domain: chim chim.cata sde

text:
Pascal Raybaud
email: pascal.raybaud@ifpen.fr

Keywords: MoS2 catalyst, -alumina, activation, sulfidation, reduction, diffusion, growth, Mo-oxide, oxysulfide, MoS3, density functional theory, mechanism

The molecular-scale understanding of the genesis of the MoS2 phase from Mooxide precursors by sulfo-reduction supported on alumina is highly challenging with a strong impact on the activation process of heterogeneous industrial catalysts. By means of density functional theory (DFT), we quantify the activation free energies of the elementary steps involved in the sulfo-reduction mechanisms of Mo-trioxide oligomers and the stability of the corresponding Mo-oxysulfide intermediates supported on the -alumina (100) surface. The Gibbs free energy profiles highlight the characteristic chemical reactivity of various oxygen sites involved in the O/S exchange mechanism and reveal that that interfacial oxygen atoms (Mo-O-Al) are the most challenging sites to be exchanged with S. We quantitatively compare the two main paths proposed experimentally: the one involving Mo-oxysulfide and Mo-trisulfide intermediates and the second one involving only Mo-oxysulfide. While O/S exchange requires moderate activation energies, the rate-determining steps correspond to S-and O-removal on small MonO3n-xSx or MonS3n (n≤3) oligomeric intermediates. To overcome these high energy steps, the small Mo-trisulfide (MonS3n) oligomers are proposed to be fast diffusing surface species and to promote the growth process towards the targeted MoS2 phase. A reconstruction from chain to triangular Mo3S9 conformer also facilitates this phase transformation.

Introduction

MoS2 based materials represent a wide interest for various catalytic and electrocatalytic applications such as hydrodesulfurization process, hydrogen evolution reaction, etc. However, the catalytic performances strongly depend on the sulfidation state of Mo resulting from the preparation steps. [START_REF] Toulhoat | Catalysis by transition metal sulphides: From molecular theory to industrial application[END_REF] More particularly, the final activation step is crucial for the genesis of the targeted disulfided Mo active phase from its Mo-oxide precursors deposited on a support (such as -alumina (-Al2O3), [START_REF] Euzen | Alumina[END_REF][START_REF] Breysse | Overview of support effects in hydrotreating catalysts[END_REF][START_REF] Breysse | Recent studies on the preparation, activation and design of active phases and supports of hydrotreating catalysts[END_REF] anatase-TiO2, [START_REF] Ramirez | Hydrodesulphurization activity and characterization of sulphided molybdenum and cobalt-molybdenum catalysts comparison of alumina-, silica-alumina-and titania-supported catalysts[END_REF] amorphous silica (SiO2), [START_REF] Huirache-Acuña | SBA-15 Mesoporous Silica as Catalytic Support for Hydrodesulfurization Catalysts-Review[END_REF] and amorphous silica-alumina) [START_REF] Ramirez | Hydrodesulphurization activity and characterization of sulphided molybdenum and cobalt-molybdenum catalysts comparison of alumina-, silica-alumina-and titania-supported catalysts[END_REF] after impregnation, drying, or calcination. This activation involves a sulforeduction process with either H2/H2S gas phase (laboratory scale) or organo-sulfur compounds in a liquid phase (industrial scale) at elevated temperature (350°C). [START_REF] Toulhoat | Catalysis by transition metal sulphides: From molecular theory to industrial application[END_REF][START_REF] Texier | Activation of alumina-supported hydrotreating catalysts by organosulfides or H2S: Effect of the H2S partial pressure used during the activation process[END_REF][START_REF] Lesage | High pressure cell for edge jumping X-ray absorption spectroscopy: Applications to industrial liquid sulfidation of hydrotreatment catalysts[END_REF][9] In the latter case, the sulfidation starts only after the liquid organo-sulfur compound decomposed into H2S. [START_REF] Lesage | High pressure cell for edge jumping X-ray absorption spectroscopy: Applications to industrial liquid sulfidation of hydrotreatment catalysts[END_REF][START_REF] Eijsbouts | Changes of MoS2 Morphology and the Degree of Co Segregation during the Sulfidation and Deactivation of Commercial Co-Mo/Al2O3 Hydroprocessing Catalysts[END_REF][START_REF] Frizi | Genesis of new gas oil HDS catalysts: Study of their liquid phase sulfidation[END_REF][START_REF] Van Haandel | Influence of sulfiding agent and pressure on structure and performance of CoMo/Al2O3 hydrodesulfurization catalysts[END_REF] Therefore, to improve the resulting properties of these catalysts, it remains critical to better understand at a molecular scale how the MoS2 active phase is engendered from its oxide precursors. Even though the activation step of -alumina supported molybdenum oxide precursor by sulfo-reductive treatment has been the subject of many spectroscopic studies, [START_REF] Chang | Infrared and Raman studies of amorphous MoS3 and poorly crystalline MoS2[END_REF][START_REF] Cramer | EXAFS studies of amorphous molybdenum and tungsten trisulfides and triselenides[END_REF][START_REF] Cattaneo | A Quick EXAFS Study of the Sulfidation of NiMo/SiO2 Hydrotreating Catalysts Prepared with Chelating Ligands[END_REF][START_REF] Weber | Basic Reaction Steps in the Sulfidation of Crystalline MoO3 to MoS2, As Studied by X-ray Photoelectron and Infrared Emission Spectroscopy[END_REF][START_REF] Rochet | Co-K and Mo-K edges Quick-XAS study of the sulphidation properties of Mo/Al2O3 and CoMo/Al2O3 catalysts[END_REF][START_REF] Rochet | Intermediate Species Revealed during Sulfidation of Bimetallic Hydrotreating Catalyst[END_REF] several mechanistic questions remain open regarding the nature of the Mo-oxysulfides (MoOxSy) and Mo-trisulfide (MoS3) intermediates, the reaction pathways, and the kinetically limiting steps (Figure 1). The oxidation state of Mo changes from VI, to V and IV during the activation process, corresponding to widely invoked MoOxSy [START_REF] Texier | Activation of alumina-supported hydrotreating catalysts by organosulfides or H2S: Effect of the H2S partial pressure used during the activation process[END_REF][START_REF] Cattaneo | A Quick EXAFS Study of the Sulfidation of NiMo/SiO2 Hydrotreating Catalysts Prepared with Chelating Ligands[END_REF][START_REF] Weber | Basic Reaction Steps in the Sulfidation of Crystalline MoO3 to MoS2, As Studied by X-ray Photoelectron and Infrared Emission Spectroscopy[END_REF][START_REF] Leliveld | The Sulfidation of γ-Alumina and Titania Supported (Cobalt)Molybdenum Oxide Catalysts Monitored by EXAFS[END_REF][START_REF] Arnoldy | Temperature-programmed sulfiding of MoO3/Al2O3 catalysts[END_REF] and MoS3 [START_REF] Cattaneo | A Quick EXAFS Study of the Sulfidation of NiMo/SiO2 Hydrotreating Catalysts Prepared with Chelating Ligands[END_REF][START_REF] Rochet | Co-K and Mo-K edges Quick-XAS study of the sulphidation properties of Mo/Al2O3 and CoMo/Al2O3 catalysts[END_REF][START_REF] Rochet | Intermediate Species Revealed during Sulfidation of Bimetallic Hydrotreating Catalyst[END_REF][START_REF] Weber | Structure of Amorphous MoS3[END_REF][START_REF] Cattaneo | An XAFS Study of the Different Influence of Chelating Ligands on the HDN and HDS of γ-Al2O3-Supported NiMo Catalysts[END_REF][START_REF] Nicosia | The effect of phosphate and glycol on the sulfidation mechanism of CoMo/Al2O3 hydrotreating catalysts[END_REF][START_REF] Payen | Genesis and characterization by laser Raman spectroscopy and high-resolution electron microscopy of supported molybdenum disulfide crystallites[END_REF] intermediates. These intermediates are complex amorphous compounds often well dispersed on -alumina. Identifying molecular structures for these amorphous compounds remains challenging. For instance, a wide structural diversity exists for the MoS3 polymorphs as a function of size even without support effects. [START_REF] Sahu | Size-Dependent Structural, Energetic, and Spectroscopic Properties of MoS3 Polymorphs[END_REF] The structural insights for Mo oxysulfides is even more elusive, particularly in the presence of the alumina support.

Considering the respective role of H2S and H2 as potential reactants during sulfo-reduction of alumina-supported Mo-oxide, H2 consumption was observed at high temperature only during temperature-programmed reduction (TPR). At the same time, H2S uptake was seen at low temperatures in temperature-programmed sulfidation (TPS). [START_REF] Texier | Activation of alumina-supported hydrotreating catalysts by organosulfides or H2S: Effect of the H2S partial pressure used during the activation process[END_REF][START_REF] Leliveld | The Sulfidation of γ-Alumina and Titania Supported (Cobalt)Molybdenum Oxide Catalysts Monitored by EXAFS[END_REF][START_REF] Arnoldy | Temperature-programmed sulfiding of MoO3/Al2O3 catalysts[END_REF] Furthermore, it has been shown that H2S is the key reactant to allow the formation of the MoS2 phase even without H2 uptake at an early stage. [START_REF] Texier | Activation of alumina-supported hydrotreating catalysts by organosulfides or H2S: Effect of the H2S partial pressure used during the activation process[END_REF][START_REF] Leliveld | The Sulfidation of γ-Alumina and Titania Supported (Cobalt)Molybdenum Oxide Catalysts Monitored by EXAFS[END_REF][START_REF] Arnoldy | Temperature-programmed sulfiding of MoO3/Al2O3 catalysts[END_REF][START_REF] Payen | Genesis and characterization by laser Raman spectroscopy and high-resolution electron microscopy of supported molybdenum disulfide crystallites[END_REF][START_REF] Baubet | Quantitative Two-Dimensional (2D) Morphology-Selectivity Relationship of CoMoS Nanolayers: A Combined High-Resolution High-Angle Annular Dark Field Scanning Transmission Electron Microscopy (HR HAADF-STEM) and Density Functional Theory (DFT) Study[END_REF] In a second stage, the observed release of a substantial quantity of H2S may feature the conversion of Mo-trisulfide intermediates into Mo-disulfide phase through H2 reduction. [START_REF] Cattaneo | A Quick EXAFS Study of the Sulfidation of NiMo/SiO2 Hydrotreating Catalysts Prepared with Chelating Ligands[END_REF][START_REF] Weber | Basic Reaction Steps in the Sulfidation of Crystalline MoO3 to MoS2, As Studied by X-ray Photoelectron and Infrared Emission Spectroscopy[END_REF][START_REF] Rochet | Co-K and Mo-K edges Quick-XAS study of the sulphidation properties of Mo/Al2O3 and CoMo/Al2O3 catalysts[END_REF][START_REF] Rochet | Intermediate Species Revealed during Sulfidation of Bimetallic Hydrotreating Catalyst[END_REF][START_REF] Weber | Structure of Amorphous MoS3[END_REF][START_REF] Nicosia | The effect of phosphate and glycol on the sulfidation mechanism of CoMo/Al2O3 hydrotreating catalysts[END_REF] Therefore, if the MoS3 intermediate is involved, the activation process is proposed to occur in two stages: O/S exchange with H2S [START_REF] Arnoldy | Temperature-programmed sulfiding of MoO3/Al2O3 catalysts[END_REF][START_REF] Scheffer | Sulfidability and HDS activity of Co-Mo/Al2O3 catalysts[END_REF] leading to the MoS3-phase [START_REF] Cattaneo | A Quick EXAFS Study of the Sulfidation of NiMo/SiO2 Hydrotreating Catalysts Prepared with Chelating Ligands[END_REF][START_REF] Payen | Genesis and characterization by laser Raman spectroscopy and high-resolution electron microscopy of supported molybdenum disulfide crystallites[END_REF][START_REF] Muijsers | Sulfidation Study of Molybdenum Oxide Using MoO3/SiO2/Si(100) Model Catalysts and Mo3 IV -Sulfur Cluster Compounds[END_REF] from MoO3-like species (steps I and II in Figure 1), followed by its transformation to MoS2 phase thanks to H2 reduction (step IV). However, at this stage, the possibility of direct reduction of oxysulfide to disulfide phase cannot be (step III) ruled out. For these reasons, our study will focus on the key role of H2S only as sulfiding agent in steps I, II, and by considering the possible role of H2 at a latter stage in steps III and IV.

Thus, identifying and characterizing Mo-oxysulfides intermediate remains crucial but challenging from an experimental point of view. In particular, in situ EXAFS enabled to follow the evolution of bond lengths such as Mo-O, Mo-S, Mo-Mo [START_REF] Lesage | High pressure cell for edge jumping X-ray absorption spectroscopy: Applications to industrial liquid sulfidation of hydrotreatment catalysts[END_REF][START_REF] Rochet | Co-K and Mo-K edges Quick-XAS study of the sulphidation properties of Mo/Al2O3 and CoMo/Al2O3 catalysts[END_REF][START_REF] Rochet | Intermediate Species Revealed during Sulfidation of Bimetallic Hydrotreating Catalyst[END_REF] and to reveal some key intermediates such as MoOxSy and MoS3. Time-resolved XAS and Raman spectroscopy on Ni promoted MoS2 catalyst supported on Al2O3 provided critical insights on such intermediates by chemometric multivariate curve regression with altering least-squares (MCR-ALS) method. [START_REF] Rochet | Influence of the Preparation Conditions of Oxidic NiMo/Al2O3 Catalysts on the Sulfidation Ability: A Quick-XAS and Raman Spectroscopic Study[END_REF] Interestingly, the molecular models of MoOxSy intermediates proposed by EXAFS are constituted from dimeric or trimeric Mo clusters. The XAS analysis also enabled to distinguish specific Mo-oxysulfide intermediates depending on gas phase or liquid sulfidation protocol. [START_REF] Lesage | High pressure cell for edge jumping X-ray absorption spectroscopy: Applications to industrial liquid sulfidation of hydrotreatment catalysts[END_REF] Another interesting trend revealed by in-situ XAS is that during liquid phase sulfidation, the delayed sulfidation temperature induces a depolymerization of the polyoxomolybdate precursor between 80 to 230°C. [START_REF] Lesage | High pressure cell for edge jumping X-ray absorption spectroscopy: Applications to industrial liquid sulfidation of hydrotreatment catalysts[END_REF] Hence, small Mo-oxide oligomers (as small as dimers or trimers) highly dispersed on the support are formed and will be the relevant oxide species involved in sulfidation. For that reason, as also explained in what follows, we will consider such small Mooxide oligomers as the starting species for the simulation of sulfo-reduction mechanisms.

Also, the disappearance of some characteristic top oxo-species Mo-Ot and the appearance of disappear more rapidly than Mo-O-Mo species. [START_REF] Weber | Basic Reaction Steps in the Sulfidation of Crystalline MoO3 to MoS2, As Studied by X-ray Photoelectron and Infrared Emission Spectroscopy[END_REF] This analysis also seems to differentiate the behavior of bulk crystalline MoO3 from the one dispersed catalyst.

Lastly, transmission electron microscopy (TEM) highlighted that the sulfidation process occurs through a layer-by-layer growing process involving the diffusion of presumably small Mooxysulfides or sulfides species on the support. [START_REF] Hansen | Growth Mechanism for Single-and Multi-Layer MoS2 Nanocrystals[END_REF] The nature and role of such small Mo-entities remain to be elucidated.

Very few density functional theory (DFT) studies addressed the sulfidation process of Mooxide supported on alumina. Some DFT investigations analyzed the interactions of Mo, or Woxide clusters of various sizes support by Al2O3, [START_REF] Handzlik | Structure of Isolated Molybdenum(VI) Oxide Species on γ-Alumina: A Periodic Density Functional Theory Study[END_REF][START_REF] Handzlik | Structure of Dimeric Molybdenum(VI) Oxide Species on γ-Alumina: A Periodic Density Functional Theory Study[END_REF] TiO2, [START_REF] Hamraoui | Computational Investigation of TiO2-Supported Isolated Oxomolybdenum Species[END_REF][START_REF] Hamraoui | Structure and reducibility of titania-supported monomeric and dimeric molybdenum oxide entities studied by DFT calculations[END_REF][START_REF] Tougerti | Synergy between XANES Spectroscopy and DFT to Elucidate the Amorphous Structure of Heterogeneous Catalysts: TiO2-Supported Molybdenum Oxide Catalysts[END_REF][START_REF] Hu | Investigation of the Reducibility of Supported Oxomolybdate Species for Mapping of Active Centers of Partial Oxidation Reaction: In Situ Mo K-Edge XAS and DFT Study[END_REF] and SiO2. [START_REF] Kiani | Existence and Properties of Isolated Catalytic Sites on the Surface of β-Cristobalite-Supported, Doped Tungsten Oxide Catalysts (WOx/β-SiO2, Na-WOx/β-SiO2, Mn-WOx/β-SiO2) for Oxidative Coupling of Methane (OCM): A Combined Periodic DFT and Experimental Study[END_REF] Several plausible mono-oxo and di-oxo Mo centers were proposed for Mo1O3, and Mo2O6 species on alumina (100) and (110) surfaces using DFT calculations. [START_REF] Handzlik | Structure of Isolated Molybdenum(VI) Oxide Species on γ-Alumina: A Periodic Density Functional Theory Study[END_REF][START_REF] Handzlik | Structure of Dimeric Molybdenum(VI) Oxide Species on γ-Alumina: A Periodic Density Functional Theory Study[END_REF] DFT was also applied to investigated the stability and interaction mode of the final sulfided MoS2 clusters on -alumina and TiO2 surface, revealing Mo-O-Al(Ti) chemical bridges. [START_REF] Arrouvel | A density functional theory comparison of anatase (TiO2)-and γ-Al2O3-supported MoS2 catalysts[END_REF][START_REF] Costa | Edge wetting effects of γ-Al2O3 and anatase-TiO2 supports by MoS2 and CoMoS active phases[END_REF] Also, the thermochemistry of sulfur-oxygen exchange at the edges of the MoS2 nano-crystallite to identify the possible residual Mo-O chemical bonds after sulfidation using DFT suggested that the MoS2 edge is the most difficult to sulfide and maybe the location of residual oxidized Mo sites. [START_REF] Hinnemann | A Density Functional Study of the Chemical Differences between Type I and Type II MoS2-Based Structures in Hydrotreating Catalysts[END_REF] Similarly, the sulfur/oxygen exchange was predicted to occur in the long-run on the MoS2 edges under electrocatalytic conditions such as hydrogen evolution reaction (HER). [START_REF] Abidi | How Stable Are 2H-MoS2 Edges under Hydrogen Evolution Reaction Conditions?[END_REF] The dissociative adsorption of H2S was investigated on multilayers of the α-MoO3 phase deposited on two different -alumina models by using DFT. The reactivity of the monolayer of MoO3 deposited on the surface of non-spinel -alumina was shown to be highest due to charge transfer from alumina to the MoO3 monolayer. [START_REF] Yu | Interfacial stability, electronic property, and surface reactivity of α-MoO3/γ-Al2O3 composites[END_REF] Other quantum simulation studies attempted to rationalize the O/S exchange thermodynamics of bulk, [START_REF] Shahrokhi | On the understanding of the optoelectronic properties of S-doped MoO3 and O-doped MoS2 bulk systems: a DFT perspective[END_REF] monolayer or large clusters of MoO3. [START_REF] Hong | Sulfurization of MoO3 in the Chemical Vapor Deposition Synthesis of MoS2 Enhanced by an H2S/H2 Mixture[END_REF][START_REF] Shi | Theoretical Cluster Studies on the Catalytic Sulfidation of MoO3[END_REF][START_REF] Misawa | Reactivity of Sulfur Molecules on MoO3 (010) Surface[END_REF] In general, it was found that replacing the terminal oxo-site by sulfur is more feasible (through vacancy formation) and exothermic in nature than the O/S exchange for bridging (two fold) or tridentate oxygen sites. Moreover, O-vacancy creation increases the reactivity of sulfiding agents (H2S or S2), which means that the use of hydrogen would enhance the sulfidation rate. As more terminal oxygens are being replaced by sulfur, they can form Sdimers leading to a stabilization of the system. [START_REF] Shi | Theoretical Cluster Studies on the Catalytic Sulfidation of MoO3[END_REF] Thermodynamic trends in thiolysis energies of Mo oxide precursors as a function of various supports (including alumina) analyzed by DFT calculations on small molecular clusters showed an appealing correlation between thiolysis energy descriptor and sulfidation degree and/or dispersion, [START_REF] Joshi | Support effects in HDS catalysts[END_REF] although no kinetic analysis was provided by this study and the realism of the small cluster models remains questionable. We have chosen to consider the sulfidation of small MonO3n oligomers (n=1, 2, and 3) deposited on the (100) -alumina surface since this surface have been suggested to have a higher degree of sulfidation than other planes of alumina. [START_REF] Bara | Aqueous-Phase Preparation of Model HDS Catalysts on Planar Alumina Substrates: Support Effect on Mo Adsorption and Sulfidation[END_REF][START_REF] Garcia De Castro | Surface-Dependent Activation of Model α-Al2O3-Supported P-Doped Hydrotreating Catalysts Prepared by Spin Coating[END_REF] The MonO3n oligomers have been suggested to be present on numerous oxide support (including alumina) [START_REF] Handzlik | Active sites of olefin metathesis on molybdena-alumina system[END_REF][START_REF] Ohler | Study of the Elementary Processes Involved in the Selective Oxidation of Methane over MoOx/SiO2[END_REF][START_REF] Fierro | Metal Oxides: Chemistry and applications[END_REF][START_REF] Stencel | Raman spectroscopic investigation of the effect of H2O on the molybdenum surface species in MoO3-Al2O3 catalysts[END_REF][START_REF] Hu | Surface Structures of Supported Molybdenum Oxide Catalysts[END_REF][START_REF] Xiong | Surface Coordination Structure of Molybdate with Extremely Low Loading on γ-Alumina Characterized by UV Resonance Raman Spectroscopy[END_REF][START_REF] Desikan | Structure and dispersion of molybdenum oxide supported on alumina and titania[END_REF][START_REF] Mestl | Raman Spectroscopy of Monolayer-Type Catalysts[END_REF] under various thermal conditions. Moreover, the Mo-oxysulfides intermediates formed in the course of sulfidation are also reported by EXAFS analysis to exhibit a very small Mo-Mo coordination number corresponding to such dimers or trimers. [START_REF] Leliveld | The Sulfidation of γ-Alumina and Titania Supported (Cobalt)Molybdenum Oxide Catalysts Monitored by EXAFS[END_REF][START_REF] Rochet | Influence of the Preparation Conditions of Oxidic NiMo/Al2O3 Catalysts on the Sulfidation Ability: A Quick-XAS and Raman Spectroscopic Study[END_REF] As mentioned before, small Mo-oxides oligomers result from the depolymerization of polyoxomolybdates in high-temperature liquid phase sulfidation. [START_REF] Lesage | High pressure cell for edge jumping X-ray absorption spectroscopy: Applications to industrial liquid sulfidation of hydrotreatment catalysts[END_REF] Finally, Mo-oxide trimers supported on alumina exhibit various types of Ospecies (top-oxo, bridging oxo, O-interfacial). These O-sites might feature characteristic reactivities towards H2S and H2, informing about the most O/S exchange-resisting sites encountered in the real experimental system.

We will thus investigate the interaction of small Mo-trioxide precursors with alumina and their sulfidation using H2S and H2 as key reactants. We will address the kinetic and thermodynamic aspects of sulfo-reduction and corresponding Mo-oxysulfide or trisulfide intermediates along the main path depicted in Figure 1. Finally, we will also discuss the effect of size, diffusion, and growth during this whole process.

Computational details

For all total energy calculations, density functional theory (DFT) as implemented in VASP [START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF][START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF] has been used relying on the Perdew-Burke-Ernzerhof (PBE) [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] functional within the framework of generalized gradient approximation (GGA). The long-range London dispersion interactions were included through a density-dependent dispersion correction (dDsC). [START_REF] Steinmann | A generalized-gradient approximation exchange hole model for dispersion coefficients[END_REF][START_REF] Steinmann | Comprehensive Benchmarking of a Density-Dependent Dispersion Correction[END_REF] The projector augmented-wave (PAW) method [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] was chosen to describe the electron-ion interaction. The kinetic energy cut-off for the plane-wave basis set has been fixed at 400 eV. For the minimization of the electronic energy, Gaussian smearing with a width of 0.2 eV was chosen.

A mixture of the blocked-Davidson scheme and residual minimization method direct inversion in the iterative subspace has been applied. Spin-polarized calculations were performed to obtain the ground state of the clusters. By scrupulously varying the difference of two spin components, we examined the spin effect, but the ground states remained nonmagnetic. Electronic convergence was assumed to be achieved at 10 -6 eV. For geometry optimization, the conjugate gradient algorithm was used. Geometric convergence cut-off has been set to 0.02 eV/Å.

For frequency calculations, the structures have been optimized with tighter convergence criteria: 10 -7 eV for electronic properties and maximum gradients below 0.01 eV/Å. The finite difference method has been used to calculate the frequencies and the density functional perturbation theory (DFPT) method to simulate the infra-red (IR) spectra within the framework of dipole approximation as implemented in VASP. [START_REF] Gajdoš | Linear optical properties in the projector-augmented wave methodology[END_REF][START_REF] Karhánek | A density-functional study of the adsorption of methane-thiol on the (111) surfaces of the Ni-group metals[END_REF][START_REF] Brüesch | Phonons: Theory and Experiments II: Experiments and Interpretation of Experimental Results[END_REF] For systems where both methods have been applied, they are found to give consistent results. To avoid the peaks from alumina support, we have only simulated the modes concerning the cluster and bonded or weakly interacting part of underneath alumina.

For determining the reaction energy (𝛥𝐸) of various reaction steps on alumina at 0 K, the following formal equation was used:

𝚫𝐆 = 𝐆(𝐏 𝐬𝐮𝐫𝐟𝐚𝐜𝐞 ) + 𝐆(𝐏 𝐠𝐚𝐬 ) -𝐆(𝐑 𝐬𝐮𝐫𝐟𝐚𝐜𝐞 ) -𝐆(𝐑 𝐠𝐚𝐬 ) (1)
where 𝐆(𝐑 𝐬𝐮𝐫𝐟𝐚𝐜𝐞 ) (respectively 𝐆(𝐏 𝐬𝐮𝐫𝐟𝐚𝐜𝐞 )) is the Gibbs free energy of the reactant (respectively product) adsorbed on the "catalytic surface", and 𝐆(𝐑 𝐠𝐚𝐬 ) (respectively 𝐆(𝐏 𝐠𝐚𝐬 )) is the Gibbs free energy of the reactant (respectively product) in the gas phase. The detailed equations of each considered reaction are reported in Supporting Information S1.

This study focused on the (100) surface of -alumina (Figure S1). This slab has been constructed following the procedure by Digne et al. [START_REF] Digne | Hydroxyl Groups on γ-Alumina Surfaces[END_REF][START_REF] Digne | Use of DFT to achieve a rational understanding of acid-basic properties of γ-alumina surfaces[END_REF] according to the bulk alumina model defined by Krokidis et al.. [START_REF] Krokidis | Theoretical Study of the Dehydration Process of Boehmite to γ-Alumina[END_REF] Moreover, it has been shown that in sulfur-reduction conditions as encountered in this work, the surface remains dehydrated and is not sulfided. [START_REF] Arrouvel | Effects of PH2O, PH2S, PH2 on the surface properties of anatase-TiO2 and γ-Al2O3: a DFT study[END_REF] We have relaxed the first two layers of the surface, and the bottom two layers have been kept fixed.

Once the most stable adsorption sites for the Mo-oxide clusters are identified on the surface, we assume that the adsorbed cluster will not move or diffuse on the surface in the course of the sulfo-reduction mechanism. This assumption is based on the strong Mo-oxide or Mo-oxysulfide support interaction shown later in the results. This does not exclude that locally the anchoring sites evolve as a function of sulfidation.

During these sulfo-reduction steps into the final disulfides, we identify the limiting steps and corresponding activation energies. To determine the activation energy, we computed the energy of the transition state (TS). We used the Nudged Elastic Band (NEB) method in conjunction with constrained force-based optimizers to determine the geometry of the transition states (TS). [START_REF] Henkelman | Methods for Finding Saddle Points and Minimum Energy Paths[END_REF][START_REF] Henkelman | A climbing image nudged elastic band method for finding saddle points and minimum energy paths[END_REF][START_REF] Sheppard | Optimization methods for finding minimum energy paths[END_REF][START_REF] Heyden | Efficient methods for finding transition states in chemical reactions: Comparison of improved dimer method and partitioned rational function optimization method[END_REF] To generate the intermediate images between reactant and product, we used the Opt'npath open-source code. [START_REF] Fleurat-Lessard | Opt'n Path[END_REF] We performed the frequency calculations to confirm TS as a first-order saddle point on the potential energy surface with only one imaginary frequency, and that the imaginary mode corresponds to the restoring force along the direction from the TS to the reactant or product. We have used an open-source code to trace the reaction energy plots. [START_REF] Angnes | mechaSVG[END_REF] All aforementioned electronic energies were corrected by the contribution of zero-point energy, thermal corrections at T=623K (experimental temperature for sulfo-reduction), and entropy corrections in order to determine the vibrational free energy:

𝚫𝑮 = 𝚫𝑯 -𝑻𝚫𝑺 2 𝚫𝐇 = 𝚫𝐔 + 𝐏𝚫𝐕 3
𝚫𝐔(𝐒) = 𝚫𝐔(𝐒) 𝐞𝐥𝐞 + 𝚫𝐔(𝐒) 𝒗𝒊𝒃 + 𝚫𝐔(𝐒) 𝒓𝒐𝒕 + 𝚫𝐔(𝐒) 𝒕𝒓𝒂𝒏𝒔 4
We assumed that the MonO3n, MonOxS3n-x, and MonS3n oligomers are immobile on the alumina surface due to their strong chemical anchorage. We included the translational and rotational U(S) contributions for the gas-phase molecules H2O, H2S, and H2.

All free energy diagrams are plotted for 1 bar partial pressure of H2O, H2S, and H2. It is possible to include a correction on the thermodynamic reference levels of these molecules in gas phase induced by pressure effects as described in Supporting Information 1.

Results

Interaction of molybdenum oxides precursors with 𝜸-alumina

Based on the experimental insights described in the Introduction, we first explore the stability of monomeric (Mo1O3), dimeric (Mo2O6), and trimeric (Mo3O9) Mo-oxides dispersed on alumina. To determine the optimal interaction and the adsorption sites of -alumina, we systematically explored the energetic stability of these species on the (100) -alumina surface.

For Mo1O3 and Mo2O6, our results (Supporting Information 3.1) are mainly consistent with previous theoretical works. [START_REF] Handzlik | Structure of Isolated Molybdenum(VI) Oxide Species on γ-Alumina: A Periodic Density Functional Theory Study[END_REF][START_REF] Handzlik | Structure of Dimeric Molybdenum(VI) Oxide Species on γ-Alumina: A Periodic Density Functional Theory Study[END_REF] The Mo3O9 oligomer may exhibit two conformers in the gas phase: either cyclic or chain-like (Figure -S2 c andd), similar to the Mo3S9 (Mo-trisulfide)

cluster where the chain and triangular conformers are competing. [START_REF] Cramer | EXAFS studies of amorphous molybdenum and tungsten trisulfides and triselenides[END_REF][START_REF] Weber | Structure of Amorphous MoS3[END_REF][START_REF] Sahu | Size-Dependent Structural, Energetic, and Spectroscopic Properties of MoS3 Polymorphs[END_REF][START_REF] Liang | Amorphous MoS3 and WS3[END_REF][START_REF] Hibble | Modeling the structure of amorphous MoS3: a neutron diffraction and reverse Monte Carlo study[END_REF][START_REF] Hibble | Chemical excision from amorphous MoS3; a quantitative EXAFS study[END_REF][START_REF] Deng | Operando Raman Spectroscopy of Amorphous Molybdenum Sulfide (MoSx) during the Electrochemical Hydrogen Evolution Reaction[END_REF][START_REF] Jiao | The Structure and Possible Catalytic Sites of Mo3S9 as a Model of Amorphous Molybdenum Trisulfide[END_REF][START_REF] Hibble | Amorphous MoS3[END_REF] The cyclic conformer is more stable than the chain by about 0.86 eV in the gas phase (Figure S4), similar to our previous finding for Mo3S9 clusters. [START_REF] Sahu | Size-Dependent Structural, Energetic, and Spectroscopic Properties of MoS3 Polymorphs[END_REF] However, the strong support effect induces an inversion of the relative stability of the two conformers: the chain conformer becomes more stable by -0.42 eV on the (100) -alumina surface (Figure S6). The same support effect is also observed for Mo3S9 clusters, as discussed later. The support interaction enables the formation of new Mo-O-Al and Mo-Osurf bonds, which cauterizes the under-coordination of Mo-atoms in the chain and leads to a square-pyramidal environment for each Mo-atom (Supporting Information 3.2), while in the absence of support, the Mo atoms are all stabilized in the tetrahedral environment by Mo-O-Mo cyclization (Figure S2). This interaction with support also impacts the nature of oxygen atoms which will be involved in the sulfur/oxygen exchange process, as described in the following. . We found two competing Mo3O9 chain conformers (Figure S6a andS6b), but we will discuss in the main text only the most relevant one (Figure S6a) based on the sulfidation thermodynamics and kinetics consideration. This chain conformer exhibits two-terminal oxo (Ot) species, three bridgings (Obr), three interfacial bidentates (Oint(bi)), and one interfacial tridentate (Oint(tri)). All three Moatoms are penta-coordinated but possess distinct geometrical orientations. The central Mo-atom has an octahedral vacancy site; however, the terminal Mo-atoms have distorted square-pyramidal conformation. The details of the second conformer are given in Supporting Information 3.2.

The analysis of the local environment of Al and O sites on MonO3n oligomers (n=1, 2, and 3) is compatible with earlier experimental ones proposed for various catalytic systems (not only HDS), where molybdenum oxides are found in a highly dispersed form on various oxide surfaces and could even exist as isolated MoOx species after thermal treatment. [START_REF] Leliveld | The Sulfidation of γ-Alumina and Titania Supported (Cobalt)Molybdenum Oxide Catalysts Monitored by EXAFS[END_REF][START_REF] Handzlik | Active sites of olefin metathesis on molybdena-alumina system[END_REF][START_REF] Ohler | Study of the Elementary Processes Involved in the Selective Oxidation of Methane over MoOx/SiO2[END_REF][START_REF] Fierro | Metal Oxides: Chemistry and applications[END_REF][START_REF] Stencel | Raman spectroscopic investigation of the effect of H2O on the molybdenum surface species in MoO3-Al2O3 catalysts[END_REF][START_REF] Hu | Surface Structures of Supported Molybdenum Oxide Catalysts[END_REF][START_REF] Xiong | Surface Coordination Structure of Molybdate with Extremely Low Loading on γ-Alumina Characterized by UV Resonance Raman Spectroscopy[END_REF][START_REF] Desikan | Structure and dispersion of molybdenum oxide supported on alumina and titania[END_REF][START_REF] Mestl | Raman Spectroscopy of Monolayer-Type Catalysts[END_REF]

Oxygen/sulfur exchange for Mo3O9 on alumina

Thermodynamic considerations

The supported oxide oligomers are expected to undergo a sulfo-reduction process to form Mooxysulfides or Mo-trisulfides intermediates, followed by their further transformation (reduction) to the final Mo-disulfide phase. The cyclic conformers remain more stable in the gas phase than the chain along the entire sulfidation path leading to the trisulfide phase (Figure S3 and S4). By contrast, this trend is again reversed by the support. As explained in detail in Introduction, numerous published experimental works underlined the key role of H2S during the early stage of sulfo-reduction of Mo-oxide, we will thus assume here that hydrogen will not react at the first steps (I and II). Instead, we consider first that O/S exchange by H2S adsorption and H2O removal is thermodynamically preferred (as illustrated in what follows), which is in line with the earlier proposal by Muijsers et al. [START_REF] Muijsers | Sulfidation Study of Molybdenum Oxide Using MoO3/SiO2/Si(100) Model Catalysts and Mo3 IV -Sulfur Cluster Compounds[END_REF] Moreover, using H2S is also coherent with some experiments that reported MoS2 formation under pure H2S environment. [START_REF] Payen | Genesis and characterization by laser Raman spectroscopy and high-resolution electron microscopy of supported molybdenum disulfide crystallites[END_REF][START_REF] Baubet | Quantitative Two-Dimensional (2D) Morphology-Selectivity Relationship of CoMoS Nanolayers: A Combined High-Resolution High-Angle Annular Dark Field Scanning Transmission Electron Microscopy (HR HAADF-STEM) and Density Functional Theory (DFT) Study[END_REF] Note that we preliminary found that the direct reduction of Mo3O9 by hydrogen is endothermic (0.2 eV -1.76 eV for first oxygen removal (Supporting Information 5.3) and 0.51 eV -1.89 eV for the second oxygen removal).

Thus,

We systematically examined the O/S exchange for multiple models: monomer, dimer, trimer (chain and cyclic) according to the various types of oxygen sites identified. Detailed results are reported in Supporting Information 4, 5, and 6); we present in what follows two thermodynamically relevant paths (path-1 and -2) for the chain Mo3O9 conformer. The O/S replacement on path-1 occurs more homogeneously than on path-2 (Figure 2 and Figure S8).

The first two steps of path-1 and path-2 are similar and involve bridging O-sites in O/S exchange. However, the main difference arises at the third and fourth steps where path-1 replaces the terminal oxygen, while path-2 replaces the interfacial (Oint(bi)). On path-1, the three Mo-atoms become all partially sulfided (connected to one S-atom) at Mo3O6S3, whereas on path-2, only two Mo-atoms are sulfided at Mo3O6S3. Figure 2 reveals that the overall trend is exergonic. Even though step three is slightly less favored for path-2, the free energy gain at the 4 th step for path-2 becomes more significant, about -0.8 eV (Figure 2). This enhanced stability comes from the formation of S2-dimer replacing two adjacent Oint(bi) by S. Interestingly, such S2 dimers are observed experimentally (see the forthcoming spectroscopic analysis). Path-1 favors the replacement Oint(bi) and Oint(tri) after the bridging and terminal oxygen. At the 7 th step, path-1 can be linked to path-2 by dissociating the half-bridged dimer formed at step 6 and creating a new S2 dimer at step 7. The formation of new terminal S2 dimer results in -0.5 eV stabilization. This observation is consistent with an earlier DFT study of MoO3 O/S exchange, where the S2-dimer formation results in ~0.5 eV further stabilization. [START_REF] Shi | Theoretical Cluster Studies on the Catalytic Sulfidation of MoO3[END_REF] We thus propose that both paths co-exist or that a mixed solution combining path-1 until step 7 and a transition to path-2 after step 7 will lead to the formation of the most stable chain-Mo3S9. The O/S exchange energies of bridging and terminal oxygens are very similar from a thermodynamic aspect, whereas exchanging Oint(tri) site costs ~0.65 eV additional energy. Except for the last few steps, every O/S exchange is exergonic by about -0.2 eV to -0.5 eV. Interestingly, this observation remains valid across the size and models (Figure -S12). This trend suggests that the last few O/S exchanges involving Oint(tri) or Oint(bi) are thermodynamically more arduous than earlier ones. The homogeneous path-1 involves the replacement of terminal and bridging oxygen first and later the interfacial ones (Oint(tri) and Oint(bi)), while the heterogeneous path-2 exchanges the two bridging species followed by two Oint(bi) out of three, then terminal ones, and finally Oint(tri) and Oint(bi), respectively (Figure 2 and Figure S8 b andc). These oxysulfides contribute to the emerging Mo-S bonds as more oxygens are replaced by sulfur from Mo3O6S3 and Mo3O3S6 (Figure S9 andS10). For instance, new terminal Mo-S bonds of 2.14 Å (2.24 Å) [START_REF] Rochet | Intermediate Species Revealed during Sulfidation of Bimetallic Hydrotreating Catalyst[END_REF] and Mo-S-Mo bonds of 2.41 Å (2.38 Å) [START_REF] Rochet | Intermediate Species Revealed during Sulfidation of Bimetallic Hydrotreating Catalyst[END_REF] appear and are evidence of the presence of different S species such as S2 2-and S 2-as also confirmed by IR/Raman, [START_REF] Weber | Basic Reaction Steps in the Sulfidation of Crystalline MoO3 to MoS2, As Studied by X-ray Photoelectron and Infrared Emission Spectroscopy[END_REF][START_REF] Rochet | Intermediate Species Revealed during Sulfidation of Bimetallic Hydrotreating Catalyst[END_REF][START_REF] Weber | Structure of Amorphous MoS3[END_REF] while Mo-Ot vanishes as more S replaced the oxygen (Figure S9 andS10). Moreover, since EXAFS revealed that a short Mo-Ot bond is still present in late oxysulfides intermediates, [START_REF] Rochet | Co-K and Mo-K edges Quick-XAS study of the sulphidation properties of Mo/Al2O3 and CoMo/Al2O3 catalysts[END_REF][START_REF] Rochet | Intermediate Species Revealed during Sulfidation of Bimetallic Hydrotreating Catalyst[END_REF] the path-2 where sulfidation occurs heterogeneously from one side, may explain that the remaining terminal oxo species until Mo3O3S6, as seen in EXAFS spectrum for short Mo-O bond. The Mo-Mo bond shrinks from 3.31 Å to 2.86 Å as more O/S exchanges take place.

Structural and vibrational analysis of key intermediates

To further assess the reliability of our Mo-oxysulfide intermediates, we also undertook a similar analysis by simulating the IR spectrum of each intermediate and compared them with available experimental data (Figure -S10). Various Mo-O stretching modes were recovered between 700-1000 cm -1 : Mo-Ot : 980 cm -1 , [START_REF] Weber | Basic Reaction Steps in the Sulfidation of Crystalline MoO3 to MoS2, As Studied by X-ray Photoelectron and Infrared Emission Spectroscopy[END_REF][START_REF] Fierro | Metal Oxides: Chemistry and applications[END_REF] Mo-Oint(bi) : 800-900 cm -1 and Mo-OSurf : 700-

Mechanism and kinetics of O/S exchange from Mo3O9 to Mo3S9 (step I and II)

As explained in detail in Introduction, numerous published experimental works underlined the key role of H2S during the early stage of sulfo-reduction of Mo-oxide, we will thus assume here that hydrogen will not be involved in the sulfidation mechanisms at the first steps (I and II).

Instead, we consider first that O/S exchange by H2S adsorption and H2O removal is thermodynamically preferred (as illustrated in what follows), which is in line with the earlier proposal by Muijsers et al. [START_REF] Muijsers | Sulfidation Study of Molybdenum Oxide Using MoO3/SiO2/Si(100) Model Catalysts and Mo3 IV -Sulfur Cluster Compounds[END_REF] Moreover, using H2S is also coherent with some experiments that reported MoS2 formation under pure H2S environment. [START_REF] Payen | Genesis and characterization by laser Raman spectroscopy and high-resolution electron microscopy of supported molybdenum disulfide crystallites[END_REF][START_REF] Baubet | Quantitative Two-Dimensional (2D) Morphology-Selectivity Relationship of CoMoS Nanolayers: A Combined High-Resolution High-Angle Annular Dark Field Scanning Transmission Electron Microscopy (HR HAADF-STEM) and Density Functional Theory (DFT) Study[END_REF] Note that we preliminary found that the direct reduction of Mo3O9 by hydrogen is endothermic (0.2 eV -1.76 eV for first oxygen removal (Supporting Information 5.3) and 0.51 eV -1.89 eV for the second oxygen removal).

Thus, we will first focus on the role of H2S and its reactivity on oxides/oxysulfides to trisulfides conversion (in line with steps I and II of Figure 1), and further, we will analyze the possible role of H2 to allow the transformation either from trisulfide to disulfide (Figure 1, step IV), or from oxysulfide to disulfide (Figure 1, step-III).

Oxygen to sulfur exchange by H2S will involve four crucial steps as described in Scheme 1. During the next step, the H2S dissociation with a proton transfer to the targeted oxygen occurs.

The activation free energy for this H2S dissociation is Δ𝐺 ‡ 𝑏𝑟 1→2 = +0.64 eV which is expected to be accessible in sulfo-reductive conditions (T = 625 K). Once H2S is dissociated, one of its protons is transferred to the bridging oxygen leading to the scission of one Mo-O bond and the simultaneous formation of one OH group. Consequently, the Mo-S bond shortens as H2S dissociates (from 2.79 Å with H2S to 2.42 Å with SH), which reveals the strengthening of the interaction of the SH group with the Mo-site with respect to the initial H2S molecule. Therefore, it is reasonable to neglect these activation steps and assume that they will not significantly impact the overall processes.

After these rearrangements, the proton transfer occurs and is coupled with S migration from top to bridging site and water formation. The S bridging process promotes water formation and desorption by cauterizing the Mo-vacancy site where O is removed. This stabilizing effect also explains why the O/S exchange process is more favored than the direct O-removal by H2

(Supplementary Information 5.3). The free energy of activation of this step is Δ𝐺 ‡ 𝑏𝑟 4→5 = +0.62 eV which is also reasonable. The final step concerns the removal of water which exhibit about free energy of activation of Δ𝐺 ‡ 𝑏𝑟 5→6 = +0.28 eV. The entropy of water makes the overall path slightly exergonic (-0.12 eV).

Top-oxygen sites. According to the thermodynamic study, terminal oxygen would not differ significantly from bridging oxygens. We explored the O/S exchange mechanism for terminal oxygen on a Mo3O7S2 oxysulfide where the two bridging atoms have been substituted (Figure S13). The same central Mo-site exhibits a slightly weaker molecular adsorption of H2S with There are two intrinsic complexities for the O/S exchange on these sites: one, O accessibility to H2S is sterically hindered, and two, strong interaction with Al sites. The adsorption of H2S on the central Mo-atom is relatively weak compared to the previous cases, and the interfacial oxygen would not be accessible with such pre-adsorbed H2S on the Mo site. Consequently, we had to consider that H2S adsorbs on one of the Al sites of support located in the close vicinity of the interfacial oxygen to be exchanged. As support Al sites initiate the mechanism, some intermediate steps might differ from the two previous cases, but the four key steps described in Scheme 1 remain the same, assuming that one Al site is involved as a free site (*). H2S is adsorbed on support with a stronger interaction (also involving some H-bonding) than on Mosite. At 625 K, the H2S adsorption step is thus slightly less endergonic (Δ𝐺 𝑖𝑛𝑡-𝑏𝑖 0→1 = +0.43

Δ𝐺 𝑡 0→1 = +0.
eV, Figure 4). than the trimeric one (Supplementary Information 4). This difference is due to the adsorption of H2S to the Mo site in the Mo1OS2 site (and not on the Al site), which facilitates its activation/dissociation and H-transfer to the interfacial O-site of Mo1OS2. This size effect will be further discussed in Section 4.

Interfacial-tridentate oxygen site. We consider the MoO2S7 oxysulfide intermediate containing one Oint(bi) and one Oint(tri) site for this step (Figure S14). After H2S adsorption on the support (Δ𝐺 𝑖𝑛𝑡-𝑡𝑟𝑖 0→1 = +0.37 eV), the hydrogen atoms of H2S cannot reach the targeted oxygen site. Hence, H2S dissociates first on a neighboring alumina µ3-oxygen and transforms it into µ2-OH with a weak activation energy of Δ𝐺 ‡ 𝑖𝑛𝑡-𝑡𝑟𝑖 1→2 = +0.43 eV. Thereafter, it diffuses and is transferred to the Oint(tri) (targeted oxygen) atom forming µ3-OH with a high activation free energy (Δ𝐺 ‡ 𝑖𝑛𝑡-𝑡𝑟𝑖 2→3 = +1.00 eV). Since the proton of SH is too far from Oint(tri) to react, the SH group must diffuse from alumina to an accessible terminal sulfide to form a Mo-S-S-H species with a low activation free energy (Δ𝐺 ‡ 𝑖𝑛𝑡-𝑡𝑟𝑖 4→5 = +0.42 eV). The proton is more easily accessible to oxygen through this S-S-H species and can be transferred smoothly with a moderate activation free energy of Δ𝐺 ‡ 𝑖𝑛𝑡-𝑡𝑟𝑖 5→6 = +0.41 eV. The newly formed water is still in strong interaction with alumina and Mo, which makes the water desorption step demanding with Δ𝐺 ‡ 𝑖𝑛𝑡-𝑡𝑟𝑖 6→7 = +0.73 eV, similar to the Oint(bi) site. In general, we observe that water desorption from support is kinetically more limited than from a Mo site of the cluster (~0.7 eV vs. ~0.2 eV). The water desorption on Mo-site is promoted by the exchanged S atom, but on the support, it occurs more or less independently. After the desorption of water, the O-vacancy should be replaced by S, which currently exists as S-S dimer with terminal S. The splitting of the S-S bond requires an activation free energy of Δ𝐺 ‡ 𝑖𝑛𝑡-𝑡𝑟𝑖 7→8 = +0.92 eV. As in the previous case, many energy levels involved are high, and the elementary steps are more numerous, making the overall mechanism much more complex.

Transformation of Mo3S9 trisulfides into Mo3S6 disulfides (step IV)

The Mo-trisulfide into disulfide conversion (step IV in Figure 1) involves H2 as a reactant and H2S as product. The three main elementary steps are described in Scheme 2. Like in previous cases, some intermediate SH reorientation and S diffusion or rearrangement are also involved. As they are not the limiting ones, we will not report their activation energies.

The detailed kinetic pathways corresponding to the different S-species (terminal and bridging) are reported in Supporting Information 7.2. One preliminary remark is that we identified possible chain to triangular reconstructions during the Mo3S9 to Mo3S6 transformation (Figure 5). It is known that the targeted MoS2 phase exhibits a triangular Mo3 pattern where Mo-atoms are connected by 3-sulfur atoms. Several Mo3S9 conformers have been proposed in the literature, such as triangular [START_REF] Weber | Structure of Amorphous MoS3[END_REF][START_REF] Jiao | The Structure and Possible Catalytic Sites of Mo3S9 as a Model of Amorphous Molybdenum Trisulfide[END_REF][START_REF] Müller | Mo3(IV)S(S2)6] 2from amorphous MoS3 by the reaction with OHand R= 0.015 strucutre of[END_REF] or chain-like ones. [START_REF] Liang | Amorphous MoS3 and WS3[END_REF][START_REF] Hibble | Modeling the structure of amorphous MoS3: a neutron diffraction and reverse Monte Carlo study[END_REF][START_REF] Hibble | Chemical excision from amorphous MoS3; a quantitative EXAFS study[END_REF][START_REF] Hibble | Amorphous MoS3[END_REF][START_REF] Chien | Local and intermediate-range structure of amorphous MoS3[END_REF] Hence, one key question for the genesis of the MoS2 phase could be linked to the kinetics of formation of this triangular pattern. eV on the alumina support in contrast with their gas-phase structures. [START_REF] Sahu | Size-Dependent Structural, Energetic, and Spectroscopic Properties of MoS3 Polymorphs[END_REF] As it was already confirmed for the Mo3O9 tri-oxide and for Mo3OxSy (x+y = 9) oxysulfides presented before.

However, the trend is inverted for the Mo3S6 species that are stabilized with a triangular shape due to the undercoordination of Mo in the chain conformer. For 1:3 stoichiometry of Mo:S/O, the interaction with the alumina site is a strong stabilizing factor for the chain conformer over triangular, which involves significant reconstruction of the chain and triangular with respect to their gas-phase ground-state structures. Nevertheless, the support can no longer stabilize chain shapes for Mo:S/O ratio of 1:2 due to the undercoordination of Mo atoms.

Several elementary steps are thus suspected of inducing the chain to the triangular reconstruction of Mo3Sy intermediates in the course of S removal. This chain to triangular reconstruction may occur at the initial Mo3S9 stage (Figure 5, bottom path) or while removing sulfur atoms from Mo3S9 into Mo3S6 (Figure 5, top path). The direct Mo3S9 chain to triangle reconstruction requires a competing activation free energy of +1.77 eV (Figure S23). The complete structural description of this reconstruction is reported in Supporting Information 8.4.

The triangular-Mo3S9 will then further transform into triangular-Mo3S6. Even though the triangular-Mo3S9 is slightly less stable, the reconstruction may compete with the S-removal on chain conformers involving higher activation energies. (bottom path). Red numbers are free energies of activation calculated for each given step (referring the highest TS to its lowest energy precursor of the given step, see Supporting Information 8.1 for the detailed free energy profiles).

To explore how the S-removal occurs, we screened the various possible sites for S removal onchain and triangular Mo3S9 and observed that the terminal-S2 dimer is kinetically the most prominent to be removed (Figure S19a concerted process for chain and separate for triangular but with no additional cost. From Mo3S9 to Mo3S8, the conformation of the cluster remains unchanged.

From Mo3S8 to Mo3S7, the bridging sulfur is thermodynamically more advantageous than the terminal ones to be removed in the chain conformer. Pulling out, the bridging S creates a vacancy initiating the chain to triangular reconstruction illustrated in Figure S19b. As mentioned earlier, the first step would be H2 dissociation that requires about +1.83 eV (Δ𝐺 ‡ 𝐵 0→2 ) as activation energy. The proton transfer and the formation of H2S involves high overall activation energy of +2.16 eV (Δ𝐺 ‡ 𝐵 0→4 ) which asserts to be the rate-limiting step. The desorption of H2S creates S vacancy and induces the bending of the Mo3-chain leading to the initiation of a triangular conformer converting bridging sulfur (µ2-S) into apical sulfur (µ3-S) with a negligible barrier. The reconstruction results in the stabilization and S-removal process from Mo3S8 into Mo3S7, which becomes exergonic, contrasting with the previous endergonic S removal. In the case of a triangular conformer, the second S removal from terminal-S2 dimer is assumed to occur in a similar fashion as the first one.

The remaining excessive sulfur of Mo3S7 is removed identically (Figure 6) with a rate-limiting step of proton transfer (Δ𝐺 ‡ 𝐶 0→4 = 1.49 eV ). As in the previous case, the H2S removal is associated with a further reconstruction, and terminal µ1-S converted into bridging µ2-S, which closes the triangular pattern of the Mo3S6 disulfide. This structure is reminiscent of the triangular pattern observed in MoS2 phases. In the triangular case, the bridging S2-dimer dissociates and converts into the triangular Mo3S7 observed from the chain conformer, and S-excess is removed in the same way (Figure 5). It could be noticed that the various calculated free energies for H2 activation through homolytic dissociation leading to two Mo-SH groups on Mo3Sx trimer, such as reported in Figure 6 or in Supplementary Information 7.2 are very consistent with those previously found on MoS2

edges. [START_REF] Prodhomme | Free-energy profiles along reduction pathways of MoS2 M-edge and S-edge by dihydrogen[END_REF] Even if we cannot fully rule out that this activation step might occur through a heterolytic dissociation (Mo-H and Mo-SH) such as found on monomeric Mo1S3 (Figure S31), the calculated values reported in Ref. [START_REF] Prodhomme | Free-energy profiles along reduction pathways of MoS2 M-edge and S-edge by dihydrogen[END_REF] indicate that the heterolytic dissociations are in the same range of the homolytic ones. Hence, the trend reported in our work might not be strongly affected. Mo3O3S6. [START_REF] Rochet | Co-K and Mo-K edges Quick-XAS study of the sulphidation properties of Mo/Al2O3 and CoMo/Al2O3 catalysts[END_REF][START_REF] Rochet | Intermediate Species Revealed during Sulfidation of Bimetallic Hydrotreating Catalyst[END_REF]

Competition between oxysulfide pathway and trisulfide pathway

The summarized free energy profile shown in +1.96 eV (Figure S21c), which is the highest value among all the individual activation energies found for the mechanisms studied in this work. After replacing this O with S, it will transform into Mo3S7, and the last S removal step, to eventually transform into Mo3S6, will be the same as the trisulfide path (Figure 6).

Considering the limitation for the last interfacial oxygen removal, the trisulfide pathway involving Mo3S9 seems to be more favorable than the direct reduction from Mo3O3S6

(oxysulfide) to Mo3S6 (disulfide). Nonetheless, Mo3S9 eventually has also to transform into disulfide Mo3S6. barrier of triangular-Mo3S9 is also lower than Mo3S6 (0.67 eV vs. 1.17 eV). Therefore, if Mo3S6 species are formed, their mobility could also allow the formation of the MoS2 phase. Since the Sremovals on chain-Mo3S9 are kinetically limited as aforementioned, the chain to triangle reconstruction followed by diffusion of triangular-Mo3S9 will preferentially occur. This diffusion process will allow their subsequent condensation into larger trisulfide Mo3nS9n 2D patches of finite size, so called 1T'-MoS3 phase in our previous study. [START_REF] Sahu | Size-Dependent Structural, Energetic, and Spectroscopic Properties of MoS3 Polymorphs[END_REF] Molecular dynamics simulation revealed that the condensation of triangular-(Mo3S9)n (n=2,3) oligomers into Mo3nS9n 2D patches is indeed possible in gas phase. [START_REF] Sahu | Size-Dependent Structural, Energetic, and Spectroscopic Properties of MoS3 Polymorphs[END_REF] Moreover, According to Ref. [START_REF] Sahu | Size-Dependent Structural, Energetic, and Spectroscopic Properties of MoS3 Polymorphs[END_REF], the energy gain by the condensation of isolated triangular-Mo3S9 into Mo3nS9n 2D patches is substantial (around -2 eV to -2.5 eV/Mo3S9 depending on n). Since the interaction energy of triangular-Mo3S9 on -alumina is about -1.5 eV (Figure S25), this implies that the formation of such 2D patches from triangular-Mo3S9 dispersed on alumina is an exothermic process. If so, the S-removal steps would occur on such larger size Mo3nS9n 2D patches rather than on the Mo3S9 for which the Sremoval is energetically too demanding. Supporting Information SI.11 and Figure 8 show that the estimated barriers for the S-removal step decrease by increasing the Mo trisulfides cluster size. This S-removal results in the transformation of Mo3nS9n 2D patches into Mo3nS6n 2D patches which could diffuse and futher grow to form the crystalline MoS2 phase.

We also expect that even smaller Mo trisulfides entities (Mo2S6 or Mo1S3, Moreover, the O/S exchange step is also influenced by the effect of size, and the monomeric Mo1O3 cluster exhibits a significantly smaller activation free energy of +1.35 eV (Supporting Information SI.4) than Mo3O9. This implies that the trisulfide pathway (steps I and II in Figure 1) should be predominant for small MoO3 oligomers, including monomeric ones. Therefore, once these small Mo oxide clusters are trisulfided, they rapidly diffuse on the alumina surface (Figure S29) and grow to form larger Mo3nS9n 2D patches before transforming into MoS2 phase by Sremovals.

Conclusions

Using DFT calculations, we examined the sulfo-reduction mechanisms of Mo-oxide oligomers on the (100) surface of 𝛾-alumina support. Mo-oxysulfides model intermediates have been validated by comparison with available structural data and IR spectra. As first perspective, we propose that the numerous Mo-oxysulfide structures identified in this work could be used for the simulation of in situ X-ray Absorption Spectra (EXAFS or XANES) in order to help for a refined identification of the key intermediates involved in the sulfo-reduction pathway. • The chain-like Mo3S9 cluster should reconstruct into a triangular one to be able to transform further (plain light blue arrows in Figure 9).

• The small size MonS3n oligomers (x≤3, including triangular Mo3S9) are fast diffusing species and oligomerize into larger species (dashed green arrows in Figure 9), last but not least into (Mo3S9)n 2D patches.

• For Mo3S9, the S-removal occurs preferentially on terminal-S2 and terminal-S while bridging S requires the highest activation energy. However, the S-removal is expected to take place at a lower cost on larger (Mo3S9)n 2D patches (dashed blue arrows in Figure 9).

• As discussed in Ref., [START_REF] Sahu | Size-Dependent Structural, Energetic, and Spectroscopic Properties of MoS3 Polymorphs[END_REF] these (Mo3S9)n 2D patches may be the precursor of the 1T-MoS2 phase, subsequently leading to 2H-MoS2.

Since we analyzed the role of H2S and H2 as individual reactant leading to sulfidation and/or reduction, we propose as a second perspective to investigate if an interplay could exist between both reactants being simultaneously involved in the elementary steps.

We found that the support shows a substantial impact on energetics and structures (with respect to isolated species): cyclic-Mo3O9 and triangular Mo3S9 are more stable in the gas phase, while the alumina (100) surface stabilizes the linear conformers through single or multiple Mo-O-Al bonds. Nevertheless, we expect that the specific alumina facet may impact the mobility of the species that we have quantified in the present work. In the future, it would thus be relevant to extend the study to other -alumina surfaces which were proposed to influence the sulfidation

Figure 1 .

 1 Figure 1. Schematic diagram of sulfidation of Mo-oxide precursors by H2S into Mo oxysulfides

S2 2 -

 2 and S 2-species was analyzed as a function of temperature by in situ Laser Raman Spectroscopy for alumina supported Ni-promoted MoS2 catalyst.[18] Temperature-dependent infra-red (IR) emission spectrum of sulfidation of crystalline MoO3 showed that around 100-200 C, the peak of bridging oxo-species Mo-O-Mo disappears, and a new peak assigned to top oxospecies Mo=Ot appears before Mo-S formation. Then, on Mo-oxysulfides, the Mo=Ot species

However, to the

  best of our knowledge, no DFT study addressed the sulfo-reduction mechanisms of Mo-oxides dispersed on a support such as -alumina. Hence, numerous open questions remain about the molecular mechanisms and key oxysulfides intermediates involved in the elementary steps of Figure 1, such as O/S exchange, S-removal, O-removal involved during activation. In particular, it would be crucial to identify the most refractory oxygen sites with respect to sulfidation, and the role of the Mo-trisulfide invoked by numerous experimental studies.

Figures 3 and

 3 Figures 3 and S6 highlight the four distinct types of oxygen atoms present in the supported

Figure

  Figure S12highlights that the second chain conformer (FigureS6b) is actually slightly less

Figure 2 .

 2 Figure 2. Gibbs free energy at 625 K for the O/S exchanges of chain-trimer Mo3O9 according

  During the O/S exchanges, the local chemical and structural environment of Mo3O9-xSx intermediates evolve, involving the disappearance of Mo-O bonds and the simultaneous formation of new Mo-S and S-S bonds as highlighted by the evolution of Mo-O(S) bond lengths and coordination number of the critical intermediates in Figure S9 where a comparison with EXAFS data is also given.[16-19,84] As detailed in Supporting Information 5.2, the DFT optimized structural values are consistent with EXAFS ones, and the calculations recover the various Mo-O bond lengths as a function of the type of O site.

  750 cm -1 . As the bridging oxygens are being replaced, several Mo-O, Mo-O-Al, and Al-O-Al peaks start diminishing while peaks of the newly formed Mo-St, and Mo-S-Mo appear (around 550 cm -1 and below).

Scheme 1 .

 1 Scheme 1. Main elementary steps for the O/S exchange involving H2S/H2O. * represent

Figure 3 .

 3 Figure 3. Free energy profile of O/S exchange involving bridging oxygen and H2S. Color

  of the product is quite close to the TS level (br(2) and br(2-3) ‡ , Δ𝐺 ‡ 𝑏𝑟 2→3 = +0.10 eV) due to their structural similarity. A slight internal arrangement, SH and OH rotations, occurs before the next proton transfer involving weak activation energy around +0.07/0.15 eV (activation for H-rotation not shown here), which is far lower than the barrier of other key steps.

Figure 4 .

 4 Figure 4. Free energy profile of O/S exchange involving interfacial bidentate oxygen and H2S.

Scheme 2 .

 2 Scheme 2. Main elementary steps for the S removal H2/H2S. * represents formally a Mo site of

Figure 5

 5 illustrates the structures of the most relevant Mo3S9-x intermediates found along the Mo3S9 to Mo3S6 transformation activated by H2. As shown in Figure S18a, the S-removal steps are almost all isergonic. The chain-like Mo3S9 is more stable than triangular-Mo3S9 by ~0.5

Figure 5 .

 5 Figure 5. Two possible pathways for the chain-Mo3S9 to triangular-Mo3S6 transformation:

  and S24). In chain-Mo3S9, it leads to a symmetrical structure, and in triangular both terminal-S2 dimers can be disintegrated likewise. Since the activation free energy of breaking the S2 dimer along with dissociative adsorption of H2 is relatively high Δ𝐺 𝐶ℎ𝑎𝑖𝑛 ‡ 𝐴 0→2 = +1.87 eV (Figure S19a) vs. Δ𝐺 𝑇𝑅 ‡ 𝑡-𝑆2 0→2 = +2.04 eV (Figure S24), this step would be a rate-limiting step. It is followed by SH rotation, and the third step is a proton transfer from one SH to the neighboring SH leading to the formation of H2S with activation energy Δ𝐺 𝐶ℎ𝑎𝑖𝑛 ‡ 𝐴 0→4 of +1.74 eV. This proton transfer is relatively more accessible for triangular case (Δ𝐺 𝑇𝑅 ‡ 𝑡-𝑆2 0→4 = +0.86 eV). The proton transfer and H2S desorption are a

Figure 6 .

 6 Figure 6. Free energy profile of S removal using H2 and formation of the triangular Mo3

29 3. 3 Figure 1 ,Figure 2 )

 29312 Figure 2), O/S exchange will follow path-1 at the early stage of sulfidation since bridging and

Figure 7 ,In Figure 7 ,

 77 is based on the dominating kinetics showing that the O/S exchange occurs in the following order: Obr > Ot > Oint-bi > Oint-tri. Based on several tests, we assume that the same types of oxygen (or sulfur) sites exhibit similar kinetic barriers (although some of them have not been calculated explicitly). We compare in what follows the free energies of activation of the Rate Determining Transition States (RDTS) and Determining Intermediates (RDI) and propose an overall discussion on kinetic effects. until the formation of Mo3O3S6, the rate-limiting step is exchanging the Oint-bi (G 𝑖𝑛𝑡-𝑏𝑖 ‡ = 1.81 eV). The next O/S exchange is competing with O removal by a direct reduction pathway (steps III in Figure 1): from Mo-oxysulfide (Mo3O3S6), removing interfacial oxygen with H2 requires comparable free activation energies as replacing the same oxygen sites by S (+1.85 eV vs. +1.79 eV). Moreover, thermodynamically the O/S exchange also competes with reduction accompanied by oxygen removal. Indeed, the RDI of the trisulfide pathway obtained for the Mo3OS8 intermediate, exhibits a very similar free energy (~ -2 eV) as for the RDI Mo3OS6 in the O-removal of the oxysulfide path. Therefore, it seems challenging to discriminate between O/S exchange leading to Mo3OS8 (step II) and oxygen removal (step III) leading to Mo3OS6 starting from the common Mo3O3S6 intermediate. Exchanging the final oxygen by sulfur (Mo3OS8→Mo3S9) is endergonic (G=+0.32 eV) and requires the maximum activation energy among all O/S exchanges (G 𝑖𝑛𝑡-𝑡𝑟𝑖 ‡ = +1.93 eV). By contrast, the last O-removal on Mo3OS6 reveals a kinetic limitation due to the high-energy intermediate generated (+2.68 eV of Mo3S6) before its reconstruction towards the most stable one. Instead of removing the last oxygen in Mo3OS6 alternatively, it can be replaced by the O/S exchange leading to Mo3S7. This alternative step reveals a free activation energy of G 𝐹(4-5) ‡

Figure 7 .

 7 Figure 7. Free energy comparison of entire sulfo-reduction pathways from chain-Mo3O9 to

Figure S29)Figure 8 .

 8 Figure 8. Comparison of Gibbs free energies of activation for O/S exchange and S-removal for

  two competing pathways of the genesis of the active phase: the first one involving Mo-oxysulfide intermediate only and the second one involving Mo-oxysulfide/Motrisulfide. A complete free energy analysis has been performed, accounting for various effects: the oligomer size, the chain to triangular shape reconstruction, and the diffusion of the Mo clusters on the alumina surface. Based on the gained understanding, we propose a comprehensive reaction network for the sulfidation/reduction process from Mo3O9 oxide to MoS3 and MoS2 active phase, as summarized in Figure 9.

Figure 9 .•

 9 Figure 9. Schematic representation of the entire reaction network during activation, starting

  The proton transfer associated with S migration is the rate-

	limiting step for this terminal O/S exchange and is higher (Δ𝐺 ‡	𝑡 3→4 = +0.92 eV) than the rate-
	limiting step for the bridging O/S one. After water formation, migration of S from bridging site
	to top site is easily leading to a precursor of the water desorption weakly activated (Δ𝐺 ‡	𝑡 5→6 =
	+0.15 eV). It must be underlined that the S/O exchange occurring on a top monomeric Mo1O3 is
	located at a lower energy level than the trimeric one (Supplementary Information 4).
	79 eV in contrast with the previously discussed O/S exchange. With a slight
	activation free energy barrier of Δ𝐺 ‡	𝑡 1→2 = +0.18 eV H2S dissociates. After subsequent SH/OH

rotation (t(2) → t(3)), the proton transfer takes place. This step is also coupled with S migration (from top to bridging site) similarly to the bridging O, which is much less energy-demanding than the direct creation of O-vacancies on top of the Mo site upon H2/H2O exchange (Supplementary Information 5.3).

Interfacial-bidentate oxygen sites. Interfacial oxygens remaining on

Mo3O4S5 can be considered as top/bridging O-sites are already replaced. Oint(bi) interacts with Al through Mo-O-Al linkage.

Acknowledgements

The authors acknowledge C. Legens from IFP Energies Nouvelles for fruitful discussions on EXAFS experimental data.

reconstruction is about +2.09 eV (related to RDI, Figure 7) which is preferred to the direct formation of Mo3S6 intermediate through S-or O-removal. However, the subsequent removals of S-atoms from TR-Mo3S9 to TR-Mo3S6 are again kinetically limited (+2.72 eV, Figure S24 and Figure 7). Chain and triangular Mo3S9 are thus kinetically accessible, but the subsequent steps of S-removals are kinetically prohibited. So, the unique alternative for the Mo3S9 intermediates to evolve could be to diffuse on the alumina surface and grow before giving rise to the MoS2 phase as discussed in the following.

Mobility, growth, and size effects

As quantified in Supporting Information 9.1, the interaction energy of Mo-oxysulfides and Mo-sulfides with alumina reveals that the Mo-sulfides oligomers are the less strongly bonded species, as expected from chemical intuition. Based on this preliminary interaction energy analysis, we have quantified the translational diffusion of 4 key Mo-sulfide species (chain-Mo3S9, triangular-Mo3S9 and triangular-Mo3S6, and Mo1S3) on the alumina (100) surface following some main principal orientations of the surface, which allow the migration of the oligomers from one O site to another (Supporting Information 9.2). The translational diffusion barrier is significantly higher for chain-Mo3S9 than for triangular conformers (1.73 eV vs. 0.67 eV). Therefore, the mobility of Mo3S9 triangular intermediates is favored with respect to chain-Mo3S9. We thus expect that the growth of MoS3-polymorphs should be predominant through Mo3S9 triangular species before their ultimate transformation into the MoS2 active phase, as suggested by the observed sizes of sulfides evaluated by EXAFS studies. [START_REF] Lesage | High pressure cell for edge jumping X-ray absorption spectroscopy: Applications to industrial liquid sulfidation of hydrotreatment catalysts[END_REF][START_REF] Rochet | Co-K and Mo-K edges Quick-XAS study of the sulphidation properties of Mo/Al2O3 and CoMo/Al2O3 catalysts[END_REF][START_REF] Rochet | Intermediate Species Revealed during Sulfidation of Bimetallic Hydrotreating Catalyst[END_REF] The diffusion degree of the MoS2 phase, [START_REF] Bara | Aqueous-Phase Preparation of Model HDS Catalysts on Planar Alumina Substrates: Support Effect on Mo Adsorption and Sulfidation[END_REF][START_REF] Garcia De Castro | Surface-Dependent Activation of Model α-Al2O3-Supported P-Doped Hydrotreating Catalysts Prepared by Spin Coating[END_REF] and which features OH groups under sulfo-reduction conditions together with other Al sites as compared to the (100) surface. Supporting Information. The gas phase sulfidation, and complementary data on thermodynamics, kinetics and frequency analyses of various pathways (including diffusion and reconstruction) for monomers and trimers, EXAFS and IR comparison for intermediates, have been reported in supporting information. The structural data for all intermediates and transition states are available from the corresponding author upon reasonable request. [START_REF] Handzlik | Structure of Dimeric Molybdenum(VI) Oxide Species on γ-Alumina: A Periodic Density Functional Theory Study[END_REF] Funding Sources Calculations were performed using HPC resources (Jean Zay and Occigen) from GENCI-CINES