Rh single atoms on TiO2 dynamically respond to reaction conditions by adapting their site

Single-atom catalysts are widely investigated heterogeneous catalysts; however, the identification of the local environment of single atoms under experimental conditions, as well as operando characterization of their structural changes during catalytic reactions are still challenging. Here, the preferred local coordination of Rh single atoms is investigated on TiO2 during calcination in O2, reduction in H2, CO adsorption, and reverse water gas shift (RWGS) reaction conditions. Theoretical and experimental studies clearly demonstrate that Rh single atoms adapt their local coordination and reactivity in response to various redox conditions. Single-atom catalysts hence do not have static local coordinations, but can switch from inactive to active structure under reaction conditions, hence explaining some conflicting literature accounts. The combination of approaches also elucidates the structure of the catalytic active site during reverse water gas shift. This insight on the real nature of the active site is key for the design of high-performance catalysts.

S upported noble metal nanoparticles are widely investigated heterogeneous catalysts due to their high activity and selectivity for valuable products. However, the high prices and finite resources of these noble metals limit their applications in large-scale production. Heterogeneous single-atom catalysts (SACs), which consist of isolated atoms anchored onto supports, maximize the efficiency of noble metal utilization [1][2][3][4][5] . Moreover, developing catalysts that precisely place the single metal atoms homogeneously at a single site on the support can offer high selectivity towards a specific product. Thus, as a bridge between homogeneous and heterogeneous catalysis, SACs have become a new frontier in catalysis science and thus attracted significant attention recently [6][7][8][9][10][11][12][13][14][15] .
A single atom (SA) on a support possesses unique chemical and physical properties due to its particular local chemical environment, inducing an electronic structure that differs from that of conventional supported nanoparticle catalysts. However, the identification of this local environment of SAs under experimental conditions, as well as operando characterization of structural changes of SAs during catalytic reactions, is still challenging despite the development of in situ microscopy and spectroscopy techniques 16 . The local environment determines the electronic structure, charge distribution, and oxidation state of the SAs, and hence also the stability, activity, and selectivity of the catalyst. Two main types of structures have been described for SACs: either substituting a cation at the oxide surface or supported on-top of the support, and these two types of SAs generally exhibit different catalytic properties 17 . Camellone and Fabris 18 reported that substitutional Au 3+ ions at the ceria surface, and not supported Au + adatoms, activate molecular CO and oxidize it to CO 2 18 . In the case of cobalt oxide (CoO)-supported Rh SACs, Rh substituted at the Co site was shown to be active and selective towards propene hydroformylation 19 , while Rh substituted at the O site (Rh 1 Co 3 bimetallic single-cluster sites) exhibits an excellent catalytic performance in the reduction of NO with CO at low temperature 20 and a potential application in ammonia synthesis via N 2 reduction 21 . Datye and co-workers 22 highlighted that atomically dispersed Pt on ceria can achieve a high activity for low-temperature CO oxidation after a steam treatment at 750°C, which affects the environment of the single Pt atom on the support.
There are several factors that can potentially affect the local structure of SACs, including specific pretreatment, reactants, intermediate species, and temperature. Here, we consider a single Rh atom supported on the rutile TiO 2 (110) surface to investigate the stability of different Rh structures under typical experimental conditions with first-principles atomistic thermodynamics, in order to show how SAs dynamically respond to reaction conditions. Stabilization of SAC requires strong interaction between the metal atom and the oxide, and although several oxides have been shown to be adequate (Fe 3 O 4 , TiO 2 , CeO 2 , Co 3 O 4 ), TiO 2 avoids additional theoretical challenges linked with magnetic properties or relativistic effects. We experimentally characterize single Rh atoms on rutile after different reduction steps under hydrogen by CO probe molecule infrared (IR) spectroscopy and scanning transmission electron microscopy (STEM) imaging 23,24 . The combination clearly demonstrates that Rh SAs change their structure and adapt their catalytic site under reaction conditions towards a structure active for CO 2 reduction to CO under hydrogen by reverse water gas shift (RWGS).

Results
Compared stability of various sites. The two main parameters controlling the structure of the Rh atom/TiO 2 (110) interface are the oxygen stoichiometry for the TiO 2 surface and the position of the Rh atom. We systematically studied the stoichiometric termination, two oxygen-deficient ones (0.65 and 1.30 vacancies by nm 2 ) and one oxygen-rich one (0.65 additional O by nm 2 ), and we explored a large range of positions for the Rh atom, in substitution of a Ti atom (denoted as Rh 1 @support) or supported on the surface (denoted as Rh 1 /support), and of relative positions between the Rh atom and the vacancies/additional O. This allowed us to generate multiple environments and electronic structures for the Rh atom. The stability of the various terminations can be compared using first-principles atomistic thermodynamics, using oxygen chemical potential (μ) as a descriptor (Ti chemical potential is then fixed from the bulk energy of TiO 2 ). For each selected TiO 2 surface termination, and each type of Rh site (supported or substitutional), all Rh atom positions have been evaluated, but only the most stable one is considered in the surface stability diagram (Fig. 1). Other positions and their relative energies can be seen in Supplementary Figs. 1 and 2.
Under oxygen-rich conditions (high chemical potential of oxygen, −1.7 < Δμ(O) < 0), Rh substituted at the 6-fold Ti site in the stoichiometric TiO 2 (Rh 1 @TiO 2 ) is the most favorable structure (Fig. 1a). Terminations with additional O atoms, and Rh appearing as a supported oxide moiety (Rh 1 @TiO 2 + x , Rh 1 / TiO 2 + 2x ), are close in energy in the highest part of the interval, but never appear as most stable. Under oxygen-poor conditions,  At the given μ(H) value, the relative stability for each model still depends on the chemical potential of oxygen, as shown in Fig. 2a, in a similar way to Fig. 1a. A major difference is that the high pressure of hydrogen drives the system into an O-poor condition. Under reduction conditions, hydrogen will react with surface O atoms to form water and if we assume an H 2 conversion of 0.01% to H 2 O, and still 0.1 atm H 2 at 500 K, Δμ(O) is then fixed at the low value of −3.23 eV. At this O chemical potential, the substitutional and supported Rh atom structures have almost the same free energy (Fig. 2b) and hence both coexist at thermodynamic equilibrium. This supported Rh becomes stable vs. the substitutional cation upon the formation of two O vacancies around Rh, and in this situation, it is liganded to two H atoms. Therefore, Rh SAs on TiO 2 adapt their site from substitutional to supported when going from oxygen-rich preparation to H 2 -reduction conditions. Mobility of the TiO 2 surface at high temperature under H 2 allows filling of the Ti vacancy formed after extraction of the Rh atom 16 .
If Δμ(O) and Δμ(H) are independent, a 2D surface stability diagram can be constructed as a function of these two descriptors ( Fig. 3). High Δμ(O) stabilizes the substitutional sites, and low Δμ (O) the supported sites, but the frontier between the stability regions of the two sites (shown as a thick black line) is moved towards lower Δμ(O) when Δμ(H) (and hence the H coverage) is increased, especially in the temperature region corresponding to reduction conditions (400-600 K). This trend is explained by the strong adsorption energy of H on Rh (−2.30 eV) in the presence of two O vacancies, which extends the stability of the green zone in Fig. 3. Hence, hydrogen pressure stabilizes both the substitutional and the supported site, but the shift to very Opoor conditions strongly favors the supported site, which becomes more stable.
Stability under a pressure of CO. Upon submitting the system to a pressure of CO, the preferred structure is governed by the O and CO chemical potentials. CO adsorbs on the supported SA and all possible adsorption sites for SA Rh with one or two CO adsorbed have been tested ( Supplementary Fig. 7). The most 3.0 μ(system) (eV) stable structure for each Rh site, TiO 2 termination, and CO coverage is chosen to establish the stability diagram. The complete 2D stability diagram, as a function of Δμ(O) and Δμ(CO), is shown in Fig. 4a. Partial diagrams constrained to one CO or two CO adsorption for a fixed Δμ(CO) value can be seen in Supplementary Fig. 8. Upon CO pressure, the zones corresponding to Rh being stable as a supported atom (purple in Fig. 4a) are strongly extended. This is especially the case for a typical condition of CO adsorption used in volumetric chemisorption or probe molecule IR experiments (a 10% gas mixture of CO, and 90% He at atmospheric pressure and room temperature), in which Δμ(CO) is calculated to be −0.59 eV, a situation where the supported Rh is more stable than the substitutional one for the almost entire range of O chemical potential considered here ( Fig. 4a and Supplementary Fig. 9). CO adsorption hence completely changes the thermodynamic site preference for the Rh atom, irrespective of the presence of O vacancies. This is explained by the fact that CO adsorbs significantly more strongly on the supported Rh (−4.89 eV for Rh 1 /TiO 2 ), compared to the substitutional Rh (−2.74 eV for Rh 1 @TiO 2−2x ). Charge density difference demonstrates that the strong interaction between Rh SAs and CO molecules results from not only Rh-C σ-bonding but also back-donation from the metal towards the antibonding π* CO orbital ( Fig. 4c, d).
Hence thermodynamics under CO pressure tends to drive all Rh atoms to a supported site, if the temperature is high enough for kinetic aspects not to be limiting. Thus, the CO molecule plays a role in stabilizing the supported Rh SAs. Experimentally, CO is typically adsorbed on Rh after H 2 reduction, so the surface is partially reduced by H 2 with the formation of two oxygen vacancies and thus the most favorable structure under CO pressure should be 2CO/Rh 1 /TiO 2−2x .
To further illustrate the potential for Rh site modification of hydrogen or CO adsorption, we can define the driving energy of the transformation as the difference of free energy between the most favorable supported site and the most favorable substituted site, a negative driving energy indicating that the site change towards the supported case is thermodynamically favorable. During CO adsorption, the driving energy is markedly negative, with a value of~−1.5 eV in the relevant region of chemical potential (see Supplementary Fig. 10b). This driving energy for site change is much stronger under a pressure of CO than under a pressure of H 2 , where it becomes negative only at very low μ(O) and remains close to energy neutral. This result further proves that CO and H 2 molecules adapt the sites of SAs via different mechanisms and with different strength due to difference in their bonding mechanism.
Stability vs. cluster formation and FTIR studies. Thermodynamic analyses hence show that Rh SACs on TiO 2 will adapt their sites in response to reaction conditions, such as under H 2 or CO pressure. Beyond its position on the oxide, the stability of the SA vs. clustering is another key aspect, especially when it is in supported situation and hence has potential mobility. Our calculations show that under a pressure of CO (2CO/Rh/TiO 2 structure), dimerization of the Rh(CO) 2 species is less stable by 1.14 eV ( Supplementary Fig. 11). Hence initial clustering of the SA is thermodynamically unfavorable. In addition, the Rh SA liganded to two CO is more stable than bulk Rh metal (Supplementary Fig. 9), precluding the formation of large nanoparticles. Similarly, under H 2 reduction condition (6H/Rh/TiO 2−x structure), the dimerization of the RhH 2 surface species into a supported Rh 2 H 4 unit is endothermic by 1.24 eV ( Supplementary  Fig. 11). However, in that case, the H-liganded Rh SA is less stable than bulk Rh (Fig. 2c). Since dimer formation is endothermic, the nucleation process is difficult, and the SA is metastable at reasonable temperature. There is hence a risk of particle formation only under H 2 at high temperature.
In order to validate our conclusions, we synthesized Rh SAs on rutile TiO 2 support, varied in situ pretreatments conditions, and used spectroscopy and microscopy to analyze the evolution of the Rh structure and TiO 2 support. CO probe molecule IR experiments were executed at −120°C, which allows us to kinetically trap the structure, avoiding any changes induced by the adsorption of CO. CO adsorption on Rh SAs supported on TiO 2 has previously been shown to yield a specific doublet of peaks at ∼2097 and ∼2028 cm −1 , associated with the symmetric and asymmetric stretches of the Rh(CO) 2 gem-dicarbonyl species 26 . Figure 5a shows the IR spectrum of CO adsorption at −120°C on four differently in situ pretreated samples (oxidized at 350°C, reduced at 100, 200, and 300°C), to correlate with the predicted structures that would form in varying oxidation and reduction conditions. The pre-oxidized (350°C in O 2 for 1 h) sample does not adsorb CO at −120°C. This is fully consistent with aforementioned calculation results, since during O 2 pretreatment, O chemical potential is high (−0.61 eV) and Rh SAs are stabilized in a +4 oxidation state in the substitutional site of Ti (Rh 1 @TiO 2 ), a situation where CO cannot adsorb on the Rh cation.
After reduction in H 2 at 100°C, CO adsorbs on Rh at −120°C with a predominant stretch at 2094 cm −1 and a very small accompanying stretch at 2026 cm −1 . The formation of a majority species with CO adsorbing to Rh atoms with a 1:1 stoichiometry agrees with calculations of the Rh@TiO 2−x species, which show preference for the adsorption of single CO with a vibrational frequency of 2071 cm −1 . This is consistent with the pathway followed in Fig. 3, where Rh@TiO 2−x forms due to exposure of Rh@TiO 2 species (that do not adsorb CO) to mild reduction conditions. Further reduction in H 2 at 200°C induces the growth of the stretch at 2031 cm −1 and a shift in the stretch at 2094 to 2097 cm −1 . This result is consistent with the calculations that predict the formation of the gem-dicarbonyl species 2CO/Rh 1 / TiO 2−2x (Fig. 4b), and the calculated frequencies for CO are 2082 and 2023 cm −1 , in good agreement with the experimental values. However, when the reduction temperature is increased to 300°C, one notes the appearance of a CO band at 2070 cm −1 , showing the agglomeration of Rh SAs in Rh clusters. The primary conclusions of the CO probe molecule IR characterization were substantiated via ex situ atomic resolution STEM imaging of the Rh/TiO 2 sample following reduction in H 2 at 100 and 300°C, see Fig. 5c, d and Supplementary  Fig. 12. For the sample that had been reduced at 100°C, single Rh atoms were primarily observed in all images. Alternatively, for the sample that had been reduced at 300°C, a mixture of Rh clusters and SAs were observed. Both observations are in agreement with the interpretation of the CO IR characterization. It is interesting to note that while 300°C reducing conditions in H 2 were observed to drive encapsulation of Rh particles by reduced TiO 2 overlayers (see Supplementary  Fig. 13), the combination of CO IR and STEM imaging presented here suggests that single Rh atoms will not be encapsulated by TiO 2 under similar conditions 27 .
When CO adsorption is performed at 20°C, all three reduced samples show similar Rh(CO) 2 spectral features, suggesting that CO adsorption, when the temperature is high enough to allow atom mobility, drives Rh atoms to similar supported Rh(CO) 2 geometries, even though they may be in different starting locations, Fig. 5b. The small difference in the CO stretch frequencies likely derives from small differences in surface Ovacancy coverage on the TiO 2 support. From the sample pretreated at 300°C, the feature at 2070 cm −1 disappears after CO adsorption at 20°C, showing that supported Rh particles can be readily fragmented to Rh SAs in the presence of CO, see Fig. 5b, in line with the calculated high stability of supported SAs in these conditions 28 . This scenario is reminiscent of the dynamic SA formation during nanogold catalysis [29][30][31] . As expected, the intensity of the symmetric stretch (~2090 cm −1 ) at 20°C is stronger than that of the asymmetric stretch (2023 cm −1 ) for the Rh(CO) 2 species due to the existence of nearby O vacancies in TiO 2 , but the exact ratio of intensity depends on reduction conditions.
It should be noted that for the pre-oxidized Rh sample, exposure to 20°C CO does not change the properties at all, Fig. 5b, and in fact exposure to CO at 300°C is required to induce O-vacancy formation that enables CO adsorption, see Supplementary Fig. 14. That is because the stable and highly coordinated substitutional site cannot provide an adsorption site for CO, so that CO is unable to interact and to transform the site to the supported structure. Hydrogen hence has a special role in creating O vacancies around the substitutional Rh cation, reducing its coordination and opening a channel for CO adsorption, and subsequent migration of the CO stabilized Rh species. The creation of oxygen vacancies when CO acts alone as a reductant at 300°C is further evident because CO 2 was observed to form, presumably through oxidation by TiO 2 lattice oxygen, and these O vacancies in turn enabled the formation of Rh(CO) 2 species (Supplementary Fig. 14).
X-ray photoelectron (XPS) spectra showed a downshift of the XPS Ti 2p core level by 0.3 eV, from 459.0 to 458.7 eV, when comparing oxidation at 350°C to reduction under hydrogen at 200°C, indicating a reduction of some of the Ti in the sample, most likely at the surface of the oxide nanoparticle as indicated by the DFT calculations. Additionally, the O1s level in the reduced case is also downshifted by 0.4 eV, together with the appearance of a new feature at higher (+1.9 eV) binding energy (Supplementary Fig. 15) 32,33 . This peak is assigned to the formation of surface hydroxyls under hydrogen pressure. In addition, by using the integrated area of the Ti and O peaks and associated sensitivity factors, it was observed that the O:Ti ratio decreased by 5% after reduction 34 . The XPS and IR results are in agreement with the DFT calculations, and that reduction of the Rh/TiO 2 catalysts induces hydroxylation and oxygen vacancy formation, which in turn drive the switch in the preferred Rh local coordination, enabling interaction with adsorbates.
Catalytic reactivity. In a nutshell, the combination of theory and experiment shows here that Rh atoms adapt their binding site to the presence of various reactants (O 2 , H 2 , and CO). It is hence important to explore whether this adaptive character has an impact on catalytic properties. We selected the RWGS reaction as an example for this purpose since when submitting a mixture of CO 2 and H 2 to a Rh on TiO 2 catalyst, it was shown that dispersed Rh SAs are active and selective for CO formation (from RWGS), while Rh nanoparticles lead to methanation 35 .
Under reaction condition (500 K, 10 CO 2 :1 H 2 ), 6H/Rh 1 @TiO 2−2x and 6H/Rh 1 /TiO 2−x are the most favorable hydrogenated structures for substitutional and supported models, respectively (Supplementary Table 1). Hence, both structures were considered as initial state for the RWGS pathways and considering two mechanisms: via CO 2 dissociation or COOH-mediated. In the first case, the key step is the direct dissociation of CO 2 to CO, while for the second possibility, adsorbed CO 2 will react with surface OH species to form COOH that dissociates to OH and CO species 36 . For the supported Rh atom structure 6H/Rh 1 / TiO 2−x , the CO 2 dissociation path is the most favorable and the first step consists in forming a second O vacancy, necessary to activate CO 2 . One of the two H on Rh reacts with a neighboring OH species, forming one water and one oxygen vacancy, with a barrier of 1.05 eV ( Fig. 6 and Supplementary Table 2). Water easily desorbs at reaction temperature, creating a vacancy site where CO 2 can adsorb in an exergonic way, with an adsorption internal energy of −1.70 eV and a bent geometry, indicating a strong activation of CO 2 at this site. Then, the dissociation of CO 2 to CO occurs with a very low activation barrier (0.26 eV), the CO naturally coordinating to the Rh atom. The final steps (H 2 dissociative adsorption and CO desorption) occur easily, but the order is important since H 2 adsorption assists CO desorption. According to the energetic span model 37 , the effective barrier of the reaction is 1.52 eV. In contrast, the reaction is much more difficult if one starts from Rh in substitution of Ti in 6H/Rh 1 @TiO 2 −2x . The Rh atom is saturated by two H atoms and, in order to create an adsorption site for CO 2 , one H must be transferred to a nearby O atom ( Supplementary Fig. 16, Supplementary Table 3). Reaction with a surface -OH species to form H 2 O is not allowed here, since it is endothermic (+1.49 eV) with a barrier of 3.00 eV. Transfer to subsurface oxygen is still not favorable, with an endothermic energy of +1.46 eV and a barrier of 2.30 eV. Activation of the Rh center for RWGS is hence not possible, and the substitutional structure for the Rh atom is not catalytically active, because the strong adsorption energy of hydrogen on Rh prevents CO 2 adsorption. This indicates clearly that the active site for Rh SAC on TiO 2 in the case of the RWGS reaction is the supported site rather than the substitutional site. Further electronic structure analysis (see Supplementary Fig. 17) shows that Rh, liganded to two H atoms, is slightly negatively charged (−0.06 |e|) in 6H/Rh 1 /TiO 2−x and that its oxidation state is zero. In the unit cell, four protons and one vacancy provide six electrons. Five Ti 3+ are located at the surface of the unit cell (representing 31% of surface Ti cations) and one electron is shared on the RhH 2 unit. After creation of another vacancy by desorption of H 2 O (2v + 4H* intermediate on Fig. 6), one more Ti 4+ is reduced to Ti 3+ on the surface and Rh gains further electronic population (charge: −0.50 |e|). This negatively charged Rh can transfer electron to CO 2 , and promote the adsorption and activation of CO 2 .
The steady-state nature of the catalyst in reaction conditions is given by the most stable intermediate along the profile. For the supported Rh on TiO 2 , this corresponds to the coadsorption of CO and H on Rh, with three additional H adsorbates and one O vacancy on the TiO 2 unit cell (Rh(H)(CO) in Fig. 6). In reaction conditions, it is 0.21 eV (Supplementary Table 1) more stable than the best substitutional site, which in the same conditions bears two H on the Rh and four H adsorbates and two O vacancy on TiO 2 . This Rh(H)(CO) structure is supported experimentally by in situ Fourier-transform infrared spectroscopy (FTIR) measurements under the same reaction conditions where a linear CO bonded to Rh appears at 2049 cm −1 , close to the calculated value 2044 cm −1 (Supplementary Fig. 18a). Post-reaction analysis showed that the Rh species retained its SA structure (Supplementary Fig. 18b). The catalytic activity (turn over frequency, TOF) was calculated from the pathway (and in the conditions) of Fig. 6 by using the energetic span approach 37 . The value obtained (0.0056 s −1 ) is in qualitative agreement with the measured TOF values in similar conditions (~0.01 s −1 ) 35 . Comparing the theoretical and experimental results obtained here for rutile TiO 2 supported single Rh atoms with reactivity measurements made on P25 mixed-phase TiO 2 supports is justified based on CO IR measurements that suggest single Rh species localized on rutile domains of the P25 TiO 2 support (Supplementary Fig. 19). Hence, the experimental and theoretical analysis agrees on the most stable species under reaction conditions and the TOF. This strongly validates our conclusion that, during RWGS reaction, Rh atoms will tend to move from the substitutional site favored during catalyst synthesis toward the supported site, more stable but also catalytically active.
By a combination of first-principles modeling and experiment, we have shown that single Rh atoms on TiO 2 could dynamically adapt their site to the reaction conditions under reduction condition. This finding is consistent with the stability analyses of SAs on oxide surface that can vary with the site and reaction conditions 29,38 . The allusion of statically anchoring for a stable single metal atom on an oxide support can be misleading under such circumstances. In oxidative conditions, Rh prefers to substitute the six-coordinated Ti atoms in the surface plane of the oxide. In contrast, under a pressure of H 2 or CO, it prefers to be supported on-top on the oxide. The roles of H 2 and CO are however distinct in this scenario. CO efficiently stabilizes the supported site when adsorbed on it, but is unable to interact with the initial saturated substitutional site. In contrast, the stabilization induced by hydrogen is weaker, but it can decrease the Rh cation coordination by creation of O vacancies and hence open a channel for CO adsorption. In addition, the single metal atom is not bare, but covered by H atoms and/or CO molecule(s) in catalytic conditions. FTIR measurements of CO adsorption on SA Rh following varied pretreatment confirms the site change trend obtained from the calculations, and show that the transformation is kinetically accessible.
This adaptive character of the SA can only be accessed by operando studies and can be crucial for its catalytic reactivity, as illustrated here with the RWGS reaction. The as-prepared SAs, placed in substitution of titanium, are inactive for this reaction even after reduction by hydrogen and vacancy creation around the Rh. Especially noteworthy is the finding that the reductive condition of the reaction promotes the change of the site from substitution toward the supported structure, a situation where the SA is covered by H and CO and becomes catalytically active. FTIR during reaction again confirms the result. The H 2 reactant, further assisted by the CO product, hence in situ switches the inactive as-prepared catalyst precursor into a highly active species. The dual character of the SAC with an off-site and an on-site, switchable through specific chemical interactions, could also explain the controversy in the literature on the inactive or active character of SAC, for example, in the case of Pt for CO oxidation and water gas shift reaction 24,39,40 .
Restructuring under reaction conditions is not a privilege of SAs, but also occurs for catalytic clusters and nanoparticles, as shown by in situ studies 41 . A key difference is that with SAs, the support plays the primary role in driving the reconstruction. In the present case, we showed that the change in oxidation state and coordination environment of Rh is driven by OH formation and O-vacancy formation at the TiO 2 surface. In contrast, the dynamical behavior of a metal cluster in reaction conditions, although affected by the state of the support, is primarily driven by the metal cluster thermodynamics.  Table 1 Our findings have provided insights on the critical questions of stability of heterogeneously supported SAs under reactive condition and the dynamic position changes of these atoms in redox reactions. The approach, and the proposed link between the transformation of the support and the restructuring of the metal, can in principle be extended to other SAC with similar metals (Rh, Pt, Ni, etc.) on reducible oxides (Fe 3 O 4 , CoO, CeO 2 ) in order to understand how the chemical nature of oxide and metal controls the restructuring process. The message from the present study is that as-prepared catalysts provide structures with the metal at high oxidation state occupying the oxide cation position, and that migration to a more reduced, supported and adequately liganded structure might be required for optimal catalytic activity. Our results provide a detailed understanding of the local structure of SAs on oxide support and their adaptive and dynamic character under realistic catalytic conditions, which are key insights that chemists should have in mind when designing single SACs.

Methods
DFT parameters. All the calculations were performed using periodic DFT methods implemented in the Vienna Ab initio simulation package (VASP) code 42,43 . The projector augmented wave 44 method was used for the interaction between the atomic cores and valence electrons. The valence orbitals of Ti (3p, 4s, 3d), Rh (4d, 5s), O (2s, 2p), C (2s, 2p), and H (1s) were described by plane-wave basis sets with cutoff energies of 400 eV. The exchange-correlation energies were calculated by the generalized gradient approximation with the Perdew-Burke-Ernzerhof functional 45 . Spin polarization was considered using unrestricted Kohn-Sham formalism. To correct the strong electron-correlation properties of these oxides, DFT + U calculations 46,47 were performed with U = 4.2 eV for Ti, which is taken from the literature 48,49 .
The force threshold on each relaxed ion was set as 0.02 eV/Å. Monkhorst-Pack (1 × 1 × 1) Γ-centered k-points grid sampling within the Brillouin zones were used because of the large size of the surface models. The location and energy of transition states were calculated with the climbing-image nudged elastic band and dimer methods 50,51 . Vibrational analysis was further used to confirm the transition states with only one imaginary frequency.
Computational models. The rutile TiO 2 (110) surface was modeled as periodic slabs with 12 layers (four tri-layers), with a vacuum gap between slabs at~15 Å. A 4 × 2 surface cell was utilized and the bottom three layers were kept fixed to their bulk position.
In this work, we calculated the adsorption energies according to the following equation: E ads = E (slab + adsorbate) − E (slab) − E (adsorbate) , where E (slab + adsorbate) , E (slab) , and E (adsorbate) are the calculated electronic energy of species adsorbed on the surface, the bare surface, and the gas-phase molecule, respectively. Similarly, the desorption energy is defined as E des = E (slab + desorbate) − E (slab) − E (desorbate) and the reaction energy is defined as ΔE = E (products) − E (reactants) . The charge density differences were evaluated using the formula Δρ = ρ A + B − ρ A − ρ B , where ρ X is the electron density of X. Atomic charges were computed using the atom-in-molecule scheme proposed by Bader 52 .
Stability descriptor. The system chemical potential μ(system) was used to measure the stability of different models with a consistent reference: where E(system) is the VASP calculated energy of Rh 1 TiO 2 structures, and E(TiO 2 ) is the energy of the bare TiO 2 surface. The μ(Rh) and μ(TiO 2 ) represent the chemical potential of bulk Rh and TiO 2 , respectively, and μ(O) is the free energy of oxygen atom. Bulk solid chemical potentials are taken from optimized DFT structures. The n values are set to balance the stoichiometry relative to a standard Rh 1 TiO 2 system, namely, the TiO 2 surface slab and bulk Rh. The relative free energy is calculated for each system by subtracting the energy of this standard system. The chemical potential of oxygen atom, μ(O), is calculated as a function of temperature T and oxygen partial pressure P, using where Δμ(O) is the value of μ(O) when using the half of E(O 2 ) as zero reference. Similar definitions are used to Δμ(H) and Δμ(CO).
When we consider the absorbed species, the chemical potential of system with adsorbed species μ(system-ads) can be estimated by μ systemÀads ð Þ ¼ μ system ð ÞþE ads À Δμ ads T; P ð Þ: ð3Þ For H 2 reduction, it should be μðsystemÀHÞ ¼ EðsystemÀHÞ À nðOÞμðOÞ À nðTiO 2 ÞμðTiO 2 Þ À ðEðTiO 2 Þ þ μðRhÞÞ À nðHÞμðHÞ; ð4Þ where μ(system) is the chemical potential of system without adsorbed species; E ads is the adsorption energy for adsorbed species and μ ads (T,P) is the chemical potential of adsorbed species. In the case of H 2 reduction, an additional variable μ (H) is introduced, and μ(O) is given by μðOÞ ¼ μðH 2 OÞ À μðH 2 Þ: ð5Þ Sample preparation. Rh SACs were synthesized by utilizing strong electrostatic adsorption principles at the low Rh weight loading of 0.05 wt%. The rutile TiO 2 support (US Nano # US3520, 30 nm diameter, 99.9% purity) and precursor (Sigma-Aldrich # 206261, Rhodium(III) chloride hydrate) were diluted in water separately at ratio of 4:1 and according to a support surface loading of 260 m 2 /l based on a measured TiO 2 surface area of 26 m 2 /g. NH 4 OH was added to the separate support and precursor solutions to target a pH of 8.25. The precursor solution was injected at a rate of 4 ml/min into the support solution while constantly stirring. Then, the solution was heated to 70°C until water evaporated and sample was dried completely. The sample was kept overnight in a 100°C in an oven and then ex situ calcined in 10% O 2 in He for 4 h at 350°C. XPS was done to indicate that no Cl remained on catalyst to influence local Rh structure ( Supplementary Fig. 20).
FTIR characterization. The catalyst was loaded in a Harrick low-temperature reaction chamber mounted inside a Thermo Scientific Praying Mantis diffuse reflectance adapter set in a Nicolet iS10 FTIR spectrometer with a Mercury Cadmium Telluride (MCT) detector and mass flow controllers (Teledyne Hastings) were used to control the gas flow rates across the reactor bed. Catalysts were pretreated in situ by either oxidation for 30 min at 350°C in 10% O 2 in He, or subsequent reduction for 1 h at a specified temperature (100, 200, and 300°C) in 10% H 2 in Ar. CO probe molecule IR was executed by decreasing the temperature following pretreatment in argon below −120°C in vacuum, then exposing to 10% CO in Ar for 10 min, followed by purging in Ar for 10 min, and spectra collection. The temperature was then increased to room temperature and 10% CO in Ar was flown to the cell for 10 min and flushed with Ar prior to room temperature spectra collection.
STEM characterization. The two samples were taken from the same batch of Rh SAC. Both samples were ex situ oxidized at 350°C for 30 min in pure O 2 and then one was reduced at 100°C and one at 300°C for 60 min in 10% H 2 in He. Atomic resolution bright field (BF) and HAADF-STEM images were taken on JEOL Grand ARM 300CF TEM/STEM with double spherical aberration correctors operated at 300 kV with probe current of 23 pA and pixel time of 4 μs. BF image was taken with outer collection angle of 31 mrad and HAADF image was taken with 53-180 mrad collection angle. Samples for STEM measurements were prepared by dropping 60 μl nanoparticles dispersion in methanol on a lacey carbon-coated copper grid.
XPS characterization. The two samples were taken from the same batch of Rh SAC. Both samples were oxidized at 350°C for 30 min in pure O 2 and then one was reduced at 200°C for 60 min in 5% H 2 in Ar. After samples were oxidized or reduced, they were vacuum sealed without exposure to air, transferred to a glovebox under inert gas, and mounted on copper tape in a sample holder for XPS analysis. The sample holder was directly transferred from the glovebox to the chamber of the XPS to prevent air and moisture exposure. XPS characterization was carried out under vacuum using a Kratos AXIS ULTRA DLD XPS system equipped with an Al Kα monochromated X-ray source and a 165 mm mean radius electron energy hemispherical analyzer. Binding energy calibrations were done with reference to the carbon 1s peak by adjusting spectra to 284.8 eV.

Data availability
All data supporting the findings of this study are available within the Article and its Supplementary Information and/or from the corresponding authors upon reasonable request.