Marwa Dhifallah

Mathilde Iachella

Adnène Dhouib

Francesco Di Renzo

David Loffreda
email: david.loffreda@ens-lyon.fr

Hazar Guesmi
email: hazar.guesmi@enscm.fr

Support Effects Examined by a Comparative Theoretical Study of Au, Cu and CuAu Nanoclusters on Rutile and Anatase Surfaces

The role of the support anatase TiO2(100) and rutile TiO2(110) on the energetics, the shape and the charge transfer of deposited CuAu nanoclusters ( 1 nm) has been examined by using density functional theory calculations including Hubbard correction (DFT+U). Regular

truncated octahedron clusters (rto), Cu(1-x)Au(x) (x being in the range 0.15-0.36), representing different alloy types (core@shell, Regular alloy, Skin-Heart) are considered. From a thermodynamic standpoint, the core-shell deposited nanoclusters present the strongest adsorption strength on both rutile and anatase supports, although they are the least stable homotops in vacuum. Interestingly, for skin-heart and regular alloy CuAu clusters, the stability on these supports decreases with the Au content. CuAu nanoclusters present larger adsorption energies on rutile than on anatase support. This result has been explained by a Bader analysis of charge transfers and an energy decomposition analysis (EDA) model which shows a larger binding energy between the metal and the rutile support than that on anatase, in part compensated by the stronger deformation of the structure of rutile. At the size of 38 atoms, the bimetallic cluster exhibits a significant propensity to distort its structure and adapt it to the geometry of the oxide surface to maximize the stability of the formed metal-oxide chemical bonds. Such an interesting property is expected to decay with the increasing size of the metallic nanocluster. This work provides an original discussion related to the support effect which is rarely evoked in the literature of DFT studies of such supported alloy clusters at the nanoscale.

I-Introduction

Supported bimetallic nanoparticles (BiM NPs) are widely used as heterogeneous catalysts [START_REF] Sankar | Designing bimetallic catalysts for a green and sustainable future[END_REF][START_REF] Gu | Shape control of bimetallic nanocatalysts through welldesigned colloidal chemistry approaches[END_REF][START_REF] Wu | Surface latticeengineered bimetallic nanoparticlesand their catalytic properties[END_REF][START_REF] Kim | Ag-Cu bimetallic nanoparticles with enhanced resistance to oxidation: A combined experimental and theoretical study[END_REF]. In the recent decade, these materials have attracted much attention due to their tunable catalytic properties. In fact, for several catalyzed reactions, alloying two metals could improve the activity and/or the selectivity compared to the properties measured for the same reactions occurring on monometallic components [START_REF] Kitchin | Role of strain and ligand effects in the modification of the electronic and chemical properties of bimetallic surfaces[END_REF][START_REF] Oguz | The effect of Pd ensemble Structure on the O2 dissociation and CO oxidation mechanisms on Au-Pd(100) surface alloys[END_REF]. The catalytic properties of the supported metals may depend on several factors, such as the size and the shape of the nanoparticles, the structure and the surface composition, the stability of the nanoparticles and their interactions with the support. Although these factors have been identified for a long time, a rational control and understanding of the catalytic properties at the atomic scale is still missing.

Many methods have been employed for the synthesis and the characterization of BiM NPs on various oxide supports [START_REF] Louis | Chemical Preparation of Supported Bimetallic Catalysts. Gold-based bimetallic, a case study[END_REF]. Supported Au-based NPs, such as AuPd [START_REF] Edwards | Direct synthesis of hydrogen peroxide from H and O using TiO -supported Au-Pd catalysts[END_REF][START_REF] Zhu | Evidence of Pd segregation and stabilization at edges of AuPd nano-clusters in the presence of CO: a combined DFT and DRIFTS study[END_REF], AuCu [START_REF] Chimentao | Propene epoxidation by nitrous oxide over Au-Cu/TiO alloy catalysts[END_REF][START_REF] Delannoy | Selective hydrogenation of butadiene over TiO2 supported copper, gold and gold-copper catalysts prepared by deposition precipitation[END_REF][START_REF] Pauwels | Transmission electron microscopy and Monte Carlo simulations of ordering in Au-Cu clusters produced in a laser vaporization source[END_REF],

AuAg [START_REF] Sandoval | Bimetallic Au-Ag/TiO catalyst prepared by 2 deposition-precipitation. High activity and stability in CO oxidation[END_REF][START_REF] Menezes | Effects of particle size, composition, and support on catalytic activity of AuAg nanoparticles prepared in reverse block copolymer micelles as nanoreactors[END_REF], and AuPt [START_REF] Gallo | H2 production by renewables photoreforming on Pt-Au/TiO catalysts activated by reduction[END_REF][START_REF] Na | Effect of preparation method on the performance of Pt-Au/TiO2 catalysts for the catalytic co-oxidation of HCHO and CO[END_REF] are highly active for many catalytic reactions, such as CO oxidation, and can be applied in catalysis, electrochemistry and nanotechnology [START_REF] Juarez | Catalytic properties of Au electrodes modified by an underlayer of Pd[END_REF][START_REF] Su | Designer titania-supported AuPd nanoparticles for efficient photocatalytic hydrogen production[END_REF]. The AuCu/TiO2 system has been employed several times for various applications such as wastewater treatment [START_REF] Hai | Modification of TiO2 by bimetallic Au-Cu nanoparticles for wastewater treatment[END_REF], photocatalysis and CO2 reduction by water [START_REF] Nahar | Advances in Photocatalytic CO2 Reduction with Water: A Review[END_REF] and photodegradation of methyl orange [START_REF] Hai | Radiolytic synthesis of Au-Cu bimetallic nanoparticles supported on TiO2: application in photocatalysis[END_REF]. Titanium dioxide is one of the most widely used and studied reducible supports in the literature [START_REF] Diebold | The surface science of titanium dioxide[END_REF]. TiO2 supports for heterogeneous catalysts provide stability in electrochemical environment and are easily commercially available [START_REF] Tauster | Strong interactions in supportedmetal catalysts[END_REF][START_REF] Kominami | Novel synthesis of microcrystalline titanium(IV) oxide having high thermal stability and ultra-high photocatalytic activity: thermal decomposition of titanium(IV) alkoxide in organic solvents[END_REF]. Different allotropic forms of TiO2 exist in the nature: anatase, rutile and brookite. Among them, anatase and rutile feature the most interesting surfaces for applications on photochemistry [START_REF] Neaţu | Gold-Copper Nanoalloys supported on TiO2 as photocatalysts for CO2 reduction by water[END_REF][START_REF] Panayotov | Surface chemistry of Au/TiO2: Thermally and photolytically activated reactions[END_REF] and photocatalysis, especially for the Au/TiO2 system [START_REF] Kominami | Novel synthesis of microcrystalline titanium(IV) oxide having high thermal stability and ultra-high photocatalytic activity: thermal decomposition of titanium(IV) alkoxide in organic solvents[END_REF][START_REF] Subramanian | Catalysis with TiO2/Gold nanocomposites: effect of metal particle size on the Fermi Level equilibration[END_REF][START_REF] Li | Mesoporous Au/TiO2 nanocomposites with enhanced photocatalytic activity[END_REF][START_REF] Murdoch | The effect of gold loading and particle size on photocatalytic hydrogen production from ethanol over Au/TiO2 nanoparticles[END_REF]. The role of the support is often considered in the literature and a classification has been proposed for catalysis by gold according to two major effects : reducibility and strong-metal support interactions [START_REF] Liu | Catalysis by gold: New insights into the support effect[END_REF]. Nevertheless, the role of the support on the chemical properties of those BiM NPs is still debatable [START_REF] Delannoy | Reducibility of supported gold (III) precursors: influence of the metal oxide support and consequences for CO oxidation activity[END_REF]. The nature and the structure of the surface active sites is still the subject of intense research and discussions [START_REF] Chen | On the origin of the unique properties of supported Au nanoparticles[END_REF][START_REF] Chen | Catalytically active gold on ordered titania supports[END_REF].

During the last decade, several theoretical works have reported on the growth of Au clusters (between 4 and 10 atoms) on titanium support [START_REF] Li | CO oxidation on TiO2 (110) supported subnanometer gold clusters: Size and shape effects[END_REF][START_REF] Turner | Selective oxidation with dioxygen by gold nanoparticle catalysts derived from 55-atom clusters[END_REF][START_REF] Pillay | Growth and structure of small gold particles on rutile TiO2 (110)[END_REF][START_REF] Pillay | Structure of small Aun,Agn, and Cun clusters (nZ2K4) on rutile TiO2(110): A density functional theory study[END_REF][START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF][START_REF] Puigdollers | Gold and silver clusters on TiO2 and ZrO2 (101) surfaces: role of dispersion forces[END_REF]. Larger Au clusters (20-24 atoms) in interaction with the rutile stoichiometric TiO2(110) surface have been modeled by combining DFT calculations with a genetic algorithm [START_REF] Vilhelmsen | Identification of the catalytic site at the perimeter of Au clusters on rutile TiO2(110)[END_REF][START_REF] Vilhelmsen | A genetic algorithm for first principles global structure optimization of supported nano structures[END_REF][START_REF] Ding | The growth pattern of Aun (n = 1-20) clusters absorbed on rutile TiO2 (1 1 0) surfaces[END_REF]. The AuCu bimetallic system has been studied several times from global optimization methods, with free clusters containing 38-56 atoms [START_REF] Barcaro | Electronic and structural shell closure in AgCu and AuCu nanoclusters[END_REF][START_REF] Darby | Theoretical study of Cu-Au nanoalloy clusters using a genetic algorithm[END_REF][START_REF] Ferrando | Quantum effects on the structure of pure and binary metallic nanoclusters[END_REF][START_REF] Rapallo | Global optimization of bimetallic cluster structures. I. Sizemismatched Ag-Cu, Ag-Ni, and Au-Cu systems[END_REF][START_REF] Hsu | Structures of bimetallic clusters[END_REF][START_REF] Tran | Theoretical study of Cu38nAun clusters using a combined empirical potential-density functional approach[END_REF]. Complex morphologies and shapes have been found including (poly)icosahedral forms [START_REF] Darby | Theoretical study of Cu-Au nanoalloy clusters using a genetic algorithm[END_REF][START_REF] Ferrando | Quantum effects on the structure of pure and binary metallic nanoclusters[END_REF], distorted and pancake shapes [START_REF] Ferrando | Quantum effects on the structure of pure and binary metallic nanoclusters[END_REF], and a wide and complex range of structures including core-shell systems [START_REF] Hsu | Structures of bimetallic clusters[END_REF][START_REF] Tran | Theoretical study of Cu38nAun clusters using a combined empirical potential-density functional approach[END_REF]. However, the deposit of AuCu on the titania support, has been studied by density functional theory calculations only by considering small clusters of 3 atoms [START_REF] Jiang | Adsorption of AuxCuy (x + y = 1, 2, 3) nanoclusters on the anatase TiO2(101) surface and their catalytic activity: a density functional theory study[END_REF] or solid-solid AuCu(001)/TiO2(101) interfaces [START_REF] Jiang | Comparison studies of interfacial energetic and electronic properties of bimetallic AuCu/TiO2 hetero-structures from DFT calculations[END_REF]. Hence, little is known about the interaction of gold-copper BiM NPs at a larger size (around 1 nm) on the titanium support and the quantitative description of the effect of the different forms (anatase vs. rutile) is still missing.

In order to fill this gap, this work aims to compare the effect of the surface of anatase and rutile supports on the shape and the stability of either monometallic gold and copper nanoparticles or gold-copper nanoalloys for 38 atoms in total (around 1 nm). The paper is organized as follows: first, the optimized parameters of both TiO2 supports are reported. Then the results of the optimizations of free nanoclusters are analyzed. In the third part, thermodynamic and geometric data of deposited Au, Cu, CuAu nanoclusters are exposed by comparison between rutile and anatase. Electronic structure calculations with the Bader charge analysis are discussed.

II-Computational details

Periodic DFT calculations were performed using the projector-augmented wave (PAW) method [START_REF] Blochl | Improved tetrahedron method for Brillouinzone integrations[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF], as implemented in the Vienna ab initio simulation package (VASP) code [START_REF] Kresse | Ab initio molecular dynamics for liquid metal[END_REF]. The generalized-gradient approximation functional of the exchangecorrelation energy was calculated within the Perdew, Burke, and Ernzerhof formulation (GGA-PBE) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF]. The cut-off energy was fixed at 400 eV and the positions of the atoms in the supercell are relaxed until the total electronic energy differences fall below 10 -6 eV.

DFT calculations of rutile and anatase oxide supports faces a classical issue of band-gap underestimation [START_REF] Morgan | A dft+u description of oxygen vacancies at the TiO2 rutile (110) surface[END_REF], with a width of 1.7 eV for rutile with GGA-PBE vs 3.05 eV experimentally and a width of 2.1 eV for anatase with GGA-PBE vs 3.2 eV experimentally [START_REF] Tang | Photoluminescence in TiO2 anatase single crystals[END_REF]. Indeed, both LDA and GGA functionals fail to describe the corresponding electron localization at a metallic center [START_REF] Bengone | Implementation of the projector augmented-wave LDA+U method: Application to the electronic structure of NiO[END_REF]. This is explained by the narrow radial extension of Ti 3d orbitals. In titanium oxide, the 3d orbitals do not overlap with the oxygen ones and they are more localized on the titanium atoms. A probative semi empirical approach has been proposed to improve the spurious delocalization provided by LDA and usual GGA functionals. An additional term U, corresponding to electron on-site repulsion and based on a Hubbard model [START_REF] Altland | Condensed matter field theory[END_REF][START_REF] Surján | Second quantized approach to quantum chemistry[END_REF], is considered to correct the self-interaction error. In this work, the Dudarev's approach (PBE+U) has been selected [START_REF] Dudarev | Electronenergy-loss spectra and the structural stability of nickel oxide: An LSDA+U study[END_REF] with an optimal value for the Coulomb interactions corrections of Ti electrons Ueff of 4.2 eV for rutile and of 3.3 eV for anatase. The systematic error of the band gap has been evaluated by changing the extension of the Ti atom valence (see for instance, M. Iachella et al. [START_REF] Iachella | Diffusion kinetics of gold and copper atoms on pristine and reduced rutile TiO2(110) surfaces[END_REF] for more details). In this study, we have chosen to describe the Ti 4+ states by selecting 12 valence electrons for Ti atoms (3s 2 3p 6 3d 2 4s 2 ). TiO2 rutile and anatase bulks were modeled using tetragonal unit cells with a = b ≠c and α = β = γ = 90°. For the DFT calculations, Monkhorst-Pack [START_REF] Monkhorst | Special points for brillouin-zone integrations[END_REF] k-points mesh of (9 × 9 × 15) and (33 × 33 × 13) have been considered, respectively, for rutile and analase. Extended surfaces (see Figure 1) were modeled by bi-dimensional periodic slabs with the vacuum space between two equivalent slabs along the z direction set to 20 Å. The rutile TiO2(110) surface has been described by a stoichiometric non-polar termination within a (6 ×3) supercell terminated by bridging oxygen rows along y (Figure 1a). As the number of atoms in a trilayer TiO2 rutile is large (36 Ti and 72 O atoms), we considered a TiO2 slab with only 3 trilayers (representing 324 atoms in total). In this model the bottommost layer was fixed in bulk optimal positions and the two topmost layers were allowed to fully relax. The anatase TiO2(100) surface was described by a (5 × 2) supercell composed of 240 atoms distributed over 4 layers with the two bottommost layers fixed to the bulk situation (Figure 1b). Converged total electronic energies of bare surfaces were calculated by choosing k-points grids (smallest supercells) (7 × 7 × 1) and (3 × 3 × 1) for rutile TiO2(110) and anatase TiO2(100), respectively. For deposited metallic nanoclusters, larger supercells have been considered so the gamma-point only approach was used.

Insert Figure 1 The surface energies γ (meV.Å -2 ) of the two TiO2 supports are calculated as the difference between the total energy of the slab and the total energy of an equal number of TiO2 units in the bulk phase, divided by the total exposed area. Spin polarized calculations were developed for free monometallic Au, Cu, and bimetallic CuAu nanoparticles (BiM NPs). During the geometric optimizations, all the degrees of freedom of the metallic atoms were relaxed. In order to avoid spurious interactions between cluster images, the considered supercells were large (30x30x30 Å 3 ). The Brillouin zones were sampled by gamma point with a convergence criterion for total electronic energy set to 10 -6 eV. Atomic positions and lattice parameters were both relaxed until residual forces are below 0.01 eV Å -1 . In this work we focused on the Cu-rich phase of Cu1-xAux nanoalloys, in which the composition on Au increased from x=0.15 to x=0.36. According to previous works related to the theoretical study of gold-copper nanoclusters in vacuum [see 43 and references therein], there exist several possible morphologies in the fluxional regime around 1 nm [START_REF] Darby | Theoretical study of Cu-Au nanoalloy clusters using a genetic algorithm[END_REF][START_REF] Ferrando | Quantum effects on the structure of pure and binary metallic nanoclusters[END_REF][START_REF] Rapallo | Global optimization of bimetallic cluster structures. I. Sizemismatched Ag-Cu, Ag-Ni, and Au-Cu systems[END_REF][START_REF] Hsu | Structures of bimetallic clusters[END_REF][START_REF] Tran | Theoretical study of Cu38nAun clusters using a combined empirical potential-density functional approach[END_REF], including octahedral, decahedral and icosahedral shapes. Due to the computational cost, the exploration of all possible shapes on TiO2 support is not possible in a reasonable time. To open the discussion of the support effect on the nanocluster stability and structure, we have chosen to represent monometallic Au and Cu and bimetallic CuAu systems by regular truncated octahedral (rto) nanoparticles of 38 atoms based on the fcc packing of the corresponding bulk crystals. Five CuAu structures representing three different nanoalloy types (core-shell (CS), skin-heart (SH) and regular alloy (RA)) were computed. Of course this Au-Cu structure selection is not inclusive. In addition to the selected structures, there are a plenty of Au-Cu structures that could exist. However, all structures can't be taken into account by conventional DFT calculations. In this work, the rto [START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] structure give the possibility to compare a "perfect" core-shell structure (6 atoms in the core and 32 atoms in the shell) with different alloyed structures, but many other possibilities could exist. In order to analyze the stability of these different chemical ordering structures of CuAu as a function of the Au content x, the excess energy per atom (ΔEexc) was calculated [START_REF] Cleveland | The energetics and structure of nickel clusters: Size dependence[END_REF][START_REF] Rapallo | Global optimization of bimetallic cluster structures. I. Size-mismatched Ag-Cu, Ag-Ni, and Au-Cu systems[END_REF][START_REF] Ferrando | From theory to applications of alloys Clusters and nanoparticles[END_REF]. This energetic descriptor is defined as follows:

∆𝐸 𝑒𝑥𝑐 (𝐶𝑢 𝑚 𝐴𝑢 𝑛 ) = 𝐸(𝐶𝑢 𝑚 𝐴𝑢 𝑛 ) -𝑚𝐸(𝐶𝑢 38 )/𝑁 -𝑛𝐸(𝐴𝑢 38 )/𝑁
Eq.1

where 𝐸(𝐶𝑢 𝑚 𝐴𝑢 𝑛 ) is the total electronic energy of the BiM NP and 𝐸(𝐶𝑢 38 ) and 𝐸(𝐴𝑢 38 )

are respectively the total electronic energies of the structures of the pure 38 rto NPs. By this way, Eexc is unbiased, being zero for pure clusters. A negative value of excess energy indicates a tendency to form stable nanoalloys (the mixing is energetically favorable), and the lower the value of excess energy, the higher the stability of the structure is. In addition, the surface energies of these free NPs are calculated as follows:

γ (x) = 𝐸𝑡𝑜𝑡(𝑥)-𝐸𝑡𝑜𝑡 ̅̅̅̅̅̅̅ (𝑥) 𝐴 Eq.2
where 𝐸𝑡𝑜𝑡( 𝑥) is the total electronic energy (calculated by DFT) of the optimized structure of the bimetallic nanoparticle of composition x, 𝐸𝑡𝑜𝑡 ̅̅̅̅̅̅ (𝑥) is the total electronic energy of the optimal alloy bulk with an equivalent composition x, and A is the surface area of the corresponding relaxed nanoparticles structure. More details concerning the surface energy calculations could be found elsewhere [66].

In order to evaluate the effect of the interaction of the nanoclusters with the oxide support, different energetic descriptors were computed. The first one corresponds to the energy gained ∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2 by the system after the deposition of the gas phase NP on the TiO2 oxide support and calculated as follows:

∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2 = 𝐸(𝑁𝑃/ 𝑇𝑖𝑂 2 ) -𝐸(𝑇𝑖𝑂 2 ) -𝐸(𝑁𝑃 𝑓𝑟𝑒𝑒 ) Eq.3
where 𝐸(𝑁𝑃/ 𝑇𝑖𝑂 2 ) is the total electronic energy of the deposited NP on the support, 𝐸(𝑇𝑖𝑂 2 ) represents the total electronic energy of the bare TiO2 support (anatase and rutile surfaces with spin-polarization) and 𝐸(𝑁𝑃 𝑓𝑟𝑒𝑒 ) is the energy of the 38 rto NP calculated in gas phase. The second energetic descriptor corresponds to the average deposition energy

< ∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2
> per bond connecting the NP to the support. This value is obviously based on the first descriptor, which has been normalized by the number of bonds between the NP and the TiO2 (

𝑁 𝑏 𝑁𝑃-𝑇𝑖𝑂 2 ) ∶ < ∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2 >= 𝐸(𝑁𝑃/ 𝑇𝑖𝑂2)-𝐸(𝑇𝑖𝑂2)-𝐸(𝑁𝑃 𝑓𝑟𝑒𝑒 ) 𝑁 𝑏 𝑁𝑃-𝑇𝑖𝑂 2
Eq.4

As described in Refs. [START_REF] Hammer | Adsorption, diffusion, and dissociation of NO, N and O on flat and stepped Ru[END_REF][START_REF] Dupont | Theoretical evidence of PtSn alloy efficiency for CO oxidation[END_REF], the deposition energy ∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2 can be decomposed in two energetic components: the deformation energy and the interaction energy. It is also interesting to quantify the deformation energy of the NP before and after the deposition on the support, named ∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑁𝑃 and defined as follows:

∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑁𝑃 = 𝐸(𝑁𝑃 * ) -𝐸(𝑁𝑃 𝑓𝑟𝑒𝑒 ), Eq.5
where 𝐸(𝑁𝑃 * ) is the total electronic energy of the NP relaxed on TiO2 support, obtained by a single point energy calculation in vacuum.

In addition to these components, it is also important to evaluate the deformation energy of the stoichiometric TiO2 support during the deposition

∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑇𝑖𝑂 2 ∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑇𝑖𝑂 2 = 𝐸(𝑇𝑖𝑂 2 * ) -𝐸(𝑇𝑖𝑂 2 )
Eq.6

Where 𝐸(𝑇𝑖𝑂 2 * ) and 𝐸(𝑇𝑖𝑂 2 ) are respectively the total electronic energies of the bare support after and before deposition. 𝑇𝑖𝑂 2 * is the bare support relaxed after the NP deposition, for which we have performed a single point energy calculation.

The last component is the interaction energy (or binding energy) between the NP and the support, obtained when the deformation and the relaxation contributions are taken off from the deposition energies, as follows:

∆𝐸 𝑖𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑁𝑃 * /𝑇𝑖𝑂 2 * = ∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2 -(∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑁𝑃 + ∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑇𝑖𝑂 2
) Eq.7

Similarly to the case of the deposition energy, it is possible to normalize the interaction energy between the NP and the support per bond:

< ∆𝐸 𝑖𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑁𝑃 * /𝑇𝑖𝑂 2 * > = ∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2 + ∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑁𝑃 + ∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑇𝑖𝑂 2 𝑁 𝑏 𝑁𝑃-𝑇𝑖𝑂 2
Eq.8

In order to quantify the geometric deformation of the NP induced by the support, we have evaluated the geometric deformation ratio 𝑟 𝑑𝑒𝑓𝑜𝑟𝑚 by calculating the average metal-metal bond length inside the NP before and after the deposition on the support. Then, we have applied the following formula:

𝑟 𝑑𝑒𝑓𝑜𝑟𝑚 = ( 𝑑 𝑀-𝑀 𝑁𝑃 * ̅̅̅̅̅̅̅̅̅ 𝑑 𝑀-𝑀 𝑁𝑃 ̅̅̅̅̅̅̅̅̅ -1) 𝑋 100 Eq.8
Where 𝑑 𝑀-𝑀 𝑁𝑃 * is the average distance of M-M bonds of the deformed NP on the support and 𝑑 𝑀-𝑀 𝑁𝑃 the average metal-metal bond length of the NP optimized in gas phase.

Finally, the electronic structure of modeled systems was studied through a charge transfer analysis based on Bader charge [START_REF] Bader | Atoms in molecules: a quantum theory[END_REF]. These calculations have been performed by using Henkelman and co-workers' approach interfaced with VASP [START_REF] Sanville | Improved grid-based algorithm for Bader charge allocation[END_REF].

III-Results

III.1. Modeling of TiO2 supports

Extended surfaces are modeled by considering bi-dimensional periodic slab, involving a finite number of atomic layers, cut from the optimized bulk materials. All geometric and energetic parameters of optimized bulk rutile and anatase are depicted in table 1S. One important characteristic of the surface models is the choice of termination and thickness of the symmetric slab on the basis of the convergence of the surface energy (systematic error due to the slab thickness). In addition, as the focus herein is on the effect of the support, it is useful to give a brief description of the atomic structure of these two surfaces.

Rutile TiO2(110) : the [110] direction in rutile TiO2 leads to three types of terminations, where only one presents a stoichiometric surface (the one considered herein). It exhibits twofold coordinated oxygen atoms (O2C) rows upon the surface and Ti5C/O3C plan. Following the (110) direction, one can distinguish a Ti2O4 layer that is composed of three plans: two plans containing one oxygen and a third one in between composed of Ti2O2 (see Figure 1a). The relaxation of a stoichiometric rutile TiO2 (110) surface has been estimated by ion-scattering spectroscopy. It appears that the height of O2C from the surface is not different from the O-(TiO) distance in the bulk structure. A detailed analysis of surface energy (Esurf ) calculations for stoichiometric surface model as a function of the slab thickness shows that absolute convergence is obtained for a 13-layer thick slab (0.362 J.m -2 with a systematic error of 10 mJ.m -2 ). This value is in fair agreement with previous DFT models (0.35 J.m -2 [START_REF] Lazzeri | Structure and energetics of stoichiometric TiO2 anatase surfaces[END_REF]). Because of the computational cost, a reasonable compromise to make the theoretical study possible is to consider 3-layer thick slab, which leads to a larger systematic error of around 70 mJ.m -2 .

Anatase TiO2(100): the (100) termination is very common in titanium oxide powder used in catalysis but the (101) facet was the most studied as it was reported to be the most thermodynamically stable TiO2 anatase facet. Indeed, the calculated average surface energies was reported to follow the order of: γ(110) 1.09 J m-2 > γ(001) 0.9 J m-2 > γ(100) 0.53 J m-2 > γ(101) 0.44 J m-2 [START_REF] Lazzeri | Structure and energetics of stoichiometric TiO2 anatase surfaces[END_REF]. Recent first-principles calculations reported by Ma et al.

predict the relative photooxidation ((100) > ( 101) > ( 001)) and photoreduction ((100) > ( 101) > ( 001)) activities, and show the higher photocatalytic activity of (100) facet compared to the (101) and (001) surfaces [START_REF] Ma | Relative photooxidation and photoreduction activities of the {100}, {101}, and {001} surfaces of anatase TiO2[END_REF]. Thus, because of its recently identified high reactivity and as very little is known about it, the TiO2 (100) anatase surface was selected in this study. The outermost layer involves five coordinated (Ti5C), two-fold (O2C) and three-fold (O3C) atoms, while the second layer exposes fully coordinated Ti and O atoms. It possesses small grooves formed by oxygen atoms (O2C) on either side of the groove along with both Ti and O atoms at the bottom. From the analysis of surface energy evolution as a function of the slab thickness, an accurate convergence could be reached for 6-layer thick slab (12 atomic plans) with surface energy of 0.67 J.m -2 . This value is slightly higher than the value reported by Lazzeri et al 0.58 J.m -2 [START_REF] Lazzeri | Structure and energetics of stoichiometric TiO2 anatase surfaces[END_REF]). To reduce the computational cost, a slab with a thickness of 2 layers was considered, which leads to a larger systematic error of 10 mJ.m -2 .

III.2. Gas phase NPs

In a recent DFT work devoted to the study of the stability of bimetallic AuCu NPs in vacuum, Iachella and coworkers [66] mixing is favorable for small compositions on gold, as it was expected in view of the bulk alloy.

Insert Table 1 Insert Figure 3 For the composition x=0.21, geometry optimizations show that the regular alloyed structure obtained from the regular AuCu3 bulk, presents an optimal volume only 3% larger than that of pure Cu. The second regular alloyed nanocluster of a composition x=0.26 was obtained by substituting 10 Cu atoms by Au; two atoms from the core and 8 from the outer-shell. The volume variation of this structure shows an expansion of 6% compared to the monometallic Cu38. Finally, the skin-heart structure presents similar characteristics as regular alloy structures but according to its low excess energy value this structure is predicted as the most favorable CuAu nanoparticle alloy type. This may be due to the occupation of Au of lower coordinated surface sites (edge sites).

III.3. Deposited nanoparticles

In the following section the effect of the interaction with the titanium oxide supports on the structure, shape and stability of the nanoclusters is analyzed. For clarity, besides Cu and Au monometallics, we focused our analysis of BiM systems on three selected NPs: CS_Cu32Au6, Insert Figure 4 In Figures 4a andb, the deposited structures of rto [START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] Au and Cu nanoparticles over rutile TiO2(110) are depicted (see the SI for complementary views). Figures 4c and4d represent the deposited NPs on anatase support and will be discussed in the next section. Geometry optimizations show that the structure of rto [START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] before and after deposition on rutile has not changed much; no strong deformation of the monometallic nanoparticles has occurred. In Tables 2 and3, the deposition energy and normalized deposition energy of rto [START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] are addressed for both Au38 and Cu38 (-201 and -28 kJ.mol -1 per bond, whereas -493 and -70 kJ.mol -1 per bond, respectively). The interaction between these nanoparticles and the support forms 7 bonds (see table 4). As shown in Table 2, the deformation energy of rto [START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] Au is roughly twice weaker than that of Cu38 (14 versus 34 kJ.mol -1 ). The trend obtained for the rutile support is concomitant with a twice larger deformation energy for the deposition of rto [START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] Cu with respect to Au. In general, the rutile surface deformation is one order of magnitude larger than that of the metallic nanoclusters. The gain in deposition energy observed for Cu nanocluster is governed by the binding energy (-829 versus -360 kJ.mol -1 )

(
between the NP and the rutile support (largest contribution in the energy decomposition analysis (EDA) model, as illustrated in Table 2). Finally, as depicted in Table 4, the computed geometric deformation ratios of -0.25% and +0.81%, show the negligible contraction of Au nanocluster and the stronger expansion of Cu cluster induced by the contact with the rutile support, respectively.

Regarding the CuAu nanoclusters, the optimal adsorption structures on rutile TiO2 (110) are depicted in Figures 5a, 5b and 5c (see also the SI for complementary views). The energetic order stability obtained from the calculated Eexc in the gas phase (CS_Cu32Au6 < RA_Cu30Au8 < SH_Cu30Au8) is strictly opposite to the stability trend on the rutile support (CS_Cu32Au6 > RA_Cu30Au8 > SH_Cu30Au8). This latter is reflected by the deposition energies of Table 2 in absolute values (698 > 473 > 440 kJ.mol -1 ). This is also consistent with the relative stability in the gas phase of the two nanoclusters with the same composition RA_Cu30Au8 and SH_Cu30Au8 (the less stable is the cluster in gas phase, the larger is its propensity to bind to the support). This analysis is explained by two major contributions of the EDA, i.e. the binding energy between the particle and the support in absolute values (913 > 741 > 705 kJ.mol -1 ), and the deformation energy of the support, at a lesser extent (168 < 200 < 223). In average, the deformation energy of the supported Au, Cu and CuAu nanoclusters is 41 kJ.mol -1 (cf. Table 2). This is a rather weak deformation which is illustrated by the analysis of the geometric deformation ratios of these clusters by comparing adsorbed structures with gas phase ones (0.8 % in average in Table 4).

Insert Figure 5 III.

Au, Cu and AuCu BiM NPs on anatase TiO2(100)

The optimal structures of rto [START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] Au and Cu on anatase TiO2(100) have been reported on Figures 4c and4d (see also the SI for complementary views), while the deposition energies and EDA are addressed in Table 5. For deposited monometallic nanoclusters, our calculations show that both Au and Cu clusters stabilize at the site of the step where the hexagonal face of NP directly interacts with the surface. In such configuration seven atoms of the hexagonal face are bound with seven surface oxygen atoms, five of which belong to the step (O2C) (see Figures 4c and4d).

The normalized energies per metal-support bond and structural complementary analyses are given in Tables 67. Similar to rutile support, rto [START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] Au adsorbed on anatase is less strongly bound (-164 kJ.mol -1 ) than rto [START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] Cu (-408 kJ.mol -1 ). This is mainly explained by the loss of interaction energy (from -600 to -269 kJ.mol -1 ). Regarding the analysis of deformation energies (weaker contributions), the trends between Au and Cu nanoclusters are also compatible with those previously predicted for rutile.

For the deposit of CuAu on anatase support, the relaxed adsorption structures are shown in and undergoes a strong deformation (see Figure 5e).

Regarding the relative stability of the three considered clusters on this support with respect to the gas phase, the trend is identical to the one previously exposed for rutile. The least stable cluster in the gas phase (CS_Cu32Au6) is the most stable one on anatase (-512 kJ.mol -1 in Table 5). Once more, this trend is mainly ruled by the binding energy as shown in Table 5 (from -672 to -461 kJ.mol -1 ). Regarding the average deformation energy of Au, Cu and CuAu nanoclusters (cf. Table 5), the obtained value is weak (44 kJ.mol -1 ) as the one previously calculated for rutile. The slight increase of energetic cost in average for the adsorbed clusters on anatase is consistent with the small increase of geometric deformation (1.2 % in average according to Table 7).

IV. Discussion

Once the analyses of the monometallic and bimetallic clusters have been examined for each support, the natural next step is the detailed comparison between energetic and structural properties of all these nanoclusters on rutile TiO2(110) and anatase TiO2(100). This important discussion related to the support effect is rarely evoked in the literature of DFT studies for such supported clusters at the nanoscale. In the following, we propose a systematic comparative analysis of the support effect on Au, Cu and various CuAu nanoclusters on the two TiO2 surfaces. In addition, we also examine and compare the atomic charge distributions from the Bader analysis of all considered deposited systems. All computed Bader charges are provided in the Supporting Information, Figure S1).

The comparative analysis of total deposition energies of all the considered rto(38) mono and bimetallic systems is addressed in Figure 6 for rutile and anatase surfaces. The first key remark is the systematic larger deposition energy predicted on rutile with respect to anatase.

Interestingly, this difference of support effect is maximum for the CuAu core-shell bimetallic cluster (-698 kJ.mol -1 on rutile versus -512 kJ.mol -1 on anatase), for which the gain is 186 kJ.mol -1 . According to the EDA, such a difference in favor of rutile is mainly explained by the gain in binding energy (-913 kJ.mol -1 for rutile versus -672 kJ.mol -1 for anatase) corresponding to 241 kJ.mol -1 . The small loss between the variation of binding energy with respect to the one of deposition energy comes from the secondary contribution in the EDA, i.e. the deformation energy of the support (168 kJ.mol -1 for rutile versus 124 kJ.mol -1 for anatase). In this global energetic balance, the main gain resulting from the interaction energy (nanoparticle-support bonding) is thus in part compensated by the larger cost to distort rutile support with respect to anatase. This exceptional effect observed for the supported core-shell clusters can also be understood by looking at the relaxed adsorbed geometries (cf. Figure 5a and 5d). On both rutile and anatase supports, the Au6 core tends to extract itself from the Cu32 outer-shell, as much as possible (any deformation inducing an energy cost).

Insert Figure 6 A second remark is related to the change of deposition energy which roughly evolves monotonously with the chemical composition (exception of the two core-shell supported systems); the nanocluster being less stable when the gold content increases. In addition, the deposition energy of regular alloy and skin-heart bimetallic clusters is intermediate between pure and supported Au and Cu nanoclusters.

Coming back to the binding energy between the cluster and the support which is mainly responsible for the stability trends, a first element of comparison is the number of metaloxygen bonds calculated in the optimal adsorbed structures (the threshold for a bond being 3 Å). In Tables 3,4 for rutile and 6, 7 for anatase, these total numbers of bonds and associated normalized interaction energies are reported, respectively. The results show that the number is relatively similar for adsorbed clusters on rutile and anatase (an average of 7 bonds), except for the core-shell deposited clusters (11 bonds on anatase versus 6 bonds on rutile). For the monometallic adsorbed clusters, the loss of binding energy between rutile and anatase is identical (26%), the number of bonds being the same. Interestingly, the Bader analysis also shows similar losses of charges for Cu (1.03 é) and Au (0.99 é) clusters between rutile and anatase. The total charge of Cu cluster being -1.595 é on anatase vs. -2.625 é on rutile; and the total charge of Au cluster being 0.57 é on anatase vs. 1.56 é on rutile.

For the bimetallic adsorbed particles, the loss of interaction energy is either similar to the pure clusters (21% for regular alloy from rutile to anatase) or twice stronger for core-shell (a loss of 60%) and skin-heart (a loss of 53%) nanoclusters. For the latter two bimetallic systems, the loss of interaction energy per bond is similar from rutile to anatase, however the origins are alternate: for core-shell the total number of bonds is twice larger as explained before, whereas for skin-heart, the number of bonds varies less. The detailed analyses of Bader charge distributions on the bimetallic systems point out a noticeable effect of the support. For instance, for core-shell structure, formed by negatively charged pure Au core (positively charged Cu shell), a charge loss of 0.24 é in the Au core and a charge gain of 0.57 é in the Cu shell are registered between anatase and rutile. Concerning the supports, the computed total charges of anatase / rutile in the cases CS_Cu32Au6 (-1.492 é / -2.298 é) > RA_Cu30Au8 (-1.457 é / -2.206 é) > SH_Cu30Au8 (-1.252 é / -1.805 é), follow the trend of deposition energy and confirm the stronger interactions of clusters with rutile support.

A last remark concerns the analysis of the deformation energy of the support which is almost the most important element to analyze for understanding the titania support effect. According to the EDA in Table 2 and5, the average energy cost to distort rutile upon the cluster deposition is 1.9 larger on rutile than on anatase. This corresponds to a significant average deformation energy of 93 kJ.mol -1 for rutile and a stronger charge transfer from clusters adsorbed on rutile support than on anatase. This counterintuitive result illustrates the effective lower propensity of anatase to adapt to the adsorption structure of the metallic cluster with respect to that of rutile, although anatase TiO2(100) exhibits a higher surface energy than rutile TiO2(110). This phenomenon is in part compensated by the higher ability of the metallic clusters to deform itself and optimize the binding with the support. As a matter of fact, the average deformation cost for the clusters on anatase is slightly larger than that on rutile (opposite trend with respect to the support) and this compensates the 93 kJ.mol -1 at the height of 13% (12 kJ.mol -1 ).

By the light of this latter analysis, one can expect that the support effect might increase with the size of the deposited metal. In fact, the larger the metallic cluster, the smaller its ability to deform (larger facets being progressively as stable as flat terraces) and to compensate the larger deformation energy registered for anatase.

V. Conclusion

In this paper, we presented and discussed the results of DFT calculations on CuAu nanoclusters deposited on both rutile TiO2 (110) and anatase TiO2 (100) supports. The objective was to explore the support effect on the adsorption properties. Regular truncated octahedron (rto) 38 atoms nanoclusters Cu(x-1)Au(x), with x in the range [0.15-0.36],

representing three alloy types (regular alloy (RA), core-shell (CS), and skin-heart (SH) structures) were fully optimized in interaction with the support. This selection of AuCu bimetallic nanoparticles has allowed the exploration of various chemical ordering in the core of the cluster but also in the outer-shell, especially for modifying the chemical composition of the facet in contact with the support. A comparative analysis of energetics and structural properties has shown that the adsorption strength of these clusters is systematically larger on rutile than on anatase chosen termination (the most stable cluster being the core-shell Au32Cu6). On the basis of an energy decomposition analysis, this gain of stability is essentially due to the enhancement of the binding energy between the nanoparticle and the rutile support, although this is in part counterbalanced by the deformation cost of the oxide which is larger for rutile than for anatase. This result is supported by the Bader analysis of charge transfers between the supports and the metallic nanoclusters. When the gold increases, the stability of the AuCu bimetallic nanoparticles tends to decrease. The larger propensity of bimetallic nanoclusters to distort themselves, aiming to promote the formation of chemical bonds with the support, has been illustrated by examining the deformation energy of the supported clusters. This ability is expected to decrease with the size of the metallic cluster since larger facets than those of rto [START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] should be more stable and thus less able to adapt to the geometry of the support. Hence this work illustrates the efficiency of theoretical studies for unraveling the question of the chemical bonding at the complex interface, at the atomic scale between a metal and an oxide surface. It paves the way to advanced DFT studies where larger pure and bimetallic nanoparticles (of several nanometers) will be modeled in interaction with reducible supports, especially with the presence of defects such as oxygen vacancies (another type of support effect).

Tables Table 1:

Figure captions

TOC Graphic

Figures 5 d

 5 Figures 5 d, 5e and 5f (see also the SI for complementary views). Except for RA_Cu30Au8, all

Figure 1 :

 1 Figure 1: Lateral (upper part) and top (downmost part) views of TiO2 support surfaces (a) TiO2 (110) rutile, (b) TiO2 (100) anatase. Red and blue balls are oxygen and titanium atoms, respectively.

Figure 2 :Figure 3 :

 23 Figure 2: Optimal structures of free Cu(x-1)Au(x) nanoclusters of composition x in the range [0.15-0.36], of truncated octahedral shape and of total number of atoms of 38. Au (yellow), Cu (orange). Notation : CS = Core-Shell, RA = Regular Alloy, SH = Skin heart

Figure 4 :

 4 Figure 4: Optimized structures of deposited monometallic Au and Cu nanoclusters on (a,b) rutile (110) and (c,d) anatase (100) TiO2 supports. The yellow, brown, blue and red colored balls represent Au, Cu, Ti and O, respectively.

Figure 5 :

 5 Figure 5: Structures of optimized CuAu nanoparticles deposited on (a,b,c) the rutile TiO2 (110) and (d,e,f) anatase (100) TiO2 supports. Ti atoms are represented in blue, O in red, Au in yellow and Cu in brown.

Figure 6 :

 6 Figure 6: Evolution of the computed energy deposition of Au, Cu and CuAu nanoclusters on anatase TiO2 (100) (red line) and rutile TiO2 (110) (blue line), as a function of Au content (x).

Figures Figure 1

 1 Figures

Figure 5 Rutile

 5 Figure 5

  have established a stability-composition relation for a set of two hundreds of BiM NP, in the range 0.8-1.8 nm, with octahedral shape. According to the reported stability diagram, the rto 38 atoms nanoparticles with different alloy types from rich gold to rich copper composition have been shown to be the most stable structures. In the following work we selected five rto 38 atoms nanoclusters representing Cu(x-1)Au(x) of composition ranging from x = 0.15 to x= 0.36 and representing three alloy types (regular alloy (RA), core-shell (CS), and skin-heart (SH) structures). As illustrated by Figure2, the coreshell structure (CS_Cu32Au6) is formed by six Au atoms in the core and 32 Cu in the shell.The two skin-heart structures at x=0.21 and x=0.36, are formed by assembling alloyed cores or outer-shells with pure outer-shell (skins) or cores (hearts), respectively. Concerning RA_Cu30Au8 and SH_Cu30Au8, at x=0.21, the difference between the two structures is that the surface Au atoms are located at the center of the facets and at the edges, respectively. The RA_Cu28Au10 is similar to the RA_Cu30Au8 but with a richer Au core.In table 2 the energetic and geometric properties of the free pure Au and Cu and alloyed

	Insert Figure 2
	Structures including a maximum of Au atoms in the outer-shell (RA_Cu30Au8, SH_Cu30Au8
	(x=0.21) and RA_Cu28Au10 with (x=0.26)) have negative excess energy values and
	concomitantly the lowest surface energies. This superior stability could be attributed to the
	preferential segregation of gold to the surface (cf. Table 1) [75-76]. These results indicate that

CuAu nanoclusters are presented. From this table one can see that CS_Cu32Au6 (x=0.15) and SH_Cu24Au14 (x=0.36) structures, where Au atoms are mainly on the core, present positive values of excess energy 𝐸 𝑒𝑥𝑐 (see Figure

3

) and form the largest volume nanoparticles.

Considering the Core-Shell structure CSAu6Cu32 alloy nanoparticles and compared to the monometallic Cu38, the substitution of 6 Cu atoms by Au, stretches the nanoparticles volume by about 8%. For skin heart x=36, which is composed of a pure core of 6 Au and an alloyed outer-shell of 8 Au and 24 Cu, the Bi NP shows a volume expansion of 11% compared to pure Cu and a volume decrease of about 14% compared to pure Au.

Table 2 :

 2 Energetic (Energy excess and surface energy) and geometric (average atomic distance and volume) descriptors of isolated pure and BiM NPs (GGA PBE level). Energetics

	Au content (x)	Free NPs	∆𝐸 𝑒𝑥𝑐 (eV/atom)	Γ(eV.Å -2 )	d(Å)	V(Å 3 )
	0	rto(38)Cu	0.000	0.043	2.48	1694.9
	0.157	CS_Cu32Au6	+0.108	0.045	2.58	1902.6
	0.210	RA_Cu30Au8	-0.037	0.040	2.52	1780.3
	0.210	SH_Cu30Au8	-0.074	0.038	2.53	1788.8
	0.263	RA_Cu28Au10	-0.052	0.040	2.56	1854.9
	0.368	SH_Cu24Au14	+0.034	0.042	2.62	1986.2
	1	rto(38)Au	0.000	0.028	2.83	2499.2
		(deposition, deformation and interaction energies) for optimized
	rto(38)Au, rto(38)Cu, Core-shell CS_Cu32Au6, regular alloy RA_Cu30Au8, skin heart
	SH_Cu30Au8 nanoparticles adsorbed on the rutile TiO2 (110) support.
	Nanocluster (kJ.mol -1 )	∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2	∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑁𝑃	∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑇𝑖𝑂 2	∑∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 ∆𝐸 𝑖𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑁𝑃 * /𝑇𝑖𝑂 2 *
	rto(38) Au	-201	14	144	158	-359
	rto(38)Cu	-493	34	302	336	-829
	CS_Cu32Au6	-698	47	168	215	-913
	RA_Cu30Au8	-473	68	200	268	-741
	SH_Cu30Au8	-440	43	223	266	-706

Table 3 :

 3 Energetics (average deposition and interaction energies) for optimized rto[START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF]Au,

	rto(38)Cu, Core-shell CS_Cu32Au6, regular alloy RA_Cu30Au8, skin heart SH_Cu30Au8
	nanoparticles adsorbed on the rutile stoichiometric TiO2 (110) support.
	Nanocluster (kJ.mol -1 )	< ∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2	>	< ∆𝐸 𝑖𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑁𝑃 * /𝑇𝑖𝑂 2 *	>
	rto(38) Au	-28		-51
	rto(38)Cu	-70		-118
	CS_Cu32Au6	-116		-152
	RA_Cu 30 Au 8	-68		-106
	SH_Cu30Au8	-62		-100

Table 4 :

 4 Geometric properties (average metal-metal bond lengths of the NP optimized gas

	phase, of the NP optimized on the support, geometric deformations and the numbers of
	bounds connecting the NP with the support) for rto(38)Au, rto(38) Cu, Core-shell
	CS_Cu32Au6, regular alloy RA_Cu30Au8, skin heart SH_Cu30Au8 nanoparticles adsorbed on
	the rutile stoichiometric TiO2 (110) support.
	Nanocluster	𝑑 𝑀-𝑀 𝑁𝑃 ̅̅̅̅̅̅̅ (Å) 𝑑 𝑀-𝑀 𝑁𝑃 * ̅̅̅̅̅̅̅ (Å)	(Å) ∆𝑑 𝑀-𝑀 ̅̅̅̅̅̅̅	(%) 𝑟 𝑑𝑒𝑓𝑜𝑟𝑚	𝑁 𝑏	𝑁𝑃-𝑇𝑖𝑂 2
	rto(38) Au	2.827	2.82	-0.01	-0.25		7
	rto(38)Cu	2.48	2.50	0.02	0.81		7
	CS_Cu32Au6	2.59	2.54	-0.05	-1.93		6
	RA_Cu30Au8	2.55	2.57	0.02	0.78		7
	SH_Cu30Au8	2.55	2.56	0.01	0.39		7

Table 5 :

 5 Energetics (deposition, deformation and interaction energies) for optimized rto[START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF]Au, rto[START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF]Cu, Core-shell CS_Cu32Au6, regular alloy RA_Cu30Au8, skin heart SH_Cu30Au8 nanoparticles adsorbed on the anatase TiO2 (100) support.

	Nanocluster (kJ.mol -1 )	∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2	∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑁𝑃	∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 𝑇𝑖𝑂 2	∑∆𝐸 𝑑𝑒𝑓𝑜𝑟𝑚 ∆𝐸 𝑖𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑁𝑃 * /𝑇𝑖𝑂 2 *
	rto(38) Au	-164	34	71	105	-269
	rto(38)Cu	-408	51	141	192	-600
	CS_Cu32Au6	-512	36	124	160	-672
	RA_Cu30Au8	-389	70	130	200	-589
	SH_Cu30Au8	-323	31	107	138	-461

Table 6 :

 6 Energetics (average deposition and interaction energies) for optimized rto[START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF]Au,

	rto(38)Cu, Core-shell CS_Cu32Au6, regular alloy RA_Cu30Au8, skin heart SH_Cu30Au8
	nanoparticles adsorbed on the anatase stoichiometric TiO2 (100) support.
	Nanocluster (kJ.mol -1 )	< ∆𝐸 𝑑𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑁𝑃/𝑇𝑖𝑂 2	>	< ∆𝐸 𝑖𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑁𝑃 * /𝑇𝑖𝑂 2 *	>
	rto(38) Au	-23		-38
	rto(38)Cu	-58		-86
	CS_Cu32Au6	-47		-61
	RA_Cu30Au8	-55		-84
	SH_Cu30Au8	-46		-66

Table 7 :

 7 Geometric properties (average metal-metal bond lengths of the NP optimized gas phase, of the NP optimized on the support, geometric deformations and the numbers of bounds connecting the NP with the support) for optimized rto[START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF]Au, rto[START_REF] Jiang | Density functional theory study on the metal-support interaction between a Au9 cluster and an anatase TiO2(001) surface[END_REF] Cu, Core-shell

	CS_Cu32Au6, regular alloy RA_Cu30Au8, skin heart SH_Cu30Au8 nanoparticles adsorbed on
	the anatase stoichiometric TiO2 (100) support.
	Nanocluster	𝑑 𝑀-𝑀 𝑁𝑃 ̅̅̅̅̅̅̅ (Å)	𝑑 𝑀-𝑀 𝑁𝑃 * ̅̅̅̅̅̅̅ (Å)	∆𝑑 𝑀-𝑀 ̅̅̅̅̅̅̅ (Å) 𝑟 𝑑𝑒𝑓𝑜𝑟𝑚 (%)	𝑁 𝑏	𝑁𝑃-𝑇𝑖𝑂 2
	rto(38) Au	2.825	2.835	0.01	0.35		7
	rto(38)Cu	2.482	2.516	0.034	1.37		7
	CS_Cu32Au6	2.580	2.640	0.060	2.32		11
	RA_Cu30Au8	2.523	2.594	0.071	2.81		7
	SH_Cu30Au8	2.527	2.570	0.043	1.70		7

Acknowledgements

This work was granted access to the HPC resources of [CCRT/CINES/IDRIS] under the allocation 2018 [x2018087369] made by GENCI (Grand Equipement National de Calcul Intensif]. A.D acknowledges funding from the Research Center, Scientific Research Deanship, IAU, KSA, under Award No. 2015208.

Supporting Information

See supporting information for the following results:


Fokou Mukum

Sandy Fomundam

Sociolinguistical Metamorphosis Of The Moghamo Speaking People Of Cameroon

Keywords: Moghamo, Sociolinguistics, culture, decentralisation, dialect continuum., language attribution

As human altitudes evolve, so too do languages change as time passes especially African languages .African languages are instrumental media through which the African identity, cosmic vision and culture can be expressed and a reliable means through which meaningful development and transformation of the African continent can take place. This paper gives an inside perspective of the synchronic metamorphosis of the moghamo language spoken in the north West region of Cameroon , it's main challenge which is language attribution caused by the bilingual and multilingual nature of the Republic of Cameroon and Remedies to these challenges.

Introduction Definition and Origin Of Sociolinguistics

The word sociolinguistics is derived from two morphemes "socio" from the greek word "socius " meaning society and "linguistics " meaning "scientific study of language ". Sociolinguistics will there be defined as the relationship between society and language that is, how the people of a particular society uses language to interact with each other and with outsiders.

According to Janet Holmes sociolinguist are interested in explaining why we speak differently in different social contexts, and they are concerned with identifying the social functions of language and the ways it is used to convey social meaning. Examining the way people use language in different social contexts provides a wealth of information about the way language works, as well as about the social relationships in a community, and the way people convey and construct aspects of their social identity through their language.

In this write-up , I am going to illustrate the way the moghHamo speaking people use language to interact with each other.

B) Literature Review Historicity :

This publication is an orthography for Moghamo, a Grassfield Bantu language spoken by about 112000 elites of Batibo Subdivision, Momo Divisionof the Northwest Region of Cameroon. SIL's (society of international Linguists) Ethnologue classifies Moghamo alongside Meta as follows: Niger-Congo, Atlantic-Congo, Volta-Congo, Benue-Congo, Bentoid, Southern, Wide Grassfield, Narrow Grassfield, Momo (Grimes, 2000:45).

According to Dieu & Renaud (1983), Moghamo has four different speech forms; (Batibo, Iyirikum, Bessi and Kugwe).ALCAM (the Atlas of central African l anguages) puts them in zone 8 under the number 866. This author agrees with Ndam (2001) that Ashong is one of the four speech forms of Moghamo (in addition to Batibo, Iyirikum and Kugwe).for Ndam, Bessi is the same as Batibo.This work is based on the Batibo speech form which is the reference dialect.

Moghamo speakers are also found in some villages of Santa subdivision (i.e., Baforchu, Baba II,Ngyiembo and Mbe) and Banjah village, all in Mezam Division of the Northwest Region. Moghamo and Meta' spoken in the Mbengwi Central Subdivision of the Momo Divivsion are sometimes considered as dialect continuum since they posses impeccable similarities.

Source:Alcam

Research Methodology

This research was done mainly on observation and Consultation of some data results and finally a positive conclusion was done with the consultation of discussion groups which has so far been accurate

Language Culture and Loncal Development

A) CULTURE Definition

Culture can be defined as a set of rules , practices and believes under which the people of a particular society are govern. However, for anthropologists and other social scientists, culture is the full range of learned human behavior patterns. The term was first used in this way by the pioneer English Anthropologist Edward B. Tylor in his book, Primitive Culture, published in 1871. Tylor said that culture is "that complex whole which includes knowledge, belief, art, law,morals, custom, and any other capabilities and habits acquired by man as a member of society."

Nature of culture

• Our written languages,governments, buildings, and other man-made things are merely the products of culture. They are not culturein themselve • Culture is a powerful human tool for survival, but it is a fragile phenomenon.

• It is constantly changing andeasily lost because it exists only in our minds. The Concept of Culture

Microculture

These are smaller groups with distinct pattern of learned and shared behavior and thinking found within larger cultures such as ethnic groups in localized regions.Some people like to think of these as "local cultures" .Microcultures can include ethnic groups within nations

Levels of Culture

There are very likely three levels of culture that are part of your learned behavior patterns and perceptions. 1. Cultural homogeneity and Perculiarity When people speak of English, French, Italian,Samoan, or Japanese culture, they are referring to the shared language, traditions, and beliefs that set each of these peoples apart from others.. In most cases, those who share your culture do so because they acquired it as they were raised by parents and other family members who have it.

2.Subculture :

In complex, diverse societies in which people have come from many different parts of the world, they often retain much of their original cultural traditions. As a result, they are likely to be part of an identifiable subculture in their new society. The shared cultural traits of subcultures set them apart from the rest of their society.An example of subculture is -Cameroon -Fulani, Bantu, Pygmies,Arabs, Semi-Bantus,-Africa -Bantu, Semi-Bantus, Maghrebian,

• 3. Cultural universals. These are learned behavior patterns that are shared by all of humanity collectively. No matter where people live in the world, they share these universal traits. An example of cultural universal is Communicating with a verbal language consisting of a limited set of sounds and grammatical rules for constructing sentences.

Characteristics of culture

• Culture Is An Adaptive Mechanism -We need our cultural skills to stay alive. Before decentralisation, it was difficult to conceptualise how to include all the local languages in the development endeavour. French and English have remained the exclusive languages of educational, public administration, media, etc. This policy has failed to consider the view that maintaining one's individual identity and ideology through language and culture broadens one's perspective and outlook' (Wang and Maroea in Sgarcoea, 2002)'. Should heritage language speakers be able to build on the linguistic and cultural inheritance that their families pass on, they will be able to achieve a high level of language proficiency that will benefit both the individual and society as a whole.

• Culture is learned -Culture is non-instinctive -Culture is cumulative • Culture is cumulative • We Do Not Know

Implications of Decentralisation On Traditional Structures, Local Languages and Cultures

Before decentralisation, the promotion of indigenous languages and culture (it remains partly) the responsibility of the Ministry of Arts and Culture, of Basic education, of secondary education, and to some extent the ministry of youth affairs. The 1996 revision as well as the 2004 Law 33 which defines the assignment of responsibilities between the State and local governments to meet the criteria of complementarity, ostensibly follows developments in the EU(World Bank2011). According to the provisions of the Law on decentralization, the promotion of local languages and culturesis the responsibility of the local councils under the supervision of the Ministry of Decentralisation and local development.

Classification Of The Moghamo Language

The languages of Africa are generally divided into four major phyla: Niger-Congo, Nilo-Saharan, Afroasiatic, and Khoisan. Moghamo being a Cameroonian language and above all an African languages is classified under the Niger-Congo Phylum which is the largest of the four phyla containing between 1350 and 1650 languages which is twothird of the African languages.

Facts About Niger-Congo Phylum

Niger-Congo is the largest language phylum in the world covering a greater area than any other phylum (Williamson & Blench 2000). Not surprisingly, then, many of the most widely spoken languages in Africa belong to Niger-Congo. One of its salient features is an elaborated noun class system with grammatical concord. A large majority of languages of this family are tonal such Yoruba, Igbo, Aghem, Ghomala, Fe'fe', Ewondo, Duala, Basaa, Fang-beti. A major branch of Niger-Congo languages is the Bantu. The Bantu Languages are believed to number at present between 400 and 600. They are spoken in almost half of all Sub-saharan countries: Cameroon, Central African Republic, Equatorial Guinea, Gabon, Congo, Democratic Republic of Congo, Rwanda, Burundi, Uganda, Kenya, Tanzania, Comoros, Angola, Zambia, Malawi, Mozambique, Namibia, Botswana, Zimbabwe, South-Africa, Lesotho, and Swaziland..

Approach Use To Classify Moghamo Language

The criteria used for classifying African languages have been and continue to be typological and even areal or geographic. In other parts of the world, languages are said to be genetically related only if they share linguistic properties and items which cannot have been borrowed, thereby demonstrating that they have a common "parent".

The approach use to classify moghamo language is the mutual intelligibility test approach .This approach tries to analyze whether speakers of language A can understand language B and vice versa . For example Moghamo speakers in Batibo Sub division and Menemo Speakers in Mbengwi sub division all in Momo Division of the northwest region of Cameroon.

One of the methods consists of playing a speech sample from Language B played to speakers of Language A. The Language A speakers then tested on how well they understand the speech sample. And then the reverse is done: speakers of Language B try to understand a speech sample from Language A. Although this method has not been put to widespread use by linguists in Africa (see [START_REF] Ladefoged | Language in Uganda[END_REF], Schuring 1985, Slabbert & Myers-Scotton 1997), it has been widely used by social psychologists and sociolinguists, e.g., Labov 1981. It features prominently, of course, in the tool box of missionaries, particularly those intent on Bible translation, e.g., Casad 1974, Grimes 1990. With the information gleaned from such an assessment, missionary analysts can make decisions as to how many different Bible translations are needed for a given area and even which dialect should be chosen as the standard.

In summary, then, an evaluation of intelligibility, in uncovering the socialpsychological dimension, tells us much more than a purely linguistic analysis. Although such measures have not often been used in genetic classification, they do provide information on the relatedness of languages at the micro level. From the data they furnish one can make social historical inferences and thus obtain information on past and future relations between language varieties, useful information for classification

Experiment Of The Mutual intelligibility Approach On Moghamo language

During A Traditional wedding Between A bride from Batibo and a groom from ku Bomie village in mbengwi subdivision where the families of the former and the later could express themselves in their respective mother tongue respectively that is moghamo and menemo, it was observed that 75 % of the attendees of could clearly understand each others language perfectly without any interpretation .5% of invitees from other neighbouring villages could slightly understand because the existence of of loan words in this languages from other dialects for example ngoshie in njikwa sub division and the rest 20% could only express themselves either in English-pidgin or English which is one of the official languages of Cameroon.

It was finally concluded that speakers of moghamo and menemo could clearly understand themselves because they have a common history and ancestor even though there is a slight variation in accent and tone in both languages.

Moghamo Dialect Continuum

Definition of Dialect

The word dialect comes from the Latin word "dialectus" meaning to dialogue or converse. A dialect can be defined as a regional variety of language distinguished by features of vocabulary, grammar, and pronunciation from other regional varieties and constituting together with them a single language.

Dialect continuum:

A dialect continuum can be a range of dialects spoken in some geographical area that are only slightly different between neighbouring areas. But these differences become larger as someone travels in any direction, so that speakers from opposite ends of the continuum, are no longer mutually intelligible, they cannot understand each other. "A traveller walking in a straight line from village to village notices successive small changes, but seldom, if ever, observes large differences.This sounds like a justification of the continuum view, but there is an added twist. Might the traveller be misled by the perspective of most recent memory"(Heeringa and Nerbonne 2002: 375).This can be explained by the assertion below.

If we travel from village to village, in a particular direction, we notice linguistic differences which distinguish one village from another. The further we get from our starting point, the larger the differences will become. At no point is there a complete break such that geographically adjacent dialects are not mutually intelligible (speakers of these dialects can't readily understand and communicate with one another),but the cumulative effect of the linguistic differences will be such that the greater the geographical separation, the greater the difficulty of comprehension. This type of situation is known as a geographical dialect continuum (Chambers and Trudgill 2004: 5). This shows us that the mutual intelligibility seems to depend on geographical distances between the villages. But the question is does this traveller notice everything or just some changes?

Moghamo language has four speech forms (Batibo, Iyirikum, Bessi and Kugwe) with just slight variation in accent and pronunciation.It is also similar to other western other core dialects of the Momo Division conspicuous amongst them is the meta dialect with the code MGO same as that of moghamo. It has six speech forms( Bameta, Chubo, Menemo-Mogamo, Metta, Mitaa, Muta) and it's spoken in the following areas east and southeast Mbengwi and east Batibo subdivisions,Bamenda1 Subdivision, Bafuchu and Nja village areas.

The Table Below

Current Situation Of Moghamo Language

Within the last decade moghamo has almost become an extinct language because of language attribution.

Language Attribution :

It is the process of losing a native or a first language .This process is generally caused by the both isolation from the speakers of the first language (L1) and acquiring a new language (2). In the case of moghamo, this can be clearly link to the large exodus of indigines of the community to Urban areas in search of greener pastures and also the promotion of official languages of Cameroon which are English and French by the state as enshrined in article1(3) of its constitution. This is clearly visible as english and french are use in all areas of the country even in education to solve the problem of linguitic and cultural diversity which is a major call of concern in the country as it has over 250 national languages. Also,the high rate of using English-Pidgin as a sociolect amongst individuals in to communicate has also cause a decline in many local languages including moghamo. A new creole known as Camfranglais which is a combination of Cameroonian languages including moghamo, English and French is currently making waves across the nation and it serves as as an idiolect for a majority of the youths and a sociolect for members of a particular social class and could be used as a regeolect in particular regions depending on how words of the three languages are permutated and commutated to make moaning.

REMEDY AND CONCLUSION

To solve the problem of language attribution, several mechanisms are being put in place by the moghamo speaking people such as the organization of cultural Jamborees to teach people the culture of the moghamo people,

The government of Cameroon is doing a great deal to promote local (national) languages through the national Commission for the promotion of bilingualism and multiculturalism (NCPBM) ,the ministry of scientific research and innovation(MINRESI) in partnership with SIL Cameroon has carried out intensive study on the moghamo orthography and have documented it. The Moghamo language Committee (MOLCOM) has done a great deal to document the moghamo language using the general alphabet of Cameroonian languages and has organised several workshop to educate people on the use of the language .In the education sector, the ministries of education in the country has encourage the teaching of local languages including moghamo at the basic and secondary level.Also the celebration of the Mother's tongue day goes a long way to instill the zeal to learn local languages.

  All of Our Own Culture • All cultures change over time • Culture Gives Us a Range of Permissible Behavior Patterns • Cultures No Longer Exist in Isolation

shows the different areas whose dialects are similar to Moghamo by virtue of the fact that they have been classified as western momo language and have so many similarities with moghamo in the areas of Morphology and graphetics in the northwest region of Cameroon

	Meta	MGO	Bameta, Chubo, Menemo-	East and
			Mogamo, Metta, Mitaa, Muta	southeast Mbengwi
				and east Batibo
				subdivisions;
				Bamenda1
				Subdivision,
				Bafuchu and Nja
				village
	Ngamambu	NBV	Bafuchu, Banja, Mbu, Mungyen,	East and
			Nga, Ngembo	southeast Mbengwi
				and east Batibo
				subdivisions;
				Mezam Division,
				Santa Subdivision,
				Bafuchu and
				Nja village areas.
	Ngoshie	NGN	Ngwaw	East Njikwa
				subdivision
	Njen	NJJ	Nyen, Nzin	Southeast of Batibo
				Nyen Village
	Ngie	NGI	Angie, Baminge, Baninge,	West mbengwi sub
			Mingi, Ngi, Ugie, Ungie	division Andek Area
	Dialect	Code	Speech forms	Area Spoken