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[Oscar Custance](https://orcid.org/0000-0001-7931-603X), [Manuel González Lastre](https://orcid.org/0009-0000-2299-6687), [Kyungmin Kim](https://orcid.org/0000-0002-3147-5100), [Estefanía Fernández-Villanueva](https://orcid.org/0000-0002-9419-0786), [Pablo Pou](https://orcid.org/0000-0002-5854-8218), [Masayuki Abe](https://orcid.org/0000-0001-5619-3911), [Hossein Sepehri-Amin](https://orcid.org/0000-0002-7856-7897), [Shigeki Kawai](https://orcid.org/0000-0003-2128-0120), [M. Verónica Ganduglia-Pirovano](https://orcid.org/0000-0003-2408-8898), [Ruben Perez](https://orcid.org/0000-0001-5896-541X)

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[Near-surface defects break symmetry in water adsorption on CeO2−x(111)](https://mdr.nims.go.jp/datasets/9a00ef23-2256-4506-b87e-93d4ce9f141b)

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Near-surface defects break symmetry in water adsorption on CeO2−x(111)communicationsmaterials ArticleA Nature Portfolio journalhttps://doi.org/10.1038/s43246-025-01011-xNear-surface defects break symmetry inwater adsorption on CeO2−x(111)Check for updatesOscar Custance 1,7 , Manuel González Lastre 2,7, Kyungmin Kim 3,Estefanía Fernández-Villanueva 2,4,5, Pablo Pou 2,6, Masayuki Abe 3, Hossein Sepehri-Amin 1,Shigeki Kawai 1, M. Verónica Ganduglia-Pirovano 4 & Ruben Perez 2,6Water interactions with oxygen-deficient cerium dioxide (CeO2) surfaces are central to hydrogenproduction and catalytic redox reactions, but the atomic-scale details of how defects influenceadsorption and reactivity remain elusive. Here, we unveil how water adsorbs on partially reducedCeO2−x(111) using atomic force microscopy (AFM) with chemically sensitive, oxygen-terminatedprobes, combined with first-principles calculations. Our AFM imaging reveals water molecules assharp, asymmetric boomerang-like features radically departing from the symmetric triangular motifspreviously attributed to molecular water. Strikingly, these features localize near subsurface defects.While the experiments are carried out at cryogenic temperatures, water was dosed at roomtemperature, capturing configurations relevant to initial adsorption events in catalytic processes.Density functional theory identifies Ce3+ sites adjacent to subsurface vacancies as thethermodynamically favoredadsorption sites,wheredefect-induced symmetry breakinggovernswaterorientation. Force spectroscopy and simulations further distinguish Ce3+ from Ce4+ centers throughtheir unique interaction signatures. By resolving how subsurface defects control water adsorption atthe atomic scale, this work demonstrates the power of chemically selective AFM for probing site-specific reactivity in oxide catalysts, laying the groundwork for direct investigations of complexsystems such as single-atom catalysts, metal-support interfaces, and defect-engineered oxides.Ceriumdioxide (CeO2, or ceria) is a cornerstonematerial in catalysis, widelyused both as an active component and as a support, owing to its exceptionalability to store, release, and transport oxygen1,2. This redox flexibility isrooted in the ease of reversible Ce4+/Ce3+ reduction, which enables ceria toform and heal oxygen vacancies under operating conditions. As a result,ceria exhibits remarkable versatility across a broad range of applications,fromautomobile exhaust gas treatment3,4 andhydrogenproduction5 to solidoxide fuel cells6 and emerging biomedical technologies7,8. In common withother reducible oxides9,10, the type, density, and spatial distribution of thesevacancies profoundly influence catalytic performance. Among the mole-cular species central to redox catalysis, water plays a pivotal role, particularlyin reactions such as the water-gas shift11 and thermochemical splittingcycles12. Understanding how water interacts with defective ceria surfaces atthe atomic scale is therefore essential for the rational design of next-generation catalysts and redox-active materials.Atomic force microscopy (AFM) has proven to be a powerful tool toexplore metal-oxide surfaces at the atomic scale, as well as adsorbates onthem13–17. Constant-height imaging with functionalized probes18–20 hasempowered this technique with unprecedented resolution that has beendeployed, among other feats, to study individual water molecules andproperties of water networks on several surface systems21–25.Molecular water on ceria surfaces has been studied with AFM26,27, aswell as with scanning tunneling microscopy (STM)28. For both techniques,and for sample temperatures ranging from room temperature to 10K,watermolecules on theCeO2(111) surfacewere imaged aswide triangular featuresextending over three surface oxygen atoms. At this surface, water adsorbswith the oxygen binding to a Ce4+ site and one of its hydrogen atomsinteracting with one of the adjacent surface oxygen atoms29. In contrast toother oxides, water onCeO2(111) can exist in two configurations,molecularform and hydroxyl pair29–31. This duality originates from the specific lateral1National Institute for Materials Science (NIMS), Tsukuba, Ibaraki, Japan. 2Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma deMadrid, Madrid, Spain. 3Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan. 4Instituto de Catálisis y Petroleoquímica (CSIC),Madrid, Spain. 5Universitat Politècnica de València, Valencia, Spain. 6Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid,Madrid, Spain. 7These authors contributed equally: Oscar Custance, Manuel González Lastre. e-mail: custance.oscar@nims.go.jp; ruben.perez@uam.esCommunications Materials |            (2026) 7:39 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s43246-025-01011-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-025-01011-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-025-01011-x&domain=pdfhttp://orcid.org/0000-0001-7931-603Xhttp://orcid.org/0000-0001-7931-603Xhttp://orcid.org/0000-0001-7931-603Xhttp://orcid.org/0000-0001-7931-603Xhttp://orcid.org/0000-0001-7931-603Xhttps://orcid.org/0009-0000-2299-6687https://orcid.org/0009-0000-2299-6687https://orcid.org/0009-0000-2299-6687https://orcid.org/0009-0000-2299-6687https://orcid.org/0009-0000-2299-6687http://orcid.org/0000-0002-3147-5100http://orcid.org/0000-0002-3147-5100http://orcid.org/0000-0002-3147-5100http://orcid.org/0000-0002-3147-5100http://orcid.org/0000-0002-3147-5100http://orcid.org/0000-0002-9419-0786http://orcid.org/0000-0002-9419-0786http://orcid.org/0000-0002-9419-0786http://orcid.org/0000-0002-9419-0786http://orcid.org/0000-0002-9419-0786http://orcid.org/0000-0002-5854-8218http://orcid.org/0000-0002-5854-8218http://orcid.org/0000-0002-5854-8218http://orcid.org/0000-0002-5854-8218http://orcid.org/0000-0002-5854-8218http://orcid.org/0000-0001-5619-3911http://orcid.org/0000-0001-5619-3911http://orcid.org/0000-0001-5619-3911http://orcid.org/0000-0001-5619-3911http://orcid.org/0000-0001-5619-3911http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0003-2128-0120http://orcid.org/0000-0003-2128-0120http://orcid.org/0000-0003-2128-0120http://orcid.org/0000-0003-2128-0120http://orcid.org/0000-0003-2128-0120http://orcid.org/0000-0003-2408-8898http://orcid.org/0000-0003-2408-8898http://orcid.org/0000-0003-2408-8898http://orcid.org/0000-0003-2408-8898http://orcid.org/0000-0003-2408-8898http://orcid.org/0000-0001-5896-541Xhttp://orcid.org/0000-0001-5896-541Xhttp://orcid.org/0000-0001-5896-541Xhttp://orcid.org/0000-0001-5896-541Xhttp://orcid.org/0000-0001-5896-541Xmailto:custance.oscar@nims.go.jpmailto:ruben.perez@uam.eswww.nature.com/commsmatdistance between the ceria site and its three neighboring oxygen atoms at theCeO2(111) surface and the low energy cost of displacing these oxygenspecies. The low energy barriers between different adsorption configura-tions successfully explain the triangular shape detected in the experiments29.In this work, we study the adsorption of molecular water on a partiallyreduced CeO2−x(111) surface using AFM operated at cryogenic tempera-tures (T ~ 4.8 K) with copper-oxide functionalized probes19,20. Our AFMimages reveal water molecules as sharp asymmetric boomerang-like fea-tures, connecting the cerium adsorption site29 with two of the neighboringsurface oxygen atoms, challenging our understanding of water adsorptionand imaging on the surface.To clarify these new findings, we combine density functional theory(DFT) simulations with constant-height AFM imaging and site-specificfrequency shift (Δf) curves32,33 on both the surface atomic sites and theatomic positions visited by the water molecule. By comparing these Δfcurves with theoretical predictions, we identified a model probe thatreproduces the experiments well.We build on thismodel to unveil the key role played by the response ofthewatermolecule to the forces exertedby theprobeduring the experimentsand explain the observed features in the AFM images, considering thepresence of sub-surface oxygen vacancies. When such a defect is produced,two Ce4+ ions are reduced to Ce3+. Our analysis suggests a particularadsorption environment created by one of these Ce3+ near a vacancy as theexplanation for the asymmetry.Furthermore, simulated Δf curves predict a stronger attractive inter-action on the Ce3+ sites relative to the Ce4+. This different interaction withthe probe originates fromdistortions on the topmost oxygen layer caused bythe excess charge localized on Ce3+, and it paves the way for a possibleexperimental identification of these so far elusive defects.Ourwork reveals the potential ofAFMas apowerful atomic-resolutionlocal technique to address and understand problems involving oxidenanostructures and their role in catalysis, such as the study of single-atomcatalysts, due to the possibility of accessing the local reactivity.Results and discussionAFM imaging of water, surface atomic sites and probeidentificationFigure 1a shows an atomic resolution AFM image of an area of theCeO2(111) surface that presents four water molecules (see Fig. S1 for ageneral view of the surface region). Since it is well established thatmolecularwater adsorbs on top of a cerium atom27,29, these water molecules were usedasmarkers13 to assign chemical specificity to the atomic features observed inthe AFM images and the Δf curves32,33 measured over them (Fig. 1b, c).The behavior of the experimental curves over the cerium and oxygensites suggests anoxygen-terminated apex,which is consistentwith the probeconditioning at the copper oxide areas19 coexistingwith the ceria islands (seethe Methods). The nature of the probe apex is further confirmed by theo-retical calculations of the Δf curves using a model probe that combines theshort-range contribution from DFT calculated forces with the long-rangeprobe-surface interaction (inset in Fig. 1d). The calculated forces are pro-vided by a rigid COmolecule—that represents the oxygen atom at the apex—interacting with a stoichiometric CeO2 slab (Fig. S9), which are thenconverted toΔf 34. The long-range vdW interaction is obtained fromafittingto the experimental Δf curves at large distances (cyan dotted line in Fig. 1d,see also Fig. S9 and Methods). The calculated curves reproduce quantita-tively the experimental spectroscopy, and allow us to estimate the value forthe imaging distance (Zexp ¼ 0 in Fig. 1d), which corresponds to a Z ~ 411pm separation with respect to the plane defined by the center of theuppermost surface oxygen atoms (Fig. 1d, see Methods). According to thisdistance and the Δf curves, the bright contrast in the constant-height AFMimages relates to the topmost oxygenatomsof the surface, and the spotswiththe lower contrast correspond to the position of the cerium atoms belowthem (see the inset models in Fig. 1d).A force curve on topof thewatermolecule informsus that themoleculeis imaged in Fig. 1 past the minimum of the Δf curve; a region where theinteraction between the probe and the surface has already become repulsive(see Fig. S2 for a detailed evolution of the AFM contrast over the watermolecule with the distance). For surface atoms that correspond to the samechemical species, and with a similar charge state, the relative position of theΔfminima could be an indication of their topographic distribution normalto the surface. Theminimumat awatermolecule is 200 to 300 pmabove thesurface oxygen atoms, which is consistent with the results of our DFTcalculations, where the oxygen atom of the molecule is 250 (220) pm abovethe cerium atom for the molecular (hydroxyl pair) adsorption state.The images in Fig. 1 display two striking differences with respect toprevious works27,28,35: (i), the triangular feature extending over three oxygenatoms is replaced by three well-defined lines connecting them; and (ii), oneof the prongs of these lines presents a dimmer contrast than the other two,breaking the surface three-fold symmetry and giving rise to a boomerang-like shape (Fig. 1). This asymmetric shape is found in the three possibleorientations compatible with the surface symmetry (see Figs. 1 and Fig. S2),and in all the cases, there is a dark shadow enclosed by two of the three lines,yet its location does not seem to correlate with the direction of the lessintense one.This asymmetric shape suggests either the stabilization of the dis-sociated state in the form of a hydroxyl pair, which naturally breaks thesymmetry in one of the directions, or the presence of defects like oxygenvacancies and the associated Ce3+ ions nearby, that locally change thestructure and energetics of water adsorption.Water dosing in the experiments reported herewas carried out at roomtemperature, resulting in a rather low coverage. Increasing the dosage by 10and 100 times did not provide a significant increase in the concentration ofwater on our CeO2(111) films. According to Mullins et al., water moleculesdo not adsorb on a fully oxidized CeO2(111) surface at room temperature36,suggesting that the adsorption of water on the CeO2(111) surface at roomtemperature is significantly affected by the presence of defects. This wouldbe consistent with our early works on the observation and manipulation ofwater molecules on CeO2(111) single crystals with AFM27,35. Those crystalshad a high density of defects (mostly subsurface defects characterized bycontrast variations in topographic AFM images of the outermost oxygensurface layer, and occasionally, surface oxygen vacancies were also found),whose concentration and appearance varied from terrace to terrace37. Thecrystals had a blackcolor, so theyprobably also contained atomic impurities.In those experiments, also carried out by similar dosing at room tempera-ture, higher water coverage was obtained. Furthermore, while water waseasily manipulated on the CeO2(111) single crystals35, our efforts tomanipulate one of the water molecules displayed in Fig. 1a using a highlyreproducible method we reported before35,38 did not succeed (see Fig. S3).Adsorption of molecular water in the presence of asubsurface defectTo understand the possible influence of defects in the adsorption of mole-cular water on the CeO2(111) surface, we have performed first-principlescalculations based on DFT as implemented in VASP39–43 using the PBE44exchange-correlation functional supplemented with the vdW dispersionenergy correction described by the DFT-D3 approach45,46 (see Methods).There are DFT-based studies on the adsorption of water on CeO2(111),(110) and (100) at low, intermediate and high coverages in the presence ofsurface oxygen vacancies47–50. However, we have previously demonstratedthat the energetically most stable near-surface defect in the CeO2(111)system is a subsurface oxygen vacancy (SSOV)51. Accordingly, we havesimulated the adsorption of a water molecule when an SSOV is locatednearby using a 3 × 3 unit cell.In this 3 × 3 slab with one SSOV, we have two equivalent Ce3+ sites andfive inequivalent Ce4+ sites, of which two are nearest neighbors of the SSOV(as in structure 3, Fig. 2), whereas the others are farther away (as in structure2, Fig. 2; see also Fig. S5 and the associated discussion in the SupplementaryInformation). In thepresence of anearby SSOV, the adsorption energy of thewater molecule on a Ce4+ atom, −0.70 eV for the pristine surface29–31(Fig. 2a), is barely affected when the Ce4+ is a second neighbor to thehttps://doi.org/10.1038/s43246-025-01011-x ArticleCommunications Materials |            (2026) 7:39 2www.nature.com/commsmatvacancy, -0.72 eV, but reduces (weaker binding) for first neighbors, withvalues in the range (−0.61,−0.66) eV (see Fig. 2b, Fig. S5). It is energeticallymore favorable for the water molecule to adsorb on a Ce3+ than on a Ce4+,−0.79 eV (Fig. 2c). Under the presence of a SSOV, the threefold symmetryobserved for the pristine surface case29 is broken, and an adsorption con-figurationwith one of the hydrogen atoms interactingwith a surface oxygenatom neighboring the SSOV becomes the less favorable of the three possiblemolecular orientations, −0.68 eV vs −0.75 and −0.79 eV (Fig. 2c). Whenconsidering the hydroxyl pair, a lower adsorption energy is obtained over aCe3+ than over a Ce4+ (−0.78 eV vs−0.75 eV, see Fig. 2d and Fig. S5), andattempting the formation of an hydroxyl with an oxygen neighboring theSSOV results in recovering the molecular form (Fig. 2d). For the adsorptionon a Ce3+, the molecular and hydroxyl pair states are separated by energybarriers of ~ 50− 60meV (Fig. S6b); smaller than those found on aCe4+ onthe fully oxidized surface 80 (130) meV for the transition from (to) themolecular state (Fig. S6c). These calculations, carried out with the DFT-D3approach to include the vdW interaction, compared well with our previousresults29 employing the optB86b-vdW functional, where binding energies of−0.73 (−0.76) eVwere found for themolecular (hydroxyl pair) states, withenergy barriers of 80 (100)meV for the transition from (to) the molecularstate.Comparisonwith published theoretical results forwater adsorptionona Ce3+52 shows that the inclusion of dispersion corrections provides anadditional binding energy but does not significantly modify the relativestability of the different adsorption configurations for both the molecularstate and the hydroxyl pair. Therefore, neither state is strongly thermo-dynamically favored, and both are expected to coexist at equilibrium.This symmetry breaking and the energetic diversity among otherwisesimilar adsorption configurations for the water molecule close to thevacancy are due to the structural surface relaxations inducedby the presenceof the SSOV and the two nearby Ce3+ ions51. Our calculations resulted in theoxygenatomsdirectly on topof the SSOV relaxing ~15 pmtowards the bulk.In contrast, the second nearest surface oxygen atoms and the Ce3+ rise~ 15 pm and ~ 7 pm, respectively, toward the vacuum (Fig. 6d, e).We havecarefully checked that all of these conclusions are not conditioned by theparticular arrangement of the Ce3+ ions forced by the 3 × 3 cell (where theyare neighbors), as shown by the results for adsorption structures (Fig. S7)and energy barriers (Fig. S8) obtained in a 4 × 4 unit cell (see Methods).Calculated AFM images of a water molecule adsorbed near asubsurface defectTo explore whether the presence of the SSOV and associated Ce3+ ionsexplain the asymmetric shape found in our experiments, we calculatedFig. 1 | Individual watermolecules, surface atom identification and probe-modelcharacterization. aAtomic-resolution constant-height AFM image of a CeO2(111)surface area displaying four water molecules, two of them enclosed by a red and acyan square. b, cWatermolecule highlightedwith a red square in (a) with hexagonallattices in red, green and black superimposed over the atomic sites of the CeO2(111)surface: cerium (Ce), oxygen (O) and coordination vacancy (CV). The comparisonof pairs of lattices with the adsorption position of the water molecule enables us toassign the black, red and green lattices to Ce, O and CV, respectively. d Frequencyshift (Δf) curves measured at the top of the water molecule (orange), and on an O(red), a Ce (black) and a CV (green) site far from the molecule in (b, c). The dottedcurves are calculated Δf curves fromDFT interatomic forces obtained over the threeCeO2(111) surface sites using a probe modeled by a rigid CO molecule (inset). Along-range van derWaals interaction derived fromfitting the experimental curves atlarge distances (cyan dotted line) has been added to each of the calculated curves toinclude the interaction with the mesoscopic part of the probe. The origin in theexperimental distance axis (Zexp) corresponds to the probe-surface separation theimages in (b, c) were acquired. The correspondence zexp = 0⇔ z = 411 pm has beendetermined by a rigid shift of all the simulated Δf curves in order to align theircharacteristic minima with those in the experiments. Acquisition parameters were:an oscillation amplitude (A) of 60 pm, and a free oscillation resonant frequency (f0)of 994230 Hz. Yellow arrows in (a) point to Ce atoms with an unusual contrast. Thescale bar represents 1 nm. See Methods for further details on AFM acquisition,model probe, calculated Δf curves, and fitting over the long-range interaction.https://doi.org/10.1038/s43246-025-01011-x ArticleCommunications Materials |            (2026) 7:39 3www.nature.com/commsmat1-0.70 eV2-0.72 eV3-0.66 eVa bc4-0.79 eV5-0.75 eV6-0.68 eVd7-0.78 eV8-0.77 eVFig. 2 |Water adsorption at the CeO2(111) surface in the presence of a subsurfaceoxygen vacancy.DFT optimized most stable structures for water adsorption on: a aCe4+ of the pristine surface; b a Ce4+ of the reduced surface, far 2 and close 3 to theoxygen vacancy; and c a Ce3+ of the reduced surface. d Hydroxyl pair (OH + H)adsorbed on a Ce3+ and a neighboring O atom of the reduced surface. The energieswith respect to the slab and water molecule energy are indicated. The position of theoxygen vacancy is highlighted by a dotted circle. Ce3+, Ce4+ and surface O andsubsurface O atoms are represented in green, beige, red and yellow, respectively. Nostable hydroxyl pair (OH + H) was obtained from structure 6; it reverts to water.https://doi.org/10.1038/s43246-025-01011-x ArticleCommunications Materials |            (2026) 7:39 4www.nature.com/commsmatconstant-height AFM images at several probe-surface separations usingrepresentative stable configurations for the adsorption of water close to aSSOV (Fig. 3). These calculations are based on the full density–basedmodel(FDBM)53,54—which retains DFT accuracy in the description of the probe-surface forces while offering the computational speedneeded for simulatinga whole image—using the probe model shown in Fig. 1. Therefore, thecalculated Δf signal for these images includes both the short-range con-tribution fromtheCOmolecule (calculatedwithFDBM)and the long-rangevdW interaction fitted from the experiments.In a constant height AFM image, the contrast will depend on therelative value of the probe-surface forces over the different surface posi-tions explored. In the images presented in this work, the dark regions(normally more negative Δf) correspond to a stronger net attractionbetween the probe and the surface, whereas brighter areas reflect a lessattractive interaction, because either the force is small or it already ascendsthe repulsive branch of the interaction, in a manifestation of the non-monotonic nature of the probe-surface interaction force. An example ofthis effect appears in the contrast of the AFM images in Fig. 1: while thecontrast over the surface oxygen atoms and over thewatermolecule seemsto be similar, the former corresponds to an attractive interaction and thelatter to the onset of a repulsive one. In the calculated images in Fig. 3, thesubsurface Ce positions appear as a relatively bright background eventhough the interaction between the terminal oxygen of the probe and theCe site remains attractive (Fig. 1d). This apparent brightness arisesbecause the strong attractive contribution from the hydrogen bondbetween the water molecule and the probe that saturates the color scaleused for the maps.Figures 3a, b present calculated Δf images of the two most stableconfigurations for the water adsorption on a Ce3+ atom in the molecularform (4 and 5 in Fig. 2, respectively). These orientations show a brightcontrast over a region close to the oxygen of the molecule, and display anextended dark feature over a wide area spanning from the position of thehydrogen atom pointing upwards towards the surface oxygen atomsopposite to the SSOV.The probe-surface separations explored (540–500 pm) covers theregimewhere thebright contrast over the oxygen atomof themolecule startsto be dominated by the Pauli repulsive interaction between the lone pairs ofthe oxygen atoms of CO and water; consistent with the appearance of abright contrast—of repulsivenature, as it develops past theΔfminimum—atthe water site in Fig. S2. The dark contrast reflects the attractive interactionassociated with the onset of a hydrogen bond formation between thehydrogen pointing upwards and the oxygen atom at the CO molecule,which is consistent with the vertical electric field resulting from the DFTsimulations (Fig. S19). For an analysis of the force contributions for therepresentative case of Fig. 3a, see Fig. S10.In the hydroxyl pair case (configuration 7 in Fig. 2d), the imagingmechanism is similar (Fig. 3c): an initial dark contrast is obtained due to anattractive interaction of the hydrogen atom pointing towards the vacuumwith the oxygen atom at the probe, that develops into a bright spot uponfurther approach towards the surface, as the repulsive interaction betweenthe oxygen of the hydroxyl and the one at the probe starts dominating thecontrast (see Fig. S11 for the corresponding force contributions).These calculated Δf images point towards the AFM being capable ofdiscriminating between the two adsorption forms upon stabilization of oneof them on the surface. However, the calculated images only partiallyreproduce the observed features in the experiments. The calculated AFMimages were obtained under the common assumption that the surfaceconfiguration is notmodifiedby the interactionwith theprobe.Yet ourDFTcalculations suggest thatwater is extremelymobile in either of the two formson CeO2(111)29. Further information about how the water molecule inter-actswith theprobe canbeobtained fromthe calculationofΔf curves over therelevant atomic positions visited by the molecule.Interaction of the probe with the water moleculesFigure 4 displays calculatedΔf curves over the atomic sites of a fully oxidizedCeO2(111) surface in the presence of a water molecule. In the calculation ofthe forces that generate these curves (Fig. S12), the outermost oxygen-cerium-oxygen trilayer of the surface and the water species were allowed toFig. 3 | Simulated constant-height AFM images. Calculated Δf maps of the moststable adsorption configurations of a watermolecule adsorbed on a partially reducedCeO2−x(111) surface characterized by the presence of a subsurface oxygen vacancy(dotted circumference). The Δf images were calculated using the full density basedmodel (including the probe-surface long-range vdW interaction fitted from theexperiments, see Methods) at three representative probe-surface separations for:a molecular water in configuration 4; b molecular water in configuration 5; and c,hydroxyl pair in configuration 7, as shown in Fig. 2. Latices with the top-most Ce andO surface atomic positions, as well as a rhomboid highlighting the unit cell, havebeen superimposed to each Δf image. The color code for the species in the atomicmodels is the same as for Fig. 2. See Figs. S18 and S19 for the corresponding chargedensity and vertical electric field maps, respectively.https://doi.org/10.1038/s43246-025-01011-x ArticleCommunications Materials |            (2026) 7:39 5www.nature.com/commsmatrelax in response to the force exerted by the probe model introduced inFig. 1. Each set ofΔf curves comprises the interactionover the ceriumsite thewater binds to (orange), the three neighboring surface oxygen atoms (yel-low, cyan and magenta), and an oxygen atom of the fully oxidized surface(red) for reference.The calculatedΔf curves for the adsorption of water inmolecular form(Fig. 4a) reveal a strong variability in the magnitude and position of theminima over the oxygen atoms. The water molecule pulls the oxygeninvolved in the hydrogen bond up by ~ 10 pmwith respect to the other twooxygenatoms,whose heights are unaffected by the presenceof themolecule.This structural modification is amplified by the water-probe interaction,causing the corresponding Δfminimum to be shifted by ~100 pm towardsthe vacuum (yellow curve) with respect to the reference surface oxygen. Theproximity of the water molecule also affects the position and magnitude oftheΔfminimum for the oxygen atom labeled inmagenta, while theΔf curveover the oxygen far from the hydrogen atom (cyan) is the closest to thereference oxygen.A dominant role of the interaction over structural effects manifests inthe curve at the cerium site: although the oxygen of the water molecule is~ 170 pm higher than the yellow-labeled oxygen, the attractive interactionprovided by the hydrogen atom pointing out of the surface reduces thedifference in the position of the curve minimum to ~ 75 pm. Despite thatthis hydrogenhas a lowerheight than in the case of the adsorption onaCe3+,the contrast evolution over the cerium site at large distances is consistentwith the one shown by the images calculated with FDBM for the reducedsurface, with the orange curve bending upward and crossing those asso-ciated with the neighboring oxygen atoms for distances below 540 pm.Thehydroxyl pair provides smaller differencesamong the three oxygensites, and shows greater flexibility of the atoms to move in response to theinteractionwith theprobe,which changes thepositionand strengthof theΔfminima for the ceriumsite and the yellow-labeled oxygenwith respect to themolecular adsorption case.Our experiments also reveal an asymmetric behavior of the Δf curvesover the atomic sites visited by the water molecule. Figure 5a displays thecurves obtained at the location highlighted by a red square in Fig. 1a; andFig. 5b, c shows two sets of curvesmeasured over themolecule enclosed by acyan square in Fig. 1a, but with a 40-minute interval between theiracquisition.A close look at the contrast of the atomic sites in the image displayed inFig. 5a reveals a discrepancy with the spectroscopic data. Two of the oxygenatoms (cyan and magenta) show a bright contrast, while the third one(yellow) has the appearance of a normal surface oxygen atom. The asso-ciated Δf curves indicate, however, that the contrast over the spots in yellowandmagenta shouldbe almost identical to the contrast on a standard surfaceoxygen. The sets displayed inFig. 5b, c show similar discrepancies: in Fig. 5b,the spot in yellow should have a dimmer contrast than the one in cyan; andin Fig. 5c, the sites highlighted in yellow and cyan should have almostidentical contrast, but in the image, the cyan spot appears dimmer than theyellow one. This discrepancy between the image contrast and the corre-spondingΔf curves, together with the variability of theΔf curves recorded atdifferent times over the same molecule, points to the existence of probe-induced dynamical effects that result in the change of the adsorption con-figurationof thewatermolecule, andpossibly, reversible transitionsbetweenmolecular and hydroxyl pair forms.Probe-induced dynamical effectsThese probe-induced changes have been verified during the simulations toproduce the calculated Δf curves. In Fig. 4a, an abrupt instability uponapproaching the probe beyond420 pmover the yellow-labeled oxygen atombrings theΔf curve very close to the one at themagenta site, generatingwhatseems to be a minimum. However, this sharp feature reflects in reality atransition between force spectroscopy curves that correspond to two dif-ferent configurations of the system. This formation originates froma probe-induced change in the adsorption configuration, in which the hydrogenatom interacting with the oxygen at the yellow site moves upward, breaksthe hydrogen bond, and then the whole molecule rotates to establish a newhydrogen bondwith the oxygen atom at themagenta site (seeMovie S1). Inthis newarrangement, the yellow siteplays an equivalent role to themagentasite in the original configuration, explaining the similarity between the twoΔf curves beyond 400 pm approach. Similar processes take place when theprobe approaches other sites, like the coordination vacancy between theoxygen atoms marked in yellow and cyan (see Movie S2), confirming thatthis event—characterized by a very low energy barrier29—is quite commonfor the probe-surface separations used in atomic resolution imaging ( ~ 411pm for the images in Fig. 5). Interestingly, the probe is also able to induce thetransition from the molecular form to the hydroxyl pair when approachingover the cerium site (see Movie S3). In this case, the proton transfer occursspontaneously—indicating a zero energy barrier—in the range of385–400 pm, close to the imaging separation mentioned above. This tran-sitionwill seamlessly switch between the orange curves in Fig. 4a, b, bringingthe position of theminimum—relative to the ones for the oxygen sites—andits strength closer to the experiment. Within the accuracy of our calcula-tions, the molecular and hydroxyl-pair states adsorbed on a cerium atom(either aCe3+or aCe4+) havenearly the same energies,whichdiffer onlyonafew tens of meV (Fig. 2), and the activation barriers for interconversion arelikewise small (Fig. S6). Therefore, the two states are thermodynamicallycomparable and expected to coexist, with switching readily triggered by theprobe under our imaging conditions at 4.8 K. In the experiments, theseparationatwhich this transitionoccurs iswell beyond theminimumin thecalculated Δf curves, entering a probe-surface interaction range dominatedby the repulsion between the oxygen atoms of the molecule and the probe.The limitation of our model to describe areas of highly repulsive forces,where the long-range elasticity of probe and surface starts playing a role,makes the theoretical curves significantly steeper than the experimental onespast the minimum of the Δf. However, considering that the water moleculeis imaged in the experiments under this repulsive interaction regime, ourcalculations strongly suggest that the transitionbetweenmolecular formandhydroxyl pairs should take place systematically during imaging.With all this information, we can address the appearance of themolecule as three well-defined lines pointing to the neighboring oxygenatoms with a boomerang-like shape.Origin of the boomerang-like shape of water in the AFM imagesWhen imaging with CO-functionalized probes, the relaxation of the COmolecule in response to the interaction with the surface enhances the AFMsignal over covalent18,55 and hydrogen53,55 bonds, which are imaged as bond-like sharp features. In our experiments and simulations, we use a rigidoxygen-terminated apex, yet the probe-induced transitions of the watermolecule between the different adsorption configurations play a similar roleto the relaxation of the COmolecule, leading to the three well-defined linesobserved in our experimental images. These transitions are not privative ofthe molecular form: Movie S4 shows a probe-induced change in theorientation of the hydroxyl pair that closely resembles the dynamics of aflexible CO-apex in the presence of a rapidly varying region of the potentialenergy surface.These probe-induced relaxations would tend to restore the threefoldsymmetry. However, the discussion above shows that both the presence ofdefects such as a SSOV and the water molecule itself—that pulls up a surfaceoxygen atom with the hydrogen bond—contribute to break the symmetryamong the three neighboring oxygen sites. A quantitative answer to thisquestion would imply DFT simulations of force curves for a water moleculeadsorbedondifferent ceriumsites on a reduced ceria surface on afine3Dgridof the probe positions. The inclusion of just a single SSOV with the twoassociated Ce3+ ions in those calculations renders the relaxation of the wholesystemto thegroundstate for eachprobepositionaherculean feat, as theCe3+ions make the electronic convergence quite cumbersome. Such calculation isbeyond our current capabilities, but we can point out that the presence of anSSOV singles out the oxygen site closer to the vacancy, making less probablethe formation of a hydrogen bond with that site in the countless times thewater molecule visits the three oxygen atoms during an AFM image.https://doi.org/10.1038/s43246-025-01011-x ArticleCommunications Materials |            (2026) 7:39 6www.nature.com/commsmatIn the experiments reported here, direct evidence of the presence ofsubsurface oxygen vacancies could not be obtained either in the Δf or in thedissipation signal; the latter is probably due to the use of amuch stiffer forcesensor56,57 than in previous works37. However, we often observe ceriumatomswith an unusual contrast (yellow arrows in Fig. 1a) in a concentrationclose to the coverage of watermolecules on the terraces after dosingwater atroom temperature.Wepropose that thesemore attractive ceriumatoms canbe candidates for Ce3+, originating from the presence of defects under thesurface.Origin of the cerium atoms with unusual contrastTo address the nature of these cerium atoms, we calculated Δf curves ondifferent cerium sites of the reduced surface (Fig. 6a) using themodel probeintroduced in Fig. 1. In order to speed up the calculation of the forces, and tosingle out the effect of the presence of the vacancy, we have not included thewater molecule in these DFT simulations.Our calculations reveal that the Ce3+ sites have the deepest Δf mini-mum (18% larger than the Ce4+ labeled 1, and 9% larger than the referenceCe4+ on the fully oxidized surface), which is associated with a significantlystronger attractive force with the probe compared to the Ce4+ sites (seeFig. S13).This outcome seems counterintuitive when considering the extrascreening provided by the additional electron localized at the Ce3+site. However, an increase in the local electric field over the Ce3+ as aresult of surface atomic relaxations accounts for this stronger inter-action. Figure 6b, c show the vertical component of the local electricfield (Ez) for the fully oxidized and the reduced ceria surface,Fig. 5 | Spectroscopic measurements over water molecules. Frequency shift (Δf)curves obtained over the center of the water molecule structure (orange) and thecenter of the three surface oxygen atoms (yellow, cyan and magenta) the moleculevisits. The inset graphs show a detail around the minima of the Δf curves. These setsof force curves were measured over: a the molecule highlighted with a red square inFig. 1a; b the molecule highlighted with a cyan square in Fig. 1a; c the samemoleculeas in b, but 40 minutes after the acquisition of the first set. Constant-height AFMimages obtained prior to the force spectroscopymeasurements are included as insets.Each image was measured at a probe-surface separation corresponding to the originof the distance axis. A set of force curves over the three surface sites of the CeO2(111)surface (Ce in black, O in red, and CV in green) far from the water molecule isincluded for reference. All curves were measured with an identical probe apextermination. Acquisition parameters were: A = 60 pm and f0 = 994230 Hz.baFig. 4 | Calculated spectroscopy curves for a water molecule on a fully oxidizedCeO2(111) surface. Sets of calculated Δf curves over the surface atoms visited by awater molecule adsorbed on the CeO2(111) surface: the Ce atom the molecule bindsto (in orange) and its three first-neighboring oxygen atoms (in yellow, cyan andmagenta). aWater in amolecular form; and bwater in hydroxyl pair form. The insetimages are top and side views of the atomic conformations of the molecule andsurface atoms. The Δf curve over a surface O atom in the absence of the watermolecule (curve in red, Fig. 1d) has been included for reference. The calculation ofthe Δf curve over the center of each surface atom (colored crosses) was performed tomatch the experimental counterparts (see Fig. 5). The probe model introduced inFig. 1, including the probe-surface long-range vdW interaction fitted from theexperiments, was used for the calculation of the Δf curves (see Methods).https://doi.org/10.1038/s43246-025-01011-x ArticleCommunications Materials |            (2026) 7:39 7www.nature.com/commsmatrespectively, at a height of 274 pm above the uppermost oxygen layer.The strong Ez over the Ce3+ sites comes from the displacement of thenearby oxygen atoms away from the Ce3+ (see Fig. S14) due to theexcess charge localized in the Ce3+ as a polaron, enhancing theattractive short-range electrostatic interaction and reducing the Paulirepulsion sensed by the AFM probe. The downward displacement ofthe oxygen atoms around the SSOV (Fig. 6d) and the slight upwardshift of the Ce4+ sites close to it (Fig. 6e) also contribute to theenhanced Ez. These simulations set the basis for the possibility ofidentifying the presence and location of the elusive Ce3+ ions usingspectroscopy measurements, supporting our interpretation for thecerium atoms with an unusual contrast found in the terraces58.We observed similar variability in the interaction with the ceriumatoms in the vicinity of the water molecules. Figure 7 summarizes Δf curvesmeasured over atomic positions around themolecule highlightedwith a redsquare in Fig. 1a (see also Fig. S4). The cerium atoms at the vertices of thetriangle formed by the water structure (curves 1, 2, 3 in cyan) show ~ 9%and ~ 6% greater minimum value than the reference cerium far from themolecule (black curve). The three cerium sites on the left (curves in orange)show similar response as the reference atom, but the three cerium sites onthe right (curves 7, 8, 9 in blue), which should be equivalent by symmetry,show a more repulsive interaction past the minimum. Similar strongrepulsion is also detected over the second line of surface oxygen atoms onthe right (positions and curves in pink). The water molecule visiting moreoften the oxygen atoms on the right and lower sides than the left oneundoubtedly plays a role in adding steepness to the Δf curves beyond theminima over the cerium atoms in blue, the oxygen sites in pink and, to alesser degree, the cerium at position 4. However, the cerium atoms atpositions 1, 2, 3 (in cyan) are far enough to be affected by thewatermolecule,and the consistency with the theoretical calculations points them out ascandidates toCe3+ ions, suggesting thepossible presenceof SSOV close to theadsorbed water molecule.At this point, we cannot rule out the presence of a SSOV close to theceriumatomswith anunusual strongattractive interaction inboth themiddleof the terraces and around thewatermolecules, but we speculate, consideringthe difficulty in increasing the water coverage on the surface when dosing atroom temperature, that the presence of one or several SSOV close to the Ce3+ions is needed to bind water molecules to the terraces of the CeO2(111)surface at roomtemperature.Addressing this andother questionswill requirefuture work, exploiting the sensitivity of AFM spectroscopy in combinationwith tunneling measurements51 that could help locate the SSOVs.ConclusionsIn summary, we have combined Non-Contact AFM and first–principlescalculations to investigate the interaction of water with a partially reducedCeO2−x(111) surface at the atomic scale. Our low-temperature experimentsusing oxygen–terminated probes reveal water molecules adsorbed on cer-ium atoms as sharp, asymmetric boomerang–like features, in contrast withprevious STM and AFM studies, in which water appeared as a triangularshape, consistent with the symmetry of the lattice surface. DFT simulationsreveal that water—in both molecular and dissociated forms—preferentiallyadsorbs at Ce3+ sites near subsurface oxygen vacancies, and the surfacerelaxations induced by these defects break the local symmetry of the lattice.Calculated force spectroscopy based on DFT exhibits distinct interactionsignatures between the Ce3+ and Ce4+ sites. These differences are attributedto local structural relaxations of surface oxygen atoms, which change thelocal electrostatic environment of the cerium species. These calculationsmatch quantitatively with experimental force spectroscopy measurementsaround the water molecule and on the reduced surface. Finally, the char-acteristic contrast in constant-height AFM images originates from a probe-induced mobility of the water molecule, enabled by low-energy barriersbetween different adsorption configurations and adsorption states, andpossibly, from the particular environment created around aCe3+ ion close toa subsurface oxygen vacancy. Beyond resolving water adsorption on theCeO2(111) surface, our work demonstrates the broader capabilities ofchemically selective AFM for probing local chemical reactivity. Thisapproach offers a unique opportunity to investigate, at the atomic level,complex catalytic systems including single-atom catalysts, metal-supportinterfaces and defect-engineered oxide surfaces, where local structure andcharge state critically influence chemical behavior.1 (Ce4 + )2 (Ce4 + )3 (Ce4 + )4 (Ce4 + )5 (Ce3 + )6 (Ce3 + )300 400 500 600 700Z [pm]0.80.60.40.2Frequency shift [Hz]Fig. 6 | Calculated frequency shift curves over cerium atoms in the presence of avacancy. aDFT-based calculated Δf over the Ce4+ (curves 1–4) and the Ce3+ (curves5 and 6) atoms of a reduced CeO2−x(111) surface in the vicinity of a subsurfaceoxygen vacancy (dotted-line circles). Curve labeling is indicated in the inset imagedisplaying the atomic arrangement, which also serves as a reference for the atomicfeatures presented in the other panels. The Δf curves for the O (red), Ce (black), CV(green) calculated for the fully oxidized surface (Fig. 1), together with the long-rangevdW component (cyan) fitted from the experiments, have been included as dottedlines for reference. This long-range vdW contribution has also been added to thecalculated Δf curves in the graph. b, c Local distribution of the vertical component ofthe electric field (Ez) for the fully oxidized surface and for the same area with asubsurface oxygen vacancy (dotted circle), respectively, both obtained at a height of274 pm above the topmost oxygen layer. d Vertical relaxation of the surface oxygenatoms near a subsurface oxygen vacancy with respect to the position of the topmostoxygen layer of the fully oxidized surface. eVertical relaxation of the cerium atoms inthe proximity of a subsurface oxygen vacancy with respect to the position of theoutermost cerium layer of the fully oxidized surface (78 pm below the uppermostoxygen layer). The parallelogram in orange highlights the unit cell used in thecalculations.https://doi.org/10.1038/s43246-025-01011-x ArticleCommunications Materials |            (2026) 7:39 8www.nature.com/commsmatMethodsScanning probe microscopy experimentsThe experiments were carried out in an ultra-high vacuum (UHV) systemequipped with tools for the in situ sample preparation and a home-madescanning probemicroscope operated at 4.8 K using a commercial controller(Nanonis SPMControl System, SPECS, Germany). AFM experiments werecarried out using the frequency modulation detection scheme59 keepingconstant the oscillation amplitude of the force sensor. Under this scheme,the AFM signal corresponds to the shift in the free-oscillation resonantfrequency of the force sensor (Δf) upon forces acting on it. Force spectro-scopy experiments were performed by initially approaching the probetowards the surface fromthe imaging separation, and then retracting it uponreaching the specified closest approach until reaching the free-oscillationregime. Both constant-height AFM imaging and spectroscopy were carriedout by setting the voltage bias to zero. CeO2(111) thin-filmswere grownon aCu(111) surface following a similar procedure to the one describedelsewhere60. The Cu(111) single crystal was cleaned by repeated cycles ofargon ion sputtering and annealing in UHV, and then the surface wasoxidized by keeping the sample at 470 ∘C in a 1.0 × 10−5 Pa oxygen envir-onment for 10min. TheCeO2(111) thin-filmswere fabricated by depositingcerium (rod, 99.9 % purity, GoodFellow) from a water-cooled e-beamevaporator in the presence of 1.0 × 10−5 Pa oxygen while keeping the pre-oxidized Cu(111) sample at 480 ∘C. After the cerium evaporation, thesample temperature was gradually reduced at a typical rate of 1∘C/sec in an1.0 × 10−5 Pa oxygen. Upon the sample reaching 200 ∘C, both heating andoxygen flow were stopped and the crystal was left to cool to room tem-perature in UHV. Ultra-clean Milli-Q water, further purified by severalfreeze-pump-thaw cycles, was dosed by backfilling the UHV preparationchamber with water vapor through a leak valve while keeping the sample at35 ∘C.Dosingwith 5, 50 and 500 Langmuir of waterwith the sample at 35 ∘Cproduced similar coverages as the one displayed in Fig. 1.Probe preparationWe used the KolibriSensor (SPECS, Germany) for the detection ofboth tunneling current and probe-surface interaction forces. Theprobe of the KolibriSensor was sharpened to a typical apex radius of~ 15 nm ex situ by using a focused ion beam, and it was furtherconditioned for atomic resolution imaging in situ on copper oxidesurface areas coexisting with the CeO2(111) thin-films. Probe con-ditioning is carried out until good and sharp atomic resolution isobtained, and force spectroscopy over the three sites of theCeO2(111) surface reproduces the trend shown in Fig. 1d. Mea-surements were done on the fourth ceria surface bilayer (see Fig. S1),in which an atomic arrangement close to the bulk ceria is expected.DFT calculationsThe adsorption and transition state structure optimizations, as well as thesimulated force-distance calculations, were performed using DFT asimplemented in the VASP code (version 5.4.4)39–43 with the slab-supercellapproach61. The projector augmented wave (PAW) method62 was used todescribe the valence electrons of the atomic species: Ce (4f, 5s, 5p, 5d, 6s), O(2s, 2p) andH (1s), with a plane-wave cutoff energy of 415 eV. The electronlocalization on Ce3+ atoms of the support has been treated by means of theDFT+U approach proposed by Dudarev et al.63, with a Ueff value ofU − J = 4.5 eV for the Ce 4f electrons. We used the PBEexchange–correlation functional, the generalized gradient approximation(GGA) suggested by Perdew, Burke, and Ernzerhof (PBE)44. The vdWdispersion energy correctionwas consideredbymeansof the so-calledDFT-D3 approach45,46.Adsorption and transition state structure calculationsCeO2(111) surfaces with (3 × 3) and (4 × 4) periodicities weremodeledwithan optimized lattice constant of 5.485Å for bulk CeO2. The (3 × 3) surfacemodels have four O–Ce–O tri-layers, whereas the (4 × 4) models were builtwithonly three tri-layers to save computational resources. Bothmodels havesufficient separationbetweenconsecutive slabs (~12and27Å, respectively).All atoms in the bottomO–Ce–Otri-layerwere keptfixed at their optimizedbulk-truncated positions during geometry optimization, whereas the rest ofthe atoms were allowed to fully relax. A (2 × 2 × 1) k-point mesh, accordingto theMonkhorst–Packmethod64, was used to sample the Brillouin zone forthe (3 × 3) models, and only the Γ-point for the (4 × 4) surface. For the gas-phase calculations of the water molecule, a (15 × 15 × 15) Å3 cell wasemployed, with Γ-point only.Two Ce4+ are reduced to Ce3+ when an oxygen vacancy is generated.Following the previous work by Pan et al.65 (which reported many dif-ferent positions for the Ce3+ on a (4 × 4) surface at the HSE level66,67), wemodeled the most stable configuration they found, where the Ce3+ arenext-nearest neighbors of the vacancy (Fig. S7a and Fig. S8b). Note thatthis causes the two Ce3+ atoms to be neighbors (to each other) on the(3 × 3) model (Fig. S5). To check that our results on the stability of waterandOH+H species were not significantly affected by this situation, and toensure that the (3 × 3) results were reliable for the subsequent spectro-scopic studies, we also calculated the crucial structures on the (4 × 4)model for the twomost stable relative positions of the twoCe3+ atoms (Fig.S7b, c and Fig. S8c, d).Fig. 7 | Spectroscopic curves measured at surface atomic sites surrounding awater molecule. a Sets of Δf curves measured over Ce and O positions around thewater molecule, highlighted with a red square in Fig. 1a. The inset is a constant-height AFM image of the molecule, acquired before the spectroscopic measurementat a separation corresponding to the origin of the distance axis. Black and red latticessuperimposed on the image highlight the cerium and oxygen surface positions,respectively. bDetail of theΔf curves close to theminima. Numbering and color linkthe corresponding curve to the acquisition location in inset image: curves over the Ceatoms are in cyan (1, 2, 3), orange (4, 5, 6) and blue (7, 8, and 9); and relevant curvesoverO atoms are displayed in pink color (see also Fig. S11). Curvesmeasured overCe(in black), O (in red), and CV (in yellow) sites far from the water molecule areincluded for comparison. Acquisition parameters were: A = 60 pm andf0 = 994230 Hz.https://doi.org/10.1038/s43246-025-01011-x ArticleCommunications Materials |            (2026) 7:39 9www.nature.com/commsmatThe adsorption energy of water was calculated as:ΔEads ¼ EðH2O=CeO2ð111ÞÞ � EðH2OÞ � EðCeO2ð111ÞÞ ð1Þwhere E(H2O/CeO2(111)) is the energy of the structure with wateradsorbed on the surface, E(H2O) is the energy of the molecule in the gasphase, and E(CeO2(111)) is the total energy of the clean model surface.To identify transition state structures, the climbing image nudgedelastic band technique (CI-NEB) was used68, and frequency calculationswere employed to check that only one imaginary frequency was found foreach of them. Activation energies (ΔEact) are defined as the differencebetween the energy of the transition state (TS) and the initial state (IS).Simulated frequency shift curvesThe frequency shift curves were calculated from the forces obtained with amodel probe that includes: i) a rigid COmolecule to describe the interactionof the sample with the oxygen-termination of the probe apex, which pro-vides chemical sensitivity and ii) themesoscopic part of the apex (the yellowcone in Fig. 1) whose only contribution is a long–range attraction. Theinteraction with the apex as a function of the probe height is calculated withDFT by vertically approaching the COprobe toward the surface, adding upthevertical componentof the forceover the twoatomsof theCOmolecule ateach approach distance. The atoms of the water molecule and the firsttrilayer of the surface were allowed to relax at each step of the approach,while the remaining atoms in the surface were kept fixed. These relaxationsare minimal for the calculation of force curves over sites of the bare ceriasurface within the probe-surface distance range explored, and can safely bedisregarded to speedupcalculations, butplay a crucial role in thedescriptionof the water response to the probe-sample interaction. The computed forcecurves were converted into frequency shift (Δf) curves using classical per-turbation theory34 and the efficient approach proposed by Giessibl69.To better compare calculated Δf curves and images with the experi-mental counterparts, we added the main contribution of the long–rangeinteraction between probe and surface in the experiments to all the calcu-lated Δf curves and images. To characterise the long–range interaction inthe experiments, we fitted the experimental Δf curves over the long-rangedistance regime considering the analytical expression for the Δf originatedby the van der Waals interaction force between a spherical probe and aplane,32,70:FvdWðzÞ ¼ Czð Þ2 ) Δf vdWðzÞ ¼ f 0ffiffiffiffiffi8πp � k � A3=2� Czð Þ3=2; ð2Þwhere f0, k, and A represent the free-oscillation resonant frequency, theeffective stiffness, and the oscillation amplitude of the force sensor,respectively, z denotes the probe-surface separation, and C is a fittingparameter that accounts for the mesoscopic geometry of the probe.For the calculation of theΔf(z) curves from the atomic forces providedbyDFT,we used the experimental values of f0, andA (Fig. 1), and the value kwas obtained from the specifications of the KolibriSensor56. The parameterCwas determined by fitting the experimental Δf(z) curves measured on thestoichiometric surface over the tail towards the free-oscillation regime,obtainingC=− 1.4311 × 10−6 N pm2 (Fig. S16). Using these parameters, weadded theΔfvdW(z) background (cyan dotted line in Figs. 1d, S9 and S12) toeach of the Δf(z) curves and images obtained from the DFT-based atomicforces.The calculated Δf(z) curves provide a reference for the probe-surfacedistance in the experiments, which is measured as the relative displacementof the sample with respect to the probe (fixed in our experimental system).In our simulations, on the contrary, the probe-surface distance is welldefined with an origin (z = 0) at the plane of the topmost oxygen layer ofCeO2 (111) surface. To estimate the probe-surface distance in the experi-ments, we shift the calculated Δf(z) curves as a block (that is, preserving therelative distance between them as defined by the DFT calculations) until anacceptable alignment of the minima of all experimental and calculatedcurves is reached. This process yields the equivalence: zexp = 0 ⇔z = 411 pm.Simulation of the constant-height AFM imagesConstant-height AFM images were simulated using the FDBM53,54,71 asimplemented in the DBSPM GitHub repository: https://github.com/SPMTH/DBSPM. This method efficiently computes frequency shift ima-ges while preserving the accuracy of theDFT-calculated forces, enabling thehigh-fidelity reproduction of atomic resolution AFM images. FDBM cal-culates the total force between a probe with an inert termination, like a COmolecule, as the sum of three contributions: the short-range Pauli repulsion(SR), the electrostatic interaction (ES), and the van der Waals dispersionenergy correction modeled by the D3-vdW method45. The SR and EScontributions were computed as:VSR ¼ V0Z½ρprobe � ρsurface�α dV ; ð3ÞVES ¼Zρprobe �Φsurface dV ; ð4Þwhere ρprobe and ρsurface represent the charge density of probe andsurface, respectively, and Φsurface is the electrostatic potential of thesurface. These quantities are obtained from independent DFT calcula-tions for the probe and sample. To obtain the short-range parameters (α,V0), we fit the total force (SR + ES + vdWDFT-D3) computed with theFDBMmethod to DFT force–distance curves calculated with a rigid COprobe positioned over representative sites of the reduced CeO2−x(111)surface (Fig. S15). This process yields α= 1.08 andV0 = 36.96 eV/Å3(2α−1),ensuring that FDBM reproduces the DFT forces accurately, in particularthe short-range contribution involving oxygen atoms. Therefore, themodel should accurately describe the interaction with water moleculesadsorbed on the CeO2(111) surface. Since the oxygen atom in the watermolecule lies ~2Å above the surface oxygens, images of water acquiredat probe–surface distances ~5Å should be well captured by the FDBMapproach. The probe-surface long-range vdW force obtained from Eq.(2) is then added to obtain the total force used to generate the Δfimages shown in Figs. 3, S10 and S11 (see Fig. S17 for a detaileddescription of the AFM image simulation workflow). The FDBMsimulated images shown in Fig. 3 were performed for water adsorbed onthe reduced CeO2−x(111) surface.Data availabilityAll DFT data supporting the findings of this study are available at Zenodounder the accession number https://zenodo.org/records/17360622. Therepository includes the following files: Structures.tar.gz, contain-ing the VASP files for all structures reported in the paper; for-ces_and_freq_shifts.tar.gz, containing the forces andfrequency-shift data used to reproduce the figures of the manuscript; andmovies.tar.gz, providing DFT spectroscopy animations in .mp4format. A detailed description of the structural data is provided inStructures_README.txt. The experimental data supporting thefindings of this study are available from the author (O.C.) upon reasonablerequest.Received: 22 August 2025; Accepted: 5 November 2025;References1. Trovarelli, A. Catalysis by ceria and related materials ∣ Catalyticscience series Vol. 2 (World Scientific Publishing Company, London,England, UK, 2002).2. Montini, T.,Melchionna,M.,Monai,M. & Fornasiero, P. Fundamentalsand catalytic applications of CeO2-basedmaterials. Chem. 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Nanoscale 13, 18473–18482 (2021).AcknowledgementsThisworkwas supportedbyNIMSgrants (AG2030andAM2100), by severalGrant-in-Aid for Scientific Research (19H05789, 21H01812, 21K18876,22H00285, 23KJ1516, 24K01350) from the Ministry of Education, Culture,Sports, Science and Technology of Japan (MEXT) and by the SpanishMinistry of Science, Innovation and Universities (MCIU), through projectsPID2023–149150OB–I00 and PID2021-128915NB-I00, and the “María deMaeztu” Program for Units of Excellence in R&D (CEX2023–001316–M).E.F.V. acknowledges support from the Margarita Salas postdoctoral fel-lowship (Spanish MIU and European Union NextGenerationEU) and theMOMENTUM Program (MMT-24-ICP-01, Plan de Recuperación, Transfor-mación y Resiliencia European Union NextGenerationEU). The SpanishSupercomputing Network (RES) is acknowledged for providing computa-tional resources at the Marenostrum Supercomputer (BSC, Barcelona).Author contributionsO.C., K.K., M.A., H.S.A. and S.K. performed the experiments and dataanalysis. M.G.L., E.F.V., P.P., M.V.G.P. and R.P. performed the DFTcalculations and AFM simulations. O.C., M.G.L., E.F.V., P.P., M.V.G.P., andR.P. wrote the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s43246-025-01011-x.Correspondence and requests for materials should be addressed toOscar Custance or Ruben Perez.Peer review information Communications Materials thanks Guangfu Liaoand the other, anonymous, reviewer(s) for their contribution to the peerreview of this work. A peer review file is available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License,which permits any non-commercial use, sharing, distribution andreproduction in any medium or format, as long as you give appropriatecredit to the original author(s) and the source, provide a link to the CreativeCommons licence, and indicate if you modified the licensed material. Youdo not have permission under this licence to share adapted materialderived from this article or parts of it. The images or other third partymaterial in this article are included in the article’s Creative Commonslicence, unless indicated otherwise in a credit line to thematerial. If materialis not included in thearticle’sCreativeCommons licenceandyour intendeduse is not permitted by statutory regulation or exceeds the permitted use,you will need to obtain permission directly from the copyright holder. Toview a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2026https://doi.org/10.1038/s43246-025-01011-x ArticleCommunications Materials |            (2026) 7:39 12https://doi.org/10.1038/s43246-025-01011-xhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/commsmat Near-surface defects break symmetry in water adsorption on CeO2−x(111) Results and discussion AFM imaging of water, surface atomic sites and probe identification Adsorption of molecular water in the presence of a subsurface defect Calculated AFM images of a water molecule adsorbed near a subsurface defect Interaction of the probe with the water molecules Probe-induced dynamical effects Origin of the boomerang-like shape of water in the AFM images Origin of the cerium atoms with unusual contrast Conclusions Methods Scanning probe microscopy experiments Probe preparation DFT calculations Adsorption and transition state structure calculations Simulated frequency shift curves Simulation of the constant-height AFM images Data availability References Acknowledgements Author contributions Competing interests Additional information