Max Schutz

Maximilian Muhr

Kerstin Freitag

Christian Gemel

Samia Kahlal

Jean-Yves Saillard

Juarez Augusto C H Da Silva

L F Da Silva

Thomas F Fässler

Roland A Fischer

Max Schütz

Jean- Yves Saillard

Juarez L F Da Silva

Contrasting Structure and Bonding of a Copper-Rich and a Zinc-Rich Intermetalloid Cu/Zn Cluster

Keywords: bimetallic cluster synthesis, X-ray crystallography, bonding analysis

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

INTRODUCTION

We have been interested for a long time in the synthesis of bimetallic, molecular complexes and cluster compounds, accessible by bottom-up synthesis from low valent ECp* ligands (E = Al, Ga, In, Zn) and organometallic transition metal (TM) precursors. [START_REF] Gonzalez-Gallardo | Cyclopentadiene based low-valent group 13 metal compounds: Ligands in coordination chemistry and link between metal rich molecules and intermetallic materials[END_REF]2 Especially for late transition metals TM many examples for intermetallic complexes [TMa(ECp*)b(L)c] and clusters [TMaEb](Rc) (R = hydrocarbon ligand such as Me = CH3, Cp* = C5(CH3)5, CN t Bu etc.) could be isolated and structurally characterized. [START_REF] Gonzalez-Gallardo | Cyclopentadiene based low-valent group 13 metal compounds: Ligands in coordination chemistry and link between metal rich molecules and intermetallic materials[END_REF]2 In particular, a variety of intermetallic Cu/Zn clusters are accessible, some of which show structural similarities to the solid-state structures of brass phases. The molecular structure of the superatom cluster [Cu4Zn4](CN t Bu)4(Cp*)4, for example, is based on interpenetrated Cu4 and Zn4 tetrahedra with a [Cu4Zn4] unit (M8) which is also found in γ-brass. [START_REF] Freitag | Molecular brass: Cu4Zn4, a ligand protected superatom cluster[END_REF] The triangular cluster [CuZn2](Cp*)3 has been identified as an "embryonic" building block of such brass clusters. 4 The species [CuZn2](Cp*)3 does indeed give access to larger clusters in defined cluster building up reactions: In presence of the substitutionally labile Zn(I) dimer [Zn2]Cp*(L)3 + (L = Et2O), the cationic M7 cluster {[Cu2Zn5](Cp*5)} + is formed. 4,5 The isoelectronic neutral analogue [Cu3Zn4](Cp*)5 is obtained by reaction of Cu(OAc) with [Zn2](Cp*)2 in very low yields. 5 Both M7 clusters are isoelectronic and highly electron deficient according to Wade-Mingos rules, remarkably Cu 3d orbitals contribute substantially to cluster bonding. 5 In all examples of molecular "embryonic brass" clusters reported so far, the Cu:Zn ratio is not far away from 1:1 with a slight bias to zinc, ranging from 1:1 in [Cu4Zn4](CN t Bu)4(Cp*)4 to 1 : 2.5 in [Cu2Zn5](Cp*)5 + .

The bimetallic metal cores of such M/E clusters are most often structurally similar to cut-outs of the respective intermetallic solid-state phases. "Structural similarity" includes the appearance of similar structural motifs such as polyhedral shapes or metal coordination numbers, but also similar interatomic distances as in intermetallic compounds. While the electronic situation in extended solid-state phases is doubtlessly different from that in a finite molecular cluster, the underlying electronic principles may well be associated, e.g. the polarization of M-M' interactions triggered by the different electronegativities of the two metals. In the case of solid-state brass phases, the Cu:Zn ratio has a strong influence on the structural and physical properties of the materials. For example, below 2:1, α-brass exhibits a regular fcc structure based on that of metallic Cu. With increasing zinc content β-brass, a bcc structure, is favored. Only with zinc contents above 50% the structurally diverse Hume-Rothery phases γ-, δand ε-brass are observed. 6 Even though it is known since a long time that the structures of Hume-Rothery phases strongly correlates with the average valence electron concentration (VEC) of the distinct compositions such as β-, γ-, and ε-brass with VEC = 1.5 (CuZn), 1.615 (Cu5Zn8, ), and 1.75 (CuZn3), respectively, no simple chemical picture exists for their understanding. [START_REF] Hume-Rothery | The Structure of Metals and Alloys, The Structure of Metals and Alloys[END_REF] Thus, the exploration of the structural variability of molecular Cu/Zn clusters is an interesting target to us. How are the electronic situations and bonding properties in such clusters affected if the abundance of one of the two metals is much higher than the other? In this contribution we like to present the synthesis and characterization based on experimental techniques and density functional theory calculations of two new molecular Cu/Zn clusters with metal core compositions far away from Cu:Zn = 1:1. Specifically, we succeeded in the isolation and characterization of the Zn-rich cluster [CuZn10](Cp*)7 (1), as well as its Cu rich congener [Cu10Zn2](Mes)6(Cp*)2 (2).

EXPERIMENTAL SECTION

General

All experiments were conducted using standard Schlenk and glovebox techniques under an atmosphere of purified argon. All solvents were carefully dried (water content < 5 ppm) and saturated with argon prior to their use. The starting compounds [Zn2](Cp*)2, CuMes = [Cu5] (Mes)5 and [( i Dipp)CuO t Bu] were prepared according to literature methods. [START_REF] Grirrane | Zinc-Zinc Bonded Zincocene Structures. Synthesis and Characterization of Zn2(η 5 -C5Me5) 2 and Zn2(η 5 -C5Me4Et)2[END_REF][START_REF] Meyer | Polynuclear aryl derivatives of Group 11 metals. Synthesis, solid state-solution structural relationship, and reactivity with phosphines[END_REF][START_REF] Jordan | Synthesis and reactivity of new copper (I) hydride dimers[END_REF] For both compounds 1 and 2 no meaningful data for elemental analyses (C, H, Cu, Zn) could be obtained due to their high sensitivity (2) as well as co-crystallization with side products (1). However in both cases the molecular ion signal in the LIFDI (liquid field injection desorption ionization) mass spectrum is consistent with the suggested elemental composition derived from crystallographic and other spectroscopic data. NMR spectra were recorded on a Bruker Avance III AV400US ( 1 H, 400 MHz; 13 C 101 MHz) and a Bruker Avance II 500 with a cryo-probe ( 13 C, 125 MHz). Variable temperature (VT) NMR spectra were recorded on a Bruker DRX 400 spectrometer ( 1 H, 400 MHz). Chemical shifts are described in ppm relative to tetramethylsilane (TMS) and referenced to the solvent residual signals. Mass spectrometry was conducted with a Micromass LCT-QTOF Micro mass spectrometer and a Thermo-Fischer Exactive Plus mass spectrometer using LIFDI as ionization method. Raman scattering was performed on a Renishaw inVia Raman microscope RE04 using an excitation wavelength of 532 nm. The data were collected with a CCD detector and evaluated using WiRE 4.2. FT-IR spectra were measured in an ATR setup with a Bruker Alpha FTIR spectrometer under an inert gas atmosphere in a glove-box. Data for X-ray crystallography were collected on a single crystal x-ray diffractometer equipped with a TXS rotating anode and an IMS microsource (see table S1) with MoKα radiation (λ = 0.71073 Å) and a Helios optic using the APEX3 software package. Measurements were performed on single crystals coated with perfluorinated ether. The crystals were fixed on top of a kapton micro sampler and frozen under a stream of cold nitrogen. Diffraction data were processed using the APEX3 software with the implemented SAINT and SADABS programs. The structures were solved using SHELXT with the aid of successive difference Fourier maps, and were refined against all data using SHELXL-2014/2017 in conjunction with SHELXLE. The unit cell of compound 1 contains one disordered molecule of diethylether, which was treated as a diffuse contribution to the overall scattering without specific atom positions using the PLATON/SQUEEZE procedure. The unit cell of compound 2 contains six disordered molecules of toluene, which were treated as a diffuse contribution to the overall scattering without specific atom positions using the PLATON/SQUEEZE procedure. We refer to the supporting information for a more detailed procedure for X-ray crystallography and refinement including literature references for the used programs and software.

Synthesis of [CuZn10](Cp*)7 = [Cu(ZnZnCp*)3(ZnCp*)4] (1)

A sample of 274 mg (0.52 mmol) of [( i Dipp)Cu(O t Bu)] were suspended in 8 ml of diethylether and cooled to -75 °C. A volume of 0.15 ml of [HSi(OEt)3] (0.81 mmol) were added dropwise to the solution leading to an immediate color change to yellow. The solution was stirred for 4 hours at -75 °C before a solution of 420 mg [Zn2](Cp*)2 (1.0 mmol) in 7 ml diethylether was added at that temperature. The resulting solution was allowed to warm to room-temperature and stirred for 2 hours, accompanied by a color change to deep-red. The solution was concentrated in vacuum, filtered and left for crystallization at -30 °C for several weeks leading to a mixture of red crystals of 1 and colorless ones of [Zn2](Cp*)2, which was isolated and washed with a minimum amount of n-hexane. The yield could not be determined due to the inseparability of the two types of crystals. The assignment of the spectroscopic data of the manually separated single crystals of 1 is as follows:

Synthesis of [Cu10Zn2](Mes)6(Cp*)2 (2)

A sample of 200 mg (1.1 mmol) of [CuMes] = [Cu5](Mes)5 and 132 mg (0.3 mmol) of [Zn2](Cp*)2 were dissolved in 25 ml of toluene and heated to 75 °C for 7 days. The dark solution was filtered via a passivated glass frit, concentrated under reduced pressure (4 ml) and left for crystallization at -30 °C for several weeks. Dark-green crystals of 2 were isolated in 9.1 % yield (based on Cu) and washed with a minimum amount of n-hexane (3 x 0.3 ml).

RESULTS AND DISCUSSION

Synthesis and characterization of the zinc-rich M11 cluster [CuZn10](Cp*)7 (1)

Synthesis

The reaction conditions for the synthesis of 1 are described in scheme 1. The reaction progress can be monitored by LIFDI-MS pointing to the formation of various Cu( i Dipp) aggregates, as well as of a complicated mixture of M8/M11/M13 mixed metal Cu/Zn clusters (see figure S1). However, when the concentrated reaction solution is cooled down to -30 °C, single crystals of Cluster 1 readily dissolves in common organic solvents (toluene, benzene, hexane, diethylether) and solutions in benzene are stable at room-temperature for several days before slow decomposition (metallic precipitate) occurs.

Notably, the excess of [Zn2](Cp*)2 in the synthesis of 1 is crucial. The use of stoichiometric amounts leads to unspecific reaction mixtures and no product can be isolated. Obviously, high concentrations of [Zn2](Cp*)2 are required to "trap" the Cu fragments formed in the competitive thermal decomposition of i Dipp-Cu-H. Due to the chemical instability of i Dipp-Cu-H we also investigated the reaction of the thermally more stable analogous PPh3 compound [Cu6](H)6(PPh3)6.

However, Cp* transfer to copper was observed in this case as the dominating mechanism and the thermodynamically very stable half-sandwich complex [(PPh3)CuCp*] was isolated as the only product. This illustrates the importance of the choice of the organometallic Cu-source and thus points to the kinetic control of the Cu/Zn cluster formation reactions.

Crystallographic characterization of 1

The molecular structure of 1 in the solid state has been investigated by SC-XRD (see figure 1).

We refer to the Supporting Information (table S1) for detailed crystallographic information. S3). Unfortunately, no [START_REF] Freitag | Zn⋯Zn interactions at nickel and palladium centers[END_REF] C-NMR spectrum could be recorded at -90 °C, due to decreased solubility of the compound at low temperatures.

The molecular ion peak of [CuZn10](Cp*)7 is detected as a weak signal at m/z = 1664 (see figure S4). Unfortunately, the isotopic pattern observed for the molecular ion peak does not satisfy high resolution standards (see figure S4, right) due to the weak intensity of the signal. However, the fragment ion [1 -ZnCp*] + is observed with high resolution and its isotopic pattern is well consistent with the calculated one for [CuZn9](Cp*)6 (see figure S4,left).

Computational analysis of 1

The assignment of the copper location in 1 was obtained by geometry optimizations based on total energy DFT calculations of seven representative configurations (see Supporting Information, figure S10) corresponding to different occupations of the metal positions, using the all-electron full-potential Fritz-Haber institute ab initio molecular simulations (FHI-aims) package [START_REF] Blum | Ab initio molecular simulations with numeric atom-centered orbitals[END_REF] with the PBE functional [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] (see computational details, Supporting Information). Unsurprisingly, the most stable structure is that with copper lying at the central position (see Supporting Information, figure S10), in full agreement with the above discussed spectroscopic and structural data. It lies 0.67 eV below in energy than the next most stable configuration in which Cu is located at a more peripheral position. In a following step, using the lowest energy structure, the electronic structure of 1 was then analysed by using the ADF program suite [START_REF] Velde | Chemistry with ADF[END_REF][START_REF] Baerends | ADF2016[END_REF] at the BP86/TZ2P-D3 level (see computational details, Supporting Information). Although slightly distorted away from Cs symmetry, the optimized geometry of 1 at this level of theory was found to be close to its X-ray structure. The computed 1 H NMR chemical shifts (av. 2.06 and 1.95 ppm for ZnCp* and ZnZnCp*, respectively) as well as the [START_REF] Freitag | Zn⋯Zn interactions at nickel and palladium centers[END_REF] C ones (av. 10.66 and 113.16 ppm for ZnCp* and av. 7.74 and 111.57 ppm for ZnZnCp*) are consistent with the experimental data. Discarding first the long Zn…Zn contact and considering that each individual ZnCp* or ZnZnCp* unit is a 1-electron donor, the 7 electrons provided by the 7 organo-zinc ligands add up to the 11 valence electrons of Cu(0), making the later a 18-electron metal centre. This electron count is consistent with the computed substantial HOMO-LUMO gap (2.06 eV). However, the 18-electron rule should be considered carefully when applied to complexes in which the number of ligands is larger than the number of metal valence orbitals available for bonding. In such situations, delocalization over the ligand sphere is expected.

This is what happens in 1 where the 3d 10 4s 1 copper centre has only four accepting orbitals (4s and 4p) to accommodate the 7 ligand electrons coming from seven organo-zinc -type orbital combinations. These seven combinations interact with the Cu orbitals in a manner roughly sketched in figure 2. Four among the seven organo-zinc combinations interact with the copper 4s and 4p orbitals, leaving three of them non-bonding with Cu. Among the seven organo-zinc combinations, those which are the closest in energy to the copper AOs are expected to interact in a stronger way. These orbitals are the lowest among the seven, thus those which have Zn…Zn Unsurprisingly, the computed Zn…Zn Wiberg indices (avg. 0.084) are much smaller than that corresponding to the Zn-Zn single bonds (avg. 0.490).

Synthesis and characterization of the copper-rich M12 cluster [Cu10Zn2(Mes)6Cp*2] (2)

Synthesis of 2

The synthesis of [Cu10Zn2](Mes)6(Cp*)2 (2) is described in scheme 2. Compound 2 was identified as the major reaction product by LIFDI-MS (see figure S9). After cooling the filtered and concentrated reaction solution to -30°C, 2 can be separated from the mixture in form of very airand moisture sensitive black-green crystals (see scheme 2). The molecular structure of 2 in the solid state has been determined by SC-XRD (see figure 3).

Cluster 2 is well soluble in toluene, but less soluble in benzene and only sparingly soluble in hexane. It can be obtained in analytically pure form after washing the isolated crystals with hexane.

It is only moderately stable under argon atmosphere at room-temperature in the solid state as well as in solution. Prolonged heating to more than 100 °C leads to the formation of a metallic precipitate. Due to the high sensitivity of 2, no meaningful data from elemental analysis could be obtained.

Scheme 2: Synthesis of cluster 2, [Cu10Zn2](Mes)6(Cp*)2.

Zn2. Most interestingly, the structural motif of two edge-sharing Cu4-tetrahedra, is also found in LAVES phases such MgCu2. [START_REF] Berry | The crystal chemistry of the Laves phases[END_REF] The Cu-Cu distances within the cluster core are all between 2.4223( 7 The six mesityl units are found in edge-bridging positions, each bridging one of the Cu-Cu contacts between the central Cu3 triangle and the Cu3 triangles of the two tetrahedral Cu4 units. The Cu-C distances are all within the range of 1.992(5) Å and 2.044(4) Å and well in line with the Cu-C distance reported for [Cu5](Mes)5. 9

Spectroscopic characterization of 2

The 1 H-and 13C-NMR spectrum of 2 in benzene-d 6 (see figure S6) is consistent with the molecular structure found in the solid state and with all other analytical data. Due to the high sensitivity of 2 small amounts of side products like mesitylene are found in the NMR spectra. The isotopic pattern of the molecular ion peak of 2 in the LIFDI-mass spectrum is in agreement with the calculated isotopic pattern for [Cu10Zn2](Mes)6(Cp*)2 (figure 4).

Computational analysis of 2

The assignment of the two zinc locations over twelve metal sites in 2 was obtained by geometry optimization based on total energy DFT calculations of ten representative configurations (see Supporting Information, figure S10) in the same manner as proceeded for 1 (see computational details and figure S10). Following the same trend, there is an excellent structural agreement between the XRD structure and the lowest energy configuration in which the two zinc atoms are located on the capping positions along the pseudo-three-fold axis. In the same way as for 1, this low energy configuration was then investigated at the BP86/TZ2P-D3 level with the ADF2017 code (see computational details, Supporting Information) for analysing its electronic structure, which, as developed below, can be explained within the framework of the superatom concept. [START_REF] Khanna | Atomic clusters: Building blocks for a class of solids[END_REF][START_REF] Walter | A unified view of ligand-protected gold clusters as superatom complexes[END_REF][START_REF] Häkkinen | Atomic and electronic structure of gold clusters: understanding flakes, cages and superatoms from simple concepts[END_REF] The computed 1 H-and [START_REF] Freitag | Zn⋯Zn interactions at nickel and palladium centers[END_REF] C-NMR chemical shifts are also consistent with their experimental counterparts (Table S2). The first question that arises with respect to electron distribution, is that of the metal oxidation states. Indeed, with six mesityl and two Cp* ligands, all formally anionic, the [Cu10Zn2] group oxidation state is +8, that is, there are [(10 x 1) + (2 x 2)] -8 = 6 metallic 4s electrons located somewhere on the metal core. This number is not a superatom closed-shell "magic" electron count, which makes sense owing to the fact that the regular superatom model assumes cluster spherical shapes, [START_REF] Khanna | Atomic clusters: Building blocks for a class of solids[END_REF][START_REF] Walter | A unified view of ligand-protected gold clusters as superatom complexes[END_REF][START_REF] Häkkinen | Atomic and electronic structure of gold clusters: understanding flakes, cages and superatoms from simple concepts[END_REF] which is not obviously the case of 2. In any case, like in superatoms of group 11 metals, metal-metal bonding in 2 is expected to be mainly ensured by these valence s-type electrons. [START_REF] Walter | A unified view of ligand-protected gold clusters as superatom complexes[END_REF][START_REF] Häkkinen | Atomic and electronic structure of gold clusters: understanding flakes, cages and superatoms from simple concepts[END_REF][START_REF] Sharma | Structurally Precise Dichalcogenolate-Protected Copper and Silver Superatomic Nanoclusters and Their Alloys[END_REF] Like in group 11 superatoms also, the computed HOMO-LUMO gap of 2 (1.51 eV), although significant, is not as large as that found usually at the GGA level for Cu(I) species. [START_REF] Dhayal | Diselenophosphate-Induced Conversion of an Achiral [Cu20H11{S2P (OiPr)2}9] into a Chiral [Cu20H11{Se2P(OiPr)2}9] Polyhydrido Nanocluster[END_REF] A careful analysis of the occupied Kohn-Sham orbitals allowed identifying three of them with important 4s character, two of pseudo-a'1 and one of pseudo-a"2 symmetry. They are plotted in figure 5. The highest one is the pseudo-a'1 HOMO which is principally composed of the 4s AO of the central Cu4 atom, with some minor antibonding admixture from the other metal atoms. The two other 4s combinations have significant bonding character and therefore much lower energies. The lowest is the pseudo-a'1 bonding counterpart of the HOMO. The other one, of pseudo-a"2 symmetry, is bonding within each of the inner Cu4 tetrahedra. Thus, in terms of a superatomic description, the electron configuration of 2 is 1S 2 1Pz 2 2S 2 , consistent with the very prolate shape of the cluster core. Thus, despite its substantial deviation from spherical symmetry, we believe that the superatom model still appears to be a useful limit reference for rationalizing the electronic structure of 2. Consistently, the two LUMO's can be tentatively identified as the We thus expect much more species to be discovered following the strategy outlined in this and our previous reports. [START_REF] Freitag | Molecular brass: Cu4Zn4, a ligand protected superatom cluster[END_REF][4][5]

CONFLICTS OF INTEREST

There are no conflicts to declare.

electron complex of Cu (0) embedded in a shell of •ZnCp* and •ZnZnCp* ligands compromising some interligand bonding. In contrast, 2 is interpreted as a 6 electron superatom with prolate distortion from spherical symmetry.

For table of contents only

1 H

 1 -NMR (298 K, 400 MHz, C6D6, manual separation of single crystals): 2.22 (s, 105H, Cp*) 1 H-NMR (208 K, 400 MHz, C6D6, manual separation of single crystals): 2.25 (s, 45H, ZnZnCp*), 2.27 (s, 60H, ZnCp*) 13 C-NMR (298 K, 400 MHz, C6D6, manual separation of single crystals): 12.21 (s, C5(CH3)5 groups), 111.10 (s, C5(CH3)5) Raman (298 K): ν [cm -1 ] = 2850 (b, w), 1575 (b), 1025 (s, w), 980 (s), 142 (s); (see Supporting Information, figure S5). LIFDI-MS: m/z (a.u.) = 1664 ([M] + ), 1462 ([M-ZnCp*] + ).

1 H

 1 -NMR (298 K, 400 MHz, C6D6): 2.16 (s, 30 H, ZnCp*), 2.24 (s, 18H, CH3 (Mes)), 2.39 (s, 36H, CH3 (Mes)), 6.84 (s, 12H, CHaryl (Mes)).

13 C

 13 -NMR (298 K, 400 MHz, C6D6): 9.41 (s, methyl groups (ZnCp*)), 21.18 (s, methyl groups (Mes)), 30.49 (s, methyl groups (Mes)), 110.23 (s, ring carbon atoms (Cp*)), 126.52 (s, ring carbon atoms (Mes)), 137.46 (s, ring carbon atom (ZnCp*)), 140.57 (s, ring carbon atoms (Mes)), 154.68 (s, ring carbon atoms (Mes)). ATR-IR (298 K): ν [cm -1 ] = 3011 (w), 2962, 2908, 2855, 1594 (s), 1444, 1413, 1380, 1283 (w), 1258 (s, i), 1081 (i), 1013 (i), 863 (w), 842 (w), 791 (i), 661-698, 574 (w), 544 (w), 527 (w); (see Supporting Information, figure S8). LIFDI-MS: m/z (a.u.) = 1751 ([M] + ).

[Scheme 1 :

 1 Scheme 1: Synthesis of cluster 1, [CuZn10](Cp*)7 = [Cu(ZnZnCp*)3(ZnCp*)4] (R = 2,6diisopropylphenyl). The Cu-Zn connecting lines illustrate short contacts.

Cluster 1

 1 crystallizes in the orthorhombic space group Pnma with four molecules per unit cell together with four molecules of heavily disordered diethylether per asymmetric unit. The molecule of 1 sits on a crystallographic symmetry plane and thus possesses Cs symmetry. The central Cu atom is hepta-coordinated by three Zn-ZnCp* units and four ZnCp* units. In all seven Zn units, the protecting Cp* ligands are  5 -coordinated, with Zn-Cp*centroid distances varying between 1.91 Å and 2.01 Å, which is typical for Zn-Cp* distances found in literature (e.g. 1.934 Å for [Pd(ZnCp*)4(ZnMe)4]). 11 The distances of the central Cu to the surrounding Zn atoms lie between

Figure 1 :

 1 Figure 1: Left: Molecular structure of 1 in the solid state as determined by SC-XRD. Thermal ellipsoids are shown at the 50 % probability level, hydrogen atoms, co-crystallized solvent molecules and disordered groups are not shown for clarity and ligands are simplified as wireframes. Selected interatomic bond distances [Å] and angles [°]: Cu1-Zn5: 2.3477(3), Cu1-Zn1: 2.335(5), Cu1-Zn2: 2.3997(5), Cu1-Zn4: 2.3662(4), Cu1-Zn3: 2.4136(5), Zn4-Zn6: 2.3686(5), Zn5-Zn7: 2.390(5), Zn2-Zn5: 2.7489(4), Zn1-Zn4: 2.713(6), Zn5-Zn3: 2.7418(4), Cu1-Zn4-Zn6: 173.08(2), Cu1-Zn5-Zn7 172.0(2). Right: Coordination geometry of Cu (orange) in 1 with Zn in the first (blue) and second coordination sphere (green). Longer Zn-Zn contacts are illustrated in blue, shorter ones as a blue-green gradient line.

  bonding character. In fact, they are the two lowest -type combinations (somewhat stabilized by 4p(Zn) AOs of the ZnZnCp* ligands) of each of the two subunits [(Cp*Zn)(ZnZnCp*)(ZnCp*)] and [(Cp*Zn)(ZnZnCp*)(ZnCp*)(ZnZnCp*)]. On the other hand those having Zn…Zn antibonding character are expected to interact to a lesser extent. This is exemplified by a fragment decomposition analysis which indicates that the four lowest -type organo-zinc combinations have a global occupation of 5.98 electrons, whereas that of three highest ones is only 1.03 electrons. It results that the highest occupied levels of 1 have some Zn…Zn bonding character, whereas those having Zn…Zn antibonding character are vacant. The diagram of figure 2 is obviouslyoversimplified, but it allows explaining where bonding delocalization between the organo-zinc ligands originates from. It is worth noting that this situation is allowed because the organo-zinc type orbitals lie at higher energy than the 3d(Cu) block. A lower energy would result in the occupation of their Zn…Zn antibonding combinations. Steric crowding among the ligand sphere tends also to favour such delocalization. The availability of 7 organo-zinc combinations to stabilize four Cu AOs is also favourable to a fluxional behaviour of the organo-zinc ligand sphere around the copper center.

Figure 2 :

 2 Figure 2: Simplified MO diagram sketching the interaction of the Cu valence AOs with the combinations of the -type frontier orbitals of the ZnCp* and ZnZnCp* fragments in 1.For the sake of simplicity Cu is considered in its +I oxidation state, making the whole ligand sphere an 8-electron donor system.

Figure 4 :

 4 Figure 4: Comparison of the experimental (as determined by positive ion-mode LIFDI-MS; bottom, red) and calculated (top, black) isotopic pattern of [Cu10Zn2]Mes6Cp*2 (2).

Figure 5 :

 5 Figure 5: The three occupied orbitals of 2 of large 4s character and responsible for metal-metal bonding in the [Cu10Zn2] core.

  Bu)4(Cp*)3Cp (2.471 3 The longest M-M distances (avg. 2.75 Å) are observed between the central Cu4 atom and the Cu triangle spanned by Cu5, Cu6 and Cu7. The Cu-Zn

		) Å and 2.7662(8) Å, which
	is well within the range of molecular compounds with direct Cu-Cu bonds reported in literature
	(2.3 Å for { i DiPPCuH}2 19	, 3.424 Å for {[Ag6Cu2(dppe)3(CCC6H4OCH3)6(MeCN)](ClO4)2}(dppe=
	1,2-bis(diphenylphosphino)ethane), 2.56 Å for Cu metal) 10, 20, 21 , but slightly shorter the mean
	Cu-Cu distance in [Cu6Al6](H)4(Cp*)6 (2.531 Å) 22 and very similar to the one in
	[Cu4Zn4](CN t

distances (avg. 2.45Å) are shorter with respect to [Cu4Zn4](CN t Bu)4(Cp*)3Cp (2.498(2) Å) 3 but very similar to those in [Cu3Zn4](Cp*)5 (2.431(2) -2.458(2) Å), 5 reflecting the similar structural motifs of Zn capped Cu triangles. The Zn-Cp*centroid distances are 1.91 Å and 1.92 Å, which is in line with literature values for terminal ZnCp* units in metal-rich molecules (1.83 Å -2.19 Å) and especially comparable to those observed in [Cu3Zn4](Cp*)5 (1.901 / 1.922 Å). 5

ACKNOWLEDGMENTS

Kerstin Mayer and Carsten Aulenbacher, Christoph Wallach and Christina Fischer are acknowledged for support in initial mass spectrometric measurements. Dr. Christian Jandl is acknowledged for help in the refinement of single crystal XRD data. S.K and J.-Y.S are grateful to GENCI (Grand Equipment National de Calcul Intensif) for HPC resources (Project A0050807367). A.C.H.S and J.L.F.S gratefully acknowledge support from FAPESP (São Paulo Research Foundation, Grant Numbers 2017/11631-2 and 2018/21401-7), Shell and the strategic importance of the support given by ANP (Brazil's National Oil, Natural Gas and Biofuels Agency) through the R\&D levy regulation.

FUNDING SOURCES

This work was supported by the Deutsche Forschungsgemeinschaft (grant Fi 502/23-2) as well as the TUM Global Incentive Fund.

Crystallographic characterization of 2

Cluster 2 crystallizes in the triclinic space group P-1 with two molecules per unit cell and three disordered molecules of toluene per asymmetric unit. We refer to the Supporting Information (table S1) for detailed crystallographic information. The metal core structure of 2 is close to ideal

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

SUPPORTING INFORMATION

Detailed description of materials and methods (including X-ray crystallography and computational details), crystallographic information for compounds 1-2, computed NMR shifts for compound 2, LIFDI-MS spectra, NMR spectra, Raman spectra and optimized geometries for M11 and M12 (M = Cu, Zn) ligand protected clusters.


Tzu-Hao Chiu

Jian-Hong Liao

Franck Gam

Ying-Yann Wu

Xiaoping Wang

Samia Kahlal

Jean-Yves Saillard

C W Liu

Hydride-containing 8-electron Pt/Ag Superatoms: Structure, Bonding and Multi-NMR Studies

Keywords: Platinum, Silver, Hydride, Neutron diffraction, Superatom

)) describe a central platinum hydride (PtH) unit encapsulated within a distorted Ag12 icosahedron, the resulting (PtH)@Ag12 core being stabilized by an outer sphere made up of seven capping silver atoms and twelve dichalcogenolates. Solid-state structures of 1 and 2 differ somewhat in the spatial configuration of their outer spheres, resulting in overall different symmetries, C1 and C3, respectively. Whereas the multi-NMR spectra of 2 in solution at 173K reveal that the structure of C3 symmetry is the predominant one, 1 H and 195 Pt NMR spectra of 1 at the same temperature disclose the presence of isomers of both C1 and C3 symmetry. DFT calculations found both isomers to be very close in energy, supporting the fact that they co-exist in solution. They also show that the [PtH@Ag12] 5+ kernel can be viewed as a closed-shell superatomic core, the 4-hydride electron contributing to its 8-electron count. On the other hand, the 1s(H) orbital contributes only moderately to the superatomic orbitals, being mainly involved in the building of a Pt-H bonding electron pair with the 5dz 2 (Pt) orbital. The two compounds display differences in photoluminescence, compound 2 exhibiting a strong phosphorescence emission at 77K.

Introduction

Researches on alloy nanoclusters (NCs) have become topical because of the presence of unique stability and distinct catalytic activities compared with homometallic counterparts. [START_REF] Jin | Atomically Precise Colloidal Metal Nanoclusters and Nanoparticles: Fundamentals and Opportunities[END_REF][START_REF] Chakraborty | Atomically Precise Clusters of Noble Metals: Emerging Link between Atoms and Nanoparticles[END_REF][START_REF] Wang | Role of Anions Associated with the Formation and Properties of Silver Clusters Acc[END_REF][START_REF] Parker | The Story of a Monodisperse Gold Nanoparticle: Au25L18[END_REF][START_REF] Jin | Doping and alloying in atomically precise gold nanoparticles[END_REF][START_REF] Sharma | Structurally Precise Dichalcogenolate-Protected Copper and Silver Superatomic Nanoclusters and Their Alloys[END_REF] In general these atomically precise NCs are protected by monothiols, dithiols, carbenes, tertiary phosphines, halogens, etc. In recent years, a class of nanoscale metal-hydride species has gradually expanded from copper-rich clusters to gold-or silver-rich clusters. [START_REF] Yuan | Combinatorial Identification of Hydrides in a Ligated Ag40 Nanocluster with Noncompact Metal Core[END_REF][START_REF] Yi | Superatom-in-Superatom [RhH@Ag24(SPhMe2)18] 2-Nanocluster Angew[END_REF][START_REF] Takano | Hydride-Doped Gold Superatom (Au9H) 2+ : Synthesis, Structure, and Transformation[END_REF][START_REF] Takano | Hydride-Mediated Controlled Growth of a Bimetallic (Pd@Au8) 2+ Superatom to a Hydride-Doped (HPd@Au10) 3+ Superatom[END_REF][START_REF] Yuan | Ultrastable Hydrido Gold Nanoclusters with the Protection of Phosphines[END_REF][START_REF] Dong | The synthesis and characterization of a new diphosphine-protected gold hydride nanocluster[END_REF][START_REF] Dong | The Synthesis, Bonding, and Transformation of a Ligand-Protected Gold Nanohydride Cluster[END_REF][START_REF] Wei | Au16Ag43H12(SPhCl2)34] 5-: An Au-Ag Alloy Nanocluster with 12 Hydrides and Its Enlightenment on Nanocluster Structural Evolution[END_REF][START_REF] Zhu | Structural determination of a metastable Ag27 nanocluster and its transformations into Ag8 and Ag29 nanoclusters[END_REF] However, most of these clusters (except copper hydrides) are metastable products and they have been extremely challenging in the characterization of hydride positions. As the smallest ligand, H -inclines to occupy positions situated inside the metal core, leading to deformation of the metal framework.

After striping the inner hydride by heating, structure changes accompanied with alteration of cluster nuclearity are frequently observed. [START_REF] Dong | The Synthesis, Bonding, and Transformation of a Ligand-Protected Gold Nanohydride Cluster[END_REF][START_REF] Wei | Au16Ag43H12(SPhCl2)34] 5-: An Au-Ag Alloy Nanocluster with 12 Hydrides and Its Enlightenment on Nanocluster Structural Evolution[END_REF][START_REF] Zhu | Structural determination of a metastable Ag27 nanocluster and its transformations into Ag8 and Ag29 nanoclusters[END_REF][START_REF] Ito | Controlled Dimerization and Bonding Scheme of Icosahedral M@Au12 (M=Pd, Pt) Superatoms[END_REF][START_REF] Zhong | A Two-Electron Silver Superatom Isolated from Thermally Induced Internal Redox Reactions of a Silver(I) Hydride[END_REF][START_REF] Charkrahari | Isolation and Structural Elucidation of 15-Nuclear Copper Dihydride Clusters: An Intermediate in the Formation of a Two-Electron Copper Superatom[END_REF] Hence more researches on metal hydrides are needed to facilitate the understanding of metal nanocluster evolutions, especially for those that were formed via reduction routes.

Upon reacting with Lewis acids such as salts of group 11 metals, interstitial hydrides can behave as 2-electron ligands to establish donor-acceptor relationships. 18- 20 Examples are explicitly demonstrated on the two encapsulated hydrides of [Cu11H2(dtp)6(C2Ph)3]. [START_REF] Silahahi | Reactivities of Interstitial Hydrides in a Cu11 Template: En Route to Bimetallic Clusters[END_REF]21 In addition, an interstitial hydride connected to noble metals, whose electronegativity values are larger than that of H, can behave as a "metallic" hydrogen. [START_REF] Yi | Superatom-in-Superatom [RhH@Ag24(SPhMe2)18] 2-Nanocluster Angew[END_REF][START_REF] Takano | Hydride-Doped Gold Superatom (Au9H) 2+ : Synthesis, Structure, and Transformation[END_REF][START_REF] Takano | Hydride-Mediated Controlled Growth of a Bimetallic (Pd@Au8) 2+ Superatom to a Hydride-Doped (HPd@Au10) 3+ Superatom[END_REF][START_REF] Yuan | Ultrastable Hydrido Gold Nanoclusters with the Protection of Phosphines[END_REF][START_REF] Dong | The synthesis and characterization of a new diphosphine-protected gold hydride nanocluster[END_REF][START_REF] Dong | The Synthesis, Bonding, and Transformation of a Ligand-Protected Gold Nanohydride Cluster[END_REF] Tsukuda and co-workers reported that the hydride dopant in (HPd@Au10) 3+ contributes to the cluster 8-electron count, (1S) [START_REF] Chakraborty | Atomically Precise Clusters of Noble Metals: Emerging Link between Atoms and Nanoparticles[END_REF] (1P) [START_REF] Sharma | Structurally Precise Dichalcogenolate-Protected Copper and Silver Superatomic Nanoclusters and Their Alloys[END_REF] . [START_REF] Takano | Hydride-Mediated Controlled Growth of a Bimetallic (Pd@Au8) 2+ Superatom to a Hydride-Doped (HPd@Au10) 3+ Superatom[END_REF] Sim and Lee put forward to a concept of superatom-in-superatom, in which the hydride dopant in [RhH@Ag24(SPhMe2)18] 2-NC provides one electron to the Rh atom, an open d-shell ([Kr]4d 8 5s 1 ), to form a RhH "superatom" corresponding to a closed shell ([Kr]4d [START_REF] Takano | Hydride-Mediated Controlled Growth of a Bimetallic (Pd@Au8) 2+ Superatom to a Hydride-Doped (HPd@Au10) 3+ Superatom[END_REF] ). [START_REF] Yi | Superatom-in-Superatom [RhH@Ag24(SPhMe2)18] 2-Nanocluster Angew[END_REF] Unfortunately, the hydride position within these two clusters was only proposed by DFT calculations. [START_REF] Yi | Superatom-in-Superatom [RhH@Ag24(SPhMe2)18] 2-Nanocluster Angew[END_REF][START_REF] Takano | Hydride-Mediated Controlled Growth of a Bimetallic (Pd@Au8) 2+ Superatom to a Hydride-Doped (HPd@Au10) 3+ Superatom[END_REF] Herein, we provide the first structure proof of hydride being a part of superatom by the synthesis of a new hydride-containing 8-electron alloy cluster, [PtHAg19{S2P(O n Pr)2}12] (1), which is fully characterized by ESI-MS spectrometry, UV-vis spectrum, multi-NMR, single crystal X-ray and neutron diffractions.

Additionally, a slightly different metal-framework is observed on its Se-analogue, [PtHAg19{Se2P(O i Pr)2}12] (2), formed via ligand-exchange induced structure transformation (LEIST) method. [START_REF] Knng | Transformation of Atomically Precise Nanoclusters by Ligand-Exchange[END_REF][START_REF] Dhayal | Diselenophosphates Induced Conversion of An Achiral [Cu20(H)11{S2P(O i Pr)2}9] into A Chiral [Cu20(H)11{Se2P(O i Pr)2}9] Polyhydrido Nanocluster[END_REF] The photoluminescence at 77K is also enhanced after LEIST. To the best of our knowledge, [PtHAg19{S2P(O n Pr)2}12] ( 1) is the first hydride-containing bimetallic superatom certified by neutron diffraction of which the hydride electron participates to the superatomic electron count, [PtH@Ag12] 5+ , forming an 8-electron species.

Results and discussion

In previous works, we have identified [M@Ag20(dtp/dsep)12] (M = Pt, [START_REF] Chiu | Homoleptic Platinum/Silver Superatoms Protected by Dithiolates: Linear Assemblies of Two and Three Centered Icosahedra Isolobal to Ne2 and I3[END_REF][START_REF] Chiu | All-selenolate-protected eight-electron platinum/silver nanoclusters[END_REF] Both simulated isotopic patterns match well with their experimental observations. The X-ray structures of 1 and 2 are depicted in Figure 2 and selected bond distances and angles are given in Table 1. Both metal frameworks of 1 and 2 show a PtH motif encapsulated in a distorted Ag12 icosahedron (Figure 2a), with seven capping Ag atoms (Agcap) around the icosahedron surface (Figure 2b). Whereas the PtHAg12 cores in 1 and 2 are similar, the arrangements of the seven Agcap atoms are different.

The difference comes from one of the seven Agcap atoms which migrates onto another Ag3 triangle upon going from 1 to 2. Hence, the PtHAg19 framework of 1 possesses C1 symmetry, while it approximates C3 symmetry in 2. Similar M20 arrangements have been shown to exist in related 8-electron M20(dtp/dsep)12 NCs, i.e., Ag20 (C1), 27 AuAg19 (C1), [START_REF] Lin | Synthesis, structural characterization and transformation of an eight-electron superatomic alloy[END_REF] Cu3.5Ag16.5 (C1 29 and C3 30 ), Cu2.5AuAg16.5 (C1), [START_REF] Yen | A Homoleptic Silver-Rich Trimetallic M20 Nanocluster[END_REF] and Ag20 (C3). [START_REF] Dhayal | Ag20{S2P(OR)2}12]: A superatom complex with a chiral metallic core and high potential for isomerism[END_REF][START_REF] Chang | Hereroatom-Doping Increases Cluster Nuclearity: From An[END_REF] However, a distinct feature of 1 and 2 is that their Ag12 icosahedron is substantially distorted away from ideal Ih symmetry. This distortion can be described as the enlargement of one of the icosahedral faces with Ag…Ag distances of 3.3143(7), 3.2140(8) and 3.2075(7) Å in the case of 1, and 3.3653(9), 3.2454(9) and 3.2304(9) Å in the case of 2 (Figure 2c and Figure S1). Such distortion is also reflected from the continuous symmetry measurement (CSM) values. [START_REF] Zabrodsky | Continuous Symmetry Measures[END_REF] With respect to an ideal icosahedron which has zero CSM value, the calculated CSM for the PtHAg12 cores in 1 and 2 are 0.16 and 0.15, which are substantially larger than that in the PtAg12 core of PtAg20(dtp)12 (0.05). [START_REF] Chiu | Homoleptic Platinum/Silver Superatoms Protected by Dithiolates: Linear Assemblies of Two and Three Centered Icosahedra Isolobal to Ne2 and I3[END_REF] It is worth noting that a much larger CSM value (0.27) was found for the RhH@Ag12 core of the [RhH@Ag24(SPhMe2)18] 2-NC, to reveal a wider open site that suggests the presence of hydride in the cluster core. [START_REF] Yi | Superatom-in-Superatom [RhH@Ag24(SPhMe2)18] 2-Nanocluster Angew[END_REF] This icosahedral distortion does not much affect the surrounding capping atoms. Although the arrangement and the number of Agcap atoms in 1 are different from those in PtAg20(dtp)12, the Agcap-Agico distances are similar (avg. 3.0151(6) Å in 1, avg. 2.9813(9) Å in PtAg20(dtp)12).

The positions of the hydride in 1 and 2 were found from the residual densities in the X-ray data and could be refined with some constraint. Furthermore, a neutron diffraction investigation was carried out on 1 (structure 1N), confirming unambiguously the hydride position inside a tetrahedron composed of a Pt and the expanded (Agico)3 triangular faces (Figure 2d) that contains Ag3, Ag4 and Ag9. The Pt-H distance (1.67(4) Å) is significantly shorter than the Agico-H ones (avg. 1.93(5) Å), revealing substantially stronger bonding. The averaged∠Agico-H-Agico and ∠Pt-H-Agico angles (114(3)˚ and 104(2)˚, respectively) are indicative of a distorted tetrahedral μ4-H coordination. Thus, the connection of the hydride to a triangular icosahedral face induces its expansion (Figure S1). The encapsulated PtH motif is iso-electronic to Au, in a similar way as the encapsulated RhH motif in [RhHAg24(SR)18] 2-is isoelectronic to Pd. [START_REF] Yi | Superatom-in-Superatom [RhH@Ag24(SPhMe2)18] 2-Nanocluster Angew[END_REF] Thus the whole structure in 1 and 2 can be described as an 8-electron [PtH@Ag12] 5+ core protected by an outer [Ag7(dtp/dsep)12] 5-shell (Figure 2e). The X-ray structure of 2 located also the hydride connected to Pt and to the expanded icosahedral triangle. As compared to 1, the different topology in the Agcap distribution (Figure 2b) induces also different orientations of the surrounding ligands. The twelve ligands in 2 can be grouped into four coordination environments related to C3 symmetry (Figure 2e, LA-LD), with three dsep ligands in each domain. LA and LD exhibit η 2 (μ2, μ1) and η 3 (μ2, μ1) connecting modes, located around the 3-fold axis, at the top and bottom respectively. LB and LC are alternatively situated around the belt, exhibiting η 3 (μ2, μ1) and η 3 (μ2, μ2) modes, respectively. On the other hand, the twelve dtp ligands in 1 are chemically inequivalent, due to the cluster C1 symmetry.

The hydride presence is unequivocally confirmed by the 1 H NMR spectra of 1 and 2, and their hydride resonances in negative values were observed at low frequencies.

The hydride chemical shift δ( 1 H) at ambient temperature displays an un-resolved resonance flanked with platinum satellites at -10.8 ppm ( 1 JPtH = 499 z) for 2 and -12.3 ppm ( 1 JPtH = 491 Hz) for 1, respectively (Figure 3 and Figure 4). The VT 1 H NMR experiment of 2 shows a gradually resolved hydride splitting pattern and slightly downfielded shift upon decreasing the temperature (Figure 3). At 173K only one pseudo quartet centered at -9.7 ppm accompanied by a set of platinum satellite can be seen. The observed splitting pattern results from the hydride coupled to three 107 Ag/ 109 Ag nuclei and one 195 Pt nuclei, which is confirmed by its simulated spectrum by using the following parameters: [START_REF] Jin | Atomically Precise Colloidal Metal Nanoclusters and Nanoparticles: Fundamentals and Opportunities[END_REF]

J( 1 H-107 Ag) = 44 Hz, 1 J( 1 H-109 Ag) = 50 Hz, 1 J( 1 H-195 Pt) = 502
Hz (Figure S2). Hence, the NMR spectroscopic result matches perfectly with the hydride coordination environment as revealed by neutron diffraction. The hydride atom is buried within a (PtAg3) tetrahedral cavity, coordinating to the central Pt and three Agico atoms. Surprisingly, the VT 1 H NMR experiment of 1 not only shows a gradually resolved hydride splitting pattern but also splits into two pseudo quartets upon lowering the temperature (Figure 4a). The 1 H{ 195 Pt} decoupling experiment removed the effect of overlapped Pt satellites and further confirmed two hydride resonances centered at -11.8 and -12.7 ppm at 173K (Figure 4b). The hydride signal of 1 does not broaden until 193K, while peak broadening of 2 is observed at 253K. A much faster movement of the peripheral Agcap atoms is assumed in 1, swapping on the triangular planes of the icosahedron. The result suggests that a rapid exchange process between two isomers of different symmetries occurs at ambient temperature. The molecular motion slows down by lowering the temperature to 173K to observe both isomers in solution. Such a fluxional behavior is also revealed in the VT 31 P{ 1 H} NMR spectrum of 2 (Figure 3b).

Two distinct broad resonances at 64.5 and 68.1 ppm were observed at ambient temperature, suggesting that both C1 and C3 isomers of 2 are present in solution. The major resonance resolves into four peaks with approximately equal intensity at 173 K, corresponding to the four coordination environments (LA-LD in Figure 2e) of the dsep ligands in the pseudo-C3 solid-state structure of 2. These results undoubtedly suggest that the two isomers of 2 existing in solution at ambient temperature transform into the more stable pseudo-C3 form at low temperature. Unfortunately, the VT 31 P{ 1 H} NMR spectrum of 1 (Figure S3) shows a complicated un-resolved pattern due to the existence of isomeric mixture at 173K. Thus the isomerization process of 1 monitored by VT 31 P{ 1 H} NMR spectroscopy is not informative.

The 195 Pt{ 1 H} NMR spectrum of 2 exhibits an extraordinary broad resonance ranging from -8320 to -8890 ppm at 293K, and appears at -8798.3 ppm at 173K (Figure S4), which is the most up-fielded shift among the reported resonances, [START_REF] Still | Pt NMRtheory and application[END_REF] such as in [Pt(H)(AuPPh3)8] + (-5673 ppm) [START_REF] Bour | Hydride platinum gold clusters: synthesis and characterization[END_REF] and [Pt(H)(AgNO3)2(AuPPh3)8] 3+ (-6348 ppm). [START_REF] Kappen | Cluster Growth: Some Representative Reactions. Crystal Structures of [Pt(H)(AgNO3)[END_REF] The 1 H{ 195 Pt} experiments were performed by recording 1 H nuclei decoupled with various ranges of 195 Pt magnetic field at 293 K (Figure S5). When the decoupling range approaches the signal of Pt, the platinum satellites in the 1 H{ 195 Pt} NMR spectrum disappear, confirming that the hydride is bound to the Pt atom. On the other hand, the 195 Pt{ 1 H} NMR spectrum of 1 (Figure 4c) at 293K shows a broad singlet at -8800 ppm due to the rapid movement of the whole molecule, suggesting the existence of fluxional behavior similar to those observed in both 31 P{ 1 H} and 1 H{ 31 P} spectra. It further splits into two singlets at -8753.6 and -8869.7 ppm upon decreasing the temperature, indicating the presence of two isomers probably those of C1 and C3 symmetries. The 1 H{ 195 Pt} NMR spectra of 1 at 293K recorded under various 195 Pt decoupling ranges show a similar pattern as 2 (Figure S6). The 1 H{ 195 Pt} experiments at 173K (Figure S7) confirm that the more down-fielded resonance at -11.7 ppm is related to the more upfielded resonance at -8869.7 ppm in the 195 Pt{ 1 H} spectrum, and vice versa.

Considering both coupling constants 1 J( 1 H-107 Ag) and 1 J( 1 H-109 Ag) related to -12.5 ppm in 1 at 173 K (Figure 4a), they are the same as those in the 1 H NMR spectrum of 2 at 173 K (Figure 3a), indicating a highly similar environment for the interstitial hydride. Therefore, the resonance at -11.7 ppm with higher intensity can be assigned to the cluster of C1 symmetry, and the minor resonance could be its C3 isomer.

The UV-Vis absorption spectrum of 1 (Figure 5a) depicts one major absorption band centered at 419 nm, which is similar to that of [PtAg20{S2P(O n Pr)2}12] (412 nm). [START_REF] Chiu | Homoleptic Platinum/Silver Superatoms Protected by Dithiolates: Linear Assemblies of Two and Three Centered Icosahedra Isolobal to Ne2 and I3[END_REF] 2 exhibits two absorption bands at 388 and 468 nm (Figure 5b), slightly red-shifted compared with 1. In addition, we found that the ligand nature can enhance the photoluminescence (PL) properties. Compound 1 did not exhibit any PL even at 77K, but its Se analogue 2 displayed a strong PL (636 nm) at 77K. The lifetime of 2 (~11 μs) suggests phosphorescence (Figure S8).

Compound 1 is thermally stable at ambient temperature in THF-d8 solution, as shown by the permanence of their [START_REF] Chang | Hereroatom-Doping Increases Cluster Nuclearity: From An[END_REF] P NMR spectra during a 3-month period (Figure S9). However, the persistence of 1 in chloro-solvents is not as good and partial decompositions into [PtAg20{S2P(O n Pr)2}12] and [Ag{S2P(O n Pr)2}]n in CDCl3 at room temperature was observed after 4 days (Figure S10). Compounds 1 and 2, were investigated by DFT calculations at the BP86/Def2-TZVP level of calculations (see Computational Details in the SI). For the sake of computational limitations, the dtp and dsep ligands were replaced by S2PH2 and Se2PH2 models, respectively, a simplification which has been proved to be reasonable in many past investigations. [START_REF] Zhong | A Two-Electron Silver Superatom Isolated from Thermally Induced Internal Redox Reactions of a Silver(I) Hydride[END_REF][START_REF] Charkrahari | Isolation and Structural Elucidation of 15-Nuclear Copper Dihydride Clusters: An Intermediate in the Formation of a Two-Electron Copper Superatom[END_REF][START_REF] Silahahi | Reactivities of Interstitial Hydrides in a Cu11 Template: En Route to Bimetallic Clusters[END_REF]21,[START_REF] Chiu | Homoleptic Platinum/Silver Superatoms Protected by Dithiolates: Linear Assemblies of Two and Three Centered Icosahedra Isolobal to Ne2 and I3[END_REF][START_REF] Barik | Mono-and Hexa-Palladium Doped Silver Nanoclusters Stabilized by Dithiolates[END_REF][START_REF] Dhayal | Ag20{S2P(OR)2}12]: A superatom complex with a chiral metallic core and high potential for isomerism[END_REF][START_REF] Lin | Synthesis, structural characterization and transformation of an eight-electron superatomic alloy[END_REF][START_REF] Zhong | Doping effect on the structure and properties of eight-electron silver nanoclusters[END_REF] For each ligand, both C1 and C3 structures were considered. The resulting computed models are labelled 1'(C1), 1'(C3), 2'(C1) and 2'(C3) in the followings. It is of note that the C1 and C3 isomers of 1' and 2' provided very similar computed results. This is exemplified by their very close total energy differences (0.6 kcal/mol for 1' and 1.7 kcal/mol for 2', the C3 isomer being the most stable in both species) and free energy differences (1.8 and 0.8 kcal/mol, respectively). At our level of modeling, these energy differences are barely significantly different from zero, thus supporting the fact that both isomers can coexist in solution.

Selected computed data are given in Table 1, Table 2 andTable S3. The computed metrics of 1'(C1) and 2'(C3) (Table 1) are in good agreement with their experimental counterparts, with a small overestimation (lower than 3%) of bond distances. In particular, the icosahedron distortion and the µ4 coordination mode of the hydride are well reproduced. In the four models, both Pt and H are negatively charged (Table 2), although the charge of H is significantly lower than that found usually for typical hydrides, for example -0.65 in [Ag7(H)(S2PH2)6]. [START_REF] Liu | Ag7(H){E2P(OR)2}6] (E = Se, S): Precursors for the Fabrication of Silver Nanoparticles[END_REF] The Wiberg bond indices are consistent with the existence of significant Pt-H covalent bonding and weaker, but nonnegligible, Ag-H bonding. The Pt-Ag and Ag….Ag interactions are of the same order of magnitude as those found in the relative 8-electron [PtAg20(S2PH2)12] (see Table 2).

Owing to the similarities between the four computed models, we only describe below the electronic structure of 1'(C3). Its Kohn-Sham orbital diagram is shown in Figure 6 besides that of the 8-electron [Ag20(S2PH2)12] and [PtAg20(S2PH2)12] models. The frontier orbitals of the three models are plotted in Figure S11. One goes from [Ag20(S2PH2)12] to 1' by replacing the encapsulated Ag in the former by an isoelectronic Pt-H unit in the latter. One goes from 1' to [PtAg20(S2PH2)12] by removing the encapsulated H in the former and adding a supplementary capping (outer) Ag atom in the latter. The diagrams of Figure 6 clearly show similar electronic features for the three compounds. Their three highest occupied orbitals can be easily identified as the 1P superatomic orbitals (with 2% H participation in the case of 1') and their five lowest vacant ones to the 1D levels (see Figure S11). For the three clusters, a unique 1S orbital cannot be identified, due to substantial mixing with metal d-type combinations. Thus, despite its distorted icosahedral core, 1' is, like its [Ag20(S2PH2)12] and [PtAg20(S2PH2)12] congeners, an 8-electron superatoms.

In order to analyze more deeply the role played by the encapsulated hydride in the electronic structure of 1' and 2', calculations were carried out on their bare superatomic core [PtHAg12] 5+ (selected results in Table 2). Its optimized structure, of C3v symmetry (Figure S12), matches reasonably well with that of 1' and 2' (Pt-H = 1.653, Ag-H = 2.238, Pt-Ag(av.) = 2.982 Å), except from the fact that, owing to its large cationic charge, free [PtHAg12] 5+ is more expanded than when stabilized as the passivated core of 1'. Its charge distribution and Wiberg indices are consistent with those of 1' and 2'.

Its electronic structure can be rationalized on the basis of the interaction between the [PtAg12] 5+ cage and its encapsulated hydrogen atom, as sketched in the qualitative MO diagram of Figure 7. Considered as isolated, the 7-electron [PtAg12] 5+ fragment is an unstable electron-deficient superatom. However, it reaches closed-shell stability by encapsulating the H-atom, through interaction of its 5dz 2 (Pt) orbital with the 1s(H) AO (assuming the z and C3 axes colinear), leading to the formation of an occupied Pt-H bonding orbital and a vacant antibonding combination that provokes the complete filling of the 1P shell. Thus, [PtHAg12] 5+ is an 8-electron superatom that contains an encapsulated Pt-H unit. Of course, the 2 electrons associated with the Pt-H bond get somewhat delocalized onto the whole cluster cage, through some participation to the superatomic orbitals of the 1s(H) and, to a lesser extent, the 5dz 2 (Pt) orbitals. Going from [PtAg20(S2PH2)12] to 1' corresponds to the replacement of a 5dz 2 (Pt) lone pair in the former by a (Pt-H) bonding pair in the latter. Of course, this rather low-lying (Pt-H) orbitals is also present in 1' (see Figure 6), with Pt, H and Ag12 participation of 15, 44 and 39%, respectively. In both [PtAg20(S2PH2)12] and 1', the electron pair in question is (moderately) involved in cluster bonding; weakly in the case of 5dz 2 (Pt) of [PtAg20(S2PH2)12] 37-39 and somewhat more importantly in the case of (Pt-H) in 1'. This stronger bonding in the latter case helps compensating the energy loss upon distortion of the icosahedral cage.

Consistently with the fact that the electron of the encapsulated hydrogen participates to the superatom electron count, adding two supplementary electrons to [PtHAg12] 5+ , i.e. making [PtHAg12] 3+ results in a structure in which the hydride is expelled outside the cage to become a regular µ3-H outer ligand (see Figure S12). Thus, the [PtHAg12] 3+ model consists of a regular 8-electron [PtAg12] 4+ superatomic core, "protected" by one capping hydride.

The TD-DFT UV-Vis spectra simulated at the CAM-B3LYP/Def2-TZVP level (see Computational Details in the SI) of both the C1 and C3 isomers of 1' and 2' are shown together with the recorded spectra of 1 and 2 in Figure 5. The spectra show little difference between isomers and there is a good overall agreement between them and their experimental counterparts. The low-energy bands are associated with 1P→1D transitions, as in the [PtAg20(dtp/desp)12] and [Ag20(dtp/desp)12] species.

Conclusion

In summary, two hydride-containing 8-electron Pt/Ag alloy NCs, [PtHAg19{S2P(O n Pr)2}12] (1) and [PtHAg19{Se2P(O i Pr)2}12] (2), were successfully isolated and the LEIST method was used to synthesize 2 via the reaction of 1 with dsep ligands. The former compound is the first hydride-containing 8-e superatom, of which the structure was fully ascertained by neutron diffraction. The encapsulated hydride leads to the expansion of one triangular face of the icosahedron and sits inside the tetrahedron formed by this face and the central Pt atom. The electron of the interstitial hydride participates in the [PtH@Ag12] 5+ superatomic electron count, which is isoelectronic to [Au@Ag12] 5+ . On the other hand, the 1s(H) orbital participates only moderately to the superatomic orbitals, but more importantly to the building of a Pt-H bonding orbital with the 5dz 2 (Pt) orbital. The hydride coordination environment is in good agreement with the NMR spectroscopy. Whereas the solid-state structure of 1 is of C1 symmetry, that of 2 is C3. This difference originates from slightly different configurations in their outer spheres. Both VT 1 H and 31 P{ 1 H} NMR spectra of 2 show that isomers with different symmetries co-exist in solution at ambient temperature and the isomer of C3 symmetry is a dominant structure at 173 K, in agreement with the DFT results. Moreover, an enhancement of photoluminescence is also observed after structure distortion induced by ligand exchange of sulfur-donors (dtp) by seleniumdonor ligands (dsep).

  Pd; 26 dtp and dsep denote dithiophosphate and diselenophosphate, respectively) alloy NCs. They consist of an 8-electron superatomic core [M@Ag12] 4+ protected by an outer shell made up of 8 peripheral capping Ag + and 12 dtp -or dsep -dichalcogenolate ligands. The heterometal M is located at the center of an Ag12 icosahedron. The alloys passivated by S-donor ligands were synthesized by a one-pot co-reduction method, as exemplified by the formation of [PtAg20(dtp)12] from the reaction of [Ag(CH3CN)4]PF6, [Pt{S2P(O n Pr)2}2], and NH4[S2P(O n Pr)2] followed by the addition of NaBH4 into the reaction flask. The residual products were separated by column chromatography. In fact, [PtHAg19{S2P(O n Pr)2}12] (1) was found in one of the several bands issuing from the same reaction and could be purified, thanks to its polarity different from that of [PtAg20{S2P(O n Pr)2}12]. A ligand replacement process was successfully performed by adding 12 equiv. of NH4[Se2P(O i Pr)2] into [PtHAg19{S2P(O n Pr)2}12] to yield [PtHAg19{Se2P(O i Pr)2}12] (2) within one minute. It is of note that a prolonged stirring results in decomposition due to the light-sensitive nature of the selenium-donor ligands. The compositions of 1 and 2 were first determined by positive-mode ESI mass spectrometry. The peak observed at m/z 4911.2669 Da in Figure 1a corresponds to the adduct ion [1 + Ag + ] + (calc. m/z: 4911.2957 Da). In the spectrum of 2 (Figure 1b), the ion peak at m/z 6038.1291 Da corresponds to [2 + Ag + ] + . (calc. m/z: 6037.9743 Da).

Figure 1 .

 1 Figure 1. (a) Positive-mode ESI mass spectrum of 1. Insets: experimental (black) and simulated (red) isotopic distribution of the ion peak [1 + Ag + ] + . (b) Positive-mode ESI mass spectrum of 2. Insets: experimental (black) and simulated (red) isotopic distribution of the ion peak [2 + Ag + ] + .

Figure 2 .

 2 Figure 2. (a) The "PtH" unit enclosed in the Ag12 icosahedral skeleton. (b) The metal framework of 1 (left) and 2 (right). (c) A schematic representation of the Agico-Agico distance distributions in 1 (PtH@Ag12, left) and [PtAg20{S2P(O n Pr)2}12] (Pt@Ag12,

Figure 3 .

 3 Figure 3. (a) The VT 1 H NMR (THF-d8, δ, ppm) of 2. The hydride resonance: -10.8 ( 1 J1H-195Pt = 499 Hz at 293K), -9.7 ( 1 J1H-195Pt = 502 Hz, 1 J1H-107Ag = 44 Hz, 1 J1H-109Ag = 50 Hz at 173K), and (b) VT 31 P{ 1 H} spectra of 2.

Figure 4 .

 4 Figure 4. (a) VT 1 H NMR (THF-d8, δ, ppm) spectra. The hydride resonance: -12.3 ( 1 J1H-195Pt = 491 Hz at 293K), -11.7 ( 1 J1H-195Pt = 485 Hz, 1 J1H-107Ag = 37 Hz, 1 J1H-109Ag = 43 Hz at 173K) and -12.5 ( 1 J1H-195Pt = 485 Hz, 1 J1H-107Ag = 44 Hz, 1 J1H-109Ag = 50 Hz at 173K), (b) VT 1 H{ 195 Pt}, and (c) VT 195 Pt{ 1 H} NMR spectra of 1.

Figure 5 .

 5 Figure 5. (a) Absorption spectra of 1 (red), 1' (C1, blue), and 1' (C3, green). (b) Absorption spectra of 2 (red), 2' (C3, green), 2' (C1, blue), and emission spectrum of 2 (brown).

Figure 6 .

 6 Figure 6. Kohn-Sham orbital diagrams of the models [Ag20(dtp)12], [PtHAg19(dtp)12] (1') and [PtAg20(dtp)12] (dtp = S2PH2).

Figure 7 .

 7 Figure 7. Simplified interaction MO diagram for the 8-electron [PtHAg12] 5+ superatom.

Table 1 .

 1 Selected experimental bond distances (Å) and angles (deg.) for 1, 1N, [PtAg20{S2P(O n Pr)2}12], 2, and [PtAg20{Se2P(O i Pr)2}12], and DFToptimized counterparts in 1'(C1) and 2'(C1).

		[PtHAg19{S2P(O n Pr)2}12]	[PtHAg19{S2P(O n Pr)2}12]	[PtHAg19(S2PH2)12]		[PtHAg19{Se2P(O i Pr)2}12]	[PtHAg19(Se2PH2)12]
					[PtAg20{S2P(O n Pr)2}12]			[PtAg20{Se2P(O i Pr)2}12]
		(1, X-ray)	(1N , neutron)	(1', DFT)		(2)	(2', DFT)
	symmetry	C1	C1	C1	C2	C3	C3	T
	CSM	0.15	0.16	0.17	0.05	0.15	0.13	0.02
	Mcent-Agico

Table 2 .

 2 Selected computed data for 1'(C1), 1'(C3), 2'(C1) and 2'(C3) and related species.

		[PtHAg12] 5+	1'(C1)	1'(C3)	[PtAg20(S2PH2)12]	2'(C1)	2'(C3)
					(C3)
	HOMO-LUMO gap (eV)	2.74	1.71	1.96	1.80	1.48	1.69
	C1 vs. C3 relative energy (kcal/mol)		0.6	0.0		1.7	0.0
	C1 vs. C3 relative free energy (kcal/mol)		1.8	0.0		0.8	0.0
	Pt	-1.67	-1.13	-1.14	-1.35	-1.09	-1.08
	H	-0.39	-0.40	-0.41		-0.42	-0.40
	NAO charges
	Agico (av.)	0.59	0.36	0.36	0.29	0.34	0.33
	Agcap (av.)		0.70	0.70	0.70	0.65	0.66
	Pt-H	0.292	0.196	0.197		0.195	0.197
	Ag-H (av.)	0.086	0.101	0.103		0.101	0.098
	Wiberg bond
	Pt-Ag (av.)	0.216	0.135	0.133	0.148	0.123	0.125
	indices
	Agico-Agico (av.)	0.086	0.082	0.082	0.042	0.081	0.082
	Agcap-Agico (av.)		0.043	0.041	0.087	0.044	0.042

For table of content only


Mitja Nikolaus
email: mitja.nikolaus@univ-amu.fr

Laurent Prévot
email: laurent.prevot@univ-amu.fr

Communicative Feedback in Response to Children's Grammatical Errors

Keywords: language acquisition, communicative feedback, clarification requests, acknowledgements

Children learning their mother tongue engage in interactive communication starting from the early stages of their development. In a large-scale study of transcribed child-caregiver conversations, we investigated the role of Communicative Feedback in response to children's grammatical errors. We found evidence for both positive and negative feedback signals that are useful for learning the grammar of one's native language: Caregivers are more likely to provide acknowledgments if an utterance is grammatical, and they are more likely to ask for clarification if an utterance is ungrammatical. Further, we investigate how children react in response to negative communicative feedback signals and find evidence that grammaticality is improved in direct follow-ups to negative feedback signals. This study provides the largest and most comprehensive evidence supporting the presence and effectiveness of communicative feedback signals in grammar learning, broadening the literature on communicative feedback in language acquisition more generally.

Introduction

Long before their linguistic skills are fully developed, children engage in conversational exchanges with people around them, which allows them to refine their linguistic knowledge by leveraging various signals of language use in interaction [START_REF] Bohn | The Pervasive Role of Pragmatics in Early Language[END_REF][START_REF] Bruner | Child's Talk: Learning to Use Language[END_REF][START_REF] Clark | Conversation and Language Acquisition: A Pragmatic Approach[END_REF][START_REF] Tomasello | Constructing a Language: A Usage-Based Theory of Language Acquisition[END_REF]. One such signal is corrective feedback (and its variants such as negative evidence, reformulations, or recasts). It describes situations in which the caregiver provides the child with a corrected form of an erroneous utterance ("I goed to school." -"You went to school?"). This phenomenon has been studied extensively in the developmental literature, but the research community has not reached a consensus regarding its availability to children and/or its effectiveness for first language acquisition (e.g., [START_REF] Brown | Derivational complexity and order of acquisition in child speech[END_REF][START_REF] Chouinard | Adult reformulations of child errors as negative evidence[END_REF][START_REF] Clark | Conversational Repair and the Acquisition of Language[END_REF][START_REF] Demetras | Feedback to first language learners: the role of repetitions and clarification questions*[END_REF][START_REF] Farrar | Negative evidence and grammatical morpheme acquisition[END_REF][START_REF] Hiller | A Data-driven Investigation of Corrective Feedback on Subject Omission Errors in First Language Acquisition[END_REF][START_REF] Marcus | Negative evidence in language acquisition[END_REF][START_REF] Maynard | Conversation management in contrast: Listener response in Japanese and American English[END_REF][START_REF] Nelson | Syntax Acquisition: Impact of Experimental Variation in Adult Verbal Interaction with the Child[END_REF][START_REF] Saxton | Negative input for grammatical errors: effects after a lag of 12 weeks[END_REF].

In the current study, we focus on the role of another kind of social signal that has come to be called Communicative Feedback (hereafter, CF). CF represents signals that the listener (here, the caregiver) sends to the speaker (i.e., the child) to indicate communicative success or failure depending on whether the listener thinks they understood the meaning intended by the speaker (for an overview, see Nikolaus & Fourtassi, 2023). The main difference with corrective feedback is that CF does not necessarily aim at correcting the child but rather at reaching and maintaining mutual understanding between interlocutors (H. H. [START_REF] Clark | Using Language[END_REF]. Despite having a communicative rather than a teaching agenda, the child can still use such signals to learn, either by revising their erroneous linguistic assumptions or by confirming/reinforcing their correct knowledge [START_REF] Nikolaus | Modeling the Interaction Between Perception-Based and Production-Based Learning in Children's Early Acquisition of Semantic Knowledge[END_REF].

Suppose the child produces an erroneous utterance. Even if the child is not corrected (as in the case of recasts), they can receive negative signals of communication breakdown (e.g., a clarification request) that they can use to revise the expression of their communicative intent ("Went to school." -"Who went to school?" -"He went to school.").1 If the child produces a well-formed utterance, the caregiver can provide acknowledgments (e.g., backchannels), offering the child positive feedback of communication success and indirectly confirming their current hypotheses about the linguistic structures they used ("He went to school." -"Oh I see!").

Previous work has provided evidence for the role of such feedback in children transitioning from non-speech to speechlike vocalizations (i.e., babbling, [START_REF] Goldstein | Social interaction shapes babbling: Testing parallels between birdsong and speech[END_REF][START_REF] Lopez | Adult responses to infant prelinguistic vocalizations are associated with infant vocabulary: A home observation study[END_REF][START_REF] Warlaumont | A Social Feedback Loop for Speech Development and Its Reduction in Autism[END_REF] and for transitioning to the first intelligible words (Nikolaus, Prévot, & Fourtassi, 2022). Here, we investigate whether similar communicative signals are available and helpful to children in regard to the development of grammatical speech (at both the morphological and syntactic levels).

We consider negative CF when caregivers provide clarification requests ("Went to school." -"What?") and positive CF when caregivers provide backchannel responses (e.g., "uh-huh") or acknowledge repetitions ("He went to school." -"He went to school."). Some previous work did study the role of clarification requests and of exact repetitions as a (weak) learning signal [START_REF] Bohannon | The issue of negative evidence: Adult responses to children's language errors[END_REF][START_REF] Demetras | Feedback to first language learners: the role of repetitions and clarification questions*[END_REF], but findings from these studies have been difficult to interpret, given several methodological issues and contradicting results [START_REF] Marcus | Negative evidence in language acquisition[END_REF][START_REF] Maynard | Conversation management in contrast: Listener response in Japanese and American English[END_REF][START_REF] Morgan | Limits on negative information in language input*[END_REF]. More recently, the effects of negative feedback have been revisited in a corpus study of one child [START_REF] Saxton | Negative evidence and negative feedback: immediate effects on the grammaticality of child speech[END_REF] as well as in an intervention paradigm [START_REF] Saxton | The prompt hypothesis: Clarification requests as corrective input for grammatical errors[END_REF]. The findings suggest that children are indeed responsive to negative feedback as shown by an increase of grammatical follow-ups in response to errorcontingent clarification requests.

The current study Here, we present the largest (in terms of sample size) and most comprehensive corpus study of CF for grammatical errors in child-caregiver naturalistic conversations. We considered a wide range of positive and negative CF signals, including exact as well as partial repetitions ("I went to school." -"You went to school."), backchannel responses, and clarification requests of various kinds (open and restricted requests, as well as recasts). Thanks to automatic measures, we analyzed these cues in large-scale data of English-learning children conversing with their caregivers [START_REF] Macwhinney | The CHILDES Project: Tools for Analyzing Talk[END_REF]. We tested both 1) the usefulness of CF as reliable signals to children (i.e., more negative CF following ungrammatical utterances and more positive CF following grammatical utterances), and 2) the effect of these signals on children's grammatically as reflected in children's immediate follow-up utterances.

To ensure reproducibility, we make the source code of all analyses publicly available: https://github.com/ mitjanikolaus/childes-communicative-feedback.

Methods

Data

We analyzed 3-part micro-structure sequences consisting of 1) child's utterance, 2) caregiver response, and 3) the child follow-up (following previous work like [START_REF] Bavelas | Doing mutual understanding. Calibrating with micro-sequences in face-to-face dialogue[END_REF]; Nikolaus, Prévot, and Fourtassi (2022); [START_REF] Warlaumont | A Social Feedback Loop for Speech Development and Its Reduction in Autism[END_REF]). Hereafter, we will call this sequence URF (Utterance, Response, Follow-up). An example for such a sequence could look as follows:

Utterance (Child): Need some milk Response (Caregiver): Hm? Follow-up (Child): I need some milk.

-EllisWeismer corpus, LT/42pc/22175.cha Our analyses are based on transcribed conversations from a subset of the English CHILDES corpora [START_REF] Macwhinney | The CHILDES Project: Tools for Analyzing Talk[END_REF]. We follow Nikolaus, Prévot, and Fourtassi (2022) for the extraction of URF sequences and discard all sequences that contain non-speech and non-intelligible utterances.

Annotations and Corpus Selection

Grammaticality Corpora in CHILDES follow the CHAT transcription format (MacWhinney, 2017), which supports the annotation of grammatical errors using dedicated coding schemes. In order to obtain a better understanding of the quality and quantity of errors annotated, we grouped all annotated errors into error type classes, using a coding scheme slightly adapted from [START_REF] Hiller | A Data-driven Investigation of Corrective Feedback on Subject Omission Errors in First Language Acquisition[END_REF] and [START_REF] Saxton | The prompt hypothesis: Clarification requests as corrective input for grammatical errors[END_REF].2 A list of error types can be found in the legend of Figure 1. We excluded all utterances for which no obvious mapping could be made (sometimes error annotations are annotations of slang, such as "I'd [: I would]", or "I was runnin' [: running]"; these cases are not considered grammatical errors).

Figure 1 presents the proportion of child errors for different corpora. We find that there are only a few corpora in which a substantial number of errors were annotated. Inspecting more closely the distribution of error types, it becomes apparent that certain corpora only focused on certain error types (e.g., in the Kuczaj corpus, there were almost exclusively tense aspect errors annotated). In the following, we only considered corpora that (1) included at least 1% errors in child utterances and (2) included a range of different error types annotated. This left us we the following set of seven candidate corpora: Thomas, Providence, MPI-EVA-Manchester, Braunwald, Lara, EllisWeismer, and Bates.

For these candidate corpora, we performed some manual annotations as a sanity check for our research purposes. For each corpus, we randomly selected 3 transcripts. The first author annotated grammaticality (on a binary scale) of all children's utterances until we reached a threshold of 100 annotated utterances within the transcript. 1, inter-annotator agreement between our annotations and the annotations in CHILDES vary to a large degree. Importantly, however, we find that error precision is overall high and recall rather low, indicating that numerous errors were not annotated in CHILDES, but the errors that were annotated are generally agreed upon.

For the remainder of the paper, we only consider corpora for which we obtained substantial agreement scores: Providence [START_REF] Demuth | Word-minimality, Epenthesis and Coda Licensing in the Early Acquisition of English[END_REF], Lara [START_REF] Rowland | The effect of sampling on estimates of lexical specificity and error rates[END_REF], and EllisWeismer (Moyle, Weis- Clarification Requests We annotated clarification requests using two complementary approaches. First, we use a model for automatic annotation of speech acts in child-caregiver conversations [START_REF] Nikolaus | Large-scale study of speech acts' development in early childhood[END_REF] and select all utterances that are labelled as "Eliciting questions (e.g., hmm?)" or "Requests to repeat utterance". The model detected mostly open clarification requests, such as "what?", or "huh?".

Secondly, in order to include other kinds of clarification requests such as restricted requests and restricted offers (Dingemanse & Enfield, 2015) we also considered questions that are marked by repetition of the previous utterance (e.g., "Went to the house" -"Who went to the house?"). Previous research has found that repair often involves a repetition (Dingemanse & Enfield, 2015;[START_REF] Fusaroli | Measures and mechanisms of common ground: backchannels, conversational repair, and interactive alignment in free and task-oriented social interactions[END_REF][START_REF] Jefferson | Side Sequences[END_REF][START_REF] Kendrick | Other-initiated repair in English[END_REF][START_REF] Purver | Computational Models of Miscommunication Phenomena[END_REF][START_REF] Schegloff | The Preference for Self-Correction in the Organization of Repair in Conversation[END_REF].

We calculated repetition scores for all child utterances followed by a caregiver utterance.

After excluding a set of stopwords and stemming, we calculated rep utt = #words overlap/#words utt and rep response = #words overlap/#words response, where #words overlap is the number of words that are both in the utterance and the response, #words utt the words of the utterance and #words response the words of the response. We only counted unique words. Then, we randomly sampled a set of 200 utterance-response pairs for which the response was a question (marked by a question mark in the transcript) and the repetition ratios were greater than 0. We manually annotated these pairs for whether the response was a clarification request or not. 3 Figure 2 shows the relationship between the two repetition ratio measures and whether a response is a clarification request. The annotated data was used to train a logistic regression model 3 We included requests for confirmation ("He went to school." -"Did he?"), as they also communicate a negative feedback signal to the speaker: The interlocutor is not sure whether they understood the speaker correctly (see also [START_REF] Kendrick | Other-initiated repair in English[END_REF].

that classifies clarification requests based on the repetition ratios. 4 This classifier reached an F-score of 0.82 on the training set. The fitted decision boundary is shown in the graph. We found that for distinguishing clarification requests from other responses, mainly the response repetition ratio (rep response) was important. We annotated another 100 utterances as evaluation set and obtained an F-score of 0.85 (precision: 0.93, recall: 0.78).5 ture [START_REF] Fernández | Classifying Non-Sentential Utterances in Dialogue: A Machine Learning Approach[END_REF]. We manually annotated another 200 utterance-response pairs, but this time including only responses that were not finished with a question mark. All responses that approve the understanding of the child's utterance were marked as acknowledgements. Figure 3 shows the relationship between the two repetition ratio measures and whether a response is an acknowledgement. 6 We also fit a logistic regression to classify acknowledgements, which reached an F-score of 0.82 for the training utterances and 0.84 (precision: 0.82, recall: 0.82) on a separate set of 100 evaluation utterances. 7Table 2 provides an overview on the automatically annotated clarification requests and acknowledgements. ances. The graph suggests that clarification requests are used more often in response to ungrammatical sentences. We supported this hypothesis using a mixed-effects GLM that predicts whether a clarification request was given as a function of whether the child utterance was grammatical and child age (in months), including a random intercept for the child identifier. The estimated fixed effect for the grammaticality of the child utterances was negative (utt is grammatical : β = -0.516, SE = 0.055, p < 0.001), validating our observation. 8 Subsequently, as illustrated in Figure 5, we were interested in whether caregivers respond with clarification requests primarily to certain kinds of grammatical errors, or whether they are used for all kinds of errors. We found that the pattern of increased use of clarification requests is not specific to certain kinds of errors, but holds for almost all error types (with the exception of syntactic object errors). 8 The other fixed effect estimates indicated that caregivers use a decreasing number of clarification requests with increasing age of the child (age : β = -0.912, SE = 0.117, p < 0.001), and a slight decrease of the main effect with increasing child age (utt is grammatical*age : β = 0.566, SE = 0.221, p < 0.05).

Caregiver's Acknowledgements

Next, we turn to positive feedback which is provided in the form of acknowledgements. Figure 6 compares the difference in proportion of acknowledgements to grammatical and ungrammatical utterances. We found that acknowledgements are used more often in response to grammatical utterances (utt is grammatical : β = 0.2, SE = 0.033, p < 0.001), but this pattern is decreasing over the child's age as indicated by a negative interaction term (utt is grammatical*age : β = -0.891, SE = 0.167, p < 0.001). 9

Children's Follow-ups

Finally, we explored whether children directly respond to the negative feedback by increasing the grammaticality in their follow-up utterances. Figure 7 compares the proportion of grammatical child utterances before (utterance) and after (follow-up) the caregiver's response. In case the caregiver's response is a clarification request (right side), we observe a slight increase in grammaticality in the children's follow-ups. We fit a mixed-effects model to predict whether an utterance is grammatical depending on whether it is a follow-up (is follow up) and whether the response is a clarification request (resp is clar req), including random intercepts for the child identifier, child age, and conversation identifier. We found a significant positive interaction term resp is clar req*is follow up : β = 0.603, SE = 0.072, p < 0.001, demonstrating that the difference in grammaticality before and after a response is larger in the case of clarification request responses, than it is for other responses. 10 In a follow-up analyses we looked more closely at the kind of clarification request provided by the caregiver. We found that the grammaticality in follow-ups increased only after repetition-based clarification requests, and there was no ef- 9 The GLM definition was the same as in the case of clarification requests, except that we were predicting the use of acknowledgements. With increasing age, the overall probability of acknowledgements decreased slightly (age : β = -0.198, SE = 0.086, p < 0.05). 10 The other fixed effects indicated that grammaticality of followups is generally lower after clarification requests (resp is clar req : β = -0.231, SE = 0.039, p < 0.001), and that it is higher in followups (is follow up : β = 0.446, SE = 0.036, p < 0.001)).

Discussion

In the present corpus study, we investigated communicative signals provided by caregivers that could support children's acquisition of syntactic and morphological aspects of their native language. We found that caregivers provide both positive and negative communicative feedback in a reliable fashion: They use acknowledgments more often in response to children's grammatical utterances, and clarification requests more often in response to ungrammatical sentences. When analyzing children's ability to capitalize on these signals, we found that, indeed, the grammaticality of children's utterances increased in direct follow-ups to clarification requests from caregivers. The current studies provide quantitative evidence supporting the presence and effectiveness of communicative feedback signals in grammar learning, enriching the growing research on CF in language acquisition (E. V. [START_REF] Clark | Conversational Repair and the Acquisition of Language[END_REF]Nikolaus & Fourtassi, 2023).

The role of negative feedback Previous research on the presence of negative feedback led to mixed results [START_REF] Bohannon | The issue of negative evidence: Adult responses to children's language errors[END_REF][START_REF] Demetras | Feedback to first language learners: the role of repetitions and clarification questions*[END_REF][START_REF] Marcus | Negative evidence in language acquisition[END_REF][START_REF] Morgan | Limits on negative information in language input*[END_REF]. In particular, these results have been put into question for several reasons. Some lack inferential statistics, some findings could possibly be explained by averaging artifacts, and some studies conflated multiple error categories (phonological, lexical, and grammatical) [START_REF] Marcus | Negative evidence in language acquisition[END_REF]. Another major limitation of these previous studies was the relatively small sample size (due to the labor-intensive nature of manual annotation), which has led to generalizability issues. Here, we were able to perform a much larger-scale analysis thanks to automatic annotation techniques and aggregation of previously made and publicly available manual annotations. Further, we ensured that our analyses were not subject to previous criticisms. We focused exclusively on grammatical errors, and we employed mixed-effect GLMs which control more efficiently for possible averaging artifacts One surprising finding of the current study was that caregivers provided negative feedback to virtually all kinds of children's grammatical errors covered in this study (Figure 5). This seems to go against the predictions made by theories of CF for language learning (Nikolaus & Fourtassi, 2023). Indeed, one would expect that, if caregivers cared more about communication (and not as much about correction), they would provide more feedback in response to grammatical mistakes that impede more significantly the understanding of children's intended meaning, which is arguably the case for only a subset of the errors and would not include, e.g., errors of past tense inflection (i.e., whether the child says "goes" or "went" does not really impact the transmission of the child's intended meaning, and therefore, should a priori receive no negative CF signals). We investigated this observation a bit deeper by focusing on the specific case of tense aspect errors. We found that the negative CF signals in response to such errors are exclusively repetition-based (no open clarification requests). By examining the corresponding URF sequences, we found that they are often recasts ("I waked your mommy right up." -"You woke my mommy right up?"), and sometimes verbatim repetitions of the error without correction: "They breaked it open." -"They breaked it open?"). This suggests, indeed, that caregivers do not glean over grammatical mistakes even when these mistakes do not impede understanding. That said, caregivers' recasts can be understood as providing the child with both corrective feedback (a candidate understanding) and negative communicative feedback. Thus, the results of the current work do not only speak to theories of communicative feedback but also to some aspects of corrective feedback. Further work is needed to determine how communicative and corrective feedback precisely interact in caregiver language use across development.

The role of positive feedback Several studies found that caregivers respond with exact repetitions more often in response to grammatical than to ungrammatical utterances, and could therefore function as positive feedback [START_REF] Bohannon | The issue of negative evidence: Adult responses to children's language errors[END_REF][START_REF] Demetras | Feedback to first language learners: the role of repetitions and clarification questions*[END_REF][START_REF] Penner | Parental Responses to Grammatical and Ungrammatical Child Utterances[END_REF]. However, as mentioned earlier, these studies have been criticized for several methodological issues. Regarding the specific case of exact repetitions, [START_REF] Marcus | Negative evidence in language acquisition[END_REF] argued that the findings could be merely driven by the fact that almost all adults' utterances are grammatical, and therefore exact repetition of children's grammatical (as opposed to ungrammatical) utterances does not constitute evidence of parental sensitivity to children's grammatical errors. This argument does not apply to our case: The current study does not study caregiver's sensitivity to errors, but, rather, the availability of communicative cues that children can leverage for learning even if they do not have a corrective intent on the part of the caregiver.

Our results suggest that positive feedback in the form of acknowledgement is provided predominantly in response to children's grammatical sentences. However, this effect decreased significantly with age (cf. Figure 6). It appears that caregivers provide such explicit positive feedback mostly in early stages of development, until around the third year of age (this result should be taken with a grain of salt, as the data in the current study is not equally distributed across ages; it is concentrated for children aged 2 to 3 years and is very sparse for the rest). One interpretation of this finding is that, as soon as children start to produce longer and more sophisticated utterances, other (more implicit) forms of positive feedback become possible such as the contingency of a caregiver's response to a child utterance (see also [START_REF] Hoff-Ginsberg | Topic relations in mother-child conversation[END_REF]Nikolaus & Fourtassi, 2023). In other words, children require less explicit encouragement after each correct utterance; as they grow older, they can feel understood merely by having a coherent exchange with their interlocutor. In order to obtain a complete picture of CF signals in language acquisition, such implicit signals should be the focus of future work.

Limitations and future research directions One possible confound of our analysis on grammaticality of children's follow-ups after clarification requests (cf. Figure 7) is that children are more likely to produce shorter utterances (e.g., one-word replies) as follow-up to clarification requests and these are more likely to be grammatical. We investigated this possibility by restricting the analysis to utterances that have a minimum length of 2 (or 3) words. In both cases, the effect on the grammaticality of the follow-ups decreased but was still significant for the case of minimum length of 2 words.

More generally, this points to limitations of evaluating children's follow-ups as a means to study the children's sensitivity to feedback (Figure 7, as well as [START_REF] Saxton | Negative evidence and negative feedback: immediate effects on the grammaticality of child speech[END_REF][START_REF] Saxton | The prompt hypothesis: Clarification requests as corrective input for grammatical errors[END_REF]: This approach is only taking into account immediate and verbalized evidence of children's learning. In many cases, the child might actually understand and take the feedback into account, but not demonstrate it overtly/immediately. Such more long-term effects on learning can be studied using longitudinal data collection coupled with in-lab testing [START_REF] Bergelson | Nature and origins of the lexicon in 6-mo-olds[END_REF].

Another limitation of the present study is that it only considered verbal instantiations of communicative feedback signals that were possible to extract from the transcripts. Future work should include signals that are communicated nonverbally (e.g., head nods, frowns) or using prosodic cues (e.g., rising pitch) using multimodal corpora (e.g., [START_REF] Bodur | Using video calls to study children's conversational development: The case of backchannel signaling[END_REF][START_REF] Shi | Prosodic modulations in child-directed language and their impact on word learning[END_REF].

Finally, the current analysis was only based on children learning English. Evidence suggests that communicative feedback signals such as clarification requests (Dingemanse et al., 2015;[START_REF] Lustigman | Exposure and feedback in language acquisition: adult construals of children's early verb-form use in Hebrew[END_REF][START_REF] Ochs | Language acquisition and socialization. Culture theory: Essays on mind, self, and emotion[END_REF] and acknowledgements [START_REF] Cutrone | A case study examining backchannels in conversations between Japanese-British dyads[END_REF][START_REF] Liesenfeld | Bottom-up discovery of structure and variation in response tokens ('backchannels') across diverse languages[END_REF][START_REF] Maynard | Conversation management in contrast: Listener response in Japanese and American English[END_REF] are universally used in human conversations, and can therefore be leveraged by children from different languages and cultures. Future work is required to investigate this hypothesis.

Figure 1 :

 1 Figure 1: Proportion of child errors normalized by total number of child utterances. We only display English CHILDES corpora that include at least 100 annotated errors.

Figure 2 :

 2 Figure 2: Clarification requests and other responses as a function of repetition ratios. As many points have the same repetition ratios, the number of points is indicated by the size of the dots. The decision boundary is shown as a striped line.

Figure 3 :

 3 Figure 3: Acknowledgements and other responses as a function of repetition ratios. Number of points is indicated by dot size. The decision boundary is shown as a striped line.

Figure 4 Figure 4 :

 44 Figure 4 compares the difference in proportion of clarification requests to grammatical and ungrammatical child utter-

Figure 5 :

 5 Figure 5: Proportion of caregiver's clarification requests to children's utterances with different error types. The baseline ratio (proportion of clarification requests after grammatical utterances) is indicated as a striped line.

Figure 6 :

 6 Figure 6: Proportion of caregiver's acknowledgements to children's grammatical and ungrammatical utterances.

Figure 7 :

 7 Figure 7: Proportion of grammatical utterances before (utterance) and after (follow-up) a caregiver response, which could be a clarification request (right side) or any other kind of response (left side).

Table 1 :

 1 Inter-annotator agreement (Cohen's κ), Precision, and Recall for the grammatical error annotations in 7 different corpora.

		Cohen's κ Precision Recall
	Bates	0.43	0.89	0.31
	Thomas	0.05	1.00	0.03
	MPI-EVA-Manchester	0.41	0.80	0.31
	Providence	0.65	0.92	0.52
	Braunwald	0.49	0.86	0.42
	Lara	0.62	0.77	0.57
	EllisWeismer	0.68	0.91	0.59
	As shown in Table

Table 2 :

 2 Number of clarification requests and acknowledgements that were annotated using speech acts, keywords and repetition features.

	Clarification Requests
	Speech Act Repetition	Total
	519	7,540	8,028
	Caregiver's Clarification Requests

See also[START_REF] Saxton | Negative evidence and negative feedback: immediate effects on the grammaticality of child speech[END_REF] about the difference between negative evidence and negative feedback.

To simplify their coding scheme, we don't distinguish errors of omission/insertion/substitution and group regular and irregular past tense errors in the group tense aspect (thereby also including errors with e.g. participles). Further, we merge regular and irregular plural errors and include all kinds of subject-verb agreement errors (third-person s, wrong use of is/are) in the group sv agreement).

We evaluated also a non-linear SVM on the data but found that performance did not improve.

Manual inspection of misclassified examples showed that cases in which the caregiver asks a follow-up question were sometimes wrongly classified as clarification requests. Other cases with synonyms in restricted offers were not classified as clarification requests (e.g., "I want spoon." -"You'd like a spoon?"). Additionally, the stemmer did not stem certain colloquial word forms ("wanna") correctly, which led to incorrect repetition ratios.

We did not stem the words for calculating the repetition ratios for this case, as this would hide small morphological modification which could in fact be corrections. In this case the utterance is not an acknowledgement, but rather the contrary.

Manual inspection showed that many misclassified examples are cases in which the response is a repetition with minimal changes, which however changes the overall semantics and therefore pragmatics of the utterance.

Acknowledgements To annotate acknowledgments, we included all responses that start with specific keywords (e.g., "uhhuh", "mhm", "okay", "alright", "yeah"). We excluded cases in which these keywords are following a question, in that case they are responses and not backchannels. This keyword-based method includes many common backchannel responses, but misses repetition-based acknowledgements (e.g., "It isn't very nice is it?" -"It isn't."). To identify such acknowledgements, repetition ratios can also be used as a fea-Acknowledgements Keyword Repetition Total 20,398 14,103 32,214

Acknowledgements

We would like to thank Abhishek Agrawal and Alex Warstadt for their insightful feedback on this work. This work, carried out within the Labex BLRI (ANR-11-LABX-0036) and the Institut Convergence ILCB (ANR-16-CONV-0002), has benefited from support from the French government, managed by the French National Agency for Research (ANR) and the Excellence Initiative of Aix-Marseille University (A*MIDEX).

The project leading to this publication has received funding from Excellence Initiative of Aix-Marseille -A*MIDEX (Archimedes Institute AMX-19-IET-009), a French "Investissements d'Avenir" Programme.