Evgenii M Roginskii
email: e.roginskii@mail.ioffe.ru

Mikhail B Smirnov

Konstantin S Smirnov
email: konstantin.smirnov@univ-lille.fr

Rita Baddour-Hadjean

Jean-Pierre Pereira-Ramos

Alexander N Smirnov

Valery Yu Davydov

A Computational and Spectroscopic Study of Electronic Structure of V 2 O 5 -based Cathode Materials

The electronic structure of α-V 2 O 5 , γ -V 2 O 5 and γ-MeV 2 O 5 (Me = Li, Na) bronzes is studied by quantum-chemical calculations completed by spectroscopic experiments.

The calculations are performed using G 0 W 0 method with DFT+U self-consistent wavefunction as an initial approximation. The electronic band gap E g = 2.89 eV calculated for α-V 2 O 5 is found to be in a fair agreement with available experimental data. The strategy was then applied to studying the electronic structure of the γ -V 2 O 5 phase and γ-MeV 2 O 5 bronzes for which no experimental band gap data exist in the literature. Computed E g values are equal to 3.17 eV, 1.21 eV and 1.18 eV for γ -V 2 O 5 , γ-LiV 2 O 5 and γ-NaV 2 O 5 , respectively. The nature of alkali metal atom is obtained to have little influence on the structure and electronic states of the bronzes. Raman spectra recorded with different wavelengths of exciting radiation have allowed the determination of energy threshold corresponding to the transition from off-resonance to resonance Raman scattering process. In this way, a band gap value in the range 2.54 -2.71 eV for α-V 2 O 5 and γ -V 2 O 5 is obtained in a good agreement with the experimental values for the α-phase. Raman spectra of γ-MeV 2 O 5 suggest the band gap smaller than 1.58 eV in these materials, whereas the photoluminescence measurements yield E g ≈ 0.95 eV for the γ-LiV 2 O 5 bronze. Remarkably, the result of the G 0 W 0 calculations lies in between the experimental estimates. Strong similarity of structures and electronic states of γ-LiV 2 O 5 and γ-NaV 2 O 5 accounts for their the same operating voltage when used as cathodes in Li(Na)-ion batteries.

Introduction

The rich chemistry and polymorphism of vanadium pentoxide (V 2 O 5 ) have made this material very interesting for fundamental research and for many applications in heterogeneous catalysis, 1 electrochromism 2 and electrochemical energy storage. [START_REF] Whittingham | Lithium Batteries and Cathode Materials[END_REF] Vanadium pentoxide is a typical intercalation compound because of its layered structure. This structural peculiarity is illustrated in Figure 1 Very early, the α-form (Figure 1a) has been identified as a promising cathode material for secondary lithium batteries. [START_REF] Whittingham | Lithium Batteries and Cathode Materials[END_REF][START_REF] Whittingham | The Role of Ternary Phases in Cathode Reactions[END_REF][START_REF] Delmas | The Li x V 2 O 5 System: An Overview of the Structure Modifications Induced by the Lithium Intercalation[END_REF] Functioning of the batteries relies on the electron transfer reaction accompanied by the electrochemical intercalation/de-intercalation of alkali metal atoms into the oxide structure. The insertion of alkali metal (Me) in the interlayer space of V 2 O 5 lattice leads to vanadium oxide bronzes with general formula Me x V 2 O 5 showing remarkable versatility as a function of the nature of intercalated alkali atom. [START_REF] Galy | Vanadium Pentoxide and Vanadium Oxide Bronzes -Structural Chemistry of Single (S) and Double (D) Layer M x V 2 O 5 phases[END_REF] The presence of two V 5+ ions per V 2 O 5 unit allows to reach a high storage capacity that can amount to 300 mAh g -1 corresponding to the reversible accommodation of two lithium ions/mole in the 2.3-3.5 V potential window. [START_REF] Whittingham | Lithium Batteries and Cathode Materials[END_REF][START_REF] Delmas | The Li x V 2 O 5 System: An Overview of the Structure Modifications Induced by the Lithium Intercalation[END_REF] The interest of the γ -V 2 O 5 polymorph (Figure 1b) for the electrochemical applications has been recently demonstrated in the case of lithium [START_REF] Baddour-Hadjean | Unraveling the Structural Mechanism of Li Insertion in γ -V 2 O 5 and Its Effect on Cycling Properties[END_REF][START_REF] Baddour-Hadjean | Kinetic Insight into the Electrochemical Lithium Insertion Process in the Puckered-Layer γ -V 2 O 5 Polymorph[END_REF] and sodium insertion. [START_REF] Safrany Renard | γ -V 2 O 5 : A New High Voltage Cathode Material for Sodium-Ion Battery[END_REF][START_REF] Baddour-Hadjean | The Richness of V 2 O 5 Polymorphs as Superior Cathode Materials for Sodium Insertion[END_REF] A higher open circuit voltage combined with lower diffusion barriers afford superior electrochemical properties to this material compared to the α-V 2 O 5 form. [START_REF] Baddour-Hadjean | Kinetic Insight into the Electrochemical Lithium Insertion Process in the Puckered-Layer γ -V 2 O 5 Polymorph[END_REF][START_REF] Baddour-Hadjean | The Richness of V 2 O 5 Polymorphs as Superior Cathode Materials for Sodium Insertion[END_REF] A readily accessible V 5+ /V 4+ redox couple and the stability of different local coordination environments of the vanadium atoms (octahedral, distorted octahedral, square pyramid, . . . ), result in the flexibility of the layered V 2 O 5 structures and in their ability to accommodate point defects through a crystallographic shear and/or charge localization/delocalization. [START_REF] Zavalij | Structural Chemistry of Vanadium Oxides with Open Frameworks[END_REF] The lattice of γ-MeV 2 O 5 bronzes (Me = Li, Na) is very close to that of γ -V 2 O 5 shown in Figure 1b and in what follows, we therefore use the same notation for the atoms V and O atoms in both the pure and intercalated structures.

The electronic structure and the energy difference between the top of the valence band and the bottom of the conduction band, the band gap E g , are fundamental characteristics of material that determine its electric conductivity and optical properties. The conductivity is directly related to the concentration of charge carriers that, in its turn, depends on the band gap, and impacts high rate capabilities of electrode materials. [START_REF] Eftekhari | Lithium-Ion Batteries with High Rate Capabilities[END_REF] The band gap is also an important factor in electrochemical applications, in particular for designing an electrode-electrolyte pair. [START_REF] Bisquert | Energy Diagram of Semiconductor/Electrolyte Junctions[END_REF][START_REF] Liu | Understanding Electrochemical Potentials of Cathode Materials in Rechargeable Batteries[END_REF] Among different structural modifications of vanadium pentoxide, a value of the band gap has been measured only for the α-V 2 O 5 polymorph, [START_REF] Kenny | Optical Absorption Coefficients of Vanadium Pentoxide Single Crystals[END_REF][START_REF] Bodó | Optical Absorption near the Absorption Edge in V 2 O 5 Single Crystals[END_REF][START_REF] Meyer | Electronic Structure of Vanadium Pentoxide: An Efficient Hole Injector for Organic Electronic Materials[END_REF] while no such data exist for γ-Me x V 2 O 5 bronzes which, as it was mentioned above, have more promising properties for the usage as cathode material for Me-ion batteries. [START_REF] Safrany Renard | γ -V 2 O 5 : A New High Voltage Cathode Material for Sodium-Ion Battery[END_REF][START_REF] Baddour-Hadjean | The Richness of V 2 O 5 Polymorphs as Superior Cathode Materials for Sodium Insertion[END_REF][START_REF] Emery | γ-Na 0.96 V 2 O 5 : A New Competitive Cathode Material for Sodium-Ion Batteries Synthesized by a Soft Chemistry Route[END_REF] Nowadays, the lack of experimental data can in part be compensated by the use of atomistic simulations that have become a valuable and reliable tool in materials research.

Most of electronic-structure calculations of materials employs methods based on the density functional theory (DFT). However, a correct description of electronic structure with DFT encounters problems due to the energy derivative discontinuity and the local character of exchange-correlation (XC) functionals of commonly used local density approximation (LDA) and generalized gradient approximation (GGA) to DFT. The derivative discontinuity makes the band gap to be known up to a constant, [START_REF] Perdew | Density Functional Theory and The Band Gap Problem[END_REF] while the local character of LDA and GGA XC functionals causes artifacts in the calculations for materials with occupied d and f states, [START_REF] Mori-Sánchez | Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction[END_REF] such as transition metal oxides. To overcome the shortcomings, computational investigations of the electronic structure of solids often rely on the DFT+U approach, that introduces an on-site repulsion for localized electrons. [START_REF] Anisimov | Density Functional Theory and NiO Photoemission Spectra[END_REF] Alternatively, the local character of the LDA and GGA XC functionals is remedied in hybrid functionals, such as PBE0 [START_REF] Perdew | Rationale for Mixing Exact Exchange with Density Functional Approximations[END_REF] and HSE06 [START_REF] Heyd | Hybrid Functionals Based on a Screened Coulomb Potential[END_REF][START_REF] Heyd | Hybrid Functionals Based on a Screened Coulomb Potential[END_REF] , that bring a non-local exchange energy of Hartee-Fock (HF) theory into DFT. While these approaches generally improve results for the electronic structure of materials, they introduce empirical parameters (Hubbard parameter U in DFT+U and the portion of HF exchange in hybrid functionals) that may not work properly outside the range of systems (properties) to which they are fitted.

In order to sidestep the deficiencies inherent to DFT, one can employ computations that use a GW approximation based on the many-body perturbation theory. The GW calculations permit a more accurate description of the electronic states in a systems of interacting electrons and nuclei, [START_REF] Shishkin | Self-Consistent GW Calculations for Semiconductors and Insulators[END_REF][START_REF] Hedin | New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem[END_REF] but at the expense of being much more computationally expensive than their DFT counterparts, especially if the self-consistent solution is sought.

Although the GW method provides results in a good agreement with experimental data, it was found that the computations overestimate the band gap if the Green's function G and the screened Coulomb interaction matrix W are updated until a self-consistency. On the other hand, a "single-shot" G 0 W 0 calculations including of one iteration step underestimate experimental values. A compromise was found in the case when only the Green's function is updated until the self-consistency, while the screened Coulomb potential is kept unchanged (GW 0 approximation). [START_REF] Shishkin | Self-Consistent GW Calculations for Semiconductors and Insulators[END_REF] Nevertheless, even GW 0 remains computationally demanding for systems with dozens of atoms in the unit cell. Bruneval and Marques 27 reported on results of G 0 W 0 calculations starting from electronic states obtained by different methods. The authors found that the accuracy of the calculations could be improved by using a solution obtained with a hybrid XC functional as an initial approximation. Alternatively, Scheffler and co-workers have shown that the use of LDA+U solution in G 0 W 0 method provides an accurate description of electronic structure in systems with occupied d-or f -electron shells. [START_REF] Jiang | Localized and Itinerant States in Lanthanide Oxides United by GW@LDA+U[END_REF][START_REF] Jiang | First-Principles Modeling of Localized d States with the GW@LDA+U Approach[END_REF] The structure, lattice dynamics and electronic states of the α-phase of vanadium pentoxide have been studied with DFT methods in a number of works. [START_REF] Kempf | Theoretical Investigations of the Electronic Properties of Vanadium Oxides. 1. Pseudopotential Periodic Hartree-Fock Study of Vanadium Pentoxide Crystal Lattice[END_REF][START_REF] Eyert | Electronic Structure of V 2 O 5 : Role of Octahedral Deformations[END_REF][START_REF] Willinger | Geometric and Electronic Structure of γ-V 2 O 5 : Comparison Between α-V 2 O 5 and γ-V 2 O 5[END_REF][START_REF] Brázdová | Periodic Density Functional Study on Structural and Vibrational Properties of Vanadium Oxide Aggregates[END_REF][START_REF] Scanlon | An ab initio Study of Reduction of V 2 O 5 through the Formation of Oxygen Vacancies and Li Intercalation[END_REF][START_REF] Londero | Role of van der Waals Bonding in the Layered Oxide V 2 O 5 : First-principles Density-functional Calculations[END_REF][START_REF] Londero | Vanadium Pentoxide (V 2 O 5 ): A van der Waals Density Functional Study[END_REF][START_REF] Carrasco | Role of van der Waals Forces in Thermodynamics and Kinetics of Layered Transition Metal Oxide Electrodes: Alkali and Alkaline-Earth Ion Insertion into V 2 O 5[END_REF] In order the calculations to correctly reproduce the layered structure of the material, the use of semi-empirical dispersion correction was found to be indispensable. [START_REF] Londero | Role of van der Waals Bonding in the Layered Oxide V 2 O 5 : First-principles Density-functional Calculations[END_REF][START_REF] Londero | Vanadium Pentoxide (V 2 O 5 ): A van der Waals Density Functional Study[END_REF] Band gap values computed in ref 30-32,34 were obtained to be smaller than the experimental data [START_REF] Kenny | Optical Absorption Coefficients of Vanadium Pentoxide Single Crystals[END_REF][START_REF] Bodó | Optical Absorption near the Absorption Edge in V 2 O 5 Single Crystals[END_REF][START_REF] Meyer | Electronic Structure of Vanadium Pentoxide: An Efficient Hole Injector for Organic Electronic Materials[END_REF] and the agreement with the experiment could be improved by the inclusion of on-site Hubbard term penalizing the electron delocalization into the Hamiltonian. [START_REF] Scanlon | An ab initio Study of Reduction of V 2 O 5 through the Formation of Oxygen Vacancies and Li Intercalation[END_REF] Like the experimental research, computational DFT studies of other V 2 O 5 structures paid little attention to their electronic states. [START_REF] Willinger | Geometric and Electronic Structure of γ-V 2 O 5 : Comparison Between α-V 2 O 5 and γ-V 2 O 5[END_REF][START_REF] Carrasco | Role of van der Waals Forces in Thermodynamics and Kinetics of Layered Transition Metal Oxide Electrodes: Alkali and Alkaline-Earth Ion Insertion into V 2 O 5[END_REF][START_REF] Zhou | Raman Spectrum of Vanadium Pentoxide from Density-Functional Perturbation Theory[END_REF][START_REF] Smirnov | Spectroscopic and Computational Study of Structural Changes in γ-LiV 2 O 5 Cathodic Material Induced by Lithium Intercalation[END_REF] Investigations of V 2 O 5 materials with the GW methods are scarce. The electronic structure of α-V 2 O 5 was investigated in self-consistent GW calculations by Bhandari and Lambrecht. [START_REF] Bhandari | Quasiparticle Self-Consistent GW Calculations of the Electronic Band Structure of Bulk and Monolayer V 2 O 5[END_REF] In line with aforementioned results, the authors obtained the band gap significantly larger than the experimental values. [START_REF] Kenny | Optical Absorption Coefficients of Vanadium Pentoxide Single Crystals[END_REF][START_REF] Bodó | Optical Absorption near the Absorption Edge in V 2 O 5 Single Crystals[END_REF][START_REF] Meyer | Electronic Structure of Vanadium Pentoxide: An Efficient Hole Injector for Organic Electronic Materials[END_REF] The discrepancy was explained as a result of enhanced screening of the Coulomb potential due to an increase of the static dielectric constant because of large LO-TO splitting in the system. To the best of our knowledge, no other attempts of exploring V 2 O 5 -based materials with GW methods were undertaken.

The present work reports on a combined computational and experimental study of the electronic structure, particulary the band gap, of pure α-V 2 O 5 , γ -V 2 O 5 and of alkali-atom intercalated γ-MeV 2 O 5 (Me = Li, Na) materials. The computations have adopted a strategy in which the electronic structure of α-V 2 O 5 was investigated by G 0 W 0 method with the self-consistent LDA+U solution as an initial approximation to the many-particle wavefunction. [START_REF] Jiang | First-Principles Modeling of Localized d States with the GW@LDA+U Approach[END_REF] To avoid the arbitrariness in the choice of Hubbard parameter, value of U was obtained using density functional perturbation theory. [START_REF] Cococcioni | Linear Response Approach to the Calculation of the Effective Interaction Parameters in the LDA + U Method[END_REF] A good agreement of the calculated band gap value with the available experimental data for this structure enabled us to extend the strategy to the computation of the electronic structure of γ -V 2 O 5 and of the MeV 2 O 5 bronzes. In the absence of any experimental information on the band gap in these materials, Raman and photoluminescence experiments performed with different wavelengths of the exciting radiation provided experimental estimates for E g and validated results of the electronicstructure calculations.

Methods

Experimental procedure and materials characterisation α-V 2 O 5 was prepared through the polyol method described in ref 42. Chemical lithiation of α-V 2 O 5 was performed under mild conditions, using lithium iodide in excess (molar ratio 2:1) to obtain the δ-LiV 2 O 5 precursor that transforms to γ-LiV 2 O 5 when heat-treated at 300 • C. [START_REF] Murphy | Lithium Incorporation by Vanadium Pentoxide[END_REF] γ -V 2 O 5 is obtained by chemical oxidation of γ-LiV 2 O 5 using NO 2 BF 4 in molar excess (2:1), as described in ref 18. γ-NaV 2 O 5 is come by chemical sodiation of γ -V 2 O 5 using anhydrous sodium iodide (molar excess 2:1). [START_REF] Zavalij | Structural Chemistry of Vanadium Oxides with Open Frameworks[END_REF] The synthesis procedure results in a change of samples color from orange for the pure V 2 O 5 phases to dark green (nearly black) for the alkali-atom intercalated compounds. The structural parameters of α-

V 2 O 5 , γ -V 2 O 5 γ-LiV 2 O 5 γ-NaV 2 O 5
are summarized in Table S1 of Supporting Information (SI). The experimental Raman spectra of the materials are plotted in Figure S1 of SI, while the assignment of spectral features in the spectra is discussed in detail elsewhere. [START_REF] Emery | γ-Na 0.96 V 2 O 5 : A New Competitive Cathode Material for Sodium-Ion Batteries Synthesized by a Soft Chemistry Route[END_REF][START_REF] Smirnov | Spectroscopic and Computational Study of Structural Changes in γ-LiV 2 O 5 Cathodic Material Induced by Lithium Intercalation[END_REF][START_REF] Baddour-Hadjean | The Raman Spectrum of the γ -V 2 O 5 Polymorph: A Combined Experimental and DFT Study[END_REF][START_REF] Safrany Renard | Crystal Structure Determination of a New Sodium Vanadium Bronze Electrochemically Formed[END_REF][START_REF] Smirnov | Unraveling the Structure-Raman Spectra Relationships in V 2 O 5 Polymorphs via a Comprehensive Experimental and DFT Study[END_REF] The Raman measurements of α-V 2 O 5 and γ -V 2 O 5 were performed at room temperature using LaBRAM HR 800 (Jobin-Yvon-Horiba) micro-Raman spectrometer equipped with a back illuminated charge coupled device detector (Spex CCD) cooled by Peltier effect to 200 K. In the measurements, the exciting light at four wavelengths was used, namely: He-Ne laser (λ= 632.8 nm), and tunable Ar+ laser (λ = 514, 488 and 458 nm). A 100x LWD objective was used to focus the laser light to a spot size of 1 µm 2 on the sample surface. To avoid a local heating of the sample, the power of the laser beam was adjusted to 0.2-0.5 mW with neutral filters of various optical densities. The Raman and photoluminescence measurements of γ-LiV 2 O 5 were performed with a T64000 (Horiba Jobin-Yvon) spectrometer equipped with a confocal microscope and a silicon CCD detector cooled by liquid nitrogen.

Room temperature Raman spectra were excited by a 442 nm HeCd laser line, 532 nm line of a Nd:YAG laser (Torus, Laser Quantum, Inc.), and λ 0 = 785 nm line of nearinfrared laser diode (TEC, Thorlabs Inc.). Photoluminescence spectra were excited by λ 0 = 785 nm (TEC, Thorlabs Inc.) and λ 0 = 244 nm (Coherent Innova 300C MotoFreD Ion Laser). The measurements in the temperature range from 78 to 300 K were carried out in a temperature controlled microscope stage Linkam THMS600. All spectra were measured in a backscattering geometry.

Computational procedure

The ab initio calculations presented in the paper were carried out with ABINIT software package. [START_REF] Gonze | ABINIT: First-Principles Approach to Material and Nanosystem Properties[END_REF][START_REF] Gonze | A Brief Introduction to the ABINIT Software Package[END_REF] The LDA calculations employed the pseudopotential method and the plane wave basis set for valence electronic states, and used the PW exchange-correlation functional. [START_REF] Perdew | Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy[END_REF] The interactions between the core and valence electrons were described with the projectoraugmented wave (PAW) method. [START_REF] Blöchl | Projector Augmented-Wave Method[END_REF][START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method[END_REF] The 3p3d4s states of V atom, 2s2p states of O atom and 2s2p3s states of sodium were considered as valence states; the Li atom was treated at the all-electron level. In order to take into account the reduction of the transition metal upon the intercalation of alkali atoms, spin-polarized calculations were performed. The localized character of the 3d states of V atoms was taken into consideration via the Hubbard term in the Hamiltonian (DFT+U method). [START_REF] Anisimov | Density Functional Theory and NiO Photoemission Spectra[END_REF] Choice of the Hubbard parameter U is discussed below in detail.

For each system studied the equilibrium structure was obtained in the following way.

First, the geometry optimization of the unit cell was performed for a series of five volumes.

In these calculations, both atomic positions and lattice parameters were allowed to vary, whereas the volume and the symmetry of the crystalline lattice were kept fixed. The Kohn-Sham equations were solved iteratively with a stopping criterion 10 -12 Ha for the energy convergence and the geometry optimization was considered to be completed if the maximum force on ions was less than 5 × 10 -5 Ha/Bohr. The obtained energy vs. volume dependence was fitted by the Murnaghan equation of state [START_REF] Murnaghan | The Compressibility of Media under Extreme Pressures[END_REF] that provided an equilibrium cell volume.

Then, the volume was used in a final optimization run that produced the equilibrium lattice parameters and atomic coordinates. This approach permitted to avoid problems related to the Pulay stress and to the variation of size of plane wave basis set that accompany calculations with simultaneous optimization of both the volume and atomic positions. The total energy was tested for the convergence with respect to the k-point grid and number of plane waves, the latter is controlled by a plane wave kinetic energy cutoff. It was found that the convergence of the total energy within 10 -4 Ha/atom was achieved with the energy cutoff of 40 Ha and 2 × 6 × 6 grids and 2 × 6 × 2 grids of k-points chosen according to the Monkhorst-Pack scheme [START_REF] Monkhorst | Special Points for Brillouin-Zone Integrations[END_REF] in the irreducible part of the Brillouin zone (BZ) of the α-V 2 O 5 , and γ -V 2 O 5 and γ-MeV 2 O 5 structures, respectively. The so-obtained equilibrium structures were employed in subsequent calculations that used the above calculation parameters and the convergence criterion. The LDA+U calculations were performed considering a partial occupation of electronic states with a gaussian smearing of 1 mHa width.

The quasi-particle GW calculations 54 used the frequency dependence of the screened Coulomb interaction obtained within the random-phase approximation by the contour deformation method. [START_REF] Lebègue | Implementation of an All-Electron GW Approximation Based on the Projector Augmented Wave Method Without Plasmon Pole Approximation: Application to Si, SiC, AlAs, InAs, NaH, and KH[END_REF] The exchange and correlation components of the self-energy were computed using the plane wave basis set with the energy cutoffs of 40 Ha and 10 Ha, respectively.

The calculation of the polarizability and Green's function employed 268 unoccupied states in the conduction band. The BZ integration was performed over the 2 × 4 × 4 and 2 × 4 × 2 grid for α-V 2 O 5 and for γ -V 2 O 5 and γ-MeV 2 O 5 , respectively. The initial single-particle Green's function G 0 and the screened Coulomb potential W 0 were constructed using the LDA+U eigenstates and eigenvalues, that is known as G 0 W 0 @LDA+U approach. [START_REF] Jiang | Localized and Itinerant States in Lanthanide Oxides United by GW@LDA+U[END_REF][START_REF] Jiang | First-Principles Modeling of Localized d States with the GW@LDA+U Approach[END_REF][START_REF] Patrick | Quasiparticle Bandgaps of Anatase TiO 2 Starting from DFT + U[END_REF] In order to exclude double-counting term contained in the LDA+U eigenvalues, 57 the quasi-particle energies E σ nk were calculated using following expression: 29

E σ nk = ¯ σ nk + Z nk (¯ σ nk ) [Σ σ nk (¯ σ nk ) -(ν xc ) σ nk ] , (1)
where σ is the spin index (up/down), k -wavevector, ¯ σ nk -single-particle energies calculated with LDA+U wave functions, Z nk -renormalization factor, and ν xc -Kohn-Sham (KS)

exchange-correlation operator. The band structure in the GW calculations was obtained from the KS band structure by applying the energy-dependent scissors operator generated by a fit of GW -KS energy differences over a dense grid of k-points as a function of the KS eigenvalues. [START_REF] Levine | Linear Optical Response in Silicon and Germanium Including Self-Energy Effects[END_REF]59 Results and discussion

Choice of Hubbard parameter U . The use of the LDA+U solution in the GW calculations requires the knowledge of the Hubbard parameter U . Previous DFT calculation of V 2 O 5 bronzes 34,39 made use of U = 4 eV that was obtained from comparison of computed band gap to E g values measured by the X-ray and UV photoelectron spectroscopies. [START_REF] Wu | Photoelectron Spectroscopic Study of Li Intercalation into V 2 O 5 Thin Films[END_REF][START_REF] Wu | Photoelectron Spectroscopic Study of Na Intercalation into V 2 O 5 Thin Films[END_REF] However, this value of U could not be simply transferred to the present calculations. In fact, the used DFT+U approach relies on two Hubbard parameters U and J which being combined give an effective parameter U ef f = U -J and it is U ef f that corresponds to U in ref 34,39. Making use of the linear response method, [START_REF] Cococcioni | Linear Response Approach to the Calculation of the Effective Interaction Parameters in the LDA + U Method[END_REF][START_REF] Shick | Implementation of the LDA+U Method Using the Full-Potential Linearized Augmented Plane-Wave Basis[END_REF][START_REF] Bennett | A Systematic Determination of Hubbard U Using the GBRV Ultrasoft Pseudopotential Set[END_REF] we have computed U = 4.5 eV and U = 4.9 eV for the α-V 2 O 5 and γ -V 2 O 5 structures, respectively. For the alkali atom intercalated γ-MeV 2 O 5 compound the method has yielded an U value of 5.2 eV. Constrained DFT calculations of U and J for several transition metal oxides have given U ≈ 5 eV and Given the likeness of the results obtained by the linear response method and the outcome of the previous calculations, [START_REF] Jiang | First-Principles Modeling of Localized d States with the GW@LDA+U Approach[END_REF] we have chosen to use U = 4.5 eV and J = 0.5 eV for all the systems in the study without adjustment.

The comparison of electron density of states (DOS) obtained for γ-LiV 2 O 5 with these values of U and J to DOS computed in ref 39 shows their a good agreement (see Figure S2).

Futhermore, auxiliary calculations have revealed a small difference between the target quantities computed with the system-specific (obtained with the linear response method) and the generic U and J parameters (Table S3). A weak dependence of the electronic structure on the parameter values indicate that their values are "physically" meaningful. [START_REF] Jiang | First-Principles Modeling of Localized d States with the GW@LDA+U Approach[END_REF] Electronic structure and Raman spectra of pure V 2 O 5 structures. The geometry optimization of the pristine V 2 O 5 structures at the LDA+U level does not notably improve the agreement between the computed and experimental structural characteristics in comparison to the conventional LDA calculations (Table S1). The result is perfectly understandable because none of the 3d states of vanadium atoms, which are subjected to the Hubbard term, is occupied in these systems. However, the use of U in the LDA calculations pushes the bottom of the conduction band up, thus increasing the electronic band gap E g . The direct band gap E d g for the α-V 2 O 5 structure computed at the LDA+U level is equal to 1.79 eV, 1.84 eV and 1.87 eV for U ef f = 0 eV, U ef f = 2.7 eV and U ef f = 4 eV, respectively. The optical absorption measurements on α-V 2 O 5 monocrystals have given E g = 2.35 ± 0.01 eV 15 and E g = 2.31 ± 0.01 eV [START_REF] Bodó | Optical Absorption near the Absorption Edge in V 2 O 5 Single Crystals[END_REF] and the band gap at T = 0 K estimated by extrapolating these experimental data is 2.49 eV to 2.54 eV. [START_REF] Bodó | Optical Absorption near the Absorption Edge in V 2 O 5 Single Crystals[END_REF] More recent photoemission spectroscopic experiments reported the band gap of 2.8 eV for this material. [START_REF] Meyer | Electronic Structure of Vanadium Pentoxide: An Efficient Hole Injector for Organic Electronic Materials[END_REF] Although the LDA+U slightly increases E g value, the band gap still remains markedly smaller than the experimental conterparts and the energy derivative discontinuity makes the quantity known up to a constant. [START_REF] Perdew | Density Functional Theory and The Band Gap Problem[END_REF] As it was mentioned in Introduction, one may expect to solve the problem, at least in part, by using the GW method while a high computational cost of such calculations can be reduced by taking the self-consistent LDA+U solution as an initial approximation. Density of electronic states (DOS) for α-V 2 O 5 computed at the LDA+U level is presented in Figure 2a while the partial DOS (PDOS) can be found in Figure S3. The first conduction band with lowest energy appears as a sharp peak in DOS (shaded with light green color in Figure 2). The nature of states in the band is important for understanding the change of the electronic structure upon the intercalation of alkali metal atoms. As it has been found previously, the conduction band is dominanted by d-states of vanadium atoms [START_REF] Willinger | Geometric and Electronic Structure of γ-V 2 O 5 : Comparison Between α-V 2 O 5 and γ-V 2 O 5[END_REF][START_REF] Bhandari | Quasiparticle Self-Consistent GW Calculations of the Electronic Band Structure of Bulk and Monolayer V 2 O 5[END_REF] and this conclusion is confirmed by the analysis of PDOS (Figure S3). Since these V 3d states are unoccupied, the vanadium atoms are in the 5+ oxidation state in the pure compound. Such a band of localized V 3d states is typical for vanadium oxides including γ-V 2 O 5 (Figure 2b) [START_REF] Porsev | Hybrid Hartree-Fock-Density Functional Theory Study of V 2 O 5 Three Phases: Comparison of Bulk and Layer Stability, Electron and Phonon Properties[END_REF] .

Anticipating the following discussion, the intercalation of alkali metal atoms injects additional electrons into the system that fill the states thus making the band valence and radically decreasing the band gap in the material.

Figure 3a presentss the band structure of α-V 2 O 5 obtained in an "one-shot" G 0 W 0 @LDA+U calculation. The top of the valence band and the bottom of the conduction band are in the vicinity of the T-point (0, [START_REF] Weckhuysen | Spectroscopy and the Role of Supported Vanadium Oxides in Heterogeneous Catalysis[END_REF] 2 , 1 2 ) and in the Γ-point of the BZ, respectively. The direct gap E d g is equal to 2.89 eV and corresponds to the transition in the (0, 1 4 , 1 2 ) point of the BZ, the indirect band gap E i g amounts to 2.42 eV. The computed E d g value is slightly greater than the estimation of 2.49 -2.54 eV at T = 0 K obtained from the UV-vis adsorption data, [START_REF] Kenny | Optical Absorption Coefficients of Vanadium Pentoxide Single Crystals[END_REF][START_REF] Bodó | Optical Absorption near the Absorption Edge in V 2 O 5 Single Crystals[END_REF] while it is close to an estimate 2.98 -3.01 eV at T = 0 K found by extrapolating the band gap measured in the photoemission experiments. [START_REF] Meyer | Electronic Structure of Vanadium Pentoxide: An Efficient Hole Injector for Organic Electronic Materials[END_REF] Our trial calculations have shown that a small variation of U ef f does not significantly influence the values of the band gap and therefore, the choice of U ef f = 4 eV seems to be reasonable. Bohr that has resulted in the convergence of exact exchange energy better than 5 × 10 -4 Ha.

Γ X S Y Γ Z U R T Z -5 -4 -3 -2
The results presented above show that the use of this approach and of a DFT solution as the input to the G 0 W 0 calculations, gives the band gap in the α-V 2 O 5 in a much better agreement with the experimental data than the E g values obtained in the self-consistent GW calculations. [START_REF] Bhandari | Quasiparticle Self-Consistent GW Calculations of the Electronic Band Structure of Bulk and Monolayer V 2 O 5[END_REF] The electronic band structure obtained for γ -V 2 O 5 in a G 0 W 0 @LDA+U calculation using the above approach is presented in Figure 3b. The top of the valence band and the bottom of the conduction band are found in the vicinity of the T-point (0, 1 2 , 1 2 ) and in the Γ-point (0, 0, 0) of the BZ, respectively. The calculation yields the direct and indirect band gaps of 3.17 eV and 3.09 eV, respectively, and the direct gap corresponds to the transition in the Γpoint of the BZ. G 0 W 0 @LDA+U calculations using the U value obtained by linear response method has given slightly lower E g values, namely 3.12 eV and 3.04 eV for the direct and indirect band gap, respectively (Table S3). To the best of our knowledge, no experimental data exist on the band gap in the material. Previously, Willinger et al. Besides the optical absorption or photoemission experiments, Raman spectroscopy can, in principle, provide information on the band gap value. Indeed, one can expect a notable change in the Raman spectrum of material as soon as the energy of exciting radiation exceeds E g and thus, the scattering process occurs in the electron resonance conditions. Figure 4 displays Raman spectra of α-V 2 O 5 and γ -V 2 O 5 samples measured with four different excitation wavelengths. One sees that all the spectra obtained with λ 0 > 458 nm are very similar to each other, whereas the spectra obtained with λ 0 = 458 nm strikingly differ from the spectra measured with excitation wavelengths of smaller energy. Despite a variation of shape of the most intense peak at ca. 500 cm -1 , the 458 nm spectra obtained from different spots on the sample's surface show a good reproducibility. Hence, such a dependence of the spectra on the excitation wavelength cannot be viewed as an artifact and the behavior allows us to suppose that the 458 nm spectra were measured in the electron resonance conditions. Then, it is reasonable to assume that the band gap value for the α-V 2 O 5 and γ -V 2 O 5 materials at room temperature lies between 2.71 eV (λ 0 = 458 nm) and 2.54 eV (λ 0 = 488 nm). Making use of the relative band gap values in these materials obtained in the G 0 W 0 @LDA+U calculations, one can estimate the band gap in α-V 2 O 5 to be slightly greater than 2.54 eV that well agrees with the previous experimental results. [START_REF] Bodó | Optical Absorption near the Absorption Edge in V 2 O 5 Single Crystals[END_REF][START_REF] Meyer | Electronic Structure of Vanadium Pentoxide: An Efficient Hole Injector for Organic Electronic Materials[END_REF] The gap in γ -V 2 O 5 can then be evaluated to be slightly lesser than 2.71 eV that provides a first experimental estimation of this quantity for the material. It should be noted that the γ -V 2 O 5 sample was obtained by the chemical deintercalation of Li atoms from the γ-LiV 2 O 5 bronze and, therefore its structure can contain a number of defects. Consequently, the above value likely underestimates the band gap in a defect-less structure of γ -V 2 O 5 .

Figure 4 shows that the resonance Raman spectra of both the pure V 2 O 5 structures are dominated by a peak at 500 cm -1 . According to our previous calculations, [START_REF] Smirnov | Spectroscopic and Computational Study of Structural Changes in γ-LiV 2 O 5 Cathodic Material Induced by Lithium Intercalation[END_REF][START_REF] Baddour-Hadjean | The Raman Spectrum of the γ -V 2 O 5 Polymorph: A Combined Experimental and DFT Study[END_REF][START_REF] Smirnov | Unraveling the Structure-Raman Spectra Relationships in V 2 O 5 Polymorphs via a Comprehensive Experimental and DFT Study[END_REF] the Raman features in this spectral region originate from vibrational modes involving stretching vibrations of V-O2 contacts in the ladder steps and of the bonds in the V-O3-V bridges [START_REF] Smirnov | Unraveling the Structure-Raman Spectra Relationships in V 2 O 5 Polymorphs via a Comprehensive Experimental and DFT Study[END_REF] (see Figure 1b). The electronic-structure calculations indicate that the main contribution to the top of the valence band comes from the O2 and O3 oxygen atoms, whereas the bottom of the conduction band is formed by the d states of vanadiums. It is, therefore, not surprising that the Raman peaks due to vibrational modes involving displacements of these atoms are the most concerned by the electron resonance effect. γ-MeV 2 O 5 bronzes. In contrast to the pure V 2 O 5 materials, a computational investigation of alkali atom intercalated MeV 2 O 5 structures necessitates the use of theoretical approach that takes into account the localized character of partially occupied 3d vanadium states. [START_REF] Scanlon | An ab initio Study of Reduction of V 2 O 5 through the Formation of Oxygen Vacancies and Li Intercalation[END_REF][START_REF] Smirnov | Spectroscopic and Computational Study of Structural Changes in γ-LiV 2 O 5 Cathodic Material Induced by Lithium Intercalation[END_REF] Figure 6 shows the G 0 W 0 @LDA+U electron band structure of γ-LiV 2 O 5 , the band structure of the γ-NaV 2 O 5 bronze is very similar with a tiny difference in a value of the band gap (Figure S3). The electronic states at the Fermi level are formed by the d orbitals of Vb atoms occupied by electrons ejected from the outer s shell of the alkali metals, while the bottom of the conduction band is formed by the d orbitals of Va atoms, Figure 1b.

From Figure 6 it follows that the γ-MeV 2 O 5 bronzes are the direct transition semiconductors with the direct optical transition at the Y-point and the band gap values obtained in the G 0 W 0 @LDA+U calculation are equal to 1.21 eV and 1.18 eV for the γ-LiV 2 O 5 and γ-NaV 2 O 5 structures, respectively. Calculations using U obtained by the linear response method results in E g values slightly greater (by 0.1 eV) than those computed with the generic U (Table S3).

In the absence of any experimental data concerning the band gap in these materials, we attempt to estimate this quantity by using the Raman and photoluminescence spectroscopies.

Note that the above theoretical E g values imply that the Raman spectra measured using the light sources in the visible region are all obtained in the resonance conditions. Figure 5 shows PDOS for the γ-LiV 2 O 5 bronze obtained in the spin-polarized LDA+U calculation (see Figure S2 for the total DOS). One readily sees the difference between "spin up" and "spin down" states in the range -0.7 to 0 eV corresponding to the band of localized 3d states of Vb atoms. The difference is explained by the fact that with four intercalated Li atoms per unit cell, four electrons ejected from the 2s orbitals of lithiums occupy the 3d states of Vb atoms in the "spin up" configuration. This leads to the splitting of conduction V 3d band to the valence one formed by filled d-states of Vb atom and to the conducting band formed by empty d-states of Va atom (Figure 6). The cation sublattice now consists of vanadium atoms in the 4+ (Vb) and 5+ (Va) oxidation states. This conclusion is in line with the results reported in ref [START_REF] Scanlon | An ab initio Study of Reduction of V 2 O 5 through the Formation of Oxygen Vacancies and Li Intercalation[END_REF] and complete the data in ref [START_REF] Smirnov | Spectroscopic and Computational Study of Structural Changes in γ-LiV 2 O 5 Cathodic Material Induced by Lithium Intercalation[END_REF] . S4). One sees that peaks in the spectra of γ-LiV 2 O 5 are characterized by larger widths and higher intensities compared to the counterpart peaks in the spectrum of the pure compound. It could be supposed that these peculiarities are due to a more disordered structure of the bronze compared to that of γ -V 2 O 5 , however, it is the contrary that should be true. Indeed, γ -V 2 O 5 is obtained by chemical de-intercalation of alkali-metal atoms from γ-LiV 2 O 5 and therefore, its resultant structure is expected to contain more defects than that of the parent material. Nevertheless, the peaks in the Raman spectrum of γ -V 2 O 5 shown in Figure 7 are characterized by a notably smaller width. Such a difference between the spectra of the pure and lithiated γphases indicates, in our opinion, that the spectra of γ-LiV 2 O 5 (and of its sodium analogue)

Γ Z T Y S X U R -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Energy, eV C A B I D E C F G H E
were measured in the electron resonance conditions. If true, this gives an estimation of the band gap in the material E g < 1.58 eV (785 nm) that is in line with the results of the calculations. Unfortunately, all our attempts to obtain the Raman spectra of MeV 2 O 5 bronzes with an excitation source of energy smaller than 1.58 eV (λ 0 > 785 nm) did not succeed due to technical problems. It is noteworthy that all the spectra in Figure 7a-c were measured with the energy of incident radiation smaller than 2.8 eV, i.e. the resonance electronic excitation corresponds to the transitions A -G, see Figure 6 and Figure 8. These transitions occur between the localized states near the Fermi level formed by the d-orbitals of Vb atoms and the bottom of the conduction band. This can account for the fact that the most marked difference between the spectra of the γ -V 2 O 5 and γ-LiV 2 O 5 samples, Figure 7, is seen for Raman peaks which, according to our calculations, correspond to vibrational modes involving displacements of Vb atoms (see Figure 1).

Conclusions

This work reports results of a combined computational and experimental study of the electronic structure of α-V 2 O 5 , γ -V 2 O 5 and γ-MeV 2 O 5 (Me = Li, Na) materials. The electronic states in these compounds were investigated with the quasi-particle GW method which used a self-consistent LDA+U solution for constructing the initial Green's function and screened Coulomb potential. Such a "single-shot" G 0 W 0 @LDA+U calculations have given the direct electronic band gap value E g = 2.89 eV for the α-V 2 O 5 structure that well agrees with the available experimental data. [START_REF] Kenny | Optical Absorption Coefficients of Vanadium Pentoxide Single Crystals[END_REF][START_REF] Bodó | Optical Absorption near the Absorption Edge in V 2 O 5 Single Crystals[END_REF][START_REF] Meyer | Electronic Structure of Vanadium Pentoxide: An Efficient Hole Injector for Organic Electronic Materials[END_REF] The strategy was subsequently applied to compute the electronic structure of the γ -V 2 O 5 phase and of the γ-MeV 2 O 5 bronzes for which no experimental information on band gap value exists. The calculations have given E g = 3.17

eV, E g = 1.21 eV and E g = 1.18 eV for the γ -V 2 O 5 , γ-LiV 2 O 5 and γ-NaV 2 O 5 structures, respectively. The calculations have shown a close similarity between the electronic structures of the two alkali-atom intercalated materials that accounts for their peculiar and attractive electrochemical characteristicsr. [START_REF] Emery | γ-Na 0.96 V 2 O 5 : A New Competitive Cathode Material for Sodium-Ion Batteries Synthesized by a Soft Chemistry Route[END_REF] Indeed, while Na insertion systematically occurs at much lower voltage than Li one (∆E ≈ 1.5 V in the case of α-V 2 O 5 [START_REF] Muller-Bouvet | Electrochemically Formed α -NaV 2 O 5 : A New Sodium Intercalation Compound[END_REF] ), the same high voltage of 3.3 V vs. Na + /Na is remarkably achieved for Li and Na reactions in γ-MeV 2 O 5 bronzes. [START_REF] Emery | γ-Na 0.96 V 2 O 5 : A New Competitive Cathode Material for Sodium-Ion Batteries Synthesized by a Soft Chemistry Route[END_REF] The results of electronic-structure calculations were accompanied with data of spectroscopic experiments. Thus, measuring Raman spectra of the materials with different wavelengths of exciting radiation has allowed to estimate a threshold energy corresponding to the transition from off-resonance to resonance Raman scattering process. The band gap value obtained in this way for α-V 2 O 5 and γ -V 2 O 5 was found to lie between 2.54 eV and the α-phase and with the result of the G 0 W 0 @LDA+U calculation. The Raman spectra of γ-MeV 2 O 5 bronzes revealed a band gap smaller than 1.58 eV, whereas the comparison of the calculated band structure of γ-LiV 2 O 5 with the photoluminescence spectra yielded the band gap E g ≈ 0.95 eV for this material. The result of the quasi-particle G 0 W 0 calculations is just between the two experimental estimates and is very close to a 0 K value extrapolated from the photoluminescence data. The present work shows that the calculations do not necessitate using adjusted parameters, i.e. they can be performed in a fully nonempirical way. The successful approach combining the ab initio calculations and spectroscopy will be applied to the investigation of other γ-Me x V 2 O 5 (Me = K + , Mg 2+ , Ca 2+ , . . . ) bronzes having a crucial interest for next generation Me-ion batteries.

Rita Baddour-Hadjean: 0000-0002-3158-1851

Jean-Pierre Pereira-Ramos: 0000-0001-5381-900X

Notes

Authors declare no competing financial interest.

  for the α-V 2 O 5 and γ -V 2 O 5 phases which are the main objects of the present work. These structures exhibit characteristics typical of all V 2 O 5 polymorphs, i.e. V 2 O 5 chains running in the b crystallographic direction and connected in layers via V-O2 "ladder" steps; the layers are then stacked in the third dimension and held together by weak interlayer interactions. Puckering layers in the γ -V 2 O 5 lattice compared to flat layers in the α-V 2 O 5 structure results in the c lattice parameter of the γ -V 2 O 5 unit cell being approximately twice of the parameter of α-V 2 O 5 one.

Figure 1 :

 1 Figure 1: Structures of α-V 2 O 5 (a) and γ -V 2 O 5 (b). The crystallographic unit cells are shown by dashed lines; atom labels correspond to those used throughout the paper.

56

 56

Figure 2 :

 2 Figure 2: Densities of states (DOS) for α-V 2 O 5 (a) and γ -V 2 O 5 obtained in the LDA+U calculations. The density of states in valence band and in the V 3d conduction band discussed in the text are shaded by the blue and light green color, respectively. The origin of the energy axis is placed at the Fermi energy.

Figure 3 : 4 . 8

 348 Figure 3: Electronic band structure of α-V 2 O 5 (a) and γ -V 2 O 5 (b) calculated in G 0 W 0 @LDA+U approximation; dashed lines indicate the positions of the Fermi level and the bottom of the conduction band. The bottom of conduction band and the top of the valence band pointed out by blue and red dots, respectively. Direct and indirect interband transitions are respectively shown by vertical and oblique arrows. The origin of energy axis is placed at E F (Fermi energy).

32 computed E g of 1 .

 1 70 eV in γ -V 2 O 5 by using the full potential linearized augmented plane waves method; the value E g = 1.75 eV was obtained for α-V 2 O 5 by the authors.

Figure 4 :

 4 Figure 4: Raman spectra of α-V 2 O 5 (a) and γ -V 2 O 5 (b) obtained with different wavelengths λ 0 of the incident radiation: λ 0 = 633 nm (red), λ 0 = 514 nm (green), λ 0 = 488 nm (blue), and λ 0 = 458 nm (violet).

Figure 5 :

 5 Figure 5: Partial densities of states (PDOS) for γ-LiV 2 O 5 obtained in the spin-polarized LDA+U calculation. For each atom type, the positive and negative parts of DOS correspond to the spin up and spin down states. The origin of the energy axis is placed at the Fermi energy.

Figure 6 :Figure 7

 67 Figure 6: Electron band structure of γ-LiV 2 O 5 obtained in G 0 W 0 @LDA+U calculation. Red and black lines stand for the spin up and spin down states, respectively; dashed lines indicate the positions of the Fermi level and bottom of the conduction band. The bottom of conduction band and the top of the valence band pointed out by blue and red dots respectively. Arrows indicate optical interband transitions, see text for details. The origin of the energy axis is placed at E F (Fermi energy)

Figure 7 :

 7 Figure 7: Experimental Raman spectra of γ-LiV 2 O 5 measured with the excitation wavelengths λ 0 = 785 nm (red), λ 0 = 532 nm (green) and λ 0 = 442 nm (blue); black line labeled γ -V 2 O 5 presents the experimental Raman spectrum of γ -V 2 O 5 obtained with λ 0 = 633 nm.

Figure 8 :

 8 Figure 8: Photoluminescence spectra of γ-LiV 2 O 5 sample: a) room temperature (RT), excitation wavelength λ = 785 nm; b) temperature T = 77 K, excitation wavelength λ = 244 nm.Letters labeling bands in the spectra refer to transitions depicted in Figure6.

Table 1

 1 collects experimental and theoretical band gap values for the α-V 2 O 5 and γ -V 2 O 5 materials. Comparison of the E g values computed at different levels of theory shows that the use of the DFT+U approach yields a better agreement with the experimental data, in line with the outcome of previous studies[START_REF] Scanlon | An ab initio Study of Reduction of V 2 O 5 through the Formation of Oxygen Vacancies and Li Intercalation[END_REF] . Computations with the hybrid PBE0 functional using both the LCAO basis set[START_REF] Porsev | Hybrid Hartree-Fock-Density Functional Theory Study of V 2 O 5 Three Phases: Comparison of Bulk and Layer Stability, Electron and Phonon Properties[END_REF] and plane waves (this work) strongly overestimate the band gap in the α phase. The HSE06 functional performs better, yet the band gap in the material is markedly greater than the experimental values. A better agreement with the experiment has been obtained at the GGA+U level in ref 34 that is not surprising as U in that study has been fitted to reproduce the experimental band gap. Despite a relatively high computational cost, the G 0 W 0 calculation using LDA+U solution gives a very good estimation of E

g obtained in a purely ab initio way with the U parameter found with the linear response method

[START_REF] Cococcioni | Linear Response Approach to the Calculation of the Effective Interaction Parameters in the LDA + U Method[END_REF]

.

Table 1 :

 1 Experimental and calculated values of band gap E g for the α-V 2 O 5 and γ -V 2 O 5 polymorphs.

	Polymorph E g (eV)	Method	Reference
	α-V 2 O 5	2.35 ± 0.01 Exp. a , OA	15
		2.31 ± 0.01 Exp., OA	16
		2.8	Exp., PES	17
		1.74	Calc. b , ASW/LDA	31
		1.6 (2.1)	Calc., PAW/GGA (GGA+U ) 66
		1.38 (2.06) Calc., PAW/LDA (PBE)	67
		1.92	Calc., PAW/PW91	68
		1.74	Calc., PAW/PBE	69
		2.26	Calc., PAW/PBE+U	34
		1.75	Calc., FPLAPW	32
		4.04	Calc., TZVP/PBE0	64
		4.83	Calc., SC GW	40
		1.79 (1.87) Calc., PAW/LDA (LDA+U ) This work
		4.17	Calc., PW-NCPP/PBE0	This work
		3.43	Calc., PW-NCPP/HSE06	This work
		2.89	Calc., G 0 W 0 @LDA+U	This work
	γ -V 2 O 5	1.70	Calc., FPLAPW	32
		4.23	Calc., TZVP/PBE0 e	64
		1.93 (2.27) Calc., PAW/LDA (LDA+U ) This work
		4.41	Calc., PW-NCPP/PBE0	This work
		3.64	Calc., PW-NCPP/HSE06	This work
		3.17	Calc., G 0 W 0 @LDA+U	This work
	a Experiment: OA -optical absorption, PES -photoemission spectroscopy;
	b Calculations: LDA, GGA -local density approximation and generalized gradient
	approximation to DFT, respectively; +U -inclusion of Hubbard term into Hamiltonian;
	PBE, PW91 -GGA exchange-correlation functionals; PBE0, HSE06 -hybrid HF-DFT
	functionals; ASW -augmented spherical wave; FPLAPW -full potential linearized
	augmented plane wave; SC GW -self-consistent GW approach; PAW -projector
	augmented wave; TZVP -polarization quality triple-zeta valence atomic basis set,
	PW-NCPP -plane wave basis set with norm-concerving pseudopotentials.

Acknowledgements E.M.R. acknowledges the financial support of Université Paris Est-Créteil in the frame of the invited professor program UPE 2020. A part of the calculations was performed using the facilities of the Computational Center of Research Park of St. Petersburg State University.

The authors also thank the anonymous reviewers for valuable comments.

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Catalysis by Metals : Contribution of Electrochemistry

In Catalysis by metals, methods of electrochemistry can be mainly used in the two following areas : -Preparation of bimetallic catalysts by surface redox reactions, -Characterization of metallic catalysts.

. PREPARATION OF BIMETALLIC CATALYSTS BY SURFACE ELECTROCHEMICAL REACTIONS

Preparation procedures of bimetallic catalysts influence the type of interaction between the two metallic species and then the catalytic performance of catalysts.

Different electrochemical methods can be used to bring into close contact the two metals responsible for the formation of the bimetallic entities. Four methods of preparing bimetallic catalysts were developed. These methods are direct redox reactions, redox reactions of adsorbed species, catalytic reduction and underpotential deposition [1].

Direct redox reactions in the preparation of bimetallic catalysts

In this case, metal-metal interactions result from surface redox reactions between the chemically prereduced metal «parent» M and the oxidized form of the modifier M'z'+.

According to Nernst's law, the equilibrium potential of the reversible oxidation of M :