Alae Eddine Lakraychi

Louis Sieuw

Darsi Rambabu

Koen Robeyns

Alia Jouhara

Gheorghe Borodi

Cristian Morari

Philippe Poizot

Alexandru Vlad

Through-Space Charge Modulation Overriding Substituent Effect: Rise of the Redox Potential at 3.35 V in a Lithium-Phenolate Stereoelectronic Isomer

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■ INTRODUCTION

One of the primary assets of current Li-ion battery technology is the availability of positive electrode chemistries that are stable to ambient air in the lithium containing, electrochemically reduced form. 1 Whereas there are many opportunities for the transition metal-based chemistries to fulfill these criteria, the organic-based compounds with alike properties remain finger-counted. [START_REF] Li | window, at a cycling 615 rate of 2 Li + equivalents exchanged in 10 h (i.e., 1Li + /5 h or a 616 C-rate of C/10). Upon charging, Li 4 -p-DOBDA undergoes a 617 two-electron process at an average oxidation potential of 3.7 V 618 vs Li + /Li 0 , yielding its full two-electron capacity (215 mAh/g). 619 This is superior to carboxyphenolate derivatives (e.g., Li 4 -p-620 DHT, Li 4 -o-DHT, and Mg(Li 2 )-p-DHT) which consistently 621 yield[END_REF] Organic batteries emerge as one of the attracting alternative technologies for the forthcoming massive adoption of electrochemical energy storage (EES) systems. Indeed, these would allow to cope with raw material supply shortages, lead to a reduced environmental production and recycling footprint, and potentially result in an enhanced manufacturing scalability, globally improving the sustainability of EES devices. [3][4][5][6][7] Whereas the gravimetric and volumetric energy metrics of organic batteries may not currently compete with their inorganic counterparts, the natural abundance of their constituent elements (e.g., C, H, N, O), and the expected mitigation of the battery life-cycle's environmental burden constitute arguments of choice to counterbalance and eventually overthrow this already receding disadvantage. [START_REF] Li | window, at a cycling 615 rate of 2 Li + equivalents exchanged in 10 h (i.e., 1Li + /5 h or a 616 C-rate of C/10). Upon charging, Li 4 -p-DOBDA undergoes a 617 two-electron process at an average oxidation potential of 3.7 V 618 vs Li + /Li 0 , yielding its full two-electron capacity (215 mAh/g). 619 This is superior to carboxyphenolate derivatives (e.g., Li 4 -p-620 DHT, Li 4 -o-DHT, and Mg(Li 2 )-p-DHT) which consistently 621 yield[END_REF] Instrumentation. 1 H NMR spectra were acquired on a 300 MHz Bruker Advance II. 13 C NMR spectra were acquired on a 500 MHz Bruker Advance III. Samples were prepared by dissolution of 5-10 mg of the product in 600-700 μL of deuterated solvent (D 2 O or d 6 -DMSO-Sigma-Aldrich). FTIR spectroscopy was carried out on pristine powders using a Bruker Alpha P or an Agilent Technologies Cary 630 spectrometer with a Single reflection ATR module. Thermogravimetry (TG) and differential scanning calorimetry (DSC) experiments were carried out under argon with a SENSYSevo instrument from Setaram using a heating rate of 5 °C min -1 between 25 and 600 °C. Scanning electron microscopy (SEM) images were collected on using a JEOL JSM-7600F microscope.

Powder X-ray powder diffraction (PXRD) patterns were collected on a STOE Stadi P diffractometer in transmission geometry equipped with a Cu anticathode (Kα radiation, operating at 50 kV to 40 mA).

For structure resolution, data were acquired at the ESRF synchrotron (Grenoble, beamline BM01) with a wavelength of λ = 0.69425 Å.

Electrochemical Assembly and Analysis. The electrochemical performances of Li 4 -p-DOBDA in the solid phase (galvanostatic charge/discharge) were determined using two-electrode coin cells assembled in an argon-filled glovebox. A typical Li 4 -p-DOBDA working electrode (cathode) was composed of 5 mg of active material (60 wt %) manually mixed with 30 wt % of Ketjenblack EC600 (denoted as KB600 carbon) and 10 wt % poly(tetrafluoroethylene) (PTFE) dry binder. The resulting mixture was pressed on stainless steel mesh disks with a pressure of 8 tons to form the working electrode (5 mg/cm 2 of active material typically). A lithium foil disk was used as counter and reference electrode (anode), two PE/PP sheets as separator and LiPF 6 1 M in ethylene carbonate/dimethyl carbonate (EC/DMC) 1:1 (v/v) as electrolyte (LP30, battery grade, Solvionic). The galvanostatic measurements were recorded using a In Situ X-ray Measurements. In situ PXRD patterns were collected in the 5.00-31.13 2θ degrees ranges, with a step size of 1.005°and total acquisition time per diffractogram of 80 min. Measurements were performed with a simple holder able to accommodate an in-house in situ coin cell. The working electrode was prepared by mixing Li 4 -p-DOBDA, KB600, and PTFE with a composition ratio of 60:30:10 wt %. The lithium metal disk was used as negative electrode, 2 sheets of PE/PP (Celgard) as separator, and LP30 as electrolyte. The galavanostatic measurements were collected on a Parstat 3000 potentiostat/galvanostat.

■ RESULTS AND DISCUSSION

Design Considerations for High Potential Organic Positive Electrode Chemistries. Our current efforts are oriented on finding n-type organic positive electrode materials capable of fulfilling the paramount criteria of a conventional Liion cathode. Whereas most results are based on conventional approaches to the electron withdrawing effect to increase the redox potential, recently we reported on a new class of organic materials based on conjugated sulfonamide (CSA) as an efficient organic Li-ion cathode material, given its intrinsic high voltage properties. 19 Various CSA chemistries were explored and found to be operating within a wide range of potential between 2.85-3.45 V vs Li + /Li 0 (with also excellent air stability) with tunable electrochemical performance.

The archetypal carbonyl redox chemistry nevertheless remains the most explored to date, owing to its tangible ability to simultaneously attain high energy and power densities combined with extended cycling stability. For s1 instance, quinone chemistry (Q 0 gQ 2-, Scheme 1), promises an impressive theoretical energy density of more than 1 kWh/ kg [two electron redox, specific capacity of 440 mAh/g (mass of the Li + cations considered), for an average electrode potential of 2.7 vs Li + /Li 0 ]. 20 However, benzoquinone presents two key drawbacks: the reduced Q 2-form is sensitive to oxidation in air, whereas the oxidized form Q 0 is highly soluble in typical liquid battery electrolytes.

Concerning the latter, many approaches have been developed in the past to counter act the solubility. [21][22][23][24][25][START_REF] Xu | Electrochemically Active, Crystalline, Mesoporous Covalent Organic Frameworks on Carbon Nanotubes for Synergistic Lithium-Ion Battery Energy Storage[END_REF] In addition to the inclusion of permanent negative charges to increase the polarity [START_REF] Poizot | Clean Energy New Deal for a Sustainable World: From Non-CO2 Generating Energy Sources to Greener Electrochemical Storage Devices[END_REF] such as in the tetralithium 2,5dihydroxyterephthalate salt (Li 4 -p-DHT also known as Li 4 DHTPA), 17,18 we have explored intermolecular H-bonding in 2,5-diamino-1,4-benzoquinone (DABQ) [START_REF] Sieuw | A H-Bond Stabilized Quinone Electrode Material for Li-Organic Batteries: The Strength of Weak Bonds[END_REF] as a new efficient strategy to reduce the solubility of the low-molecular weight quinone-based systems. However, the electron-donor nature of the amine and carboxylate substitution comes along with the reduction of the redox potential (Scheme 1).

One key element to enable ambient air stability of lithiated (reduced state) organic electrode materials, which will also translate into higher energy content, is to increase the redox potential above the limit of 2.91 V vs Li + /Li 0 ; the redox potential at which oxygen reduction occurs vs Li. 17,[START_REF] Laoire | Influence of Nonaqueous Solvents on the Electrochemistry of Oxygen in the Rechargeable Lithium -Air Battery[END_REF] Considering that few lithiated reduced organic phases comply to this criterium, it is not surprising that most organic battery chemistries proposed thus far are assembled out of the oxidized phase, requiring a lithium reservoir counter electrode, and thus suitable only for lithium-metal (rechargeable or primary) cells. Since this latter technology is still facing major challenges, [START_REF] Liu | Advancing Lithium Metal Batteries[END_REF][START_REF] Liu | Pathways for Practical High-Energy Long-Cycling Lithium Metal Batteries[END_REF] organic materials do not yet make the cut for Lithium-ion batteries. All-organic Li-ion cells have nevertheless 206 been made possible by synthesizing the reduced phases of 207 organic quinone-based compounds. 6,18,[START_REF] Zhao | Nanostructured Organic Electrode Materials Grown on Graphene with Covalent-Bond Interaction for High-Rate and Ultra-Long-Life Lithium-Ion Batteries[END_REF] However, these 208 phases are reactive toward oxygen and moisture, making 209 them hardly practical, as many are impossible to handle even in 210 dry rooms. It should be mentioned that there exist organic 211 battery chemistries with a formal redox potential above 3 V vs 212 Li + /Li 0 , however their redox mechanisms is based on the 213 ingress/removal of anions (also known as p-type redox 214 systems). 6,[START_REF] Deunf | Reversible Anion Intercalation in a Layered Aromatic Amine: A High-Voltage Host Structure for Organic Batteries[END_REF][START_REF] Jouhara | Tuning the Chemistry of Organic-Nitrogen Compounds for Promoting All-Organic Anionic Rechargeable Batteries[END_REF] Whereas such chemistries are suitable for Li-215 free batteries [START_REF] Deunf | Reversible Anion Intercalation in a Layered Aromatic Amine: A High-Voltage Host Structure for Organic Batteries[END_REF][START_REF] Macinnes | Organic Batteries: Reversible n-and p-Type Electrochemical Doping of Polyacetylene, (CH)X[END_REF][START_REF] Kaneto | Characteristics of Polythiophene Battery[END_REF][START_REF] Deunf | Solvation, Exchange and Electrochemical Intercalation Properties of Disodium 2,5-(Dianilino)Terephthalate[END_REF][START_REF] Deunf | A Dual -Ion Battery Using Diamino -Rubicene as Anion -Inserting Positive Electrode Material[END_REF][START_REF] Wild | All-Organic Battery Composed of Thianthrene-and TCAQ-Based Polymers[END_REF][START_REF] Dong | Organic Batteries Operated at -70[END_REF][START_REF] Dai | Manipulation of Conjugation to Stabilize N Redox-Active Centers for the Design of High-Voltage Organic Battery Cathode[END_REF][START_REF] Duḧnen | Reversible Anion Storage in a Metal-Organic Framework for Dual-Ion Battery Systems[END_REF] or better known as molecular-ion 216 batteries, [START_REF] Yao | Molecular Ion Battery: A Rechargeable System without Using Any Elemental Ions as a Charge Carrier[END_REF] these cannot comply with conventional Li-ion 217 design.

218

In accordance with the inductive or mesomeric effects 219 rationales (Scheme 1), several electron-deficient quinones have 220 been designed, with effectively increased redox potentials. 44-47 221 But it is only very recently that practical organic Li-ion cathode 222 chemistriesdefined as Li-containing in the reduced form, 223 while also being stable in ambient airhave been proposed. pointed to be sensitive to moisture). [START_REF] Lakraychi | An Air-Stable Lithiated Cathode Material Based on a 1,4-Benzenedisulfonate Backbone for Organic Li-Ion Batteries[END_REF] The same year, Jouhara 229 et al. reported an innovative approach to achieve significant 230 increase of the redox potential in p-DHT 4-. [START_REF] Jouhara | Raising the Redox Potential in Carboxyphenolate-Based Positive Organic Materials via Cation Substitution[END_REF] The authors 1). The measured half-272 wave redox potential of p-DODBA 4-obtained by cyclic 273 voltammetry (aqueous solution, pH 13.4) was found to be 274 approximately 120 mV lower than that of hydroquinone (Q 2-) 275 measured in similar conditions: -0.365 V and -0.485 V vs 276 [Fe(CN) 6 ] 3-/ [Fe(CN) 6 ] 4-for Q 2-and p-DODBA 4-, 277 respectively (Figure 1A). This observation corroborates the 278 rationale presented in Scheme 1 and is in accordance with the 279 through bond electronic effects at play. The acetate groups 280 (-CH 2 -COO -) in p-DOBDA 4-have an inductive donor 281 nature and would thus enrich the electronic density of the 282 quinone/enolate redox center, resulting in a lower (than for 283 Q 2-) redox potential. A similar dependence is also known for 284 other substituted p-benzoquinones. [START_REF] Yokoji | Rechargeable Organic Lithium-Ion Batteries Using Electron-Deficient Benzoquinones as Positive-Electrode Materials with High Discharge Voltages[END_REF] When an electron 285 withdrawing group (e.g., -CF 3 , giving 2.5-bis-286 (trifluoromethyl)-1,4-benzoquinone -CF 3 -BQ) was used, 287 the redox process occurred at -0.41 V vs Ag + /Ag 0 , while it 288 dropped to -1.08 V vs Ag + /Ag 0 when an electron donating group (e.g., -CH 3 in 2.5-dimethyl-1,4-benzoquinone -CH 3 -BQ) was used. [START_REF] Yokoji | Rechargeable Organic Lithium-Ion Batteries Using Electron-Deficient Benzoquinones as Positive-Electrode Materials with High Discharge Voltages[END_REF] Counterintuitively, when tested as solid in a lithium half-cell, the reversible electrochemical activity of Li 4 -p-DOBDA occurred at an impressively higher, but also practical potential around 3.35 V vs Li + /Li 0 (Figure 1B), about 700 mV higher than what could be predicted from comparative experimental study and through-bond electronic effect (Scheme 1 and Figure 1B). The chemical nature and similarity of Li 4 -p-DOBDA to Li 4 -p-DHT did not allow prediction of this peculiarly high potential value, and the large discrepancy between the redox activity in the dissolved phase as compared to the solid-state further adds to the exotics of this system.

In Li 4 -p-DHT, the electron donating nature of the carboxylates effectively lowers the redox potential to 2.55 V vs Li + /Li 0 as compared to 2.8 V vs Li + /Li 0 for Li 2 Q (Figure 1B). While the methylene group increases the distance between the quinone center and the negatively charged carboxylate and should effectively reduce the inductive donor effect, -CH 2is not an electron-withdrawing group and thus cannot, in terms of electronic effects, explain the potential gain.

Moreover, the disubstituted p-benzoquinones studied by Modeling of the correlation through linear regression. 312 solution. Indeed, CF 3 -BQ revealed an average redox potential 313 of 3.0 V vs Li + /Li 0 , while CH 3 -BQ operated at 2.7 V vs Li + / 314 Li 0 , indicating that the potential is tuned in accordance with 315 the conventional through-bond electronic effects, independ-316 ently of whether the measurement was performed in solid 317 phase or through molecule electrochemistry analysis. Follow-318 ing the same rationale, the redox potential of Li 4 -p-DOBDA 319 should be at best somewhere between the redox potentials of 320 Li 4 -p-DHT (2.55 V vs Li + /Li 0 ) and of Li 2 Q (2.8 V vs Li + /Li 0 ). 321 Whereas this is the case for molecular electrochemistry analysis 322 (cyclic voltammetry in solution, Figure 1A), it is no longer 323 valid for the solid phase behavior (half-cell, Figure 1B).

324

Correlating the Redox Potential Gain with the Bond 325 Vibration Energy. The high redox potential of Li 4 -p-DOBDA 326 in the solid state is nearly on par with the recently investigated 327 Mg(Li 2 )-p-DHT [START_REF] Jouhara | Raising the Redox Potential in Carboxyphenolate-Based Positive Organic Materials via Cation Substitution[END_REF] and is among the highest observed yet for a 328 lithiated n-type organic positive electrode material. This 329 previous investigation suggested a theory that correlated the 330 influence of spectator cation (M n+ = Li + , Mg 2+ , Ca 2+ , Ba 2+ ) in 331 the --

+ p M (Li ) DHT n n 2/ 2
system by tuning of the π-electron 332 density distribution in the aromatic unit depending on the 333 electronegativity value of M. It was put forward that the 334 blueshift of the ν as (COO -) band as well that of the aromatic 335 bandwhen varying the countercation in the following order: 336 M n+ = Ba 2+ , Li + , Ca 2+ , and Mg 2+ demonstrate the nature of 337 M-O bonds can affect the electronic distribution along the 338 aromatic system. This interaction resulted notably in a 339 mitigation of the inductive donor (+I) effect of the carboxylate 340 groups with a resulting electronic density decrease. This model 341 perfectly explained the 800 mV potential gain in Mg(Li 2 )-p-342 DHT via the through-bond electronic effect (Scheme 1). 343 However, the respective rationale, relying on the effect of the 344 electro-attracting spectator metal cations, cannot be applied to 345 the Li 4 -p-DOBDA chemistry presented in this work.

346

To explore the link between redox potential and FTIR 347 spectrum, we have analyzed a series of quinone derivatives (all 348 selected to be in the reduced, lithium-containing form) with 349 well-established redox properties and available FTIR data. The f2 350 results of this analysis are shown in Figure 2, and the 351 chemistries included are the following: Li 2 -DABQ, [START_REF] Sieuw | A H-Bond Stabilized Quinone Electrode Material for Li-Organic Batteries: The Strength of Weak Bonds[END_REF] Li 2 Q, and 352 Li 4 -p-DHBDS, [START_REF] Lakraychi | An Air-Stable Lithiated Cathode Material Based on a 1,4-Benzenedisulfonate Backbone for Organic Li-Ion Batteries[END_REF] as well as the four --

+ p M (Li ) DHT n n 2/ 2
(M n+ = 353 Ba 2+ , Li + , Ca 2+ , Mg 2+ ) derivatives studied in Jouhara's work. [START_REF] Jouhara | Raising the Redox Potential in Carboxyphenolate-Based Positive Organic Materials via Cation Substitution[END_REF] 354 For Li 4 -p-DOBDA, data include the partially deprotonated 355 products of H 4 -p-DOBDA (Figure S16 of the Supporting 356 Information, SI) as well as the IR data acquired in the solid and 357 dissolved states. Whereas the former set of data helped to 358 better identify the specific vibration feature in Li 4 -p-DOBDA, 359 the latter was motivated by the discrepancy observed between 360 molecular and solid phase electrochemistry results (Figure 361 1). [START_REF] Lakraychi | An Air-Stable Lithiated Cathode Material Based on a 1,4-Benzenedisulfonate Backbone for Organic Li-Ion Batteries[END_REF]

362

The position of the ν as (COO -) band in solid Li 4 -p-DOBDA 363 is almost identical to that of Li 4 -p-DHT1576 and 1573 364 cm -1 whereas the formal redox potentials are 3.35 and 2.55 365 V vs Li + /Li 0 , respectively. Both compounds share the same 366 spectator cation in the solid phase, and the electron density of 367 the carboxylate remains thus relatively unaffected. Further, the 368 -COO -vibration frequency for dissolved Li 4 -p-DOBDA is 369 located at a lower frequency (1560 cm -1 , Figure 2A). Indeed, 370 in aqueous solution, Li 4 -p-DOBDA is fully dissociated, with 371 minimal ion-pairing interaction (as confirmed with a slight 372 shift of Li + at -0.11 ppm with respect to LiOH•H 2 O and lithium benzoate, Figure S17). Clearly, there is no correlation between the vibration frequency of ν as (COO -) band and the redox potential when including the solid and dissolved Li 4 -p-DOBDA phases in this correlation analysis. The IR band shift of the aromatic stretch ν(CC aromatics ) tends to correlate to a certain extent with the redox potential (Figure 2A). However, given the complexity in unambiguously assigning the specific bands in this region of the spectrum, we decided to concentrate our investigation on an additional key vibration bandthe enolate vibration ν(C-O -).

The wavenumber of the enolate ν(C-O -) vibration band (Figure 2A, inset to the right) was found to scale linearly (R 2 = 0.91) with the redox potential (Figure 2B) for all analyzed compounds in the solid phase, confirming the existence of a correlation between both parameters. A higher vibration energy of the enolate bond is thus at the origin of the higher redox potential of solid Li 4 -p-DOBDA. This additionally corroborates with the seminal work of Josien et al., where the redox potential of quinones was linearly correlated to the carbonyl ν(CO) stretching frequency. [START_REF] Josien | An Infrared Spectroscopic Study of the Carbonyl Stretching Frequency in a Group of Ortho and Para Quinones[END_REF] Importantly, this correlation could be used as guideline for future developments of quinone-based redox chemistries to estimate the redox potential from simply measuring or estimating the vibration frequency of the respective band.

It is further interesting to point out the noticeable red shift of the ν(C-O -) and ν as (COO -) for dissolved Li 4 -p-DOBDA as compared to the solid Li 4 -p-DOBDA. According to the rationales presented above, this should correspond to a lower redox potential, which is actually the case. However, correlating the potential with only ν as (COO -) would imply a much lower potential than was actually measured, additionally supporting the idea that the carboxylate group has a different impact on the redox of Li 4 -p-DOBDA as compared to Jouhara's work. [START_REF] Jouhara | Raising the Redox Potential in Carboxyphenolate-Based Positive Organic Materials via Cation Substitution[END_REF] Furthermore, the vibration frequency of the enolate bond in dissolved Li 4 -p-DOBDA has a value of 1208 cm -1 , which would correspond to a redox potential of approximately 2.7 V vs Li + /Li 0 , following the linear regression presented in Figure 2B. Measuring the redox potential of dissolved Li 4 -p-DOBDA vs Li + /Li 0 is experimentally complicated and may be prone to additional errors and redox potential shift due to differences in ionic strengths and ion solvation structures between aqueous and aprotic solution required. [START_REF] Ernould | Negative Redox Potential Shift in Fire-Retardant Electrolytes and Consequences for High-Energy Hybrid Batteries[END_REF] However, it is possible to estimate its value from the data shown in Figure 1. Since a redox potential difference of approximately 100 mV exists between the standard quinone (Q 2-) and p-DOBDA 4-in aqueous solution, and Q 2-has a potential of 2.8 V vs Li + /Li 0 , the redox of dissolved Li 4 -p-DOBDA should indeed evolve around 2.7 V vs Li + /Li 0 . This further supports the validity of the linear correlation analysis (Figure 2B) and that the strength of the enolate bond is a more generalized approach to understand and predict the redox potential in quinone derivative battery materials.

Crystal Structure, Molecular Conformation, and

Correlation with the Redox Potential. In terms of donor inductive effects (+I), the acetate groups in Li 4 -p-DOBDA should have an influence on the electronic density of the aromatic cycle similar to that of the carboxylate groups in Li 4p-DHT (Scheme 1). If these were to be considered as dominantly affecting the redox potentials of both chemistries, then it would be reasonable to expect comparable values. This approximation is however significantly distant from the reality of our experimental observations (Figure 1B), which led us to investigate another possible influence factor: the through-space E between the -CH 2 -COO -bond and the plane formed by the benzene ring (blue double arrow).

The significant +650 mV redox potential difference detected in the solid phase as compared to measurements in solution can thus be understood by major molecular conformation differences, translated into electronic charge perturbation, between the carboxylate and phenolate groups in the solid and dissolved phases. To verify this hypothesis, additional DFT calculations were carried out to predict the conformation as well as atom charge distribution in p-DODBA 4-in both solid and dissolved phases. On the basis of DFT calculations, p- In the solid phase, the lower dihedral angleand thus the proximity between the ortho-phenolate and carboxylate groupsis the consequence of the local tetrahedral oxygen coordination environment (LiO 4 ) of the lithium cations (Figure 3, and SI Section S2). Metal induced conformational change in ligands is a known process, especially significant in biological systems. For small ligand molecules, along with the effect of metal on electronic configuration, conformation changes are also possible, unless for ligand molecules that are so rigid that coordination cannot promote a conformational change. The acetate groups in DOBDA 4-allow for structural flexibility so that the system displays stereoelectronic chameleonic behavior dependent on the countercation.

The redox potentials of the solid and dissolved p-DOBDA 4- (averaged) molecular conformations were also computed using the SIESTA and GAMESS software for solid state and solvent model calculations, respectively. [START_REF] Soler | The SIESTA Method for Ab Initio Order-N Materials Simulation[END_REF][START_REF] Schmidt | General Atomic and Molecular Electronic Structure System[END_REF] The solvent effects were taken into account using the density polarized continuum model. [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF] Total energies for each of the oxidation states in the solvent were computed for the relaxed structures using the Minessota M11 exchange-correlation functional [START_REF] Peverati | Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation[END_REF] The results are presented in Table 1 and the full calculation details and methods are presented in SI Section S3. Computed and experimental redox potential values for solid p-DOBDA 4- are in good accordance, whereas larger differences are observed for computed redox potentials in solution (i.e., around 0.35 V).

These are assigned to errors arising from the solvation energy as well as solvent reorganization effects, since a relatively important change in the geometric structure occurs between the p-DOBDA 4-and p-DOBDA 2-. Indeed, the dihedral angle α formed by the -CH 2 -COO -bond with the benzene ring To grasp further insight into the structure-property 533 correlation of solid and solvated phases of p-DOBDA 4-, t2 534 Bader charge analysis [START_REF] Tang | A Grid-Based Bader Analysis Algorithm without Lattice Bias[END_REF] was carried out (Table 2, SI Section 535 S3.5). While the charge distribution is minimally affected for 536 the aromatic C2, C3, and aliphatic C4 atoms (see the notations 537 for carbons in the graphic associated with Table 2), the charge 538 differences between oxygen and carbon atoms in the 539 carboxylate (O2, O3, C5) and enol (O1, C1) groups are 540 significantly higher in solid phase as compared to aqueous 541 solution. The dipole charges (C1-O1, C5-O2/3 DC) are 542 estimated to be larger in the respective carboxylate and enol 543 groups in the solid p-DOBDA 4-, leading to stronger bonding 544 and thus higher vibration energy. This closely correlates with 545 the FTIR analysis presented in Figure 2 (higher vibration 546 frequency-wavenumbers for the respective bonds for solid 547 when compared to dissolved p-DOBDA 4-) and confirms the higher redox potential displayed by Li 4 -p-DOBDA in its solid crystalline form.

Combining these analyses, we can ascribe the increase of the redox potential in the solid phase to a pronounced throughspace charge modulation arising between the carboxylate (COO -) and enol (CO -) groups. In solution, the molecule adopts a relaxed conformation in which the carboxylate groups are far afield from the adjacent enolate groups, resulting in a reduced interaction and higher charge density. In this case, the redox potential can solely be rationalized by the through-bond electronic effects (Scheme 1) with the measured and computed formal redox potential values being indeed lower than those of the parent quinone system (Figure 1A). The From the FTIR spectra, it can be concluded that no oxidation occurs upon exposure to air, since no additional carbonyl band (corresponding to the quinone) is observed (Figure 4A). There is also no hydrolysis of the phenolate or acetate groups. The band at 1220 cm -1 is preserved and no phenolic O-H vibration band (3400 cm -1 ) or characteristic For the Q 0 /Q 2-couple, the redox potential was not possible to compute in solid phase since the crystal structure of Li 2 Q is not available. reduced over the subsequent cycles with good capacity retention (Figure 5B).

The dynamic molecular conformation of the p-DOBDA 4- skeleton (Figure 3) prompted us further to investigate the structural reversibility of the redox process in the solid phase. The tetrahedral LiO 4 coordination is imposing significant strain on p-DOBDA 4-skeleton in solid, resulting in unexpected molecular conformation (Figure 3B). Upon oxidation, with two lithium atoms (as well as the two negative charges from the phenolate groups) removed, it is reasonable to assume that Li 2 -p-DOBDA will adopt a different conformation, also with modified crystal packing. The quality of the in situ XRD patterns did not allow us to unambiguously refine the structure of the oxidized phase. However, the DFT calculations confirm drastic conformational changes upon oxidation in solution and in vacuum (refer to SI Section S3.4

for details) and alike process can be also considered to take place in the solid phase. This would imply possible subtle H gliding or rotation of the phenyl/acetate groups, resulting in turn in possible particle shape and volume changes, grinding and ultimately electrode degradation. This conformation changes in the solid phase could also explain the slow kinetics (or experimentally observed high polarization) of the solidphase Li 4 -p-DOBDA electrodes.

In terms of specific gravimetric capacity and energy metrics, Li 4 -p-DOBDA is already on par with LiFePO 4 and LiCoO 2 and is expected to outperform these once the energy efficiency and degradation issues are fixed. The slow kinetics and polarization can be assigned to various parameters, typical of organic battery materials, and including charge and mass transport, molecular orbital, as well as conformation reorganization. The estimated electrical conductivity of Li 4 -p-DOBDA is of the order of 10 -12 to 10 -13 S/cm. No significant ionic conductivity was measured in macroscale pellet-form samples even at 70 °C. Combining these with the significant structural and conformational changes, the rather elevated electrode polarization and slow kinetics of the Li 4 -p-DOBDA electrodes are not surprising.

Further improvements required to render this chemistry practically appealing could thus focus on electrode and active material morphology optimization to achieve better reversibility and cycling stability. Nanostructuration with conductive carbon allotropes 18 or other 2D materials could be viable solutions to explore. In terms of chemical stability, further investigation of the intrinsic stability of the oxidized phase (Li 2 -p-DOBDA) is needed, and oxidative decarboxylation at the high operation voltage required for this chemistry is an additional factor not to be excluded. 67 High voltage organic redox chemistries, close to and above 4 V, remain hitherto unexplored, and high energy advantages arise with yet to be investigated intrinsic stability toward decarboxylation, as well as the nature and reactivity toward products of electrolyte anodic decomposition.

■ CONCLUSIONS

With this work we disclose a new member in the very young, yet highly promising family of quinone-based organic Li-ion positive electrode materials. The high capacityfrom the reversible two electron exchange, combined with the high redox potential of Li 4 -p-DOBDAis the result of an exotic intramolecular charge modulation, providing in an impressive theoretical gravimetric energy density in the 700 Wh/kg range, placing this new organic chemistry above all other lithiated organic LIB positive electrode materials. Moreover, Li 4 -p-DOBDA can be synthesized and handled in ambient air without impact on either its molecular and structural nature or on its electrochemical behavior, meaning this robust material can be processed in conditions similar to conventional inorganic LIB compounds. Further developments should focus on cycling stability and energy efficiency optimization to allow this chemistry to practically compete with typical inorganic materials such as LiCoO 2 (LCO, 600 Wh/kg) or LiFePO 4 (LFP, 550 Wh/kg).

■ ASSOCIATED CONTENT

* sı Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.0c02989.

  Scheme 1. Modulation of the Redox Potential in Quinone Derivatives a

224

  Lakraychi et al. were the first to report on the tetralithium salt 225 of 2,5-dihydroxy-1,4-benzenedisulfonic acid (Li 4 -p-DHBDS), 226 with a redox potential of ∼3.25 V vs Li + /Li 0 , making it 227 processable under dry air conditions (the materials however

  228

  spectator cation (M n+ ). Impressively, 234 substituting lithium for magnesium in Li 4 -p-DHT, to yield 235 Mg(Li 2 )-p-DHT, led to a voltage gain of nearly +800 mV, 236 raising the redox potential up to 3.4 V vs Li + /Li 0 . 237 Taking a global look at these different investiga-238 tions, 2,15,45-49 the possible approaches to tune the redox 239 potential can be broadly resumed to one fundamental rationale 240 (Scheme 1): the through-bond electronic effect, with either 241 increase or decrease in the charge density, resulting in redox 242 potential decrease or increase, respectively. The strength of 243 these effects correlates with the redox potential and effectively 244 explains the redox potential values of many studied materials 245 and those under development. 3,46,49,50 However, adding 246 substituents always compromises the specific capacity given 247 the increase in the molecular weight. 248 Alternatively, there are few reports on exotic effects, which 249 have proven effective in increasing the redox potential of 250 organic materials with limited impact on the capacity. For 251 example, Banda et al. have exploited steric hindrance in 252 perylene diimide derivatives and found that molecular 253 distortion can lead to increased redox potential as compared 254 to a planar equivalent. 51 In the same category, the investigation 255 of Li 4 -o/p-DHT, where the carbonyls switch from the para to 256 ortho position, also resulted in an increased potential. 52 257 Through our explorations of high voltage n-type organic 258 materials, we found that Li 4 -p-DOBDA is another example of 259 organic battery material with unusually elevated redox 260 potential due to an exotic effectnamely, the through-space 261 intramolecular electronic charge modulation. Whereas a similar 262 effect could also explain the para to ortho (Li 4 -o-DHT, as well 263 as in catechol vs quinone) increased redox potential, in Li 4 -p-264 DOBDA this effect is found to be unexpectedly amplified, 265 leading to a 650 mV increase in potential as compared to 266 traditional (through bond) rationalized values. C The Curious Case of Li 4 -p-DOBDA Electrochemical 268 Response. The striking point that triggered our interest for 269 extensive analysis of Li 4 -p-DOBDA was the major discrepancy 270 between the electrochemical responses in aqueous solution as f1 271 compared to the solid phase (Figure

Figure 1 .

 1 Figure 1. (A) Typical cyclic voltammetry curves of Q 2-and p-DOBDA 4-measured in aqueous solutions (pH 13.4). The pH of all solutions was adjusted with NaOH 0.1 M, in addition to the 0.5 M KCl electrolyte carrier salt. A glassy carbon working electrode was used, and a scan rate of 5 mV/s was applied. (B) Potential-composition profiles at the first galvanostatic charge-discharge cycle of Li 4 -p-DHT, Li 2 Q and Li 4 -p-DOBDA measured in a lithium half-cell with a nonaqueous electrolyte [cycling rate: 1 electron (1 Li + ) per equivalent exchanged in 5 h].

Figure 2 .

 2 Figure 2. (A) Overlaid FTIR spectra of selected quinone derivatives in their respective reduced state. The IR spectra are displayed from bottom to top in the order of increased redox potential. The _aq and _cr subscripts for Li 4 -p-DOBDA are used to indicate the dissolved and solid crystalline forms used for measurement, respectively. Insert to the right: close up on the enolate vibration band ν(C-O -Li + ). The ν(C-O -) vibration band is identified by comparison of the lithiated and protonated form for each compound. The evolution of the enolate (C-O -) vibration band is highlighted by the red dotted line and the band shift between Li 4 -p-DOBDA_cr and Li 4 -p-DOBDA_aq is highlighted by the blue arrow. (B) Modeling of the correlation through linear regression.

DOBDA 4 -

 4 adopts on average a different configuration in vacuum, or in aqueous solvated phase, than in the solid state (Figure 3B, and SI Section S3). The larger dihedral angle (111.3°) formed in average by CH 2 -COO -with the benzene ring can be related to steric and electrostatic repulsions between enolate and carboxylate groups, allowed by free rotation in the solvated or gas phase. An additional interesting feature is the asymmetry of C-O bonds in the carboxylate functional groups. While in the solid state a clear distinction between the two oxygen occurs (i.e., a difference about 0.05 Å between the bonds), in vacuum or in solution the effect is completely removed, the two C-O bonds being of same length (refer to SI Section S3.4 for more details). It is also interesting to note that a similar conformation (with a low dihedral angle) is also observed for the parent protonated version, H 4 -p-DOBDA, with the Hbonding being at the origin of the peculiar molecular conformation (SI Section S4).

  and the 6-31G** Pople basis set. For the solid state calculations, the vdW-DF-cx exchange-correlation functional of Berland and Hyldgaard 61 and a double-ζ polarization basis set was used.

  t1

Figure 3 .

 3 Figure 3. (A) Rietveld refinement of the PXRD pattern of Li 4 -p-DOBDA. The red circles correspond to the experimental data, whereas black, blue, and gray lines respectively correspond to the simulated, difference, and background patterns. Inset: crystal structure view along b-axis with a representation of the tetrahedral oxygen environment of the lithium cations. (B) Molecular conformation of p-DOBDA in the solid phase (as determined from PXRD data) and aqueous solution (as determined from DFT calculations). Views along the CH 2 -C AR and perpendicular to the AR-ring.

  532

  constrained molecular conformation in the solid state leads to a hitherto undocumented type of intramolecular charge perturbation and redox potential gain of +650 mV, when switching from liquid to solid phase. Air-Stability of Li 4 -p-DOBDA. Air-stability of the positive electrode materials is a key requirement in battery materials handling, storage and cell manufacture. 63,64 Therefore, beyond the Li-reservoir characteristic, air-stability is an additional important parameter to be considered for Li-ion positive electrode materials. The fact that Li 4 -p-DOBDA undergoes redox in the solid phase at a potential above 2.91 V vs Li + /Li 0 already indicates that this chemistry should be resistant to oxidation in air, but not necessarily to moisture, as previously observed with Li 4 -p-DHBDS 48 (i.e., air exposure of Li 4 -p-DHBDS lead to poor electrochemical performances). In order to investigate the air-stability, Li 4 -p-DOBDA powders was exposed to ambient air for a week, and a comparative FTIR and PXRD analysis was carried out. Remarkably, as displayed f4 in Figure 4, both analyses yielded identical features as compared to the pristine material.

Figure 4 .

 4 Figure 4. FTIR (A) and PXRD (B) survey of the as synthesized Li 4 -p-DOBDA and after being exposed to ambient air for 1 week. No changes can be detected.

Figure

  Figure 5C displays the in situ PXRD data for the first two cycles (rate of 1Li + exchanged in 15 h). Upon Li extraction the XRD pattern of the Li 4 -p-DOBDA electrode is strongly modified, with the progressive disappearance of the intense Bragg peaks near 2θ (Cu Kα) = 19.5°, 21.5°, and 24.6°, accompanying the appearance of new intense peaks at 2θ = 18.5°and 24.0°. The Li 4 -p-DOBDA undergoes a biphasic twoelectron process with no intermediate semiquinone phase being detected (possibly because the respective radicals are short-lived), corroborating the direct two-electron mechanism as also observed in the galvanostatic charge-discharge profile (only one plateau).To should be noted that this process is unusual for quinone derivatives, most of which display sequential charge transfer (one-by-one electron) in the solid state or in aprotic environment.17,[START_REF] Sieuw | A H-Bond Stabilized Quinone Electrode Material for Li-Organic Batteries: The Strength of Weak Bonds[END_REF]45,[START_REF] Shimizu | Nitrogen-Containing Polycyclic Quinones as Cathode Materials for Lithiumion Batteries with Increased Voltage[END_REF][START_REF] Stinner | Effect of Ambient Storage 998 on the Degradation of Ni-Rich Positive Electrode Materials 999 (NMC811) for Li-Ion Batteries[END_REF][START_REF] Quan | Voltammetry of Quinones in Unbuffered Aqueous Solution: 1003 Reassessing the Roles of Proton Transfer and Hydrogen Bonding in 1004 the Aqueous Electrochemistry of Quinones[END_REF] Upon discharge, the phase transition proved to be perfectly reversible, proceeding again through a direct two-electron, biphasic process. The collection of XRD patterns during the second cycle show the occurrence of the same phases and transitions, which indicate that the molecular conformation along with the crystal structure are preserved with cycling. In other words, the electrochemical pathway observed during the first cycle is completely reversible and maintained during the second cycle even though the oxidation profile is being slightly modified.

Figure 5 .

 5 Figure 5. (A) Overlaid potential-composition profiles for Li 4 -p-DOBDA and LiFePO 4 (binder-free) electrodes galvanostatically cycled in lithium half-cell configuration, with LP30 electrolyte, at a Li + insertion/extraction rate of 1 Li + /5 h (C/10). (B) Cycling stability of Li 4 -p-DOBDA electrodes with LP30 electrolyte and at a Li + insertion/extraction rate of 1 Li + /4 h (C/8). (C) In situ PXRD data collected during the first two cycles. LP30 used as electrolyte, at a Li + insertion/extraction rate of 1 Li + /15 h (C/30).

  Institute of Condensed Matter and 734 Nanosciences, Université Catholique de Louvain, 1348 735 Louvain-la-Neuve, Belgium; orcid.org/0000-0002-0059-736 9119; Email: alexandru.vlad@uclouvain.be

Table 1 .

 1 Computed Equilibrium Redox Potentials of Quinone and p-DOBDA 4-Redox Couples in the Solid State and Water Solvated Phases a redox potential (V vs Li + /Li 0 )

	redox couple	dissolved	solid
	Q 0 /Q 2-	2.69	a
	p-DOBDA 2-/p-DOBDA 4-	2.33	3.45
	a

Table 2 .

 2 Bader Charges Analysis, N 0 -N, with N 0 being the Number of Electrons in the Isolated Atom, N is the Bader Population of the Atom in Molecule a

		solution (_aq)	solid (_cr)
	O1	-1.34	-1.78
	O2/O3	-1.34/-1.34	-1.79/-1.82
	C1	0.7	1.22
	C2	-0.13	-0.03
	C3	-0.05	0.03
	C4	0.0	0.04
	C5	1.66	2.80
	C1-O1 DC	2.04	3.00
	C5-O2/3DC	3.00	4.60

a DC is the dipole charge. Top scheme, atom labeling.

(2)


Nicolas Huchet
email: huchet@univ-tln.fr

Bénédicte Serbini
email: benedicte.serbini@univ-savoie.fr

Public finance, banking sector and sovereign bond risk premiums in the Eurozone

Keywords: JEL Classifications: F34, G12, E43, E62 Interest rate premium, Public investment, Primary Balance, Sovereign debt, Bank credit risk, Liquidity

Based on a panel of Member States of the Eurozone between 2008 and 2013, we focus on the effect of both public expenditure and banking on ten-year sovereign spreads. By using fixedeffects' estimations and cluster-robust standard errors with a monthly frequency, we highlight that investors kept on scrutinizing fundamentals about debt sustainability during the sovereign debt crisis, despite the importance of risk aversion. In addition to budgetary balance and debt, distances to the stabilizing primary balance and public investment indicate that markets are sensitive to specific items of public expenditures and not only their level, which put the interest of austerity measures into proportion. Then, our findings support the hypothesis of a risk transfer between private and public sectors, which legitimates long-term refinancing operations by the central bank and put the emphasis on the need to go further as regards European integration, especially the single resolution mechanism.

I. Introduction

The markets for public debt establish the cost of debt and so the price of government bonds.

Following standard theory, asset prices reflect all available information and depend on monetary drivers (including official interest rates and future inflation) and counterparty risk premium. Borrowing rates also include a liquidity premium linked to trade volumes on secondary markets. However, in case of crisis, assets prices may be disconnected from fundamentals. If so, risk aversion and uncertainty become main drivers of sovereign spreads.

So the question we answer is the remaining role of public expenditure and interbank troubles for long-term interest rates during the sovereign debt crisis.

Even though a common monetary policy offers the advantage of ignoring exchange rates matters, the European debt crisis is an interesting topic for empirical research mainly because it may result in the death of redistributive models, or by contrast it may only mean that markets need credible and reassuring information about consistency between public finance management and chosen growth models. The question is all the more important that Member States at the same time reduce (and streamline) debt and deficit ratios and implement measures aimed at enhancing economic growth.

From late 2008 and especially 2010, long-term interest rate premiums (relative to German benchmark bonds) increase, sometimes dramatically. We explain it from 2008 to 2013 for ten Member States of the Eurozone, by taking into account both banking sector and public finance features. Section II depicts related literature and usual findings. Section III presents monthly data and estimation methods. Section IV highlights interesting results: first, investors are sensitive to the composition of public finance in times of crisis, by considering the distance to the stabilizing primary balance, public investment, government balance and (squared) debt, so that resources reallocations are as important as debt levels. Second, liquidity providing to banks reduces bond market stress but bank credit risk remains negatively related to sovereign spreads, which supports the hypothesis of a risk transfer.

Indeed, the central bank may reduce risk aversion but resolving solvency troubles is necessary to restore confidence, hence the need to go further as regards the single resolution mechanism. Section V concludes.

II. Related Literature

Debt sustainability is achieved when government finance is not supposed to be drastically adjusted in the near future. So two issues at least derive from the inter-temporal budget constraint: short-term refinancing (liquidity) and long-term repayment ability (solvency), which in turn define the duration of sovereign debt [START_REF] Hatchondo | Sudden stops, Time inconsistency, and the Duration of Sovereign Debt[END_REF].

Regardless the reason, a rise in debt burden that is superior to the rise in GDP implies a decrease in primary balance as there is a ceiling for public deficit (i.e. 3 per cent in the Eurozone), hence a lower deal of control in public spending. That is why the later structural fiscal adjustments3 are, the more painful they get. Fiscal consolidation is thus necessary, but at the same time austerity measures may have a severe impact in terms of unemployment, especially if fiscal multiplier is underestimated [START_REF] Blanchard | Growth forecast errors and fiscal multipliers[END_REF]. That is also why it is important to better understand determinants of long-term bond risk premiums, assuming that they bear no more relation to the fundamentals if confidence is lost.

Many indicators aim at stabilize debt-to-GDP ratio, usually through primary balance and tax rate [START_REF] Blanchard | Suggestions for a new set of fiscal indicators[END_REF]. That is why [START_REF] Borgy | Fiscal sustainability, default risk and Euro area sovereign bond spreads markets[END_REF] use expected changes in debt-to-GDP ratios for each country in order to assess fiscal sustainability and then sovereign bond yields.

On the basis of projections of public debt ratios including age-related spending, [START_REF] Cecchetti | The Future of public debt: Prospects and Implications[END_REF] find that "the path pursued by fiscal authorities in a number of industrial countries is unsustainable" and advocate drastic measures both to support monetary stability and longterm growth. Indeed demographic ageing put additional pressure on public finances in many countries, as shown by [START_REF] Rother | Challenges for the EU fiscal framework: Fiscal sustainability, Government debt and monetary Policy[END_REF]. [START_REF] Barrios | Determinants of intra-euro government bond spreads during the financial crisis[END_REF] and [START_REF] Manganelli | What drives spreads in the Euro Area Government Bond Market?[END_REF] explain that the high degree of risk aversion in the Eurozone also appears as a key factor of bond yield spreads. A refinement is yet necessary because the lack of confidence can be interpreted as a cause of the crisis and at the same time as a result. The work carried out by [START_REF] Attinasi | What explains the surge in euro area sovereign spreads during the financial crisis of 2007-09?[END_REF] is thus helpful, by including dummies related to support measures to the banking sector. The model's ability to forecast is successful, but the study ends in 2009 and cannot encompass recent developments in the European debt crisis. Over a longer period of time, [START_REF] Seremetis | Government bond yield spreads determination: a matter of fundamentals or market overreaction? Evidence from over-borrowed European countries[END_REF] point that the counterparty risk associated to each country is similar in good times, but huge differences appear in bad times as individual macroeconomic fundamentals become closely scrutinized by investors. Still over a long period, [START_REF] Gerlach | Banking and sovereign risk in the Euro area[END_REF] show that an aggregate risk factor is a main driver of spreads. In case of increase, the level of equity ratios and the size of the banking sector also play a major role in widening yields spreads, as financial markets expect for bank bailouts.

According to [START_REF] Assman | Determinants of government bond spreads in the Euro area: in good times as in bad[END_REF] and [START_REF] Bernoth | Sovereign bond yield spreads: A time-varying coefficient approach[END_REF], such a (long) study period reveals the need of time-varying coefficient models. So face to heterogeneous results in the literature (except for global environment), [START_REF] Maltritz | Determinants of sovereign yield spreads in the Eurozone: A Bayesian approach[END_REF] applies Bayesian Model Averaging to annual panel data over the period 1999-2009, and highlight the role of fiscal variables (budget balance and government debt).

Despite risk and liquidity premium, [START_REF] Dötz | What can EMU countries' sovereign bond spreads tell us about market perceptions of default probabilities during the recent financial crisis?[END_REF] find that the third component of spreads, namely the expected loss component, rises during the recent financial crisis, such as sovereign spreads rise too. [START_REF] Alexopoulou | Determinants of Government bond spreads in new EU countries[END_REF] use a dynamic panel error correction model for new EU countries over the period 2001-2008 and highlight the role of fundamentals for the assessment of creditworthiness (by including exchange rates or even trade openness). Domestic fundamentals but also swings in market perception of sovereign risks are more relevant when countries are characterised by large external imbalances and historically high levels of spreads. [START_REF] Sgherri | Euro area sovereign risk during the crisis[END_REF] show that sovereign risk premium differentials tend to co-move over time as they are mainly driven by global risk; however, markets are more and more concerned about specific criteria for countries in the Euro area, including liquidity risk.

The aim of this paper is to provide a similar analysis over the period 2008 to 2013, by focusing on banks' involvement and public finance on a monthly basis. Indeed both are supposed to affect sovereign bond yields and bond risk premiums. In particular, we compute for each country the distance to the stabilizing primary balance as the level of budget balance for which debt-to-GDP ratio is constant over time. In order to take into account the role of public spending for sovereign spreads, we also estimate the share of public investment in government spending. Indeed the relative shares of investment expenditure and operating costs may be taken into account by investors during any tender, because it tends to matter for future economic growth. We also use monetary and banking data to assess the relationship between banking sector and sovereign spreads.

III. Data and Methodology

A. Data

After the financial crisis triggered in 2007 and mostly 2008, economic theory predicts a flight to quality, usually in favour of public claims. At the same time, sovereign bonds are no more considered as risk-free assets [START_REF] Schuknecht | Government bond risk premiums in the EU revisited: The impact of the financial crisis[END_REF], what may be consistent with market sanction (bail-in) and accountability of Member States. Up to the end of 2009, sovereign spreads increase in the same proportions for all countries and then come back to a low level: the investors are more risk adverse but they still do not operate huge discrimination among countries. Then, Greece is the first country really concerned by the debt crisis in December 2009, as soon as its budget deficit is updated, and sovereign bond risk premiums sharply increase in the Euro area, especially for Greece, Portugal and Ireland (Table 1). Spanish and Italian premiums move in the same direction, and then this trend is reversed between July 2011 (Ireland) and July 2012 (Greece), though Greek troubles last until summer 2015, and probably more.

Insert Table 1 here

From 2010 to 2012, Greece, Portugal and Ireland accessed International Monetary Fund, European Union (EU) and European Central Bank (ECB) resources. Premiums react strongly when Greece asks for a financial rescue, and after first debates about ways to restructure Greek sovereign debt in July 2011 (Figure 1). Then the decrease in spreads is not coordinated and they remain at a higher level in 2013 than at the beginning of period.

Insert Figure 1 here So, the dependent variable is the monthly spread between national and German long-term interest rates. The sample consists of the first countries that adopt the euro on 1st January 1999 (except Luxembourg4 ): Germany, Austria, Belgium, Spain, Finland, France, Greece (2001), Ireland, Italy, the Netherlands and Portugal. As indicated in the summary table of variables (Annex 1), each (monthly) explicative variable is defined in difference against Germany, the referent country, from January 2008 to December 2013. Indeed, although there is no sign of a debt crisis until 2009, the year 2008 presents a major financial crisis that weakens banks and may play an important role in determining government spreads.

Firstly, depending on the risk profile of each country, a credit risk premium is required. To measure counterparty risk, we use public debt (debt) and budgetary balance (bal). We also calculate the balance that stabilizes debt, in other words the proceeds of previous gross public debt and current growth rate of Gross domestic product. By subtracting the interest burden from this stabilizing balance (i.e. the difference between budgetary and primary balances), we obtain the stabilizing primary balance. Then, the (widespread) gap to the stabilizing balance (denoted effort) is obtained by difference between theoretical and observed balances, i.e. the difference between the stabilizing primary balance and the current primary balance. Another interest variable complements the evaluation of counterparty risk, since we recover (on a quarterly basis) the share of public investment in public spending (gfcf).

Banking variables are also part of sovereign risk in the literature. In case of a decline in the value of public securities, the value of banks' balance sheets declines too, due to financial reporting standards. In this case, a credit crunch lowers growth, hence a negative feedback effect on future tax revenues and a self-sustaining spiral of higher long-term interest rates. In the extreme case, financial losses reduce levels of capital positions and a recapitalisation scheme reinforces public over-indebtedness 5 . We take into account recapitalization and guarantee schemes over the studied period through a binary variable (recap). We also use time series through the spread between EURIBOR and EUREPO three-month interest rates (borrepo). The maturity is the same but the risk is different because REPO markets are collateralized, so that the variable borrepo indicates banking credit risk. On the opposite, we have not included the yield curve of money markets (i.e. the difference between three-month and one-month or one-day interest rate on unsecured markets) because of excessive correlation with other control or interest variables that could bias our findings.

Secondly, as regards monetary factors, we take into account liquidity provision by the ECB.

As unconventional monetary policy is implemented over the period, main refinancing operations are excluded from dataset in order to take into account long-term refinancing operations. Moreover, assets purchase must be considered as an important part of liquidity providing, so that the best indicator of the monetary policy stance seems to be the excess liquidity (excliq) in the Eurozone. Because of the specific Inflation-targeting framework (given by the 2% threshold), the break-even inflation rate (bir) 6 may also inform about the anticipation of a monetary policy tightening or easing. The variable is associated with an ambiguous expected sign as a lower anticipation of inflation may increase spreads, by indicating a recessive scenario or a liquidity trap, but it also may decrease spreads, by implying a lower inflation premium in long-term interest rates or by reassuring market's participants as regards further monetary policy easing.

Sovereign credit risk, banking and monetary data constitute interest variables of estimations, which are then completed by control variables. So, another component of the determination of central bank has reached the "zero lower bound": a possible rise in official interest rates would also reduce the value of securities on secondary markets, notably in banks' balance sheets. 6 The break-even inflation rate corresponds to the spread between nominal and inflation-linked bonds. It represents an indicator of inflation expectations as it reflects the overall inflation compensation requested to hold nominal bonds (the spread includes both the expected level of inflation and a premium to compensate for inflation risks).

spreads is the bond liquidity risk. We calculate a liquidity premium (liq) for each country characterized by a higher borrowing cost than Germany. We do not retain the bid-ask spread, neither the amount of issuances, but we prefer the share of outstanding (fixed-rate denominated) long-term securities issued by each central government, within total outstanding at the end of the month for the whole sample, as do Bernoth et al. (2012). More specifically, we use data on gross public debt, which include the first bilateral loan to Greece (May 2010) and then financial assistance from the European financial stability fund (EFSF)7 to supported countries.

Next, global risk is an important component in works focused on sovereign spreads. As for D'Agostino and Ehrmann (2013), it is measured through the yield differential between BAA and AAA American corporate bonds (spreadba). Indeed, contrary to [START_REF] Haugh | What drives sovereign risk premiums? An analysis of recent evidence from the Euro area, OECD Working Paper[END_REF] we do not retain the yield spread between high rated short-term securities issued by the nonfinancial sector and securities with worse signature, which also comes from the Fed, because it is more interesting to take into account foreign financial sector ratings. Alternatively, and as in the literature, we also use the S&P 500 (sp500) index to control the international environment.

As indicators of risk aversion, we do not use the implied volatility given by Vstoxx or VIX indexes, as both are based on equity markets (and excessively correlated with many other variables). Futures contracts listed on the Chicago Board of Trade measures the implied volatility of bond markets, but do not give any significant result compared to the implied volatility of the Eurozone bond market (eurex), which is therefore used to control risk aversion. In the same way, because of the features of the debt crisis, a binary variable (break) is introduced in order to consider the breakdown from which sovereign spreads' dynamics changes.

B. Methodology

X1 represents the liquidity risk, X2 the sovereign risk, X3 the global risk and the economic environment, X4 the risk aversion, X5 monetary variables and X6 is a breakdown. We estimate the following equation:

!"#$%& !,# = ( ! + * $ (, $ ) !,# + * % (, % ) !,# + * & (, & ) !,# + * ' (, ' ) !,# + * ( (, ( ) !,# + * ) (, ) ) !,# (1)
Our sample confirms a partly heterogeneous specification, as intra-individual variability ("within") is superior to inter-individual variability ("between"), and as the number of periods exceeds the number of observations. A Breusch-Pagan test rejects OLS method, and statistical properties of data do not imply random-effects estimations, so our coefficients are unbiased when using a fixed-effect model, which takes into account the features of the countries in the sample. 8 The equation is estimated with a monthly frequency9 from January 2008 to December 2013. Besides common variables, each country-specific variable is defined in difference against Germany, and stationary transformations (growth rates) of all variables (except break) are implemented in order to avoid spurious regressions. As modified Wald tests reveal heteroscedasticity, all specifications of the equation are estimated by robust standard errors. Moreover, each estimate successfully passes the Wooldridge test, which systematically implies the absence of first order autocorrelation.

With a fixed effects model, the standard errors are only adjusted for clustering at the level of country (in our case, standard errors are adjusted for 10 clusters by country). But with panel data, the residuals may be correlated both for countries and time [START_REF] Peterson | Estimating standard errors in finance panel data sets: comparing approaches[END_REF][START_REF] Thompson | Simple formulas for standard errors that cluster by both firm and time[END_REF]. Thus, it is useful to conduct additional regressions with double clustered standard errors (by country and by month). Finally, as Greece is excluded from financial markets from May 2010, we implement regressions for the full sample (10 countries) but also for all countries without Greece (9 countries).

IV. Results

A. Baseline model

Initially we do not retain the qualitative aspect of public finances or the banking sector: the purpose is to define the baseline model and to select the better indicator of monetary conditions (Table 2), either inflation concerns (bir) or financial stability issues (excliq).

Not surprisingly, liquidity risk (liq) measured by the share of outstanding amounts of longterm government securities slightly affects sovereign spreads. International conditions (measured by the spread between different classes of corporate bonds, by including the financial sector: spreadba) are strongly and positively associated with European government spreads, by using fixed effects models but also double clustered standard errors, and with or without including Greece in the sample. A usual indicator of the international environment such as the S&P 500 index (sp500) gives the same result, but is not presented because of excessive correlation together with interest variables (Annex 2) such as interbank spreads (borrepo) and the breakeven inflation rate (bir).

Risk aversion is measured by the implied bond volatility of the Eurozone (eurex), and highlights a statistically significant positive relationship with the dependent variable, as expected. Other indexes based on equity markets, such as the VIX index and the Vstoxx index, are less interesting as regards the need to highlight the functioning of bond markets.

Moreover, the VIW index would be excessively correlated with other variables such as borrepo and spreadba. Additional tests show that the implied volatility of U.S. bond markets (i.e. given by futures contracts listed on the Chicago Board of Trade) is not significant, which confirms the European specificity of the crisis (besides the role for international environment)

and the interest to focus on Eurex indexes to assess the changes in risk aversion. Again, this finding is robust, as it appears whatever the method is (even when removing Greece from the sample).

We pay particular attention to monetary conditions as interest variables. The monetary policy stance is introduced through the breakeven inflation rate of the Eurozone (bir): sovereign spreads decrease when this variable rises, but the relationship only appears when using fixed effects method. Such a result is in line with the literature, as expectations of further increases in consumer prices mean that growth is also likely to increase in the next future, hence a decrease in sovereign spreads. However, unconventional monetary policies are implemented over the studied period and the liquidity provision by the ECB includes both higher refinancing operations (longer term and larger amounts) and assets buyouts. In this context, the excess liquidity (excliq) given by the ECB is chosen for next estimations: excess reserves of credit institutions are systematically significant with the expected sign. In a context of debt deleveraging, liquidity provision is officially used to rescue banks but also directly reduces strains on sovereign bond markets, giving that the ECB is not allowed to directly help Member States and that banks are important players on debt markets (including collaterals faced to credit lines). Finally, a "breakdown" is implemented for each country over the period from May 2010 to December 2011. So, whatever the country risk profile is, investors considerably differentiate the studied countries from May 2010. Despite the aid plan for Greece, this date also corresponds to the massive European recovery plan, with the implementation of the EFSF, and to an important asset-purchase program from the ECB (as in December 2011, with a massive liquidity provision towards banks for an extended period of time of three years).

B. Composition of public finance and banking sector

A new set of tests allows introducing qualitative features of public finances and interbank troubles, still by using both fixed effects and double clustered standard errors (Table 3).

Insert Table 3 here

As regards banking, the three-month Euribor-Eurepo spread (borrepo) represents bank credit risks as Repo markets are secured by guarantees. We could have expected for a positive sign, as disturbance on interbank markets indicates strains and then unwillingness or unability to lend, hence the absence of recovery. On the opposite, the (systematically) negative sign supports the hypothesis of a risk transfer from banks to public sector, as shown by [START_REF] Attinasi | What explains the surge in euro area sovereign spreads during the financial crisis of 2007-09?[END_REF]. Indeed, in spite of the common policy interest rate, money interest rates and longterm interest rates move in the opposite direction in case of recapitalization scheme. We note that Euribor-Eurepo spreads are just weakly significant (and only through fixed-effects models) because of the use of monthly variables and so a loss in information when computing monthly averages. This pivotal variable complements the excess liquidity (excliq) and highlights that sovereign spreads are likely to decrease even in a context of banking troubles, if the central bank eases its policy. Further estimations highlight the absence of significance for recapitalizations schemes (recap) in any case, as for [START_REF] Barrios | Determinants of intra-euro government bond spreads during the financial crisis[END_REF]. The absence of instruments for weighting rescue packages (with a binary variable) can explain this feature.

Mostly, it is uneasy to assess the effect of rescue packages that clean balance sheets of banks, as the recovery of bank activity may be offset by the increase in sovereign debts. Here, the absence of significance also tends to validate the hypothesis of a risk transfer from banks to Member States.

Additional results related to government spending are obtained for the entire sample but also by excluding the Greek case, whose difficulties are still topical at the summer 2015 (Table 4).

Insert Table 4 here

First, debt levels are weakly significant with the expected sign, but this finding remains true whatever the estimation method and the sample are, which points out robustness of the relationship. Moreover, the squared debt is highly significant. Even if coefficients are low, this remains true by implementing double-clustered standard errors, and when excluding Greece from the sample. In other words, results highlight non-linear reactions face to changes in the risk perception by market operators [START_REF] Filbien | Macroeconomic, financial and institutional determinants of Eurozone sovereign crisis -Evidence from daily data[END_REF]. Budgetary balance (bal) is less interesting, as the positive relationship with sovereign spreads is very weakly significant.

Then, public effort (effort) is measured by the changes in the distance to stabilizing primary balances, and indicates whether markets are interested or not in the composition of public spending, including the debt burden. Despite weak coefficients, estimations confirm that public efforts are granted by lower long-term interest rates on sovereign bond markets, which in turn confirms the existence of thorough debt sustainability assessments even when risk aversion supports high risk premiums.

Finally, the share of public investment over total public spending (gfcf) is supposed to denote if bond yields consider or not the allocation of expenditure, especially towards public investment: if so, a higher debt could result in a decrease in spreads, by supporting future economic growth. On the opposite, as indicated by Table 3, public investment is not significant for the whole sample. However, when removing Greece from the sample (Table 4), the relationship becomes significant with unexpected positive sign. First, it is essential to remove Greece from the sample, because of the very specific context of crisis: over the period, the changes in investment expenditure do not reflect choices with regard to public expenditure management, as they depend on ongoing adjustment programs. For the same reason, we note that budgetary balance is not significant when considering Greece in the sample. Second, additional public expenditure systematically increases yield spreads, even by considering only investment expenses: two opposite views can be put forward to account for the positive sign of gfcf. A first reading leads to conclude that any expenditure (operating but also investment expenditure) increases sovereign spreads, which tends to validate the hypothesis of a very short-term horizon of financial markets, contrary to the possibility of exhaustive debt sustainability assessments. However, when subjected to closer scrutiny, rises in public investment rises correspond to economic downturns and to subsequent decreases in public expenditure. In other words, a rise in gfcf does not indicate an increase in public spending but, on the contrary, a recession resulting in a decrease in operating expenditure.

Though this is the most likely scenario, the question whether sovereign spreads are due to recession or austerity cannot be answered.

Overall, this significant variable mainly confirms that the structure of public spending remains scrutinized by investors during a sovereign debt crisis, except for countries under assistance that are excluded from financial markets: even in a context of sovereign debt crisis associated with huge risk aversion, sovereign spreads remain partly driven by fundamentals, and debt sustainability cannot be summarized as a threshold expressed in percent of GDP. Indeed, removing Ireland or Portugal from the sample does not change above-mentioned results. It is also possible to conclude that governments seems to have restrain spending in an orderly way, by decreasing unproductive spending faster than public investment.

V. Conclusions

Over the period 2008-2013, we implement a panel model with country fixed-effects to highlight the main drivers of the European debt crisis. Stationary variables prevent from taking into account base effects, for example on government debt or balance. As a consequence, the explanatory power is limited to the main drivers in changes in sovereign spreads, on a monthly basis. Except for public investment, the removal of Greece and the double clustered method act as robustness tests and validate our findings.

As for previous studies on this topic, the increase in risk aversion is the most important driver of spreads, especially if based on bond markets. Unsurprisingly, the international environment also explains the crisis, especially if assessed through U.S. corporate bond spreads. Then unconventional monetary policies decrease sovereign spreads by providing liquidity to interbank markets through collateral enlargements. Yet, even though impairments on bond markets are supposed to weigh on banking health, interbank spreads (bank credit risk) are negatively related to the dependent variable (sovereign credit risk), which is due to a risk transfer with public sectors. So, the well-functioning of public bond markets depends on banking, which highlights the role for the central bank face to a sovereign debt crisis (partly due to recovery plans following the 2007-2008 banking and financial crisis). Giving that recapitalization schemes do not give any helpful information in our study, such a relationship between bank and sovereign credit risk also put the emphasis on the importance of the second key element of the European banking union, namely the Single Resolution Mechanism.

As regard public finances, the study reveals that fiscal efforts (measured by the changes in the distance to the stabilizing primary balance) and debt (especially when squared) are highly significant, even in the short-term horizon of financial markets. In other words, despite the need to decrease the level of debt, it is necessary to take into account its composition in terms of primary balance. This finding is interesting as it highlights that such fundamentals keeps on being scrutinized by investors in a context of crisis with strong risk aversion. Here, usual mechanisms are distorted as Greek debt sustainability is also assessed through the ability to satisfy creditors' requirements. By removing this country from the sample, a positive relationship appears between public investment and sovereign spreads, but the explanation is that downturns and cuts in expenditure (that mechanically result in an increase in gfcf) are accompanied by an increase in sovereign spreads. Overall, we show that financial markets take into account qualitative features of public expenditure and public efforts, and that austerity measures are far from an obvious solution.

Annex 2. Correlation matrix with statistical significance (* significant at 1%)

Table 1 .

 1 Figure 1. Ten-year government bond spreads in Euro area, compared to German benchmark bonds (% points) Descriptive statistics, ten-year government bond spreads (2008-2013)Fixed-effects regressions; 10 u. of cross-section. Note: (standard error). *** Significant at 1%, ** Significant at 5%, * Significant at 10%. Fixed-effects regressions; 10 u. of cross-section. Note: (standard error). *** Significant at 1%, ** Significant at 5%, * Significant at 10%.

		spread	liquidity	debt	debt2	bal	effort	gfcf
	gspread	1.0000
	liquidity	-0.0191	1.0000
	debt	-0.0017	-0.0012	1.0000
	debt2	0.0017	-0.0003	0.9721*	1.0000
	bal	0.0838	0.0008	0.0067	0.0054	1.0000
	effort	0.0555	-0.0073	0.0051	0.0022	0.0405	1.0000
	gfcf	0.0210	0.0048	0.0003	0.0004	0.0088	0.0023	1.0000
	borrepo	0.2937*	-0.0118	-0.0195	-0.0124	-0.0679	-0.0032	0.0120
	recap	0.0706	-0.0603	0.0537	0.0689	0.0102	-0.0175	0.0536
	sp500	-0.4139*	-0.0065	-0.0308	-0.0288	0.0369	-0.0053	0.0183
	spreadba	0.3599*	-0.0322	-0.0363	-0.0294	-0.0285	-0.0158	-0.0068
	eurex	0.2402*	0.0166	-0.0095	-0.0167	-0.0262	0.0269	0.0246
	bir	-0.2492*	0.0018	-0.0190	-0.0170	0.0474	-0.0393	-0.0082
	excliq	-0.1176	0.0090	-0.0066	-0.0052	-0.0081	0.0051	-0.0057
	break	-0.1337*	-0.0378	0.0370	0.0280	0.0619	-0.0370	0.0380
		borrepo	recap	sp500	spreadba	eurex	bir	excliq
	borrepo	1.0000
	recap	0.0074	1.0000
	sp500	-0.5910*	-0.0672	1.0000
	spreadba	0.6429*	0.0711	-0.6102*	1.0000
	eurex	0.3094*	0.0239	-0.1713*	0.2493*	1.0000
	bir	-0.4724*	-0.0615	0.5189*	-0.3997*	-0.3206*	1.0000
	excliq	-0.1159	-0.0625	0.0584	-0.0150	-0.1231	0.2751*	1.0000
	break	-0.0225	0.0147	0.1392*	-0.0108	0.0084	0.0197	0.0927
		break
	break	1.0000

Structural adjustments refer to reforms imposed to countries under assistance (Greece, Portugal and Ireland) by their institutional creditors (European Commission, European Central Bank and International Monetary Fund). Basically, it is recommended to restructure fiscal policy and to reduce public spending, to increase markets' flexibility and to strengthen international competitiveness.

Luxembourg is excluded of the sample as dataset on sovereign spreads is not significant before 2010 (too small government bond market, especially for long-term debt securities with a residual maturity of close to ten years).

This is all the more likely, that prudential rules will keep on tightening and especially solvency ratios will be higher, as EU promised to adopt next recommendations of the Basel Committee on Banking Supervision. So one can expect a decrease in excess demand for (downgraded) public securities, which is all the more likely when the

The European Financial Stability Facility (EFSF) was the first European temporary crisis resolution mechanism. The EFSF provided financial assistance to Ireland, Portugal and Greece, through the issuance of bonds and other debt instruments on financial markets. Then on October 2012 a permanent rescue mechanism was created and provided loans to Spain and Cyprus: the European Stability Mechanism (ESM), which is currently the sole mechanism responding to new requests for financial assistance by euro area Member States.

Besides economic analysis, fixed-effects are preferred as the number of periods exceeds the number of individual, even if Hausman tests do not systematically reject random-effects estimations.

Variables collected on a quarterly basis (debt, budgetary balance and public investment) are treated by cubic spline interpolation.

liq -0,0040*** (0,0007) -0,0035*** (0,0006) -0,0056*** (0,0007) -0,0051*** (0,0007) -0,0036* (0,0022) -0,0032 (0,0024) -0,0052** (0,0024) -0,0047* (0,0026) -0,0039*** (0,0006) -0,0034*** (0,0006) -0,0053*** (0,0006) -0,0048*** (0,0006) -0,0037* (0,0022) -0,0032 (0,0024) -0,0051** (0,0025) -0,0045* (0,0027) spreadba 0,469*** (0,0327) 0,521*** (0,0341) 0,468*** (0,0328) 0,518*** (0,0344) 0,469*** (0,157) 0,521*** (0,138) 0,468*** (0,166) 0,518*** (0,146) 0,460*** (0,0352) 0,514*** (0,0374) 0,459*** (0,0353) 0,511*** (0,0378) 0,460*** (0,163) 0,514*** (0,140) 0,459*** (0,170) liq -0,0056*** (0,0006) -0,0057*** (0,0007) -0,0052*** (0,0007) -0,0056*** (0,0007) -0,0056*** (0,0007) -0,0052*** (0,0006) -0,0055*** (0,0006) -0,0054** (0,0025) -0,0054** (0,0025) -0,0050* (0,0026) -0,0054** (0,0025) -0,0054** (0,0025) -0,0049* (0,0025) -0,0053**

Except the breakdown, which is a dummy variable, growth rates of variables mentioned above are used in the estimates. Only the most significant results are reported in Tables 2 to 4. Additional estimations and complete tests are available upon request.