Challenging the Oxidation State Paradigm at the Sub-Nanometric Scale

The concept of oxidation state, first introduced by Lavoisier in the 18th century, remains a fundamental principle across numerous scientific disciplines today. For example, the abundance of carbon on Earth is intricately linked to the oxidation state of iron under the extreme pressures of the Earth's upper mantle, where specific oxidation conditions significantly influence seismic waves. In medicine, Pt⁴⁺ complexes have been found to be more effective as anticancer agents compared to Pt²⁺, while copper's redox properties are essential for a variety of biological processes. The concept also plays a central role in materials science where the oxidation state of an element is most critical, as it governs its chemical and physical properties. However, even in recent decades, the concept of oxidation state has been the subject of debate and critical assessments within the scientific community, culminating in the establishment of a new definition by IUPAC and alternative frameworks. 

From an experimental standpoint, it is widely accepted that X-ray Photoelectron Spectroscopy (XPS) provides fingerprints for determining atomic oxidation states. Since its widespread adoption through the pioneering work of Kai Siegbahn, XPS has become an essential analytical tool in various fields of materials science. Its elemental and surface sensitivity make it especially suited for determining oxidation states in both bulk and surface environments. In this study, we explore whether this approach can be successfully applied at the sub-nanometric scale, where atomic aggregates consist of only few atoms. To address the challenge, we conducted high-resolution XPS experiments at the SuperESCA beamline on size-selected tungsten clusters composed of only a few atoms and produced by ENAC (Exact Number of Atoms in each Cluster), the source developed at the Nanoscale Materials Laboratory. 

We deposited W₁₃ and W₂₅ tungsten clusters at 40 K onto graphene and with an extremely low atomic density (0.06% of MonoLayer) to suppress surface diffusion and avoid any sintering. We then exploited the intense photon flux available at the beamline, enabling real-time acquisition of W 4f core-level spectra during O₂ exposure (Fig. 1a). The spin–orbit split W 4f peaks progressively shift to higher binding energies with increasing exposure, stabilizing after a few Langmuirs, which is indicative of saturation in oxygen. However, the resulting spectral complexity, much greater than that observed on solid surfaces, required a theoretical framework for interpretation. We therefore employed DFT to support the analysis. In the initial structural investigations, we systematically introduced a growing amount of O atoms into the clusters, which induces pronounced structural distortion and a notable increase in the average W–W distance. For all investigated configurations, W 4f core levels were calculated using DFT.

Figure 1.  (a) Selected W 4f core level spectral sequence acquired during oxygen exposure at 40 K of the W₁₃ and W₂₅ nanocluster deposited on graphene/Ru(0001) interface. Colored bar indicates the binding energy of the metallic 4f_7/2 components. ΔE is the spin-orbit splitting (ΔE=2.15 eV). (b) Dependence of the calculated W 4f_7/2 core levels on atomic valence. Each rectangle represents the standard deviation around the average values of the core levels and valences variables. Black line stand for the data fit. For comparison, core levels values of W bulk and surfaces are also reported. Adapted from J. Am. Chem. Soc. 147, 25, 21501–21511 (2025); Copyright ©️ 2025 The Authors. Published by American Chemical Society.

To understand the correlation between core levels and oxidation states, we than applied Pauling’s bond valence formalism. Using this method, we computed valences for all W atoms across oxygen coverages. The calculated core levels plotted against valences are shown in Fig. 1b. The graph shows a strong linear correlation between core levels and valence with mean core levels, valences, and standard deviations for each W-nO family indicated by colored rectangles (n=number of bond between W and O). Two key observations emerge: (i) for each atomic coordination, core level dispersion is significant and (ii) notable overlap occurs between different coordination families. The distribution of calculated core electron binding energy where than used to fit the experimental spectra with excellent agreement. This clearly indicates that even high-resolution XPS measurements cannot precisely determine in a straightforward way atomic oxidation state in small clusters.

This variability stems from the fluctuating interatomic distances in nanoclusters composed of few atoms. In bulk material, despite identical oxygen coordination, W–O bond lengths are fixed and vary between compounds; this is not the case for nanostructures, thus challenging conventional oxidation state assignments. The difficulty to directly determine oxidation states in sub-nanometric materials has important implications for chemical property assessments. Since valence states strongly influence reactivity, selectivity, and catalytic pathways, recognizing the heterogeneity in interatomic distances and valences is critical, not only for tungsten oxides but broadly across nanocluster oxides.

Deborah Perco¹, Monica Pozzo^2,3, Andrea Berti¹, Federico Loi^1,4, Paolo Lacovig⁵, Silvano Lizzit⁵, Aras Kartouzian⁶, Ueli Heiz⁶, Dario Alfè^7,8 and Alessandro Baraldi^1,5.

¹ Dipartimento di Fisica, Università di Trieste, Trieste, Italy
² Faculty of Technological & Innovation Sciences, Universitas Mercatorum, Roma, Italy
³ Institute for Materials Discovery, UCL, London, United Kingdom
⁴ Dipartimento di Scienze Fisiche e Chimiche, University of L’Aquila, L’Aquila, Italy
⁵ Elettra - Sincrotrone Trieste S.C.p.A., Trieste, Italy
⁶ Chemistry Department & Catalysis Research Center, Technical University of Munich, Garching, Germany
⁷ Department of Earth Sciences and London Centre for Nanotechnology, University College London, London, United Kingdom
⁸ Dipartimento di Fisica Ettore Pancini, Università di Napoli Federico II, Napoli, Italy

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