Jérôme Cuny
email: jerome.cuny@irsamc.ups-tlse.fr

Jesus Cerda Calatayud

Narjes Ansari

Ali A Hassanali

Mathias Rapacioli

Aude Simon

Simulation of Liquids with the Tight-Binding Density-Functional Approach and Improved Atomic Charges

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Introduction

Molecular liquids are complex systems which theoretical description is of paramount importance to complement experiments in order to provide deeper insights into their structural, dynamical and thermodynamical properties. In particular, liquid water displays a variety of anomalous behaviours which make it a fascinating substance that has motivated a considerable amount of studies, [START_REF] Gillan | Perspective: How Good is DFT for Water?[END_REF][START_REF] Pettersson | Water-The Most Anomalous Liquids[END_REF][START_REF] Gallo | Water: A Tale of Two Liquids[END_REF][START_REF] Cisneros | Modeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy Functions[END_REF][START_REF] Fransson | X-Ray and Electron Spectroscopy of Water[END_REF][START_REF] Amann-Winkel | X-Ray and Neutron Scattering of Water[END_REF][START_REF] Ceriotti | Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges[END_REF] and in particular, theoretical investigations. [START_REF] Pettersson | Water-The Most Anomalous Liquids[END_REF][START_REF] Gallo | Water: A Tale of Two Liquids[END_REF][START_REF] Cisneros | Modeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy Functions[END_REF][START_REF] Fransson | X-Ray and Electron Spectroscopy of Water[END_REF][START_REF] Amann-Winkel | X-Ray and Neutron Scattering of Water[END_REF][START_REF] Ceriotti | Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges[END_REF][START_REF] Cho | Understanding all of Water's Anomalies with a Nonlocal Potentials[END_REF][START_REF] Robinson | Isosbestic Points in Liquid Water: Further Strong Evidence for the Two-State Mixture Model[END_REF][START_REF] Stanley | The Puzzling Behavior of Water at Very Low Temperature[END_REF][START_REF] Errington | Relationship between Structural Order and the Anomalies of Liquid Water[END_REF][START_REF] Angell | Insights into Phases of Liquid Water from Study of Its Unusual Glass-Forming Properties[END_REF][START_REF] Pallares | Anomalies in Bulk Supercooled Water at Negative Pressure[END_REF][START_REF] Perakis | Vibrational Spectroscopy and Dynamics of Water[END_REF] However, despite continuous theoretical and methodological developments in the field, the simulation of liquid water is still challenging and raises a number of theoretical issues which always necessitate to chose the correct balance between accuracy and computational cost. As such, various levels of approximation have been proposed to describe liquid water. On the one hand, a number of force fields (FF) such as TIP4P/2005, 15 TIP5P, [START_REF] Mahoney | A Five-Site Model for Liquid Water and the Reproduction of the Density Anomaly by Rigid, Nonpolarizable Potential Functions[END_REF] Thole-type (TTM) potentials, [START_REF] Thole | Molecular Polarizabilities Calculated with a Modified Dipole Interaction[END_REF][START_REF] Burnham | The Parametrization of a Thole-Type All-Atom Polarizable Water Model from First Principles and its Application to the Study of Water Clusters (n=2-21) and the Phonon Spectrum of Ice Ih[END_REF][START_REF] Burnham | Development of Transferable Interaction Models for Water. IV. A Flexible, All-Atom Polarizable Potential (TTM2-F) Based on Geometry Dependent Charges Derived from an Ab Initio Monomer Dipole Moment Surface[END_REF][START_REF] Burnham | Development of Transferable Interaction Models for Water. III. Reparametrization of an All-Atom Polarizable Rigid Model (TTM2-R) from First Principles[END_REF][START_REF] Fanourgakis | The Flexible, Polarizable, Thole-Type Interaction Potential for Water (TTM2-F) Revisited[END_REF] SPC/E, [START_REF] Berendsen | The Missing Term in Effective Pair Potentials[END_REF] and others, [START_REF] Cisneros | Modeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy Functions[END_REF][START_REF] Jorgensen | Comparison of Simple Potential Functions for Simulating Liquid Water[END_REF][START_REF] Habershon | Competing Quantum Effects in the Dynamics of a Flexible Water Model[END_REF][START_REF] Wu | Flexible Simple Point-Charge Water Model with Improved Liquid-State Properties[END_REF][START_REF] Paesani | An Accurate and Simple Quantum Model for Liquid Water[END_REF] have been developed to model liquid water under a wide range of temperatures and pressures. These potentials are computationally inexpensive and allow for long simulation even for large system sizes but they are limited as soon as an explicit electronic structure description is required. On the other hand, since the pioneering study by Laasonen et al. in the mid-1990's, [START_REF] Laasonen | Ab initio" Liquid Water[END_REF] density functional theory (DFT) has also been intensively used to model liquid water. Indeed, a number of DFT studies have probed the properties of water at the atomic level while rationalising the strengths and weaknesses of DFT for this particular system. [START_REF] Gillan | Perspective: How Good is DFT for Water?[END_REF] Nowadays, it is well recognised that an accurate description of liquid water at the DFT level should combine an hybrid functional, [START_REF] Todorova | Molecular Dynamics Simulation of Liquid Water: Hybrid Density Functionals[END_REF][START_REF] Guidon | Ab-Initio Molecular Dynamics using Hybrid Density Functionals[END_REF][START_REF] Zhang | First Principles Simulations of the Infrared Spectrum of Liquid Water Using Hybrid Density Functionals[END_REF][START_REF] Distasio | The Individual and Collective Effects of Exact Exchange and Dispersion Interactions on the Ab Initio Structure of Liquid Water[END_REF] dispersion interaction corrections [START_REF] Lin | Importance of Van der Waals Interactions in Liquid Water[END_REF][START_REF] Jonchiere | Van der Waals effects in ab initio water at ambient and supercritical conditions[END_REF][START_REF] Zhang | Structural and Vibrational Properties of Liquid Water from van der Waals Density Functionals[END_REF][START_REF] Møgelhøj | Ab Initio van der Waals Interactions in Simulations of Water Alter Structure from Mainly Tetrahedral to High-Density-Like[END_REF][START_REF] Distasio | The Individual and Collective Effects of Exact Exchange and Dispersion Interactions on the Ab Initio Structure of Liquid Water[END_REF] for a proper description of the potential energy surface on the one side, and the inclusion of nuclear quantum effects (NQEs) on the other side. [START_REF] Ceriotti | Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges[END_REF][START_REF] Chen | Hydrogen Bonding in Water[END_REF][START_REF] Morrone | Nuclear Quantum Effects in Water[END_REF][START_REF] Ceriotti | Nuclear Quantum Effects and Hydrogen Bond Fluctuations in Water[END_REF][START_REF] Fritsch | Nuclear Quantum Effects in Water: A Multiscale Study[END_REF][START_REF] Marsalek | Ab initio Molecular Dynamics with Nuclear Quantum Effects at Classical Cost: Ring Polymer Contraction for Density Functional Theory[END_REF] For instance, DiStasio et al. were able to obtain very accurate pair radial distribution functions (g(r)) using both an hybrid functional and dispersion interaction corrections. [START_REF] Distasio | The Individual and Collective Effects of Exact Exchange and Dispersion Interactions on the Ab Initio Structure of Liquid Water[END_REF] Chen and co-workers were also able to obtain a quite good structural description of liquid water using the SCAN functional. [START_REF] Chen | Ab Initio Theory and Modeling of Water[END_REF] The inclusion of NQEs was missing in those studies but such a simulation would be computational extremely costly and hardly applicable to questions such as reactivity in aqueous solution and solvation of large molecular species.

In contrast to liquid water, liquid benzene has sustained much less interest lately, although aromatic solvents are of particular interest in the petroleum industry where benzene and its derivatives are used as solvent for asphaltenes. [START_REF] Speight | Catalysis on the Energy Scene[END_REF] Much fewer experimental and theoretical studies were thus conducted. The structure of liquid benzene was studied by X-ray [START_REF] Narten | X-Ray Diffraction Pattern and Models of Liquid Benzene[END_REF] and neutron diffraction [START_REF] Misawa | Structure of Liquid Benzene and Naphthalene Studied by Pulsed Neutron Total Scattering[END_REF] experiments and few theoretical studies were achieved using FF potentials based on a Lennard-Jones description of the intermolecular interactions. [START_REF] Jorgensen | Aromatic-Aromatic Interactions: Free Energy Profiles for the Benzene Dimer in Water, Chloroform, and Liquid Benzene[END_REF][START_REF] Cabaço | Neutron Diffraction and Molecular Dynamics Study of Liquid Benzene and Its Fluorinated Derivatives as a Function of Temperature[END_REF][START_REF] Tassaing | The Structure of Liquid and Supercritical Benzene as Studied by Neutron Diffraction and Molecular Dynamics[END_REF][START_REF] Chelli | Simulated Structure, Dynamics, and Vibrational Spectra of Liquid Benzene[END_REF][START_REF] Chelli | The Fast Dynamics of Benzene in the Liquid Phase. Part II. A Molecular Dynamics Simulation[END_REF][START_REF] De La Peña | Discontinuous Molecular Dynamics for Rigid Bodies: Applications[END_REF][START_REF] Trumpakaj | Molecular Dynamics Simulation of Benzene[END_REF] To go a step further into the description of these liquids, it is desirable to develop an intermediate approach in between DFT and FF which computational cost would allow for the description of large systems (of several hundreds of molecules) while conserving an accuracy close to DFT results and an explicit description of the electronic structure. The selfconsistent-charge density-functional based tight-binding approach (SCC-DFTB, also referred to second-order DFTB or DFTB2) [START_REF] Porezag | Construction of Tight-Binding-Like Potentials on the Basis of Density-Functional Theory: Application to Carbon[END_REF][START_REF] Elstner | Self-Consistent-Charge Density-Functional Tight-Binding Method for Simulations of Complex Material Properties[END_REF][START_REF] Frauenheim | A Self-Consistent Charge Density-Functional Based Tight-Binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology[END_REF][START_REF] Elstner | The SCC-DFTB Method and its Application to Biological Systems[END_REF] meets these requirements due to the use of a minimal valence basis-set and parameterized integrals. Two important studies tested the ability of SCC-DFTB to model liquid water. In the first one, Maupin and co-workers discussed the performances of two SCC-DFTB formulations: the original formulation and a modified scheme proposed by Elstner that includes an optimized hydrogen-bond (HB) damping function. [START_REF] Elstner | The SCC-DFTB Method and its Application to Biological Systems[END_REF][START_REF] Maupin | The Self-Consistent Charge Density Functional Tight Binding Method Applied to Liquid Water and the Hydrated Excess Proton: Benchmark Simulations[END_REF] Both models lead to oxygen-oxygen, oxygen-hydrogen and hydrogen-hydrogen g(r)

that significantly differ from both DFT and experimental curves. In particular, they display g OO (r) functions that are almost flat beyond 3.5 Å which is associated to an overestimated water self-diffusion coefficient. In the second one, which extends a first study published in 2011 by the same authors, [START_REF] Goyal | Application of the SCC-DFTB Method to Neutral and Protonated Water Clusters and Bulk Water[END_REF] Goyal et al. applied various formulations of third-order DFTB (referred to as DFTB3) to liquid water. [START_REF] Goyal | Molecular Simulation of Water and Hydration Effects in Different Environments: Challenges and Developments for DFTB Based Models[END_REF] The author showed that standard DFTB3 does not improve significantly the g(r) with respect to SCC-DFTB results although an ad hoc correction of the O-H repulsive potential, obtained by means of an iterative Boltzmann inversion procedure to tune it, could highly improve the results. These studies show that there are still possibilities for improvement of the SCC-DFTB description of liquid water, as demonstrated by another very recent study that again uses the iterative Boltzman inversion procedure to fine tune the O-H and O-O repulsive potentials. [START_REF] Lourenço | Accurate SCC-DFTB Parametrization for Bulk Water[END_REF] Although SCC-DFTB has been applied to the description of other molecular liquids, [START_REF] Addicoat | Assessment of the Density Functional Tight Binding Method for Protic Ionic Liquids[END_REF] it has to our knowledge never been applied to liquid benzene.

The Mulliken definition of atomic charges used in the SCC-DFTB potential can be replaced by other approaches like the Class IV/Charge Model 3 (CM3) charge scheme,. [START_REF] Li | New Class IV Charge Model for Extracting Accurate Partial Charges from Wave Functions[END_REF][START_REF] Thompson | Parameterization of Charge Model 3 for AM1, PM3, BLYP, and B3LYP[END_REF] It can been used as a post-analysis scheme to improve the computation of electric dipoles, [START_REF] Kalinowski | Class IV Charge Model for the Self-Consistent Charge Density-Functional Tight-Binding Method[END_REF] or introduced in the DFTB potential to replace the Mulliken charge. [START_REF] Rapacioli | Correction for Dispersion and Coulombic Interactions in Molecular Clusters with Density Functional Derived Methods: Application to Polycyclic Aromatic Hydrocarbon Clusters[END_REF] In the latter case, it appeared to improve the structural and energetic properties of polycyclic aromatic hydrocarbon (PAH) clusters [START_REF] Rapacioli | Correction for Dispersion and Coulombic Interactions in Molecular Clusters with Density Functional Derived Methods: Application to Polycyclic Aromatic Hydrocarbon Clusters[END_REF][START_REF] Dontot | Structures and Energetics of Neutral and Cationic Pyrene Clusters[END_REF][START_REF] Zamith | Thermal Evaporation of Pyrene Clusters[END_REF][START_REF] Joblin | Size Effect in the Ionization Energy of PAH Clusters[END_REF] and water clusters isolated, with impurities or deposited on a PAH surface. [START_REF] Simon | Vibrational Spectroscopy and Molecular Dynamics of Water Monomers and Dimers Adsorbed on Polycyclic Aromatic Hydrocarbons[END_REF][START_REF] Simon | Water Clusters Adsorbed on Polycyclic Aromatic Hydrocarbons: Energetics and Conformational Dynamics[END_REF][START_REF] Simon | Conformational Dynamics and Finite-Temperature Infrared Spectra of the Water Octamer Adsorbed on Coronene[END_REF][START_REF] Oliveira | Phase Changes of the Water Hexamer and Octamer in the Gas Phase and Adsorbed on Polycyclic Aromatic Hydrocarbons[END_REF][START_REF] Korchagina | Structural Characterization of Sulfur-Containing Water Clusters Using a Density-Functional Based Tight-Binding Approach[END_REF] Encouraged by these results, we demonstrate in the present article how the use of an alternative formulation of the atomic charges, based on a non-symmetric repartition of the overlapping density between two centers, can improve the SCC-DFTB description of liquid water and benzene under ambient conditions. Furthermore, as mentioned above, NQEs have been shown to influence the g(r)'s of liquid water within the DFT framework (see [START_REF] Ceriotti | Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges[END_REF] and references therein). Consequently, we also report the coupling of the deMonNano 86 and i-PI [START_REF] Ceriotti | A Python Interface for Ab Initio Path Integral Molecular Dynamics Simulations[END_REF] codes which are used to probe the impact of NQEs through the path-integral molecular dynamics (PIMD) scheme [START_REF] Marx | Ab Initio Path-Integral Molecular Dynamics[END_REF][START_REF] Marx | Ab Initio Path Integral Molecular Dynamics: Basic Ideas[END_REF][START_REF] Habershon | Quantum Mechanical Correlation Functions, Maximum Entropy Analytic Continuation, and Ring Polymer Molecular Dynamics[END_REF][START_REF] Habershon | Ring-Polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space[END_REF] within the SCC-DFTB framework. Finally, the anisotropy of the hydration shell of a benzene molecule in water has also sustained a lot of interest lately [START_REF] Choudhary | Dynamics of Water in Conical Solvation Shells around a Benzene Solute under Different Thermodynamic Conditions[END_REF][START_REF] Choudhary | Anisotropic Structure and Dynamics of the Solvation Shell of a Benzene Solute in Liquid Water from Ab Initio Molecular Dynamics Simulations[END_REF] (and references therein) and we demonstrate that SCC-DFTB provides results of near-DFT quality for such system.

The paper is organized as follow: the computational methods and simulation details employed along the article are described in the Computational Details section. The results are presented in the Results and Discussion section where are first discussed the results obtained for liquid water, classical then quantum, and then the results for liquid benzene and a benzene molecule in liquid water. The main outcomes and perspectives are summarized in the Conclusion.

Computational Details

SCC-DFTB Potential and Weighted Mulliken Charges. Molecular dynamics simulations were performed using the SCC-DFTB formalism, [START_REF] Porezag | Construction of Tight-Binding-Like Potentials on the Basis of Density-Functional Theory: Application to Carbon[END_REF][START_REF] Elstner | Self-Consistent-Charge Density-Functional Tight-Binding Method for Simulations of Complex Material Properties[END_REF][START_REF] Frauenheim | A Self-Consistent Charge Density-Functional Based Tight-Binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology[END_REF][START_REF] Elstner | The SCC-DFTB Method and its Application to Biological Systems[END_REF] an approximated DFT scheme whose computational efficiency relies on the use of an atomic minimal valence basis-set {φ µ } and parameterized integrals. We recently introduced a modification consisting in replacing the Mulliken atomic charges used to compute the SCC-DFTB energy by the so-called Weighted Mulliken charges (hereafter, called WMull) [START_REF] Michoulier | Theoretical Determination of Adsorption and Ionisation Energies of Polycyclic Aromatic Hydrocarbons on Water Ice[END_REF][START_REF] Simon | Contribution of the Density-Functional-Based Tight-Binding Scheme to the Description of Water Clusters: Methods, Applications and Extension to Bulk Systems[END_REF] which introduce a non-symmetric bias directly into the Mulliken repartition of the overlapping density:

φ µ (r)φ ν (r) 1 2 S µν ((1 + t µν )|φ µ (r)| 2 + (1 -t µν )|φ ν (r)| 2 ) ( 1
)
where t µν is a free parameter ranging from -1 to 1, describing the polarity of a given chemical bond. The role of this parameter is similar to that of the empirical parameters used to compute CM3 charges, although not strictly equivalent. In the following, we investigate two approaches to determine t µν : (i) empirically as an atomic pair parameter (t µ∈A,ν∈B = t AB ), hereafter called the Weighted Mulliken (WMull) scheme or (ii) derived from atomic orbital energies through the expression t µν = µ µ+ ν , hereafter called the -Mulliken ( Mull) scheme. One interest of the WMull scheme with respect to the CM3 approach is its ease of implementation for periodic condition, mandatory for the present work. We may note that the WMull scheme has been recently used in an astrophysical context to describe water ice, [START_REF] Michoulier | Theoretical Determination of Adsorption and Ionisation Energies of Polycyclic Aromatic Hydrocarbons on Water Ice[END_REF] to compute IR spectra of PAH clusters (unpublished results) as well as in the study of the conformational change free-energy surface of alanine dipeptide in vaccum and in liquid water. [START_REF] Cuny | Metadynamics Combined with Auxiliary Density Functional and Density Functional Tight-Binding Methods: Alanine Dipeptide as a Case Study[END_REF] We also use an empirical correction term to take into account dispersion interactions [START_REF] Rapacioli | Correction for Dispersion and Coulombic Interactions in Molecular Clusters with Density Functional Derived Methods: Application to Polycyclic Aromatic Hydrocarbon Clusters[END_REF] with the atomic C 6 parameters derived by Wu and Yang et al.. [START_REF] Wu | Empirical Correction to Density Functional Theory for Van der Waals Interactions[END_REF] We used the mio-set for Slater-Koster tables. [START_REF] Elstner | Self-Consistent-Charge Density-Functional Tight-Binding Method for Simulations of Complex Material Properties[END_REF] All calculations were performed with the deMonNano code. [START_REF] Heine | deMon-Nano Experiment[END_REF] Classical Molecular Dynamics Trajectories. The SCC-DFTB classical trajectories of liquid water were performed for 128 water molecules in a 15.64 Å cubic box in the canonical ensemble at 300 K using a global Nose-Hoover chain of five thermostats with frequencies of 800 cm -1 and a 0.5 fs time step. [START_REF] Nosé | A Unified Formulation of the Constant Temperature Molecular Dynamics Methods[END_REF][START_REF] Hoover | Canonical Dynamics: Equilibrium Phase-Space Distributions[END_REF][100] In order to insure that the nature of the thermostat has no influence on the results, Figure S1 in Supporting Information compares g(r) functions of liquid water obtained with the Nose-Hoover chain and the stochastic velocity rescaling thermostat with a 1.0 ps time constant. 101 Comparisons with simulations performed in the microcanonical ensemble are also provided. The systems were equilibrated during 20 ps at 6 A similar procedure was conducted on two 31.28 Å cubic unit cells containing 1024 water molecules each. One of these simulations was obtained using Mulliken charges, the other one with the WMull scheme with t OH = 0.28. These two simulations were used to characterize the voids that exist within the hydrogen bond network of the simulated liquid water. To analysis the geometry of these voids, we used the Voronoi-Delaunay method 102 which is implemented in the VNP code. 103 In general, two radii, namely probe (R P ) and bottleneck (R B ), are needed to construct the Voronoi voids. The former is used for identification of the empty space between the molecules and the latter for merging the connected regions. Here, we used R P and R B equal to 1.2 and 1.1 Å, respectively. The interested reader may refer to references 104-106 for more details. For comparison, the voids obtained at the SCC-DFTB level were compared to those obtained using a FF simulation. In that case, a molecular dynamics simulation of TIP4P-Ew 107 liquid water (4096 molecules) was performed using the GROMACS 5.0 package 108 in a cubic box with an average side length 49.68 Å. The system was equilibrated for 2 ns with the time step of 2 fs, and the final production run was carried out over another 40 ns at NPT ensemble. The Nose-Hoover thermostat and the Parrinello-Rahman barostat 109 was used to fix the system temperature and pressure at 300 K and 1 bar, with coupling time constants of 2 ps and 1 ps respectively.

The SCC-DFTB simulations of liquid benzene consisted in 36 benzene molecules in a 17.47 Å cubic box to respect the density of liquid benzene, ∼0.87 g.cm -3 , at 300 K. In that case, a frequency of 400 cm -1 for the Nose-Hoover thermostat chain and a 0.5 fs time step were used with 100 ps of production run acquired for each simulation.

Simulations of one benzene molecule solvated in liquid water consisted in one benzene molecule and 126 water molecules in a 15.64 Å cubic box, a time step of 0.5 fs, and the frequency of the thermostat was set to 800 cm -1 . 200 ps of production run were used for analysis of the simulations.

Quantum Molecular Dynamics Trajectories of Liquid Water. The SCC-DFTB quantum simulations were performed by combining the deMonNano code with the i-PI code developed by Ceriotti et al. [START_REF] Ceriotti | A Python Interface for Ab Initio Path Integral Molecular Dynamics Simulations[END_REF] The simulations were performed under canonical conditions using a system of 128 water molecules in a 15.64 Å cubic box at 300 K. All the simulations used the PIGLET formalism that affords to use a lower number of replicas as compared to conventional PIMD simulations. 110,111 All our simulations were performed using 8 beads and a time step of 0.5 fs. In supporting information, a comparison with a PIMD simulation with 16 replicas and a PILE-g thermostat 112 with a 1.0 ps time constant is presented to insure the convergence of our PIGLET results. As for the classical simulations, the systems were equilibrated during 20 ps prior to 100 ps production run.

Results and Discussion

Description of Liquid Water Classical Description. Figure 1 provides a comparison between the g OO (r), g OH (r) and g HH (r) functions obtained using different values of the t OH parameter defined in the WMull formalism (see equation 1). We tested values going from 0.0, which corresponds to the original Mulliken charges, to 0.58. For comparison, we report on Figure 1 the DFT curves obtained by Marsalek and Markland using the revPBE-D3 functional to benchmark the present SCC-DFTB results. [START_REF] Marsalek | Ab initio Molecular Dynamics with Nuclear Quantum Effects at Classical Cost: Ring Polymer Contraction for Density Functional Theory[END_REF] It is well documented that different functionals lead to different g(r) functions for liquid water and that few of them lead to data quantitatively comparable to the experiment. In particular, no generalized-gradient approximated (GGA) functional properly describe the structure of liquid water. As a consequence, finding reference GGA-DFT radial distribution functions can hardly be done and is subject to randomness. Here, we choose the revPBE-D3 calculations by Marsalek and Markland as reference as it is a GGA functional derived from PBE, that is used to generate the SCC-DFTB parameters, [START_REF] Elstner | Self-Consistent-Charge Density-Functional Tight-Binding Method for Simulations of Complex Material Properties[END_REF] and that gives correct g(r) for liquid water.

In absence of charge correction, i.e. t OH = 0.0, the curves we report are similar to the [START_REF] Marsalek | Ab initio Molecular Dynamics with Nuclear Quantum Effects at Classical Cost: Ring Polymer Contraction for Density Functional Theory[END_REF] ones previously obtained for the description of liquid water at the SCC-DFTB level. [START_REF] Maupin | The Self-Consistent Charge Density Functional Tight Binding Method Applied to Liquid Water and the Hydrated Excess Proton: Benchmark Simulations[END_REF][START_REF] Goyal | Molecular Simulation of Water and Hydration Effects in Different Environments: Challenges and Developments for DFTB Based Models[END_REF] The shortcomings of this original SCC-DFTB formulation have already been pointed out and discussed, [START_REF] Maupin | The Self-Consistent Charge Density Functional Tight Binding Method Applied to Liquid Water and the Hydrated Excess Proton: Benchmark Simulations[END_REF][START_REF] Goyal | Molecular Simulation of Water and Hydration Effects in Different Environments: Challenges and Developments for DFTB Based Models[END_REF]113 we briefly remind them in the following. First, g OO (r) is significantly less structured than the DFT curve (see top panel of Figure 1) with a too broad first peak, the absence of minimum in the region around 3.3 Å and the absence of a well defined second solvation shell. Indeed, only a very weak maximum is obtained at ∼5.5 Å whereas the DFT curve displays such a maximum at ∼ 4.5 Å as well as a minimum at ∼5.5 Å. This latter does not exist in the SCC-DFTB curve. In contrast to the g OO (r), the g OH (r) and g HH (r) obtained at the SCC-DFTB level display the correct shapes with the correct number of maxima and minima. Nevertheless, the g OH (r) in the intermolecular region (i.e. for distances larger than 1.4 Å, see middle panel of Figure 1) also displays a lack of structuration: (i) the g OH (r) value at the maximum of the first peak is too low (1.08 instead of 1.38 at the revPBE-D3 level) although its position is reasonable at 1.87 Å (1.79 at the revPBE-D3 level) ; (ii) the g OH (r) value is too high for the first minimum and its position is shifted (2.36 Å against 2.50 Å at the revPBE-D3 level) ; (iii) the second maximum is too small and slightly shifted ; (iv) there is no maximum in the region around 5.2 Å. Similarly, the g HH (r) in the intermolecular region (i.e. for distances larger than 1.8 Å, see bottom panel of Figure 1), presents the following differences with respect to revPBE-D3 results: (i) a too low value for the first maximum with an up-shift of 0.09 Å ; (ii) a too high value for the first minimum with an up-shift of 0.17 Å ; (iii) a too low value for the second maximum with a down-shift of 0.07 Å. All these discrepancies demonstrate that the original SCC-DFTB formulation provides a very poor description of the structure of liquid water. As demonstrated by Maupin et al., [START_REF] Maupin | The Self-Consistent Charge Density Functional Tight Binding Method Applied to Liquid Water and the Hydrated Excess Proton: Benchmark Simulations[END_REF] this is associated to very poor dynamical properties. In particular, the self-diffusion coefficient of water is 1.11 ±0.04 Å2 .ps -1 at the SCC-DFTB level as compared to 0.1 and 0.23 Å2 .ps -1 at the DFT level (using the HCTH/120 functional) 114 and experimentally, 115 respectively. This much too high diffusion coefficient is explained by the flatness of g OO (r) above 3.5 Å and the absence of a well defined second solvation shell.

When the WMull correction is introduced, the three g(r) are significantly impacted. Indeed, increasing the t OH value results in a better structuration of the g OO (r) which partly corrects the aforementioned defaults of the original Mulliken charges: (i) a minimum progressively appears around 3.3 Å ; (ii) the structuration of the second solvation shell improves with the appearance of a maximum and a minimum at ∼4.6 and ∼5.7 Å, respectively. If compared to the revPBE-D3 curve, the higher t OH , the better the comparison is between the SCC-DFTB and revPBE-D3 curves beyond 3 Å. However, as t OH increases, the height of the first peak of the g OO (r) also increases to very high values. The same behavior is observed for g OH (r) and g HH (r). Indeed, in both case, increasing t OH makes the SCC-DFTB curves closer to the DFT ones at the first minimum and second maximum. However, a too large value leads to a too high first peak (see middle and bottom panels of Figure 1). For g OH (r), whatever t OH , the positions of the first minimum and second maximum remain down-shifted with respect to the revPBE-D3 curve. In contrast, for g HH (r), increasing t OH leads to peak positions that are closer to the DFT ones.

As first conclusions, the use of improved charges clearly leads to g(r) that are closer to DFT curves. In particular, it allows to recover the correct shape of the g OO (r) which was totally missing with the original Mulliken charges. Consequently, a much better description of the second solvation shell of the water molecules is obtained. However, from the present tests, it is clear that no t OH value can lead to perfect results. Indeed, while a better description of this second solvation shell is obtained by increasing t OH , this also leads to an over-structuration of the first solvation shell reflected in a too high first intermolecular peak in the three g(r). So a balance has to be chosen. t OH values of 0.28 and 0.38 appear as good compromises to correctly describe both regions of the three g(r). At this point, it is important to notice that the WMull scheme was previously used in the context of the description of water clusters. [START_REF] Michoulier | Theoretical Determination of Adsorption and Ionisation Energies of Polycyclic Aromatic Hydrocarbons on Water Ice[END_REF] and in that study, the authors determined a t OH value so as to reproduce the binding energies of water clusters previously obtained with the CM3 charge correction. Interestingly, a t OH value of 0.39 was obtained, close to the higher limit for liquid water determined in this work. The present results can be discussed in the light of the work by Goyal et al. on the modelling of liquid water with DFTB3. [START_REF] Goyal | Molecular Simulation of Water and Hydration Effects in Different Environments: Challenges and Developments for DFTB Based Models[END_REF] As for SCC-DFTB, original formulation of DFTB3 does not provide a good description of the liquid water structure.

However, using a reverse Monte Carlo algorithm based on the experimental curve, which has also been done in other studies, 116 the authors determined the shape of E rep OH that would leads to the a correct g OO (r). Interestingly, this a priori repulsive function becomes attractive in the 1.6-3.5 Å region. This demonstrates that SCC-DFTB (and DFTB3) miss some physics in the description of the water-water interaction at mid-distance and one hypothesis is the absence of atomic polarizability resulting from the use of a minimal basis set. An ad-hoc introduction of atomic polarizabilities in SCC-DFTB has already been proposed but it has not yet been considered for the description of liquid water. 117

To go a step further into describing the impact of the charge correction, Figure 2 displays the g OO (r), g OH (r) and g HH (r) functions obtained from the WMull scheme, with t OH values of 0.0, 0.28, 0.38, as well as from the Mull scheme. For comparison, the revPBE-D3 curves and the experimental data by Sopper and Benmore are also reported. 118 In the Supporting Information, comparison with the experimental data by Skinner et al. 119 for g OO (r) and Wikfeldt et al. for g OH (r) and g HH (r), 120 are provided and discussed. In the three cases, the Mull scheme for charge correction leads to equivalent results as the WMull scheme with t OH = 0.28. The most striking feature in Figure 2 is the correct qualitative agreement between the SCC-DFTB g(r) and the experimental curves. Indeed, although the match between SCC-DFTB and revPBE-D3 curves is far from being perfect due to the well-known over-structuration obtained from conventional GGA-based functionals, comparison with experiment is better. This is true for all g(r) features displayed in Figure 2 except for the first peak of g OO (r) which is still too high even compared to experiment.

As a conclusion to this analysis, it appears that the atomic charges corrections proposed in Eq. ( 3) lead to a general improvement of the water g(r). Within the WMull scheme, a correcting factor of t OH = 0.28 appears as a good compromise to recover the main features of g OO (r), g OH (r) and g HH (r) without introducing artefacts and without additional computational cost. Interestingly, the WMull scheme with t OH = 0.28 gives similar results as the Mull scheme, therefore also suitable. This gain in accuracy is also true for other properties. In particular, the self-diffusion coefficient of water, which is 1.11 ±0.04 Å2 .ps -1 at the original SCC-DFTB level, 69 is 0.78 Å2 .ps -1 using t OH = 0.28. This lower value results from the more structured liquid water obtained with the improved charges. The heat of vaporization was also calculated following the procedure described in ref. [START_REF] Maupin | The Self-Consistent Charge Density Functional Tight Binding Method Applied to Liquid Water and the Hydrated Excess Proton: Benchmark Simulations[END_REF] Using t OH = 0.28 and 0.38 leads to values of 7.93 and 9.17 kcal.mol -1 , respectively, which are both closer to the experimental value, 10.50 kcal.mol -1 , than the original SCC-DFTB formulation which gives 4.09 kcal.mol -1 . This arises from the better description of the hydrogen bonding energy when improved charges are included. Finally, Figure S5 of the Supporting Information presents how the proton-transfer energy barrier changes with the inclusion of the weighted Mulliken charges. As can be seen, while the original SCC-DFTB formulation is characterized by a very low energy barrier, both t OH = 0.28 and 0.38 lead to a drastic improvement as compared too MP2/aug-cc-pVTZ calculations, although still underestimating the barrier. Although more complete investigations are necessary, these preliminary results are encouraging in the view of describing reactive processes in liquid water using SCC-DFTB with improved charges.

As mentioned above, an optimized t OH value of 0.39 was obtained for water clusters based on the energetics of finite-size systems. [START_REF] Michoulier | Theoretical Determination of Adsorption and Ionisation Energies of Polycyclic Aromatic Hydrocarbons on Water Ice[END_REF] This demonstrates that, although an overall improvement of the description of liquid water can be obtained using the WMull and Mull schemes, some empirical insight must be introduced for a refined tuning of the charge correction. Finally, it is worth mentioning that such correction does not solve all the discrepancies of DFTB for the simulations of liquid water. In particular, the appearance of large voids in the simulations, which was already highlighted by Choi et al.,113 is still present as demonstrated in Figure 3. Indeed, the distributions of void volumes at the SCC-DFTB level is found to be very similar to the TIP4P-Ew distribution except for void volumes larger than 200 Å3 for which they are higher. Unfortunately, the WMull correction is found to have nearly no effect. This was expected as Choi et al. attributed this deficiency to the too intense first peak in g OO (r). This suggests that further improvement of the O-H and O-O SCC-DFTB parametrization will be needed to attenuate the intensity of the first g OO (r) peak in order to counterpart this default. Impact of NQEs. As stated in introduction, the role of nuclear quantum effect can be non negligeable on the liquid water g(r), in particular g OH (r) and g HH (r). [START_REF] Ceriotti | Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges[END_REF][START_REF] Chen | Hydrogen Bonding in Water[END_REF][START_REF] Morrone | Nuclear Quantum Effects in Water[END_REF][START_REF] Ceriotti | Nuclear Quantum Effects and Hydrogen Bond Fluctuations in Water[END_REF][START_REF] Fritsch | Nuclear Quantum Effects in Water: A Multiscale Study[END_REF][START_REF] Marsalek | Ab initio Molecular Dynamics with Nuclear Quantum Effects at Classical Cost: Ring Polymer Contraction for Density Functional Theory[END_REF] To probe their impact on the present simulations, we now present simulations performed using the PIMD technique as implemented in the i-PI code. [START_REF] Ceriotti | A Python Interface for Ab Initio Path Integral Molecular Dynamics Simulations[END_REF] Figure 4 provides a comparison between the g OO (r), g OH (r) and g HH (r) functions obtained at 300 K using the WMull scheme with t OH = 0.28 and 0.58. Results from both classical and quantum simulations are displayed along with the experimental data of Sopper and Benmore. 118

The g OO (r) is only slightly affected by NQEs, the main difference with classical simulation being a small decrease of the first peak intensity. For t OH = 0.28 , behind 3 Å the classical and quantum curves are identical. For t OH = 0.58, slight differences exist between the classical and quantum curves as the first and second maximum are slightly higher and lower, respectively, in the quantum simulation. Those effects on g OO (r) are expected from PIMD simulations and have already been highlighted theoretically. [START_REF] Morrone | Nuclear Quantum Effects in Water[END_REF][START_REF] Marsalek | Ab initio Molecular Dynamics with Nuclear Quantum Effects at Classical Cost: Ring Polymer Contraction for Density Functional Theory[END_REF] This is also what is observed experimentally when going from H 2 O to D 2 O. 118 Interestingly, Figure 4 demonstrates that the impact of NQEs is stronger when applied to a more structured liquid water, in the present case going from t OH = 0.28 to 0.58. This explains why in the SCC-DFTB g OO (r) case the impact of NQEs is rather low while it is much stronger when considering DFT simulations that lead to a more structured liquid. [START_REF] Chen | Hydrogen Bonding in Water[END_REF][START_REF] Morrone | Nuclear Quantum Effects in Water[END_REF][START_REF] Fritsch | Nuclear Quantum Effects in Water: A Multiscale Study[END_REF][START_REF] Gasparotto | Probing Defects and Correlations in the Hydrogen-Bond Network of ab Initio Water[END_REF][START_REF] Marsalek | Ab initio Molecular Dynamics with Nuclear Quantum Effects at Classical Cost: Ring Polymer Contraction for Density Functional Theory[END_REF] As expected, the impact of NQEs is stronger on g OH (r) and g HH (r). As for g OO (r), the effect is enhanced for t OH = 0.58 with resepct to 0.28, as the liquid is more structured and thus more sensitive to NQEs. More specifically, the two maxima of g OH (r) at 1.82 and 3.25 Å decrease while the minimum at 2.38 Å increases. Overall, inclusion of NQEs leads to a better agreement with the experimental curve although the aforementioned discrepancies remain. These effects are similar to those reported from DFT simulations. [START_REF] Morrone | Nuclear Quantum Effects in Water[END_REF][START_REF] Fritsch | Nuclear Quantum Effects in Water: A Multiscale Study[END_REF][START_REF] Marsalek | Ab initio Molecular Dynamics with Nuclear Quantum Effects at Classical Cost: Ring Polymer Contraction for Density Functional Theory[END_REF] Although the same general remarks can be drawn for g HH (r), the inclusion of NQEs now makes the t OH = 0.28 curve match very well with the experimental data up to ∼4 Å.

To conclude, combining the PIMD algorithm to the present SCC-DFTB potential leads to g(r) modifications similar to what was reported at the DFT level. NQEs leads to g(r)

functions that are closer to the experimental data in terms of intensities but do not correct the fundamental errors of the SCC-DFTB potential. The present simulations also show that their impact on the intensities varies with charge correction.

Description of Liquid Benzene

In this section, we focus on the description of liquid benzene restricting the study to classical MD. We investigate the influence of the t CH value on the carbon-carbon (g CC (r)), center of mass-center of mass (g CM -CM (r)) and all atoms-all atoms (g BzBz (r)) intermolecular pair radial distribution functions. Three t CH values were tested: 0, corresponding to the Mulliken scheme, 0.30 which was used to study PAHs in interaction with water ice, [START_REF] Michoulier | Theoretical Determination of Adsorption and Ionisation Energies of Polycyclic Aromatic Hydrocarbons on Water Ice[END_REF] and the intermediate value of 0.15. The results are reported in Figure 5 along with experimental [START_REF] Narten | X-Ray Diffraction Pattern and Models of Liquid Benzene[END_REF] and FF results from other works. [START_REF] Cabaço | Neutron Diffraction and Molecular Dynamics Study of Liquid Benzene and Its Fluorinated Derivatives as a Function of Temperature[END_REF][START_REF] Chelli | The Fast Dynamics of Benzene in the Liquid Phase. Part II. A Molecular Dynamics Simulation[END_REF] The limitation of our approach in comparison with previous studies is the size of the system: we are only able to compare our data for C-C and Bz-Bz distances up to 8 Å although experimental and other FF data are provided for distances up to about 15 Å.

As can be seen in Figure 5, the influence of WMull is little for g CC (r), but can be clearly seen for g CM -CM (r), and also for g BzBz (r) to a lesser extent, as an increase of the t CH value leads to enhanced structuration, similarly to what we observe for water. Regarding g CC (r), one shoulder is found at 4 Å (intensity of 0.9), and two maxima are found at 4.9 Å

(1.08) and 6 Å (1.16). The SCC-DFTB g CC (r) appears in very good agreement with FF results obtained with an intermolecular potential aiming at describing anisotropic interactions (Anisotropic United Atoms intermolecular potential) 121 and to a lesser extent with the experimental ones. [START_REF] Narten | X-Ray Diffraction Pattern and Models of Liquid Benzene[END_REF][START_REF] Jorgensen | Aromatic-Aromatic Interactions: Free Energy Profiles for the Benzene Dimer in Water, Chloroform, and Liquid Benzene[END_REF] Indeed, similarly to FF simulations, the SCC-DFTB approach appears to underestimate the correlation fluctuations of the CC pairs for all t CH values.

Regarding g CM -CM (r), one broad peak is observed for distances smaller than 8 Å, with a maximum located at 5.4 Å in the case of Mulliken charges, down to 5.2 Å for a t CH value of 0.30. When increasing t CH the peak becomes more assymetric, with a maximum slightly shifted towards smaller r. This can be explained as follow: based on the results for the benzene dimer in the gas phase, we show that the maximum at 5.2-5.4 Å is due to T-shape configurations between benzene molecules, the equilibrium intermolecular distance for such configuration in the gas phase being ∼ 4.8 Å. [START_REF] Rapacioli | Correction for Dispersion and Coulombic Interactions in Molecular Clusters with Density Functional Derived Methods: Application to Polycyclic Aromatic Hydrocarbon Clusters[END_REF] As an increase of t CH leads to an enhanced C-H bond polarity, the CM-CM distance is expected to decrease when increasing t CH . Interestingly, the starting rise of g CM -CM (r) starts at shorter distance, which would be more in line with the intermolecular distance within benzene molecules in π interaction (3.5 Å in the gas phase [START_REF] Rapacioli | Correction for Dispersion and Coulombic Interactions in Molecular Clusters with Density Functional Derived Methods: Application to Polycyclic Aromatic Hydrocarbon Clusters[END_REF] ). Below 4.0 Å, g CM -CM (r) diminishes as t CH increases. This can be understood [START_REF] Cabaço | Neutron Diffraction and Molecular Dynamics Study of Liquid Benzene and Its Fluorinated Derivatives as a Function of Temperature[END_REF][START_REF] Chelli | The Fast Dynamics of Benzene in the Liquid Phase. Part II. A Molecular Dynamics Simulation[END_REF] For g CC (r), the experimental curve of Narten is reported. [START_REF] Narten | X-Ray Diffraction Pattern and Models of Liquid Benzene[END_REF] The inset of the middle panel is a zoom in the 4-10 Å region.

because, as mentioned above, the WMull scheme increases the C-H bond polarity and therefore is expected to lead to a higher T-shape/π stacking ratio. These curves, not accessible by experiments, can be compared to those obtained from FF simulations. [START_REF] Cabaço | Neutron Diffraction and Molecular Dynamics Study of Liquid Benzene and Its Fluorinated Derivatives as a Function of Temperature[END_REF][START_REF] Chelli | The Fast Dynamics of Benzene in the Liquid Phase. Part II. A Molecular Dynamics Simulation[END_REF] Increasing t CH improves the agreement with the FF results as it tends to increase the intensity of the peak maximum. However it remains more asymmetric. This is expected as the anisotropic character of the interactions is inherently described with SCC-DFTB whereas it is not the case for most FF potentials. Finally, for g BzBz (r), the agreement is very good with the FF curve obtained by Cabacao et al., [START_REF] Cabaço | Neutron Diffraction and Molecular Dynamics Study of Liquid Benzene and Its Fluorinated Derivatives as a Function of Temperature[END_REF] with the main discrepancy located in the 4.9-5.1 Å region where the SCC-DFTB intensity is lower. The SCC-DFTB g BzBz (r) curve is also found slightly lower than the FF curve published by Chelli et al.. [START_REF] Chelli | The Fast Dynamics of Benzene in the Liquid Phase. Part II. A Molecular Dynamics Simulation[END_REF] To conclude, it appears that the influence of the WMull scheme is only visible on g CM -CM (r) as increasing the t CH value slightly favor T-shape configurations while decreasing CM-CM distance for this configuration. As the best agreement with previous FF simulations is obtained for t CH = 0.30, this value can be considered for further studies. However, the agreement with experimental data is not perfect as the structuration of g CC (r) remains underestimated at the SCC-DFTB level.

From a dynamical point of view, t CH = 0.30 leads to a self-diffusion coefficient of benzene of

Application: Benzene Molecule Solvated by Water

In the view to describe the behaviour of asphaltene molecules and clusters at a aromatic solvent/water interface, one has to first evaluate the accuracy of SCC-DFTB to describe the interaction of aromatic hydrocarbons with liquid water. We therefore conducted SCC-DFTB simulations of one benzene molecule solvated in water using t OH , t CH and t CO values of 0.28, 0.30 and 0.08, respectively. The first two values are determined in the present work, the third one is taken from reference. [START_REF] Michoulier | Theoretical Determination of Adsorption and Ionisation Energies of Polycyclic Aromatic Hydrocarbons on Water Ice[END_REF] We calculated the radial distribution functions between the center of mass of benzene and the oxygen atoms of water molecules (g CM -O (r)) located in a cone of angle θ axial around the benzene axial axis or θ equatorial from the equatorial plane (see inset in Figure 6), as previously achieved by Choudary et al. [START_REF] Choudhary | Anisotropic Structure and Dynamics of the Solvation Shell of a Benzene Solute in Liquid Water from Ab Initio Molecular Dynamics Simulations[END_REF] Focusing on the evolution of g CM -O (r) as a function of θ axial (Figure 6 (a)), a very sharp peak is observed at r = 3.1 Å (g = 6.3) for an angle of 15 • . In terms of intermolecular orientation, this corresponds to the water molecule interacting via a hydrogen atom with the π cloud of benzene, that we previously found as the most stable configuration of the isolated benzene-water dimer within our SCC-DFTB approach. [START_REF] Simon | Vibrational Spectroscopy and Molecular Dynamics of Water Monomers and Dimers Adsorbed on Polycyclic Aromatic Hydrocarbons[END_REF]123 The r = 3.1 Å value is the smallest possible distance that can be obtained for such dimer. When increasing θ axial , the sharpness of the peak decreases, it becomes flatter up to θ = 45 • and becomes a shoulder for θ axial > 45 • . This is due to the progressive average of water-benzene orientations with θ axial .

The agreement for both peak position and intensity between the SCC-DFTB and the DFT-D results is very satisfactory. For θ axial = 15 • , we obtain a peak position of 3.1 Å (g = 6.3) whereas a value of 3.2 Å (g = 6.8) was obtained at the DFT-D level (see Figure 3 (a) of ref. [START_REF] Choudhary | Anisotropic Structure and Dynamics of the Solvation Shell of a Benzene Solute in Liquid Water from Ab Initio Molecular Dynamics Simulations[END_REF] for comparison). The evolution of the peak as a function of θ axial is identical (see Figure 2 atom with the H atoms of benzene in its plane. We found that such conformation was slightly less stable at the SCC-DFTB level than the π-H conformation or the dimers in the gas phase. 123 Besides, when θ equatorial increases, a shoulder appears for r values between 3 and 4 Å, which corresponds to the π-H intermolecular interactions accounting for the sharp peak observed at θ axial = 15 • (see above). The minimum obtained at ∼6.4 Å is steady in position and intensity (g = 0.8) when θ equatorial increases, and similar steadiness is found for the next maximum located at r = 7.7 Å (g = 1.2). These behaviors are found to be identical to those determined at the DFT-D level (see Figure 3 (c) of ref. [START_REF] Choudhary | Anisotropic Structure and Dynamics of the Solvation Shell of a Benzene Solute in Liquid Water from Ab Initio Molecular Dynamics Simulations[END_REF] ).

Such a good agreement with one of the most accurate simulation that can be achieved on that type of system validates the description of aromatic molecule-liquid water intermolecular interactions within our SCC-DFTB scheme and, due to its computational efficiency, opens the way to further applications dedicated to the study of aromatic solvent/water interfaces.

Conclusions

In this work, we benchmarked the recent introduction of Weighted Mulliken charges in the SCC-DFTB potential for the description of liquids. Those charges allow for a better description of bond polarities as compared to the original Mulliken charges. Three systems were considered: liquid water, liquid benzene, and a benzene molecule in water. In the case of liquid water, the main effect of the improved charges is to increase the structuration of the g(r). These lead to a significant improvement of the three pair radial distribution functions of liquid water with respect to those obtained with the original Mulliken charges.

The improvements are obtained at no computational cost and no re-parametrization of the SCC-DFTB integrals is required. This study is thus a step forward in the description of liquid water at the SCC-DFTB level that demonstrates the need for using well defined atomic charges. However, all the actual limitations of the SCC-DFTB formalism cannot be solved this way, and an accurate description of liquid water at this level of theory will require further developments. We also tested the impact of NQEs on the g(r) using the PIMD formalism. The effects are similar to those observed at the DFT level. They mainly consist in a slight decrease of the structuration of the g OH (r) and g HH (r) curves as compared so classical simulations.

Correction of the atomic charges also leads to a good description of the structure of aromatic hydrocarbon solvents, although the effect of the charge definition is more limited than for liquid water. More importantly, we can achieve a rather good description of a benzene molecule in liquid water. This, in addition to studies performed on aqueous molecular clusters in the gas phase and alanine dipeptide in water, [START_REF] Korchagina | Structural Characterization of Sulfur-Containing Water Clusters Using a Density-Functional Based Tight-Binding Approach[END_REF][START_REF] Simon | Contribution of the Density-Functional-Based Tight-Binding Scheme to the Description of Water Clusters: Methods, Applications and Extension to Bulk Systems[END_REF][START_REF] Cuny | Metadynamics Combined with Auxiliary Density Functional and Density Functional Tight-Binding Methods: Alanine Dipeptide as a Case Study[END_REF] suggests that the actual formulation of the SCC-DFTB potential, although not perfect, can be used to describe the solvation of molecules in liquid water. In that domain the efficiency of the SCC-DFTB formalism could be of use to circumvent the computational cost of DFT simulations. Of course, further investigations would be needed to check the accuracy of the presently proposed charges for a larger variety of molecules. However, our results suggest that benzene/toluene solvent at

Figure 1 :

 1 Figure 1: g OO (r) (top), g OH (r) (middle) and g HH (r) (bottom) functions obtained at 300 K for classical liquid water using different t OH parameters in the WMull formalism. Comparison with the DFT results obtained with the revPBE-D3 functional by Marsalek and Markland are provided for comparison.54

Figure 2 :

 2 Figure 2: g OO (r) (top), g OH (r) (middle) and g HH (r) (bottom) obtained at 300 K for classical liquid water using the WMull scheme with three t OH values: 0.0, 0.28 and 0.38, as well as the Mull scheme. The results obtained with the original Mulliken charges correspond to t OH = 0.0. Comparison with the DFT results obtained with the revPBE-D3 functional by Marsalek and Markland are provided for comparison, 54 as well as the experimental curves of Sopper and Benmore. 118

Figure 3 :

 3 Figure 3: Volume distribution of voids in simulations of 1024 water molecules using Mulliken (black curve) and Wmull with t OH = 0.28 (red curve) of liquid water at T = 300 K. For comparison, the volume distribution of voids obtained from a TIP4P/Ew 107 simulation of 4096 water molecules is also presented (blue curve).

Figure 4 :

 4 Figure 4: g OO (r) (top), g OH (r) (middle) and g HH (r) (bottom) obtained at 300 K for classical and quantum liquid water using the WMull scheme with two t OH values: 0.28 and 0.58. The experimental curves of Sopper and Benmore are provided for comparison. 118

Figure 5 :

 5 Figure 5: Influence of the WMull parameter on the g CC (r) (top), g BzBz (r) (middle) and g CM -CM (r) (bottom) functions obtained at 300 K for a classical 36 benzene molecules simulation. The results obtained with the original Mulliken charges (t CH = 0.0) are provided along with two values of t CH , 0.15 and 0.30. For g BzBz (r) and g CM -CM (r), comparison with previous theoretical results performed with FF are provided for comparison.[START_REF] Cabaço | Neutron Diffraction and Molecular Dynamics Study of Liquid Benzene and Its Fluorinated Derivatives as a Function of Temperature[END_REF][START_REF] Chelli | The Fast Dynamics of Benzene in the Liquid Phase. Part II. A Molecular Dynamics Simulation[END_REF] For g CC (r), the experimental curve of Narten is reported.[START_REF] Narten | X-Ray Diffraction Pattern and Models of Liquid Benzene[END_REF] The inset of the middle panel is a zoom in the 4-10 Å region.

  from DFT and DFT-D simulations, DFT refering to BLYP and DFT-D to BLYP plus Grimme dispersion. When comparing the SCC-DFTB g(r) reported in Figure 6 (a) and (b) with those reported in Figure 2 (a) and (c) of ref., 93respectively, the agreement between the SCC-DFTB and the DFT-D results is found to be extremely good. The dependence of g CM -O (r) on the cone angle illustrates the anisotropy of the solvation shell of a benzene solute within liquid water, as studied in details by Choudary et al..[START_REF] Choudhary | Anisotropic Structure and Dynamics of the Solvation Shell of a Benzene Solute in Liquid Water from Ab Initio Molecular Dynamics Simulations[END_REF] Next two paragraphs are dedicated to a more detailed description of the SCC-DFTB results and to their comparison with DFT(-D) simulations.

  Figure 3 (a) of ref. 93 ).The peak corresponding to the second solvation shell appears broader and less structured at the SCC-DFTB level, starting at shorter CM-O distance (∼ 4.3 vs ∼5.0 Å at the DFT-D level). Focusing on the evolution of g CM -O (r) as a function of θ equatorial (Figure 6 (b)), a sharp peak is observed at r = 4.7 Å (g = 2.2) for θ equatorial = 15 • . When θ equatorial increases, the position of this peak is slightly shifted to smaller r down to r = 4.6 Å with an intensity decrease down to g = 1.6 for θ equatorial = 75 • . The CM-O distance corresponds to the benzene-water dimer conformation in which the water molecule interacts through its oxygen

Figure 6 :

 6 Figure6: g CM -O (r) obtained for benzene solvated by water at 300 K (classical MD) using the WMull scheme with t OH = 0.28, t CH = 0.30 and t CO = 0.08. The curves were obtained for fixed θ axial (a) and θ equatorial (b) (see scheme for the definition of θ axial and θ equatorial angles). These curves can be compared to those of the top of Figure2in Choudary et al..[START_REF] Choudhary | Anisotropic Structure and Dynamics of the Solvation Shell of a Benzene Solute in Liquid Water from Ab Initio Molecular Dynamics Simulations[END_REF]

  1.33 cm 2 .s -1 as compared to 2.27 cm 2 .s -1 at 298 K experimentally.122 Although the SCC-DFTB value is half the experimental one, it is similar to the one determined by Cabaço et al., 1.2 cm 2 .s -1 .[START_REF] Cabaço | Neutron Diffraction and Molecular Dynamics Study of Liquid Benzene and Its Fluorinated Derivatives as a Function of Temperature[END_REF] This demonstrates that, similarly to liquid water, there is still room for improvement of the SCC-DFTB model although the present agreement with experimental data is reasonable.

Acknowledgement

The author thank the supercomputing facility of Toulouse III University, CALMIP, for allocation of computer resources (Project P1320 and P17002). We also would like to thank Elise Duboué-Dijon for fruitful discussions.This work has been funded by the Agence Nationale de la Recherche (ANR) project MUSCOFI ANR-18-CE05-0028.

Supporting Information Available

Discussion on the impact of the thermostat on the pair radial distribution functions of liquid water. Discussion on the convergence of the PIMD Simulations. Comparison of the theoretical g(r) to additional experimental data are provided as well as the SCC-DFTB proton-transfer energy barrier as compared to MP2/aug-cc-pVTZ calculations. This material is available free of charge via the Internet at http://pubs.acs.org/.


Lauren Thevin
email: lthevin@uco.fr

Tonja Machulla
email: tonja.machulla@ifi.lmu.de

Guidelines for Inclusive Avatars and Agents: How Persons with Visual Impairments Detect and Recognize Others and their Activities

Realistic virtual worlds are used in video games, in virtual reality, and to run remote meetings. In many cases, these environments include representations of other humans, either as stand-ins for real humans (avatars) or artificial entities (agents). Presence and individual identity of such virtual characters is usually coded by visual features, such as visibility in certain locations and appearance in terms of looks. For people with visual impairments (VI), this creates a barrier to detecting and identifying co-present characters and interacting with them. To improve the inclusiveness of such social virtual environments, we investigate which cues people with VI use to detect and recognize others and their activities in real-world settings. For this, we conducted an online survey with fifteen participants (adults and children). Our findings indicate an increased reliance on multimodal information: vision for silhouette recognition; audio for the recognition through pace, white cane, jewelry, breathing, voice and keyboard typing; sense of smell for fragrance, food smell and airflow; tactile information for length of hair, size, way of guiding or holding the hand and the arm, and the reactions of a guide-dog. Environmental and social cues indicate if somebody is present: e. g. a light turned on in a room, or somebody answering a question. Many of these cues can already be implemented in virtual environments with avatars and are summarized by us in a set of guidelines.

Introduction

Virtual reality (VR) technology allows users to visit virtual environments and to interact with them. This increasingly includes interactions with virtual representations of other human users and artificial characters controlled by the computer, termed avatars and agents, respectively. Much recent research focuses on improving the appearance of such virtual humans and how different characteristics such as emotional expressiveness, personalization, or motion profiles influence the quality of the interpersonal interaction. As with many other features of VR environments, current representations of human characters rely heavily on visual aspects. As a result, they are less accessible to users with visual impairments. Difficulties include not being aware of the presence of other characters, or not being able to discern their location, identity, or activity. As a result, persons with visual impairments face a higher threshold when it comes to joining in social or collaborative VR experiences. Recently, there have been efforts to increase the accessibility of VR for people with VI [START_REF] Zhao | Seeingvr: A set of tools to make virtual reality more accessible to people with low vision[END_REF]. So far, these efforts have focused on improving interactions with physical features of the VR environment. Our work aims to also improve inclusiveness in terms of social and collaborative aspects of VR. To this end, we investigated how people with VI determine presence, identity, and activity of other humans in real-world settings. These factors are likely to influence whether a person will approach others with the goal of engaging in a social interaction: first, a person with VI has to be aware of the presence of potential interaction partners; second, the identity of co-present persons might play a role for certain types of interactions (such as a banter between friends); and third, the activity might determine whether the other person is available for an interaction or not (e.g., a working colleague should not be interrupted). We created an online survey answered by fifteen adults and minors with VI. We present the results of this survey and propose guidelines for the creation of inclusive virtual characters, that can be implemented at present with currently available technological solutions.

State of the Art

Representation of Avatars and Agents in Interactive Virtual Environments. Virtual environments support more and more interactive and collaborative activities [START_REF] Pan | Why and how to use virtual reality to study human social interaction: The challenges of exploring a new research landscape[END_REF], such as physical and cognitive therapies [START_REF] Mölbert | Assessing body image in anorexia nervosa using biometric self-avatars in virtual reality: Attitudinal components rather than visual body size estimation are distorted[END_REF][START_REF] Cornelissen | Body size estimation in women with anorexia nervosa and healthy controls using 3d avatars[END_REF], training [START_REF] Nakanishi | Virtual cities for real-world crisis management[END_REF][START_REF] Rudinsky | Designing soundscapes of virtual environments for crisis management training[END_REF][START_REF] Paiva | Simcec: A collaborative vr-based simulator for surgical teamwork education[END_REF], gaming, telepresence for meeting [START_REF] Shachaf | Cultural diversity and information and communication technology impacts on global virtual teams: An exploratory study[END_REF], and communication with conversational agents [START_REF] Pejsa | Who, me? how virtual agents can shape conversational footing in virtual reality[END_REF][START_REF] Negrón | Collaborative interaction analysis in virtual environments based on verbal and nonverbal interaction[END_REF]. All of these applications require the representation of oneself or others in virtual space, in the form of (self-)avatars or virtual agents. These representations rely strongly on visual cues, as these are considered essential for the realism and faithfulness of avatars [START_REF] Steed | Collaboration in immersive and non-immersive virtual environments[END_REF]. Hence, many research efforts focus on photo-realistic avatars as well as visual rendering of life-like motions and nonverbal cues. For example, research on therapy to counter perceived body image distortion in anorexia has used biometrically correct virtual bodies, so the visual representation is realistic [START_REF] Mölbert | Assessing body image in anorexia nervosa using biometric self-avatars in virtual reality: Attitudinal components rather than visual body size estimation are distorted[END_REF][START_REF] Cornelissen | Body size estimation in women with anorexia nervosa and healthy controls using 3d avatars[END_REF]. Crisis management training [START_REF] Nakanishi | Virtual cities for real-world crisis management[END_REF][START_REF] Rudinsky | Designing soundscapes of virtual environments for crisis management training[END_REF] and surgery training [START_REF] Paiva | Simcec: A collaborative vr-based simulator for surgical teamwork education[END_REF] aims to teach collaboration with virtual agents and other users to improve collective work. The representation of others and virtual agents has mostly made use of visual feedback.

Occasionally, multisensory cues are used to increase the realism and individuality of avatars, e. g., in the context of communication. Here, it is increasingly common to additionally implement auditory cues (synthetic voices, Voice Over Internet Protocol (VoIP), etc.; e.g., [START_REF] Rudinsky | Designing soundscapes of virtual environments for crisis management training[END_REF] and [START_REF] Paiva | Simcec: A collaborative vr-based simulator for surgical teamwork education[END_REF]. Voices rendering is known as a key part of collaborative skills and avatar realism, combined with visual cues [START_REF] Steed | Collaboration in immersive and non-immersive virtual environments[END_REF]. Rarely, social interactions in VR include other auditory cues and tactile feedback to the user, such as a touch to the forearm or shoulder [START_REF] Haans | Mediated social touch: a review of current research and future directions[END_REF][START_REF] Hoppe | A human touch: Social touch increases the perceived human-likeness of agents in virtual reality[END_REF].

As of yet, it is unclear whether these developments are conducive to creating inclusive virtual environment. Improving on fine visual detail is unlikely to create strong cues for people with VI, and the current focus on voices ignores other potential auditory sources as cues to the presence and identity of others.

Accessibility of Virtual Reality for People with VI. Multiple projects have specifically investigated VR for people with VI. It is now possible to navigate auditory, sometimes audio-visual, virtual environments without vision using a force-feedback joystick and environmental cues through audio-tactile feedback [START_REF] Lahav | Construction of cognitive maps of unknown spaces using a multi-sensory virtual environment for people who are blind[END_REF], with a keyboard to explore an virtual audio environment [START_REF] Connors | Virtual environments for the transfer of navigation skills in the blind: a comparison of directed instruction vs. video game based learning approaches[END_REF], with smartphone applications using and gesture [4,?], and by physically walking in a virtual or augmented room [START_REF] Kunz | Virtual navigation environment for blind and low vision people[END_REF][START_REF] Thévin | X-road: Virtual reality glasses for orientation and mobility training of people with visual impairments[END_REF]. Two works propose virtual white canes: one simulates a whitecane with a braking system [START_REF] Zhao | Enabling people with visual impairments to navigate virtual reality with a haptic and auditory cane simulation[END_REF], and another work designed a virtual white cane through vibration in the hand controller of the VR system [START_REF] Kreimeier | First steps towards walk-in-place locomotion and haptic feedback in virtual reality for visually impaired[END_REF]. In all of these works, the user interacts with physical aspects of the VE only, such as exploring virtual environments and interact with them. As far as we are aware, there are no virtual characters present, thus ignoring the potential for collaborative experiences.

Method and Participants

Design of the Survey

We created a questionnaire to gather insights into the strategies and cues used by persons with VI in real-world settings when attempting to detect and identify others with the goal of initiating an interaction. To this end, we developed 20 questions, falling into several different categories. The full set of questions is provided table 1. A first set of categories covers four types of mutual awareness in social and collaborative settings: environmental awareness, user and interaction awareness, action awareness, and organization awareness [START_REF] Ahn | Utilizing knowledge context in virtual collaborative work[END_REF]. As summarized in [START_REF] Thévin | How to move from inclusive systems to collaborative systems: the case of virtual reality for teaching o&m[END_REF], environmental awareness refers to sharing the same space (Q1), action awareness is being aware of the concurrent actions of the other users (Q6), interaction and user awareness concerns knowing the available interactions and knowing who the other users are (Q2, Q3, Q4, Q5, Q8, Q9), and organizational awareness is about knowing and sharing the implications of context on the group (Q7). The question Q8, Q9, Q19 and Q20 aim to identify the good practices for both representing people and initiating interaction in virtual environment. Further, we asked about the use of the senses (Q10 to 15), as well as potential other information found in literature and blogging (Q16-17) and one open question (Q18).

Protocol

The survey was self-administered. It was organized as follow:

-presentation of the goal of the study, confidentiality and consent form. For minors, this part was read and agreed upon by the participants' legal guardian, for legal reasons (it was the only part that required another person to answer for the minor participants). -demographic information. Information regarding age, gender, and the level of vision was collected. -survey. the twenty questions presented table 1.

Participants

We send our survey to three blind adults first, so they could verify the accessibility and the questions. We then distributed our survey to professionals of two schools for people with visual impairments in France. The schools send our surveys to former students and to parents of current students. Questionnaire responses were returned by fifteen participants in total, i.e., eight adults and seven minors under the age of eighteen years old. For confidentiality reasons and to respect the consent form terms, we do not provide the individual demographics. However, we will describe here individually each demographics dimension (gender, age, and level of vision). Regarding the adults' group, 6 participants were male, 2 were female, and 0 other. The average age is 38 years old, with a standard deviation of 18 years. The range is from 19 to 67 years old, with the following values: 19, 20, 21, 26, 48, 48, 52 and 67. 2 participants were low vision, 5 were blind with light perception, and 1 was blind without light perception. Regarding the minors' group, 5 participants were male, 1 was female, and 1 was other. The average age is 12 years old, with a standard deviation of 4 years. The range is from 6 to 16 years old, with the following values: 6, 10, 10, 10, 14, 15, 16. 1 participant was low vision, 2 were blind with light perception, and 4 were blind without light perception.

Results

In the following, we analyze participants' responses in terms of their own observational and behavioral strategies as well as strategies by others that are used to: detect and subsequently identify a person as known or unknown (4.1-4.3), and identify their activity (4.4). In section 4.5, we summarize strategies that others might use to initiate an interaction. Numbers in round brackets indicate the number of participants who mentioned a particular fact.

Detecting the presence of others

Observation strategies: Vision is used to identify silhouettes (2 participants), although audition is more commonly used, by paying attention to noises people make (9 participants) through their activities (indistinct noise, voice, breathing, typing on a computer, pace noise) or by being directly greeted by somebody in the room. Participants also use smells (4 participants), such as parfume, food, hygiene products such skin care and aftershave, touch for airflow perception and clothes, and, interestingly, a sense of a co-presence (5 participants) in form of passive echolocation or a feeling of being observed. Smell can help to estimate the distance of another person.

Behavioral strategies: Participants mention saying hello and then waiting whether somebody answers. The direction of the answer can help to visually search for the other person. An indirect strategy is trying to detect whether the light in a room is turned on since rooms containing people are often illuminated. This is useful when visual capabilities are insufficient to recognize silhouettes but light perception is possible.

Identifying a known person

Observation strategies: People can be identified visually by the individual shape of their silhouettes (2 participants), and their face if close enough (2 participants). However, eleven of the participants do not use vision at all to identify others. Visual or tactile feedback is used to recognize somebody by their hair (tactile, 2 participants; visually, 2 participants), their clothes (3 participants), the size (silhouette, tactilely when guiding by the height of the leading arm, with audio when talking). Audition is used to pay attention to the voice (14 participants; sample needs to be long enough to disambiguate identity), to personspecific sounds like laughter (2 participants), way of breathing (3 participants), moving and walking (3 participants). Other person-specific sounds mentioned were the way to playing with a pen, typing on a keyboard, and sounds from jewelry. Jewelry can also help to identify a person by touch. Two participants said they do not dare too much using active tactile exploration, as it may make others uncomfortable. Passive tactile feedback is used to recognize close relatives (e.g., by the way how another person grabs one's arm or how they guide, how their hands feel, musculature). Smell and fragrance can help (10 participants), but do not always give a clear cue to identity. Participants also mentioned using passive echo-location signature for identification (2 participants). Lastly, guidedog reactions indicate that a person is known; however, this does usually not help to identify the person (2 participants).

Behavioral strategies: Some participants let people approach and present themselves (5 participants). To this end, they define a precise meeting point (3 participants) and make their arrival known (4 participants; by phone, calling out loud, or hitting the white cane on the floor). The context can help to disambiguate persons (colleagues in the workplace, landlord inside a specific house). Other people can draw attention to themselves by calling out or waving at the person with VI.

Miscellaneous: One participant reports never going out without a sighted guide; two others report they are not able to identify people and have to rely on others approaching them. A person that is easy to identify has a recognizable voice (9 participants) or breath, a particular smell or fragrance (3 participants), makes distinctive noises (wrist bands, keys, heels, personal style of walking (3 participants), person in a wheelchair). A person is difficult to recognize if it is difficult to identify their voice (7 participants; person not talking, or too quiet, strong similarity to the voice of another person). Similarly, a person that does not move or is encountered out of their usual context is difficult to recognize, as well as encounters within large public spaces, with too many people (4 participants) and too much noise (3 participants). Lastly, familiarity plays a role-a person that is encountered less often is more difficult to recognize (4 participants) because there were insufficient opportunities to learn distinctive elements for identification (clothes, pace, voices, way of grabbing).

Identifying that a Person is unknown

Observation strategies: In general, the cues are the same as when identifying a known person; however, without any correspondence in memory: participants use the voice (10 participants), typical words or gestures, way of grabbing the arm or guiding, silhouette and smell.

Behavioral strategies: The fact that participants do not know a person is usually confirmed during the conversation and by asking questions. Sometimes, the course of the conversation will lead to the realization that the participant wrongly assumed to be talking to a known person.

Identifying An Activity

Observation strategies and joining an activity: Ongoing activities can be identified visually from gestures and, in case of physical activities, movements of human silhouettes (2 participants). Audition is particularly helpful to pick up noises that humans or materials emit (9 participants; e.g., from a keyboard, specific sounds of a familiar activity such as board games tokens or cooking tools) as well as the density of the noise, the of different voices and the content of the conversation are considered useful cues to the activity (6 participants), or the general atmosphere of the room (2 participants; e.g., tavern vs. meeting). Smell and touch give information about the material used (cooking, smell of a pen when drawing). Three participants indicated they would not participate in an activity or a conversation if they are not explicitly included by the others or invited to join.

Approaching a person with VI to start an activity

In the following, we summarize good and bad strategies mentioned by our participants regarding how others can identify themselves and initiate an activity.

Good practices:

In many situations, it is helpful if the approaching person states their name (8 participants), their function or job (3 participants), and the context of previous encounters (5 participants). If the person is unknown, they should indicate why they are approaching and, if applicable, the name of the person who send them. When others did not present themselves properly, our participants' strategies are to ask who it is (4 participants), asking possible past memories or if there have been previous encounters (2 participants), and asking questions in general. Bad practices: Several participants stated that sudden and unannounced physical contact is undesirable, such as catching somebody who is moving with a white cane by the arm to stop them (2 participants), pat them on the shoulder (2 participants), or touching otherwise without prior consent (4 participants). Approaching somebody silently can generate negative effects, like surprise or making the participants uncomfortable because they failed to hear the person's approach. Addressing a person with VI verbally has its pitfalls, as well: others may not speak up long enough for them to be identified (e.g., "Hello" is too short), a call out from too far away can lead to a visual search for the caller but without a successful localization, and calling and speaking loudly at close distance may have startling effects (3 participants). First impression: What influences the first impression somebody makes on a person with VI? Participants stated that they rely on concrete cues: the handshaking, the tone and intonation of the voice (10 participants), if there is a warm feeling in the voice, the way of speaking and the words used (three participants), the attention the person pays, the face, and the overall behavior (2 participants). One participant stated that he or she can notice if the visual handicap will be an obstacle from the voice and the intonation.

Creating Inclusive Virtual Characters

The responses to our questionnaire suggest a number of extensions that can be made to virtual characters to increase their accessibility for persons with VI with current technologies that we describe in the first subsection. The answers also open future perspectives that we describe in the second subsection.

Adaptation possible with Current Technologies

Visual attributes. Avatars and agents should have distinctive silhouettes, clothes (shapes, color), and faces, to be easily recognized even with low vision. They could have personalized movement patterns, e.g., with idle animation or when talking. A light turned on in a virtual room can indicate that an avatar or agent is present. Some adjustments make VR potentially more accessible, for instance avoiding the necessity of eye to have to adapt to differences in brightness, e.g., when changing virtual environments (e.g., rooms, or from outside to inside). Audio attributes. Voice is a highly valuable cue to identify people, in particular if the avatar is talking long enough. Distinctive voices, e.g., in terms of pitch, differentiate between characters. With only three voices with referring to gender (feminine, masculine, mixed) a user can differentiate between three characters. Vocabulary, speed, and rhythm add specificity. Other person-specific sounds such as breathing, laughter, way of walking, or wearing different types of shoes (heels, sport shoes, squeaky shoes) improve the chances of identifying the virtual character. Pace can be a cue to decide whether to start an interaction or not (e.g., walking fast may imply little time). Identity and social cues could be conveyed by any sound-generating activity linked to a habit (playing with a pen, tapping finger nails on the table), to objects (keys, chains, sword), or to jewelry (wristbands, ear rings). Multimodal attributes. The height of a person can be represented visually as well as via spatialized audio feedback. The cloth of virtual characters' garments can be represented visually by a texture as well as by distinctive sounds like rustling and swishing. Avatars in a wheelchair can be a very recognizable by their silhouette and associated sounds. Airflow. Airflow from a fan could simulated that someone just came closer or walked by. Interactions. Initiating an interaction is a crucial prerequisite for collaboration. Therefore, it is important that it is transparent to the user how they can join activities. The user should be able to address the entire virtual room, equivalent to "Hello?", using voice or through a controller. The virtual characters, either agents or avatars, should detect it (broadcast to remote users or audio recognition for agents). The user may want to send a directed call to a particular character (virtual phone call, virtual poke) or semi-directed call (like making noise with the white can). The virtual characters should be able to answer, wave at the person or get closer. They may spontaneously address the user and present themselves or even invite the user to join. The virtual space should ease recognition of characters and activities (e.g., by being a meeting point, providing distinctive activity sounds, or good separation of multiple voices). The place of meeting (noisy, full of people or not) make the recognition difficult or not.

Future Implementations for Virtual Reality

Smell. Combined with airflow, a fragrance dispenser could indicate that someone is in the room; the distance from this person could be indicated by smell intensity. Many flavors, fragrances and spices exist, liquid or other (vanilla, chocolate, coconut, mint, banana, musk, cedar, cumin, curry, basil, cinnamon), even scent kits, and can be used to give smell feedback. Tactile feedback for shapes. Tactile feedback helps to recognize jewelry by touch, the face and objects that help identifying the person. Tactile feedback for materials. Tactile feedback could indicates hair (long, short, no hair) with only on actuator at the hand level for the user. Tactile feedback for cloth can be added to visual and audio-feedback. Tactile feedback for human contact. Tactile feedback can give a lot of information, to identify a person and to make a first impression. In real life, tactile feedback for recognition is used during handshakes, guiding and even to know the size and the musculature of the person. Guide dog A virtual guide dog could react differently depending on the time spent with a virtual character or a real person controlling the avatar. Passive echo-location. Passive echo location is the ability to feel shapes and obstacles from reverberations without emitting a sound purposefully for echoing. If it can be more efficiently modeled in VR, it could be a new means to feel spaces and people.

Discussion & Perspectives

We presented the results of an online survey on the strategies used by people with VI for detecting and identifying people as well as on-going activities in real environments. We use the findings to propose solutions for inclusive collaborative VE, with inclusive representations of virtual characters and activities. Many of these solutions can already be implemented, while others will become achievable with future technological developments. Further, our work is applicable to any virtual environment such as for multiplayer games, applications with non-player characters, training environments, telepresence scenarios, or video conferencing. It may require new ways of recording and broadcasting people, to add information beyond the currently predominant video stream. Our future research will focus on designing and evaluating such virtual characters with people with and without VI.

Fig. 1 .

 1 Fig. 1. Avatars with cues usable by sighted and people with visual impairments: wristband and jewelry making noise with the movement of the avatar, distinctive voice or laughter and telling the identity, different size (audio and tactile cues), pace, loud or specific breathing pattern.

Table 1 .

 1 When you enter a room, how do you notice a person is present? Interaction and User Q2. When you meet up with people you know for a social appointment in a public space, how do you recognize them? Interaction and User Q3. When you meet people you know by coincidence in a public space, how do you recognize them? Interaction and User Q4. When you meet people you do not know, how do you know you have never met them? Interaction and User Q5. In the first few second after meeting a person for the first time, which factors (such as perceptual cues) influence your first impression of this person (a nice person, an unsympathetic person, a shy person, an extrovert person)? How do you identify that a group of people is present in a room you enter? How do you identify the activity of the group? Organizational Q7. How do you know if it is socially appropriate to join the activity of a group of people, for instance a conversation? Use of the senses Q10. Do you use vision for it? If you use vision to identify people, what cues do you use to recognize them? Use of the senses Q11. Do you use touch for it? If you use touch to identify people, what cues do you use to recognize them? Other potential cues Q16. Do you use location and context for it? If you use location and context to identify people, what cues do you use to recognize them? Other potential cues Q17. If you have one, do you use information from your guide dog for it? If you use information from your guide dog to identify people, what cues do you use to recognize them? What do you want people not to do to alert you from their presence or to identify themselves? For example, because the action startles or annoys you or is not helpful. The twenty questions of the survey, and the categories. Awareness categories: Environmental, Interaction and User, Action and Organizational. Other categories: Use of senses, Other potential cues, Open question, and Good practices.

	Category	Question
	Environmental Q1. Action Q6. Interaction and User, Q8. When do you find a person easy to recognize?
	Good practices
	Interaction and User;	Q9. When do you find a person difficult to recognize?
	Good practices
	Use of the senses	Q12. Do you use temperature perception for it? If you use
		temperature perception to identify people, what cues do you
		use to recognize them?
	Use of the senses	Q13. Do you use air flow perception for it? If you use air flow
		perception to identify people, what cues do you use to recognize
		them?
	Use of the senses	Q14. Do you use audio perception for it? If you use audio
		perception to identify people, what cues do you use to recognize
		them?
	Use of the senses	Q15. Do you use smell perception for it? If you use smell per-
		ception to identify people, what cues do you use to recognize
		them?
	Open question	Q18. What other cues do you use to recognize people?
	Good practices	Q19. When somebody approaches you and you can't identify
		the person because you either don't know or remember the per-
		son, what are the most helpful cues to identify who it is?
	Good practices	Q20.

Acknowledgments

We thank the participants and the institutions that distributed our survey, especially IRSA and Ocens. This work was supported by the European Union's Horizon2020 Program under ERCEA grant no. 683008 AMPLIFY.