Laura Scalfi

Maximilian R Becker

Roland R Netz

Marie-Laure Bocquet

Enhanced interfacial water dissociation on a hydrated iron porphyrin single-atom catalyst in graphene

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

I. INTRODUCTION

Since two decades, the field of heterogeneous catalysis has seen a surge of interest in single atom catalysts (SAC) comprised of single transition metal atom active sites [START_REF] Sykes | Fundamental insights into heterogeneous single-atom catalysis[END_REF][START_REF]Single atom catalysts push the boundaries of heterogeneous catalysis[END_REF] . The original experiments were performed on oxide supports, with the insertion of individual Au or Pt atoms into cerium oxide for the water-gas shift reaction [START_REF] Fu | Active nonmetallic au and pt species on ceria-based water-gas shift catalysts[END_REF] and later with single Pt atoms inserted into an iron oxide for CO oxidation [START_REF] Qiao | Single-atom catalysis of co oxidation using pt1/feox[END_REF] . Single-atom catalysts quickly invested the active field of electrocatalysis, where these diluted catalysts were immersed into liquid electrolytes. The SAC now even extends to the field of bionanocatalysis with promising anti-bacterial results [START_REF] Fan | A Copper Single-Atom Cascade Bionanocatalyst for Treating Multidrug-Resistant Bacterial Diabetic Ulcer[END_REF] . In search of scalability, individual noble metals like Pt and non-noble metals like Co and Fe have been successfully inserted into various carbonaceous supports, such as porous graphene [START_REF] Li | Photochemical solid-phase synthesis of platinum single atoms on nitrogen-doped carbon with high loading as bifunctional catalysts for hydrogen evolution and oxygen reduction reactions[END_REF] , graphene oxide [START_REF] Fei | Atomic cobalt on nitrogen-doped graphene for hydrogen generation[END_REF] and also other 2D materials like MoS 2 [START_REF] Li | 3.4% solar-to-ammonia efficiency from nitrate using fe single atomic catalyst supported on mos2 nanosheets[END_REF] .

a) Electronic mail: marie-laure.bocquet@ens.fr A practical question that arises is how to best graft single metals on 2D materials, while avoiding metal sintering or clustering. Several synthesis strategies have successfully been implemented: the most common technique consists in first pre-doping graphitic materials like graphene or graphene oxide with nitrogen atoms N via heating under NH 3 atmosphere. Upon addition of the metal as a salt and subsequent pyrolysis, single metal ions coordinate in the vacancies forming 4 strong metal-N bonds [START_REF] Fei | Atomic cobalt on nitrogen-doped graphene for hydrogen generation[END_REF][START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF][START_REF] Fei | General synthesis and definitive structural identification of mn4c4 single-atom catalysts with tunable electrocatalytic activities[END_REF] . Two other synthesis strategies for SACs include high-energy ball-milling of the metal phthalocyanine molecule with graphene nanosheets [START_REF] Deng | A single iron site confined in a graphene matrix for the catalytic oxidation of benzene at room temperature[END_REF] and a surfactant-assisted synthesis method using a mixture of metal salt, a graphitic carbon nitride and a polymer surfactant [START_REF] Yang | Unveiling the high-activity origin of single-atom iron catalysts for oxygen reduction reaction[END_REF][START_REF] Yang | Single-atom cobalt electrocatalysts for foldable solid-state zn-air battery[END_REF] .

With the aid of XANES (X-ray Absorption Near Edge Structure) spectroscopy and density functional theory (DFT) modelling [START_REF] Li | Photochemical solid-phase synthesis of platinum single atoms on nitrogen-doped carbon with high loading as bifunctional catalysts for hydrogen evolution and oxygen reduction reactions[END_REF][START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF] or X-ray photoelectron spectroscopy [START_REF] Fei | Atomic cobalt on nitrogen-doped graphene for hydrogen generation[END_REF][START_REF] Yang | Unveiling the high-activity origin of single-atom iron catalysts for oxygen reduction reaction[END_REF] , two possible SAC grafting geometries around the metal core were proposed: one of pyridine type, with the metal coordinated by 4 pyridinic ligands (six-membered rings), and one of porphyrin type, with the metal coordinated by 4 pyrroles ligands (five membered rings). Both defects have been found to coexist in these SACs, and recently Zhang et al. [START_REF] Zhang | High-purity pyrrole-type fen4 sites as a superior oxygen reduction electrocatalyst[END_REF] have successfully converted the iron pyridine defects into the iron porphyrin ones after a NH 3 -assisted pyrolysis. These fourfold motives, labelled M-N 4 SACs, have been widely tested experimentally in a large range of electrochemical reactions, in particular for the oxygen reduction reaction (ORR), and using different metal centers, where Fe was found to be a promising catalytically active non-noble metal [START_REF] Sa | A general approach to preferential formation of active fe-nx sites in fe-n/c electrocatalysts for efficient oxygen reduction reaction[END_REF] . Interestingly, a recent study compared the two defects mentioned above and found a different predicted reactivity [START_REF] Chen | Identification of the highly active co-n 4 coordination motif for selective oxygen reduction to hydrogen peroxide[END_REF] . Indeed, by a combined experimental and theoretical study, the Co SAC porphyrin motif (also called pyrrole in the literature) was found most efficient for the 2 electrons ORR pathway, leading to H 2 O 2 formation, while the Co SAC pyridine motif works better for the 4 electrons ORR, leading to H 2 O production. Note that the latter selectivity for ORR drastically depends on the metal atom: for example, high-purity Fe SAC porphyrin defects in protonexchange membrane fuel cells rather exhibit complete 4 electrons reaction selectivity [START_REF] Zhang | High-purity pyrrole-type fen4 sites as a superior oxygen reduction electrocatalyst[END_REF] .

From a theoretical point of view, these SACs are easily modelled at the quantum level either as molecular models or as small periodic models, allowing for the quantitative prediction of electrochemical pathways in vacuum adding electrons and protons (including several studies with Fe [START_REF] Liu | Bridging the homogeneous-heterogeneous divide: Modeling spin for reactivity in single atom catalysis[END_REF][START_REF] Wang | Orbital dependence in single-atom electrocatalytic reactions[END_REF] ). However, modelling an explicit solution environment around solids plays an important role and has recently revealed many un-expected interfacial reactivities like charge adsorption on 2D materials [START_REF] Grosjean | Versatile electrification of two-dimensional nanomaterials in water[END_REF] and enhanced water dissociation on defected [START_REF] Comtet | Direct observation of water-mediated single-proton transport between hbn surface defects[END_REF] or hybridized 2D materials [START_REF] Grosjean | Spontaneous liquid water dissociation on hybridised boron nitride and graphene atomic layers from ab initio molecular dynamics simulations[END_REF] , or in nanoconfined water [START_REF] Muñoz-Santiburcio | Nanoconfinement in Slit Pores Enhances Water Self-Dissociation[END_REF][START_REF] Muñoz-Santiburcio | Chemistry in nanoconfined water[END_REF] . Regarding single atom catalysis, Patel et al. [START_REF] Patel | Theoretical Approaches to Describing the Oxygen Reduction Reaction Activity of Single-Atom Catalysts[END_REF] recently suggested by comparing a Cu-modified covalent triazine framework catalyst with a Cu(111) surface that solvation effects are probably larger for SACs than for conventional metal catalysts. Up to now however, only a single theoretical study considered the Fe-pyridine defect embedded in a graphene sheet and immersed in an active chemical environment, i.e. including the solvent water molecules interfacing the SAC, using extensive DFT molecular dynamics (DFT-MD) [START_REF] Chen | Pseudo-adsorption and long-range redox coupling during oxygen reduction reaction on single atom electrocatalyst[END_REF] . That study also emphasized the crucial need for taking into account explicit solvation in order to represent correctly the dynamical reactive interfacial processes at stake. On a technical level, static DFT studies [START_REF] Liu | Bridging the homogeneous-heterogeneous divide: Modeling spin for reactivity in single atom catalysis[END_REF][START_REF] Liberto | Universal principles for the rational design of single atom electrocatalysts? handle with care[END_REF] highlighted the importance of performing quantum calculations with care and using spin-polarized simulations as soon as dealing with magnetic atoms like Fe or Co. Another important aspect often poorly discussed is the full atomistic model in which the SAC is embedded. In previous studies, the simulation box was only slightly larger than the catalytic center itself. However, this imposes large constraints on the geometry of the SAC defects and is not a realistic representation of the graphene support. Indeed, the reported experimental density of these defects is between 0.5 and 4 wt% [START_REF] Zhang | Single atoms on graphene for energy storage and conversion[END_REF] . Therefore, we argue here that larger unit cells should be used to ensure a better representation of the systems and that the local defect created by the SAC insertion induces only small local perturbations [START_REF] Liberto | Universal principles for the rational design of single atom electrocatalysts? handle with care[END_REF] .

In this theoretical work, we investigate iron-based SAC embedded in graphene, motivated by the low cost of the materials. We compare the reactivity of two Fe-N 4 SAC defects in operando, i.e. including explicit liquid water by means of extensive spin-polarized DFT-MD simulations and employing large periodic unit cells (corresponding to a density of defects of 2.8-2.9 wt%) to mitigate the induced strain in graphene. As a result, we demonstrate that, while two water molecules of the solvent readily coordinate in an axial fashion the Fe atom on both defects, the Fe-porphyrin defect has a significant stabilizing effect on an adsorbed hydroxide ion. By applying a moderate electric field perpendicular to the graphene support, the Fe-porphyrin defect leads to the deprotonation of one of the adsorbed water molecules. In contrast, the Fe-pyridine defect remains inactive under the same external stimulus; the adsorbed water molecules stay coordinated to the Fe metal ion, effectively passivating or protecting the Fe core. This shows that Fe-porphyrin is better suited for water protolytic applications then Fe-pyridine.

II. RESULTS AND DISCUSSION

A. Embedding Fe SAC catalytic structures in graphene 1. Geometries and electronic structure of bare SAC defects in gas phase

As mentioned in the introduction, two configurations for embedding Fe in N-doped graphene were proposed in earlier studies [START_REF] Li | Photochemical solid-phase synthesis of platinum single atoms on nitrogen-doped carbon with high loading as bifunctional catalysts for hydrogen evolution and oxygen reduction reactions[END_REF][START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF][START_REF] Yang | Unveiling the high-activity origin of single-atom iron catalysts for oxygen reduction reaction[END_REF][START_REF] Liu | Bridging the homogeneous-heterogeneous divide: Modeling spin for reactivity in single atom catalysis[END_REF] . The structure most widely studied, which we denote Fe-pyridine defect, is pictured in Fig. 1a: two consecutive carbon atoms forming a vertical bond are removed (not shown) and this di-vacancy is filled by one metal cation, while the four edge carbon atoms of the as-formed di-vacancy are substituted by nitrogen atoms. A second configuration has been proposed by periodically replicating a porphyrin macrocycle, leading to a compensation of each pyrrole group by one eight-member ring placed in anti-position along the diagonal directions [START_REF] Chen | Identification of the highly active co-n 4 coordination motif for selective oxygen reduction to hydrogen peroxide[END_REF][START_REF] Liu | Bridging the homogeneous-heterogeneous divide: Modeling spin for reactivity in single atom catalysis[END_REF][START_REF] Zhao | Selective electroreduction of CO2 to acetone by single copper atoms anchored on N-doped porous carbon[END_REF] . Here, we propose an alternative way to embed the Fe-porphyrin defect: as shown in Fig. 1b (see also Supplementary Figure 1), we incorporate a porphyrin into a large graphene sheet (approximately 20 by 20 Å) and solve the non-commensurability of porphyrin with the graphene structure by inserting two seven-member rings and a five-member ring on the left and right sides of the porphyrin, reminiscent of a Stone-Wales defect [START_REF] Banhart | Structural Defects in Graphene[END_REF] , highlighted in yellow on Fig. 1b. We have checked that the induced strain in graphene remains small and localized to the defect. Indeed, after geometryoptimization at the DFT level, the obtained C-C bonds are only slightly longer than the average bond length for the pristine graphene d graphene CC = 1.42 Å: the maximal C-C length is d max CC = 1.5 Å in the five-member rings only and the full bond distribution is given in Supplementary Figure 2. This allows our Fe-porphyrin structure to stay stable throughout all further simulations and to maintain a planar catalytic site. The main geometrical difference between the two SAC structures resides in the Fe-N distance: d pyr FeN = 1.88 Å in the Fe-pyridine defect is significantly smaller than d porph FeN = 2.06 Å for the Feporphyrin defect, in fine agreement with recent EXAFS (Extended X-ray Absorption Fine Structure) measurements made for related cobalt SAC defects [START_REF] Chen | Identification of the highly active co-n 4 coordination motif for selective oxygen reduction to hydrogen peroxide[END_REF] .

Because the Fe cation center can be magnetic, we perform static DFT and DFT-MD simulations with the simulation package CP2K [START_REF] Kühne | CP2K: An electronic structure and molecular dynamics software package -Quickstep: Efficient and accurate electronic structure calculations[END_REF] on the PBE level [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF][START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] using unrestricted (spin-polarized) Kohn Sham equations (UKS) with imposed spin multiplicity M of the total system. Simulation details are given in the Methods section and in the Supplementary Methods.

Because of the localized d-orbitals on the isolated Fe metal ion, the delocalization error of GGA (generalized gradient approximation) functionals might lead to inaccurate results, while hybrid functionals such as PBE0 [START_REF] Adamo | Toward reliable density functional methods without adjustable parameters: The PBE0 model[END_REF] correct for this and are therefore more reliable for predicting properties of the transition metal ions present in SACs [START_REF] Liu | Bridging the homogeneous-heterogeneous divide: Modeling spin for reactivity in single atom catalysis[END_REF][START_REF] Patel | Theoretical Approaches to Describing the Oxygen Reduction Reaction Activity of Single-Atom Catalysts[END_REF][START_REF] Liberto | Universal principles for the rational design of single atom electrocatalysts? handle with care[END_REF] . However, this is prohibitively computationally expensive for running MD simulations. To check for the severity of this approximation, we provide a comparison of adsorption energies of sin-gle molecules onto the defects and of the energy difference between spin states calculated with PBE and PBE0. The data is given in Supplementary Figures 5 and6 and discussed in sections II.B and III.

We investigate the impact of spin settings in our DFT simulations by comparing results for two different spin multiplicities of the whole system -UKS M = 1 and UKS M = 3. As expected, the spin polarization (taken as the number of unpaired electrons) mostly localizes on the Fe atom [START_REF] Liu | Bridging the homogeneous-heterogeneous divide: Modeling spin for reactivity in single atom catalysis[END_REF] . In Table I, we report extracted charges q Fe and spin polarizations s Fe on the Fe atom for different settings. For Fe-pyridine, both a low and a high spin states can be found, with s Fe = 0 (no unpaired electrons localized on Fe) and s Fe ≈ 2 (2 unpaired electrons localized on Fe) respectively. For Fe-porphyrin, we observe the high spin state with s Fe ≈ 2 for both UKS settings (M = 1 and M = 3). In both bare defects, the high spin state (corresponding to a Fe triplet spin state, which does not necessarily correspond to the total system multiplicity M) is energetically favorable by about 10-20 kcal mol -1 . We also observe that the high spin states have higher charges on the iron atom and the Fe-porphyrin defect shows slightly higher charge values with respect to Fe-pyridine. Interestingly, a combined experimental and theoretical study has raised similar conclusions stating that the valence state of Fe in the Fe-porphyrin defect is more positive than that in the Fe-pyridine, pointing to a higher chemical reactivity of the Fe-porphyrin defect [START_REF] Zhang | High-purity pyrrole-type fen4 sites as a superior oxygen reduction electrocatalyst[END_REF] . This demonstrates the importance of using spin-polarized simulations allowing for non-zero spin on the Fe core for bare defects in vacuum.

We further analyze spin-polarized densities of states projected on atomic orbitals of the Fe atom (pDOS, schematized in Fig. 1c-d and shown in Supplementary Figure 3). The Feporphyrin defect pDOS is very similar to the pDOS of the molecular porphyrin, except that the d xz and d yz degeneracy is slightly lifted due to the rectangular distortion of the Fe environment. For both defects, we find the following occupation of the d-orbitals: d

(2) xy [d xz , d yz ] (3) d (1)
z 2 (where we cannot assign the d xz and d yz separately), which is consistent with ligand field theory and previous calculations for porphyrins [START_REF] Zerner | Porphyrins[END_REF][START_REF] Scheidt | Spin-state/stereochemical relationships in iron porphyrins: implications for the hemoproteins[END_REF] . The Fe d z 2 and the d xz(yz) orbitals (drawn in Fig. 1c-d) are therefore magnetic orbitals i.e containing one unpaired electron each. In line with the smaller Fe-N distance d FeN in Fe-pyridine, we measure a higher ligand field splitting in Fe-pyridine: the two orbitals lie further apart and there is a larger destabilisation of the d xz(yz) magnetic orbital. In contrast, the lengthening of Fe-N bond in the Fe-porphyrin defect leads to a smaller ligand field destabilisation of the d xz(yz) orbital, placing it close to but below the d z 2 orbital, leading to an energetic inversion between the two magnetic orbitals.

Single adsorbed waters in gas-phase

To investigate the reactivity of these Fe SAC defect in aqueous conditions, we first report static DFT results for single water molecules adsorbed on the catalytic site in gas-phase. From a chemical point of view, the electron-deficient (positively charged) Fe core of SAC defects should ligate water spontaneously via a nucleophilic addition of the lone pair of the water oxygen, as drawn in Fig. 1e, and eventually induce the adsorbed water to auto-dissociate, loose one proton and form an adsorbed hydroxide anion.

We explore two different situations: the adsorption of two water molecules on either side of the catalytic site, as in Fig. 1f and noted H 2 * O, and the adsorption of a water molecule and a hydroxide ion, as in Fig. 1g, noted * OH -. (Here and in the following, * O denotes oxygen atoms adsorbed on the Fe metal ion). In the case of * OH -, a single proton is added far from the hydroxide ion to ensure the neutrality of the simulation cell. Note that to ensure a +1 charge on the proton, no basis set is attributed to the H atom. We prepare different initial configurations and optimize their ground-state geometry at the PBE-DFT level. The results for these complexes are similar and the values for the lowest energy configuration are shown in Table II for different spin settings. In the * OH 2 configuration, we find distinct low and high spin states for both defects, with a slightly lower energy reported for the high spin states (≤ 5 kcal mol -1 ). For each system, we compute adsorption energies of the water molecules and/or the hydroxide ion onto the Fe-defect. The adsorption energy of two water molecules is about -20 kcal mol -1 , while we observe a very strong adsorption of * OH -onto both defects with as adsorption energy between -110 to -135 kcal mol -1 . Interestingly, ∆E ads is globally more negative for Fe-porphyrin configurations than for Fe-pyridine ones, i.e. water molecules and the hydroxide ion adsorb more strongly on Fe-porphyrin than on Fe-pyridine. Values obtained from PBE0, given in Supplementary Figure 5, are in qualitative agreement with the conclusions above. The relative adsorption energies between Fe-pyridine and Fe-porphyrin are similar, nevertheless we find that ∆E ads is more negative for PBE, with differences of about 2.5 kcal mol -1 for absorption of water molecules and 10 kcal mol -1 for adsorption of * OH -. Among the different optimized systems, we observe different adsorption geometries on the catalytic site. For 2 adsorbed water molecules, we note that in the low spin states the distance between Fe and the adsorbed oxygen atom * O d Fe * O ≈ 2.06 Å is smaller than for high spin states, where it equals 2.3 -2.4 Å. Additionally, we observe that water molecules carry a positive partial charge, with a total charge on each water molecule of about 0.2 e in the low spin states and 0.1 e in the high spin states. This indicates a net electron transfer from the two water molecules to the graphene sheet of 0.4 e in the low spin state, and suggests a Lewis acid-type mechanism for the Fe- * OH 2 interaction, as pictured in Fig. 1e. We also note that high spin states have a weaker interaction with water, as suggested by the larger Fe- * O distance and the smaller charge transfer. For the * OH -configuration, we observe an intermediary spin state with s Fe ≈ 0.9 -1.0 (with a slightly higher value for Fe-pyridine). Upon water deprotonation, the Fe- * O distance of the hydroxide oxygen shortens to d Fe * OH -= 1.8 Å. At the same time, the Fe- * O distance of the opposite water molecule lengthens up to d pyr Fe * OH 2 = 2.35 Å for Fe-pyridine and d porph Fe * OH 2 = 2.2 Å for Fe-porphyrin, leading to a reduced positive charge on the water molecule with respect to the previous calculations, with a charge transfer of 0.1-0.15 e. Such structural asymmetry between axial ligands is a direct signature of the trans-effect well-known in coordination chemistry [START_REF] Deimel | Direct quantitative identification of the "surface trans-effect[END_REF] . The charge on the hydroxide anion is between -0.2 and -0.3 e so that a large portion of the additional negative charge is transferred to the graphene substrate.

Therefore, we observe that the spin state of the Fe core evolves with water chemisorption and water dissociation, which confirms the importance of using spin-polarized DFT simulations to model these gas-phase systems. Both M = 1 and M = 3 system spin multiplicities give similar results for the * OH -case, leading to an intermediary spin state. In the H 2 * O case in contrast, the setting M = 3 leads to a weaker interaction with water molecules. This is consistent with PBE0 results shown in Supplementary Note 3.

B. SAC in liquid water

In the following, we investigate the activity of the Feembedded graphene structures in liquid aqueous conditions, using extensive DFT-MD simulations of the hydrated system shown in Fig. 2a, where the simulation box containing the Fe SAC defects is filled with liquid water. Although we are aware that in many experiments the doped graphene sheet is often exposed to water on one side and to a solid support on the other side, we choose this model because this configuration is frequently adopted in the literature and is also computationally advantageous to simulate.

For completeness, we run both UKS simulations with a system multiplicity M = 1 and M = 3. For a selection of configurations along these DFT-MD trajectories, we calculate the difference between these two settings and found the M = 1 setting to be the lowest in energy in the vast majority of the cases (see Supplementary Figure 6, where we also give a comparison with PBE0 results). Therefore, in the following, we only show results of DFT-MD simulations using a system multiplicity M = 1. Other spin settings in DFT-MD runs are analyzed in Supplementary Table 1 and Supplementary Fig- ure 4. During the equilibration of the DFT-MD simulations, we observe that two water molecules from both sides of the liquid slab readily adsorb onto the Fe metal ion at a distance of approximately 2 Å, in agreement with the previous section. In the following, we note the related adsorbed oxygens by * O to differentiate them from the rest of the water solvent molecules. During the production runs, we do not observe any exchange of these adsorbed water molecules on the timescale of our simulations (∼ 10-20 ps -details are given in Tab. III). Fig. 2c shows the distribution of the * O-H bond length for the adsorbed water molecules for both defects (solid red line for the Fe-porphyrin and solid blue line for the Fe-pyridine), compared to the O-H bond length distribution in the bulk region far from the graphene sheet (dashed black line). We observe a significant lengthening of the * O-H bonds of the adsorbed water molecules with respect to the bulk value, which hints at a weakening of the * O-H bond and a decrease of the free energy barrier to water dissociation at the defect. It is interesting to note that no * O-H bond lengthening was observed in the gas phase calculations without surrounding solvent, de-picted in Fig. 1e, which suggests that the hydrogen bonding in liquid water is crucial to facilitate water dissociation via proton transfer.

Quantifying the free energy barrier of deprotonation in the adsorbed state is however not possible because no spontaneous deprotonation occurs during the limited length of our unbiased simulations. Thus, we examine the stability of hydroxide in aqueous conditions, i.e. of the product of this deprotonation process. We prepare configurations with a hydroxide ion adsorbed on the right side of the catalytic site (z > 0) and a hydronium ion to ensure charge neutrality, placed initially as far as possible in the liquid water from the hydroxide, as shown in Fig. 2b. Fig. 2d indicates the average Fe- * O distance in the * OH 2 case by a vertical gray line (the distribution is identical for both defects). In the * OH - case, the Fe- * O distance on the hydroxide side (shown by the solid lines) is shorter, similar to what we observed previously in single molecule calculations, while for the opposite adsorbed water it increases slightly (dotted lines). This transeffect is larger for Fe-porphyrin (red lines) than Fe-pyridine (blue lines), indicating a stronger Fe- * OH -bond in the Feporphyrin case. Fig. 2e shows the total energy distributions along simulations with two adsorbed water molecules * OH 2 (solid lines) and with initially an adsorbed hydroxide anion * OH -(dashed lines). Upon water deprotonation we find a decrease in average energy for Fe-porphyrin but not for Fepyridine. Although the distributions significantly overlap, the average total energy of the * OH -simulations for Fe-pyridine is about 60 kcal mol -1 higher than in the pure water simulations, while it is approximately 50 kcal mol -1 lower in the case of Fe-porphyrin, as confirmed in Table III. Other characteristics of these MD simulations are reported in Table III. In particular, we find spin states consistent with the previous gas-phase single molecule calculations, except for a quenching of the spin in Fe-pyridine with an adsorbed hydroxide ion, instead of an intermediary spin state with s Fe ∼ 1.

In the trajectories reported in Table III, we observe that the hydroxide ion remains continually adsorbed for the whole simulation length (18 ps) in the case of Fe-porphyrin. On the other hand there are several proton transfers from neighbouring water molecules in the case of Fe-pyridine, eventually leading after 7 ps to the recombination of the hydroxide with the hydronium ion (such recombination was also observed for M = 3 for Fe-pyridine). The trajectories are given in Supplementary Figure 7. We follow the proton transfer reaction (here from liquid water to the adsorbed * OH -) by computing the coordination number of the adsorbed oxygen atom * O of the hydroxide, using the switch function

n * O = n H ∑ 1 1 - r * OH r 0 6 1 - r * OH r 0 18 , (1)
where the sum runs over all hydrogens in the simulation box, r * OH is the distance to the adsorbed oxygen and we choose r 0 = 1.4 Å. The choice of exponents in Eq. 1 and cutoff value r 0 influences the average number of hydrogen atoms ac-counted for * O but not the shape of the distributions nor its qualitative behavior. In Fig. 3, we plot a transient free energy profile, taken as the negative logarithm of the frequency distributions of n * O , ∆F transient = -k B T ln(P(n * O )). For simulations starting from two adsorbed water molecules (see Fig. 3a), the coordination number has a single minimum at 1.75, while for simulations with an initial hydroxide ion (see Fig. 3b) the distributions initially show a minimum at 0.95, as expected. These simulations have large energy barriers. For the lack of multiple barrier crossing events the free energies shown in Fig. 3 (and Fig. 4c) are not converged to equilibrium profiles and thus are transient quantities. Nonetheless, in Fig. 3b, we observe in the case of Fe-porphyrin a single stretched well corresponding to the hydroxide species, while for Fe-pyridine we observe a reprotonation of the anion, leading to a second minimum corresponding to H 2 * O. We stress that for Fe-pyridine only three barrier crossings are observed during the simulation, so that the height of the energy barrier is not equilibrated and depends on the trajectory length. These results show that our proposed Fe-porphyrin structure stabilizes the product of water deprotonation, i.e. the hydroxide anion coordinated to the Fe atom, which adopts an intermediary spin state. On the contrary, for the Fe-pyridine configuration the hydroxide ion is only metastable and will eventually accept a proton from the liquid water so that the adsorbed hydroxide and free hydronium recombine on the 5-10 ps timescale.

C. Biasing the deprotonation with E-fields

To go further in the characterisation of the proton transfer, we apply a moderate electric field to trigger the water deprotonation at the surface, which is both a sampling bias method but can also be realized experimentally. We use an external electric field, with a nominal field strength of D/ε 0 = 1 V nm -1 , which is small enough to avoid the disruption of the hydrogen bond network. Due to the way electrostatics are treated in periodic boundary conditions in conjunction with polarization of the water in our simulation box the effective electric field is different from the applied one. We evaluate the effective electric field in the bulk water to be E bulk = 0.12 ± 0.02 V nm -1 (see Supplementary Figure 8 for details). Notably, this electric field stimulus is around 30 times smaller that the one applied in recent DFT-MD simulations of bulk water in order to trigger water dissociation [START_REF] Saitta | Ab Initio Molecular Dynamics Study of Dissociation of Water under an Electric Field[END_REF][START_REF] Cassone | Ab initio molecular dynamics studies of the electric-field-induced catalytic effects on liquids[END_REF] . Upon application of the external field, we observe an asymmetry in the Fe- * O distance, shown in Fig. 4b: given that the field is applied in the z direction, the right adsorbed molecule in the z > 0 plane aligns strongly with the field and its Fe- * O distance shortens (solid lines), while the left molecule is pulled away from the surface, leading to a lengthening of the bond (dashed lines), with values close to those obtained from the adsorption of a hydroxide anion (see Fig. 2d). This bond shift is pronounced for Fe-porphyrin but weaker for Fe-pyridine. For the Fe-pyridine, we only observe a low spin state with s Fe ≤ 0.5 and no water deprotonation event occurs over the length of the simulation (around 17 ps), as shown by the distribution of the coordina-tion number of the right water molecule in Fig. 4c (blue line), which displays a single well corresponding to H 2 * O. We note that the well is asymmetric and stretched toward the low coordination numbers compared to Fig. 3a, because of the bias due to the applied electric field. In the case of Fe-porphyrin, we observe low and intermediary spin states with s Fe = 0.5 and 0.9.

Most interestingly, for Fe-porphyrin we observe deprotonation and reprotonation events, as indicated by the doublewell structure in Fig. 4c. The data is collected along two independent biased simulations of Fe-porphyrin for a total of 35 ps, during which we detect ∼ 120 proton transfer events (including both deprotonation and protonation events). Here and in the following analysis, we define a proton transfer event when a proton's nearest oxygen changes to or from the adsorbed oxygen * O. In these biased simulations, the created proton eventually diffuses away, pushed by the electric field, so that we do not observe any more recombinations between the adsorbed hydroxide and the solvated hydronium ion on the timescale of our simulation. An example of such a trajectory is given in Fig. 4d, where we plot the timeseries of the coordination number n * O along a 20 ps trajectory. We additionally plot the lifetime distribution of the * OH -species in Fig. 4e. We observe several short-lived proton transfers, with a lifetime of less than 25 fs, and a few long-lived transfers of a few hundreds of fs. These short proton transfers are mostly resulting in contact ion pairs (such as in Fig. 4f), or solvent separated ion pairs (with a single water molecule separating the hydroxide and the hydronium ions, see Fig. 4g). At 11 ps, there is a water deprotonation event that lasts for 2.5 ps, where the created hydronium ion hops relatively far from the adsorbed hydroxide, along an oxygen chain containing 5-6 oxygens, highlighted in blue in Fig. 4h. The hydronium and the hydroxide ions then recombine by travelling backwards through the same water chain, but another proton transfer occurs after 1 ps, using once again the same water chain, and the hydronium ion diffuses away without returning to the catalytic site for at least 6 ps. As known in the literature [START_REF] Garofalini | Subpicosecond Molecular Rearrangements Affect Local Electric Fields and Auto-Dissociation in Water[END_REF][START_REF] Hassanali | Proton transfer through the water gossamer[END_REF][START_REF] Chen | Hydroxide diffuses slower than hydronium in water because its solvated structure inhibits correlated proton transfer[END_REF] , this highlights the importance of hydrogen bond networks for long-lived water dissociation. In the second independent simulation we observe qualitatively the same behavior.

Finally, using the simulations for Fe-porphyrin with an applied electric field, we analyse the proton transfers occurring at the catalytic site. In Fig. 5, we show four properties as a function of the time difference to a transfer, by plotting the timeseries 300 fs before and after each event and aligning them such that the proton transfer occurs at 0. We show averages over all observed deprotonation (green lines) and protonation (purple lines) trajectories. Fig. 5 shows, for a proton transfer between the right adsorbed * O (see Fig. 4a) and a second O from the solvent, the * O-H distance (panel a), the * O-O distance (panel b), the Fe- * O distance (panel c) and the Fe spin polarization s Fe (panel d). The plots highlight how these properties change during the proton transfer: all trajectories closely overlap, as shown by the small spread of data indicated by the shaded areas, pointing to a common mechanism. Importantly, there is a time-reversal symmetry between protonation and deprotonation trajectories with respect to tt PT = 0, so that there is no time delay in the proton transfer. The * O-H distance increases from 1.05 Å to around 1.6 Å upon deprotonation (and vice-versa for protonation) as expected, while the * O-O distance decreases during the proton transfer, as shown in Fig. 5b. This mechanism was already pointed out in bulk water and it was explained by the fact that the proton transfer barrier is sensitive to the oxygen-oxygen distance, so that shortening the distance favors the proton transfer [START_REF] Garofalini | Subpicosecond Molecular Rearrangements Affect Local Electric Fields and Auto-Dissociation in Water[END_REF][START_REF] Brünig | Spectral signatures of excess-proton waiting and transfer-path dynamics in aqueous hydrochloric acid solutions[END_REF][START_REF] Brünig | Proton-transfer spectroscopy beyond the normal-mode scenario[END_REF] . Contrary to the * O-H and * O-O distances, both the Fe- * O distance and the spin polarization s Fe are symmetric with respect to the initial and final states, i.e. they cross t = t PT in the middle between the two minima: for example, s Fe goes from 0.5 to 0.9 during the proton transfer and crosses t = t PT at 0.7. Finally, for both protonation and deprotonation events, it takes the system around 100 fs to dissipate the perturbation created by the proton transfer: all depicted properties start deviating from their average value around 50 fs before the event and reach their new equilibrium value 50 fs after the event, indicating proton transfer several times faster than what has been reported for bulk water auto-dissociation in the literature, where deviations from the average values up to 600 fs before the proton transfer have been reported [START_REF] Garofalini | Subpicosecond Molecular Rearrangements Affect Local Electric Fields and Auto-Dissociation in Water[END_REF] . This speed up of reaction time can be interpreted with respect to the catalytic action of the Fe-SAC, combined with the action of the electric field, as well as a difference in hydrogen bonding of the adsorbed water molecule.

III. CONCLUSION

In this work, we have used static DFT and DFT-MD with spin-polarized calculations to thoroughly study the chemical reactivity of two Fe-SAC defects in aqueous conditions in order to mimic an in-situ electrocatalyst. We showed that both defects are reactive in liquid water, adsorbing two interfacial water molecules on both sides. We also highlight a different reactivity of both defects with respect to the water dissociative adsorption process. Indeed, the Fe-porphyrin defect shows a stronger interaction with adsorbed water molecules and a larger stabilization of the product of water dissociation, i.e. of hydroxide ions, with respect to Fe-pyridine. The Feporphyrin defect therefore lowers the energy barrier to water dissociation more than Fe-pyridine. This is confirmed by biased simulations with an applied electric field, in which we observe deprotonation of an adsorbed water molecule only in the case of Fe-porphyrin and not for Fe-pyridine. This points to a higher intrinsic chemical reactivity of the Fe-porphyrin defect with respect to deprotonation. Based on our simulations, we therefore recommend that the SAC synthetic route promotes selectively porphyrin-like defects to catalyze water.

In a more general perspective, very few metal catalysts are prone to water dissociation in aqueous media [START_REF] Ramzan | Toward a realistic surface state of ru in aqueous and gaseous environments[END_REF] , such as Ru(0001). Even on the prototypical highly reactive Pt(111) catalyst, interfacial water molecules are predicted to remain intact [START_REF] Khatib | The nanoscale structure of the pt-water double layer under bias revealed[END_REF] . Such favorable water activation into its self-ions permitted by the Fe-porphyrin SAC defect becomes therefore of great importance to guide the next generation of sustainable electrocatalysts.

METHODS

The two Fe-SAC considered in this study are composed of one iron (Fe) atom coordinated by 4 nitrogens embedded in a single graphene sheet. The geometry of the Fe-porphyrin and Fe-pyridine defects is optimized with density functional theory (DFT) to obtain the lateral dimensions of the simulated box: 19.6896 × 21.3146 Å 2 for the Fe-pyridine defect and 19.6907 × 21.0636 Å 2 for the Fe-porphyrin defect. The hydrated Fe-SAC defects contain 201 additional water molecules, with a periodic box length of 17.7206 Å in the direction perpendicular to the defects. All the MD simulations are then run with a CSVR thermostat at 323.15 K, with a timestep of 0.5 fs for at least 10 ps. If not stated otherwise, DFT calculations (static and MD) are performed with the software CP2K [START_REF] Kühne | CP2K: An electronic structure and molecular dynamics software package -Quickstep: Efficient and accurate electronic structure calculations[END_REF] , using the PBE-D3 functional [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF][START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] with Grimme's dispersion correction [START_REF] Grimme | A consistent and accurate ab initio parametrization of density functional dispersion correction (dft-d) for the 94 elements h-pu[END_REF] and the DZVP-MOLOPT-SR basis set [START_REF] Vandevondele | Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases[END_REF] , combined with GTH pseudopotentials [START_REF] Goedecker | Separable dual-space gaussian pseudopotentials[END_REF] , and with a cutoff of 600 Ry. Extensive simulation details and in particular for the spin constraints are provided in Supplementary Methods and Notes 1-5. resources of GENCI for the grant A0130807364 and funding from the EU H2020 Framework Programme/ERC Synergy Grant agreement number 101071937 n-AQUA. II. Water and hydroxide adsorption on Fe SAC defects in gas phase BSSE-corrected adsorption energy ∆E ads of the water molecules and/or hydroxide ion onto the Fe-defects, Fe spin polarization s Fe , Fe charges q Fe , total charges on the adsorbed H 2 * O and * OH -and Fe- * O distances for different spin settings (UKS M = 1 and UKS M = 3). Data is shown for DFT-optimized configurations coordinated by either two water molecules or a water molecule and a hydroxide ion in gas phase, corresponding to the structures given in Fig. 1F-G 20.5 + 16.9 0.5 & 0.9 0.45 TABLE III. Fully hydrated Fe SAC defects Data is given for DFT-MD simulations (UKS M = 1) of fully hydrated Fe SAC defects with two adsorbed water molecules ( * OH 2 ), with one water and one hydroxide ion adsorbed ( * OH -) and with an applied electric field: total running time, average Fe spin polarization s Fe and average Fe charges q Fe . When two values are indicated, the distribution has two peaks during the simulation time, as can be seen in Supplementary Figure 4.

FIG. 1 .FIG. 2 .

 12 FIG. 1. Bare defects in gas-phase Top views of the DFT-optimized Fe-pyridine (a) and Fe-porphyrin defects (b) embedded in graphene. The simulation box is cropped in the vertical direction: for snapshots of the entire unit cell, see Supplementary Figure 1. The colors are as follows: C -gray, Fe -orange, N -blue, O -red, H -white. Pink areas highlight the defect pattern and the yellow areas show the graphene reconstruction with seven-and five-membered rings. (c-d) Representation of the magnetic d-orbitals of the Fe atom in SAC extracted from spin-polarized projected densities of states (pDOS, explicitly shown in Supplementary Figure 3), together with corresponding Fe spin polarizations s Fe . Water as a ligand : (e) Mechanism of a single water molecule adsorption on the Fe SAC defect, where the Fe atom acts as a Lewis acid followed by auto-dissociation of the adsorbed water. Close-up DFT structures of the Fe SAC coordinated by either two water molecules (f) or a water molecule and a hydroxide ion (g), along with computed total charges of the adsorbed H 2 * O or * OH -and Fe spin polarizations s Fe . The full box is shown in Supplementary Figure 1. Both defects yield similar charge and spin values, for more details see Tab. II.

→ * OH 2 b

 2 FIG. 3. Characterisation of adsorbed water and hydroxide stability Transient free energy profile ∆F transient , taken as the negative logarithm of the frequency distribution of the coordination number of the right adsorbed oxygen atoms n * O , defined in Eq. 1, as a function of n * O , for simulations with two adsorbed water molecules (a) and for simulations with initially a single hydroxide ion adsorbed at the catalytic site (b), for the Fe-porphyrin defect (red lines) and the Fe-pyridine defect (blue line). These distributions are taken along the finite length of our simulations (approximately 10-20 ps).

FIG. 4 .

 4 FIG. 4. Deprotonation an electric (a) Schematic representation of fully hydrated simulations with a small applied electric field D/ε 0 = 1 V nm -1 , with initially two adsorbed water molecules on the catalytic site. We show results for the Fe-porphyrin (red lines) and the Fe-pyridine (blue lines) hydrated defects. (b) Fe- * O distance d Fe * O distributions for simulations with an applied electric field, for the right adsorbed oxygen (solid lines) and for the left adsorbed oxygen (dotted lines). The vertical gray line shows the average distance for the simulations with two adsorbed water molecules without electric field. (c) Transient free energy profile ∆F transient , taken as the negative logarithm of the probability distribution of the coordination number of adsorbed oxygen atoms n * O , defined in Eq. 1, as a function of n * O . (d) Coordination number of the right adsorbed oxygen n * O along a Fe-porphyrin trajectory with an applied electric field (red line). Horizontal dashed lines indicate the two maxima in the n * O distributions, corresponding to the adsorbed water being protonated ( * OH 2 ) or deprotonated ( * OH -). (e) Distribution of the lifetime of the deprotonated species * OH -along the previous trajectory. (f-h) Snapshots of the proton transfer at t = 11 ps: contact ion pair (f), solvent separated ion pair (g) and snapshot with separated hydroxide and hydronium ions where we highlighted in blue the water chain through which the proton has hopped (h).

FIG. 5 .

 5 FIG. 5. Proton transfer dynamics * O-H distance d * OH (a), * O-O distance d * OO (b), Fe- * O distance d Fe * O (c) and Fe spin polarization s Fe (d) as a function of the time delay to a deprotonation (green line) or a protonation event (purple line), averaged over all proton transfer events (between an adsorbed oxygen * O and a second oxygen O from the solvent) in the simulations of Fe-porphyrin under an applied electric field. Shaded areas correspond to the standard error.

TABLE I .

 I Bare Fe SAC defects in gas phase Potential energy E, Fe spin polarization s Fe and Fe charges q Fe for different spin settings (UKS M = 1 and UKS M = 1). See Methods section and Supplementary Methods for more details.O L and * O R H - Spin Settings ∆E ads s Fe q Fe q H * 2 O d Fe * O ∆E ads s Fe q Fe q H * 2 O L q * O R H -d Fe * O L d Fe * O R [kcal mol -1[e] [e] [Å] [kcal mol-1 ]

			H 2	* O		H 2 [e] [e]	[e]	[Å]	[Å]
					Fe-pyridine
	UKS M = 1	-22.2	0.0 0.12 0.20 2.06	-122.3	1.0 0.21 0.11 -0.20 2.38 1.81
	UKS M = 3	-14.2	2.1 0.24 0.08 2.50	-110.9	0.9 0.20 0.12 -0.20 2.32 1.81
					Fe-porphyrin
	UKS M = 1	-27.6	0.0 0.40 0.20 2.07	-135.6	0.9 0.44 0.15 -0.19 2.18 1.80
	UKS M = 3	-22.3	2.4 0.52 0.11 2.32	-124.8	0.9 0.44 0.15 -0.17 2.18 1.79
	TABLE

*

  . See Methods section and Supplementary Methods for more details.Initial setup Time [ps]⟨s Fe ⟩ ⟨q Fe ⟩[e]

			Fe-pyridine
	* OH 2 * OH -E-field * OH 2	17.3 11.4 16.9	0.0 0.05 0.0	0.16 0.17 0.17
			Fe-porphyrin
	* OH 2 * OH -E-field	20.8 18.1	0.4 0.8	0.44 0.46

* OH 2

ACKNOWLEDGMENTS

We acknowledge support provided by the European Research Council under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 835117), the Deutsche Forschungsgemeinschaft, Grant No. CRC 1349, Code No. 387284271, Project No. C04 and CRC 1609. We gratefully acknowledge computing resources from the Hochleistungsrechenzentrum Norddeutschland, Project No. bep00106 as well as from the CURTA HPC cluster at ZEDAT, FU Berlin 50 . M.L.B. acknowledges the French HPC

CONFLICT OF INTEREST

The authors declare no competing interests.

DATA AVAILABILITY

The data that support the findings of this study are openly available on Zenodo 49 at https://doi.org/10.5281/zenodo.8406389.

All other data are available from the corresponding author upon reasonable request.


domain: shs info sdv

text:
Arthur Longuefosse

Baudouin Denis De Senneville

Gaël Dournes

Ilyes Benlala

François Laurent

Pascal Desbarats

Fabien Baldacci

Denis Baudouin

De Senneville

MR to CT synthesis using GANs : a practical guide applied to thoracic imaging

Keywords: GAN, CT Synthesis, Lung

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

Introduction

In clinical practice, computed tomography (CT) is typically used to diagnose lung conditions. However, this modality exposes patients to ionizing radiation, which may have negative effects on their health. Recently, lung MRI with ultrashort or zero echo-time (UTE/ZTE) has shown promise for high-resolution structural imaging of the lung [START_REF] Dournes | Quiet Submillimeter MR Imaging of the Lung Is Feasible with a PETRA Sequence at 1[END_REF][START_REF] Dournes | 3D ultrashort echo-time MRI of the lung using stack-of-spirals and spherical k -Space coverages: Evaluation in healthy volunteers and parenchymal diseases: Lung MRI With 3D UTE Spiral VIBE Sequence[END_REF]. However, the appearance of images obtained using this technique is substantially different from those obtained using CT, notably imaging texture, blurring, and noise which has limited its adoption in clinical practice (cf Figure 1). The generation of CT images from MRI may be a good alternative and could improve patient diagnosis by providing high quality images to radiologists based solely on the safe and non-invasive nature of MRI. Over recent years, deep learning approaches, particularly generative adversarial networks (GANs) [START_REF] Goodfellow | Generative adversarial nets[END_REF], have been extensively studied for image synthesis in medical imaging. This type of network is made of a generator and a discriminator, and is able to produce high quality synthetic data similar to a given dataset by learning a complex non-linear relationship between MR and CT. Previous research on cross-modality synthesis has used GANs to synthesize images in several different regions of the body, such as the brain [START_REF] Wolterink | Deep MR to CT Synthesis using Unpaired Data[END_REF][START_REF] Nie | Medical Image Synthesis with Context-Aware Generative Adversarial Networks[END_REF], pelvic region [START_REF] Lei | MRI-Only Based Synthetic CT Generation Using Dense Cycle Consistent Generative Adversarial Networks[END_REF], and also in the lungs using Dixon MRI [START_REF] Baydoun | Dixon-based thorax synthetic CT generation using Generative Adversarial Network[END_REF]. Many studies have been conducted on the development of specific GAN models, including unpaired methods based on cycleGAN [START_REF] Zhu | Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks[END_REF] and paired methods based on pix2pix [START_REF] Isola | Image-to-Image Translation with Conditional Adversarial Networks[END_REF]. In addition, research also focused on the development of various loss functions, such as cycle consistency [START_REF] Zhu | Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks[END_REF], feature-matching [START_REF] Wang | High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs[END_REF], perceptual [START_REF] Johnson | Perceptual Losses for Real-Time Style Transfer and Super-Resolution[END_REF], and contrastive loss [START_REF] Andonian | Contrastive Feature Loss for Image Prediction[END_REF]. However, most state-of-the-art studies are limited to these developments and do not properly address the full range of steps involved in medical translation tasks, such as preprocessing and robust evaluation. In this paper, we present a general guideline for image-to-image translation applied to thoracic MR to CT synthesis, covering key topics such as pre-processing steps, data normalization and quantization, and the importance of an adapted resampling before registering the input. We review the different types of GANs and losses and compare their performances in thoracic image-to-image translation. A quantitative evaluation of the different models and parameters is presented, using traditional metrics as well as a comparison of the segmentations of airways in synthesized CT images versus ground truth CT images, to help identify the factors that have the biggest impact on the performance of medical image-to-image translation. Overall, our evaluation helps to provide a better understanding of the different models and parameters used for medical image-to-image translation and can serve as a useful reference for researchers and practitioners in this field.

Methods

Data acquisition

The dataset used in this study consists of UTE MR and CT thoracic images of 110 patients. Both modalities were acquired on the same day, from 2018 to 2022. CT images were obtained using a Siemens SOMATOM Force, in end-expiration, with sharp filters. The parameters used were a DLP of 10 mGy.cm and a SAFIRE iterative reconstruction. UTE MR images were acquired using the SpiralVibe sequence on a SIEMENS Aera scanner, with the following parameters: TR/TE/flip angle=4.1ms/0.07ms/5°. Since the slice plane is encoded in Cartesian mode, the native acquisition was performed in the coronal plane with field-of-view outside the anterior and posterior chest edges to prevent aliasing. It should be noted that resolutions, voxel spacings, and fields of view are not identical in CT and MR images. In addition, modalities may have been taken at different points in the respiratory cycle. To obtain a paired dataset, an adequate resampling and a deformable registration will thus be required between CT and MR volumes.

Preprocessing

Resampling In multimodal registration, it is typically advised to use the image with the highest resolution as the fixed image and the image with the lower resolution as the moving image, since a higher level of detail and accuracy in the fixed image can help improve the performance of the registration process. In our case, we have to register the CT volume, with a voxel size of 0.6 × 0.6 × 0.6 mm 3 , on the MRI, with a voxel size of 1 × 1 × 1 mm 3 , which implies a resampling of the CT to the MRI resolution, and thus a loss of information, as shown in Figure 2. To avoid this issue, we propose to upsample the MRI voxel size to the CT voxel size, allowing to keep the initial resolution of the CT, which implies a better convergence of the registration algorithm as well as better performances for the GAN. The two modalities are therefore resampled on a common grid of 0.6 × 0.6 × 0.6 mm 3 using tricubic interpolation. For comparison purposes, CT and MR volumes were also resampled on a 1 × 1 × 1 mm 3 grid.

Multimodal registration Accurate alignment of images from different modalities often requires non-rigid registration, especially in parts of the body subject to severe periodic deformations, such as cardiac and respiratory motions. Edgealignment methods seems particularly well suited for multimodal medical registration since they don't rely on input landmarks and can overcome differences in intensity and contrast between modalities, by focusing on boundary information. In our dataset, a rigid translation is estimated to ease convergence, before the EVolution algorithm [START_REF] Denis De Senneville | Evolution: an edge-based variational method for non-rigid multi-modal image registration[END_REF] is employed to estimate the elastic deformation, a patch-based approach that includes a diffusion regularization term and a similarity term that favors edge alignments. To prevent physically implausible folding of the volumes during the registration process, a diffeomorphic transformation is ensured by minimizing the inverse consistency error ( [START_REF] Christensen | Consistent image registration[END_REF], [START_REF] Heinrich | MIND: Modality independent neighbourhood descriptor for multi-modal deformable registration[END_REF]). Intensity normalization CT and MR modalities have fundamental differences that must be taken into account when normalizing intensity values. CT intensity values are defined in Hounsfield units (HU) and have a physical meaning, whereas MR intensity values strongly depend on acquisition parameters. Therefore, methods used for intensity normalization must be tailored to the specific characteristics of each modality.

In our study, CT intensities are cropped to [-1000; 2000] HU window to remove irrelevant values from the table or background and rescaled to [-1; 1] using the same window limits. MR intensity inhomogeneities, also known as bias field, are first corrected using the popular N4 bias field correction algorithm [START_REF] Tustison | N4ITK: improved N3 bias correction[END_REF]. MR values are then normalized using z-score, i.e. zero mean and unit variance, cropped to [-3σ ; 3σ] to remove outliers, σ being the standard deviation, and rescaled to [-1; 1] based on minimum and maximum intensities. Nyul histogram matching [START_REF] Nyúl | New Variants of a Method of MRI Scale Standardization[END_REF] was also considered, but the findings of Reinhold et al. [START_REF] Reinhold | Evaluating the impact of intensity normalization on MR image synthesis[END_REF] indicated that the synthesis process was robust to the choice of MR normalization method used. As a result, we opted for a traditional Z-score normalization approach.

Field of view standardization As shown in Figure 1, modalities may have different fields of view (FOV). Due to the use of a narrow beams of X-rays to produce images, CT field of view is typically limited to a small area of the body, whereas MRI allows capturing a wider field of view. In our dataset, patients may also be in a different position depending on the modality. This is reflected by the visibility of the arms on the MRI, as opposed to the CT image. To uniformize FOV, which can be useful to speed up calculations and guide training, one common approach is to identify a region of interest (ROI) using segmentation methods. Few methods for lung segmentation in MRI have been developed due to the lower signal and contrast, as well as the lack of data. On the other hand, many effective methods are available for CT, such as the U-Net R-231 convolutional network [START_REF] Hofmanninger | Automatic lung segmentation in routine imaging is primarily a data diversity problem, not a methodology problem[END_REF]. The CT volume being registered on the MRI, it is then possible to apply the segmentation of the lungs from the CT on the MRI, allowing to obtain the same FOV on both modalities. All axial slices are then either cropped or zero-padded to 512 × 512, depending on the CT lung mask size.

Impact of intensity quantization

In this study, we also investigate the impact of the bit depth of input medical images on the performance of a GAN in lung MR to CT translation. We create two datasets, one in line with most of the current state-of-the-art papers in the field with 8-bit images, and another dataset with 16-bit images, and evaluate the GAN's performance on each dataset. This allows us to determine whether using higher bit-depth images can improve the performance of the GAN for thoracic CT synthesis.

Image-to-image translation

Conditional generative adversarial networks (cGANs), are a variant of GANs trained with additional constraints on a specific input image and have demonstrated significant potential for image-to-image translation tasks. CGANs are typically divided into two main categories: unpaired methods, often based on the CycleGAN model [START_REF] Zhu | Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks[END_REF], designed for image-to-image translation without the need for corresponding pairs of images, and paired methods, based on the pix2pix model, using corresponding pairs of images.

Since the introduction of the cycle consistency loss in CycleGAN, many unpaired methods have been developed, including NICE-GAN [START_REF] Chen | Reusing Discriminators for Encoding Towards Unsupervised Image-to-Image Translation[END_REF], a decoupled network training method that uses the discriminator to encode the image of the target domain. As for the paired methods, pix2pix improvements are described in the method pix2pixHD [START_REF] Wang | High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs[END_REF], which is no longer dependent on the pixel-wise loss, but on a new feature matching loss, as well as a multi-scale discriminator and a perceptual loss. SPADE [START_REF] Park | Semantic Image Synthesis with Spatially-Adaptive Normalization[END_REF] also enhanced the performance of paired methods by injecting class-specific information into the generator network. This model introduces a spatially adaptive normalization based on the inputs, that improves the performance and reliability of the generator, allowing synthesized images that are conditioned on the input class. The SPADE architecture can be integrated in other models, such as pix2pixHD, to apply additional constraints on the inputs and guide training. Finally, recent works on paired image-to-image translation developed a new type of bidirectional contrastive loss, called PatchNCE loss [START_REF] Andonian | Contrastive Feature Loss for Image Prediction[END_REF], that assesses the similarity between two images based on the mutual information from embedded patches, unlike GANs discriminator that only evaluates the realism of a synthesized image. This contrastive loss produces a smooth and interpretable loss trajectory, which makes it easier to evaluate the convergence of the training process and determine the number of epochs needed. This is a common challenge with GANs since their traditional loss functions tend to be noisy and provide no clear indication of training progress.

Assesment of the MR to CT synthesis

In order to evaluate the performance of generative models, past research has proposed several extrinsic evaluation measures, most notably Inception Distances (FID [START_REF] Heusel | GANs trained by a two timescale update rule converge to a local nash equilibrium[END_REF], KID [START_REF] Bińkowski | Demystifying MMD GANs[END_REF]), which compare the generated images to a set of real images and assess their quality and similarity. Such measures have been proven to be insensitive to global structural problems [START_REF] Tsitsulin | The Shape of Data: Intrinsic Distance for Data Distributions[END_REF], and may not be sufficient for the evaluation of medical image translation. Traditional image processing metrics, such as MSE, PSNR, SSIM, are the stateof-the-art reference metrics for evaluating synthetic images. They can provide information on how well the model preserves spatial structure and content of the original images, but are still highly sensitive to noise and distortion, and may not accurately reflect the visual quality of an image with low-level artifacts [START_REF] Toderici | Full Resolution Image Compression with Recurrent Neural Networks[END_REF].

Our assumption is that task-specific metrics are required to accurately quantify synthesized images and evaluate the performance of a model, by taking into account the structure and semantics of the images. In our dataset, we defined them as Dice score, precision, and sensitivity between synthesized and ground truth bronchial tree segmentations, by using NaviAirway [START_REF] Wang | NaviAirway: a bronchiolesensitive deep learning-based airway segmentation pipeline for planning of navigation bronchoscopy[END_REF], a bronchiole-sensitive airway segmentation pipeline designed for CT data. This allows us to accurately quantify false positives and false negatives at the bronchial level for each synthetic CT image. A qualitative evaluation conducted by radiologists or other medical experts can also be valuable, to ensure that the translation has preserved overall fidelity with the ground truth, as well as key diagnostic information.

Experiments and results

The initial dataset of 110 MR-CT thoracic images is split in a training set of 82 patients, and testing set of 28 patients. Although 3D GANs allow perception of volumetric and neighborhood spatial information, they involve an excessive computational cost and a reduction of the number of samples, which can be challenging to implement for some datasets. Therefore, we choose to train the models on the 2D axial slices of the CT and MR volumes, and define datasets that will allow us to assess the impact of each preprocessing step :

unpaired dataset with unregistered 0.6 × 0.6 × 0.6 mm 3 CT, 8-bit unpaired dataset with registered 0.6 × 0.6 × 0.6 mm 3 CT, 8-bit paired dataset with registered 0.6 × 0.6 × 0.6 mm 3 CT, 8-bit paired dataset with registered 0.6 × 0.6 × 0.6 mm 3 CT, 16-bit paired dataset with registered 1 × 1 × 1 mm 3 CT, 16-bit

The NICE-GAN model was trained using unpaired datasets, while the pix2pixHD and SPADE models were trained using paired datasets. We also evaluated the performance gain of the contrastive loss when applied to these paired methods.

Table 1: Mean squared error (MSE), cross-correlation (CC) and structural similariy index (SSIM) between synthesized CT and real CT inside the lungs.

Model MSE CC SSIM NICE-GAN
88,45 ± 9,91 0,9283 ± 0,023 0,9725 ± 0,024 NICE-GAN registered 82,41 ± 9,74 0,9406 ± 0,015 0,9776 ± 0,022 pix2pixHD 78,46 ± 13,03 0,9499 ± 0,011 0,9834 ± 0,032 pix2pixHD w/ contrast 75,51 ± 12,05 0,9557 ± 0,010 0,9900 ± 0,030 SPADE 67,82 ± 8,18 0,9635 ± 0,083 0,9915 ± 0,016 SPADE w/ contrast 67,53 ± 7,31 0,9646 ± 0,088 0,9927 ± 0,017 SPADE 8-bit w/ contrast 67,76 ± 7,70 0,9630 ± 0,096 0,9932 ± 0,018 SPADE 1mm 3 w/ contrast 76,36 ± 8,79 0,9505 ± 0,016 0,9830 ± 0,026 All models are trained using the same procedure and architecture defined in the respective papers, apart from pi2pixHD/SPADE dataloader and inference parts, which have been adapted to support 16-bit input and output arrays. Table 1 lists the quantitative evaluation using mean squared error, cross-correlation and structural similarity index between synthesized CT images and ground truth CT. Calculations are constrained within the intersection between CT and synthesized CT lung masks, to avoid comparing the backgrounds and narrow the results inside the lungs. Figure 3 shows an example axial slice between input MR, ground truth CT and synthetic CT from SPADE model with different samplings. SPADE results based on CT with a voxel size of 0.6 × 0.6 × 0.6 mm 3 present enhanced contrast and sharpness, and therefore allow a more accurate distinction of vessels and bronchi inside the lungs. To validate these assumptions, we performed the airways segmentation of synthesized and ground truth CT using NaviAirway [START_REF] Wang | NaviAirway: a bronchiolesensitive deep learning-based airway segmentation pipeline for planning of navigation bronchoscopy[END_REF], a bronchiole-sensitive airway segmentation pipeline designed for CT data, and computed dice score, precision, and sensitivity. To enable comparison, the SPADE 1 × 1 × 1 mm 3 was resampled to the same resolution as the ground truth CT before calculating the airways segmentation. 0,590 ± 0,088 0,636 ± 0,0752 0,583 ± 0,1298 NICE-GAN-registered 0,640 ± 0,071 0,665 ± 0,069 0,642 ± 0,104 pix2pixHD 0,707 ± 0,054 0,796 ± 0,060 0,660 ± 0,102 pix2pixHD w/ contrast 0,741 ± 0,031 0,787 ± 0,052 0,715 ± 0,088 SPADE 0,733 ± 0,068 0,829 ± 0,060 0,681 ± 0,108 SPADE w/ contrast 0,743 ± 0,060 0,819 ± 0,054 0,706 ± 0,104 SPADE 8-bit w/ contrast 0,742 ± 0,055 0,802 ± 0,057 0,719 ± 0,098 SPADE 1mm w/ contrast 0,687 ± 0,078 0,766 ± 0,068 0,652 ± 0,120

Discussion

Results from Table 1 based on image processing metrics and Table 2 based on the evaluation of airways segmentation are strongly correlated, with identical trends. Unpaired methods seem to benefit from the elastic registration but produce less satisfactory results than paired methods, which is in agreement with statements in state-of-the-art [START_REF] Kaji | Overview of image-to-image translation by use of deep neural networks: denoising, super-resolution, modality conversion, and reconstruction in medical imaging[END_REF]. Paired pix2pixHD method combined with the conditional normalization layer SPADE provides better performances than the pix2pixHD method alone since it can overcome false positives and false negatives by adding constraints on the inputs. The introduction of the PatchNCE [START_REF] Andonian | Contrastive Feature Loss for Image Prediction[END_REF] contrastive loss has improved the performance of paired methods, particularly for the pix2pixHD model that tends to diverge. This addition had only a minor impact on the SPADE model, but still provided better control over convergence during training and a more accurate way to differentiate epochs. The performance of the SPADE model with a voxel size of 0.6 × 0.6 × 0.6 mm 3 is significantly superior to that of the model with a voxel size of 1 × 1 × 1 mm 3 , both in terms of signal quality and bronchi reconstruction. These results confirm our initial hypothesis that input data should be registered based on the voxel size of the modality with the highest resolution, since downsampling the ground truth reference leads to a loss of information, especially in fine structures such as vessels and bronchi. Surprisingly, the intensity quantization in the input dataset images does not appear to have a significant impact on GAN performances; both SPADE 16bit and SPADE 8-bit models performed similarly. The reason for this could be that our dataset is composed of highly contrasted information, such as vessels and bronchi in the lungs, and the representation in 8-bit instead of the initial 12-bit would barely impact the reconstruction using GANs. Future works will aim to confirm this hypothesis by conducting similar experiments using different medical datasets in other parts of the body.

Conclusion

In this paper, we present a comprehensive guide for medical image translation using GANs. We focus on the importance of data preprocessing, and its impact on performance; the benefits of using a resampling based on the modality with the highest resolution, as opposed to state-of-the-art statements, have been demonstrated. We advocate the use of contrastive loss methods, such as PatchNCE, to address one of the most significant challenges of GANs, which is assessing convergence and stability during training. In addition, we argue that traditional GAN metrics commonly used in the field, such as FID and KID, as well as standard image processing metrics, do not provide sufficient information to adequately evaluate GAN performances in medical image-to-image translation tasks. We recommend defining task-specific quantitative evaluation methods, ideally in conjunction with a qualitative evaluation by experts, in order to robustly assess the performance of a model in this context. In future work, we plan to investigate the validity of our assumptions on different datasets for other parts of the body and provide guidance on incorporating 3D information into the training process for medical image-to-image translation.

Fig. 1 :

 1 Fig. 1: Visual comparison of thoracic UTE MR and CT modalities of the same patient at a corresponding axial slice. The CT scan shows a higher signal quality, greater contrast and sharpness, and fewer artifacts compared to the MRI.

3 Fig. 2 :

 32 Fig. 2: Visual comparison of identical CT slices at different voxel spacing, with zoomed regions that highlight bronchi, circled in yellow. Pulmonary bronchi are nearly indistinguishable in the 1 mm 3 version due to the lower resolution of the image.

3 Fig. 3 :

 33 Fig. 3: Comparison between MR, synthetic CT from SPADE 1 × 1 × 1 mm 3 and SPADE 0.6 × 0.6 × 0.6 mm 3 and ground truth CT axial slices.

Fig. 4 :

 4 Fig. 4: Airways segmentation example based on SPADE with contrastive loss (yellow) and real CT (red) using the NaviAirway pipeline [27].

Table 2 :

 2 Dice, precision and sensitivity between synthesized and ground truth airways segmentations

	Model	Dice	Precision	Sensitivity
	NICE-GAN


Harry Ramadasse
email: harry.ramadasse@gmail.com

Aurélie Dudézert
email: aurelie.dudezert@imt-bs.eu

The role of digital work in the new normal way of working

Introduction

The world has witnessed what is perhaps the most dramatic transformation of work in the digital era. In the wake of the global pandemic, much has been written regarding the "new normal" of work. However, defining what the "new normal" is today seems very complex. Before the crisis, most companies had initiated their digital transformation to adapt to a changing environment. Covid-19 has subsequently forced organizations into rapid "big bang" adoption of "tech-driven" practices under severe time pressure [START_REF] Carroll | Normalising the "new normal" : Changing tech-driven work practices under pandemic time pressure[END_REF]. This transformation was particularly forced by the introduction of teleworking [START_REF] Ng | Remote work as a new normal? The technology-organizationenvironment (TOE) context[END_REF]. In the aftermath of the crisis, workers are back to work, at least partially, and new forms of organization are appearing; leading to unprecedented hybrid work situations. Therefore, we can define the "new normal" as the development of new ways of working based on the adoption of digital work [START_REF] Wibowo | Understanding Digital Work and its Use in Organizations from a Literature Review[END_REF][START_REF] Baiyere | Digital Work : A Conceptual Clarification[END_REF].

This article explores the place of digital work in this new normal way of working. While it seems clear that white-collar workers have reorganized themselves adopting digital work, the same question also arises for blue-collar workers. Although they did not benefit from teleworking, they are also in a new normal way of working after the crisis, leveraging the opportunities from a digital landscape of work. More specifically, this article addresses the following question: What is the role of digital work in the new normal way of working of white-collar and blue-collar workers? To address this question, we have analyzed a sample of 206 398 responses from an employee satisfaction survey conducted in a pre-digital [START_REF] Sebastian | How big old companies navigate digital transformation[END_REF] industrial international company employing more than 110 000 workers (60% blue collar and 40% white collar). The responses were collected by the company's Human Resources Department all through the Covid-19 crisis: 2020 (beginning of the crisis), 2021 (during the crisis) and 2022 (after the crisis).

Our research has two main contributions. The first is theoretical, as our work contributes to understand the employees' perception of digital work in the new normal way of working. The second contribution is methodological, as we have structured a textual data analysis method [START_REF] Garnier | Analyse des données textuelles[END_REF][START_REF] Moscarola | Quantitative and Qualitative Methods[END_REF] based on Sphinx IQ3 and DataViv software [START_REF] Boughzala | Sphinx Quali : Un nouvel outil d'analyses textuelles et sémantiques[END_REF].

Context & background

A study conducted in an international industrial context

This study is part of a PhD initiated in May 2021 within the HR Department of a large industrial group. This company is a leader in its industrial field with a presence in over 30 countries. The organization employs more than 110 000 employees, 60% work in industrial production-related jobs (blue-collar) while the remaining 40% are office workers, with an "intellectual" occupation (white-collar). Over the past few years, the company has conducted an annual employee satisfaction survey. In total, employees are requested to answer more than sixty closed-ended questions on more than 10 dimensions including different aspects of work such as: customer, leadership, respect for people, quality of worklife, career & development, and digital work. The survey then concludes with two openended questions: (1) Please tell us one improvement requested during the past year, (2) Please tell us the most positive experience you've had in the past year. These last two questions invite employees to share their perceptions of their work, either by taking up a dimension of the survey or by highlighting new themes. These responses therefore appear to be adequate to answer our research question. This enables us to study the role of digital work in the new normal way of working.

The role of digital work in the new normal

The Covid-19 pandemic has forced organizations into rapid a "big bang" adoption of "tech-driven" practices under severe time pressure [START_REF] Carroll | Normalising the "new normal" : Changing tech-driven work practices under pandemic time pressure[END_REF]. The pandemic has had massive implications for the nature of work and the role technology plays within the workplace [START_REF] Carroll | Normalising the "new normal" : Changing tech-driven work practices under pandemic time pressure[END_REF]. Further, Information Technology has played "a central role" in many aspects of the pandemic, including "behavioral, temporal, societal, and organizational" (Ågerfalk et al., 2020) although the belief that "technology is the remedy of all things", has also been criticized [START_REF] Zilber | Technology in the time of corona : A critical institutional reading[END_REF]. This central role of technology is especially induced by the massive introduction of remote work. Even though, many organizations found themselves introducing remote working practices with very little time to plan, consider alternative options, and set-up remote working with their employer and manager (Ågerfalk et al., 2020); the Covid-19 pandemic has established remote work as the new normal. Our work builds upon recent studies on digital work. This is a broad concept that still lacks a commonly accepted definition [START_REF] Messenger | Three generations of Telework : New ICTs and the (R)evolution from Home Office to Virtual Office[END_REF][START_REF] Duan | An Integrated Framework for Understanding Digital Work in Organizations[END_REF]. Based on a systematic literature review, [START_REF] Wibowo | Understanding Digital Work and its Use in Organizations from a Literature Review[END_REF] propose the following definition of digital work "work arrangement between individuals and organizations for performing job-related tasks using digital technologies through processing diverse kinds of data from remote location". They then detail this definition with four characteristics: Use of Technology, Remote Location, Flexible Working Hours and Contractual Arrangements. [START_REF] Baiyere | Digital Work : A Conceptual Clarification[END_REF] recently provide another perspective with a typology of digital work arguing that digital work requires three rationales to be fulfilled: process (How?), outcome (What?), and objective (Why?). Based on this, the authors highlight three variationsdigital enabled work, digital engaged work, and digital embedded work. In this paper we focus on digital enabled work.

Nevertheless, there is a theoretical gap in the literature that seems to exclude blue-collar workers from debate. For this paper, we will then focus on the following definition: "digital work is the use of digital technologies in the process of work" [START_REF] Mrass | Towards a Taxonomy of Digital Work[END_REF]. Finally, though this research we aim at exploring the role of digital work in white-collar ways of working, and in blue-collar workers' who are part of these same organizations.

Method

Alongside the development of Web 2.0, social networks, and Big Data, we notice the development of textual data analysis software to meet the new needs and requirements, in terms of data, of researchers and companies, such as DataViv or N-vivo software [START_REF] Garnier | Analyse des données textuelles[END_REF][START_REF] Mothe | L'analyse de données textuelles assistée par ordinateur. Les discours sur les réseaux de chaleur[END_REF]. Given that our corpus of responses was sizable, we used Sphinx IQ3 and DataViv software. Textual data analysis is "all approaches, methods and computer tools that aim to discover the information contained in a textual corpus" (Boughzala et al., 2014, p. 1-2). The objective is to qualify the essential elements of a corpus using lexical and/or semantic categories and to quantify them by analyzing the statistical distribution of the corpus elements. Our textual data analysis method is divided into two phases: (3.1) the sampling approach and (3.2) the thesaurus design and the top-down hierarchical classifications.

The sampling approach: identification of a significant and calibrated sample

The objective of this first methodological phase is to identify a subset of the sample that is significant, documented, and calibrated. Our sampling approach was conducted in several steps defined below.

(1) Selection of expert responses: among the 206 398 responses, we excluded answers of less than 10 words. We consequently retained 117 313 responses qualified as 'expert' because they are long enough, documented, and they commonly develop multiple and varied points of view. (2) From answer to sentence granularity: we subsequently split the expert responses into sentences. Each answer is made up of several sentences which can represent several ideas. This step is necessary because within the same answer, several complementary or contradictory arguments can be found. The granularity of the sentence is therefore closer to the idea and thus allows a better identification of emerging themes. The sample is therefore composed of 227 732 sentences. (3) Selection of significative sentences: among these sentences, we excluded sentences containing no verb or sentences of less than 10 words. This allows us to retain 177 541 fully constructed and documented sentences. (4) Sample calibration: at this stage the sample is uncalibrated. For example, we had more white-collar sentences in 2020 for the positive experience question than blue collar sentences in 2021 for the improvement question. Given our objective in this article, which is to compare the expectations of white-and blue-collar workers over the period 2020 to 2022, we calibrated the sample. Having reached saturation in terms of responses, we were able to perform this calibration. The calibration is a random selection from the sample of significant sentences, in order to obtain as many responses as possible for the two context variables studied: socio-professional category (blue-and white-collar workers), year (2020, 2021 and 2022), question (improvement requested and positive experience). We finally identified a significant sentences sample of 82 848 sentences, in other words 6 904 sentences per sub-population.

Thesaurus design and top-down hierarchical classification

The objective of this second phase is to create a thesaurus to extract sentences related to our research question and then structure the data to make the corpus intelligible.

In the Information System field, the "thesaurus" is a vague concept, referring to synonym dictionaries, analog dictionaries, document dictionaries, semantic networks or networks, or more complex structures such as ontologies (Da Sylva, 2015, p. 150). The use of the thesaurus offers many advantages, one of them is useful for our extraction. The thesaurus solves the problem of expressing the same concept in different ways. For example, it allows a program to recognize that, the two strings of characters c-o-m-p-u-t-e-r and l-a-p-t-o-p express the same concept. As a result, the thesaurus feature allows us to extract sentences from a corpus based on a selection of words. For this paper, we needed to extract all the sentences related to digital work. To design this thesaurus, we selected words from a list of words occurring at least 50 times in our corpus. For each word, there are two possibilities:

(1) if the word refers necessarily to digital work, it is selected in our thesaurus (e.g. "teleworking", "software", "digitalize"); (2) otherwise, the word is excluded (e.g. "employee", "collaboration", etc., which can refer to other concepts, so they are not taken into account). The thesaurus designed at this phase allowed us to extract a sample of 3 749 sentences related to digital work.

After extracting a corpus of sentences related to our research object, a manual coding (Thiétart, 2014, p. 555-559) would have been time consuming, so we conducted a top-down hierarchical classification on this sample [START_REF] Reinert | Une méthode de classification descendante hiérarchique : Application à l'analyse lexicale par contexte[END_REF][START_REF] Moscarola | Recherche Qualitative : Analyse lexicale et sémantique de grands corpus d'entretiens ou de documents[END_REF]. This classification is based on a sequence of multiple factorial analyses, dividing the elementary meaning units (sentences) of a corpus into two classes composed of similar elements in terms of the words that compose them. The class with the largest number of meaning units is then divided into two classes by a new factorial analysis. This process continues by dividing at each step the largest class. Finally, it stops when the class with the highest number of units is too small to be divided again or when a fixed number of classes is reached. Concretely, the top-down hierarchical classification gathers sentences with a similar meaning to identify emerging themes. However, given the size of the sample there is still a large thematic diversity within each class. At this stage, we can't read all the sentences of a class to identify a common theme. We therefore proceeded to a second classification on each class.

Results and discussion

Our textual data analysis method highlights the following initial findings. The place of digital work in employees' discourse on their work is modest. The digital thesaurus extracted 3 749 sentences on the sample of 82 848 sentences (i.e 4,5%). The first level top- The second class addresses the need of digitalization of work practices (31%). The last class is related to the technological dimension needs (device, software, system) (20%).

Next steps

The next steps will consist in exploring the three emerging classes. To that end, we will study the level 2 top-down hierarchical classifications that divide each class into multiple sub-classes. This will allow us to identify the specific themes mentioned by the employees. An initial exploration of the teleworking class highlighted the positive impact of teleworking on white-collar workers in several areas, such as work-life balance, flexibility of working hours, work environment, etc. It would therefore be interesting in the next steps to identify the dimensions impacted by the introduction of telework among white-collar workers, and then to carry out a comparative analysis with blue-collar workers' perceptions on these same dimensions. There seems to be a gap between the two populations, with bluecollar workers showing a deterioration in the dimensions mentioned above.

Figure 1 :

 1 Figure 1: Top-down hierarchical classification of digital work corpus