Breakdown of the correlation between oxidation states and core electron binding energies at the sub-nanoscale

X-ray photoelectron spectroscopy is a powerful analytical tool to ﬁngerprint the atomic oxidation state. However, the well-established trend that is found for bulk, ultra-thin ﬁlms and surface oxides, which is usually characterized by an incremental binding energy shift upon increasing oxidation state, may not apply at the sub-nanoscale where reduced dimensionality and quantum size eﬀects play a relevant role. Here we investigate through a combined experimental and theoretical approach the oxidation of size-selected Ag 7 and Ag 11 clusters supported on graphene, revealing an anomalous Ag 3d 5 / 2 core level shift trend upon increasing O coverage. We show that the negative core


Introduction
The concept of oxidation state or oxidation number constitutes an essential trait of a material, intimately connected with its specific electronic structure and the nature of chemical bonds [1].Besides the widespread application of theoretical approaches, ranging from the bond valence sum method [2] to density functional theory calculations [3] and the most recent applications of the state-of-the-art machine learning [4], x-ray photoelectron spectroscopy (XPS) has proven to be an extremely powerful experimental technique to study this aspect of matter since the pioneering work by Kai Siegbahn and co-workers [5].The composition and chemical nature of solid surfaces has been deeply investigated thanks to the ability to distinguish spectral components separated even by only a few hundred meV, allowing to create an extensive XPS database of the oxidation state of many elements of the periodic table.Copper provides a textbook example of this, since the 1s core level shifts by +4.4 eV going from the metallic to the oxide phase [6].The capability to identify exactly the oxidation state in copper compounds is nowadays of paramount importance for a wide set of chemical processes [7,8,9,10].
For heavier elements, such as tantalum and tungsten, the observation of discrete, evenly spaced 4f 7/2 core level shifts (CLS) brought to reveal a large number of possible non-equivalent oxidation states [11].The nature behind these shifts relies on the correlation of the exact peak position of the core level lines to the oxidation level of the emitting atom and to the electric field generated by adjacent atoms.In general, when the emitting atom is bound with a more electronegative ligand such as oxygen, it undergoes a withdrawal of electrons, making it harder to photoexcite its core electrons, which thus have a higher binding energy (BE).Ag represents and exception to this rule, as atoms with a higher oxidation state show lower BEs [12,13].This applies also to the oxidation of ultra-thin Ag films, which potentially allow to achieve higher oxidation conditions compared to bulk foils.In this case, the BE of the Ag 3d 5/2 core level assigned to Ag(0), Ag(I) and Ag(III) oxidation states was respectively 368.24, 367.30 and 366.80 eV [14].Similarly, for Ag (111) the absolute value of the CLS increases linearly with the number of oxygen neighbors as for a wide range of transition metals [15,16,17], but with a negative trend.Calculated Ag 3d 5/2 CLS for the p(4 × 4) configuration of the oxidized Ag(111) surface are found to be -0.28,-0.60 and -0.81 eV when Ag forms a bond with one, two and three oxygen atoms respectively [18].
The same behavior was found also in the case of Ag(100) with a number of O neighbors up to four [19], thus suggesting that the trend has a general validity for Ag surfaces.The motivations behind this trend is attributed to the peculiar electronic band structure of Ag.Calculations on the valence electronic structure and for the initial state effect contributions to the CLS of a Ag(111) surface at different O coverage showed that the onsite Ag core potential is almost not affected by oxidation, despite a clear metal-to-oxygen charge transfer.For this reason, the calculated CLS was attributed to final state effects arising from the inefficient screening of bonding s states [18,20].
The recent observation that the oxidation of a size-selected Ag 11 cluster leads to a bulk-like hybrid structure composed of both Ag(III) and Ag(I) ions [21], prompted us to investigate the CLS anomaly of Ag oxides at the subnanoscale.In this work we studied the oxidation of Ag 7 and Ag 11 clusters supported on graphene by means of high-resolution XPS and ab initio DFT calculations.We found that the Ag 3d 5/2 CLS of the atoms in the clusters follows the negative trend typical of Ag until the number of Ag-O bonds (N B ) is below 3. When moving to N B = 4, which corresponds to Ag(III) ions [21], the CLS suddenly moves back towards Ag(0).The final result of this trend is that Ag(III) ions in oxidized Ag 7 and Ag 11 clusters show a Ag 3d 5/2 BE higher than Ag(I).We interpret this effect as a result of the direct response of the d-band center d of the Ag atoms in the clusters to the increasing number of Ag-O bonds which enhances the initial state contribution to the overall CLS.This is a striking difference compared to bulk, ultra-thin films and surface Ag oxides which indicates that the well-established trends found in bulk matter and on solid surfaces might differ greatly for atomic clusters because of their reduced dimensionality and unique electronic properties.

Sample Preparation
A Ru(0001) single crystal was cleaned by repeated cycles of Ar + sputtering and annealing in O 2 atmosphere between 600 and 1000 K.The residual oxygen was removed by a final flash annealing up to 1500 K. Graphene was grown by thermal decomposition of ethylene (C 2 H 4 ) at 1100 K.The precursor pressure was initially set to 5 × 10 −9 mbar and successively increased in steps up to 5 × 10 −8 mbar to ensure that entire surface was covered by graphene.The resulting graphene layer showed the typical low energy electron diffraction (LEED) pattern with sharp moiré spots reported in Figure S4 [22].

Deposition of Ag Nanoclusters
Ag 7 + and Ag 11 + positive clusters were produced using the cluster source ENAC.This cluster source is based on the laser ablation of a metal target.
The mass selection of clusters is performed with a quadrupole mass analyzer and a mass scan reported in Supplementary Information.A more detailed description of the source is reported elsewhere [23,24].The clusters were deposited on graphene/Ru(0001) (Gr/Ru), on which they are electrically neutralized.The amount of clusters reaching the Gr/Ru surface was monitored by reading directly the current on the sample, on which we applied a positive voltage to reduce the kinetic energy E k of the clusters to ensure the soft landing conditions (E k < 1 eV/atom) [25].To avoid Ag cluster sintering, the cluster density was below 9 × 10 −3 cluster/nm 2 and the temperature of the sample was kept at 20 K during the deposition, reaction, and measurements.

High-Resolution X-Ray Photoelectron Spectroscopy
High-resolution X-ray photoelectron spectroscopy (HR-XPS) measurements were performed in-situ at the SuperESCA beamline at Elettra Sin-crotrone Trieste, Italy.The photoemission spectra were collected by means of a Phoibos 150 mm mean radius hemispherical electron energy analyzer from SPECS, equipped with a delay line detector developed in-house.The overall energy resolution was better than 50 meV for the photon energies and parameters employed.The binding energy scale was calibrated to the Fermi level position of the metallic substrate.The XPS spectra were acquired by tuning the photon energy to have a photoelectron kinetic energy of about 100 eV, to enhance surface sensitivity.For each spectrum, the photoemission intensity was normalized to the photon flux and the BE scale was aligned to the Fermi level of the Ru(0001) substrate.Core level spectra were analyzed using a Doniach-Šunjić [26] line profile for each spectral component, combined with a Gaussian distribution to account for the experimental, phonon and inhomogeneous broadening.The background was modeled with a second-degree polynomial curve for every Ag 3d 5/2 spectrum.

Theoretical Methods
The calculations have been performed using density functional theory (DFT) as implemented in the VASP code [27].The systems were described with a slab with 4 layers of Ru in a 12 × 12 hexagonal supercell and a layer of 13 × 13 unit cell of graphene placed on top with an overall number of 914 atoms, excluding the Ag 11 and Ag 7 cluster.The Ag cluster was placed on the valley of the corrugated graphene layer, with his center on a fcc site, where the stronger interaction with the Ru(0001) substrate increases its stability [28].The bottom two layers of Ru were kept frozen at their bulk geometry, with a lattice parameter of 2.724 Å, and the rest of the system was fully relaxed using the rev-vdw-DF2 functional [29] until the largest residual force was less than 0.015 eV/ Å.We employed the projector augmented method (PAW) [30] using PBE [31] potentials.The plane wave cutoff was set to 400 eV, and the relaxations were performed by sampling the Brillouin zone using the Γ point only.To obtain the partial density of states (PDOS) we have performed single point DFT calculations, using geometries obtained with the rev-vdw-DF2 functional.Core-electron BEs have been estimated in the final-state approximation, therefore including also final state effects due to core-hole screening.

Deposition of Ag nanoclusters on graphene/Ru(0001)
Positive Ag 7 + and Ag 11 + clusters were generated using the cluster source ENAC, whose detailed description is reported elsewhere [23,24].The clusters were deposited under soft landing conditions on graphene/Ru(0001) (Gr/Ru), on which they are electronically neutralized.The Gr monolayer supported on Ru was chosen for its low interaction with Ag [32] and for its corrugated morphology [33].The weak interaction is required to reduce the modifications of the properties of the unsupported size-selected clusters, while the corrugation decreases the mobility of the atomic aggregates on the surface and prevents their coalescence as proved for several systems [34,35,36,21].To further reduce the probability of sintering, the cluster density on Gr/Ru was kept below 9 × 10 −3 cluster/nm 2 (about one cluster every 3000 carbon atoms).For the same reasons, the sample temperature during deposition, reaction and measurements was always maintained at 20 K.These conditions prevent the occurrence of oxidative dispersion of clus-ters, a mechanism that has been found in the case of Ag clusters after oxygen exposure in the mbar pressure range and at temperature of 700 K [37].We focused our interest on two different clusters: Ag 11 for its ability to reach a bulk-like hybrid structure composed of atoms with different oxidation states, namely 1+ and 3+ [21], and Ag 7 , the largest planar Ag cluster according to our DFT calculations, with the aim to understand if the core electron binding energy behaviour is affected by the cluster morphology.It is interesting to note that even Au 7 assumes the same planar hexagonal configuration on Al 2 O 3 surfaces, according to DFT calculations [38] The minimum energy configurations of the positively charged clusters in the gas-phase are shown in Supplementary Information.

High-resolution XPS of pristine Ag clusters
High-resolution XPS measurements were performed in situ at the Su-perESCA beamline of the Elettra synchrotron radiation facility, Trieste.The Ag 3d 5/2 spectra were acquired in normal emission and with a photon energy of 470 eV, with a total energy resolution better than 50 meV.Figure 1a shows a comparison between the Ag 3d 5/2 core level of an Ag(111) single crystal surface, an Ag polycrystalline slab and the two size selected clusters.The Ag(111) surface was fitted with two components separated by 150 meV, one associated to bulk atoms (368.20 eV) and the second to surface atoms (368.05eV) [24].The polyscristalline and the cluster spectra were fitted using a single component located at 368.17 eV for the slab, 368.17 eV for Ag 11 and 368.24 eV for Ag 7 .The Ag 3d 5/2 binding energies of the clusters are rather similar to bulk and polycrystalline sample, in agreement with previous results on Ag sieze-selected clusters [39] and nanoparticles deposited on highly oriented pyrolytic graphite (HOPG) [40].Our fitting analysis indicates that Ag 7 has a BE 70 meV higher than Ag 11 , following a trend similar to that found for Pd size-selected clusters [41].This trend was confirmed by DFT calculations that were carried out placing isolated Ag preserved with respect to the the one found for the corresponding gas-phase ion, Ag 7 show a slightly modified conformation, with silver atoms moving out from the planar configuration, an indication that the interaction with the carbon network is not completely negligible [42].
It is worth comparing the full width at half maximum (FWHM) of the Ag 3d 5/2 core level measured for the clusters with that one observed for our reference sample, which appears to be narrower.Such outcome is not totally unexpected and it is determined by a concurrence of factors.First of all, it is important to stress that the broadening observed for clusters results from the different local configurations and different coordination numbers of the non-equivalent atoms.An important parameter to consider in such case is the effective coordination, which accounts for the presence of the first-neighbor atoms, but also for the local modifications of the interatomic distances.Second, it cannot be neglected that different non-equivalent atoms undergo slightly different screening effects.Last, it is not possible to completely rule out the vibrational effects, intrinsic to the photoemission process, which contribute to the line broadening even if the sample temperature is very low.We are indeed studying systems which are not in their bulk form and to which we can associate a set of vibrational frequencies producing a general broadening of the photoemission peak.Such phenomenon has been already well documented for core levels of molecules adsorbed on surfaces [43].
Earlier work reporting photoemission data on small size-selected Ag clusters deposited on sputter damaged HOPG have already pointed out that the core levels are considerably larger in terms of FHWM than metallic surfaces.For the latter the lower surface-to-volume ratio will indeed lead to a less heterogeneous chemical environment of Ag atoms with respect to the cluster case and, therefore, to the narrowing of the line-shape [39].In particular, the FWHM increases inversely with the cluster size [44], in good agreement with our experimental results, where the Gaussian parameter obtained from the spectral analysis is 0.97 eV for Ag 7 and 0.73 eV for Ag 11 .and Ag 7 nanoclusters, as well for oxidized silver surfaces [19].The CLSs are expressed using the bulk Ag 3d 5/2 BE (368.20 eV) as reference.respectively.Hence, we can conclude observing the trends in Figure 3a that the CLS for Ag(III) ions is lower than for Ag(I).This is a striking difference with respect to Ag bulk oxides and thin films [14], where the BEs are ordered as Ag(0)>Ag(I)>Ag(III).
To explain the origin of this anomalous trend of the Ag oxdiation state vs CLS, we performed (i) a Bader charge analysis [21,18,46] (see Figure 3b) and (ii) calculated the shift of the Ag d-band center d (∆ d ) of the atoms of the oxidized clusters (see Figure 3c), mimicking the approach used to study the oxidation of Ag(111), which lead to the attribution of the negative CLS to the dominant final state contribution [18].The trend of the calculated Bader charge vs. N B for both Ag clusters, which is reported in Figure 3b, is still linear even for N B = 4 (linear correlation coefficient = 0.97 ± 0.02 and slope 0.21 e/bond).No anomalies can be appreciated in the whole range.This outcome mirrors indeed entirely the results of the calculations reported for the Ag(111) surface [18], for which a very similar slope of the Bader charge (0.22 e/bond) can be extrapolated.This trend clearly indicates that the oxidation state of the Ag atoms in both Ag 11 and Ag 7 clusters increases linearly with N B as it happens for the oxidation of the Ag(111) surface.Therefore, the non-monotonic trend of the CLS is not directly linked to anomalous charge transfer effects between oxygen and Ag atoms upon increasing N B .
The second part of the analysis we performed was focused on the study of the trend of ∆ d (expressed with respect to the bulk Ag value which we calculated to be bulk d = 3.92 eV) projected onto each of the Ag atoms for all the configurations of the two oxidized clusters as a function of N B (Figure 3).
The average ∆ d value for each N B is shown as green square.Remarkably, such behavior follows the evolution of the calculated CLS reported in Figure 3a and whose average values are also included in the Figure 3c for comparison.
This is a striking difference with respect to the case of Ag single crystal surfaces, where d is clearly not affected by N B [18].This is a sign that, in the case of clusters, the Ag -O bonds involve also electronic d-states, while for single crystal surfaces the bonding is attributed mainly to s-states.Moreover, in the oxidation of the Ag surface, CLSs and d are not interdependent, because of a dominant contribution arising form final-state effects.On the other hand, the observation that for the clusters the two quantities follow a similar trend is indicative of a dominance of initial-state effects in determining the CLSs [47,48], as proven in the case of atomic and molecular adsorbates on solid surfaces [49,50,51].
To investigate the origin of this result, we analyzed the Ag 4d and O 2p partial density of states (PDOS).In Figure 4 we report the Ag 4d PDOS of a representative set of atoms in the oxidized clusters for each N B and the associated O 2p PDOS.Generally, the interaction of O 2p states with the d states of transition metals such as Ru [16], Rh [52] and Pd [18]  to experimentally find the density of oxygen atoms on the cluster.We have indeed found a O:Ag ratio close to 1 for both clusters, although this is not enough to experimentally show the inversion of the CLS for the 3+ oxidation state.
The changes in the d-band center d and the different initial and final state contribution to the total CLS is strongly connected to the quasi-zero dimensional character and low nuclearity of the Ag clusters, since this behavior is not observed for solid surfaces, where d remains substantially unaltered by the oxygen coverage and there is no correlation with the number of O-Ag bonds.Shifts of the d are of particular interest because, according to the Hammer-Nørskov model [53], they are generally associated to changes in the chemical reactivity of a system, as also proved in the case of nanoclusters [54].
Recent works discussed possible ways to modify d doping a nanomaterial to enhance its catalytic properties [55,56,57,58].For example, it was possible to shift d of Ag-based nanoparticles by almost 0.2 eV by doping them with Pd atoms and forming an alloy [59].According to this well-established rule, the adsorbed O progressively enhances the reactivity of the Ag 7 and Ag 11 clusters, as the d-band center moves up to 1.0 eV closer to the Fermi level for N B = 2.Moreover, the dominant contribution of the initial state effects to the total CLS allows to follow the d shifts, and thus the reactivity changes by means of XPS, thanks to their direct proportionality.The ability to disentangle the initial state contribution to the CLS in metallic clusters has allowed in the past to link their catalytic and electronic properties [41].
Achieving a similar result also in the case of oxidized atomic clusters or, more in general, low nuclearity systems involving oxidized atoms, could help in bridging the gap between the understanding of catalytic reaction dynamics and the atomic level description of their geometric and electronic properties with the final goal of improving the methods for catalyst design [60,61].
Our results show that the well-established trend studied for bulk and surface oxides may be different in low-nuclearity oxidized systems.This could have implications, for example, in the study of SiO 2 , one of the most important bulk-oxides studied in materials science, which is often considered as a model system to explain the correlation between core-level shifts and oxidation state [62,63].Since Si has 4 valence electrons, its oxidation number can range from 1+ to 4+ when it binds to oxygen..The core level of Si 2p then scales with the oxidation state, with an increase in 2p binding energy of approximately 1 eV/oxidation state.Therefore, considering the bulk behavior, it would be very interesting to evaluate the trend of the 2p levels of Si in the case of clusters formed by only a few atoms to verify if the anomaly found in our case can be extended also to other nano-oxides.

Conclusion
We have shown that core levels of quasi-zero dimensional Ag oxides behave in a radically different way from the bulk or surface case, given their unique electronic structure.The different behavior of the Ag 3d 5/2 CLS in the low nuclearity clusters compared to Ag surface oxides and ultra-thin films manifests through an anomalous trend when increasing the number of Ag to O bonds.An in-depth analysis of the Ag 4d-band based on DFT calculation allowed us also to directly link such anomaly to the shift of the d-band center, thus suggesting that CLS are dominated by initial state effects and related to changes in chemical reactivity.In addition, we conclude that moderate O adsorption on Ag 7 and Ag 11 clusters could enhance their reactivity, with the adsorbents that indirectly interact through the metal d-band.Finally, our results suggest that oxidized size-selected Ag clusters can be taken in consideration as low-nuclearity supported catalysts, also in the form of alloy [64], to maximize the reaction and cost efficiency, as already proved in the case of other single-atoms and subnanometer metallic oxides [65,66,67,68,69,70], specifically in the case of the epoxidation reaction [71,72], or for biomedical applications [73].

Figure 1 :
Figure 1: (a) Ag 3d 5/2 core level spectra of Ag(111) (with surface and bulk component displayed in light and dark gray, respectively), Ag polycrystal and of the size-selected Ag 7 and Ag 11 clusters supported on Gr/Ru.The blue lines represents the fitting curves resulting from the data analysis.Top and side views of the DFT calculated relaxed structures of the Ag clusters: (b) Ag 11 and (c) Ag 7 .White balls represent C atoms, gray and black balls represent first layer and bulk Ru atoms, respectively, red and light blue stand for Ag.
7 and Ag 11 in a Gr/Ru moiré cell supported by 4 Ru layers.In Figure 1b and 1c we show zoomed side and top views on the resulting relaxed structures.The complete unit cell is shown in Supplementary Information.While the structure of adsorbed Ag 11 is almost

3. 3 .
High resolution XPS and DFT calculations: core level shift anomaly in the oxidized clustersThe oxidization of the clusters was achieved by using a photon-induced dissociation process, where atomic oxygen is obtained by irradiation of physisorbed O 2 with soft x-rays at T = 20 K[21,45].Figure2shows that an exposure to 0.1 L (low oxidation), where 1L = 1 × 10 −6 torr × 1 s, leads to a CLS towards lower binding energies for both Ag 11 and Ag 7 .The CLS further increases upon a second exposure to 0.5 L (high oxidation).This behavior reminds us the trend observed for the oxidation of (111) and (100) single crystal silver surfaces, where, as reported above, the CLS is attributed to final state effects and increases linearly with N B[18,19].For larger oxygen exposures and prolonged photon irradiation, the Ag 3d 5/2 spectra of the Ag 7 and Ag 11 clusters did not change.To understand how the measured data are related to the Ag oxidation at the atomic scale, we employed DFT to calculate the minimum energy configurations and the electronic structural modifications induced by an increasing O density on the clusters.To compare the effects of oxidation of the clusters with the oxidation of Ag surfaces and to understand if the trend observed

Figure 2 :Figure 3 :
Figure 2: (a) Ag 3d 5/2 core level spectra following the oxidation of the Ag 11 and (b) Ag 7 size-selected cluster on Gr/Ru.We report the clean (light gray), mild (0.1 L of O 2 , light blu) and highly (0.5 L of O 2 , blu) oxidized clusters.(c) DFT calculated 3d 5/2 core level binding energy for each Ag atom composing the oxidized Ag 11 O m supported clusters, with m = 0 − 10 and 12. d Similar calculations for the atoms of the Ag 7 O m supported clusters, with m = 0 − 8.

Figure 3a indicates that
Figure 3a indicates that the amplitude of the negative CLS in the clusters increases linearly for N B = 0 − 2, but the trend surprisingly breaks-down for larger values.Specifically, for Ag 7 the trend is linear (as one can see by fitting the whole set of data points) in the range N B = 0 − 2 with a slope of -0.34 eV/N B , while for Ag 11 the linear trend continues up to N B = 3 with a steeper slope of -0.41 eV/N B .Such values are similar to those found for a Ag(100) surface up to N B = 4, where the CLS increases by -0.29 eV/N B [19].On the contrary, when moving to N B = 4, the Ag 3d 5/2 CLS in the clusters decreases.For Ag 7 , it goes from -0.65 eV for N B = 3 to -0.45 eV, while the difference is even more pronounced for Ag 11 , where the CLS decreases from -1.40 eV for N B = 3 to -0.65 eV for N B = 4.In a recent publication [21], we have demonstrated that Ag atoms in the clusters with N B = 2 and N B = 4 possessing the typical planar morphology observed in AgO bulk oxide correspond to d 10 Ag(I) and d 8 Ag(III) ions,

Figure 4 :
Figure 4: (a) Ag 4d and O 2p PDOS of atoms composing the Ag 11 and (b) Ag 7 clusters for each N B in the range N B = 0 − 4. On the right-hand side of each plot, we reported ball model of the associated relaxed structures for each N B .d-band centers, illustrated in Figure 3(c), are reported as green vertical lines.Grey balls represent C atoms, red balls stand for O, light blue represents Ag.

Figure 5 :
Figure 5: (a) Average DFT calculated Ag 4d CLS of Ag 11 and (b) Ag 7 oxidized clusters as a function of the O : Ag ratio.