Marilia T C Martins-Costa

Josep M Anglada

Joseph S Francisco

Manuel F Ruiz-López

The Aqueous Surface as an Efficient Transient Stop for the Reactivity of Gaseous NO 2 in Liquid Water

The heterogeneous reaction of NO 2 with water on diverse surfaces is broadly considered as a possible source of atmospheric HONO in dark conditions, but associated mechanisms are not fully understood. We report data from first-principles simulations showing that the lifetime of the putative reactive NO 2 dimer on the surface of pure water droplets is too small to host the whole process. One infers from our results that the hydrolysis of NO 2 in clouds must be catalyzed by organic or inorganics species adsorbed on the droplets.

Recently, the chemistry of NO 2 on aqueous surfaces has attracted great attention. Photochemical processes in aqueous media have been studied both experimentally [START_REF] Crowley | OH formation in the photoexcitation of NO2 beyond the dissociation threshold in the presence of water vapor[END_REF][START_REF] Li | Atmospheric hydroxyl radical production from electronically excited NO2 and H2O[END_REF][START_REF] Carr | Comment on Atmospheric Hydroxyl Radical Production from Electronically Excited NO2 and H2O[END_REF][START_REF] Amedro | Direct observation of OH radicals after 565 nm multi-photon excitation of NO2 in the presence of H2O[END_REF][START_REF] Li | Response to Comment on" Atmospheric Hydroxyl Radical Production from Electronically Excited NO2 and H2O[END_REF][START_REF] Dillon | Reactive quenching of electronically excited NO2 * and NO3 * by H2O as potential sources of atmospheric HOx radicals[END_REF] and theoretically, [START_REF] Minaev | Photochemical Water Decomposition in the Troposphere: DFT Study with a Symmetrized Kohn-Sham Formalism[END_REF][START_REF] Fang | The conical intersection dominates the generation of tropospheric hydroxyl radicals from NO2 and H2O[END_REF][START_REF] Wu | Two photon dissociation dynamics of NO2 and NO2+ H2O[END_REF] and simulations at the air-water interface [START_REF] Martins-Costa | Theoretical Investigation of the Photoexcited NO2+H2O reaction at the Air-Water Interface and Its Atmospheric Implications[END_REF] have shown that they are a significant additional source of OH radicals in the troposphere. Many experimental studies have focused, however, on the thermal hydrolysis of NO 2 (1), which has been studied for a long time. [START_REF] Kameoka | Absorption of Nitrogen Dioxide into Water, Sulfuric Acid, Sodium Hydroxide, and Alkaline Sodium Sulfite Aqueous Solutions[END_REF][START_REF] Sakamaki | Formation of nitrous acid and nitric oxide in the heterogeneous dark reaction of nitrogen dioxide and water vapor in a smog chamber[END_REF] This key process produces HONO, whose photolysis (2) is a main source of tropospheric OH, and nitric acid, related to acid rain.

2 NO 2 + H 2 O  HONO + HNO 3 (1) HONO + h  NO + OH (2) The great interest generated by reaction (1) is principally due to the failure of current atmospheric models to predict observed concentrations of HONO and OH, so that "unknown" sources of these species are suspected. Reaction (1) might represent one of such "unknown" sources for HONO (see [START_REF] Spataro | Sources of atmospheric nitrous acid: State of the science, current research needs, and future prospects[END_REF][START_REF] Lammel | Nitrous acid and nitrite in the atmosphere[END_REF] for a review on HONO sources).

Reaction (1) is not favorable in gas-phase, but according to experiments it is enhanced through NO 2 adsorp-tion on different surfaces, [START_REF] Finlayson-Pitts | Chemistry of the upper and lower atmosphere: theory, experiments, and applications[END_REF][START_REF] Finlayson-Pitts | The heterogeneous hydrolysis of NO2 in laboratory systems and in outdoor and indoor atmospheres: An integrated mechanism[END_REF] such as soot, mineral dust, soils, urban surfaces and foliage. The surface of water droplets may also participate to this chemistry, which is supported by field studies reporting the presence of HONO in aqueous aerosols and clouds. [START_REF] Finlayson-Pitts | The heterogeneous hydrolysis of NO2 in laboratory systems and in outdoor and indoor atmospheres: An integrated mechanism[END_REF] Though the reaction mechanism has not yet been completely elucidated, experiments on thin films supported by solid substrates [START_REF] Finlayson-Pitts | The heterogeneous hydrolysis of NO2 in laboratory systems and in outdoor and indoor atmospheres: An integrated mechanism[END_REF] suggested (Figure 1) that NO 2 associates to form the symmetric dimer O 2 N-NO 2 . Upon adsorption on the surface, this dimer isomerizes to the less stable asymmetric dimer ONO-NO 2 , which ionizes to (NO + )(NO 3 -) stabilized by interactions with water. Finally, the charge separated species reacts with water to form HONO, which desorbs to gas phase, and HNO 3 , assumed to remain at the surface in molecular or nitrate ion forms. [START_REF] Ramazan | New experimental and theoretical approach to the heterogeneous hydrolysis of NO2: key role of molecular nitric acid and its complexes[END_REF] The charge-separated dimer (NO + )(NO 3 -) is therefore considered as the reactive species for hydrolysis. It has also been proposed to be involved in the reaction of NO 2 with HCl leading to ClNO. [START_REF] Raff | Chlorine activation indoors and outdoors via surface-mediated reactions of nitrogen oxides with hydrogen chloride[END_REF][START_REF] Hammerich | NOx Reactions on Aqueous Surfaces with Gaseous HCl: Formation of a Potential Precursor to Atmospheric Cl Atoms[END_REF] However, the mechanism of ( 1) is still unresolved and under discussion. [START_REF] Spataro | Sources of atmospheric nitrous acid: State of the science, current research needs, and future prospects[END_REF][START_REF] Jenkin | Laboratory studies of the kinetics of formation of nitrous acid from the thermal reaction of nitrogen dioxide and water vapour[END_REF][START_REF] Gustafsson | The molecular mechanism of tropospheric nitrous acid production on mineral dust surfaces[END_REF][START_REF] Ramazan | The photochemical production of HONO during the heterogeneous hydrolysis of NO2[END_REF] One difficulty is the low gas phase concentration of NO 2 and its low water solubility (H between 9.9x10 -5 and 4x10 -4 molm -3 Pa -1 ), [START_REF] Sander | Compilation of Henry's law constants (version 4.0) for water as solvent[END_REF] making the participation of dimers doubtful. [START_REF] Colussi | Tropospheric aerosol as a reactive intermediate[END_REF] Two observations can be made here. First, we have recently reported the free-energy of adsorption of NO 2 at the interface (-1.6 kcal•mol -1 ), predicting an excess concentration by a factor of 10 with respect to gas phase. [START_REF] Martins-Costa | Theoretical Investigation of the Photoexcited NO2+H2O reaction at the Air-Water Interface and Its Atmospheric Implications[END_REF] And second, N 2 O 4 has a significant solubility in water (H=1.4x10 -2 molm -3 Pa -1 ), [START_REF] Sander | Compilation of Henry's law constants (version 4.0) for water as solvent[END_REF] both factors advocating in favor of the mechanism described above. [START_REF] Finlayson-Pitts | The heterogeneous hydrolysis of NO2 in laboratory systems and in outdoor and indoor atmospheres: An integrated mechanism[END_REF] Experiments on aqueous microjets have shown that (1) is dramatically accelerated by anions, [START_REF] Kinugawa | Conversion of gaseous nitrogen dioxide to nitrate and nitrite on aqueous surfactants[END_REF] and the catalytic effect has been ascribed to NO 2 uptake increase in their presence. [START_REF] Colussi | Tropospheric aerosol as a reactive intermediate[END_REF][START_REF] Colussi | Detecting intermediates and products of fast heterogeneous reactions on liquid surfaces via online mass spectrometry[END_REF] Clarifying HONO formation mechanisms is therefore a pressing issue for improving current atmospheric models, and the hydrolysis of NO 2 on the surface of liquid water is certainly one of the most important questions that remain to be addressed. To shed light on this topic, a number of theoretical studies in gas phase, [START_REF] Pimentel | The isomerization of dinitrogen tetroxide: O2N-NO2 -> ONO-NO2[END_REF][START_REF] Zhu | Ab Initio Chemical Kinetics for the Hydrolysis of N2O4 Isomers in the Gas Phase[END_REF] water clusters, [START_REF] Miller | Ionization of N2O4 in Contact with Water: Mechanism, Time Scales and Atmospheric Implications[END_REF][START_REF] De Jesus Medeiros | New Insights in the Atmospheric HONO Formation: New Pathways for N2O4 Isomerization and NO2 Dimerization in the Presence of Water[END_REF][START_REF] Luo | Ground-State Intermolecular Proton Transfer of N2O4 and H2O: An Important Source of Atmospheric Hydroxyl Radical?[END_REF][START_REF] Varner | Reaction of a charge-separated ONONO2 species with water in the formation of HONO: an MP2 Molecular Dynamics study[END_REF] or bulk water, [START_REF] Pimentel | The isomerization of dinitrogen tetroxide: O2N-NO2 -> ONO-NO2[END_REF] have been done using several methods. In general, these studies have confirmed the key role of (NO + )(NO 3 -) in the mechanism described above. Moreover, it has been shown that the non-ionized asymmetric species ONO-NO 2 , which has been experimentally detected [START_REF] Seifert | The gas-phase structure of the asymmetric, trans-dinitrogen tetroxide (N2O4), formed by dimerization of nitrogen dioxide (NO2), from rotational spectroscopy and ab initio quantum chemistry[END_REF] and computationally described in the gas phase, [START_REF] Liu | First-Principles Study of the Role of Interconversion Between NO2, N2O4, cis-ONO-NO2, and trans-ONO-NO2 in Chemical Processes[END_REF] is essentially unstable in water environments, spontaneously leading to (NO + )(NO 3 -). [START_REF] Miller | Ionization of N2O4 in Contact with Water: Mechanism, Time Scales and Atmospheric Implications[END_REF] The formation of the dimer is the bottleneck of the whole process. [START_REF] Putikam | A novel mechanism for the isomerization of N2O4 and its implication for the reaction with H2O and acid rain formation[END_REF] It may proceed by direct NO 2 dimerization, [START_REF] Zhu | Ab Initio Chemical Kinetics for the Hydrolysis of N2O4 Isomers in the Gas Phase[END_REF][START_REF] De Jesus Medeiros | New Insights in the Atmospheric HONO Formation: New Pathways for N2O4 Isomerization and NO2 Dimerization in the Presence of Water[END_REF] or by isomerization of the symmetric dimer N 2 O 4 through a roaming-like transition state. [START_REF] Putikam | A novel mechanism for the isomerization of N2O4 and its implication for the reaction with H2O and acid rain formation[END_REF] To the best of our knowledge, only two theoretical studies have considered the (NO + )(NO 3 -) species on a realistic air-water interface model: Hammerich et al [START_REF] Hammerich | NOx Reactions on Aqueous Surfaces with Gaseous HCl: Formation of a Potential Precursor to Atmospheric Cl Atoms[END_REF] in a study of the NO 2 +HCl reaction, and Li et al [START_REF] Li | Formation of HONO from the NH3promoted hydrolysis of NO2 dimers in the atmosphere[END_REF] in a study of the NH 3 -promoted hydrolysis reaction. In these works, ab initio molecular dynamics (MD) simulations (DFT level) were carried out on a water slab with periodic boundary conditions. However, owing to a high computational cost, the simulations were relatively short (~20 ps), and this time scale may not be sufficient to understand all the complex dynamic behavior of the liquid water-vapor interface. [START_REF] Ruiz-Lopez | Molecular reactions at aqueous interfaces[END_REF] Hereafter, we report important new findings about the aqueous chemistry of NO 2 by carrying out QM/MM MD simulations approaching the nanosecond time scale (QM/MM stands for combined Quantum Mechanics and Molecular Mechanics potentials). The theoretical model has successfully been used to study other atmospheric OH sources, [START_REF] Zhong | Atmospheric Spectroscopy and Photochemistry at Environmental Water Interfaces[END_REF][START_REF] Anglada | Photoinduced Oxidation Reactions at the Air-Water Interface[END_REF] and it is detailed in the Supporting Information (SI). Specifically, we describe the reactive NO 2 asymmetric dimer at the quantum mechanical level (DFT) at the surface of a liquid water slab at 298K. The slab contains 499 flexible water molecules described classically; we assume periodic boundary conditions in the XY directions (Z is the axis perpendicular to the interface). During equilibration, the NO 2 dimer is forced to stay at the interface by constraining its Z-position. After equilibration, the Z-constraint is released, and the simulation is run for 300 ps. Since the dimer migrates to the bulk (see below), additional 300 ps are run after reequilibration assuming periodic boundary conditions in the XYZ directions.

The equilibration process at the interface is started with the covalent symmetric dimer ONO-NO 2 . However, the later spontaneously reorganizes into (NO + )(NO 3 -) at femtosecond time scale, and therefore it is this ionpair that is actually equilibrated and simulated. A similar fast reorganization process has been observed in small water clusters through ab initio MD simulations. [START_REF] Miller | Ionization of N2O4 in Contact with Water: Mechanism, Time Scales and Atmospheric Implications[END_REF] When the Z-constraint is released after equilibration (Figure 2), the ion-pair initially stays at the interface for a few tens of picoseconds, deeply solvated in the inner water layer, but after 100 ps, the system migrates to bulk. The trend of (NO + )(NO 3 -) to spread into the bulk may be explained by extensive long-range electrostatic interactions with the solvent (due to a large charge separation in the solute, 0.63e on average) but also to the presence of strong hydrogen-bonds in the NO 3 -moiety (Figure S2 in the SI). The short residence time predicted for the reactive ion-pair at the interface (100 ps) has important consequences for the interfacial NO 2 aqueous chemistry, as we discuss now.

To this purpose, it is pertinent to calculate the lifetime of (NO + )(NO 3 -) in respect to its reaction with water. In principle, reaction lifetimes can directly be obtained from ab initio simulations, but the computational cost becomes prohibitive for large activation barriers (>>k B T). Here, we obtain the reaction lifetime  indirectly, using accurate thermodynamic data for the process to calculate the kinetic constant k, so that =k -1 .

The energetics for the process:

(NO + )(NO 3 - )(H 2 O) n  (HONO)(HNO 3 )(H 2 O) n-1 (3
) has been studied in several works [START_REF] Zhu | Ab Initio Chemical Kinetics for the Hydrolysis of N2O4 Isomers in the Gas Phase[END_REF][START_REF] Luo | Ground-State Intermolecular Proton Transfer of N2O4 and H2O: An Important Source of Atmospheric Hydroxyl Radical?[END_REF][START_REF] Varner | Reaction of a charge-separated ONONO2 species with water in the formation of HONO: an MP2 Molecular Dynamics study[END_REF][START_REF] Putikam | A novel mechanism for the isomerization of N2O4 and its implication for the reaction with H2O and acid rain formation[END_REF] but accurate activation free-energies are not available. Li et al [START_REF] Li | Formation of HONO from the NH3promoted hydrolysis of NO2 dimers in the atmosphere[END_REF] have reported values at DFT level lying between 5.6 and 8.2 kcal•mol -1 , depending on cluster model. With the aim of determining more accurate kinetic data, we have carried out CCSD(T)/6-311+(3df,2p)//B3LYP/6-311+G(3df,2p) calculations for a cluster with two explicit water molecules immersed in a medium of variable dielectric constant. The contribution from tunneling effects has been calculated as well. The computational details and results are provided in the SI. When the system is in vacuum (=1), the obtained barrier is 8.6 kcal•mol -1 , and the pseudo-first order kinetic constant is k=3.4x10 6 s -1 (~300 ns). In bulk solution (=78), the barrier lowers to 6.1 kcal•mol -1 , and k=2.4x10 8 s -1 (~4 ns). At the interface, the kinetics is probably intermediate; one can estimate it using the dielectric constant of a low-polar sol-vent (=3). [START_REF] Wang | Generalized interface polarity scale based on second harmonic spectroscopy[END_REF][START_REF] Wang | Polarity of liquid interfaces by second harmonic generation spectroscopy[END_REF][START_REF] Zimdars | Static and dynamic solvation at the air/water interface[END_REF][START_REF] Martins-Costa | Solvation effects on electronic polarization and reactivity indices at the air-water interface: insights from a theoretical study of cyanophenols[END_REF] One gets 7.1 kcal•mol -1 , and k=5.2x10 7 s - 1 (~20 ns). From these values, it is found that the dimer lifetime is much larger than the (very short) interfacial residence lifetime, and accordingly, hydrolysis is more likely to occur in bulk. Only when a catalyst such as NH 3 is present, [START_REF] Li | Formation of HONO from the NH3promoted hydrolysis of NO2 dimers in the atmosphere[END_REF] the free energy barrier is significantly lowered (between 0.5 and 3.4 kcal mol -1 , depending on model), and the corresponding half lifetimes (0.4-50 ps) becomes closer to the residence lifetime of the reactive species at the interface. Simulations at the interface and in bulk also show that the contact ion-pair (NO + )(NO 3 -) is quite stable. The two ions remain in direct contact with one short N•••O distance fluctuating around 1.98 Å, and no ion dissociation, formation of solvent-separated ion pair structures, or dissociation into NO 2 monomers is observed. Nevertheless, despite a high stability, the dimer displays a huge internal mobility of the charged moieties, with fast dynamical exchange between cis-and trans-configurations, and frequent jumps of the (NO + ) cation to adjacent oxygen atoms in the anionic (NO 3 -) moiety. The mechanism for these jumps is illustrated in Figure 3. They occur mainly between O atoms that are pointing towards the (NO + ) direction (O2 and O5 in Figure 3). Jumps to the third oxygen atom (O6 in Figure 3) are much less frequent (it has been observed only once in our simulation). From probability histograms (see Figure S3 in the SI), we estimate the free energy barriers for these processes to 3.2 kcal•mol -1 (cis-trans conformational change) and 0.8 kcal•mol -1 (jump to an adjacent Oatom). For comparison, in the gas phase, the corresponding values are 2.8 and 5.1 kcal•mol -1 for the non-ionized form of the asymmetric dimer, [START_REF] Liu | First-Principles Study of the Role of Interconversion Between NO2, N2O4, cis-ONO-NO2, and trans-ONO-NO2 in Chemical Processes[END_REF] showing that the solvation effect on the O-exchange is quite large, as expected (though part of the effects has to be ascribed to the use of different quantum mechanical methods). The trans conformation is predicted to be more stable than the cis one by approximately 0.9 kcal mol -1 in bulk solution. In summary, the new data reported here help progress further understanding of the aqueous chemistry of NO 2 . Dimerization to form a reactive ion-pair is the first-step and bottleneck in the hydrolysis process; [START_REF] Putikam | A novel mechanism for the isomerization of N2O4 and its implication for the reaction with H2O and acid rain formation[END_REF] owing to significant interface affinity of NO 2 , 10 dimerization is likely to occur at the surface of water microdroplets. Reaction of the ion-pair with water is the subsequent step. Despite it is a fast reaction (k~10 7 -10 8 s -1 ), we have shown that the residence time of the ion-pair at the airwater interface (100 ps) is too short for the reaction to occur there. This result contrasts with the surface-enhanced processes reported for different solid surfaces, where HONO escapes to the gas phase and thus contributes to the atmospheric budget of OH through photolysis in daylight hours. On the contrary, in the droplet scenario, HONO appears to form preferably in the bulk rather than on the surface, therefore having little chance of escaping into the gas phase. The chemistry of HONO in bulk water encompasses a complex set of coupled reactions, including acid dissociation (pK a =3.16), [START_REF] Da Silva | Ab initio procedure for aqueous-phase pKa calculation: the acidity of nitrous acid[END_REF] disproportionation, and photolysis, which yield nitric oxide and nitrate as main final products. Process (1) also yields the strong acid HNO 3 , which in aqueous solution dissociates to nitrate (pK a = -1.38) and contributes to acidify the medium, contrasting again with hydrolysis in thin films on solid surfaces. In the latter case, nitric acid is at least partially undissociated [START_REF] Ramazan | New experimental and theoretical approach to the heterogeneous hydrolysis of NO2: key role of molecular nitric acid and its complexes[END_REF] and produces OH radicals by direct photolysis in daytime (ref [START_REF] Anglada | Photoinduced Oxidation Reactions at the Air-Water Interface[END_REF] and references cited therein). In future theoretical studies, modeling the chemistry of the ion-pair on water films as a function of the film thickness and the nature of the support will be most valuable and we are currently working in this direction.

Nonetheless, aerosols and water droplets are not pure water environments but contain species that may play a catalytic role on NO 2 hydrolysis in nighttime. Some interfacial catalytic mechanisms have been described, with electrolytes [START_REF] Colussi | Tropospheric aerosol as a reactive intermediate[END_REF] or ammonia [START_REF] Li | Formation of HONO from the NH3promoted hydrolysis of NO2 dimers in the atmosphere[END_REF] as catalysts, but other organic or inorganic compounds can be envisaged and future work needs to consider this possibility. This catalytic chemistry in nighttime together with photoenhanced reactions in daytime [START_REF] George | Photoenhanced uptake of gaseous NO2 on solid organic compounds: a photochemical source of HONO? Faraday Discuss[END_REF][START_REF] Liu | Photoenhanced Uptake of NO2 and HONO Formation on Real Urban Grime[END_REF][START_REF] Wall | Uptake of nitrogen dioxide (NO2) on acidic aqueous humic acid (HA) solutions as a missing daytime nitrous acid (HONO) surface source[END_REF] are plausible sources contributing to the yet unexplained excess concentrations of HONO found in the troposphere.

ASSOCIATED CONTENT Supporting Information

Details on computational methods and Figures S1-S3 are provided as Supporting Information. The Supporting Information is available free of charge on the ACS Publications website.

Figure 1 .

 1 Figure 1. Schematic NO 2 hydrolysis reaction on a surface and different structures of NO 2 dimers.

Figure 2 .

 2 Figure 2. Center of mass position of (NO + )(NO 3 -) along the QM/MM MD simulation at the air-water interface. The horizontal dashed line represents the Gibbs dividing surface. The thickness considered for the interface (yellow background) is based on the water density profile shown in Figure S1 in the SI.

Figure 3 .

 3 Figure 3. QM/MM MD simulation of (NO + )(NO 3 -) at the air-water interface. The bottom panel illustrates the jumps of the NO + moiety between the O2 and O5 atoms of the NO 3 -moiety along the first 20 ps of the simulation. The upper panel shows three snapshots for the first jump. The central snapshot corresponds roughly to the transition structure for which N3O2 and N3O5 distances are equal. The left and right snapshots correspond to -600 fs and +600 fs with respect to the middle snapshot, respectively.

ACKNOWLEDGMENT

MMC and MFRL are grateful to the French CINES (project lct2550) for providing computational resources. JMA thanks the Catalan CSUC for providing computational resources.

Funding Sources

This project has been supported by the Generalitat de Catalunya (Grant No. 2017SGR348) and Spanish Ministerio de Economía y Competitividad (Project No. PID2019-109518GB-I00).

AUTHOR INFORMATION

Corresponding Author frjoseph@sas.upenn.edu (JSF) manuel.ruiz@univ-lorraine.fr (MFRL)


Gabriel A B Marais

Bérénice Batut

Vincent Daubin

Genome Evolution: Mutation is the Main Driver of Genome Size in Prokaryotes

Despite intense research on genome architecture since the 2000's, genome-size evolution in prokaryotes has remained puzzling. Using a phylogenetic approach, a new study found that increased mutation rate is associated with gene loss and reduced genome size in prokaryotes.

 and later in 2007 in his book "The Origins of Genome Architecture" [2], Lynch developed his influential theory that a genome's complexity, represented by its size, is primarily the result of genetic drift. More genetic drift would result in larger genomes. This view relies on population genetic models as well as (AU:OK?) an analysis comparing prokaryotes and eukaryotes. On one side, prokaryotes undergo little genetic drift as they typically have large effective population sizes (Ne) and small genomes. On the other side of

the spectrum, multicellular eukaryotes have large genomes. Because of their small Ne and a large amount of drift, selection is inefficient in purging the genome of genomic parasites, such as transposable elements, and slightly deleterious indel mutations such as gene duplications.

As a consequence, their genome sizes increase. Unicellular eukaryotes are found in between.

Immediately after these publications, it was pointed out that the theory of 'mutational hazard,' as it is now referred to, does not sufficiently explain (AU:OK?) the diversity of genome size within Bacteria and Archaea (for example, see [START_REF] Daubin | Comment on" The origins of genome complexity[END_REF]). In particular, bacterial endosymbionts such as Buchnera aphidicola living in aphids have very small Ne (similar to that of their obligatory hosts) and are among the smallest known bacterial genomes. In 2009, Kuo et al. [START_REF] Kuo | The consequences of genetic drift for bacterial genome complexity[END_REF] showed that the relationship between genome size and Ne is the reverse in bacteria: that is, bacteria with small Ne have small genomes. Bacterial genomes, even large ones, usually contain very few transposable elements, and genome size is mainly driven by gene content. In small Ne bacteria such as Buchnera, the selective pressure to keep genes is low. Many nonessential genes become non-functional and are deleted, resulting in organisms with few genes and thus small genomes. However, Kuo et al.'s study did not include the mysterious marine bacteria Prochlorococcus. In the early 2000's, marine biologists discovered that Prochlorococcus, one the most abundant free-living bacteria on earth, has a reduced genome compared to its relative, Synechococcus (for example [START_REF] Dufresne | Accelerated evolution associated with genome reduction in a free-living prokaryote[END_REF][START_REF] Partensky | Prochlorococcus: advantages and limits of minimalism[END_REF]). Given its abundance, genome reduction in Prochlorococcus cannot be explained by a small Ne. A number of hypotheses have been proposed to fit Prochlorococcus into the general picture [START_REF] Batut | Reductive genome evolution at both ends of the bacterial population size spectrum[END_REF], including an adaptation to a marine environment deficient in nitrogen and phosphorus (the genome streamlining hypothesis) or an increase in mutation rates. Interestingly, Prochlorococcus genomes lack key DNA-repair genes, and increased mutation rates can result in gene loss (AU:OK?) under weak selection [START_REF] Marais | Mutation rate and genome reduction in endosymbiotic and free-living bacteria[END_REF]. These hypotheses, however, have remained untested, and our understanding of the evolution of genome size in bacteria still has to deal with a number of inconsistencies [START_REF] Batut | Reductive genome evolution at both ends of the bacterial population size spectrum[END_REF]. In this issue of Current Biology, Bourguignon et al. [START_REF] Bourguignon | Increased mutation rate is linked to genome reduction in prokaryotes[END_REF] provide for the first time strong evidence that the main driver of genome size in bacteria is mutation rate, both in free-living bacteria and in bacterial endosymbionts [START_REF] Bourguignon | Increased mutation rate is linked to genome reduction in prokaryotes[END_REF]. This study is a first step towards a new theory for explaining genome size in prokaryotes.

To disentangle the effects of Ne and mutation rates, Bourguignon et al. have updated a classical approach using the rate of nonsynonymous substitutions (dN) and the rate of synonymous substitutions (dS) in a set of conserved genes. dN is affected by mutation rates and the intensity of selection (which depends on Ne). In contrast, dS is affected mainly by mutation rates (neglecting selection on synonymous codon usage. Looking at dN and dS together provides information about(AU:OK?) mutation rates, whereas looking at the classical dN/dS ratio provides insights into selection and Ne. This approach has been used in the past (for example by [START_REF] Kuo | The consequences of genetic drift for bacterial genome complexity[END_REF]) but very distant species were compared, which can be misleading. Here, Bourguignon et al. [START_REF] Bourguignon | Increased mutation rate is linked to genome reduction in prokaryotes[END_REF] have sequenced new genomes and collected some from public databases to assemble a very large dataset comprising nine bacterial and archaeal lineages, with seven being free-living, including the marine cyanobacteria Prochlorococcus and Synechococcus. The authors analyzed each lineage separately and compared close relatives with varying genome size, an analysis never done before. In this paper, they restricted their analysis to sets of genes shared by all species of a lineage undergoing supposedly similar selection, thus making dN/dS a good proxy for Ne. In addition, using a model for gene content evolution, they could infer gene loss and gain for each branch of the phylogenetic trees. For the marine cyanobacteria, they used the alignment of 31 core genes to estimate dS and dN along the branches. Dividing the estimates by branch length, they obtained gene loss, dS, and (AU: is this what you mean? Each parameter measured per unit time?) dN per unit of time and found out that gene loss is correlated with dS (strongly) and dN (moderately), but is not correlated with dN/dS. Their result obtained on a small number of genes is however robust to a number of potential biases: phylogenetic inertia (AU:OK?)(as this can lead to spurious correlations), G+C content (which can affect dS and dN estimates), codon bias (as selection on codon bias decreases dS), and moreover, they used residuals from linear regression instead of ratio (as this can affect the output of statistical tests). Genome reduction in Prochlorococcus is then predominantly driven by an increased mutation rate.

But is this effect specific to a lineage of photosynthetic bacteria that has to cope with a deprived and mutagenic environment? Apparently not. In the other six free-living lineages, similar results are found in four of them, Thermococcus, Corynobacterium, Micrococcineae, Flavobactericeae, which represent very contrasting lifestyles and ecology. In the remaining two lineages (Gammaproteobacteria, Mycobacteria+Nocardiaceae), the results were different. They either found no correlation at all (Gammaproteobacteria) or a correlation between gene loss and dN/dS (Mycobacteria+Nocardiaceae), suggesting that in the latter (AU:OK?) lineage Ne does matter with respect to genome size. Hence, the association between mutation rates and genome size clearly applies to free-living prokaryotes, albeit not universally. And what about endosymbionts? Could mutation rate also play a role in genome reduction? The study included two endosymbiont lineages: Blattabacterium and the iconic Buchnera. To estimate the gene content evolution they used a different model with gene loss only-as gene gain by horizontal transfer is extremely rare in intracellular endosymbiont bacteria-and inferred gene loss along the branch of the trees. (AU: preceding sentence restructuring ok? Did I understand your intent correctly?) From a set of 353 core genes, they also estimated dS and dN using the same methods as explained before and obtained per unit of time estimates of gene loss, dS and dN. They found that gene loss is strongly correlated with dS, moderately with dN, and very weakly with dN/dS. In most of the controls they used (AU:OK?) the correlation between gene loss and mutation rate (dS and dN) remained, whereas the correlation between gene loss and Ne (dN/dS) disappeared.

These findings suggest that mutation rate plays a central role in the evolution of genome size in prokaryotes, both in free-living bacteria and endosymbionts. This represents (AU:OK?) a substantial change in our view on how genome size evolves in prokaryotes in general and in endosymbionts in particular. It is well known that mutation rates are determined by the presence of DNA-repair genes. Now, the data on DNA-repair genes that Bourguignon et al.

obtained (along with others from the literature; for example, [START_REF] Acosta | genome-size evolution in prokaryotes has remained puzzling. Using a phylogenetic approach, a new study found that increased mutation rate is associated with gene loss and reduced genome size in prokaryotes[END_REF]) (AU:OK?) clearly indicate that genome size and the number of DNA repair genes are correlated. As DNA-repair genes are lost, mutation increases and counteracts relatively weak selection for gene function (AU:OK?), resulting in gene loss and genome reduction in prokaryotes [START_REF] Marais | Mutation rate and genome reduction in endosymbiotic and free-living bacteria[END_REF]. Why DNA-repair genes are lost in the first place remains to be explained and may correspond to different situations. For instance, a large body of work has shown that mutator strains (with increased mutation rates) can adapt faster than wild-type strains in a changing environment, simply because advantageous mutations arise faster in the former [START_REF] Batut | Reductive genome evolution at both ends of the bacterial population size spectrum[END_REF][START_REF] Marais | Mutation rate and genome reduction in endosymbiotic and free-living bacteria[END_REF]. In this scenario, mutation rate is the main target of selection and genome reduction is just a side effect. In general though, the initial mutation rate can be restored by recombination or gene transfer once an adaptive solution to the environment has been found. In endosymbionts however, the genetic material for restoring a functional repair machinery may not be available because the symbiont does not come into contact with other bacteria, hence initiating an irreversible decay of the genome. It is also possible that a streamlined genome is beneficial in some environments, such as nitrogen-and phosphorus-poor tropical waters [START_REF] Dufresne | Accelerated evolution associated with genome reduction in a free-living prokaryote[END_REF][START_REF] Partensky | Prochlorococcus: advantages and limits of minimalism[END_REF]. In this case, genome size could be the main target, and the loss of DNA-repair genes is just a means to an end. Losing DNArepair genes could also be due to drift, especially at the initial stages of endosymbiosis, but the general lack of correlation between gene loss and Ne does not support this as a general explanation. More work is needed to test the mutator versus genome streamlining hypotheses and the consequences for genome evolution in Bacteria and Archaea (AU:OK?). However, this study is certainly a major step towards the development of a comprehensive theory of prokaryote genome-size evolution.


Andrey Tverjanovich

Maxim Khomenko

Sergei Bereznev

Daniele Fontanari

Anton Sokolov

Takeshi Usuki

Koji Ohara

David Le Coq

Pascal Masselin

Eugène Bychkov
email: bychkov@univ-littoral.fr

Eugene Bychkov

Glassy GaS: transparent and unusually rigid thin films for visible to mid-IR memory applications

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Phase-change materials (PCMs) based on tellurides (GeTe-Sb2Te3, metal-doped Sb2Te, etc.) are widely used for optical storage (DVD and Blu-ray disks), non-volatile random access memories and for development of bioinspired computing systems. [START_REF] Ovshinsky | Reversible electrical switching phenomena in disordered structures[END_REF][START_REF] Yamada | Rapid-phase transitions of GeTe-Sb2Te3 pseudobinary amorphous thin films for an optical disk memory[END_REF][START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF][START_REF] Ríos | Integrated all-photonic non-volatile multi-level memory[END_REF][START_REF] Zhang | Designing crystallization in phase-change materials for universal memory and neuro-inspired computing[END_REF] High optical absorption of the narrow-gap tellurides below λ = 2 µm intrinsically limits their applications in the telecom spectral range, where wider gap materials are needed. Recent studies of Sb2S3 and related sulfides have shown a growing interest toward visible to mid-IR optical memory applications. [START_REF] Dong | Wide bandgap phase change material tuned visible photonics[END_REF]7 Gallium sulfides, GaS and Ga2S3, are promising materials in this field because a glass-crystal phase transition might be accompanied by a drastic change in nonlinear optical (NLO) properties, opening up a new dimension in the PCM photonics.

Gallium sesquisulfide Ga2S3 in bulk chalcogenide glasses promotes dissolution of rare earth ions in the glass matrix [START_REF] Barnier | Etude de verres de chalcogénures contenant de l'europium divalent système EuS-Ga2S3-GeS2[END_REF][START_REF] Yu | Rare-earth doped chalcogenide glasses[END_REF] allowing further development of optically active materials (bulk, planar and fibers). [START_REF] Seddon | Progress in rare earth-doped midinfrared fiber lasers[END_REF][START_REF] Heo | Rare-earth-doped chalcogenide glass for lasers and amplifiers[END_REF] Monoclinic and cubic Ga2S3 also exhibit excellent laser-induced damage threshold, 174 and 590 MW cm -2 at 1064 nm, respectively, vs. 5.58 MW cm -2 in tetragonal AgGaS2; [START_REF] Zhang | Two phases of Ga2S3: promising infrared secondorder nonlinear optical materials with very high laser induced damage thresholds[END_REF] the silver thiogallate is a commercially available NLO crystal served as a light conversion reference in the mid-IR spectral range. Simultaneously, monoclinic Ga2S3 shows a strong phase-matchable second harmonic generation (SHG). [START_REF] Zhang | Two phases of Ga2S3: promising infrared secondorder nonlinear optical materials with very high laser induced damage thresholds[END_REF] Hexagonal β-GaS has centrosymmetric structure, space group 𝑃6 3 /𝑚𝑚𝑚, [START_REF] Kuhn | Charge-density analysis of GaS[END_REF] and cannot possess the second order NLO properties. Nevertheless, native GaS crystals reveal the existence of non-centrosymmetric rhombohedral GaS domains and exhibit rather intense SHG. Pure rhombohedral GaS, space group 𝑅3 � 𝑚, [START_REF] Pardo | Sur une nouvelle forme de GaS, rhomboédrique 3R métastable: Formation et étude structurale[END_REF] shows a strong second order response. [START_REF] Allakhverdiev | Second-harmonic generation in GaS crystals[END_REF] In contrast, gallium sulfide bulk glasses exhibit a large and ultrafast thirdorder nonlinear susceptibility [START_REF] Wang | Large and ultrafast third-order optical nonlinearity of GeS2-Ga2S3-CdS chalcogenide glass[END_REF][START_REF] Dong | Study on the third and second-order nonlinear optical properties of GeS2-Ga2S3-AgCl chalcohalide glasses[END_REF] suggesting a dramatic crossover in NLO properties on crystallization.

Both GaS and Ga2S3 are extensively studied in bulk and thin film forms. [START_REF] Micocci | Conductivity and optical absorption in amorphous gallium sulphide thin films[END_REF][START_REF] Suh | Chemical vapor deposition of gallium sulfide thin films[END_REF][START_REF] Mejía | Gallium-containing conducting metallopolymers which display chemically tunable reactivity for the growth of Ga2S3 semiconducting nanoparticles[END_REF][START_REF] Kato | Sellmeier equations for GaS and GaSe and their applications to the nonlinear optics in GaSxSe1-x[END_REF][START_REF] Huang | Ga2S3: Optical properties and perspectives for THz applications[END_REF][START_REF] Popescu | Amorphous thin films in the gallium-chalcogen system[END_REF][START_REF] Wang | Chemical vapor deposition growth of two-dimensional monolayer gallium sulfide crystals using hydrogen reduction of Ga2S3[END_REF][START_REF] Kim | Simultaneous growth of Ga2S3 and GaS thin films using physical vapor deposition with GaS powder as a single precursor[END_REF] Nevertheless, the structure, composition and properties of amorphous gallium sulfide thin films are far from a full understanding and often contradictory. For example, the band gap of amorphous GaS obtained by thermal evaporation was found to be 𝐸 g ≈ 1.1 eV, [START_REF] Micocci | Conductivity and optical absorption in amorphous gallium sulphide thin films[END_REF] while crystalline GaS shows 𝐸 g = 2.50 eV at room temperature. [START_REF] Brebner | The optical absorption range of GaS[END_REF] X-ray diffraction and EXAFS results at the Ga K-edge for amorphous Ga2S3 thin films were reported to reveal trigonal gallium and two-fold sulfur local coordination. [START_REF] Popescu | Amorphous thin films in the gallium-chalcogen system[END_REF] In contrast, crystalline gallium sulfides and gallium in bulk Ga2S3-GeS2 sulfide glasses exhibit tetrahedral Ga environment. [START_REF] Kuhn | Charge-density analysis of GaS[END_REF][START_REF] Pardo | Sur une nouvelle forme de GaS, rhomboédrique 3R métastable: Formation et étude structurale[END_REF][START_REF] Tomas | Détermination des structures des formes α et β de Ga2S3[END_REF][START_REF] Jones | Refinement of the crystal structure of digallium trisulfide, Ga2S3[END_REF][START_REF] Hindle | Structural analysis of 𝑥CsCl(1-𝑥)Ga2S3 glasses[END_REF][START_REF] Pethes | Local motifs in GeS2-Ga2S3 glasses[END_REF] Often, the chemical composition of gallium sulfide thin films depends on deposition technique and technical details, [START_REF] Kim | Simultaneous growth of Ga2S3 and GaS thin films using physical vapor deposition with GaS powder as a single precursor[END_REF] leaving room for uncertainty in the relationships between nominal composition, suggested structure and observed properties.

The main objective of the present study was (i) to obtain high-quality gallium sulfide thin films using pulsed laser deposition and verify their chemical composition, (ii) to study the optical properties including fundamental absorption edge, refractive index and laser-induced damage threshold, and (iii) to elucidate their atomic structure using Raman and high-energy X-ray diffraction measurements supported by first-principles molecular dynamics simulations. A deep insight into molecular architecture of vitreous gallium sulfide layers in relation with their macroscopic characteristics will be crucial in the assessment of the required potential for memory applications over visible to mid-IR spectral ranges.

A c c e p t e d M a n u s c r i p t 2 Experimental and simulation details

Material preparation

Gallium sesquisulfide Ga2S3 powder was synthesized from pure gallium (99.999 %, Alfa Aesar) and sulfur (99.999 %, Sterm) by mechanical milling. The two elements were placed in stoichiometric proportion (the total mass of 8 g) into a tungsten carbide WC vessel (the internal volume of 45 mL) with 10 WC balls (10 mm in diameter) meaning a mass ratio balls/powder was 10:1. The mechanochemical processing was operated in a planetary ball mill (Fritsch, Pulverisette 7) for 4 h at a rotation speed of 400 rpm in dry N2 atmosphere. The amorphous powder was collected, and the target (16 mm in diameter and 4 mm in thickness) was prepared by spark plasma sintering process at 700 K and 50 MPa for 5 min.

Pulsed laser deposition (PLD) of gallium sulfide films was performed by Neocera Pioneer 120 PLD system equipped with 248 nm KrF excimer laser (Coherent Compex Pro 102 F) under high vacuum. The target to substrate distance was 9 cm. The conditions of the deposition were as follows: 40,000 laser pulses, 200 mJ pulse energy, 10 Hz repetition rate. The laser beam was focused on ~5 mm 2 spot on the surface of the target. The substrate and target were rotated during the deposition process for uniform distribution of the ablated materials onto the substrate of ambient temperature. Before PLD, soda lime glass substrates, 5 cm in diameter, were ultrasonically cleaned for 15 min in 20 % solution of Decon 90 and deionized water at 323 K, respectively, dried under filtered air flow and then exposed to Nova Scan Digital UV-Ozone cleaning system for 15 min.

Thin film characterization, optical and Raman spectroscopy measurements

Gallium sulfide PLD layer morphology and chemical composition were characterized by scanning electron microscopy using a Zeiss EVO 40EB instrument equipped with EDX microanalysis system Oxford Instrument INCA 350. A Shimadzu UV-3600 spectrophotometer was used for optical absorption spectra measurements in the wavelength range of 300-2400 nm. Raman spectra were measured at room temperature in backscattering geometry using a Senterra Raman spectrometer (Bruker) equipped with a microscope. The spectra were excited by a 785 nm laser with power 10 mW and recorded in the 75-1500 cm -1 spectral range (reliable data are above 100 cm -1 ). The spectrometer resolution was 3 cm -1 . Additionally, some samples were measured using a LabRam HR microRaman spectrometer (Jobin Yvon Horiba Group). Raman scattering was excited by a 785 nm solid-state laser and recorded in the 50-850 cm -1 spectral range. The laser power was 1.5 mW in the majority of measurements, and the acquisition time was 100 to 300 s. Two to three spectra were registered for each sample at different positions to verify the sample homogeneity and the absence of photo-induced phenomena.

A femtosecond laser Mira Optima 900-D (Coherent) with acousto-optic modulator Pulse Switch in cavity dumping operation mode was used to study a laser-induced high-power density damage threshold at 790 nm. The pulse frequency was 272 kHz, and the pulse duration was 100 fs. The beam energy on the samples was about 10 nJ. A gallium sulfide layer sensitivity to UV irradiation was studied using a 250 W mercury lamp.

A c c e p t e d M a n u s c r i p t

Diffraction measurements

Tiny pieces of gallium sulfide thin film material were placed into thin-walled silica capillary for high-energy X-ray diffraction measurements, Figure S1 in Electronic Supplementary Information (ESI). A dedicated two-axis diffractometer at the BL04B2 beamline of the SPring-8 facility (Hyogo Prefecture, Japan) equipped with four CdTe detectors at low angles and three Ge diodes at high diffraction angles [START_REF] Ohara | Accurate synchrotron hard Xray diffraction measurements on high-temperature liquid oxides[END_REF] was used for these measurements. The 7-detector setup allows the diffraction pattern to be collected up to 𝑄 = 30 Å -1 with high signal-to noise ratio and sufficient energy resolution to discriminate both fluorescence from the sample and higher harmonics reflections from the monochromator crystal. The empty silica tube was also measured and used for background intensity subtraction. Further data analysis included absorption, Compton scattering, and polarization corrections using standard procedures [START_REF] Kohara | Structural studies of disordered materials using high-energy X-ray diffraction from ambient to extreme conditions[END_REF] giving the total X-ray structure factor 𝑆 X (𝑄).

First-principles simulations

Modeling of the high-energy X-ray diffraction data was carried out using the Born-Oppenheimer molecular dynamics with the CP2K package. [START_REF] Hutter | CP2K: Atomistic simulations of condensed matter systems[END_REF] The generalized gradient approximation and the PBEsol [START_REF] Perdew | Generalized gradient approximation made simple[END_REF][START_REF] Perdew | Restoring the density-gradient expansion for exchange in solids and surfaces[END_REF] or PBE0 hybrid [START_REF] Perdew | Rationale for mixing exact exchange with density functional approximations[END_REF][START_REF] Adamo | Toward reliable density functional methods without adjustable parameters: the PBE0 model[END_REF] exchange-correlation functionals have been used. The applied first-principle molecular dynamics (FPMD) technique was similar to that used previously. [START_REF] Akola | Experimentally constrained density-functional calculations of the amorphous structure of the prototypical phase-change material Ge2Sb2Te5[END_REF][START_REF] Matsunaga | From local structure to nanosecond recrystallization dynamics in AgInSbTe phase-change materials[END_REF] The initial atomic configurations for glassy gallium sulfide were created and optimized using the RMC_POT++ code [START_REF] Gereben | A new version of the RMC++ Reverse Monte Carlo programme, aimed at investigating the structure of covalent glasses[END_REF][START_REF] Gereben | RMC_POT, a computer code for Reverse Monte Carlo modeling the structure of disordered systems containing molecules of arbitrary complexity[END_REF] against the derived X-ray structure factor 𝑆 X (𝑄) in order to obtain a good agreement with experimental data. The size of the cubic simulation box at room temperature, containing 200 atoms (100 Ga and 100 S), was chosen to match the experimental number density. Further optimization has been carried using density functional theory (DFT), applying the molecularly optimized correlation consistent polarized triple-zeta valence basis set TZVP [START_REF] Vandevondele | Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases[END_REF][START_REF] Weigend | Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy[END_REF] along with the norm-conserving relativistic Goedecker-Teter-Hutter type pseudo-potentials. [START_REF] Goedecker | Separable dual-space Gaussian pseudopotentials[END_REF][START_REF] Hartwigsen | Relativistic separable dual-space Gaussian pseudopotentials from H to Rn[END_REF] The FPMD simulations were started at 300 K. In order to deal with a canonical NVT ensemble, a Nosé-Hoover 46,47 chain of length 3 has been employed as a thermostat. The PBEsol or PBE0 systems were heated up to 700-1300 K using 100 K steps for 10 to 30 ps each. At 700, 800 or 1300 K, the systems were equilibrated for 20-35 ps and cooled down to 300 K using the same temperature steps and similar simulation time. Final equilibration and data collection at 300 K was done for 25-45 ps. The connectivity and ring statistics were analyzed using the R.I.N.G.S. [START_REF] Roux | Ring statistics analysis of topological networks: New approach and application to amorphous GeS2 and SiO2 systems[END_REF] and modified connectivity [START_REF] Kohara | Lead silicate glasses: Binary network-former glasses with large amounts of free volume[END_REF] codes. For analysis of voids and cavities, the pyMolDyn [START_REF] Heimbach | pyMolDyn: Identification, structure, and properties of cavities/vacancies in condensed matter and molecules[END_REF] program was used.

Results and discussion

Chemical composition, Raman spectra and optical properties

The pulsed laser deposition yields transparent, uniform and vitreous gallium sulfide layers, Unexpected result was given by EDX chemical analysis. The film composition was found to be Ga53 ±2 S47 ±2 , that is, close to stoichiometric monosulfide GaS instead of Ga2S3. The Raman spectra of gallium sulfide PLD films are consistent with that conclusion. Figure 2 summarizes the measured Raman spectra of GaS PLD layer, semi-crystalline MM-Ga2S3 and MM-GaS2, obtained by mechanical milling (MM) and plotted together with crystalline references: hexagonal β-GaS, 51 monoclinic α-Ga2S3, and (c) plastic sulfur. We note that the most intense vibrational feature of vitreous PLD film at 183 cm -1 is similar to the 𝐴 1g symmetric in-phase Ga-Ga stretching mode in β-GaS, 189 cm -1 . [START_REF] Taylor | Raman and infrared spectra and vibrational assignments of gallium (II) sulphide[END_REF][START_REF] Van Der Ziel | Raman scattering from β-GaS[END_REF] The 183 cm -1 peak position is markedly lower than the 𝐴' in-phase Ga-S breathing of GaS4 tetrahedra of 𝐶 s symmetry in α-Ga2S3 at 233 cm -1 . [START_REF] Lucazeau | Etude vibrationnelle de α Ga2S3[END_REF] In contrast, the most intense vibrational feature of semi-crystalline MM-Ga2S3 is perfectly consistent with the 𝐴' mode, Fig. 2(b). High-frequency Ga-S stretching modes in β-GaS, 290 ≤ 𝜔 ≤ 360 cm -1 , are also very similar to broad unresolved peaks in glassy GaS in this frequency range, as well as the intense 𝐸 1g bending vibrations at ≈76 cm -1 . We also note a broad and weak feature at ≈475 cm -1 , specific only of g-GaS. Vibrational modes in this range usually belong to S-S stretching as shows a typical Raman spectrum of sulfur-rich MM-GaS2, Fig. 2(c). The excessive sulfur in MM-GaS2 exists as a plastic S allotrope, [START_REF] Eckert | Molecular spectra of sulfur molecules and solid sulfur allotropes[END_REF] characterized by strong bending and S-S stretching modes at 150, 220 and 475 cm -1 , respectively. One can hardly imagine the presence of plastic sulfur in vitreous sulfurpoor GaS. Nevertheless, a small concentration of S-S dimers seems to be realistic.

A c c e p t e d M a n u s c r i p t

The observed composition difference between the Ga2S3 target and gallium sulfide PLD layers may have various origins. First, stoichiometric Ga2S3 at high temperatures transforms into nonstoichiometric sulfides Ga 4 S 𝑥 , where 4.8 ≤ 𝑥 ≤ 5.2. [START_REF] Barron | Gallium: inorganic chemistry[END_REF] This disproportionation should occur mostly during thermal evaporation. In addition, the vapor phase above Ga2S3 essentially consists of Ga2S and S2 stable molecules instead of molecular fragments Ga2S3. [START_REF] Roberts | Anomalous temperature dependence for a partial vapor pressure[END_REF] Finally, the laser ablation of solid Ga2S3 generates the dominant atomic species 32 S + , 34 S + , [START_REF] Zakery | Optical Nonlinearities in Chalcogenide Glasses and their Applications[END_REF] Ga + , and [START_REF] Bérubé | Tailoring the refractive index of Ge-S based glass for 3D embedded waveguides operating in the mid-IR region[END_REF] Ga + , while the molecular clusters Ga 𝑚 S 𝑛 + , where 2 ≤ 𝑚,𝑛 ≤ 6, represent the minority species. [START_REF] Belbruno | Structural calculations and experimental detection of small Ga 𝑚 S 𝑛 clusters using time-of-flight mass spectrometry[END_REF] The observed effect can also be attributed to the evaporation of S during the deposition process under high dynamic vacuum, ≈3 × 10 -6 Torr, before the nucleation stage on the substrate surface. 58 The transparency of the GaS PLD layer and its uniformity were confirmed by optical absorption measurements with distinct interference fringes, Fig. 3(a). Using the Swanepoel technique, [START_REF] Swanepoel | Determination of the thickness and optical constants of amorphous silicon[END_REF] the layer thickness 𝑑 and the refractive index 𝑛 R over the 0.8 ≤ λ ≤ 2.5 µm spectral range were calculated from the transmission spectrum derived from absorption. The calculated thickness 𝑑 = 3.8±0.2 µm was consistent with that observed visually, Fig. 1(a). The refractive index 𝑛 R = 2.50±0.01, derived using the substrate refractive index 𝑛 S = 1.58, was similar to that of crystalline GaS 15 and higher than for majority of sulfide glasses. [START_REF] Hilton | Chalcogenide Glasses for Infrared Optics[END_REF][START_REF] Yang | Composition dependence of physical and optical properties in Ge-As-S chalcogenide glasses[END_REF] The fundamental absorption range of chalcogenide glasses is described by the following equation 62

𝛼 = 𝐴(ℎ𝜈-𝐸 g ) 𝑘 ℎ𝜈 , (1)
where 𝛼 > 10 4 cm -1 is the absorption coefficient, 𝐸 g the optical band gap, ℎ𝜈 the incident photon energy, 𝑘 is the parameter, characterizing the optical transition between the valence and A c c e p t e d M a n u s c r i p t conduction bands (𝑘 = 2 for most chalcogenide glasses), [START_REF] Mott | Electronic Processes in Non-Crystalline Materials[END_REF] and 𝐴 ≈ 10 5 cm -1 eV -1 is a constant. The experimental absorption data for glassy GaS layer are well described by Eq. ( 1), Fig. 3(b). The derived optical band gap 𝐸 g = 2.34 eV is very similar to that for crystalline GaS, 2.50 eV, [START_REF] Brebner | The optical absorption range of GaS[END_REF] and remarkably lower than 𝐸 g for Ga2S3 polymorphs, 2.74 eV ≤ 𝐸 g ≤ 3.30 eV. [START_REF] Ho | Optically decomposed near-band-edge structure and excitonic transitions in Ga2S3[END_REF][START_REF] Kokh | Study of Ga2S3 crystals grown from melt and PbCl2 flux[END_REF][START_REF] Caraman | Optical and photoelectric properties of planar structures obtained by thermal annealing of Ga2S3 plates in Zn vapors[END_REF] A characteristic feature of chalcogenide glass thin films is their ability to change optical, structural and chemical properties under light irradiation with photon energy close to 𝐸 g . [START_REF] Frumar | Photo-induced phenomena in amorphous and glassy chalcogenides[END_REF] A shift of the fundamental absorption edge, a change of the optical constants or different etching rates in alkaline solutions are only few examples of photo-structural transformations, used for photolithographic processes, creation of diffraction gratings, Bragg reflectors, etc. The initial properties can be recovered after annealing in the vicinity of the glass transition temperature 𝑇 g . The photo-structural transformations have also negative consequences. Typical chalcogenide glasses like As2S3 cannot transmit a high-power light because of photoinduced changes.

In contrast to this typical behavior, the obtained GaS PLD layers appear to be extremely stable to high-intensity UV light. A 250 W mercury lamp irradiation for 65 minutes does not change the spectral position of the fundamental absorption edge, see the inset in Fig. 3(a). No photoinduced changes were observed using a femtosecond laser irradiation at the wavelength λ = 780 nm. The laser-induced peak power density damage threshold was found to be above ≈1.4 TW cm -2 . For comparison, the permanent changes of the refractive index for CsCl-Ga2S3-GeS2 glasses occur above 62 GW cm -2 at 800 nm, [START_REF] Caulier | Free carrier accumulation during direct laser writing in chalcogenide glass by light filamentation[END_REF] as well as for other chalcogenide glasses. [START_REF] Tanaka | Nonlinear optical properties of photonic glasses[END_REF] A high-power laser-induced damage threshold for vitreous gallium sulfide PLD layers is crucial for NLO-related applications. Typically, isotropic chalcogenide glasses are optically highly nonlinear. [START_REF] Zakery | Optical Nonlinearities in Chalcogenide Glasses and their Applications[END_REF] The nonlinear optical susceptibility of the third order 𝜒 3 is mainly defined by the refractive index 𝑛 R according to simplified expression 70

𝜒 3 ≅ 𝐵�𝑛 R 2 -1� 4 (4𝜋) 4 , (2)
where 𝐵 ≈ 1.7 × 10 -10 esu is a constant. Chalcogenide glasses with high 𝑛 R values exhibit the 𝜒 3 susceptibility by two orders of magnitude larger than oxide glass systems and appear to be attractive materials for all-optical ultrafast switches, frequency converters, electro-optic modulators, etc. [START_REF] Zakery | Optical Nonlinearities in Chalcogenide Glasses and their Applications[END_REF] However, the third-order NLO generation needs propagation of a high power light, limited in glassy chalcogenides by photo-structural transformations and respective changes of the optical constants. [START_REF] Bérubé | Tailoring the refractive index of Ge-S based glass for 3D embedded waveguides operating in the mid-IR region[END_REF] Consequently, the obtained gallium sulfide PLD layers have three promising features: (1) the refractive index 𝑛 R = 2.50 is higher than in usual sulfide glasses, e.g. the Ge-S glass system is characterized by 2.0 ≤ 𝑛 R ≤ 2.1; [START_REF] Todorov | Thin chalcogenide films for photonic applications[END_REF] (2) the high-power laser-induced damage threshold allowing high-intensity NLO applications, and (3) the good optical transparency from visible to mid-IR spectral range.

The question arises what is the structural basis of these features. Going in opposite direction, the photo-structural transformations are promoted by (a) two-fold coordinated chalcogen species (S, Se, Te) providing flexible network structure, and (b) sufficient free volume, that is, a large number of voids and cavities delivering enough space for atomic mobility. [START_REF] Frumar | Photo-induced phenomena in amorphous and glassy chalcogenides[END_REF] The structural studies supported by first-principles simulations are expected to give some answers.

A c c e p t e d M a n u s c r i p t

High-energy X-ray diffraction

The X-ray structure factor 𝑆 X (𝑄) of the obtained PLD gallium sulfide layer is shown in Fig. 4 𝑆 X (𝑄) = 𝑤 GaGa (𝑄)𝑆 GaGa (𝑄) + 𝑤 GaS (𝑄)𝑆 GaS (𝑄) + 𝑤 SS (𝑄)𝑆 SS (𝑄),

where 𝑤 ij (𝑄) are 𝑄-dependent X-ray weighting coefficients and 𝑆 ij (𝑄) the Faber-Ziman partial structure factors. The sample is fully amorphous without any crystalline impurities. The first sharp diffraction peak (FSDP) at 𝑄 0 = 1.03 Å -1 is small in comparison with both Ga2S3-GeS2 glasses and semi-crystalline MM-Ga2S3, prepared by mechanical milling, see the inset in Fig. 4.

The amplitude of high-𝑄 oscillations (𝑄 > 12 Å -1 ) is also remarkably smaller vis-à-vis MM-Ga2S3 and g-(Ga2S3)0.3(GeS2)0.7. Similar trend was observed for (GeS)x(GeS2)1-x glasses with increasing GeS content 𝑥. 73

Fig. 4. X-ray 𝑆 X (𝑄) or neutron 𝑆 N (𝑄) structure factors for MM-Ga2S3 (neutrons), glassy GaS and (Ga2S3)0.3(GeS2)0.7 (X-rays). The inset shows isolated FSDP for these samples derived using a previously reported [START_REF] Bychkov | Compositional changes of the first sharp diffraction peak in binary selenide glasses[END_REF][START_REF] Kassem | Bent HgI2 molecules in the melt and sulfide glasses: Implications for nonlinear optics[END_REF] subtraction procedure.

Fig. 5. X-ray total correlation functions 𝑇 X (𝑟) for (a) glassy GaS, and (b) hexagonal polymorph β-GaS, space group 𝑃6 3 /𝑚𝑚𝑚. [START_REF] Kuhn | Charge-density analysis of GaS[END_REF] The Ga-S, Ga-Ga and S-S partials are highlighted in light green, green, and yellow, respectively.

The total correlation function 𝑇 X (𝑟) of g-GaS, derived through the usual Fourier transform, is shown in Fig. 5 𝑇

X (𝑟) = 4𝜋𝜌 0 𝑟 + 2 𝜋 ∫ 𝑄[𝑆 X (𝑄) -1] sin 𝑄𝑟𝑄(𝑄)d𝑄 𝑄 max 0 , (4)
where 𝑄(𝑄) is the Lorch window function, [START_REF] Lorch | Neutron diffraction by germania, silica and radiation-damaged silica glasses[END_REF] 𝜌 0 the number density and 𝑄 max = 25 Å -1 . The asymmetric peak at ≈2.35 Å suggests a mixed gallium local environment similar to that in crystalline GaS polymorphs, [START_REF] Kuhn | Charge-density analysis of GaS[END_REF][START_REF] Pardo | Sur une nouvelle forme de GaS, rhomboédrique 3R métastable: Formation et étude structurale[END_REF][START_REF] Kuhn | Refinement of the 2H GaS β-type[END_REF] parameters are similar to those in hexagonal GaS: (i) 2.332 Å, 𝑁 GaS = 3; and (ii) 2.449 Å, 𝑁 GaGa = 1. [START_REF] Kuhn | Charge-density analysis of GaS[END_REF] The position and shape of a broad unresolved second neighbor peak at ≈3.75 Å is also rather reminiscent of those in crystalline GaS polymorphs including a gap between 4.4 and 5.1 Å. However, more distant correlations are considerably broader or featureless reflecting the structural disorder in glassy gallium sulfide. Further details related to static and dynamic features in g-GaS were obtained using the first-principles simulations.

First-principles molecular dynamics (FPMD)

The standard PBE [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] or PBEsol [START_REF] Perdew | Restoring the density-gradient expansion for exchange in solids and surfaces[END_REF] exchange-correlation functionals overestimate interatomic distances in chalcogenides and pnictides, [START_REF] Le Roux | Structural properties of glassy Ge2Se3 from firstprinciples molecular dynamics[END_REF][START_REF] Bachhuber | The extended stability range of phosphorus allotropes[END_REF] also confirmed in our FPMD simulations. The use of hybrid functionals B3LYP [START_REF] Le Roux | Structural properties of glassy Ge2Se3 from firstprinciples molecular dynamics[END_REF] or PBE0 [START_REF] Kassem | Chemical and topological variety in sodium thioarsenate glasses studied by neutron diffraction and supported by first-principles simulations[END_REF] improves the agreement with experiment. Figure 6(a) shows the experimental and FPMD/PBE0 interference functions 𝑄[𝑆 X (𝑄) -1] for glassy GaS, revealing a close similarity. The only notable difference is related to underestimated principle peak at 2.25 Å -1 often associated with the small size of the FPMD simulation box, [START_REF] Ohkubo | Conduction mechanism in 70Li2S-30P2S5 glass by ab initio molecular dynamics simulations: Comparison with Li7P3S11 crystal[END_REF] 16.58 Å at 300 K in our case. As expected, the FPMD/PBEsol structure factor exhibits a systematic shift to lower scattering vectors, resulting in larger distances in 𝑟-space, Fig. S2 in ESI. 2) a low-𝑟 shoulder (≈3.1 Å) of the Ga-Ga second neighbor peak, related to short Ga-Ga correlations in edge-sharing structural units. These two features are absent in crystalline GaS polymorphs. [START_REF] Kuhn | Charge-density analysis of GaS[END_REF][START_REF] Pardo | Sur une nouvelle forme de GaS, rhomboédrique 3R métastable: Formation et étude structurale[END_REF][START_REF] Kuhn | Refinement of the 2H GaS β-type[END_REF] The gallium and sulfur local coordination distributions are shown in Fig. 7. As expected, the average gallium environment is tetrahedral, 〈𝑁 Ga-X 〉 = 3.93±0.03, X = S or Ga; and the four-fold coordinated Ga species are predominant, 93±2 %. Nevertheless, a small fraction of under-and over-coordinated gallium is present in g-GaS. The average mixed gallium coordination, 〈𝑁 Ga-X 〉 = 〈𝑁 Ga-S 〉 + 〈𝑁 Ga-Ga 〉 ≅ 3 + 1, is consistent with that in crystalline GaS polymorphs. [START_REF] Kuhn | Charge-density analysis of GaS[END_REF][START_REF] Pardo | Sur une nouvelle forme de GaS, rhomboédrique 3R métastable: Formation et étude structurale[END_REF][START_REF] Kuhn | Refinement of the 2H GaS β-type[END_REF] However, a wide NN distribution around central tetrahedral gallium is observed: one fifth of pure GaS4 tetrahedra, 62±2 % of Ga(S3Ga) mixed units (100 % in crystalline GaS), and the remaining fraction of Ga-rich mixed entities including 1.1 % of Ga(SGa3) polyhedra, see the inset in Fig. 7(b). Similar trends are observed for sulfur, Fig. 7(a). The average sulfur coordination is 〈𝑁 S-X 〉 = 2.95±0.02, and the trigonal S species appear to be dominant, 80±2 %. The NN distribution around central trigonal sulfur is narrow, just 5±1 % of mixed S(Ga2S) units, the inset in Fig. 7(a). Resuming we note a very rigid network of glassy GaS with the average coordination number 〈𝑚〉 = 〈𝑁 Ga-X 〉 × ½ + 〈𝑁 S-X 〉 × ½ = 3.44±0.03, comparable with that of amorphous silicon or germanium. The observed unusually rigid connectivity of g-GaS is atypical for chalcogenide glasses with a much lower average coordination, in most cases 2.2 ≤ 〈𝑚〉 ≤ 2.8. S-Ga-Ga, and (c) Ga-S-Ga triplets in glassy gallium sulfide in comparison with those in hexagonal GaS polymorph. [START_REF] Kuhn | Charge-density analysis of GaS[END_REF] A bimodal fitting of 𝐵(𝜃), related to edge-and corner-sharing polyhedra, is also shown.

A c c e p t e d M a n u s c r i p t

Angular dependences 𝐵(𝜃) of S-Ga-S, S-Ga-Ga, and Ga-S-Ga triplets are shown in Fig. 8 in comparison with hexagonal GaS. [START_REF] Kuhn | Charge-density analysis of GaS[END_REF] Broad 𝐵(𝜃) distributions appear to be a common feature for glassy gallium sulfide related to structural and topological disorder. The connectivity of Gacentered polyhedra is reflected by the Ga-S-Ga bond angles. The 𝐵 GaSGa (𝜃) distribution is broad and asymmetric. The 𝐵 GaSGa (𝜃) maximum at 100.7° is consistent with that in hexagonal GaS. A low-𝜃 shoulder at ≈80° indicates a non-negligible fraction of edge-sharing (ES) Ga-S tetrahedra. Similar ES-contribution at 𝜃(GeSGe) = 82° was observed in high-temperature GeS2 polymorph, consisting of edge-and corner-sharing CS-GeS4 tetrahedra, [START_REF] Dittmar | Die Kristallstruktur von H.T.-GeS2[END_REF] and Ge-S glasses. [START_REF] Blaineau | Physical properties of a GeS2 glass using approximate ab initio molecular dynamics[END_REF][START_REF] Ori | Surface of glassy GeS2: A model based on a first-principles approach[END_REF] The fractional area of the 80° feature, 14 %, is coherent with the ES/CS connectivity analysis of Ga-centered polyhedra and fitting results of the short (3.11 Å, ES-units) and long (3.66 Å, CS-polyhedra) Ga-Ga second neighbor correlations, Fig. 6(c).

The geometry of Ga-S polyhedra, mostly Ga(S4-mGam) tetrahedra, is revealed by the S-Ga-S and S-Ga-Ga bond angles. The mixed Ga(S3Ga) tetrahedra in hexagonal GaS have an axial distortion along the Ga-Ga bond and consequently different S-Ga-S (100.76°) and S-Ga-Ga (117.2°) bond angles, Fig. 8. [START_REF] Kuhn | Charge-density analysis of GaS[END_REF] The maximum of a broad and asymmetric 𝐵 SGaS (𝜃) distribution in glassy gallium sulfide is similar to the crystal value, while that of 𝐵 SGaGa (𝜃) is shifted to a tetrahedral angle, 109.6±0.4°. In other words, the average axial distortion of Ga(S4-mGam) tetrahedra appears to be reduced in g-GaS despite a strong structural disorder. A bimodal fitting of asymmetric angular distributions 𝐵 SGaS (𝜃) and 𝐵 SGaGa (𝜃) unveils a low-𝜃 contribution of nearly identical fractional area, 13±1 %, Fig. 8(a,b). These low-𝜃 contributions are related to additional geometry distortions of the ES-polyhedra in glassy GaS. The connectivity analysis reveals that 98 % of Ga and S species in the FPMD simulation box are forming a single continuous network. A few homopolar S-S bonds in g-GaS are related to S2

A c c e p t e d M a n u s c r i p t dimers. In contrast, the Ga-Ga connected fragments show a wide size distribution, 𝑃 GaGa (𝑛), dependent on temperature, Fig. 9(a,b), instead of only Ga-Ga dimers in crystalline GaS, Fig. 9(b,d). In liquid GaS at 1300K, the maximum size 𝑛 of Ga-Ga connected long-living species is limited to tetramers, Ga4, but the majority of Ga fragments, 60±4 %, are monomers. In other words, the dimeric Ga-Ga connectivity of the crystal is broken in the melt. Cooling down the liquid, one observes the increasing Ga 𝑛 size up to 𝑛 = 7, corresponding to a few Ga-S polyhedra forming a chain, Fig. 9(d). Nevertheless, the dominant Ga-Ga connections in g-GaS are dimers, 34.2±1.2 %. Plotting the ratio 𝑃 GaGa (1)/𝑃 GaGa (2) as a function of temperature, one observes that dissociation of oligomers starts above 700 K, Fig. 9(c), suggesting that the glass transition temperature 𝑇 g in g-GaS presumably appears within 700 K ≤ 𝑇 g ≤ 800 K range.

The intermediate range order in gallium sulfide is represented via Ga 𝑝 S 𝑞 ring statistics. The 2D layers in hexagonal GaS are exclusively built-up by 6-fold rings of two types: Ga4S2 and Ga3S3, Fig. 9(d). The topological disorder in glassy and liquid GaS is well illustrated by the ring population 𝑅 𝑐 (𝑝+𝑞), [START_REF] Roux | Ring statistics analysis of topological networks: New approach and application to amorphous GeS2 and SiO2 systems[END_REF] where 3 ≤ 𝑝+𝑞 ≤ 11, Fig. 10. Basically, the small rings are present in a glass and normal liquid above the melting point, 𝑇 𝑚 = 1228±6 K. [START_REF] Lieth | The P-T-X phase diagram of the system Ga-S[END_REF][START_REF] Pardo | Diagramme de phases gallium-soufre et études structurales des phases solides[END_REF][START_REF] Zavrazhnov | The phase diagram of the Ga-S system in the concentration range of 48[END_REF] The 𝑅 𝑐 (𝑝+𝑞) maximum in glassy GaS is peaked at 𝑝+𝑞 = 6 as in crystalline gallium sulfide. In liquid GaS, a bimodal distribution is observed centered on both 4-and 6-fold rings. The ring size fluctuations are remarkably larger in a liquid, reflected by the ring population uncertainty, calculated over one picosecond of FPMD simulation time and shown as error bars in Fig. 10. A c c e p t e d M a n u s c r i p t

Glassy GaS has a higher packing density compared to usual gallium sulfide glasses reflected by the macroscopic number density, 0.04390 atoms Å -1 (g-GaS) vs. 0.037-0.041 atoms Å -1 (Ga2S3-GeS2 glasses) or molar volume. At a microscopic level, the volume of cavities in glassy GaS, calculated using the Dirichlet-Voronoi tessellation [START_REF] Heimbach | pyMolDyn: Identification, structure, and properties of cavities/vacancies in condensed matter and molecules[END_REF] , Fig. 11, is also lower compared to that in glassy Ga2S3 (a preliminary FPMD modeling), 34.4 % vs. 38.4 %, respectively. Consequently, a small FSDP in g-GaS compared to gallium sulfide glasses and semi-crystalline MM-Ga2S3, Fig. 4, is related to frustration in the disordered network, associated with small available free space [START_REF] Moss | Random packing of structural units and the first sharp diffraction peak in glasses[END_REF] and decreasing spatial repeatability of Ga-centered tetrahedra at intermediate range scale. Similar trend was found earlier in GeS-GeS2 glasses. [START_REF] Bytchkov | Unraveling the atomic structure of Ge-rich sulfide glasses[END_REF] Figure 12 shows typical Ga and S mean-square displacements (MSD), 〈𝑟 2 (𝑡)〉, as a function of the FPMD simulation time 𝑡 and temperature

〈𝑟 2 (𝑡)〉 = 〈 1 𝑁 𝑖 �∑ [𝑟 𝑖 (𝑡) -𝑟 𝑖 (0)] 2 𝑁 𝑖 𝑖=1 �〉, (5)
where 𝑟 𝑖 (0) and 𝑟 𝑖 (𝑡) are the positions of particle 𝑖 for the initial time and time 𝑡, respectively, 𝑁 𝑖 the total number of particles in the simulation box, and the angle brackets represent the average over initial times. Three characteristic regimes are seen in Fig. 12(a-c). The ballistic regime is observed at 𝑡 ≲ 30 fs and characterized by a slope 𝑠 = 2 on a log-log scale [START_REF] Huang | Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid[END_REF] 〈𝑟 2 (𝑡)〉 ∝ (𝑘 B 𝑇/𝑚) 𝑡 2 , (

A c c e p t e d M a n u s c r i p t

where 𝑘 B and 𝑇 are the Boltzmann constant and temperature, and 𝑚 is the particle mass. The diffusive behavior appears at high 𝑇 and 𝑡 and exhibits a slope 𝑠 = 1, Fig. 12(c)

〈𝑟 2 (𝑡)〉 ∝ 𝐷 𝑖 𝑡, (7)
where 𝐷 𝑖 is the average diffusion coefficient of particles 𝑖. Finally, a plateau is observed between the two regimes at intermediate time scales and temperatures related to atomic vibrations and localized motion. [START_REF] Berthier | Theoretical perspective on the glass transition and amorphous materials[END_REF] The MSD is either constant or 〈𝑟 2 (𝑡)〉 ∝ 𝑡 𝑠 , where 0 ≤ 𝑠 < 1.

Except the ballistic regime, the mobility of gallium species is higher than that of sulfur. In addition, the sulfur MSD exhibit a plateau, 〈𝑟 2 (𝑡)〉 ≈ const, over a wide time window, 0.3 ≲ 𝑡 ≲ 30 ps, below 𝑇 ≤ 700 K, see Fig. S3 in ESI. Above 800 K, the localized motion becomes predominant for both Ga and S, and in the vicinity of the melting point, 𝑇 𝑚 ≈ 1230 K, the atomic mobility follows the Einstein relation (7). Different temperature domains are visible more clearly using the Arrhenius plot, log〈𝑟 2 (𝑡 = 10ps)〉 vs. 𝑇 -1 , Fig. 12(d). The localized motion/vibrations at 𝑇 ≤ 700 K are characterized by small apparent activation energy, ≈0.14 eV, and negligible sulfur MSD range, 0.08 ≤ 〈𝑟 2 (𝑡)〉 ≤ 0.3 Å 2 . The long-range diffusion/viscous flow, 𝑇 ≳ 1000 K, shows a much higher activation barrier, ≈1.2 eV, comparable with that found in macroscopic viscosity measurements. [START_REF] Tverjanovich | Temperature dependence of the viscosity of chalcogenide glass-forming melts[END_REF][START_REF] Koštál | Viscosity of chalcogenide glass-formers[END_REF] The observed difference is well illustrated by two snapshots of the FPMD simulation boxes taken at 300 K and 1300 K, the insets in Fig. 12(e). The results are consistent with previous assumption, Fig. 9 and the related text, that the presumable glass transition in g-GaS occurs between 700 K < 𝑇 g < 800 K. We also note that this estimation of 𝑇 g scales with the melting point of gallium sulfide, 1223 K ≤ 𝑇 𝑚 ≤ 1235 K, and a well-known principle, 𝑇 g ≈ ⅔𝑇 𝑚 .

Finally, the average relative energy per atom, 〈𝐸 𝑖 〉, in the FPMD simulation box exhibits a drastic increase of the 𝜕〈𝐸 𝑖 〉/𝜕𝑇 derivative by a factor of 2 above 800 K, presumably related to the onset of viscous flow and changing the accessible energy landscape above 𝑇 g . [START_REF] Sastry | Signatures of distinct dynamical regimes in the energy landscape of a glass-forming liquid[END_REF] Resuming, the diffraction results supported by FPMD simulations are consistent with exceptionally high laser-induced damage threshold of glassy GaS suggesting the superior NLO properties and a possible NLO crossover during a glass-crystal phase transition.

Conclusions

Pulsed laser deposition yields transparent, uniform and vitreous gallium sulfide layers of nearly stoichiometric GaS composition starting from a Ga2S3 target. The difference in chemical composition is certainly related to a disproportionation of Ga2S3 molecular fragments in the plasma plume. The gallium monosulfide PLD layers are characterized by a good transparency from visible to mid-IR spectral region, 0.53 ≤ λ ≤ 12 µm, with the band gap of 2.34 eV and high refractive index 𝑛 R = 2.50±0.01 at 0.8 ≤ λ ≤ 2.5 µm. The excellent high-power UV and laserinduced damage threshold, 1.4 TW cm -2 at 780 nm, superior to a vast majority of the studied chalcogenide glasses, suggests a large nonlinear optical susceptibility of the third order 𝜒 3 .

The structural basis of exceptional NLO properties, studied by Raman spectroscopy, high-energy X-ray diffraction and supported by first-principles molecular dynamics, resides in rigid tetrahedral structure of the obtained layers with the average coordination number 〈𝑚〉 = 3.44±0.03, drastically different from typical chalcogenide glasses having 2.2 ≤ 〈𝑚〉 ≤ 2.8.

A c c e p t e d M a n u s c r i p t

Tetrahedral Ga and three-fold coordinated S species are forming a continuous network, whose molecular architecture is characterized by a strong chemical and topological disorder compared to crystalline GaS polymorphs. In addition, this rigid network has a relatively small fraction of microscopic voids and cavities (34.4 %) reducing the atomic mobility. The FPMD simulations also reveal a glass transition in the GaS PLD layers between 700 < 𝑇 g < 800 K detectable through Ga-Ga oligomer dissociation, local and long-range diffusional motion and a change in the average energy per atom. The estimated 𝑇 g is consistent with a well-known relation, 𝑇 g ≈ ⅔𝑇 𝑚 , where the melting point of GaS is 𝑇 𝑚 = 1228 K.

glass-crystal phase transition in gallium monosulfide is expected to be accompanied by a drastic change in the NLO properties from a large 𝜒 3 in isotropic glass to a strong SHG in a noncentrosymmetric crystal, opening up a new dimension in the PCM photonics and memory applications from visible to mid-IR.

Fig. 1 .

 1 The cross-sectional view shows a smooth vitreous layer of 3.5-4.0 µm in thickness. The surface topography is uniform revealed by a secondary electron image. Finally, the obtained films are transparent from visible to mid-IR spectral window, 0.53 ≤ λ ≤ 12 µm.

A c c e p t e d M a n u s c r i p tFig. 1 .

 1 Fig. 1. GaS layer obtained by PLD: (a) crosssectional view revealing a 3.5-4 µm thick vitreous GaS layer and soda lime glass substrate, (b) layer surface image in secondary electrons, and (c) the entire transparent GaS film on glass substrate.

Fig. 2 .

 2 Fig. 2. Raman spectra of (a) GaS PLD layer, (b) MM-Ga2S3 and (c) MM-GaS2, plotted together with crystalline references: (a) β-GaS, 51 (b) α-Ga2S3, and (c) plastic sulfur. The S-S stretching vibrations in g-GaS are highlighted in yellow.

Fig. 3 .

 3 Fig. 3. Optical characteristics of GaS PLD layers: (a) absorption spectrum of the film with interference fringes, the inset shows a negligible difference in optical absorption between the virgin layer (blue) and that irradiated with a 250 W mercury lamp for 65 min (magenta); (b) optical band gap 𝐸 g determination.

Fig. 5 (

 5 b). A Gaussian peak fitting allows the two contributions to be identified: (i) the Ga-S nearest neighbors (NN) at 2.31±0.01 Å, the partial coordination number 𝑁 GaS = 2.92±0.03; and (ii) the Ga-Ga NN at 2.46±0.01 Å, 𝑁 GaGa = 0.96±0.05. The derived

A c c e p t e d M a n u s c r i p t

Fig. 6 .

 6 Fig. 6. Derived FPMD/PBE0 total and partial functions in 𝑄-and 𝑟-space for glassy GaS: (a) the experimental (circles) and FPMD (green line) X-ray interference function 𝑄[𝑆 X (𝑄) -1], (b) the partial structure factors 𝑆 ij (𝑄), and (c) the partial pair-distribution functions 𝑔 ij (𝑟), where Ga-Ga (dark green), Ga-S (light green) and S-S (orange) atomic pairs are color-coded.The partial structure factors 𝑆 ij (𝑄) are summarized in Fig.6(b) revealing the main contribution to the FSDP comes from Ga-Ga correlations. The 𝑟-space partials, Fig.6(c), confirm mixed gallium local environment consisting of Ga-S (≈2.30 Å) and Ga-Ga (≈2.40 Å) nearest neighbors. The NN peaks are asymmetric having a higher-𝑟 tail. The 𝑔 ij (𝑟) exhibit also two unexpected features: (1) a small fraction of S-S homopolar bonds at ≈2.07 Å, also visible in Raman spectra of

Fig. 7 .

 7 Fig. 7. Local coordination distributions for (a) sulfur and (b) gallium in glassy gallium sulfide. The insets show the nearest neighbor distributions for (a) trigonal central sulfur, and (b) tetrahedral central gallium.

Fig. 8 .

 8 Fig. 8. Angular dependences 𝐵(𝜃) for (a) S-Ga-S, (b)S-Ga-Ga, and (c) Ga-S-Ga triplets in glassy gallium sulfide in comparison with those in hexagonal GaS polymorph.[START_REF] Kuhn | Charge-density analysis of GaS[END_REF] A bimodal fitting of 𝐵(𝜃), related to edge-and corner-sharing polyhedra, is also shown.

Fig. 9 .

 9 Fig. 9. Ga-Ga connected oligomer statistics in (a) liquid, and (b) glassy and crystalline GaS; (c) the Ga-Ga monomer-to-dimer ratio as a function of temperature, and (d) typical examples of Ga-Ga connected fragments in various forms of gallium sulfide.

Fig. 10 .

 10 Fig. 10. Ring population 𝑅 𝑐 (𝑝+𝑞) in (a) liquid, (b) glassy and (c) crystalline GaS calculated using the R.I.N.G.S. software.[START_REF] Roux | Ring statistics analysis of topological networks: New approach and application to amorphous GeS2 and SiO2 systems[END_REF]

Fig. 11 .

 11 Fig. 11. Cavities in glassy (a) Ga2S3 and (b) GaS calculated using the pyMolDyn program 50 and Dirichlet-Voronoi tessellation.

Fig. 12 .

 12 Fig. 12. Mean-square displacements in (a) glassy, (b) supercooled, and (c) normal GaS liquid at 300 K, 800 K and 1300 K, respectively, plotted as a function of FPMD simulation time; (d) Ga and S mean-square displacements at 10 ps in Arrhenius coordinates; (d) the average relative energy per atom as a function of temperature; the insets show the snapshots of the FPMD simulation boxes at 300 K and 1300 K, respectively. See text for further details.

Fig. S1 .

 S1 Fig. S1. High-energy X-ray diffraction measurements at SPring-8 (Hyogo Prefecture, Japan): (a) glassy GaS in thin-walled silica capillary and empty capillary for background subtraction, (b) a vacuum chamber of the dedicated two-axis BL04B2 diffractometer, (c) a 7-detector setup of BL04B2 including four cadmium telluride detectors at low angles and three Ge diodes at high diffraction angles.

Fig. S2 .

 S2 Fig. S2. Experimental (red) and simulated FPMD/PBEsol (blue) X-ray pair-distribution functions 𝑔 X (𝑟) of glassy GaS. A typical problem of FPMD simulations using the general gradient approximation with classical PBEsol exchange-correlation functional resides in overestimation of the nearest neighbor interatomic distances resulting in a higher-𝑟 shift of the NN peak.

  A c c e p t e d M a n u s c r i p t

Fig. S3 .

 S3 Fig. S3. Mean-square displacements 〈𝑟 2 (𝑡)〉 of Ga and S species as a function of FPMD time 𝑡 and temperature 𝑇. Three characteristic regimes are clearly seen: (1) the ballistic regime below 𝑡 ≲ 30 fs, 〈𝑟 2 (𝑡)〉 ∝ 𝑡 2 , (2) the intermediate regime related to vibrations and local diffusion, 〈𝑟 2 (𝑡)〉 ∝ 𝑡 𝑠 , where 0 ≤ 𝑠 < 1, and (3) the long-range diffusion motion at high 𝑇 and 𝑡, 〈𝑟 2 (𝑡)〉 ∝ 𝑡 1 .

  A c c e p t e d M a n u s c r i p t

Acknowledgments

This work was supported by the Ministry of Science and Higher Education under agreement 075- 15-2019-1950; state assignment FSRC 'Crystallography and Photonics' Russian Academy of Sciences. The experiments at the SPring-8 were approved by the Japan Synchrotron Radiation Research Institute (proposal No. 2017A1067) and supported by the Centre for Advanced Science and Technology (Japan). The work at Tallinn University of Technology (Estonia) was supported by the European Union through the European Regional Development Fund project 'Center of Excellence' TK141. The optical measurements in part were carried out in the resource center of St. Petersburg State University: 'Center for Optical and Laser Materials Research'. The FPMD simulations were carried out using the HPC computing resources at Lomonosov Moscow State University and at the ILIT RAS in Shatura (Moscow Region). This work was also granted access to the HPC resources of IDRIS (France) under the allocation 2019-A0070910639 made by GENCI (Grand Equipement National de Calcul Intensif) and using the CALCULCO computing platform, supported by SCoSI/ULCO (Service COmmun du Systeme d'Information de l'Université du Littoral Côte d'Opale). E. B. is also grateful to Dr. F. Sava (National Institute of Materials Physics, Romania) for providing a gallium sulfide film used in preliminary measurements.

Supplementary information

High-energy X-ray diffraction measurements at SPring-8 (Hyogo Prefecture, Japan); experimental and simulated FPMD/PBEsol X-ray pair-distribution functions 𝑔 X (𝑟) of glassy GaS; mean-square displacements 〈𝑟 2 (𝑡)〉 of Ga and S species as a function of FPMD time 𝑡 and temperature 𝑇.