Olesea Cuzan-Munteanu

Dumitru Sirbu

Michel Giorgi

Sergiu Shova

Elizabeth A Gibson

Marius Réglier

Luísa M D Maylis Orio

R S Martins

Andrew C Benniston

Luísa M D R S Martins

Neutral Lipophilic Palladium(II) Complexes and their Applications in Electrocatalytic Hydrogen Production and C-C Coupling Reactions

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

Introduction

Palladium chemistry is a highly investigated field of study and is the basis for many industrially important processes. [1] The oxidative activity of palladium-based catalysts is one main dynamic area of investigation, [2] and several groups are interested not only in the catalytic activity of palladium complexes, but also in the reaction mechanism, isolation of intermediates and characterization of different redox-active species. [3] Another pertinent feature of palladium is its ability when complexed to perform reductive-based reactions thus making it a truly versatile metal. Focusing in the first instance on reductive chemistry, palladium and its complexes are considered to be good catalysts for hydrogen evolution reaction, [4] though there is still much scope for improvement especially in the area of electrocatalytic hydrogen generation from protons. The dinuclear palladium(I)1,3-bis[(2-chloro)benzene]triazenide complex, [5] for instance, was shown to produce hydrogen from acetic acid in dichloromethane (DCM), based on cyclic voltammetry experiments, but no detection of the electrolysis product was performed. The palladium(II) meso-tetraferrocenylporphyrine [6] also showed some promising results for electrocatalytic H2 production and in this case the product could be identified. A faradaic efficiency of 70% was obtained for proton reduction in dimethylformamide (DMF) at -1.5 V vs. saturated calomel electrode (SCE) at a glassy carbon working electrode. A mononuclear palladium complex based on a thiosemicarbazone ligand [7] has shown electrocatalytic behaviour for proton reduction in DMF in the presence of TFA, however the faradaic efficiency of this compound was only 34% with a turnover number of 2 after 4h.

The reductive carbon-carbon bond forming capabilities of in-situ palladium species is dominated by coupling reactions such as Suzuki, [8] Sonagashira, [9] Heck [10] and Negishi, [11] relying in many cases on the production of zero-valent palladium in the first instance. The coordination sphere of the palladium is provided by ligands generally comprising soft donor atoms such a phosphorus (e.g., PPh3), but other donor atoms have found [a] Prof A C Benniston, Dr E Gibson, Dr D

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application. For example, the 1,2,4-triazole-based palladium complex PdI[η 3 -(C6H3-2,6-(CH2Tz)2)-N,C,N] [10] was successfully tested as catalyst for the Heck coupling reaction. Another palladium complex derived from a 1,2,4-triazolin-5-ylidene containing ligand which coordinates through the CNC atoms [9] has shown good catalytic performance in Sonogashira coupling with a turnover number of 8000. Also noted is the recently reported series of palladium(II) complexes with 3-(2-pyridyl)-5R-1,2,4triazoles, where R = ethyl, n-propyl, i-propyl and t-butyl, [8] which are capable to catalyse the microwave-assisted Suzuki-Miyaura cross-coupling reaction in the presence of base.

As a follow up to our own work, [6,12] the focus was to develop palladium(II) coordinately unsaturated complexes based on robust and readily accessible ligands. A compound based upon the triazole-phenol moiety (Figure 1) offers a bidentate binding motif, and when deprotonated and complexed to palladium(II) in a 2:1 ratio forms a neutral complex. To increase solubility in common organic solvents the phenol group is a suitable unit to incorporate lipophilic alkyl groups. The three complexes (PdL1-PdL3) which were developed are promising for the electrocatalytic proton reduction into hydrogen and for Sonogashira and Heck C-C bond formation.

Results and Discussion

Synthesis and characterization

The

Single crystal X-ray diffraction analysis

By using careful crystallization methods, a number of the products afforded crystals suitable for single-crystal X-ray diffraction analysis. Collected in Table S1 of Supporting Information are the relevant data for the structures HL3, PdL2.H2O, PdL3, and PdL3.(CH3)2CO. The ligand HL3 crystallized in the monoclinic centrosymmetric space group P2/c with two independent molecules in the asymmetric unit, one of them showing some disorder at one phenyl site (two positions). The molecular structure of one molecule of HL3 is shown in Figure 3. All bond lengths and angles are within expected ranges. The hydroxyl group is intramolecular hydrogen bonded to one of the nitrogen atoms within the triazole unit to generate a six membered ring. The phenyl groups are positioned anti with respect to each other, although this is undoubtedly not the lowest energy arrangement; a basic MM + molecular mechanics calculation identified several close in energy conformations (see Supporting Information). The structure of HL3 also reveals the presence of intermolecular

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interactions within the crystal as at least four relevant stacking and five CH/ interactions can be reported (see Table S2 of Supporting Information). The molecular structure for the palladium complex with two L3 ligands is illustrated in Figure 4. Complex PdL3 crystallized in the P21/c space group. The coordination mode at the palladium ion is a slightly distorted square planar arrangement, so that oxygen atoms of the hydroxyl are positioned trans, with the same arrangement observed for the nitrogen atoms of the triazole moieties. The N4-Pd1-N1 and O1-Pd1-O2 bond angles are 170.91(9) and 176.14 (8), respectively. The Pd1-N1 and Pd1-N4 bond lengths of 2.001(2) Å and 2.013(2) Å are as expected. The Pd1-O1 and Pd1-O2 bond lengths of 1.995(2) Å and 1.999(2) Å are not within the standard deviation error different from the Pd-N bond lengths. Unlike the ligand alone, the complex is stabilized by two pairs of intramolecular stacking interactions between the benzotriazoles and two phenyl groups: the distances between centroids of rings N1/N2/N3/C60/C55 and C8/C9/C10/C11/C12/C13 and between centroids of rings N4/N5/N6/C30/C25 and C38/C39/C40/C41/C42/C43 are equal to 3.5566(18) Å and 3.572(2) Å, respectively, while the dihedral angles between these pairs of rings are equal to 1.28(16)° and 6.01(18)°, respectively. Thus, the complex adopts a rooftop conformation with one side of the Pd plane fully accessible, while the other side is partially protected by the two phenyl cycles involved in the -stacking interactions (Figure 4). Compound PdL3.(CH3)2CO crystallized in the C2/c space group with two independent molecules in the asymmetric unit (see Supporting Information). The Pd atoms reside on the 2fold axis and their coordination sphere is identical to that of complex PdL3. Indeed the geometrical features observed in PdL3.CH3CO are comparable to those observed in PdL3, with two pairs of intramolecular -stacking interactions between the benzotriazoles and two phenyl groups, but the accessible sides of the Pd planes are now facing each other thus forming a pseudo dimer with the Pd1-Pd2 distance close to 4.2 Å.

Compound PdL2.H2O crystallized in the P21/n space group with two independent molecules in the asymmetric unit. The asymmetric unit (see Supporting Information) comprises one palladium(II) atom surrounded by two molecules of deprotonated L2 ligand, coordinated to the metal through two nitrogen and two oxygen atoms. The carbon atoms of the methyl and ethyl groups are partially delocalized and the structure contains a delocalized co-crystallised half water molecule.

Theoretical calculations

To elucidate both their structural and electronic features, the neutral, monoreduced and monooxidized complexes were subjected to DFT geometry optimizations (Figure 5A-C).

Comparison of the DFT-optimized structure of PdL3 with the crystallographic one showed a pretty good agreement between the two sets of data, which confirmed that PdL3 can be best described as a diamagnetic square planar Pd(II) complex (PdL3, S = 0). Whereas the Highest Occupied Molecular 10.1002/ejic.201901283

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Orbital (HOMO) for PdL3 resides on the ligand, the Lowest Unoccupied Molecular Orbital (LUMO) is very much centred on the palladium metal (Figure 6A-B), and is identified as the 4dx 2y 2 orbital which is classically the unoccupied frontier orbital for a square planar complex. The mono-reduced PdL3 complex is best described as a Pd(I) paramagnetic species, S = ½, because of the elongation of the Pd-N and Pd-O bond lengths which supports that reduction occurs at the metal centre consistent with a Single Occupied Molecular Orbital (SOMO) being mainly distributed over the Pd centre and its coordinating atoms (Figure 6C). In the case of the mono-oxidized PdL3 complex it would appear that removal of an electron occurs at the ligand since the computed C-O and C-C bond lengths of the phenolate groups are affected. The species produced is therefore best described as paramagnetic Pd(II)-ligand radical species (S = ½) which is attested by the composition of the SOMO of the system (Figure 6D).

Cyclic voltammetry

The redox behaviour of the ligands HL1, HL2, HL3 (Figure 7, Table 1) were studied by cyclic voltammetry in dried DMF at a glassy-carbon electrode using 0.1 M tetra-Butylammonium PF6 (TBAPF6) as the supporting electrolyte. All potentials are referenced to the Fc + /Fc redox couple. The redox behaviour for the ligands (Figure 7) is relatively straightforward and similar.

The cathodic part of the CV is dominated by a quasi-reversible redox signal with E1/2 0 = -2.20 V, -2.22 V, -2.15 V for HL1, HL2, HL3, respectively. In the anodic region an irreversible signal is observed at Ep a,1 = 0.80 V, 0.90 V, 0.95 V for HL1, HL2, HL3, respectively. The redox behaviour of the complexes PdL1, PdL2 and PdL3 (Figure 8, Table 1, Table S6) were studied by cyclic voltammetry in dried DMF at a glassy-carbon electrode using 0.1 M TBAPF6 as the supporting electrolyte. All potentials are referenced to the Fc + /Fe redox couple. There are clear similarities in the cyclic voltammograms for all three complexes. Upon oxidative scanning two clear irreversible waves are observed, which by comparison to the CVs of Figure 7, are ligand-based oxidations. The presence of two clear peaks is interpreted as oxidation at one ligand site affects the oxidation of the second ligand presumably by electronic communication via the Pd centre. The reduction side of the voltammograms are more interesting since they display a new wave at ca. -1.5 V and are associated with the redox process at the metal site (Pd 2+ /Pd + ). By increasing the potential window an additional irreversible wave is observed at a potential that is very close to the ligand-based redox process (cf. Figure 7). There is presumably some degradation process since upon reversing the scan an additional wave is observed at around -0.3 V. More breakdown products are evident when the potential scanning window is increased further, arising from the additional irreversible wave at ca. -2.9 V.

UV-Visible absorption spectroscopy

The room temperature electronic absorption spectra recorded for HL1, HL2 and HL3 in DMF show two broad bands with absorption maxima λmax at 305 and 340 nm for HL1 and HL2 and with λmax at 305 and 345 nm for HL3 (Figure 9), and the relevant parameters are summarized in Table S6 of Supporting Information. In addition to ligand-based electronic transitions the absorption spectra recorded for PdL1, PdL2 and PdL3 in DMF also show two broad bands with absorption maxima λmax at 390 nm for PdL1 and PdL2 and with λmax at 395 nm for PdL3 (Figure 9). For the complexes we also observe a minor shift for the first transition from 305 to 310 nm. The second electronic transition present for the ligands at 340-350 nm is absent for the case of the palladium complexes. This observation would suggest that the transition is associated with the hydroxyl group and likely of n- character. The new band which appears at around 390 nm is related to the coordination of the ligand to the palladium and is of ligand-to metal charge transfer (LMCT) character.

The addition of up to 100 equivalents of TFA or acetic acid to a solution of PdL3 in DMF did not result in any significant changes to the absorption profile. There is a decrease in intensity and change in shape of the absorption band located at 390 nm upon formation of the mono-reduced species as expected since the LMCT transition is altered slightly. This new band does not change significantly in the presence of excess TFA. It would appear that the complex and its mono-reduced form are stable in the presence of excess acid (see Supporting Information).

Electrocatalysis

Given the behaviour of the complexes upon reduction we were interested to see if they also presented an electrocatalytic activity and were able to drive hydrogen production. The addition of either trifluoroacetic acid or acetic acid as a proton source to complexes PdL1, PdL2 and PdL3 resulted in the formation of catalytic waves in the cathodic region of the cyclic voltammograms (see Supporting Information). A typical experiment is shown in Figure 10 for PdL3. By using the "first derivative technique" the number and potential of the formed waves was estimated. For complex PdL3 three distinct waves were observed at -1.1 V, -1.6 V and -1.8 V, respectively. The current response increased with the addition of acid and the maximum for the peak shifted from -1.5 V to -1.9 V vs. Fc + /Fc.

Gas analysis

A continuous flow-rig with in-line GC analysis was used to detect the molecular hydrogen produced during electrocatalytic proton reduction using PdL3 in DMF in the presence of TFA. [13] Applying a potential of -0.36 V vs NHE to a boron-doped diamond working electrode resulted in detection of molecular hydrogen (Figure 11). The rate of H2 produced was determined by calibration with a known flow rate 10.1002/ejic.201901283

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of a H2/Ar mixture, by checking the proportionality between the peak area and the volume of injected hydrogen per minute. When no complex was employed no hydrogen was detected during five hours of electrolysis. The presence of 1 mM of PdL3 resulted in three orders of magnitude increase of current at the same applied potential and immediate constant production of hydrogen as indicated by the GC analysis. Almost seven turnovers were reached after five hours of electrolysis and no sign of hydrogen production decrease was observed at the end of this time. At the same time a low constant faradaic yield of about 50 % was noticed. The UV-Vis spectrum and the cyclic voltammogram of the electrolysis solution did not change significantly during electrolysis. This would suggest that the low faradaic yield of the detected hydrogen is more likely to be a result of substrate reduction. Palladium complexes are well known catalysts for chemical and electrochemical hydrogenation of organic compounds. [14] As the produced hydrogen cannot be removed immediately from the solution hydrogenation of the electrolysis mixture components is quite likely.

Interestingly, after performing similar gas analysis experiments using a working mercury pool electrode no gaseous hydrogen formation was observed. This finding does suggest that the molecular complex is not the active catalyst, and that it is more likely a precursor for generation of the catalytic species. The simplest answer is metallic palladium formation upon reduction of Pd(II) to Pd(0) in the complex accompanied by loss of the ligands. As most of the Pd complex seems to be still present in solution after electrolysis, most likely only a small percentage of PdL3 is initially converted to metallic Pd and is responsible for the electrocatalysis. The reductive hydrogenation of the free ligand seems to be the most likely candidate to compete with hydrogen production.

Sonogashira and Heck C-C cross couplings

The industrially important Sonogashira Pd-catalysed C-C coupling of a sp-hybridized carbon from a terminal alkyne with a sp 2 -hybridized carbon from an aryl halide to afford a substituted acetylene traditionally requires the presence of a copper co-catalyst which brings some problems (e.g., competitive homocoupling to the diyne) to the catalytic system. [15,16] To address such issues, copper-free synthetic strategies are in high demand. Herein, the Cu-free Sonogashira C-C cross coupling of phenylacetylene and iodobenzene (as a model reaction) was attempted in the presence of PdL2 or PdL3, under microwave (MW) irradiation (Figure 12a). At room temperature no C-C coupling products were detected, therefore MW irradiation was the chosen (green) heating mode. In order to probe the synthetic scope of this Cu-free Pd-catalysed MW-assisted Sonogashira-type reaction, experimental conditions were optimized by using different bases, solvents, as well as MW power and reaction temperatures, and the results for the best combinations are presented in Table 2. As seen from the data in Table 2 very similar results for both compounds were obtained, leading to maximum yields of 87% and 84% of diphenylacetylene for the Pd-complexes PdL2 and 10.1002/ejic.201901283

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PdL3, respectively, after 15 mins of MW irradiation at 70 °C in an acetonitrile/water medium. The catalytic activity of complexes PdL2 and PdL3 was also tested for the versatile and industrially important [17][18][START_REF] Martins | Green Chemistry Series[END_REF] Csp 2 -Csp 2 coupling of organic halides with olefins (Heck reaction). The selected halide substrates were styrene and iodobenzene. The reaction was performed according to Figure 12b using triphenylphosphine as the reducing agent, in the presence of triethylamine, in a sealed reactor and under microwave irradiation, typically at 80 °C. In all Heck experiments, the selectivity for trans-stilbene was 100% (the only product detected). After 1 h of MW irradiation (90 W power) at 80 °C under optimized conditions, similar yields, 91% and 88%, respectively, of trans-stilbene were obtained in the presence of PdL2 and PdL3.

It is worth noting that for both Sonogashira and Heck C-C cross couplings, the catalytic performance of PdL2 and PdL3 was clearly superior to that exhibited by their Pd precursor, Pd(OAc)2. As presented in Table 2 (entry 7) for the Sonogashira reaction, the coupling product maximum yield of 40% was obtained when Pd(OAc)2 was used as catalyst. In addition, the Heck reaction carried out in the presence of Pd(OAc)2 led only to 54% of trans-stilbene. The coordination sphere at the palladium metal for PdL2 and PdL3 during the catalytic cycle is evidently disposed to facilitate the stereoselective reaction. Noting that the molecular structure of PdL3 does show that one face of the complex is hindered by the phenyl groups, this feature may play a significant role in controlling the reductive elimination step.

Conclusions

Neutral lipophilic palladium complexes are readily prepared through the employment of cheap and readily available organic benzotriazolyl phenolate precursors. The complexes show limited capabilities as electrocatalytic hydrogen producers, since it appears that they decompose during repeating cycling, likely forming metallic palladium particles. Nevertheless, they are more productive in C-C coupling reactions outperforming the simple neutral complex Pd(OAc)2 in Sonogashira and Heck reactions. The lipophilic nature of the complexes does open up the opportunity to possibly perform cross-coupling reactions in more controlled environments such as oil droplets or emulsions that have application in flow chemistry. [START_REF] Misuk | [END_REF] In addition, the basic ligand structure is also set up for the addition of other functionality. For example, the R1 and R2 groups (Figure 1) could readily contain sites for attachment to surfaces, polymers and beads to support heterogeneous coupling reactions. Future work is intended to explore the development of the ligands along the outlined lines.

Experimental Section

All chemicals were purchased from commercial sources and used as received unless otherwise stated. Basic solvents for synthesis were dried using literature methods. Solvents for spectroscopic investigations were of the highest purity available.

Electrochemical investigations were carried out on Pd incorporated complexes in DMF/n-NBu4PF6 (0.1 M) solution at ambient temperature using a three-electrode configuration (glassy carbon working electrode, Pt counter electrode, Ag/AgNO3 reference). All potentials are presented vs Fc + /Fc redox couple. Gaseous H2 detection was performed using the method described by Summers et al. [13] 1 mM solutions of catalyst in DMF containing TFA (90 mM) and TBAPF6 (0.1 M) were prepared from thoroughly degassed stock solutions and stored under argon. Argon gas was continually flowed through the solution and into a 6-port 2-position switch (VICI) at a constant flow (10 mL min -1 ), which was maintained using a mass flow controller (Bronkhorst, E-Flow series). A 200 µL sample was analysed automatically every 3.2 mins using a gas chromatograph (Shimadzu GC2014) with a thermal conductivity detector operating at 50 °C. The sample was initially passed through a dry ice trap to remove any condensable solvents. Argon was used as the carrier gas and H2 was detected on an activated molecular sieve column (Shincarbon ST, Restek). Integration of a plot of the production rate versus time yielded the total amount of H2 produced. A voltage was applied using an IVIUMSTAT potentiostat, a boron doped diamond working electrode, platinum mesh counter electrode, Ag/AgNO3 (0.01 M) reference electrode were employed and the potentials were converted to the NHE scale by adding 0.54 V. [START_REF] Scott | Applications of Physical Methods to Inorganic and Bioinorganic Chemistry[END_REF] Elemental analyses were performed using a Thermo Finnigan EA 1112 instrument. The results were validated by at least two measurements. UV-Vis spectra were recorded on a Varian Cary 50 spectrophotometer from 200-800 nm with samples in a 1.0 cm pathlength quartz cuvette. FT-IR spectra were recorded in attenuated total reflection (ATR) mode on a Bruker TENSOR 27 spectrometer equipped with a single-reflection DuraSamplIR diamond ATR accessory. Intensities are mentioned in the parenthesis as vs = very strong, s = strong, m = medium, w = weak, vw = very weak and sh = shoulder. NMR spectra were recorded on a BruckerAvance III nanobay spectrometer (300 or 400 MHz) using TMS as internal reference. ESI-MS analyses were performed using a SYNAPT G2 HDMS (Waters) spectrometer equipped with a pneumatically assisted Atmospheric Pressure Ionization (API) source. The ion-spray voltage was 2.8 kV, the orifice lens was 20 V, and the nitrogen flux (nebulization) was 100 L h -1 . The HR mass spectra were obtained with a time-of-flight (TOF) analyzer. The sample was placed in a methanol/3mM ammonium acetate.

Synthesis of bis[2-(2H-benzotriazol-2-yl)-6-dodecyl-4methylphenolato]palladium(II) (PdL1)

To a solution of 2-(2H-benzotriazol-2-yl)-6-dodecyl-4methylphenol (HL1) (0.25 g, 0.6 mmol) in THF (3 mL) at ambient temperature was added dropwise a solution of Pd(OAc)2 (0.07 g, 0.3 mmol) in THF (4 mL). The obtained orange mixture with 10.1002/ejic.201901283

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European Journal of Inorganic Chemistry FULL PAPER the total volume of 7 mL was stirred at 20 °C. The reaction was monitored by TLC. After 48 h volatile materials were removed under vacuum. The oily product obtained was purified by flash chromatography on silica gel using the eluent petroleum ether/methylene chloride (99:1). Compound PdL1 was isolated as an orange oily product. Yield: 0.2325 g, 83.7%. IR,  (cm -1 ) = 2954.9 (m), 2922.1 (s), 2852.7 (m), 1608.6 (w), 1572.0 (w), 1556.5 (w), 1490.9 (m), 1465.9 (s), 1411.9 (w), 1377. The reaction was monitored by TLC. After 48 h volatile materials were removed under vacuum. The product obtained was purified by flash chromatography on silica gel using the eluent petroleum ether/methylene chloride (99:1). Compound PdL2 was isolated as an orange solid. 0.7309 g, 92.4 %. Suitable crystals for single crystal X-ray diffraction study of (PdL2.H2O) were grown by recrystallization from chloroform. Elemental Anal.: Calcd.: C, 65.46; H, 6.99; N, 10.41; (C44H56N6O2Pd); Found: C, 65.66; H, 6.95; N, 10.15 %. IR,  (cm -1 ) = 2960.7 (m), 2910.5 (w), 2873.9 (w), 1573.9 (w), 1460.1 (m), 1440.8 (m), 1404.1 (m), 1381.0 (w), 1352.1 (w), 1328.9 (w), 1309.6 (m), 1282.6 (m), 1244.1 (m), 1228.6 (m), 1199.7 (w), 1166.9 (w), 1149.6 (w), 1137.97 (w), 1111.0 (w), 1057.0 (w), 1006.8 (w), 987.5 (w), 974.0 (vw), 939.3 (w), 896.9 (vw), 871.8 (w), 840.9 (vw), 825.5 (w), 808.2 (w), 781.2 (w), 763.8 (w), 740.7 (vs), 723.3 (m), 690.5 (w), 663.5 (w), 638.4 (w), 592.1 (w), 563.2 (m), 538.1 (w), 516.9 (m), 505.3 (w), 474.5 (w), 441.7 (m), 395.4 (w), 356.8 (w), 314.4 (m). (d,8H, J = 8.7 Hz CH2-ethyl), 1.34 (s, 12H, CH3-methyl), 1.16 (s, 6H, CH3-methyl), 1.00 (s, 6H, CH3-methyl), 0.81 (t, 6H, J = 7.3 Hz CH3-ethyl), 0.45 (t, 6H, J = 7.9 Hz CH3-ethyl). ESI-MS (DCM): m/z 807.36 [M+H] + . UV-Vis (DMF): λmax, nm (ε, 10 3 L mol -1 cm -1 ): 310 (34.2), 390 (13.9).

Synthesis of bis[2-(2H-Benzotriazol-2-yl)-4,6-bis(1-methyl-1-phenylethyl)phenolato]palladium(II) (PdL3)

To a solution of 2-(2H-benzotriazol-2-yl)-4,6-bis(1-methyl-1phenylethyl)phenol (HL3) (0.90 g, 2.0 mmol) in THF (10 mL) at ambient temperature was added dropwise a solution of Pd(OAc)2 (0.22 g, 1.0 mmol) in THF (15 mL). The obtained deep red mixture with the total volume of 25 mL was stirred at 20 °C. The reaction was monitored by TLC. After 48 h volatile materials were removed under vacuum. The obtained product was purified by flash chromatography on silica gel using the eluent petroleum ether/methylene chloride (99:1). Compound PdL3 was isolated as an orange solid. Yield: 0.9165 g (93.95 %. Suitable crystals for single crystal X-ray diffraction study of (PdL3) were grown by recrystallization from DMF (orange hexagons). Elemental Anal.: Calcd.: C, 72.10; H, 5.65; N, 8.41; (C60H56N6O2Pd); Found: C, 72.17

Single crystal X-ray diffraction analysis

The intensity data for compounds HL3, PdL3 and PdL3.(CH3)2CO were collected on a Rigaku Oxford Diffraction SuperNova diffractometer and on a Rigaku Oxford Diffraction Xcalibur, Eos diffractometer for PdL2.H2O using CuKα radiation (λ = 1.54184 Å) for the ligand HL3 and MoKα radiation (λ = 0.71073 Å) for the Pd complexes. Data collection, cell refinement and data reduction were performed with CrysAlisPro (Rigaku Oxford Diffraction), the structure were solved with SIR92 [START_REF] Altomare | [END_REF] or SHELXS [23] and SHELXL-2013 [23] was used for full matrix least squares refinement. The hydrogen atoms were found experimentally for compounds HL3 and PdL3, except for the disordered phenyl for HL3 were they were introduced at geometrical positions. For compounds PdL3.(CH3)2CO and PdL2.H2O the H-atoms were all introduced at geometrical positions. For each structure the hydrogen atoms were refined as riding atoms with their Uiso parameters fixed to 1.2Ueq (parent atom) for the aromatics carbons and to 1.5Ueq (parent atom) for the remaining atoms.

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supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre.

DFT calculations

All theoretical calculations were performed with the ORCA program package. [24] Full geometry optimizations and signle point calculations were carried out using the hybrid functional B3LYP [25,26] in combination with the TZV/P [27] basis set for all atoms and by taking advantage of the resolution of the identity (RI) approximation in the Split-RI-J variant [28] with the appropriate Coulomb fitting sets. [29] Increased integration grids (Grid4 in ORCA convention) and tight SCF convergence criteria were used. Solvent effects were accounted for according to the experimental conditions. For that purpose, we used the DMF ( = 38.3) solvent within the framework of the conductor like screening (COSMO) dielectric continuum approach. [30] Molecular orbitals were generated using the orca plot utility program and were visualized with the Chemcraft program. [START_REF]Chemcraft -graphical software for visualization of quantum chemistry[END_REF] The microwave-assisted C-C cross coupling reactions were performed in G10 borosilicate glass tubes (10 mL capacity reaction tube with a 13 mm internal diameter) in a focused Anton Paar Monowave 300 reactor fitted with a rotational system and an IR temperature detector.

Sonogashira C-C coupling

The desired amount of catalyst (0.001-0.010 mmol), phenylacetylene (1.0 mmol), iodobenzene (1.1 mmol), Et3N (1.2-3.0 mmol) and the solvent (3.0 mL) were introduced into the Pyrex tube, closed, placed in the microwave reactor and maintained under stirring and under low power (10-100 W) irradiation for the desired temperature and reaction time. After the reaction, the obtained mixture was cooled to room temperature, the organics extracted with diethyl ether (5.0 mL) and the 1,2-diphenylethyne isolated and spectroscopically characterized. Control experiments were performed under the optimized reaction conditions but in the presence of Pd(OAc)2 instead of any complex catalyst. Blank experiments (without a metal catalyst) were performed and no C-C coupling products were detected. In addition, a mercury drop experiment was performed by adding two drops of metallic Hg to the abovementioned reaction mixture and running the reaction under the optimized reaction conditions. After the reaction, the obtained mixture was to room temperature, filtered, and treated and analysed as above. No significant difference in conversion was observed.

Heck C-C coupling

The desired amount of catalyst (0.001-0.010 mmol), styrene (2.0 mmol), iodobenzene (1.0 mmol), PPh3 (0.05-0.10 mmol), Et3N (1.0-2.0 mmol) and acetonitrile (2.5 mL) were introduced into the Pyrex tube, closed, placed in the microwave reactor and maintained under stirring and under low power (50-150 W) irradiation for the desired temperature and reaction time. After the reaction, the obtained mixture was cooled to room temperature, the organics extracted with diethyl ether (5.0 mL) and evaporated to dryness under a stream of dinitrogen. Then, the residue was dissolved in CDCl3 and analysed by 1 H NMR at Bruker 300 and 400 UltraShield™ spectrometers. The yield of C-C coupling product (relatively to iodobenzene) was established using an internal standard. [START_REF] Xu | [END_REF] Control experiments were performed under the same reaction conditions but in the presence of Pd(OAc)2 instead of any complex catalyst. Blank experiments (without a metal catalyst) were performed and no C-C coupling products were detected. In addition, a mercury drop experiment was performed by adding two drops of metallic Hg to the abovementioned reaction mixture and running the reaction under the optimized reaction conditions. After the reaction, the obtained mixture was cooled to room temperature, filtered, and treated and analysed as above. No significant difference in conversion was observed.

Figure 1 .

 1 Figure 1. Representation of the palladium(II) complexes discussed in the text and their nomenclature.

  commercially available compounds 2-(2H-benzotriazol-2-yl)-4,6-di-tert-pentylphenol (HL2) and 2-(2H-benzotriazol-2-yl)-4,6bis(1-methyl-1-phenylethyl)phenol (HL3) were used as received, while 2-(2H-benzotriazol-2-yl)-6-dodecyl-4-methylphenol (HL1) was purified by column chromatographically before use. The three new palladium(II) coordination compounds (Figure1) were obtained by the complexation of the ligands with palladium(II) acetate in very good yields (>80%). The requirement of chromatographic purification is one reason for non-quantitative yields. The 1 H NMR spectra of the free ligands (see Supporting Information) show the presence of a signal in the region 11.78 -11.07 ppm which is attributed to the OH proton. The OH signal is not present in the spectra for the complexes supporting that the metal coordinates to the deprotonated oxygen-atom. A representative 1 H NMR spectrum for PdL3 is shown in Figure2, highlighting the four signals of the inequivalent methyl groups. It is interesting to note that the 1 H NMR spectrum for HL3 displays two signals for the methyl groups. The aromatic region between 6 and 8 ppm is dominated by clear signals attributed to the benzotriazole: 11 signals are attributed to 32 protons, while in the aliphatic region 1-3 ppm are observed 5 different proton species: 4 signals are attributed to 24 protons from the methyl groups and the co-crystallized acetone peak.

Figure 2 .

 2 Figure 2. A 400 MHz 1 H NMR spectrum for PdL3 in CDCl3 showing the four inequivalent methyl proton signals and the aromatic region. * = acetone.

Figure 3 .

 3 Figure 3. Single crystal X-ray diffraction determined molecular structure for HL3 drawn at 40% probability level showing the intramolecular hydrogen bond.

Figure 4 .

 4 Figure 4. Single crystal X-ray diffraction determined molecular structure for PdL3 drawn at as 40% probability level ellipsoids showing selected labelling of atoms and distances in Å (top) and a view down the N4-Pd1-N1 axis (bottom).

Figure 5 .

 5 Figure 5. DFT-optimized structures of the neutral PdL3 complex (A), the mono-reduced PdL3 complex (B) and the one-electron oxidized PdL3 complex (C). Hydrogen atoms were omitted for clarity.

Figure 6 .

 6 Figure 6. DFT-computed HOMO (A) and LUMO (B) for the neutral PdL3 complex, SOMO for the mono-reduced PdL3 (C) and SOMO for the oneelectron oxidized PdL3 (D). Hydrogen atoms were omitted for clarity.

Figure 7 .

 7 Figure 7. Cyclic voltammogram recorded for HL1, HL2 and HL3 in N2-purged DMF containing 0.1M TBAPF6 vs Fc + /Fc at a glassy carbon working electrode.

Figure 8 .

 8 Figure 8. Cyclic voltammograms recorded for PdL1, PdL2 and PdL3 in N2purged DMF containing 0.1M TBAPF6 vs Fc + /Fc at a glassy carbon working electrode over different potential ranges both in the reduction mode (red, blue and green lines) and in oxidation mode (purple lines).

Figure 9 .

 9 Figure 9. Electronic absorption spectra for ligands HL1, HL2 and HL3 and for complexes PdL1, PdL2 and PdL3 in DMF.

Figure 10 .

 10 Figure 10. Selected cyclic voltammograms for PdL3 (1 mM) at a glassy carbon electrode in dry DMF in the presence of increasing quantities of TFA. Conditions: T = 298 K, scan rate 100 mV/s, supporting electrolyte: 0.1M TBAPF6.

Figure 11 .

 11 Figure 11. Electrocatalytic hydrogen production vs. time and charge vs. time by applying -0.36 V vs. NHE to a glassy carbon electrode in 0.1 M TBAPF6 solution of DMF containing 90 mM TFA and 1 mM PdL3 complex.

Figure 12 .Table 2 .

 122 Figure 12. Microwave (MW) assisted a) Sonogashira C-C cross-coupling reaction of phenylacetylene and iodobenzene or b) Heck C-C cross-coupling between styrene and iodobenzene, catalysed by PdL2 or PdL3.

  1 (w), 1352.1 (m), 1342.4 (m), 1307.7 (m), 1288.4 (m), 1244.1 (s), 1203.6 (m), 1149.6 (m), 1134.1 (w), 1114.8 (w), 1078.2 (w), 1037.7 (w), 987.5 (w), 976.0 (w), 947.0 (w), 906.5 (m), 856.4 (m), 819.7 (m), 763.8 (m), 734.9 (vs), 680.9 (w), 648.1 (w), 636.5 (w), 557.4 (m), 511.1 (w), 443.6 (w). 1 H-NMR (400 MHz, CDCl3, ppm): δ 8.48 (broad singlet, 2H, CH), 8.00 (d, 2H, J = 9.0 Hz, CH), 7.59 (s, 2H, CH), 7.55 (t, 4H, J = 6.5Hz CH,), 6.81 (s, 2H, CH), 2.26 (s, 6H, CH, CH3-methyl), 1.22 (t, 6H, J = 7.0 Hz, CH, CH3-dodecyl), 0.86 (m, 44H, CH, CH2-dodecyl). ESI-MS (DCM): m/z 891.45 [M+H] + . UV-Vis (DMF): λmax, nm (ε, 10 3 L mol -1 cm -1 ): 310 (22.0), 390 (8.6).Synthesis of bis[2-(2H-Benzotriazol-2-yl)-4,6-di-tertpentylphenolato]palladium(II) (PdL2)To a solution of 2-(2H-benzotriazol-2-yl)-4,6-di-tertpentylphenol (HL2) (0.70 g, 2.0 mmol) in THF (10 mL) at ambient temperature was added dropwise a solution of Pd(OAc)2 (0.22 g, 1.0 mmol) in THF (15 mL). The obtained dark red mixture with the total volume of 25 mL was stirred at 20 °C.

  1 H-NMR (400 MHz, CDCl3): δ 8.34 (d, 2H, J = 8.3 Hz CH), 8.04 (d, 2H, J = 6.7 Hz CH), 7.78 (s, 2H, CH), 7.58 (t, 4H, J = 9.3 Hz CH), 7.19 (s, 2H, CH), 1.69

  ; H, 5.57; N, 8.28 %. IR,  (cm - 1 ) = 2964.5 (w), 2933.7 (w), 2868.1 (w), 1597.0 (w), 1492.9 (w), 1462.0 (m), 1440.8 (m), 1408.0 (m), 1384.9 (w), 1354.0 (w), 1311.6 (m), 1288.4 (m), 1251.8 (m), 1230.6 (m), 1220.9 (m), 1188.1 (w), 1145.7 (w), 1128.3 (w), 1107.1 (w), 1072.4 (w), 1030.0 (w), 987.5 (w), 933.5 (w), 896.9 (w), 873.7 (w), 856.4 (w), 815.9 (m), 761.9 (s), 748.4 (s), 715.6 (w), 696.3 (vs), 667.4 (w), 650.0 (m), 636.5 (w), 615.3 (w), 605.6 (m), 578.6 (w), 561.3 (m), 551.6 (m), 528.48 (w), 509.2 (w), 497.6 (m), 472.6 (w), 455.2 (m), 443.6 (m), 410.8 (m), 403.1 (m), 383.8 (w), 366.5 (w), 326.0 (m). 1 H-NMR (400 MHz, CDCl3, ppm): δ 7.82 (d, 2H, J = 8.7 Hz CH), 7.67 (d, 2H, J = 8.7 Hz), 7.64 (s, 2H, CH), 7.39 (d, 4H, J = 7.4 Hz CH,), 7.36 (t, 2H, J = 7.6 Hz CH,) 7.29 (s, 2H, CH), 7.27 (d, 6H, J = 8.2 Hz, CH), 7.12 (t, 2H, J = 7.6 Hz, CH,) 6.65 (d, 4H, J = 7.7 Hz CH), 6.24 (t, 4H, J = 7.4 Hz CH), 6.03 (t, 2H, J = 7.4 Hz CH), 1.79 (s, 6H, CH3), 1.76 (s, 6H, CH3), 1.51 (s, 6H, CH3), 1.18 (s, 6H, CH3). ESI-MS (DCM): m/z 999.36 [M+H] + . UV-Vis (DMF): λmax, nm (ε, 10 3 L mol -1 cm -1 ): 310 (35.8), 390 (14.8). Recrystallization of (PdL3) from acetone gave the compound (PdL3.(CH3)2CO). Orange needles. For [Pd(C30H28N3O)2•0.5(CH3)2CO]: Elemental Anal.: Calcd.: C, 71.81; H, 5.78; N, 8.17; (C61.5H59N6O2.5Pd); Found: C, 71.90; H, 5.61; N, 8.10 %.

  CCDC 1965954 (for HL3), 1966865 (for PdL2.H2O), 1965953 (for PdL3) and 1965955 (for PdL3.(CH3)2CO) contain the 10.1002/ejic.201901283 Accepted Manuscript European Journal of Inorganic Chemistry This article is protected by copyright. All rights reserved.

Table 1 .

 1 CV data containing the half-wave potential of the first reduction

	process for complexes. [a]
		E1/2 2
	PdL1	-1.57
	PdL2	-1.51
	PdL3	-1.59

[a]

Data collected in dry DMF (0.1 M TBAPF6) and referenced to Fc + /Fc. 10.1002/ejic.201901283

Accepted Manuscript

European Journal of Inorganic Chemistry This article is protected by copyright. All rights reserved.

Acknowledgments

Dr. Amélie Kochem is thanked for useful discussions and advice. This work has been partially supported by the Fundação para a Ciência e a Tecnologia (FCT), Portugal; projects UID/QUI/00100/2019 and PTDC/QEQ-ERQ/1648/2014 are acknowledged. Newcastle University is thanked for support to the project.

Keywords: Palladium complexes • Electrocatalysis • Heck • Sonogashira • X-ray structures

FULL PAPER

Entry for the Table of Contents


Willème Verdeaux

Clément Moreau

Nicolas Labroche

Patrick Marcel

Causality based explanations in multi-stakeholder recommendations

This paper introduces two novel contributions in the context of multi-stakeholder recommender system. First, we present a simple and intuitive method for multi-objective and multistakeholder recommendation that relies on preferences for each stakeholder. The second contribution is the adaptation of Halpern and Pearl's definition of causality to introduce definitions of causes and explanations for multi-stakeholder recommender systems. Experiments conducted on real data study the tractability of such explanation approach in the context of RS.

INTRODUCTION

Recommender systems solve the problem of predicting the value of a user-item relationship to propose the most appropriate list of items to each user based on personalization and contextualization mechanisms [START_REF] Adomavicius | Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions[END_REF][START_REF] White | Interactions with Search Systems[END_REF]. Traditional approaches like content-based, KNN systems or Latent Factor Models can generate recommendations for which simple, limited explanations can be derived (e.g., "other customer also bought that item"). However, modern, multi-objective, multi-stakeholder recommender systems [START_REF] Sürer | Multistakeholder recommendation with provider constraints[END_REF][START_REF] Zheng | Utility-based multi-stakeholder recommendations by multi-objective optimization[END_REF] make the generation of explanations more challenging.

In this paper, we introduce two novel contributions in this regard. First, we introduce a simple and intuitive method for multi-objective and multi-stakeholder recommendation that relies on preferences of each stakeholder. Following previous works on multi-stakeholder recommenders [START_REF] Abdollahpouri | Beyond personalization: Research directions in multistakeholder recommendation[END_REF][START_REF]Towards multi-stakeholder utility evaluation of recommender systems[END_REF][START_REF] Nguyen | A multi-objective learning to re-rank approach to optimize online marketplaces for multiple stakeholders[END_REF], we express the multi-stakeholder recommendation problem with an additive gain-based formulation. We compute a profile for each stakeholder, and define the gain brought by the recommendation using the classical NDCG measure, to confront the profile with the ranks of the recommended items.

The second contribution is the adaptation of Halpern and Pearl's definition of causality [START_REF] Halpern | Causes and explanations: A structural-model approach: Part 1: Causes[END_REF] and more precisely, its adaptation in the context of databases as developed in [START_REF] Meliou | The complexity of causality and responsibility for query answers and non-answers[END_REF], to introduce definitions of causes and explanations for multi-stakeholder recommender systems. This so-defined framework allows to explain both the recommendations given but also each individual stakeholder profile, in terms of the items rated by this stakeholder.

The outline of the paper is as follows. The next section presents related work and Section 3 motivates our approach with an example. We present our first contribution, the multi-stakeholder recommender, in section 4. Section 5 introduces our second contribution, namely explanation generation. Section 6 presents preliminary tests and Section 7 concludes by discussing future work.

As stated by [START_REF] Abdollahpouri | Beyond personalization: Research directions in multistakeholder recommendation[END_REF] "multi-stakeholder recommendation has emerged as a unifying framework for describing and understanding recommendation settings where the end user is not the sole focus". Practically, a multi-stakeholder recommender produces an aggregated recommendation that maximizes the utility for several , with possibly conflicting objectives, stakeholders at once. Burke et al. [START_REF]Towards multi-stakeholder utility evaluation of recommender systems[END_REF] describe the utility space to explore as a tuple where each tuple's component is the utility of a stakeholder computed as the sum of items utility for this stakeholder. Other works consider more complex models with multiple objectives per stakeholder [START_REF] Nguyen | A multi-objective learning to re-rank approach to optimize online marketplaces for multiple stakeholders[END_REF].

This improvement of the traditional recommendation problem allows to model different stakeholders' types such as consumer, providers or system [START_REF] Abdollahpouri | Recommender systems as multistakeholder environments[END_REF][START_REF] Nguyen | A multi-objective learning to re-rank approach to optimize online marketplaces for multiple stakeholders[END_REF] and to take into account new evaluation metrics such as novelty or fairness among stakeholders (to counter the popularity bias as in [START_REF]Towards multi-stakeholder utility evaluation of recommender systems[END_REF]). Several approaches have been proposed in the recent years [START_REF] Abdollahpouri | Beyond personalization: Research directions in multistakeholder recommendation[END_REF][START_REF] Abdollahpouri | Recommender systems as multistakeholder environments[END_REF][START_REF] Adomavicius | Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions[END_REF] and [START_REF] Abdollahpouri | Beyond personalization: Research directions in multistakeholder recommendation[END_REF] introduces a first effort to structure this novel domain by proposing a classification of multi-stakeholder systems depending on: (1) the types of stakeholders involved, (2) if they are active or passive or (3) if the recommendation is neutral or personalized for each stakeholder.

As recalled in [START_REF] Nguyen | A multi-objective learning to re-rank approach to optimize online marketplaces for multiple stakeholders[END_REF], and similarly to business rules, multi-stakeholders approaches [START_REF]Towards multi-stakeholder utility evaluation of recommender systems[END_REF][START_REF] Sürer | Multistakeholder recommendation with provider constraints[END_REF] are most of the time a posteriori methods applied on top of existing traditional recommender systems.

For example, [START_REF] Sürer | Multistakeholder recommendation with provider constraints[END_REF] proposes an approach that inputs a user × item matrix as provided by a traditional recommender system, and then finds an optimal binary assignment for items by providers to enforce constraints related to providers and enhance the distributions of recommendations across retailers. Similarly to these approaches, in our proposal, we also rely on a traditional recommender system to compute a profile for each stakeholder.

Finally, in [START_REF] Nguyen | A multi-objective learning to re-rank approach to optimize online marketplaces for multiple stakeholders[END_REF] the adaptation to multiple-objective multistakeholder is done as a post-processing step after a first ranking of items is already obtained for each consumer. The proposed approach aims to re-rank it such that the new ranking remains close to the initial one and optimizes the commission perceived by the "system" stakeholder. Interestingly, the proposed approach computes a ranking of items instead of predicting scores, to produce the recommendations. To combine all conflicting stakeholders objectives, [START_REF] Nguyen | A multi-objective learning to re-rank approach to optimize online marketplaces for multiple stakeholders[END_REF] introduces a new learn to (re-)rank optimization approach based on the kernel version of the Kendall tau correlation metric. A similar approach that learns to rank is also used in [START_REF] Zheng | Utility-based multi-stakeholder recommendations by multi-objective optimization[END_REF] to determine ratings that would be unknown to the multi-stakeholder recommender.

In our proposal, we consider a more straightforward rankbased approach that involves Normalized Discounted Cumulative Gain to measure to which extent the ranking preferences of a stakeholder are respected. The solution space is explored with a simple simulated annealing. Similarly to [START_REF] Zheng | Utility-based multi-stakeholder recommendations by multi-objective optimization[END_REF], we use a recommender system to predict user item scores that are missing in the data to construct a complete ranking over the set of items, as our stakeholder profile.

Explanations

Explaining recommendations. Explainable recommendations refers to personalized recommendation algorithms that "not only provide the user with recommendations, but also make the user aware why such items are recommended" [START_REF] Zhang | Explainable recommendation: A survey and new perspectives[END_REF]. Gedikli et al. [START_REF] Gedikli | How should I explain? A comparison of different explanation types for recommender systems[END_REF] evaluate different explanation types and propose a set of guidelines for designing and selecting suitable explanations for recommender systems.

Various forms of explanations have been explored. For instance, in [START_REF] Das | MRI: meaningful interpretations of collaborative ratings[END_REF], the authors introduce the problem of meaningful rating interpretation (MRI) in the context of recommendation systems and as such provide two main heuristics for explaining collaborative ratings. Explanations are here provided as a subset of reviewers presented to the user and described by metadata attributes shared among all reviewers in the group. Groups are build under constraints to minimize a description error while maximizing the coverage of ratings. Similarly, meaningful differences are provided by determining the most unbalanced subset of reviewers in terms of positive / negative ratings and are meant to highlight controversial items, i.e. items for which groups of users consistently disagree.

Interestingly, it turns out that so far, to our knowledge, explanations based on the notion of causality have not attracted attention in the recommender system community.

Explanation and causality. Causality has been studied and defined algorithmically by Judea Pearl, in a highly influential work primarily using the concepts of counterfactuals and degree of responsibility [START_REF] Pearl | Causal inference in statistics: An overview[END_REF].

At the core, causality is defined in terms of intervention: an input is said to be a cause if we can affect the output by changing just the value of that input, while keeping all others unchanged. Importantly, causality can only be established in a controlled physical experiment, and cannot be derived solely from data, while an explanation only requires that a change in the input affects the output: the more it affects the output, the better the explanation [START_REF] Pearl | Causal inference in statistics: An overview[END_REF].

Recently, many authors in the database community (e.g., [START_REF] Meliou | The complexity of causality and responsibility for query answers and non-answers[END_REF][START_REF] Roy | A formal approach to finding explanations for database queries[END_REF]) adapted these notions to explain the results of database queries. In this context, a major challenge in finding explanations is the difficulty of defining and computing in real time interventions for complex datasets and queries. Noticeably, in both [START_REF] Das | MRI: meaningful interpretations of collaborative ratings[END_REF] and [START_REF] Roy | A formal approach to finding explanations for database queries[END_REF] data cube operations are used to compute explanations, hence benefiting from built-in database optimizations. We leave as future work an in-depth study of optimization mechanisms for computing explanations in our context of multi-stakeholder recommendations.

The approach we present in this paper, depicted in Figure 1, is particularly inspired by that of Meliou et al. [START_REF] Meliou | The complexity of causality and responsibility for query answers and non-answers[END_REF], who borrowed from Pearl and Halpern's theory of causality the following important concepts:

• Partitioning of variables into exogenous and endogenous: exogenous variables define a context determined by external, unconcerned factors, deemed not to be possible causes, while endogenous variables are the ones judged to affect the outcome and are thus potential causes. In their work, Meliou et al. propose to partition a database instance into exogenous and endogenous tuples [START_REF] Meliou | The complexity of causality and responsibility for query answers and non-answers[END_REF], and look for explanations among the endogenous tuples only. We follow a similar approach in this paper, partitioning the set of events in exogenous and endogenous events. • Contingencies: a piece of information (tuple in [START_REF] Meliou | The complexity of causality and responsibility for query answers and non-answers[END_REF]) t is a cause for the observed outcome only if there is a hypothetical setting of the other endogenous variables under which the addition/removal of t causes the observed outcome to change. Therefore, in order to check that t is a cause of an outcome based on a given dataset, one has to find a data set (called contingency) to remove from (or add to) the data set, such that t immediately affects the outcome in the new state of the data set. In theory, in order to compute the contingency one has to iterate over the subsets of the data set, meaning that checking causality is NP-complete in general [START_REF] Eiter | Complexity results for structure-based causality[END_REF]. In the context of this paper, the considered outcome is a set of recommended items and the dataset is the set of ratings used by the recommendation algorithm.

• Responsibility measures the degree of causality as a function of the size of the smallest contingency set. In applications involving large datasets, it is critical to rank the candidate causes by their responsibility, because the outcome may have large lineages and large numbers of candidate causes. In theory, in order to compute the responsibility one has to iterate over all contingency sets meaning that computing responsibility in general is hard [START_REF] Chockler | Responsibility and blame: A structural-model approach[END_REF]. 1: Toy example of user purchases Figure 1 gives the intuition of our approach. Assume a set of events relating users to items (e.g., purchases), expressing implicit user preferences. From this set, a profile σ u 1 can be inferred for a given user u 1 , e.g., by predicting scores for unseen items. To explain this profile to u 1 , one could look for events that are the most responsible of it. To do so, we compute interventions on the set of events, by removing some events from it. Each intervention leads to another profile σ ′ u 1 for u 1 . If the two profile σ u 1 and σ ′ u 1 are different, this means that the removed events have, to a certain degree, a responsibility in σ u 1 . As there can be many such events, instead of presenting them as explanations to u 1 , we summarize them using pattern extraction, and present the extracted patterns. We next illustrate this approach with a detailed example. Consider Table 1, that details consumption events of three users. An event corresponds to a quantity purchased, and a user can purchase different quantities of the same item at different moments. For instance, user u 1 purchased initially 5 items i 3 and then another 6 items i 3 subsequently. Assume we have two categories of stakeholder: that of users u i and that of a provider p. Each purchased item i j is described by two properties, price and popularity (see Table 2.

MOTIVATING EXAMPLE

i 1 i 2 i 3 i 4 i 5 u 1 1 2 2 5 6 u 2 11 3 7 u 3 2 5 Table
i 1 i 2 i 3 i 4
i 5 price med med med high high popularity high med high high high Table 2: Item description for the toy example Stakeholder preferences can be modeled following a strategy particular to each stakeholder category, and computed using the set of events. For instance, users' preferences should be such that most purchased items are preferred. The provider's preferences could be that the same number of each item is purchased. For instance, according to Table 1, the preferences of user u 1 are that i 3 is preferred over i 2 that in turns is preferred over i 1 , that in turn is preferred over both i 4 and i 5 . The preferences of stakeholder p is that i 4 is preferred (since it sold less) over i 2 , in turns preferred over i 5 , in turns preferred over i 1 and then over i 3 .

Assume now that we have a way of constructing a user profile from each user's preferences so that the profile corresponds to a total order of the items, consistent with that user's preferences. For instance, a simple baseline approach, where prediction is the sum of consumptions by item, would allow to deduce that the profile σ u 1 of u 1 ranks all items as follows:

σ u 1 = [i 3 , i 2 , i 1 , i 5 , i 4 ].
Now, assume that we want to issue a recommendation achieving a compromise between all stakeholders. A multi-stakeholder multi-objective recommendation algorithm can be used to compute this recommendation from the profiles. This recommendation can take the form of a total ranking of the items, proposed to all stakeholders, noted σ * . In our example, suppose this recommendation is

σ * = [i 4 , i 3 , i 1 , i 2 , i 5 ].
As stakeholders' profiles and recommendation σ * have the same form, both can be explained in the same way. We illustrate here how profiles can be explained. Suppose we would like to explain σ u 1 , considered as the outcome of the process that computes the profile. We then intervene on the set of events by removing those of the events responsible for the current profile. For instance, we can see that removing any of the events in entries (u 1 , i 1 ) (u 1 , i 2 ) or (u 1 , i 3 ) would leave σ u 1 unchanged, while removing the event in entry (u 2 , i 5 ) would alter σ u 1 . Therefore, the event in entry (u 2 , i 5 ) can be said to be a direct cause, or counterfactual cause, for σ u 1 . Note that both purchases made by u 1 and not made by u 1 can be counterfactual causes for u 1 's profile. Indeed, event (u 3 , i 4 ) is not a counterfactual cause.

Note also that events pertaining to preferences can also be counterfactual causes. Consider indeed user u 2 , whose profile is

σ u 2 = [i 1 , i 5 , i 3 , i 2 , i 4 ].
It can be seen that events (u 2 , i 1 ), (u 2 , i 5 ) are counterfactual causes for σ u 2 , as is (u 3 , i 2 ).

Understanding the responsibility of non counterfactual causes in the profile can be done by trying to remove more than one event and measuring the responsibility as a function of the number of events to remove (called contingency set) before the non counterfactual cause becomes a counterfactual cause. For instance, removing both events in entry (u 1 , i 3 ) changes σ u 1 , meaning that both events in that entry have a responsibility in the profile, but with a lesser degree than that of (u 2 , i 5 ) (which does not need another event to be removed to be counterfactual).

Explaining a profile σ u i means presenting to u i the events most responsible for their profile. Consider for instance user u 2 . The events most responsible for u 2 's profile are the counterfactual causes (u 2 , i 1 ), (u 2 , i 5 ) and (u 3 , i 2 ).

However, since the number of causes can be large, presenting the events themselves may not be user-friendly. A better way is to summarize them using patterns extracted from the properties of the items concerned by the events. Indeed, consistently with earlier literature on deriving explanations using causality theory [START_REF] Roy | A formal approach to finding explanations for database queries[END_REF], we propose to present explanations under the form of predicates P = v where P is property and v is a value. In our example, suppose we use frequent itemset mining [START_REF] Giacometti | 20 years of pattern mining: a bibliometric survey[END_REF] to extract properties appearing more than two third of the time in items i 1 , i 2 , i 5 . Two frequent itemsets can be extracted from these counterfactual events' properties: (i) price=med and (ii) popularity=high.

MULTI-STAKEHOLDER RECOMMENDATION 4.1 Stakeholders and their profiles

We formalize the problem as follows. We assume a set O of n objects, where each object is described by a list of properties. Let F be a set of property names and V be a set of property values, function properties : O × F → V denotes the values of a given property for a given object. We assume a set S of stakeholders and a set R of stakeholder roles, like : "user", "provider", "system owner", etc. The role of a stakeholder is given by a surjective function role : S → R. Finally, we have a set E of events, where an event is a 4-tuple ⟨s, o, r, t⟩ with s a stakeholder in S, o an object in O, a numerical value r ∈ R, representing e.g., a rating or an amount, and t a timestamp.

Preferences. Each stakeholder s is associated with their preferences, expressed as a weak order (a partial order that is negatively transitive) over the set O, noted ⪯ s . This preference relation induces a partition of the set O.

Example 4.1. Consider the example of the previous section. The preferences of u 1 can be deduced from Table 1. They correspond to the following weak order over the set of consumption events

i 3 ⪯ u 1 i 2 ⪯ u 1 i 1 ⪯ u 1 {i 4 , i 5 }.
Profile. The profile of a stakeholder s ∈ S consists of a total order σ s over the objects of O that is consistent with the preference relation ⪯ s , i.e., σ s is obtained by composing ⪯ s with a total order ≺ using priority composition [START_REF] Chomicki | Preference formulas in relational queries[END_REF], where the total order ≺ is expressed in a quantitative way through function utility : S × O → R.

These preferences can be noted by a vector ⟨utility(s, o 1 ), . . . , utility(s, o n )⟩, where the o i 's are the objects of O, and utility's are pairwise different, or alternatively by a permutation σ s of the objects in O. We note P the set of permutations of size n. Let a permutation σ , we note σ s (o) = i the rank i given by s to object o, and σ s [i] = o the object ranked i by s.

Example 4.2. Assume that it is predicted, based on u 1 's preferences, that u 1 is more likely to prefer i 5 to i 4 . The profile of u 1 therefore consists of the total order σ u

1 = [i 3 , i 2 , i 1 , i 5 , i 4 ].

Recommendation objective

Our recommendation objective is to find the optimal permutation σ * in the sense of a compromise between a subset S of all stakeholders of S. Given a subset S ⊆ S the recommendation σ * for S is given by function R : 2 S → P:

R(S) = σ * = argmax σ ∈P s ∈S α s Q(σ, s) (1)
where α s is the weight of the stakeholder s such that s ∈S α s = 1 and Q : P × S → R + is a quality function measuring how well a permutation σ is for stakeholder s.

In this work, we have chosen the classical NDCG to measure the quality of the solution. In other words, the quality is measured in terms of the gain brought by σ * for the stakeholder s with respect to their preference. Equation 1 becomes:

σ * = argmax σ ∈P s ∈S α s DCG(s, σ ) IDCG(s) (2)
where:

DCG(s, σ ) = n r =1 utility(s, σ [r ]) log 2 (1 + r ) (3)
IDCG(s) = DCG(s, σ s ) (4)
This formulation makes the recommendation problem an instance of the well-studied rank aggregation problem, aiming at aggregating the total order preferences of multiple agents [START_REF] Lin | Rank aggregation methods[END_REF]. Particularly, our problem is similar to the Kemeny optimal aggregation problem that determines the best consensus ranking minimizing the number of permutations as a Kendall-tau distance with the rankings of each agent. This problem is known to be NP-Hard even when there are only few rankings to aggregate. Because of this complexity, stochastic or evolutionary algorithms are often proposed as an efficient way to explore the space of possible rankings and then solve what is known as Mallows problem [START_REF] Aledo | Tackling the rank aggregation problem with evolutionary algorithms[END_REF]. In this work, we follow a similar idea and use simulated annealing to find the consensual ranking based on all stakeholders rankings.

EXPLAINING PROFILES AND RECOMMENDATIONS

Our framework is inspired by that of Meliou et al. for explaining query answers in relational databases [START_REF] Meliou | The complexity of causality and responsibility for query answers and non-answers[END_REF].

Profile explanations

Inspired by Meliou et al [START_REF] Meliou | The complexity of causality and responsibility for query answers and non-answers[END_REF], it makes sense to partition the set of all events E into endogenous and exogenous events. However, in this preliminary work, and without loss of generality, we consider all events as endogenous, and in what follows, only the set of all events E is used in the definitions. Let E be a set of (endogenous) events and a stakeholder s with preference ⪯ s , we note E |= σ s if the profile σ s is obtained using E and ⪯ s .

Counterfactual cause. Given a stakeholder s with preference relation ⪯ s and profile σ s , and a set of events E, an event e = ⟨s, o, r, t⟩ of E is a counterfactual cause in E for σ s if E |= σ s and E -{e} |= σ ′ s with σ ′ s σ s . In other words, removing event e from E causes the profile of s to change.

Actual cause. Given a stakeholder s with preference relation ⪯ s and profile σ s , and a set of events E, an event e = ⟨s, o, r, t⟩ of E is an actual cause in E for σ s if there exists a set Γ ⊆ E called contingency for e, such that e is a counterfactual cause for σ s in E -Γ. An event is an actual cause if one can find a contingency under which it becomes a counterfactual cause.

Responsibility. If an event e is a cause, the responsibility of e for σ s is ρ e = 1 1+min |Γ | where Γ ranges over all the contingency sets for e.

The responsibility is a function of the minimal number of events to remove from E before the event becomes counterfactual.

Causality problem. Compute the set C ⊆ E of actual causes for σ s .

Responsibility problem. For each actual cause e ∈ C, compute its responsibility ρ e .

Explanation. Given a set C of causes for σ s , consider the set

O C = {o ∈ O |∃e = ⟨s, o, r, t⟩ ∈ C}. An explanation for σ s is a set of frequent patterns extracted from {⟨properties(o, f 1 ), . . . , properties(o, f |F | )⟩|o ∈ O C , f i ∈ F }.

Explanations for σ *

In this case, we look for what causes the differences between σ * and σ s , in the profiles (and then preferences) of the stakeholders other than s. Intuitively, we want to explain to stakeholder s why is the compromise σ * not more favorable to them. Precisely, an event e is a counterfactual cause for σ * if we remove e from E then σ s does not change but there are some change in σ s ′ for some stakeholder s s ′ and σ * improves the score Q for s. Formally:

• E |= σ * • for all stakeholders (including s) s i ∈ S, E |= σ s i • E -{e} |= σ s • E -{e} ̸ |= σ * but E -{e} |= σ * ′ with σ * ′ σ * , • Q E-e (σ * ′ , s) > Q E (σ * , s)
Actual cause, responsibility and explanations are defined accordingly.

WORK COUNCIL USE CASE

The recommender system and the explanation framework are implemented in Python 3.6. User profiles are computed from raw data using the Surprise Scikit1 . Simulated annealing for exploring the space of permutations is an in-house development. We experimented on a real use case based, with purchase data from Kalidea-Up, a company that provides a service platform to works councils. We considered two stakeholder roles: "workers" who can purchase discounted services from works councils, and "system" to represent Kalidea-Up system. Available purchase data correspond to the 2014-2018 period, gathering over 5, 840 workers for 540 services and 168, 965 transactions, where each transaction corresponds to an event as defined in Section 4.

Testing the recommender system

These purchases are used to build profiles for the workers, using Surprise's off the shelve k-NN prediction algorithm, and baseline predictions to ensure a total ranking of the services. The profile for the system is a ranking computed based on the subsidies collected from the work councils for the services. As such, system preferences may not coincide with those of the users that may prefer discounts on other types of services. Simulated annealing. The objective function optimised by the simulated annealing is provided in Equation 2. In order to crawl the space of possible permutations to determine the best σ * , each new candidate permutation is generated by a random mutation that swaps 2 elements of the previous permutation at random. A temperature parameter allows to retain a solution that is not optimal after a mutation. In order to force the convergence, a geometric progression with common ratio 0.996 is applied to the temperature. The maximum number of iterations for simulated annealing was set to 500 in our experiment.

We consider the following settings in our experiments:

• as in [START_REF] Sürer | Multistakeholder recommendation with provider constraints[END_REF], we first observe to which extent the addition of new stakeholders decreases the quality of recommendation for each stakeholder: we vary the number of stakeholders from 2 : 1 recipient and the system as represented by Kalidea-Up, to 10 : 9 recipients and the system ; • for each of the previous settings, we vary the distribution of weights α s of Equation 2, for each stakeholder s ∈ S. Settings for α s are: either a uniform distribution, meaning that all stakeholders have the same weight in the final decision, or a 80% weight given to all workers, meaning that the system only accounts for 20%, or finally the symmetric situation where 80% of the weight is set to the system ;

For these settings, we expect the following results:

• if our approach performs well, it should be able to produce a good quality consensus aggregation of all stakeholders' preferences. In this case, the overall quality, as measured by our objective function should be as close to 1 as possible. This would reflect that our choice of a simple simulated annealing algorithm is a fair enough solution in our context of multi-objective optimization ; • we should observe that the decrease for each stakeholder is moderate and comparable to the one observed in other works such as [START_REF] Sürer | Multistakeholder recommendation with provider constraints[END_REF], indicating that our approach manages to accommodate all stakeholders simultaneously and with approximately the same effectiveness for each of them ;

Results. As can be seen in Table 3, our approach obtains satisfactory optimization results in terms of NDCG with approximately 0.82 as a global optimization score when weights α are uniform. As expected, our approach proves to be efficient when biasing the convergence towards one of the stakeholder or the other by adjusting the weights accordingly. Interestingly, when favoring one stakeholder, the global NDCG decreases reflecting that both stakeholders had contradictory profiles.

To provide the reader with a range for acceptable NDCG values, it can be noticed that [START_REF] Sürer | Multistakeholder recommendation with provider constraints[END_REF] have achieved very high NDCG score (above 0.95) on a tweaked MovieLens dataset where providers have been set manually for each movie. We have reproduced this data set and on the aforementioned 2 stakeholders settings and by tuning system preferences based on fairness we have achieved 0.96 NDCG which proves that simulated annealing paired with NDCG are a fair choice for the problem of multi-stakeholder optimization.

Testing explanation generation

For those tests, we used Surprise's off the shelf Baseline only predictor to compute profiles. Figure 2: Average "Mean NDCG scores" for all users, and reported for the system and globally for 3 distinct settings with 2, 5 and 10 stakeholders.

to be simple, fast and yet quite accurate. Our experiments aim to answer 2 main questions:

(1) is the approach presented in Section 5 feasible in the context of multi-stakeholder recommendation algorithms? In this case, there are possibly 2 E contingency sets to evaluate to determine the responsibility of each event of E. For this reason, we propose to first limit our experiments to small sets E ranging from 8 to 14 events, where all workers (resp., services) are pairwise different, resulting in a very sparse workers services matrix. Computation times are reported in Figure 3 ; (2) how is the responsibility distributed and can this measure be used in the context of recommender system to discriminate between events to explain a recommendation? Are all events equally discriminant regarding this measure? This paper answers the question by computing for each event the minimum size of its contingency set min |Γ| as defined in Section 5.1. Then for all events, and depending on the size of |E|, a distribution for min |Γ| is computed. Results are presented in Figure 4. The machine configuration for the tests is a Core i7-6500U CPU @ 2.50GHz, with 8 Gb of RAM, running Ubuntu 18.04.1 LTS. As can be seen from Figure 3, the causal explanation approach expectedly has an exponential time complexity behavior, which opens new research direction to avoid the exploration of all contingency sets and make this approach tractable. Interestingly, when the size of |E| increases, the training time of the multi-stakeholder recommender system tends to be negligible when compared to the explanations of the recommendation. This clearly indicates that causal explanation is even more challenging in terms of optimization than our quite resource intensive RS.

Then, considering Figure 4 it can be seen that most events in both scenarios have a majority of (close to) counterfactual events (|Γ| ≈ 0) that directly impacts the recommendation process and a minority of sensibly less "responsible" events as shown by the 2-modes distribution. This was expected as the events test sets have been built in a way making the workers × services matrix very sparse.

DISCUSSION

This paper introduces an on-going work on explaining recommendations in a multi-stakeholder context. Our immediate future work includes the optimization of the computation of responsibilities and the evaluation of the approach on the explanation of σ * . Our short term goal is mainly a complete validation of the current framework, including a user study to validate the usefulness of explanations to the different stakeholders. Our long term goal is to define a thorough framework for explanation generation in a multi-stakeholder recommendation context. Such a framework should cover: (i) The clear distinction of endogenous and exogenous causes. In Halpern and Pearl's framework, exogenous variables define a context determined by external, unconcerned factors, deemed not to be possible causes, while endogenous variables are the ones judged to affect the outcome and are thus potential causes. In the present work, we considered all the events as endogenous causes. (ii) The modeling of different types of causes. In the present work, we addressed the problem of modeling why so cause, i.e., explaining why the recommendation is what it is. Other forms of explanations can be addressed, like for instance why not so, i.e., why recommendation is not like this. (iii) The distinction between explanations of profiles and recommendations. In the present work, all explanations are generated through interventions over the set of events. Recommendation explanations may be more intuitively understood if we allow interventions directly on the stakeholders' profile (e.g., permuting the ranks of two objects). A challenge is then to investigate how to map such interventions to interventions over the set of objects.

(iv) The modification of the responsibility measure to include the assessment of the perturbations on the ranking brought by causes.

Figure 1 :

 1 Figure 1: Overview of a user's profile explanation

Figure 3 :Figure 4 :

 34 Figure 3: Executions and training times for different size of the events set |E|

Table 3 :

 3 The advantage of this predictor is Mean NDCG over 3 runs for the setting with 2 stakeholders: 1 recipient user and the system. "Uniform", "80% system / user" refer to the settings for parameters α

		Uniform	User	System		Global
		2
	α	NDCG user NDCG System NDCG Global 0,79 0,81 0,79
		5
	Uniform	0.79 ± 0.05	0.85 ± 0.03 0,85	0,86	0.82 ± 0.01 0,89
	80% system 0.63 ± 0.07 10	0.89 ± 0.04	0.76 ± 0.04
	80% user	0.95 ± 0.01	0.56 ± 0.04 0,82	0,82	0.75 ± 0.02 0,8
		Uniform		Number of stakeholders	80% system
				2		5	10
		NDCG user		0,79		0,81	0,79	NDCG user
		NDCG System		0,85		0,86	0,89	NDCG System
		NDCG Global		0,82		0,82	0,80	NDCG Global
		User		System	Global
		1
		0,75
	Mean nDCG	0,5
		0,25
		0
	Number of	2	5		10
	stakeholders

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