neuromuscular excitability in vivo. Finally, CyrTx-1a exhibits analgesic effects in mice by significantly increasing reaction time in the hot-plate assay ②. These results pave the way for further engineering studies aimed to optimize the potential anti-nociceptive properties of CyrTx-1a.

  Evelyne Benoit 1 , Michel De Waard 2 , Rémy Béroud 3 , Michel Partiseti 4 , and Denis Servent 1 Institut du Thorax, Inserm UMR 1087 / CNRS UMR 6291, Nantes, France 3 Smartox Biotechnology, Saint-Egrève, France 4 Sanofi R & D, Integrated Drug Discovery -High Content Biology, Vitry-sur-Seine, France

1 Service d'Ingénierie Moléculaire pour la Santé, ERL CNRS/CEA 9004, Gif-sur-Yvette, France 2


Rafika Boutalbi
email: rafika.boutalbi@ipvs.uni-stuttgart.de

Mira Ait-Saada
email: mira.ait-saada@u-paris.fr

Anastasiia Iurshina
email: anastasiia.iurshina@ipvs.uni-stuttgart.de

Steffen Staab
email: steffen.staab@ipvs.uni-stuttgart.de

Mohamed Nadif
email: mohamed.nadif@u-paris.fr

Tensor-based Graph Modularity for Text Data Clustering

Keywords: CCS CONCEPTS, Unsupervised learning, • Clustering → Tensor data, • NLP → Word embedding, • Graph theory, Text clustering, Tensor, Graphs, NLP, Word embedding

Graphs are used in several applications to represent similarities between instances. For text data, we can represent texts by different features such as bag-of-words, static embeddings (Word2vec, GloVe, etc.), and contextual embeddings (BERT, RoBERTa, etc.), leading to multiple similarities (or graphs) based on each representation. The proposal posits that incorporating the local invariance within every graph and the consistency across different graphs leads to a consensus clustering that improves the document clustering. This problem is complex and challenged with the sparsity and the noisy data included in each graph. To this end, we rely on the modularity metric, which effectively evaluates graph clustering in such circumstances. Therefore, we present a novel approach for text clustering based on both a sparse tensor representation and graph modularity. This leads to cluster texts (nodes) while capturing information arising from the different graphs. We iteratively maximize a Tensor-based Graph Modularity criterion. Extensive experiments on benchmark text clustering datasets are performed, showing that the proposed algorithm referred to as Tensor Graph Modularity -TGM-outperforms other baseline methods in terms of clustering task. The source code is available at https://github.com/TGMclustering/TGMclustering.

Green for word co-occurrence, Red for named entities, and Yellow for semantic meaning.

INTRODUCTION

Text clustering is an unsupervised learning task that aims at grouping a set of texts based on some extracted features (words, entities, embedding, etc.) into classes (or clusters). It relies on explicit or implicit similarity/dissimilarity measures for evaluating the similarity between texts. It is an essential task for many applications such as document retrieval, sentiment analysis, Spam e-mail detection, etc. The Bag-Of-Words (BOW) is a popular model for text representation [START_REF] Khan | Mining opinion from text documents: A survey[END_REF][START_REF] Sharma | Recent developments in text clustering techniques[END_REF], where the word occurrences describe the text. Then some specific clustering algorithms, such as Kmeans [START_REF] Macqueen | Some methods for classification and analysis of multivariate observations[END_REF] or SphericalKmeans [START_REF] Buchta | Spherical k-means clustering[END_REF], are applied using the BOW representation to group text into classes [START_REF] Aggarwal | A survey of text clustering algorithms[END_REF][START_REF] Guan | Deep feature-based text clustering and its explanation[END_REF]. The BOW representation could achieve excellent clustering results, especially when the clusters' topics are quite different. However, BOW does not record the text's sequence information or rich contextual information. In figure 1, the example exposes the limits of the BOW representation. The two text fragments belong to the same topic, but the occurrence of common words based on the BOW representation is very low (only one-word 'research'). To tackle these issues, several works made use of another way of representing text, which is the word embedding representations derived from a Language Model (LM) like Word2vec [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF] and GloVe [START_REF] Pennington | Global vectors for word representation[END_REF]. Unlike BOW, the dense representations provided by word embeddings have a better ability to capture the sense of words and sentences. Some authors use these representations to improve text clustering [START_REF] Ganguly | Contextual word embedding: a case study in clustering tweets about emergency situations[END_REF][START_REF] Ge | Improving text classification with word embedding[END_REF][START_REF] Tache | Clustering word embeddings with self-organizing maps. application on laroseda-a large romanian sentiment data set[END_REF] and they show that the clustering benefits from the two representations, BOW, and word embeddings, and from the mutual information that arises from each representation. More recently, sophisticated language models like the famous Bidirectional Encoder Representations from Transformers (BERT) achieved state-of-the-art results on a wide range of NLP (Natural Language Processing) tasks, including question answering and text generation [START_REF] Devlin | Pre-training of deep bidirectional transformers for language understanding[END_REF]. In contrast to the previous word embedding techniques, which provide one unique vector for each word of the vocabulary, the word representations delivered by transformers depend on the context of the given word. They are therefore referred to as contextual word embeddings.

Few works related to Transformer embeddings and entity embeddings are devoted to the purpose of text-clustering [START_REF] Ait-Saada | How to Leverage a Multi-Layered Transformer Language Model for Text Clustering: An Ensemble Approach[END_REF][START_REF] Nadif | Unsupervised and self-supervised deep learning approaches for biomedical text mining[END_REF]. In [START_REF] Walkowiak | Evaluation of vector embedding models in clustering of text documents[END_REF], several text representations (CBOW, BERT, ELMo, etc.) are compared by performing popular clustering algorithms such as Kmeans, SpectralClustering. The authors showed that the bestperforming representation depends on the dataset, and it is impossible to choose the best representation in the unsupervised context. Therefore it is essential to develop new algorithms to leverage several text representations.

A suitable way of combining the different available representations consists in using them as part of a 3-way tensor model representation [START_REF] Romeo | Semantic-based multilingual document clustering via tensor modeling[END_REF] or 3-way similarity tensor [START_REF] Boutalbi | Implicit consensus clustering from multiple graphs[END_REF]. To achieve the latter for a given dataset, we first compute different representation matrices (using BOW, static and contextual embeddings, and entity linking). Then, we compute from each data representation a similarity matrix viewed as the adjacency matrix of a graph that connects the documents (nodes). Finally, the similarity matrices are structured as a 3-way tensor (cf. figure 2).

This paper proposes a general, practical, and parameter-free method to learn a consensus clustering from multiple similarity graphs via tensor-based graph modularity. The advantage of the proposed approach is taking into account the graphs' properties through the modularity measure. The proposed approach, referred to as Tensor Graph Modularity (TGM), optimizes a modularity criterion from multiple similarity matrices organized in a three-way data (cf. figure 2). We summarize our main contributions in this work as follows:

• We propose a tensor representation that encloses different text similarities in the same data structure. • We develop a novel algorithm TGM for clustering of multiple graphs based on tensor representation and graph modularity. • We show that improvements can be achieved by using TGM compared to more commonly used clustering and tensor decomposition approaches.

MODULARITY MEASURE

Modularity is a measure that is commonly used to evaluate the quality of graph clustering. This measure has received considerable attention in several areas since the fundamental work presented in [START_REF] Newman | Finding and evaluating community structure in networks[END_REF] quantifies the edge density of a graph relative to the expected edge density of a random graph [START_REF] Shao | Modularity measures: Concepts, computation, and applications to manufacturing systems[END_REF]. The modularity takes values between -0.5 and 1 [START_REF] Brandes | On modularity clustering[END_REF]. An optimal graph clustering maximizing the modularity measure can be used for document clustering [START_REF] Ailem | Co-clustering document-term matrices by direct maximization of graph modularity[END_REF]. Given an undirected graph 𝐺 = (𝑉 , 𝐸) where 𝑉 is the set of vertices (or nodes) and 𝐸 the set of edges between nodes. Let X ∈ R 𝑛×𝑛 be a binary-symmetric adjacency matrix with (𝑖, 𝑗) as entry. The entry 𝑥 𝑖 𝑗 = 1 if there is a link between the nodes 𝑖 and 𝑗, and 0 otherwise. The modularity measure 𝑄(X, Z) for the partition matrix (or one-hot encoding of the label vector) Z ∈ R 𝑛×𝑔 of the graph 𝐺 represented by the adjacency matrix X is defined as follows:

𝑄(X, Z) = 1 2|𝐸| 𝑛 ∑ 𝑖,𝑗=1 (𝑥 𝑖 𝑗 - 𝑥 𝑖. 𝑥 .𝑗 2|𝐸| ) 𝑔 ∑ 𝑘=1 𝑧 𝑖𝑘 𝑧 𝑗𝑘 ( 1
)
where 𝑔 is the number of clusters, 𝑛 the number of nodes, 2|𝐸| = 𝑖 𝑗 𝑥 𝑖 𝑗 = 𝑥 .. is the number of edges, 𝑥 𝑖. = 𝑗 𝑥 𝑖 𝑗 , and 𝑥 .𝑗 = 𝑖 𝑥 𝑖 𝑗 the degree of the node 𝑖. The expected probability of edges 𝑚 𝑖 𝑗 = 𝑥 𝑖. 𝑥 .𝑗 2|𝐸| can be represented by the matrix M. We can rewrite the modularity expression as: 𝑄(X, Z) = 1

𝑥 .. 𝑛 𝑖,𝑗=1 𝑔 𝑘=1 (𝑥 𝑖 𝑗 -𝑚 𝑖 𝑗 )𝑧 𝑖𝑘 𝑧 𝑗𝑘 .

TENSOR-BASED GRAPH MODULARITY

We represent the different similarity matrices using a three-way tensor. A three-way tensor or third-order tensor has three dimen- )𝑧 𝑖𝑘 𝑧 𝑗𝑘 .

(

) 2
which be written as

Q(X, Z) = 𝑣 ∑ 𝑏=1 1 𝑥 𝑏 .. 𝑛 ∑ 𝑖=1 𝑔 ∑ 𝑘=1 𝑧 𝑖𝑘 𝑛 ∑ 𝑗=1 (𝑥 𝑏 𝑖 𝑗 - 𝑥 𝑏 𝑖. 𝑥 𝑏 .𝑗 𝑥 𝑏 .. )𝑧 𝑗𝑘 (3)
Taking

𝑥 𝑏 𝑘. = 𝑖 𝑧 𝑖𝑘 𝑥 𝑏 𝑖. = 𝑗 𝑧 𝑗𝑘 𝑥 𝑏 .𝑗 = 𝑥 𝑏 .𝑘 and 𝑥 𝑏 𝑖𝑘 = 𝑗 𝑥 𝑏 𝑖 𝑗 𝑧 𝑗𝑘 leads to Q(X, Z) = 𝑣 ∑ 𝑏=1 1 𝑥 𝑏 .. Trace[(X 𝑏 Z -M 𝑏 Z)Z ⊤ ] ( 4
)
where

M 𝑏 = (𝑚 𝑏 𝑖 𝑗 ) = 𝑥 𝑏 𝑖. 𝑥 𝑏 .𝑗
2|𝐸 𝑏 | . Using (3), the goal is to maximize the modularity through all graphs. The optimal hard clustering partition is given as follows. At iteration (𝑡 + 1) we have (

𝑧 (𝑡 +1) 𝑖𝑘 = 1 if 𝑘 = arg max 1≤𝑘 ≤𝑔 𝑣 𝑏=1 1 𝑥 𝑏 ..
) 5
The proposed approach deals to propose the Tensor Graph Modularity algorithm TGM presented in Algorithm 1. The convergence is achieved when the difference between iteration (𝑡) and iteration (𝑡 + 1) is smaller than 𝜖.

Algorithm 1: TGM Input: X, 𝑔.

Initialization: Z (0) randomly at 𝑡 = 0 repeat (1) Compute Q(X, Z (𝑡 ) ) (2) Compute Z (𝑡 +1) maximizing Q(X, Z (𝑡 ) ) using (5) (3) Compute Q(X, Z (𝑡 +1) ) until Convergence Q(X, Z (𝑡 +1) ) -Q(X, Z (𝑡 ) ) < 𝜖; return Z, Q(X, Z)

EXPERIMENTS

In our experiments, we used benchmark datasets for text clustering with the available true partitions. We evaluate all algorithms using metrics that compare the obtained clustering partitions and the true partitions. Three datasets are used to assess the performance of the different clustering techniques. DBLP1 is proposed in [START_REF] Boutalbi | Sparse tensor co-clustering as a tool for document categorization[END_REF], classic3 by Cornell University and we also used an extract of size 8,000 of the AG-news 1 dataset. The number of samples, clusters, and features' dimensions are given for each dataset in Table 1.

Experimental settings

In order to evaluate the partitions provided by each clustering, we rely on two well known metrics dedicated to clustering evaluation: Normalized Mutual Information (NMI) [START_REF] Strehl | Cluster ensembles-a knowledge reuse framework for combining multiple partitions[END_REF] All the clustering algorithms are run 30 times with different initializations, and their average scores are compared. In our experiments, we use three representations for each dataset, depending on the algorithm intended to be run. Here, we detail the three data representations that we exploit:

Feature-based representations. In order to use and evaluate standard clustering algorithms on the three datasets, we represent each document by a vector of fixed size, determined by the method that is used to compute the document representations. Given a dataset of 𝑛 documents, we compute 𝑣 = 5 different data matrices E 𝑏 , 𝑏 = 1, . . . 𝑣, each one of size 𝑛 × 𝑚 𝑏 , where 𝑚 𝑏 is the number of features of the representation and is given in Table 1. The feature-based representations are:

The obtained representations are represented by E 𝑏 , 𝑏 = 1, . . . , 𝑣, as shown in Figure 2, and are given as input for two standard clustering algorithms, namely Kmeans or SKmeans. In addition, we consider an AE learning a low-dimension representation of size 15 on which a Kmeans is applied.

1 http://groups.di.unipi.it/~gulli/AG_corpus_of_news_articles.html Pair-wise similarity representations. Another way of representing a dataset of 𝑛 samples consists in assigning a pairwise similarity measure 𝑥 𝑏 𝑖 𝑗 to each pair (𝑖, 𝑗) of document samples as part of the X 𝑏 similarity matrix of size 𝑛 × 𝑛, as shown in figure 2. To compute the matrix X 𝑏 , we use the corresponding representation E 𝑏 of the documents, that is described in the previous section. e 𝑏 𝑖 and e 𝑏 𝑗 are the 𝑖th and 𝑗th row of E 𝑏 respectively. In the case of the BOW and Entity representations, the similarity is computed by the dot product e 𝑏 𝑖 • e 𝑏 𝑗 which represents the number of words or entities in common in documents 𝑖 and 𝑗. For the representations obtained by embedding models (GloVe, BERT, SRoBERTa), we use a binarized cosine similarity measure, computed as:

𝑥 𝑏 𝑖 𝑗 = 1 if e 𝑏 𝑖 • e 𝑏 𝑗 ∥e 𝑏 𝑖 ∥ ∥e 𝑏 𝑗 ∥
≥ 𝑝 and 0 otherwise, where 𝑝 is the percentile that depends on the sparsity we expect the similarity matrix to have. For the dense embedding representations, we use the percentile that leads to a sparsity of 97%. The obtained representations X 𝑏 , 𝑏 = 1, . . . , 𝑣 of size 𝑛 × 𝑛 are used as input for three graph clustering algorithms ITCC [START_REF] Dhillon | Information-theoretic co-clustering[END_REF][START_REF] Govaert | Mutual information, phi-squared and model-based co-clustering for contingency tables[END_REF], CoclustMod2 [START_REF] Ailem | Co-clustering document-term matrices by direct maximization of graph modularity[END_REF][START_REF] Role | Coclust: A python package for co-clustering[END_REF] and SPLBM [START_REF] Ailem | Model-based co-clustering for the effective handling of sparse data[END_REF][START_REF] Ailem | Sparse poisson latent block model for document clustering[END_REF].

Tensor representations. The information provided by each of the 𝑣 representations of documents is intrinsically different, we posit that each brings some information that are not necessarily present in the others (cf. the example in Figure 1). In order to harness all the useful information brought by each representation, we simply reorganize the similarity matrices X 𝑏 , 𝑏 = 1, . . . , 𝑣 described in the previous section as part of a tensor X of size 𝑛 × 𝑛 × 𝑣. This tensor is used as input to tensor-based clustering techniques which are PARAFAC [START_REF] Harshman | Parafac : parallel factor analysis[END_REF], TUCKER [START_REF] Tucker | Some mathematical notes on three-mode factor analysis[END_REF], TSPLBM3 [START_REF] Boutalbi | Sparse tensor co-clustering as a tool for document categorization[END_REF][START_REF] Boutalbi | Implicit consensus clustering from multiple graphs[END_REF][START_REF] Boutalbi | Tensorclus: A python library for tensor (co)-clustering[END_REF] and our proposed algorithm TGM.

Clustering results

Figure 3 reports the performance obtained by 12 combinations of slices where 𝑣 ∈ {2, 3, 4, 5} using TGM. We first observe that the configuration BOW-SRoBERTa is the best performing 2-slices configuration, achieving competitive NMI scores. Then, adding the BERT and Entity slices improves the performance for all datasets. Finally, adding the GloVe slice lead us to 𝑣 = 5 and further improves the results for 4 datasets out of 6. This shows that TGM is capable to harness the useful knowledge provided by the different representations; it overcomes the possible noise induced by some representations.

The numerical results (NMI) 4 obtained by each clustering algorithm on the three datasets are depicted in Table 2, where TGM ALL stands for the TGM algorithm applied to a tensor containing all of the five slices (BOW, BERT, SRoBERTa, GloVe and Entity). We first observe that the best scores are achieved by TGM in the majority of cases. The scores obtained by TGM are still competitive. Also, the (max-min) values on unique representation indicate that none of the five ways of representing the documents are robust enough when used individually as input to any of the clustering or graph clustering algorithms, in comparison to TGM. This also supports the idea that each of the five representations brings some valuable information, potentially not available in the others. Also, it is important to note that, being in an the unsupervised setting where labels are not supposed to be available, it is impossible to know in advance which slice is more likely to perform best in practice. Furthermore, among the tensor-based clustering algorithms, TGM is the one that seems to combine the different representations in the most effective way, directly followed by TSPLBM [START_REF] Boutalbi | Sparse tensor co-clustering as a tool for document categorization[END_REF]. Figure 4 shows the evolution of the TGM's final objective function Q (normalized to a [0, 1] interval) along with the NMI external measure of the partitions. First, we observe that the worst values of Q coincide with the lowest NMI scores. Then, we can notice an increasing tendency of the NMI that approximately fits the evolution of Q for most of the datasets, which is confirmed by a high correlation coefficient. This indicates that, in the absence of labeled supervision, the modularity optimized by TGM is an effective unsupervised indicator that can be used to select a run that is likely to have a good performance. In order to further improve model selection, we perform a consensus clustering approach [START_REF] Strehl | Cluster ensembles-a knowledge reuse framework for combining multiple partitions[END_REF]. For this purpose, we use the Clus-ter_Ensembles 5 implementation that is based on graph partitioning and aims to find a consensual partition from several input clusterings. In Table 3, we compare between the average NMI w/o (without) consensus (corresponding to the TGM ALL values presented in Table 2) and the NMI obtained by the consensual partition provided by the ensemble (combining the 30 runs into a single partition). We can see that for all datasets there is an improvement in terms of NMI, particularly significant for DBLP1 and AG-news.

ASSESSING THE NUMBER OF CLUSTERS

Assessing the number of clusters still remains a challenge whatever the chosen approach. In our proposal, to deal with this problem we conducted a series of experiments with the number of clusters varying from 2 to 10. In Figure 5, we show the relationship between the number of clusters and the corresponding value of the modularity measure for the 3 datasets. The red lines indicate the real number of clusters for each data set. We can see that even though the maximum value of modularity does not always correspond to the real number of clusters, in many cases it is close the true value, especially if we look at the largest difference between values of modularity (e.g., DBLP1, Classic3). Therefore the moduarity can serve as an additional point of information when choosing the number of clusters.

CONCLUSION

It is now well established that different representations are required to capture the syntactic and semantic meaning of several NLP tasks, including text clustering. In this paper we proposed the Tensor Graph Modularity -TGM-algorithm, which harnesses this idea by iteratively maximizing a Graph Modularity criterion. TGM relies on a tensor representation that allows us to combine several representations and take advantage of the different similarity aspects, namely syntactic and semantic. We evaluated our method through in-depth experiments with three document datasets and compare the results with three categories of clustering baselines: classical clustering, graph clustering, and tensor clustering. Then We showed how improve performance of TGM by providing a consensual partition from several input clusterings. Finally, we addressed the issue of the number of clusters which is often unknown and showed that the modularity can be harnesses for this task.

A potential future work might be to introduce a schema for different representations. This would allow to evaluate the impact of each type of representation on the clustering performance.

Figure 1 :

 1 Figure 1: BOW drawbacks for similar text fragments topic. Green for word co-occurrence, Red for named entities, and Yellow for semantic meaning.

Figure 2 :

 2 Figure 2: Goal of Tensor-based Graph Modularity (TGM) clustering for text data.

  sions and is accessed by way of three indices. Notice that scalars are represented by lowercase letters e.g., 𝑥, and vectors are expressed by a bold lowercase letter e.g., x. The matrices are denoted by bold capital letters e.g., X. And finally, tensors are indicated by bold capital Euler letters e.g. X. The element (𝑖, 𝑗) of a matrix is expressed by 𝑥 𝑖 𝑗 , and 𝑥 𝑏 𝑖 𝑗 represents the element (𝑖, 𝑗, 𝑏) of a tensor. Given a three-way tensor X, each slice 𝑏 represents a graph 𝐺 𝑏 via an adjacency matrix X 𝑏 . The value 𝑥 𝑏 𝑖. = 𝑗 𝑥 𝑏 𝑖 𝑗 represents the degree of node 𝑖 with regard to the graph 𝐺 𝑏 , and 𝑥 𝑏 .. = 𝑖 𝑗 𝑥 𝑏 𝑖 𝑗 . Hereafter, we propose to tackle the tensor clustering problem by maximizing a modularity-based criterion. More specifically, we aim at maximizing the following criterion: Q(X, Z) = 𝑣 ∑

Figure 3 :

 3 Figure 3: Comparison of TGM results for different combinations of similarity slices.

Figure 4 :

 4 Figure 4: Evolution of the objective function of TGM ALL and NMIs for the 10 top runs. (Correlation) between the objective function and the NMI values.

Figure 5 :

 5 Figure 5: Estimation of the number of clusters according the objective function.

Table 1 :

 1 Description of datasets.

						Features
			Documents Clusters
					BOW Entity GloVe BERT SRoBERTa
		DBLP1	1,949	3	1,585 1,210
	Datasets	classic3	3,891	3	8,555 5,341	300 1,024	768
		AG-news	8,000	4	7,873 5,538

Table 2 :

 2 Evaluation of documents clustering in terms of NMI.The bold blue values represent the best performances and the bold ones the second best performances. SPLBM 0.32 ± 0.09 0.32 ± 0.11 0.33 ± 0.06 0.06 ± 0.03 0.20 ± 0.05 0.13 SPLBM 0.36 ± 0.30 0.53 ± 0.08 0.65 ± 0.10 0.43 ± 0.05 0.38 ± 0.25 0.29 PARAFAC and TUCKER followed by Kmeans.

			Metrics		NMI
	Data Evaluation			Max-Min
			Algorithms	BOW	BERT SRoBERTa GloVe	Entity
			Kmeans 0.20 ± 0.00 0.28 ± 0.00 0.25 ± 0.00 0.08 ± 0.00 0.01 ± 0.00 0.27
		Clustering	SKmeans 0.25 ± 0.04 0.18 ± 0.17 0.37 ± 0.06 0.28 ± 0.03 0.13 ± 0.04 0.24
			AE	0.16 ± 0.07 0.16 ± 0.05 0.15 ± 0.02 0.32 ± 0.03 0.09 ± 0.05 0.23
			ITCC	0.33 ± 0.08 0.35 ± 0.07 0.34 ± 0.05 0.10 ± 0.02 0.20 ± 0.03 0.25
	DBLP1	Graph (Similarity)	CoclustMod 0.32 ± 0.06 0.36 ± 0.11 0.35 ± 0.06 0.13 ± 0.03 0.18 ± 0.04 0.23
			PARAFAC		0.09 ± 0.05
		Tensor	TUCKER		0.08 ± 0.00
			TSPLBM		0.50 ± 0.10
			TGM ALL		0.53 ± 0.09
			Kmeans 0.63 ± 0.00 0.85 ± 0.00 0.33 ± 0.00 0.88 ± 0.00 0.62 ± 0.00 0.55
		Clustering	SKmeans 0.84 ± 0.12 0.84 ± 0.08 0.73 ± 0.12 0.86 ± 0.08 0.82 ± 0.00 0.13
			AE	0.24 ± 0.09 0.87 ± 0.01 0.20 ± 0.03 0.88 ± 0.02 0.66 ± 0.06 0.68
	Classic3	Graph (Similarity)	ITCC CoclustMod 0.84 ± 0.09 0.38 ± 0.09 0.47 ± 0.06 0.46 ± 0.03 0.81 ± 0.00 0.46 0.88 ± 0.00 0.45 ± 0.10 0.59 ± 0.12 0.45 ± 0.08 0.81 ± 0.00 0.43
			PARAFAC		0.30 ± 0.17
		Tensor	TUCKER		0.44 ± 0.00
			TSPLBM		0.89 ± 0.07
			TGM ALL		0.91 ± 0.10
			K -means 0.04 ± 0.00 0.45 ± 0.00 0.29 ± 0.00 0.53 ± 0.00 0.02 ± 0.00 0.51
		Clustering	SKmeans 0.12 ± 0.03 0.46 ± 0.11 0.51 ± 0.01 0.53 ± 0.00 0.07 ± 0.02 0.46
			AE	0.30 ± 0.04 0.5 ± 0.03 0.29 ± 0.03 0.54 ± 0.01 0.20 ± 0.04 0.34
	AG-news	Graph (Similarity)	ITCC CoclustMod 0.11 ± 0.03 0.33 ± 0.10 0.48 ± 0.07 0.43 ± 0.05 0.07 ± 0.02 0.41 0.13 ± 0.03 0.37 ± 0.09 0.52 ± 0.06 0.39 ± 0.04 0.07 ± 0.02 0.32 SPLBM 0.06 ± 0.02 0.34 ± 0.10 0.44 ± 0.06 0.33 ± 0.06 0.08 ± 0.03 0.38
			PARAFAC		0.07 ± 0.03
		Tensor	TUCKER		0.05 ± 0.00
			TSPLBM		0.51 ± 0.06
			TGM ALL		0.55 ± 0.05
	1 AE,

Table 3 :

 3 Evaluation of TGM ALL ; ↑ % denotes the percentage of improvement in terms of NMI.

	Datasets	without	with	↑ %
		Consensus	Consensus
	DBLP1	0.53	0.60	13.21
	Classic3	0.91	0.95	4.40
	AG-news	0.55	0.60	9.09

https://coclust.readthedocs.io/en/v0.2.1/

https://tensorclus.readthedocs.io/en/latest/

We provide results of TGM using other clustering metrics such as accuracy, purity, and ARI. The GPU version of TGM for larger datasets is also provided.

https://pypi.org/project/Cluster_Ensembles/

ACKNOWLEDGEMENT

Our work is funded by the German Federal Ministry for Economic Affairs and Climate Action under Grant Agreement Number 01MK20008F (Service-Meister).