1 Introduction

Due to their particular local environment, single-atom catalysts (SACs) represent a new frontier in heterogeneous catalysis, resulting in a unique electronic structure in comparison with supported nanoparticle catalysts [1,2,3,4,5,6,7]. Metal atoms adsorbed on solid supports and their resulting catalytic properties combine the advantages of homogeneous catalysts (high activity and selectivity) and heterogeneous catalysts (stable and easy to separate), while minimizing the amount of precious metal used in heterogeneous catalysis [3, 8]. Therefore, SACs are expected to bridge the gap between heterogeneous and homogeneous catalysts. However, the tendency of isolated atoms to aggregate into small clusters due to their relatively high surface energy is problematic. A strong covalent metal-support interaction is capable of stabilizing SACs [9]. However, adsorption of SACs in atomic defects on the substrate surface is the most effective way to avoid clustering and stabilize isolated metal atoms on the support [10, 11], expanding the applicability and efficiency of single-atom catalysis.

Nonetheless, such defective surfaces can affect the properties of adsorbed adatoms, whether within or outside the defect itself, and must be carefully investigated. Further, the presence of point defects on transition-metal oxide surfaces can inject excess electrons which can locally couple with ionic vibrations and form small polarons [12]. Adsorbate/oxide-surface interactions are known to be significantly affected by defects and their associated polarons [13,14,15], but their effect on catalysis has been rarely considered [16, 17]. For instance, the properties of metal atom (Me1) species on reduced rutile TiO2(110) surface, a prototypical polaronic system, has been extensively studied as a SAC [18,19,20,21,22,23], but the potential effects of polarons are generally neglected. On the reduced TiO2(110) surface, polarons tend to localize at a 6-fold coordinated Ti atom (Ti6c) in the subsurface layer in the vicinity of the 2-fold coordinated oxygen vacancy (VO2c) site, reducing Ti4+ to Ti3+ ions [24]. At elevated temperatures, polaron diffusion between subsurface and surface layers may occur, altering the properties and nature of the polaronic state [24,25,26], and potentially affecting the stability and properties of the adatoms as well.

In recent years, computational studies have become a powerful tool to accurately describe catalytic reactions at the atomic scale in heterogeneous catalysis [27,28,29]. In particular, first-principles calculations, within the density functional theory (DFT) framework, have revealed several useful insights into the nature of active sites and the reaction mechanisms in the SAC models [30]. Furthermore, the advances brought about by DFT studies facilitate the interpretation of experimental measurements, and might propose specific substrate materials and metal atoms as optimal candidates for efficient SAC processes.

The purpose of this study is to investigate the effect of polarons on the stability and properties of single-metal atom catalysts. We consider the adsorption of Rh1, Pt1, and Au1 transition metals on the reduced rutile TiO2(110) surface. To investigate the interplay between electron polarons, oxygen vacancies, and the adatom on the TiO2(110) surface, we performed DFT + U calculations and compared the results with experimental data taken from existing literature (Au1 [31,32,33,34,35]) as well as new scanning tunneling microscopy data for the Pt1 and Rh1 systems. Accordingly, we confirm that charge transfer occurs for Pt1 and Au1 adatoms located in O vacancies (VO), making them the preferred adsorption configurations, by carefully studying the most stable adsorption sites, the appropriate oxidation states, and the interactions among adatoms, O vacancies, and polarons. A low diffusion barrier on the surface of TiO2(110) allows Pt1 adatoms to reach O vacancies when dosed in low amount at room temperature. Au1 adatoms exhibit the same behavior but at a lower temperature with an even lower diffusion barrier. Rh1 is found to have no preference for such defects, leaving the polarons essentially unaffected in the subsurface. Our results show that the properties of single-atom catalysts on metal-oxide surfaces can be accurately described only by carefully considering the interaction with point defects and polarons, as well as the reduction of the adsorbed metals.

2 Methods

2.1 Computational Methods

All calculations were performed by using the Vienna ab initio simulation package (VASP) [36, 37]. The projector augmented wave method [38, 39] was used for the electron and ion interaction, with the plane-wave basis set cutoff energy set to 400 eV, optimized to include van der Waals interactions as proposed by Dion et al. [40] with the optimized functional (optPBE-DF) [41, 42]. However, DFT calculations have known drawbacks when dealing with electron localization effects [43]. Therefore, it is preferable to use first-principle schemes that account for the localized charge, such as the DFT + U method used here [44, 45]: we dressed the d orbitals of the Ti atoms with an effective on-site Coulomb repulsion term (Ueff of 3.9 eV) [46], previously determined by constrained-random-phase-approximation calculations in bulk rutile [25]. The unreconstructed rutile surface was modeled using an asymmetric slab containing five TiO2 tri-layers in a large two-dimensional 6 × 2 unit cell and including a vacuum space region greater than 12 Å along the z-axis. The top three tri-layers were allowed to relax, while the bottom two tri-layers were kept fixed at their bulk positions. An alternative slab model in which the broken bonds at the bottom layer were saturated by pseudo-hydrogen atoms did not affect our conclusions regarding the adsorption energies and polaron stabilities. The convergence is achieved when the electronic energy step of 10− 5 eV is obtained and forces acting on ions become smaller than 0.01 eV/Å. The adsorption energies were computed according to the formula:

$$E_{{{\text{ads}}}} = E_{{{\text{TiO}}_{2} \left( {110} \right) + {\text{adatom}}}} - \left( {E_{{{\text{TiO}}_{2} \left( {110} \right)}} + E_{{{\text{adatom}}}} } \right)$$

where \(E_{{{\text{TiO}}_{2} \left( {110} \right) + {\text{adatom}}}}\) is the total energy of the TiO2(110) surface with the adsorbed adatom, \(E_{{{\text{TiO}}_{2} \left( {110} \right)}}\) is the total energy of the clean TiO2(110) surface with an oxygen vacancy and the most stable polaronic configuration [47, 48]. The \(E_{{{\text{adatom}}}}\) represents the energy of the atom in the gas phase. The surface slab is displayed in Fig. 1a.

The diffusion barriers of an adatom on the reduced TiO2(110) surface were evaluated using the climbing image nudged elastic band (CI-NEB) method [49, 50] with three interpolated images. As initial and end states we carefully selected solutions including adatoms in the same oxidation state.

Fig. 1
figure 1

Structure of the TiO2(110) surface, Ti atom, O atom, and oxygen vacancy are depicted in big blue sphere, small red sphere and dashed-circle, respectively. a Side view of a 6 × 2 unit cell and b top view with possible adsorption sites: a 2-fold oxygen vacancy (VO2c), hollow1 (h1), hollow2 (h2), a 5-fold titanium atom (Ti5c), a 3-fold oxygen atom (O3c) and a 3-fold oxygen vacancy (VO3c)

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In order to inspect the different charge states of the metal atoms on different adsorption sites and the effect of the presence of polarons, we adopted the following strategy (see Fig. 2).

  1. (1)

    To inhibit polaron formation, we manually removed the two excess electrons (changed the flag NELECT in VASP), resulting in a positively charged slab. By doing so, we remove polaron-related energy contributions, such as polaron formation energies or polaron-Me interactions, which allows for a more systematic and controlled approach to study Me single-atom sites.

  2. (2)

    Adsorption sites were selected based on existing literature [22, 23, 31, 33,34,35, 51,52,53,54] (see Fig. 1). The Me-single atoms are adsorbed at the different adsorption sites as neutral species Me0 on the previously prepared surface (i.e., without polarons to interact with). The obtained Me0 adsorption energies can be considered initial reference values.

  3. (3)

    To account for the variation in relative adsorption strengths due to the oxidation state of the Me1 atom, charge is slowly re-added to the system. By adding one and then two electrons, the single atom is able to achieve its most favorable oxidation state Me0, Me− or Me2−:

    1. (a)

      Adding one electron: The Me1 can either retain its additional charge displaying the Me− oxidation state or become neutral again by moving the electron to the support where it forms a polaron [Me0 + 1pol.] vs. [Me− + 0pol.].

    2. (b)

      Adding two electrons: Me0, Me− and Me2− become available oxidation states as a result of adding one more electron. Three different configurations can be obtained: [Me0 + 2pol.] vs. [Me− + 1pol.] vs. [Me2− + 0pol.].

    As a result of step 3(b), we have retrieved the initial charge neutrality, artificially altered in step 1. At this step, we have ensured that polarons are located at the lowest energy polaronic sites (in S1 in the vicinity of VO2c) as they would in the pristine slab. Therefore, the remaining optimizations left are the interactions of polarons, if present, with the Me single atom, which is covered in step 4. Clearly, if the Me2− state results as the preferred one, no polarons are formed in the slab.

  4. (4)

    When polarons are formed (Me0 and Me−), we inspect the energy stability with respect to different polaronic trapping sites (in S0 and S1). In this way we consider the effect of the spatial polaron-VO2c and polaron-Me separation. It is known that the adatom adsorption energy is affected by the polaron orbital topology, degree of localization, and associated local structural distortions [24]. By comparing the final total energies of these charge-neutral slabs we determine the final ground state structure with the most favorable Me oxidation state previously determined and preferable polaron configurations.

Fig. 2
figure 2

 A flow diagram shows the strategy to obtain the proper charge states of metal atoms adsorbed on different adsorption sites on a charge-neutral reduced TiO2(110) surface with one VO2c

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The actual Me oxidation state is determined by counting the number of Ti3+ in the charge-neutral slab (i.e. the number of polarons in the slab), the local spin moment at the Me single atom itself, and integrated pDOS.

To selectively control the charge localization in different Ti3+ sites, we used the occupation matrix control tool [55], which consists of an initial constrained calculation (with an input occupation matrix kept fixed during the calculation) followed by an unconstrained calculation.

2.2 Experimental Details

Low temperature scanning tunneling microscopy (STM) was performed in a two-vessel UHV chamber consisting of a preparation chamber (p < 1 × 10− 10 mbar) and an analysis chamber (p < 2 × 10− 11 mbar). The preparation chamber is equipped with a commercial X-ray photoelectron spectroscopy (XPS). The analysis chamber is equipped with an Omicron LT-STM with a Qplus sensor and an in-vacuum preamplifier [56]. Room-temperature STM was performed in a second two-vessel UHV chamber consisting of a preparation chamber (p < 1 × 10− 10 mbar) and an analysis chamber (p < 5 × 10− 11 mbar). The analysis chamber is equipped with a nonmonochromatic Al Kα X-ray source (VG), a SPECS Phoibos 100 analyzer for XPS, and an Omicron µ-STM. STM in both UHV chambers was conducted in constant current mode with an electrochemically etched W tip on synthetic TiO2(110) single crystals (from CrysTec GmbH) prepared in UHV by sputtering (1 kV, Ar+, 15 min) and annealing (20 min, 700 °C). Rh and Pt were deposited using an e-beam evaporator (FOCUS), with the flux calibrated using a temperature-stabilized quartz microbalance (QCM). The STM images were corrected of distortion and creep of the piezo scanner as described in ref [57].

3 Results

The rutile TiO2(110) surface is one of the most intensively studied metal-oxide surfaces [58,59,60]. This surface layer consists of bridging oxygen rows (O2C) and 5-fold coordinated titanium (Ti5c) rows (see the structural model in Fig. 1). Bridging oxygen vacancies (VO2c) can be easily created in UHV conditions by sputtering and annealing. Each VO2c defect donates two excess electrons to the surface, which are trapped in Ti sites forming small polarons, clearly identified by sharp in-gap peaks [12, 48, 61,62,63]. We aim to elucidate the impact of polarons on the stability and properties of single-metal atoms (Pt1, Au1, and Rh1) adsorbed on the rutile TiO2(110) surface. The adsorption sites are labeled in Fig. 1b.

3.1 Pt1 on the TiO2(110) Surface

In order to investigate the adsorption of Pt1 on TiO2(110), we considered possible adsorption sites as reported in the available literature [21, 22, 51, 52] but including the presence of polarons. Figure 3a-c shows the three most stable adsorption sites and their corresponding calculated projected DOS (pDOS) as well as their oxidation states, taking polaronic effects into account. Pt1 adsorbed at a bridging oxygen vacancy is the most stable adsorption site (Eads = − 3.22 eV). The Pt1 atom in this configuration shows an oxidation state of Pt2− due to the charge transfer of two excess electrons from the reduced surface to the Pt1 adatom, meaning that it is more favorable to transfer the electrons to Pt1 rather than using the excess charge to form polarons. The calculated pDOS indeed shows no in-gap Ti polaronic peaks. We note that Pt− in this configuration is less stable than Pt2− by 0.39 eV (Fig. S6). Pt1 at the h1 site is next in energy (Eads = − 2.84 eV), with Pt0 being the most stable oxidation state. In this case, the two excess electrons prefer to be trapped in polaronic sites, and no evident net charge transfer to Pt1 occurs. The pDOS also shows two polaronic in-gap peaks for two Ti3+ sites, similar to the clean surface (Fig. S1). When polaron formation is maintained, as in the case of Pt0, polarons prefer to be trapped near the oxygen vacancy in the S1 layer [24]. The last possible adsorption site with comparatively large adsorption energy is Pt1 adsorbed atop a 3-fold coordinated oxygen atom on the basal plane. Pt− is the most stable oxidation state at this site, with one polaron again preferably located in the S1 layer near the oxygen vacancy. Overall, the polarons prefer to be located in the S1 layer in the proximity of the VO2c and maximize their distance with the adsorbed Pt1 adatom due to the repulsive interaction between the negatively charged polaron and the adsorbed metal atom. A variation of the order of 300 meV in the adatom adsorption energy can be seen depending on polaron position and its distance to the adatom (Fig. S2).

Fig. 3
figure 3

Minimum energy configuration of possible adsorption sites of Pt1 on the TiO2(110) surface. a Pt1@VO2c without polarons resulting in a Pt2− configuration. b Pt1 in h1 with two polarons resulting in a Pt0 configuration. c Pt1 atop O3C atom with one polaron resulting in a Pt− configuration, where O, Ti4+, Ti3+(polaron), Pt1 are small red, big blue, big yellow, big green spheres and VO is a dashed-circle, respectively. Each configuration is aligned with its respective DOS panels, where the total DOS, pDOS of Pt (5d), pDOS of Pt (6s), and pDOS of Ti3+(3d, polarons) are filled light blue, red line, green line, and black line, respectively. d Empty-state room temperature STM images of 0.007 ML Pt on the reduced rutile TiO2(110) surface deposited at room temperature, with surface oxygen vacancies (VO2c), OH groups (OHb), pairs of OH groups (2(OHb)), Pt adatoms (circle) and Pt clusters (dashed circle) labelled in the image. e Diffusion path of Pt1 adatom on TiO2(110) from one hollow site to the next in the neighboring unit cell without the perturbation from any VO

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The room-temperature STM image (Fig. 3d) shows Pt1 adsorbed on the reduced rutile TiO2(110) surface. The TiO2(110) surface is characterized in STM by bright rows of 5-fold coordinated Ti4+ alternating with dark rows of 2-fold bridging O2−, which run along the [001] direction [60]. Small protrusions over the dark rows can be assigned to oxygen vacancies VO2c, and brighter features on the dark rows can be assigned to bridging OH [64] and pairs of bridging OH. These originate from water dissociation at the VO2c [65,66,67]. Pt adatoms can be stabilized at low coverage, but clusters dominate the higher the coverage. The Pt adatoms adsorb in the 2-fold oxygen vacancies (marked in circle), which can be identified directly when rare events of adatoms diffusion occur. In this case, the Pt adatom diffuses from one VO to another (Fig. S7). Both the initial and final vacancies are imaged in STM. Dosing water or oxygen gas (O2) at room temperature (2 L; 100 s 2 × 10− 8 mbar) prior to the Pt deposition leads to the reparation of the VO site [66,67,68]. In such an experiment, only Pt clusters are observed (as seen in Fig. S8). These results show the direct correlation between oxygen vacancies and the Pt adatoms stabilization.

In order to account for dynamical effects involving diffusion of the metal species, we calculated the diffusion barrier of the adsorbed Pt1 along the [001] direction. The calculated energy barrier is low (0.59 eV, see Fig. 3e) so that Pt1 can diffuse already at room temperature and reach the best adsorption site (at the oxygen vacancies). The calculated results are therefore in-line with our room-temperature STM images, where only Pt1 at oxygen vacancies have been observed on the reduced TiO2(110) surface at low coverage. At lower dosing temperature, possible metastable adsorption configurations outside the VO2c can exist.

3.2 Au1 on the TiO2(110) Surface

Au1 adsorbed on TiO2(110) exhibits a similar structure than Pt1, as shown in Fig. 4. The most stable adsorption site for Au1 is located at VO2c (Eads = − 2.06 eV). Au1 located at this site becomes negatively charged with an oxidation state of Au−. Polaronic configurations are most favorable when the remaining polaron forms in the S1 layer close to the VO2c (Fig. 4a). We also considered the on-top 5-fold Ti atom adsorption site, as it was previously considered in other theoretical works [31, 32, 69]. The most stable valence state of Au1 at this site is Au− with one polaron remaining in the S1 layer close to VO2c, as shown in Fig. 4b (Eads = − 1.46 eV). The calculated pDOS in both cases shows that the valence d and s states are filled, with one characteristic in-gap polaronic peak. Similarly to Pt1, the different polaronic configurations can modify the adsorption energy up to 300 meV (Figs. S3, S4).

Fig. 4
figure 4

Minimum energy configuration of possible adsorption sites of Au1 on the TiO2(110) surface. a Au1@VO2c with one polaron resulting in a Au− configuration. b Au1 atop Ti5c atom with one polaron resulting in a Au− configuration. Each configuration is aligned with its respective DOS panels, where the total DOS, pDOS of Au (5d), pDOS of Au (6s), and pDOS of Ti3+(3d, polarons) are filled light blue, red line, green line, and black line, respectively. c Diffusion path of Au1 atom on TiO2(110) from atop Ti5c to the VO2c site, where O, Ti4+, Ti3+(polaron) and Au1 are small red, big blue, big yellow and big yellow-brown spheres, and VO is a dashed-circle, respectively

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The diffusion barrier of Au1 on the TiO2(110) from the 5-fold Ti atom to the next 5-fold Ti atom along [001] direction is low (0.2 eV), and even lower is the corresponding barrier for diffusing from the 5-fold Ti atom to the oxygen vacancy which is almost barrierless, indicating a facile diffusion (Fig. 4c). Based on our results, we can conclude that at very low Au coverage, all Au1 adatoms will be trapped in the oxygen vacancies on the surface. This result agrees with the room temperature STM measurement at low coverage [35] and with the observation of the nucleation of gold clusters at oxygen vacancy sites at high coverage [31, 32].

3.3 Rh1 on the TiO2(110) Surface

We studied the adsorption of Rh1 adatoms on TiO2(110) by combining DFT + U calculations with XPS and STM experiments. The adsorption sites with their respective adsorption energy are summarized in Fig. 5. Interestingly, Rh1 adsorbed at VO2c (Fig. 5c) is not the preferential configuration (Eads = − 2.82 eV). We assign a Rh− state to this configuration, due to the presence of an in-gap polaronic peak from one Ti3+ atom. Two configurations at hollow sites are shown in Fig. 5a and b. The oxidation state of the Rh1 adatom at hollow sites depends on the nearest oxygen atoms binding to it. For instance, the relaxed structures show that Rh0 binds to the O3c and O2c atoms (Eads = − 3.24 eV), whereas the Rh− at the hollow site near VO2c binds to only the O3c atom (Eads = − 3.05 eV). A charge transfer occurs for Rh1 near the VO2c where one excess electron transfers to Rh1, leaving the second excess electron to form a polaron in the S1 layer near VO2c. The pDOS also shows that there is one characteristic in-gap polaronic peak. The Rh1 at a hollow site that is distant from VO2c is assigned to Rh0 and has two remaining polarons in a preferential S1 configuration. The calculated pDOS shows the two in-gap polaronic peaks from Ti3+ atoms. Polarons reside in the S1 layer minimizing the distance from VO2c while maximizing the distance from the Rh1. However, the adsorption energies of Rh0 and Rh− are almost degenerate.

Fig. 5
figure 5

Minimum energy configuration of possible adsorption sites of Rh1 on the TiO2(110) surface. a Rh1 in h1 with two polarons resulting in a Rh0 configuration. b Rh1 in h1 near the VO2c with one polaron resulting in a Rh− configuration. c Rh1@VO2c with one polaron resulting in a Rh− configuration. Each configuration is aligned with its respective DOS panels, where the total DOS, pDOS of Rh (4d), pDOS of Rh (5s), and pDOS of Ti3+(3d, polarons) are filled light blue, red line, green line, and black line, respectively. d Diffusion path of Rh1 atom on TiO2(110) from the h1 site to the next h1 site, where O, Ti4+, Ti3+ and Rh1 are small red, big blue, big yellow and big silver spheres, and VO is a dashed-circle, respectively

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The adsorption of an adatom at the 3-fold oxygen vacancy (VO3c) has been proposed to rationalize the result from scanning transmission electron microscopy (STEM) experiments and DFT calculations for Pt1 and Rh1 [22, 23]. Other works argued that this adsorption does not exist on TiO2(110) due to the energetically unfavorable formation of the 3-fold oxygen vacancy (VO3c) on the bare TiO2(110) surface [35, 52]. Our calculations also show that the formation of VO2c defects is much more favorable than the VO3c vacancy by 1.39 eV on the pristine surface. Figure S5 shows, however, that when Rh1 is present and adsorbs at a VO3c, it becomes the most thermodynamically stable adsorption site (Eads = − 3.42 eV) with respect to the V2Oc formation.

Despite the unfavorable 3-fold oxygen vacancy formation energy found for the pristine surface, the presence of adatoms can alter the energetic cost of creating different vacancies other than VO2c and therefore should not be excluded. While Rh1 in VO3c is the most stable configuration found, the question arises whether it can be reached or not, as the as-prepared surface does not exhibit such defects prior to the deposition of Rh. We calculated the oxygen migration from VO2c to VO3c with the presence of Rh1 (Fig. 6), ignoring the presence of polarons and changes in the oxidation state of Rh. A barrier of 0.62 eV is obtained, significantly higher than the diffusion of Rh (0.28 eV, Fig. 5d) on the bare surface, suggesting that prior to the formation of in VO3c adsorbed Rh, the adatoms would sinter into clusters (assuming these would be favorable in energy).

Fig. 6
figure 6

Energy profile of VO migration between the initial state (Rh− at hollow site) and the final state (Rh− at 3-fold VO). In order to match the oxidation state of the final state in the NEB, the initial state is set to − 1 instead of 0, giving an offset of ~ 0.2 eV

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Figure 7a–c shows STM images of TiO2(110) before (a) and after deposition of 0.04 ML of Rh (b) and (c) at 100 K, where 1 ML corresponds to 1 Rh atom per surface unit cell. The images were acquired using liquid nitrogen as the cryogen for the LT-STM, giving the sample a temperature of 78 K. Features on the bright Ti4+ rows (Fig. 7a, b) with an apparent height of 90–100 pm can be assigned to molecular water adsorbed to Ti4+ [70]. Rh adatoms (marked in circles) are located atop the bright Ti4+ rows but slightly tilted towards the dark rows (bridging O2−). All Rh adatoms adsorb at the same site but vary in apparent height between 140 and 180 pm. This behavior differs from the behavior of Au and Pt adatoms, which preferentially adsorb in the VO2c of the TiO2(110) surface [35]. Our data suggest no preferential interaction between Rh and VO2c as the density of the visible VO2c is identical before and after Rh deposition. This result agrees with our DFT calculations, where the best adsorption of Rh1 is located at the hollow between the bridging oxygen row and the Ti row.

Fig. 7
figure 7

Experimental investigation of 0.04 ML Rh adsorbed on TiO2(110). a STM image (acquired at 78 K) of the clean TiO2(110) surface. Surface oxygen vacancies (VO2c), OH groups (OHb), pairs of OH groups (2(OHb)), and adsorbed water (H2O) molecules can be seen. b and c Following the evaporation of 0.04 ML Rh at 100 K, Rh adatoms (circle) can be seen. d XPS spectra and STM images of the Rh 3d peak after gradually increasing the temperature

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Figure 7d shows XPS spectra and the corresponding STM images of the Rh 3d peak of the as-deposited Rh at 100 K and after subsequent annealing to 873 K. Between 100 K and 150 K the Rh 3d peak shifts to higher binding energy. This core-level shift could be related to a final state effect linked to the small size of the clusters, which appear in STM at 150 K. A similar effect can be recognised when comparing Au1 and Au3 to Au nanoparticles on the reduced TiO2(110) surface. The Au 4f binding energies of the Au1 and Au3 are similar to those at a higher coverage of Au. This effect occurs from a cancellation of initial and final state effects for Au1 and Au3. By increasing the coverage, the binding energy first decreases and finally increases [71]. Between 150 and 250 K the peak stays the same but when heating the sample to temperatures above 300 K the peak shifts gradually to lower binding energy. This is related to the formation of bigger clusters with increasing temperature. These experimental observations, where Rh is seen to cluster after heating just to 150 K (Fig. 7d) agree with our previous calculated diffusion barriers and preference to sintering.

4 Discussion and Conclusions

The presence of localized charges on surfaces in form of small polarons, unavoidably impacts adsorption and reaction processes and surface dynamics. Previous studies have shown that adsorbed CO exhibit different coupling regime (from attractive to repulsive) depending on the position and density of small polarons, revealing a polaron-mediated correlation between CO adsorption energy and reduction state of the sample [13]. Substantial polaron-charge transfer has been found in O2 adsorption, leading to the formation of superoxo and peroxo species [14]. Here, we have shown that single-atom adsorption is also strongly coupled with polaron-charge transfer effect, which affects the adsorption energy and, importantly, the oxidation state of the metal atoms. For example, a Pt2− binds stronger than a Pt− at the VO site by 0.39 eV. This also implies that the reduction level and associated polaron density does affect the stability of the adsorbed metal atoms, and therefore its surface dynamics, but also its reactivity (i.e. charge transfer between the single-atom catalysts and adsorbed molecules).

For our model system, we found that Pt1 and Au1 adatoms have low diffusion barriers and preferably adsorb in VO2c. At higher dosing amounts, clusters can be observed. Rather than forming polarons, the VO2c excess electrons are transferred to the metal atoms, altering their electronic structure by filling their valence states and result in modifying their relative stabilities. The fact that negatively Pt1 and Au1 adatoms form cluster means that during the diffusion process there must be a substantial charge transfer from the Pt1 and Au1 adatoms to the substrate [72, 73]. Rh1 adatoms, however show no preference for the VO2c defect, leaving the excess charge to form polarons and instead adsorb at hollow sites, which is in agreement with our experimental STM observations where they quickly sinter into clusters with increasing temperature at low coverage.

The interaction between adsorbates and polarons is further complicated by the presence of additional species which could alter the surface charge balance. In this respect, it is also important to note that the TiO2(110) surface is fully oxidized under realistic conditions. Therefore, VO is repaired by H2O or O2 molecules, leading to hydroxylated TiO2(110) or oxidized TiO2(110) surfaces. The oxidized TiO2(110) surface was suggested to bind Au1 stronger than the VO site on the reduced TiO2(110) surface [53]. Contrary to the Au case, only Pt clusters were observed on the oxidized TiO2(110) surface.

Nevertheless, the presence of small polarons is important even for a realistic TiO2(110) surface, because repair of an oxygen vacancy by H2O results in two electron polarons arising from two surface OH groups. Clearly, the modeling of such complicated multi-polaron configurational space (which might also involve the simultaneous formation of electron and hole polarons) is clearly unfeasible via conventional DFT. In order to efficiently explore the energy landscape, novel automated machine-learning based methods must be implemented and employed to determine the most favorable (structural and electronic) configurations and the most likely dynamical paths [74].