Youssef Berro

Michael Badawi
email: michael.badawi@univ-lorraine.fr

Fouad El

Haj Hassan

Mounir Kassir

Frederik Tielens
email: frederik.tielens@vub.be

Water-silanol interactions on the amorphous silica surface: A dispersion-corrected DFT investigation

Keywords: dispersion-corrected DFT, amorphous silica, silanol defects, water interaction, SCAN

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

INTRODUCTION

Being one of the most famous materials used in adsorption and catalysis applications due to its structural properties [START_REF] Brunel | New trends in the design of supported catalysts on mesoporous silicas and their applications in fine chemicals[END_REF][START_REF] Jin | Amorphous silica nanohybrids: Synthesis, properties and applications[END_REF][START_REF] Gibson | Mesosilica materials and organic pollutant adsorption: part A removal from air[END_REF][START_REF] Li | Adsorption property and mechanism of PAMAM dendrimer/silica gel hybrids for Fe(III) and Ag(I) from N,Ndimethylformamide[END_REF][START_REF] Naghavi | Quantum molecular study of mesoporous silica nanoparticle as a delivery system for troxacitabine anticancer drug[END_REF][START_REF] Berro | Imprinting isolated single iron atoms onto mesoporous silica by templating with metallosurfactants[END_REF], the amorphous silica (silicon dioxide) has been investigated using density functional theory (DFT) calculations during the last decade [START_REF] Sautet | Catalysis and Surface Organometallic Chemistry: A View from Theory and Simulations[END_REF][START_REF] Handzlik | Paired interacting orbitals (PIO) study of Mo/SiO2 and Mo/HZSM-5 catalysts for olefin metathesis[END_REF][START_REF] Conley | Heterolytic Activation of C-H Bonds on Cr III -O Surface Sites Is a Key Step in Catalytic Polymerization of Ethylene and Dehydrogenation of Propane[END_REF][START_REF] Floryan | Strain effect and dual initiation pathway in CrIII/SiO2 polymerization catalysts from amorphous periodic models[END_REF]. The physicochemical properties of the amorphous silica are ruled by the presence of silanol groups [START_REF] Sauer | Quantum chemical investigation of interaction sites in zeolites and silica[END_REF][START_REF] Somorjai | Major Successes of Theory-and-Experiment-Combined Studies in Surface Chemistry and Heterogeneous Catalysis[END_REF], which are characteristic defects in the bulk and at the surface or interface of the finite particles.

Due to the intrinsic properties of the amorphous structure of silica, different types of silanol groups can be distinguished which geometrical parameters are spread over a distribution function depending of the origin and synthesis protocol followed. This statistical feature makes it difficult to assign one property to one specific type of silanol group. The prediction of macroscopic or global properties such as hydrophobicity, or acidity is also challenged by this statistical distribution of silanol groups, because one type of silanol groups can show opposite properties depending on the local environment and surface concentration [START_REF] Rimola | How Does Silica Catalyze the Amide Bond Formation under Dry Conditions? Role of Specific Surface Silanol Pairs[END_REF][START_REF] Tielens | Characterization of amorphous silica based catalysts using DFT computational methods[END_REF][START_REF] Douhal | Chemistry of silica and zeolite-based materials: synthesis, characterization and applications[END_REF]. In order to understand the evolution of the chemistry within one type of silanol group over the property range (mainly ruled by the local geometry), the silanol group interactions should be accurately described. It is the combination of the accurately described properties of the silanol groups over a statistical distribution that might enable the overall description of the investigated amorphous silica.

The construction of models is in the case of amorphous silica the most delicate milestone [START_REF] Sauer | Theoretical Study of van der Waals Complexes at Surface Sites in Comparison with the Experiment[END_REF][START_REF] Ugliengo | Realistic Models of Hydroxylated Amorphous Silica Surfaces and MCM-41 Mesoporous Material Simulated by Large-scale Periodic B3LYP Calculations[END_REF][START_REF] Coasne | Atomistic Model of Micelle-Templated Mesoporous Silicas: Structural, Morphological, and Adsorption Properties[END_REF][START_REF] Ewing | Accurate Amorphous Silica Surface Models from First-Principles Thermodynamics of Surface Dehydroxylation[END_REF][START_REF] Comas | Amorphous SiO 2 surface models: energetics of the dehydroxylation process, strain, ab initio atomistic thermodynamics and IR spectroscopic signatures[END_REF][START_REF] Tielens | Ab Initio Study of the Hydroxylated Surface of Amorphous Silica: A Representative Model[END_REF]. In recent years, some of us specialized in combining the amorphicity, size and periodicity in one model, with the aim to perform DFT calculations on amorphous silica [START_REF] Tielens | Characterization of amorphous silica based catalysts using DFT computational methods[END_REF][START_REF] Tielens | Ab Initio Study of the Hydroxylated Surface of Amorphous Silica: A Representative Model[END_REF][START_REF] Guesmi | Chromium Oxide Species Supported on Silica: A Representative Periodic DFT Model[END_REF][START_REF] Handzlik | Structure of Monomeric Chromium(VI) Oxide Species Supported on Silica: Periodic and Cluster DFT Studies[END_REF][START_REF] Cimas | The amorphous silica-liquid water interface studied by ab initio molecular dynamics (AIMD): local organization in global disorder[END_REF][START_REF] Pfeiffer-Laplaud | Bimodal Acidity at the Amorphous Silica/Water Interface[END_REF][START_REF] Guesmi | Characterization of molybdenum monomeric oxide species supported on hydroxylated silica: a DFT study[END_REF][START_REF] Tranca | Supported and inserted monomeric niobium oxide species on/in silica: a molecular picture[END_REF][START_REF] Guesmi | Characterization of tungsten monomeric oxide species supported on hydroxylated silica; a DFT study[END_REF][START_REF] Gierada | Hydration in silica based mesoporous materials: a DFT model[END_REF][START_REF] Suek | Characterization of hydroxylated amorphous silica: a numerical approach[END_REF][START_REF] Gierada | Understanding the Acidic Properties of the Amorphous Hydroxylated Silica Surface[END_REF][START_REF] Berro | Atomistic description of phenol, CO and H2O adsorption over crystalline and amorphous silica surfaces for hydrodeoxygenation applications[END_REF], and in particular to investigate its hydration and acidity [START_REF] Pfeiffer-Laplaud | Bimodal Acidity at the Amorphous Silica/Water Interface[END_REF][START_REF] Gierada | Hydration in silica based mesoporous materials: a DFT model[END_REF][START_REF] Gierada | Understanding the Acidic Properties of the Amorphous Hydroxylated Silica Surface[END_REF]. The chemistry of the silanol groups at the amorphous silica surface is dependent on: a) the coverage, b) the type of silanol (isolated, vicinal, geminal, and in nests), and c) the inter-molecular interactions between the silanol groups (mainly H-bonds) [START_REF] Tielens | Characterization of amorphous silica based catalysts using DFT computational methods[END_REF][START_REF] Gueddida | Grafting of iron on amorphous silica surfaces from ab initio calculations[END_REF][START_REF] Gueddida | Interaction between transition metals (Co, Ni, and Cu) systems and amorphous silica surfaces: A DFT investigation[END_REF]. The accurate description of H-bonds in quantum chemistry is not new and present a recurrent problem [START_REF] Gordon | Understanding the Hydrogen Bond Using Quantum Chemistry[END_REF][START_REF] Sun | Water dissociation and H migration on metal decorated B40: A density functional theory (DFT) study[END_REF]. In 2006, van der Wijst et al. [START_REF] Van Der Wijst | Performance of various density functionals for the hydrogen bonds in DNA base pairs[END_REF] compared the performance of different popular density functionals (B3LYP, BLYP, BP86, mPW, OPBE, PBE, PW91) for describing the geometry and stability of hydrogen bonds in DNA base pairs. They showed that results obtained from BP86 and PW91 were consistent with ab initio and experimental results, while B3LYP functional underestimates the strengths and overestimate the distances of hydrogen bonds. In contrast, the B3LYP functional overestimates the strength of hydrogen bonds in the case of clusters of methanol when using insufficiently complete basis set [START_REF] Pogorelov | Structural transformations in bulk and matrix-isolated methanol from measured and computed infrared spectroscopy[END_REF], meaning that the capability of the DFT methods to determine the strength of H-bonds can be assessed with the used basis sets. Some years later, Grimme et al. [START_REF] Goerigk | Benchmarking Density Functional Methods against the S66 and S66x8 Datasets for Non-Covalent Interactions[END_REF] evaluated the performance of 17 dispersion corrected density functional methods on the new S66 and S66x8 benchmark sets for non-covalent interactions showing that double-hybrid functionals are the most robust and accurate methods.

Nowadays, within the periodic DFT framework [START_REF] Burke | The ABC of DFT[END_REF], different methods are able to tackle this problem ranging from adapted functional to empiric London-dispersion corrections [START_REF] Albavera-Mata | Long-range exchange limit and dispersion in pure silica zeolites[END_REF][START_REF] Fischer | Benchmarking the performance of approximate van der Waals methods for the structural and energetic properties of SiO2 and AlPO4 frameworks[END_REF][START_REF] Hessou | Adsorption of NO, NO2, CO, H2O and CO2 over isolated monovalent cations in faujasite zeolite: a periodic DFT investigation[END_REF].

Indeed, the last decade has witnessed tremendous effort in the development of various correction methods to account for the missing London dispersion interactions in conventional Kohn-Sham DFT calculations [START_REF] Grimme | Accurate description of van der Waals complexes by density functional theory including empirical corrections[END_REF]. Two types of approaches are mainly used. One can use specific non-local correlation functionals that approximately account for dispersion interactions, as originally developed by Dion et al. [START_REF] Dion | Van der Waals Density Functional for General Geometries[END_REF] and improved by other groups [START_REF] Lee | Higher-accuracy van der Waals density functional[END_REF][START_REF] Klimeš | Van der Waals density functionals applied to solids[END_REF]. However, due to the relatively high cost of calculation, we decided to focus in the present work on the second approach that considers the additive correction schemes to include dispersion interactions [START_REF] Zimmerli | Dispersion corrections to density functionals for water aromatic interactions[END_REF].

According to this approach, different methods have been developed during the few precedent years, among them the D2 [START_REF] Grimme | Accurate description of van der Waals complexes by density functional theory including empirical corrections[END_REF][START_REF] Grimme | Semiempirical GGA-type density functional constructed with a long-range dispersion correction[END_REF][START_REF] Bučko | Improved Description of the Structure of Molecular and Layered Crystals: Ab Initio DFT Calculations with van der Waals Corrections[END_REF], D3 [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], D3-BJ [START_REF] Grimme | Effect of the damping function in dispersion corrected density functional theory[END_REF], TS [START_REF] Tkatchenko | Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data[END_REF][START_REF] Bučko | Tkatchenko-Scheffler van der Waals correction method with and without self-consistent screening applied to solids[END_REF], TS-HI [START_REF] Bučko | Improved Density Dependent Correction for the Description of London Dispersion Forces[END_REF][START_REF] Bučko | Extending the applicability of the Tkatchenko-Scheffler dispersion correction via iterative Hirshfeld partitioning[END_REF], MBD [START_REF] Tkatchenko | Accurate and Efficient Method for Many-Body van der Waals Interactions[END_REF][START_REF] Ambrosetti | Long-range correlation energy calculated from coupled atomic response functions[END_REF][START_REF] Bučko | Many-body dispersion corrections for periodic systems: an efficient reciprocal space implementation[END_REF], and FI-MBD [START_REF] Gould | A Fractionally Ionic Approach to Polarizability and van der Waals Many-Body Dispersion Calculations[END_REF] methods that will be described in the computational details section.

The performances of these dispersion-corrected methods will be compared with the recently developed meta-GGA SCAN functional, which should correctly describe hydrogen bonds [START_REF] Sun | Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional[END_REF].

This method, at almost GGA cost, matches or improves on the accuracy of expensive hybrid functional when used to predict geometries and energies of diversely bonded molecules and materials (including covalent, ionic, metallic, hydrogen, and van der Waals bonds) [START_REF] Sun | Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional[END_REF].

In the present paper, we study the interaction between the amorphous silica and water, as a probe for the silanol chemistry, using the DFT-D toolbox in order to describe as accurate as possible the different types of silanol groups (isolated, vicinal, geminal, and in nests) independently. This will help to the understanding of the complex amorphous silica-water interface investigated since a decade [START_REF] Cimas | The amorphous silica-liquid water interface studied by ab initio molecular dynamics (AIMD): local organization in global disorder[END_REF][START_REF] Pfeiffer-Laplaud | Bimodal Acidity at the Amorphous Silica/Water Interface[END_REF].

COMPUTATIONAL DETAILS

Calculation settings

The Vienna Ab initio Simulation Package (VASP) software has been employed to perform DFT periodic calculations [START_REF] Hafner | Ab-initio simulations of materials using VASP: Density-functional theory and beyond[END_REF][START_REF] Kresse | Ab initio molecular-dynamics simulation of the liquid-metal-amorphoussemiconductor transition in germanium[END_REF]. Perdew Burke Ernzerhof (PBE) [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] semi-local exchangecorrelation functional is chosen, and electronic wave functions are expanded into plane waves with a cut-off energy of 450 eV. Electron-ion interactions have been described using the projected-augmented-wave (PAW) method [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF]. Kohn-Sham equations are solved selfconsistently until an energy difference of 10 -6 eV is reached [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF]. Atomic positions relaxation has been done until all forces become smaller than 0.01 eV/ Å per atom. The Γ-point is used in the Brillouin-zone integration. London dispersion interactions have been taken into account using several correction additive schemes to the PBE calculations. All these corrective methods provide an Edisp term to be added to the Kohn Sham energy and are available now in the VASP package [START_REF] Bučko | Improved Description of the Structure of Molecular and Layered Crystals: Ab Initio DFT Calculations with van der Waals Corrections[END_REF][START_REF] Bučko | Tkatchenko-Scheffler van der Waals correction method with and without self-consistent screening applied to solids[END_REF][START_REF] Bučko | Improved Density Dependent Correction for the Description of London Dispersion Forces[END_REF][START_REF] Bučko | Extending the applicability of the Tkatchenko-Scheffler dispersion correction via iterative Hirshfeld partitioning[END_REF][START_REF] Bučko | Many-body dispersion corrections for periodic systems: an efficient reciprocal space implementation[END_REF][START_REF] Gould | A Fractionally Ionic Approach to Polarizability and van der Waals Many-Body Dispersion Calculations[END_REF]. These methods include pairwise additive correction schemes of Grimme [START_REF] Grimme | Accurate description of van der Waals complexes by density functional theory including empirical corrections[END_REF][START_REF] Grimme | Semiempirical GGA-type density functional constructed with a long-range dispersion correction[END_REF][START_REF] Bučko | Improved Description of the Structure of Molecular and Layered Crystals: Ab Initio DFT Calculations with van der Waals Corrections[END_REF][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][START_REF] Grimme | Effect of the damping function in dispersion corrected density functional theory[END_REF] in which the C6 coefficients are available in literature (semi-empirical D2 [START_REF] Grimme | Semiempirical GGA-type density functional constructed with a long-range dispersion correction[END_REF] or corrected depending on the coordination number D3 [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]). In the D3-BJ version, the damping function has been improved [START_REF] Grimme | Effect of the damping function in dispersion corrected density functional theory[END_REF]. Tkatchenko and Scheffler (TS) have developed another approach based on the determination of C6 on the fly, depending on the chemical environment [START_REF] Tkatchenko | Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data[END_REF][START_REF] Bučko | Tkatchenko-Scheffler van der Waals correction method with and without self-consistent screening applied to solids[END_REF]. The Tkatchenko-Scheffler scheme with iterative Hirshfeld partitioning, TS/HI, is later developed and implemented in VASP by Bučko and co-workers [START_REF] Bučko | Improved Density Dependent Correction for the Description of London Dispersion Forces[END_REF][START_REF] Bučko | Extending the applicability of the Tkatchenko-Scheffler dispersion correction via iterative Hirshfeld partitioning[END_REF] and proved to describe more accurately dispersion interactions in both covalent and ionic systems [START_REF] Hessou | Adsorption of NO, NO2, CO, H2O and CO2 over isolated monovalent cations in faujasite zeolite: a periodic DFT investigation[END_REF][START_REF] Chebbi | Evaluation of volatile iodine trapping in presence of contaminants: A periodic DFT study on cation exchanged-faujasite[END_REF]. The more sophisticated nonadditive many-body variants of the TS scheme based on the adiabatic connection fluctuationdissipation (ACFD) theorem [START_REF] Tkatchenko | Accurate and Efficient Method for Many-Body van der Waals Interactions[END_REF][START_REF] Ambrosetti | Long-range correlation energy calculated from coupled atomic response functions[END_REF], without (MBD) [START_REF] Bučko | Many-body dispersion corrections for periodic systems: an efficient reciprocal space implementation[END_REF] and with (MBD-FI) [START_REF] Gould | A Fractionally Ionic Approach to Polarizability and van der Waals Many-Body Dispersion Calculations[END_REF] taking account of the ionicity effect, are discovered recently. The meta-GGA SCAN (Strongly Constrained and Appropriately Normed) functional obeys all 17 known exact constraints that a meta-GGA can and it is nearly exact for a set of appropriate norms including rare-gas atoms and non-bonded interactions, which make it more accurate to describe weak interactions [START_REF] Sun | Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional[END_REF][START_REF] Sun | Strongly Constrained and Appropriately Normed Semilocal Density Functional[END_REF].

Structural model

The amorphous silica model structure developed and studied by Tielens and his co-workers [START_REF] Tielens | Ab Initio Study of the Hydroxylated Surface of Amorphous Silica: A Representative Model[END_REF], which present a silanol density of 5.8 OH/nm 2 has been employed. The surface unit cell parameters are a = 12.77 Å, b = 17.64 Å, c = 25.17 Å (including 15 Å of vacuum) and it is composed of 27 Si, 67 O, and 26 H atoms. Figure 1 shows, from different views, the structure of the amorphous silica model and the types of studied silanols within. Silanol sites present on the Six sites were studied, (i) the isolated site, (ii) the geminal site, (iii) the vicinal site, (iv) the gemvic site, (v) the nest-1 site, and (vi) the nest-2 site. andc) top view (oxygen atom sphere in red, silica in grey, hydrogen in white).

Adsorption model

Figure 2 shows the various methods and starting geometries used to perform the calculations. Starting from a first initial geometry ("fromGeom0"), we relaxed the geometry of all systems (silica surface, water molecule, silica and water) using PBE functional or different dispersion-corrected PBE methods (PBE + D2, D3, D3-BJ, TS, TS-HI, MBD, FI-MBD). Using the new geometry obtained after the relaxation using the PBE method ("fromPBE") we performed single point dispersion-corrected PBE, dispersion-corrected PBE and meta-GGA SCAN geometry relaxations. As well, using the geometry obtained after the relaxation using PBE+D2 ("fromD2"), we performed dispersion-corrected PBE single point and geometry relaxation calculations.

Figure 2. Scheme showing the various methods (GGA PBE, dispersion-corrected PBE, and meta-GGA SCAN) and starting geometries used to perform single point and relaxation calculations.

For each method, the interaction energy between one type of silanol and water molecule has been determined through several sets of DFT calculations that allow to obtain the energy of pure silica surface E , the energy of isolated water molecule in the gaseous phase E , and the energy of the system (water molecule on silica surface) E . This energy, E , having a positive value corresponding to an exothermic process is determined as follows:

E = E + E -E (1)
In the case of dispersion-corrected PBE methods, the interaction energy can be described as the sum of the PBE (E ) and dispersion (E ) energies.

E = E + E (2)

RESULTS AND DISCUSSIONS

Protocol of relaxation

The interaction energies, between water and silanols, and their relative PBE and dispersion contributions have been evaluated, they are computed using DFT+D calculations over each site of the amorphous surface using different dispersion-correction methods. The integration of the vdW forces effect using those correction methods is made via three different routes (Figure 2).

The first route is called "fromGeom0", in which the non-corrected PBE, the corrected D2, D3, D3-BJ, TS, TS-HI, MBD, and FI-MBD methods were applied directly for a randomly placed water molecule over the selected site. The second route is called "fromPBE", in which firstly a geometry relaxation of the system for a randomly placed water molecule on the chosen site is done using PBE calculations, and then the dispersion-correction methods are added to perform new corrected relaxation on the PBE pre-relaxed configuration. The third route is called "fromD2", which is similar to the second route but with the relaxation using various correction methods (D3, D3-BJ, TS, TS-HI, MBD, FI-MBD) of the PBE+D2 pre-relaxed geometry. As well, single point dispersion-corrected PBE calculations were performed on those two prerelaxed configuration ("fromPBE" and "fromD2"). All those calculations aim to define a protocol of calculation in order to include the effect of the dispersion forces using the most accurate method keeping also in mind the calculation time. For the isolated, vicinal, geminal, and nest-1 silanols, a full relaxation calculation always lead to the same minima for a given level of theory, whatever the starting geometry, see Tables S1 to S4 in Supplementary Material.

However, the interaction energies over the Gem-Vic (Table 1) and the nest-2 (Table 2) sites are affected by the calculation procedure. The accuracy of the calculation procedure is assessed by comparing the total interaction energies following various routes, and by comparing the PBE contribution part of the interaction energy for dispersion-corrected calculation, with the noncorrected PBE interaction energy. These two criteria can give us an information about the reliability of the obtained results following the various method and routes in order to define a protocol of calculation that can be used to other similar systems. 2 shows that the best route to follow, in the search for the optimal calculation procedure, is to perform firstly a non-corrected PBE calculation to relax the geometry of a randomly placed water molecule over the site of the amorphous silica surface. Then relaxing again the "fromPBE" configuration using DFT+D calculation by adding one of the dispersioncorrection methods. Using this procedure, we can always attain the most stable state of the system, as we obtain the minimal total energy of the system which is inversely proportional to the total interaction energy (as the total energy of silica surface and water are not highly affected by the method or route used). In fact, when relaxing directly the "fromGeom0" using DFT+D, one can underestimate the PBE contribution (e.g. in Table 1, when using PBE + D2, TS, TS-HI, MBD, and FI-MBD to relax "fromGeom0" system). Therefore, we performed single point and relaxation dispersion-corrected calculations on the pre-relaxed non-corrected configuration ("fromPBE") and on the pre-relaxed D2-corrected configuration ("fromD2") aiming to attain a better accuracy with less computational costs. However, single point calculations of the prerelaxed "fromPBE" configuration does not allow reaching the best ground state energy of the system, which implicate a misestimating of the PBE part (e.g. in Table 1, when performing single point calculations for the "fromPBE" configuration using the PBE + TS, TS-HI, MBD, and FI-MBD methods). When performing geometry relaxation calculations on the pre-relaxed "fromD2" configuration using more sophisticated dispersion-correction methods, the structure can be trapped in the local energetic minimum state found using the D2 method (e.g. in Table 2, when using PBE + D3, D3-BJ, MBD, and FI-MBD to relax "fromD2" system). An additional evidence of this observation is that performing single point calculations using those vdW methods (D3, D3-BJ, MBD, FI-MBD) of "fromD2" configuration give the same interaction energies as the full relaxations. This was not the case for "fromPBE" full relaxations, meaning that the system always get out from the local minima (e.g. in Table 1, single point and full relaxation of "fromPBE" configuration using PBE+MBD method).

It is noticeable that by using the pre-relaxed "fromPBE" system, all dispersion-correction methods (from the simple D2 to the more sophisticated FI-MBD) proved to possess the ability to estimate the interaction energy within 5%, which can be considered as the standard error of the DFT calculation itself. However, the D2 method tends to give higher interaction energies than other methods and the TS-HI method tends to underestimate those energies. Finally, from an accuracy/cost point of view, applying D2 on a pre-relaxed "fromPBE" system can be sufficient to calculate the interaction energy of the water molecule on the selected site of the amorphous silica surface. To summarize, relax the pre-relaxed "fromPBE" configuration appears as the best option to reach the best local minima of the potential energy surface and describe more accurately the interaction between water and the different silanols types.

Analysis of the water interaction over different sites of the amorphous silica

The interaction (electrostatic PBE and dispersion contribution) energies of water on selected sites of the silica surface computed by relaxing the pre-relaxed "fromPBE" system using various dispersion-correction PBE methods (PBE + D2, D3, D3-BJ, TS, TS-HI, MBD, FI-MBD) or using the meta-GGA SCAN method, as well as the percentage contribution of the vdW forces on the interaction energies, are investigated and presented in Table 3. When comparing the results of the full relaxation using the PBE (GGA) and meta-GGA SCAN methods, we can confirm that the SCAN method take into consideration the vdW forces as interaction energies obtained are larger than those found by PBE calculations (except for the isolated site). Moreover, the meta-GGA SCAN gives interaction energy values very similar to those obtained by dispersion-corrected PBE methods. This indicates that the meta-GGA SCAN method describes as well accurately the vdW forces. In order to study the interaction types and distances, the FI-MBD corrected-DFT geometry relaxation of the pre-relaxed "fromPBE" system is considered. The initial and final (after relaxation) position of water molecule interacting with the silanols of the amorphous surface defines each selected site, those sites and the water-silanol interaction (expressed in the O-H bond distances e.g.) types are described in Table 4. They are presented in Figure 3 where the O-H bond distances are revealed. The water-silanols interactions are defined as acceptor or donor H-bonds depending on the site on the silica surface, the number and distances of those H-bonds are interpreted on each site. The H-bond is defined as acceptor when the oxygen atom of the water molecule interacts with a hydrogen atom of the silanol group, while it is defined as donor when the hydrogen atom of water molecule interacts with an oxygen atom of the silanol group of the silica surface. Each site on the silica surface is characterized by a number of H-bonds between water and different types of silanol groups. The length of those H-bonds varies between 1.60 and 2.20 Å depending on the number of H-bonds and the surrounding silanols. A graphical comparison of the interaction energies computed over the selected sites, using various dispersion-correction methods, is displayed in Figure 4. The comparison of the interaction energies over the selected sites of the silica surface shows that water is more likely to adsorb on vicinal silanols than on geminal ones. Water interaction energy for vicinal sites is higher than for geminal sites. This statement is also confirmed on the Gem-Vic site where the water molecule desorbs from its initial position close to the geminal silanol and adsorbs on a neighbor vicinal silanol. This behavior is expected to be related to the effect of steric hindering which affect the formation of H-bonds. Moreover, it is remarkable that the nest-2 site with three combined geminal-vicinal H-bond interactions shows higher water interaction energy than the nest-1 site with four vicinal H-bond interactions. Among all studied sites, the nest-2 with combined vicinal-geminal H-bond interactions shows the highest interaction energy, about 95 kJ/mol, compared to other sites. This contribution proved to be important over all studied sites, to reach up to 25% of the interaction energy on the vicinal site. It is clearly seen that on the nest-1 site with four H-bond interactions, the vdW contribution is the lowest comparing to other sites (around 10% depending on the dispersion-correction method). Since the pure electrostatic contributions to the Eint is well described in pure DFT (PBE) formalism, and that H-bonds have a strong electrostatic character; one can observe from Figure 5 that the more H-bonds formed, the higher is the electrostatic contribution and the smaller is the vdW contribution. Therefore, the Eint on hydrated silica is indeed electrostatically stabilized while dry/calcined silica surfaces are stabilized through vdW interactions.

The TS-HI method shows the lowest dispersion energy contribution to the interaction energy on most sites, which confirms the underestimation of the interaction energy using this method, as discussed previously.

The effect of water-silanol interactions on the deformation of the silica surface

Table 5 enables to interpret more properly the water interaction energetics on the silica surface, from which we can conclude that the FI-MBD dispersion correction method is the most accurate to relax the pre-relaxed "fromPBE" system. The interaction energy can be affected by two main phenomena, the deformation of the silica surface due to the interaction with the water molecule and the adsorption of the water molecule on the surface. This allows us to decompose the interaction energy in two parts (deformation and adsorption energies, see equation 3) in order to interpret the effect of water-silanol interactions on the deformation of the silica surface.

E = E + E (3)
The surface deformation E is therefore dependent on the silanol type and the number of H-bonds formed on each site. It can be evaluated as follows:

E = E . , + E . (4)
Where E . , the energy of the clean relaxed silica slab, and E . the energy of the relaxed hydrated silica slab without the water molecules. Silica is known to host water molecules and stabilizes according to its surrounding environment due to its structure flexibility. Indeed, the deformation of the surface until restructuration plays 20 an important role in the physico-chemical properties of silica [START_REF] Tielens | Characterization of amorphous silica based catalysts using DFT computational methods[END_REF]. The degree of hydration modulates the surface via the H-bonds formed with the surface silanols. From the surface deformation energies (See Table 5) one can observe a trend of relation between the type and number of H-bonds formed and the deformation energy. The largest effect is found for the nest-1 site (-46 kJ/mol), and the smallest effect is found for the isolated silanol involved in only one Hbond. Yet, this reconstruction energy is moderate compared to other systems such as furan or thiophene over MoS2 (around -200 kJ/mol) [START_REF] Badawi | DFT study of furan adsorption over stable molybdenum sulfide catalyst under HDO conditions[END_REF][START_REF] Cristol | DFT study of thiophene adsorption on molybdenum sulfide[END_REF].

Comparison with crystalline silica surfaces

Historically, amorphous silica models have been elaborated from cuts of crystal structure and contain segments resembling the (100) [START_REF] Simonetti | β-Cristobalite (001) surface as 4formaminoantipyrine adsorbent: First principle study of the effect on adsorption of surface modification[END_REF] and (111) β-cristobalite cuts [START_REF] Juan | Study of zirconocene and MAO interaction with SiO2 surfaces[END_REF], as admitted by

Simonetti and coworkers [START_REF] Simonetti | Density functional theory based-study of 5-fluorouracil adsorption on β-cristobalite (1 1 1) hydroxylated surface: The importance of H-bonding interactions[END_REF][START_REF] Compañy | 5-fluorouracil adsorption on hydrated silica: density functional theory based-study[END_REF] when studying the importance of H-bonds interactions during the adsorption of 5-fluorouracil on silica surface. Thus, it would be important to compare the water interaction over the studied amorphous surface with those over various crystalline structures. Three layers of (111), ( 101) and (001) β-cristobalite surfaces having silanol densities of 4.29, 5.24, and 7.42 OH/nm 2 , respectively, are constructed by cutting the bulk geometry of SiO2 parallel to the (111), ( 101) and (001) crystallographic planes [START_REF] Rozanska | Reconstruction and stability of β-cristobalite 001, 101, and 111 surfaces during dehydroxylation[END_REF][START_REF] Handzlik | Structure of Isolated Molybdenum(VI) and Molybdenum(IV) Oxide Species on Silica: Periodic and Cluster DFT Studies[END_REF]. The two bottom layers are frozen in the geometry of the bulk and the top layer is set free to relax. All silanol groups present at the (111) surface are isolated, those at the (101) surface are vicinal, while those at the (001) surface are geminal. Figure 6 shows the water interaction configuration on the three β-crystobalite silica surfaces and the H-bonds distances.

2.09Å

configuration, as well the same method was used to interpret the water interaction with the crystalline surfaces. Results show that water-silanol interaction on various sites of crystalline surfaces is more exothermic than on "look-alike" sites of the amorphous surface. This can be clearly seen from the vicinal site which shows the highest water interaction energy, while the geminal site shows the lowest on both amorphous and β-cristobalite surfaces. This observation can be very interesting to select an appropriate silica support for separation processes involving water, or for catalytic applications such as hydrodeoxygenation processes in order to decrease the inhibiting effect of water on the adsorption of oxygenated aromatics [START_REF] Olcese | Gas-phase hydrodeoxygenation of guaiacol over iron-based catalysts. Effect of gases composition, iron load and supports (silica and activated carbon)[END_REF][START_REF] Badawi | Effect of water on the stability of Mo and CoMo hydrodeoxygenation catalysts: A combined experimental and DFT study[END_REF]. Nevertheless, the silanols used in this study are chosen to be representative, as is supported by the previous studies undertaken with the same model [START_REF] Tielens | Ab Initio Study of the Hydroxylated Surface of Amorphous Silica: A Representative Model[END_REF].

CONCLUSIONS

Silica-based materials have attracted tremendous interest these recent years in many applications.

However, little is known regarding the role of each specific type of surface silanol group. Thus, a molecular description of these silanols and their interaction with water is needed for further ß-Crystobalite Silica Amorphous Silica BJ, TS, TS-HI, MBD, and FI-MBD) and meta-GGA SCAN methods to quantify the water interaction energies with the silica surface in order to distinguish the silanols sites, which allow to tune its properties.

We identified a protocol of calculation, where firstly the system is relaxed using non-corrected PBE method, and then the dispersion-correction relaxations are performed on the pre-relaxed system, in order to reach the correct minima of the potential energy surface. Comparing those correction methods, we found that all of them could be considered reliable when following the supposed protocol of calculation, with a preference for the FI-MBD method for geometrical optimization. Moreover, they all provide very close results, as well does the meta-GGA SCAN method, which strengthen our computed results. However, the TS-HI method provides smaller dispersion energies and thus interaction energies compared to the other dispersion-corrected methods.

We were able to identify the various silanol sites; each of them is characterized by a specific water interaction behavior (number and types of H-bonds) depending on its silanols coverage, types and surrounding environment. This is crucial for understanding the effect of each site on the silica properties and allows suggesting new synthesis methods to control those properties. Furthermore, the possible deformation of the surface due to the water interaction with the silanol nest proved to be important which need an additional interpretation of the defects generated from applying new synthesis methods. Finally, the comparison of similar sites of amorphous and crystalline surfaces highlighted the fact that the studied amorphous surface is less hydrophilic, which may be promising for catalytic [START_REF] Berro | Atomistic description of phenol, CO and H2O adsorption over crystalline and amorphous silica surfaces for hydrodeoxygenation applications[END_REF][START_REF] Badawi | Guaiacol derivatives and inhibiting species adsorption over MoS2 and CoMoS catalysts under HDO conditions: A DFT study[END_REF] or separation [START_REF] Chibani | A DFT investigation of the adsorption of iodine compounds and water in H-, Na-, Ag-, and Cu-mordenite[END_REF][START_REF] Jabraoui | Ab initio screening of cation-exchanged zeolites for biofuel purification[END_REF] applications where water can inhibit the adsorption of molecules of interest.

In summary, we discussed the singularity of selected silanol sites of the amorphous surface when interacting with water molecule, the necessity and reliability of dispersion correction methods in DFT calculations, and the effect of water interaction on the silica surface deformation. This study motivates the development of new synthesis of amorphous silica enabling to control the physicochemical properties of the surface.

Figure 1 .

 1 Figure 1. Different silanols sites of the amorphous silica model from various views: a) side view-1, b) side view-2, and c) top view (oxygen atom sphere in red, silica in grey, hydrogen in white).

Figure 3 .

 3 Figure 3. Water-silanols interaction (O-H bonds) types and distances on various sites of the amorphous silica: a) isolated, b) vicinal, c) geminal, d) Gem-Vic, e) nest-1, and f) nest-2.

Figure 4 .

 4 Figure 4. Water interaction energies over selected sites of the silica surface using various dispersion-correction methods.

  The contribution of the vdW forces on the interaction energy assessed through various dispersion-correction methods are compared in Figure5over various sites of the silica surface.

Figure 5 .

 5 Figure 5. Percentage contribution of the vdW forces on the interaction energies over the selected sites of the silica surface using different dispersion-correction methods.

Figure 6 .Figure 7 .

 67 Figure 6. Water interaction and H-bonds distances on the β-cristobalite silica: a) (111), b) (001), and c) (101) surfaces.A comparison of water interaction (PBE and dispersion contribution) energies on the vicinal isolated, and geminal sites of the (101), (111), and (001) β-crystobalite surfaces, respectively, versus "look-alike" sites of the amorphous surface is presented in Table6, and illustrated graphically in Figure7. The interaction energy values of water on amorphous surface admitted for this comparison are those found using FI-MBD-corrected PBE relaxation of "fromPBE"

Figure 7

 7 Figure 7 is of course only a snapshot of the complete picture in which the complete set of silanol groups should be considered in the comparison. A distribution of the silanol geometries per type can unfortunately not be considered due to the geometrical limitations of the model.

  improvement of silica formulations. Therefore, DFT calculations (single point and full relaxation) have been performed using different dispersion-correction PBE (PBE + D2, D3, D3-

Table 1 .

 1 Water interaction energies (PBE and dispersion contribution) over the gem-vic site of the amorphous surface obtained by single point and geometry relaxation calculations usingvarious procedure routes (different starting geometries and correction methods).

	Eint (EPBE/Edisp) (kJ/mol)	PBE	PBE +D2	PBE +D3	PBE+D3-BJ	PBE +TS	PBE+TS-HI	PBE +MBD	PBE+FI-MBD
	fromGeom0 relaxation	58	64 (46/18)	69 (57/12)	70 (57/13)	62 (49/13)	59 (50/9)	62 (48/14)	59 (49/10)
	fromPBE single point	*	72 (57/15)	69 (58/11)	71 (59/12)	81 (67/14)	83 (71/12)	93 (71/22)	91 (71/20)
	fromPBE relaxation	*	72 (58/14)	69 (58/11)	71 (58/13)	70 (58/12)	67 (57/10)	72 (57/15)	69 (58/11)
	fromD2 single point	*	*	60 (47/13)	61 (47/14)	61 (47/14)	56 (46/10)	61 (46/15)	59 (46/13)
	fromD2 relaxation	*	*	61 (48/13)	61 (47/14)	61 (48/13)	57 (47/10)	62 (47/15)	60 (47/13)

Table 2 .

 2 Water interaction energies (PBE and dispersion contribution) over the nest-2 site of the amorphous surface obtained by single point and geometry relaxation calculations using various procedure routes (different starting geometries and correction methods).

	Eint (EPBE/Edisp) (kJ/mol)	PBE	PBE +D2	PBE +D3	PBE+ D3-BJ	PBE +TS	PBE+TS -HI	PBE +MBD	PBE+FI -MBD
	fromGeom0 relaxation	74	61 (49/12)	93 (77/16)	95 (77/18)	96 (77/19)	88 (76/12)	90 (74/16)	93 (76/17)
	fromPBE single point	*	97 (76/21)	88 (77/11)	88 (79/9)	99 (87/12)	106 (92/14)	116 (91/25)	115 (92/23)
	fromPBE relaxation	*	97 (77/20)	93 (76/17)	94 (75/19)	96 (74/22)	88 (76/12)	95 (75/20)	93 (76/17)
	fromD2 single point	*	*	60 (49/11)	59 (49/10)	61 (49/12)	56 (50/6)	60 (49/11)	58 (49/9)
	fromD2 relaxation	*	*	61 (52/9)	60 (50/10)	95 (77/18)	88 (78/10)	60 (50/10)	58 (50/8)

Table 1 and

 1 Table

Table 3 .

 3 Water interaction (PBE and dispersion contributions) over selected sites of the silica surface using various dispersion-correction PBE methods and the meta-GGA SCAN method.

	Site	isolated geminal vicinal	Gem-Vic nest-1	nest-2
	Eint (kJ/mol)	PBE	34	29	45	58	56	74
		PBE+D2 41(36/5) 35(28/7) 60(44/16) 72(58/14) 68(59/9) 97(77/20)
		PBE+D3 42(35/7) 34(29/5) 59(44/15) 69(58/11) 64(57/7) 93(76/17)
	Eint (EPBE/Edisp) (kJ/mol)	PBE+D3-BJ PBE+TS 41(35/6) 33(28/5) 60(44/16) 70(58/12) 65(57/8) 96(74/22) 42(34/8) 33(29/4) 58(44/14) 71(58/13) 64(58/6) 94(75/19) PBE+TS-HI 40(35/5) 32(29/3) 54(44/10) 67(57/10) 64(55/9) 88(76/12)
		PBE+MBD 42(34/8) 34(28/6) 58(42/16) 72(57/15) 64(57/7) 95(75/20)
		PBE+FI-MBD	41(36/5) 32(29/3) 56(44/12) 69(58/11) 63(58/5) 93(76/17)
	Eint (kJ/mol)	meta-GGA SCAN	31	43	55	70	71	95
		PBE+D2	12	20	27	19	13	21
		PBE+D3	17	15	25	16	11	18
		PBE+D3-BJ	19	12	24	18	9	20
	Edisp/EPBE (%)	PBE+TS PBE+TS-HI	15 13	15 9	27 19	17 15	12 14	23 14
		PBE+MBD	19	18	28	21	11	21
		PBE+FI-MBD	12	9	21	16	8	18

Table 4 .

 4 Water-silanol interaction (O-H bonds) types over defined sites of the silica surface.

	Sites	isolated geminal vicinal Gem-Vic	nest-1	nest-2
	Initial position of water molecule	isolated geminal vicinal geminal	nest	isolated
	Final position of water molecule (after relaxation)	isolated geminal vicinal	vicinal	nest	nest
	H-bonds	one	2	2	2	4	3
	acceptor	one isolated	one geminal	one vicinal	one vicinal	three vicinal	one vicinal & one geminal
	donor	-	one geminal	one vicinal	one vicinal	one vicinal	one vicinal

Table 5 .

 5 Water-silanol interactions effect on the deformation of the silica surface (FI-MBDcorrected relaxation of the pre-relaxed "fromPBE" configuration).

	Sites

isolated geminal vicinal Gem-Vic nest-1 nest-2

		Interaction Eint	41	32	56	69	63	93
	Energies (kJ/mol)	Adsorption Eads Surface Edeform deformation	46 -5	48 -16	69 -13	78 -9	109 -46	113 -20

Table 6 .

 6 Comparison of water interaction energies on similar sites of the amorphous and crystalline surfaces (relaxation of "fromPBE" configuration using FI-MBD-corrected PBE calculations).

	Silica surface	Site	Eint (kJ/mol)	EPBE (kJ/mol)	Edisp (kJ/mol)
	(101) β-cristobalite	vicinal	82	70	12
	Amorphous silica	vicinal	56	44	12
	(111) β-cristobalite	isolated	74	61	13
	Amorphous silica	isolated	41	36	5
	(001) β-cristobalite	geminal	69	56	13
	Amorphous silica	geminal	32	29	3

Acknowledgements

HPC resources from GENCI-CCRT (Grant 2020-A0080910433) are acknowledged. YB thanks the Lebanese University and the CNRS-Lebanon for funding his Ph.D. We also acknowledge financial support through the PHC CEDRE Future Materials the COMETE project (COnception in silico de Matériaux pour l'EnvironnemenT et l'Energie) co-funded by the European Union under the program "FEDER-FSE Lorraine et Massif des Vosges 2014-2020". Computational resources and services were also provided by the Shared ICT Services Centre funded by the Vrije Universiteit Brussel, the Flemish Supercomputer Center (VSC) and FWO. "FT wishes to acknowledge the VUB for support, among other through a Strategic Research Program awarded to his group.

Data availability

The data that support the findings of this study are available from the corresponding author upon request.

Supplementary Material

See Supplementary Material for additional tables S1, S2, S3 and S4 presenting the water-silanols interaction energies (in addition to the PBE and dispersion contributions) over the isolated, geminal, vicinal, and nest-1 sites respectively obtained by single point and geometry relaxation calculations using various dispersion-corrected DFT methods and starting configurations.

Conflicts of interest


Unusual dysphagia

Antoine Schein (1)*, Martin Garcier (1), Anne Neuhart [START_REF] Hilton | Schwannomas and Their Pathogenesis: Schwannomas and Their Pathogenesis[END_REF] (1) Service d'Oto-rhino-laryngologie et Chirurgie cervico-faciale, Centre hospitalier universitaire Dijon-Bourgogne, 14 Rue Paul Gaffarel, 21000 Dijon, France

(2) Service d'Anatomo-pathologie, Centre hospitalier universitaire Dijon-Bourgogne, 14 Rue Paul Gaffarel, 21000 Dijon, France 1) Case report:

Mr R., 40 years old, was referred to the outpatients department by his general practitioner with high dysphagia to solids, progressively worsening over a period of 2 years, and recent onset of dysarthria. He had no notable medical or surgical history, no history of alcoholism or smoking and presented a good general state of health with no fever.

Physical examination demonstrated healthy mucosa, but palpation revealed a painless, indurated mass of the right lingual submucosa with normal tongue mobility. The patient did not present any signs of dyspnoea or any palpable cervical lymph nodes.

Neck MRI was requested (Figure 1.a).

Treatment consisted of surgical resection of the lesion and the specimen was sent for histological examination (Figure 1.b).

One month after the operation, the initial symptoms had completely resolved with satisfactory wound healing, but with deviation of the tongue towards the right.

2) Questions:

-What is your interpretation of the MRI? -What diagnoses would you consider? -What is your analysis of the histological section? -What is your final diagnosis?

What is your diagnosis?

3) Answers:

-MRI of the neck, post-gadolinium T1-weighted sequence, coronal section (left image) and sagittal section (right image) demonstrated a well circumscribed solid lesion on the right side of the base of the tongue with a necrotic component in the centre. It showed marked gadolinium enhancement with no invasion of adjacent soft tissues.

-Rhabdomyoma, Neurofibroma, Schwannoma, Leiomyoma.

-The following stains and magnifications were used: HES stain (Haematoxylin Eosin Saffron) examined at a magnification of x2.5 for the section on the left, immunohistochemical study of S100 protein examined at a magnification x5 for the section on the right of the figure.

Histological examination revealed a nodular lesion, clearly circumscribed peripherally by a fibrous capsule of variable thickness. The tumour was composed of a proliferation of fusiform cells with clearly defined cytoplasmic limits, an elongated and sometimes nucleolated nucleus (not visible at this magnification).

These cells were mainly arranged in intermingled bands. This proliferation was sometimes densely cellular (right image), sometimes looser, with zones of oedematous infiltration (left image). The tumour was richly vascular and comprised haemorrhagic zones (left image). No mitotic figure or necrotic zones were observed. The encapsulated tumour did not invade the surrounding striated muscle.

The immunohistochemical study showed diffuse and intense anti-PS100 antibody labelling of tumour cells, which did not express caldesmon, smooth muscle actin, CD31 and CD34. The coefficient of proliferation evaluated with Ki-67 antibody (MIB-1) was low, estimated at about 3%.

-The lesion was a right hypoglossal nerve schwannoma.

4) Discussion:

Schwannomas are usually benign nerve tumours arising from cells of Schwann's sheath. They rarely occur in the tongue. These tumours are difficult to diagnose because of the minimal symptoms. Schwann cells appear during the fourth week of embryological development. These glial cells ensure myelinization of axons, i.e. insulation and nerve conduction of the peripheral nervous system including spinal somatic and autonomic nerves as well as cranial nerves, except for the olfactory nerve (I) and the optic nerve (II) [START_REF] Ferner | Neurofibromatosis 1 and neurofibromatosis 2: a twenty first century perspective[END_REF].

The aetiology of these tumours remains unknown. However, several predisposing factors have been proposed: external trauma, chronic irritation, exposure to radiation [START_REF] Hilton | Schwannomas and Their Pathogenesis: Schwannomas and Their Pathogenesis[END_REF].

The classical clinical presentation is that of a solitary, round, encapsulated, indurated, painless and non-ulcerated nodule.

The clinical features of lingual schwannoma described in the literature often consist of progressive dysphagia. Patients may also experience odynophagia, referred otalgia, obstructive sleep apnoea, dysarthria, disorders of tongue mobility [START_REF] Sitenga | Clinical Features and Surgical Treatment of Schwannoma Affecting the Base of the Tongue: A Systematic Review[END_REF].

In this setting of nonspecific symptoms, a malignant tumour must also be considered, even in the absence of risk factors. Odynophagia is often unilateral and persistent, associated with ipsilateral referred otalgia. Neck palpation may demonstrate painless, indurated lymph nodes.

The main differential diagnoses of a benign, non-congenital lesion of the base of the tongue are rhabdomyoma, neurofibroma, plexiform neurofibroma, and leiomyoma. On contrastenhanced CT scan, schwannomas have a heterogeneous appearance, sometimes comprising zones of cystic or fat degeneration. On MRI, schwannomas are well circumscribed lesions, with a low-intensity signal on T1-weighted sequences and a high-intensity signal on T2weighted sequences with intense gadolinium enhancement. Several more specific radiological signs have been described, such as "split fat sign" (thin rim of enhancement of adipose tissue at the periphery of the lesion), "target sign" (central low-intensity signal), and "fascicular sign" (multiple circular images within the lesion). Plexiform neurofibromas are invasive lesions with a high-intensity signal on T2-weighted sequences, and rhabdomyosarcomas are lesions with indistinct margins with lymph node involvement [START_REF] Badar | Tongue base schwannoma: differential diagnosis and imaging features with a case presentation[END_REF].

Histological examination reveals elongated or fusiform cells with poorly defined cytoplasmic limits, with palisading nuclei (Antoni A histological pattern), often associated with Verocay bodies, and less densely cellular areas with looser stroma (Antoni B). Immunohistochemistry reveals diffuse and intense positivity for S100 protein [START_REF] Hilton | Schwannomas and Their Pathogenesis: Schwannomas and Their Pathogenesis[END_REF].

Treatment consists of complete surgical resection without safety margins. Cervical lymph node dissection is not indicated. The surgical incision must be adapted to the site and size of the schwannoma: transoral approach, suprahyoid pharyngotomy, mandibulotomy, submandibular incision.

Transoral robotic surgery can be performed when it allows sufficient exposure, resulting in decreased morbidity. The use of a robot provides better visualization of the operative site, with endoscopes providing high definition and highly magnified images. Dissection and haemostasis are more precise and avoid the effects of tremor [START_REF] Kayhan | Treatment of tongue base masses in children by transoral robotic surgery[END_REF]. Particular attention must be paid to lingual arteries, which are associated with a considerable bleeding risk.

The site of the tumour at the base of the tongue may require endoscopy-guided intubation, tracheotomy in the event of complications (oedema, secondary haemorrhage), as well as postoperative surveillance in an intensive care unit.

Postoperative enteral feeding by nasogastric tube with oral feeding as soon as healing is considered to be satisfactory appears to be the most commonly adopted approach.

Rare cases of malignant transformation of sporadic tumours have been reported, in a context of neurofibromatosis, or after irradiation. [START_REF] Hilton | Schwannomas and Their Pathogenesis: Schwannomas and Their Pathogenesis[END_REF].

Conflict of interest: The authors have no conflicts of interest to disclose.