Exploring the properties of Ag 5 – TiO 2 interfaces: stable surface polaron formation, UV-Vis optical response, and CO 2 photoactivation † Society of Chemistry 2020 Journal of

Using a combination of ﬁ rst-principles modelling, X-ray absorption spectroscopy, and di ﬀ use re ﬂ ectance spectroscopy measurements, we explore the properties of Ag 5 -modi ﬁ ed TiO 2 surfaces. A general electron polarization phenomenon associated with surface polarons on TiO 2 has been revealed theoretically and con ﬁ rmed experimentally. First, the Ag 5 cluster donates an electron to TiO 2 , leading to the formation of polaronic Ti 3+ 3d 1 states on the rutile TiO 2 (110) surface. The analysis of polarization e ﬀ ects in the nearby electronic structure accompanying the polaron formation is con ﬁ rmed with X-ray absorption spectroscopy measurements at the Ti K-edge of TiO 2 nanoparticles. Next, the UV-Vis optical absorption spectrum of the polaronic state is also computationally modelled and an enlargement of the polaron wavefunction is predicted. Moreover, we ﬁ nd an overall improvement of the UV-Vis optical response of the material through di ﬀ use re ﬂ ectance spectroscopy measurements. Finally, we predict that charge-transfer processes at the Ag 5 – TiO 2 interface triggered by solar photons might allow for a photoinduced activation of CO 2 by sunlight.


Introduction
Highly stable metal clusters of subnanometer size, as required in industrial applications, have recently emerged as a new generation of catalysts and photocatalysts with fascinating properties arising from their molecule-like electronic structures. As opposed to metal nanoparticles in the visible region, 1 these 'atomic' or sub-nanometer-sized clusters neither sustain their metallicity, nor show their plasmonic behaviour. Instead, the presence of a molecule-like HOMO-LUMO gap drastically transforms their chemical and physical properties, thus creating innovative materials for applications including luminescence, 2 sensing, 3 therapeutics, 4 energy conversion, 5 catalysis, 6 and electrochemistry. 7,8 Nowadays, these so-called atomic quantum clusters (AQCs) can be synthesized by kinetic control using electrochemical methods, [9][10][11] showing an exceptional chemical and thermo-dynamical stability in solution over the whole pH range. 9 As discussed in ref. 9, high monodispersity of synthesized AQCs (e.g., Cu 5 ) has been achieved since the method of cluster synthesis is extremely size-selective. Moreover, the air stability of AQCs (e.g., Cu 5 ) with respect to oxidation up to a temperature of 150 C has been experimentally observed. 12 The resistance of Cu 5 clusters against an irreversible oxidation by a single O 2 molecule has been explained in theoretical studies. [12][13][14] It is well known that new catalytic and optical properties with technological projections are acquired by certain materials when modied with AQCs. 15 The TiO 2 surface has been previously selected as the AQC support due to its abundance, nontoxicity, biological inertness, and chemical stability, being one of the most popular materials for (photo-)catalytic applications and solar energy conversion. However, its large band-gap (3-3.2 eV) makes ultraviolet irradiation necessary to trigger photocatalytic reactions. The UV part is less than 8% of the solar radiation so that the reaction rate divided by the photon ux is typically less than 10% for TiO 2 -based photocatalysts. 16,17 Several techniques have been developed to extend the photoactivity of TiO 2 to the visible region, most of which involve the direct modication of the electronic structure of the bulk. Very recently, in a joint theoretical-experimental study, 15 we have proposed an alternative technique relying on the deposition of a single monolayer of Cu 5 clusters. It takes advantage of the slightly different electronic structure at the phase boundary and the ability to create electron-hole pairs close to the surface. As a result, much more energy can be harvested from sunlight, and the coated titanium dioxide stores this energy temporarily in the form of charge pairs, electrons and holes, which is a perfect prerequisite to follow-up chemistry. 18 Moreover, a very recent theoretical study 19 has indicated that TiO 2 -supported Cu 5 clusters might allow CO 2 activation through sunlight, as well as a spontaneous decomposition, leading to CO desorption.
AQCs made of a few silver atoms seem to display better chemical and physical properties. The stability of Ag n clusters (n # 5) on the rutile surface has also been theoretically analysed, 20 predicting an enhanced light absorbance intensity of the material upon their deposition, as well as the appearance of secondary broad peaks with positions depending on the size and shape of the supported clusters. In particular, intense peaks have been identied in the visible region of the spectrum for the specic case of the Ag 5 AQC. 20 In this work, for completeness, the visible spectrum of Ag 5 -modied TiO 2 surfaces is experimentally determined using diffuse reectance spectroscopy. Theoretically, the following relevant aspects are addressed: (1) the existence of surface polarons on TiO 2 through surface activation with Ag 5 AQCs; (2) the stability of the resulting polaronic states as compared to non-polaronic ones as previously reported; [20][21][22] and (3) the UV-Vis optical absorption spectrum of the polaronic states.
Polaron formation is a fundamental and well-known phenomenon in transition metal oxides, for example, reduced titanium dioxide surfaces (e.g., for a comprehensive overview see ref. 23). Excess electrons from surface defects such as oxygen vacancies and Ti interstitials locally couple to lattice distortions forming small polarons, 24 typically hosted at Ti sites close to the defects. The existence of intrinsic small polarons as self-trapped electrons at Ti 4+ ions in rutile TiO 2 (i.e., forming stable Ti 3+ 3d 1 states) has been both theoretically predicted 23,25-31 and experimentally conrmed. [32][33][34] Gono et al. 35 have theoretically shown that the presence of surface polarons reduces overpotentials in the oxygen evolution reaction (OER). This reaction is the major problem to solve in water splitting. Thus, the quest for experimental systems forming stable surface polarons (clusters on TiO 2 melt at temperatures greater than 700 C) opens new ways to the experimental work on new catalysts. Very recently, a direct observation of magnetic polarons in a doped Fermi-Hubbard system has been reported by Koepsell and co-workers. 36 A theoretical analysis of polaronic states has been provided in studies of Cu n -TiO 2 (n # 5) interfaces. 15,37 X-ray absorption spectroscopy measurements at the Cu K-edge have conrmed the theoretical prediction that the 3d levels of the Cu 5 clusters become depopulated upon adsorption on TiO 2 for both polaronic and non-polaronic states. 15 However, no conclusive experimental evidence of the modications of the electronic structure of the Ti atoms upon deposition of Cu 5 AQCs on TiO 2 nanoparticles has been found (see the ESI of ref. 15). In this work, X-ray absorption spectroscopy measurements at the Ti K-edge provide unambiguous evidence that these modications occur at the Ag 5 /TiO 2 interface. Moreover, the experimentally determined modications are related to electronic polarization effects due to the formation of polarons (Ti 3+ 3d 1 states). In this way, we extend previous experimental studies proving the existence of Ti 3+ 3d 1 states in reduced TiO 2 samples, 32-34 including their direct views through scanning tunneling microscopy. 34 Furthermore, photoexcitation spectra of the polaronic state with light in the UV-Vis region of the solar radiation are also presented. Clearly, the photoexcitation of polarons is still an unexplored area, for which the rst ground-breaking experimental studies have been very recently reported. 38 Finally, the possibility of using TiO 2 -supported Ag 5 AQCs for photocatalysis applications is also studied. Due to its importance in the context of climate change and global warming (see ref. 39 for a very recent and comprehensive review on heterogeneous CO 2 reduction), the photoactivation of CO 2 over Ag 5 has been addressed. A deterrent in the CO 2 elimination is the high stability of the C]O bond, which necessitates an energy as high as 7.8 eV (ref. 40) in order to be broken in the gas phase. The radical CO 2 c À is a clear precursor state for CO 2 dissociation due to its weakened C]O bond. The question analysed in this work is twofold: (1) whether CO 2 can be trapped in a dispersiondominated physisorption state and (2) if it is irradiated with visible light, whether this molecule can be transformed into the radical CO 2 c À over TiO 2 -supported Ag 5 clusters, as already found for copper clusters. 19 The different topics covered in this work are addressed by applying density functional theory (DFT), time-dependent DFT, and an approach combining DFT with reduced density matrix theory. We chose a DFT-D3 ansatz 41,42 on the basis of its excellent performance in describing the adsorption of the Ag 2 cluster on the rutile TiO 2 (110) surface. 20 For an appropriate determination of the electronic structure, we employed the HSE06 hybrid functional of Heyd, Scuseria and Ernzerhof 43,44 on top of the structures optimized via the DFT-D3 approach instead. It has been previously shown that the HSE06 functional allows description of localized midgap states below the conduction band which are associated with polarons in reduced TiO 2 (ref. 45) and Cu 5 -modied TiO 2 surfaces. 15 In order to calculate the UV-Vis absorption spectra, we employed reduced density matrix (RDM) theory within the Redeld approximation, 46 combined with DFT calculations using the HSE06 functional. This combination of RDM and DFT, proposed by Micha and collaborators, [47][48][49] has been successfully applied to silver 20,50-52 and copper 15,19 clusters on semiconductor TiO 2 and silicon surfaces. 15,19,20,[50][51][52][53] The results from our computational calculations and spectroscopy (diffuse reectance and X-ray absorption) measurements are presented and discussed in Section 2. This section is split in several subsections in order to emphasize at each step the importance of the presence of polarons and, in the last subsection, the prediction of CO 2 photo-activation is briey described. Section 3 summarizes the main ndings. Finally, in Section 4, further details about the materials used as well as the experimental and computational methods developed are provided.

Surface polaron formation at the Ag 5 /TiO 2 interface
We carried out structural optimizations and interaction energy calculations with the Perdew-Burke-Ernzerhof (PBE) density functional and the Becke-Johnson (BJ) damping 41 for the D3 dispersion correction, including spin-polarization. We refer to this combination as the PBE-D3(BJ) scheme. The Hubbard DFT+U term 54 was added in PBE-D3(BJ) minimizations to describe localized 3d-electrons on Ti cations.
The optimization of the bare cluster Ag 5 gives rise to a planar trapezoidal structure as in experimental observations. 55 We then inserted the Ag 5 cluster into our slab model and optimized the whole Ag 5 -slab geometries. The pyramidal-and trapezoidalshaped Ag 5 structures shown in Fig. 1 are thus predicted. Both structures are highly stable, with adsorption energies (À4.53 eV for the pyramidal-shaped geometry at the PBE-D3(BJ)/U level) being of the same order of magnitude as in previous studies. 20,21 Next, we used the wavefunctions calculated at the PBE-D3(BJ)/U level in a follow-up HSE06 calculation at the relaxed geometries. It was thus found that the Ag 5 cluster donates its unpaired electron to the TiO 2 surface and loses its magnetic moment in either pyramidal-and trapezoidal-shaped structures. Using a Bader decomposition scheme, 56 we estimated charge donations of about À1 and À0.8|e| from the Ag 5 cluster for pyramidal-and trapezoidal-shaped geometries, respectively. As can be observed in Fig. 1, the donated electron becomes localized in one specic 3d orbital lying at the surface plane and centered at the Ti(5f) atom right below the Ag 5 cluster.
The charge trapping via the localization of one electron on the Ti(5f) atom is correlated with the typical lattice distortion accompanying the formation of a small polaron in reduced TiO 2 surfaces (see, e.g., ref. 23). Thus, as we can see in Fig. 1, the oxygen ions depart from the Ti atom hosting the polaron by 0.08 A in average. For the pyramidal-shaped Ag 5 structure, the polaronic solution is À0.9 eV more stable than the nonpolaronic counterpart. For the latter, the "extra" electronic charge donated by the Ag 5 cluster becomes delocalized over several neighboring Ti atoms. As reported in ref. 20 for nonpolaronic Ag 5 -TiO 2 states, the pyramidal-like structure is preferred over the trapezoidal-shaped arrangement also in polaronic solutions. The adsorption energy differences are ca. 0.3 and 1.5 eV at the HSE06 level and PBE-D3(BJ)/U levels, respectively. This is consistent with previous studies, reporting the hollow site as the most favored position for single Ag atoms adsorbed on both rutile 20,57 and anatase 22 TiO 2 surfaces. Accordingly, as shown in Fig. 1, four Ag atoms locate at hollow sites in the pyramidal-shaped structure. The central Ag atom is localized on top of one vefold (5f) Ti atom instead.
Besides the Ti(5f) ion, alternative locations of the polarons exist with similar energies in hydroxylated and reduced TiO 2 (110) surfaces. 26,27 Very recent molecular dynamics simulations under experimental conditions 23 indicate that a subsurface Ti atom is the most stable polaron site on reduced TiO 2 (110) surfaces. The stabilization of the surface polaron induced by the Ag 5 cluster is favored by an attractive electrostatic interaction between the localized Ti 3+ 3d 1 electron and the positively charged Ag 5 cluster. As pointed out in a theoreticalexperimental study, 58 an adsorbate (a CO molecule) is capable of promoting polaron transfer from the subsurface to surface sites also in reduced TiO 2 samples. Similar to the case of the Ag 5 /TiO 2 interface, the favored surface location is caused by an attractive (repulsive) interaction of the CO molecule with the surface (subsurface) polaron.

Polarization effects induced by surface polarons
In order to analyze the polarization effects induced by the polaronic charge, we calculated the net population (number of electrons) of d-type orbitals centered at Ti atoms for Ag 5 -modied and unmodied TiO 2 surfaces. We considered the two different (trapezoidal and pyramidal) Ag 5 isomers and both polaronic and non-polaronic states. We found the main modi-cations in the population of 3d(Ti) orbitals upon Ag 5 adsorption while those of s(Ti) and p(Ti) orbitals (not shown) were kept almost unperturbed. As can be deduced from Table 1, a net depopulation of 3d(Ti) orbitals can be observed upon the polaron formation (see Table 1). This is clearly seen when comparing the 3d(Ti) orbital populations in the unmodied (2nd column) and Ag 5 -modied (3rd and 4th columns) TiO 2 surfaces hosting the polaron. Note that this is also clearly apparent in the population difference between polaronic (3rd and 4th columns) and non-polaronic (last column) states.
The depopulation of 3d(Ti) orbitals might be an outcome challenging common intuition. As a localized Ti 3+ 3d 1 electron state, the polaron is in fact characterized by excess charge (i.e., one "extra" electron) trapped at the Ti site hosting it. Accordingly, the unpaired electron of the Ag 5 cluster becomes trapped at the 3d orbital of one specic Ti(5f) atom. As a result, the difference in the population of 3d(Ti) orbitals with majority and minority spin components is unity (3rd and 4th columns of Table 1). However, we must consider that the polaron becomes effectively screened by the polarization of the surrounding electronic cloud and it is not only manifested in structural lattice distortions. This polarization is also manifested in the formation of a delocalized hole accompanying the trapped Ti 3+ 3d 1 electron in the 3d-network of occupied orbitals centered at neighboring (mostly surface) Ti atoms. Actually, this polarization effect extends to subsurface layers. As a result, the net population of 3d(Ti) orbitals decreases in the Ag 5 -modied polaronic state with respect to that existing in the unmodied TiO 2 surface. In a slightly simplied picture, the localized Ti 3+ 3d 1 electron attracts positively charged Ti 4+ centers, which become even more positively charged upon polaron formation in order to favour the attractive electrostatic electron-Ti 4+ attraction. The electronic charge is transferred to the p orbitals of neighboring O 2À ions which, being repelled by the localized Ti 3+ 3d 1 electron, move away from it (see Fig. 1). Note that this polarization effect holds for both trapezoidal-and pyramidalshaped structures of the Ag 5 cluster.
The nding that the polaron formation (as a localized Ti 3+ 3d 1 electron state) is accompanied by a polarization of the crystal electronic cloud becomes even more clear, when the analysis of orbital populations is restricted to 3d(Ti) and 2p(O) orbitals of titanium and oxygen atoms located at the polaron plane. Thus, as can be observed when comparing these populations in polaronic and non-polaronic states (values indicated in the 2nd and 4th columns and 2nd and 3rd rows, of Table 1), the electron, having le an effective hole delocalized over the 3d-network of surface Ti atoms, is transferred to 2p orbitals of oxygen atoms lying at the polaron plane. It can be noted from Table 1 that one electron located at 3d orbitals of titanium atoms in the non-polaronic state becomes localized at 2p orbitals of oxygen atoms in the polaronic counterpart. The Bader charge of surface oxygen atoms is also larger (by ca. 0.6|e|) in the polaronic state, as opposed to the surface titanium atoms.

Experimental evidence of polarization effects induced by surface polarons
We found experimental evidence of the described modications in the electronic structure of Ti atoms through X-ray absorption near edge structure (XANES) spectroscopy. This technique is characterized by a high chemical selectivity. Fig. 2 shows the XANES spectra at the Ti K-edge of bare TiO 2 nanoparticles (NPs) and TiO 2 NPs bearing supported Ag 5 AQCs. We observed a shi of the edge position (ca. 0.1 eV) when adding Ag 5 AQCs to the TiO 2 NPs. An additional peak at 4990 eV was also found. As previously shown, 59 the multiple structure appearing immediately aer the main 1s / 4p transition emerges from a two-electron transition. It consists in the simultaneous excitation of one core electron, associated with 1s / n4p transitions, and one valence electron. 59 In particular, resonances appearing at ca. 4990 eV are attributed to 2p(O) / 3d(Ti) transitions. 59 The increase of the XANES area in this region indicates charge transfer from Ti atoms to the ligands (i.e., oxygen ions), resulting in a decrease of the Ti electron density at the 3d levels in average. Thus, the experimental measurements conrm our nding that there is an effective depopulation of 3d(Ti) orbitals favouring 2p(O) orbitals as a result of the polaron formed. As will be next discussed, our interpretation is further supported by the theoretical modelling of the polaron photo-excitation.
As mentioned in the introduction, no modication of the XANES spectra at the K-edge of Ti atoms was found in the case of the Cu 5 cluster 15 as the adsorbate so that no unambiguous proof of the polaron formation could be provided. On the one hand, one key difference between Ag 5 and Cu 5 as adsorbates is that the 3d orbitals of the latter present a very pronounced hybridization with 2p orbitals of oxygen atoms from the TiO 2 surface. Hence, from our analysis above, the polarization process, which involves the transfer of electronic charge from 3d(Ti) to 2p(O) orbitals, might be somehow constraint at the Cu 5 /TiO 2 interface. On the other hand, the employment of smaller TiO 2 nanoparticles has allowed for a larger Ag 5 -TiO 2 contact region than in our previous work. 15 Table 1 Net population (number of electrons) of d(Ti) orbitals in the unmodified TiO 2 surface (2nd column) and the modified TiO 2 surface bearing supported Ag 5 clusters in both pyramidal-and trapezoidal-shaped structures (3rd and 4th columns). For the most stable pyramidalshaped isomer, the d(Ti) orbital population is also presented for the non-polaronic state (last column). The population of d and p orbitals of surface titanium and oxygen atoms (referred to as Ti S0 and O S0 ) is presented for the pyramidal-shaped isomer in polaronic and non-polaronic states. The difference between the occupation of orbitals with majority and minority spin components is also indicated as values between parenthesis We note that the depopulation of 3d(Ti) orbitals is the same for Ag 5 and Cu 5 clusters. Also, we obtained similar values for the surface polaron formed from oxygen vacancies in the reduced TiO 2 (110) rutile surface (see Section S1 of the ESI †). Hence, we have provided general microscopic details of polarons: the mechanism leading to their internal structure through the polarization effects in the electronic structure of the environment. This important aspect of the polaron formation is deduced theoretically not from a model Hamiltonian but from our extended ab initio calculations. The strategy followed has been obviously motivated by the presence of Ag 5 clusters which seems to be determinant. Fig. 4 (bottom panel) shows the photo-absorption spectra of the Ag 5 -modied TiO 2 surface, with the Ag 5 cluster in the most stable (i.e., pyramidal-shaped) structure. The photo-adsorption spectrum for the trapezoidal-shaped structure is very similar (see Section S2.2 of the ESI †). For the sake of clarity, the density of states is presented in the upper panel of Fig. 4 while the most relevant frontier orbitals are shown in Fig. 3, with the Ti 3+ 3d 1 electron characterizing the highest-energy single-occupied (referred to as SOMO) orbital of the system (see also Fig. 3 and Section S2 of the ESI †). As can be observed in the projected electronic density of states, the localized Ti 3+ state (marked with a yellow arrow in the upper panel of Fig. 5) appears about 1.2 eV below the bottom conduction band. The same value was reported by Di Valentin et al. for a Ti(5f) 3d 1 state in hydroxylated and reduced rutile TiO 2 (110) surfaces. 25 Moving to the photo-excitation processes, the rst thing to note from Fig. 4 is that the excitation of the Ti 3+ 3d 1 electron with a photon energy at the end of the visible region (marked with a yellow arrow at about 3.1 eV) leads to its transfer to 3d orbitals of Ti atoms spread all over the TiO 2 surface. Essentially, the delocalized hole accompanying the formation of the polaronic Ti 3+ 3d 1 state becomes lled, indicating the existence of the delocalized hole itself. This is further conrmed by an analysis of the acceptor orbital, being mainly composed of 3d states of surface Ti atoms (ca. 64%). Alternatively, our nding could also be viewed as the photo-induced conversion of a small polaron into a large polaron. Previous experimental measurements 60 have shown that visible light excitation of Ti 3+ centers on reduced TiO 2 nanoparticles leads to the transfer of the localized 3d 1 electrons into the conduction TiO 2 band.

Improvement of the UV-Vis optical response of TiO 2 : experimental conrmation
As found for non-polaronic states 20 and the Cu 5 /TiO 2 interface, 15 it can be noted from Fig. 4 (bottom panel) that the Ag 5 cluster increases the UV and extends into the visible the optical response of TiO 2 . Fig. 5 shows the comparison of the theoretical and experimental absorbance in the visible region going from 1.65 to about 3.08 eV. All the DRS spectra show the typical behavior expected in TiO 2 -based semiconductors consisting of a nearly at region, at small photon energies, that is dominated by reection and scattering due to the high refractive index of the investigated material. The milling process decreases the nanoparticle size increasing the surface area. In this way, the amount on deposited clusters increases and the light absorption is higher (by about a factor of three) than for nanoparticles without milling. The abrupt increase when radiation becomes more intensively absorbed with increasing photon energy corresponds to an onset of transmission near the optical absorption. The experiment corroborates the theoretical prediction that Ag 5 clusters are capable of extending the optical response of TiO 2 into the visible.
As can be seen in the bottom panel of Fig. 4, the main absorption peaks in the visible (pink and forest-green arrows) involve the electron transfer from 'isolated' midgap states (the HOMOÀ1 and HOMO orbitals) to acceptor Ti(3d) states in the TiO 2 conduction band (the LUMO+26 and LUMO+76 orbitals). In contrast with the case of the Cu 5 /TiO 2 interface, 15 the frontier HOMOÀ1 orbital bears a dominant Ag(5s) atomic contribution (see Section S2 of the ESI †) and not chemical mixing of Cu(3d) orbitals with O(2p) and Ti(3d) states. For the Ag 5 -TiO 2 system, there is also photo-induced electron transfer from frontier Ag(4d) orbitals having chemical mixing with O(2p) and Ti(3d) states such as the HOMOÀ2 orbital (see Section S2 of the ESI †). However, the associated absorbance contribution (dotted blue arrow in Fig. 4) is located in the UV and not the visible region.
Our results are consistent with previous studies 15, 20 indicating that the main mechanism driving photoabsorption is a single electron 'jumping' from 5s (Ag 5 ) or 3d (Cu 5 ) orbitals to the conduction band, leaving behind a long-lived 'hole' at the subnanometer clusters. Similar to the case of the Cu 5 -TiO 2 interface, 15 the Ag 5 cluster induces a spatial separation of photogenerated holes and electrons. It can be noted from the orbital pictures of Fig. 4 that the acceptor state bears a depleted region of charge (empty region) at the Ag 5 -TiO 2 layer, hindering

Prediction of CO 2 photo-activation
A previous theoretical study 19 has indicated that subnanometer Cu 5 clusters could enable the photo-activation of the CO 2 molecule and we analyse here if similar conclusions hold for unsupported and TiO 2 -supported Ag 5 clusters. By relaxing the whole CO 2 /Ag 5 geometry (see the inset of Fig. 6), we estimated a physisorption energy of À0.10 (À0.12) eV for the CO 2 molecule over the Ag 5 cluster at the MP2 (DFT-D3) level. We also estimated the Helmholtz free energy of formation, 62 nding that the CO 2 /Ag 5 complex is still stable at room temperature but by À0.03 eV only. Follow-up TDDFT calculations of the UV-Vis spectrum (see Fig. 6) show that the bare Ag 5 clusters induce CO 2 activation with photon energies in the UV region (from about 3.4 eV). When considering TiO 2 -supported Ag 5 clusters as the photocatalysts, we nd that the physisorption state and energy (0.11 eV) are very similar to the case of the unsupported cluster. However, it can be noted from Fig. 7 that a photon energy in the visible region is already capable of inducing CO 2 activation. The transition responsible for the peak in the visible involves an electron "jump" from the HOMO orbital and the nal state is the CO 2 c À radical attached to the Ag 5 -supported cluster. It is well-known that the radical CO 2 c À is a clear precursor-state for dissociation of the CO 2 molecule due to its weakened C]O bond.
Also, we found that both the physisorption and the photoactivation of CO 2 are possible over the pyramidal-shaped Ag 5 isomer shown in Fig. 1, with an almost identical physisorption energy (À0.12 eV). The order of magnitude of our estimated physisorption energies are the same as in previous studies on CO 2 capture through TiO 2 nanoparticles (between À0.16 and À0.28 eV in ref. 63). In view of the similar properties of Ag n clusters (n < 5) when adsorbed on rutile and anatase phases, 20,22 we expect that the photoinduced activation of CO 2 occurs also on anatase-supported Ag 5 clusters. We also calculated the UV-Vis spectra of CO 2 adsorbed on the bare TiO 2 for one specic conguration (over the Ti(5f) site). However, no transition with a signicant oscillator strength has been found for a photoexcited electron from the bare TiO 2 surface to the CO 2 molecule. This outcome also indicates that the Ag 5 cluster is responsible for the predicted CO 2 photoactivation.

Conclusions
The very recent development of cutting-edge experimental techniques making the synthesis of subnanometer metal clusters possible is pushing our understanding of molecule-like catalysts and photocatalysts far beyond the theory developed for metal nanoparticles and bulk materials. As an example, it has been previously shown how new photocatalytic and optical properties with technological projections are acquired by TiO 2 surfaces upon deposition of Cu 5 clusters. 15,19 In this work, we computationally and experimentally explored the properties of Ag 5 -modied TiO 2 surfaces instead, taking advantage of the high monodispersity of the method for Ag 5 cluster synthesis.
On the one hand, we have clearly shown that these Ag 5 clusters are capable of inducing the formation of stable surface   polarons, as localized Ti 3+ 3d 1 states, as well as photogenerated large polarons at the Ag 5 /TiO 2 interface of the material. Moreover, new fundamental insights have been gained on general electronic polarization effects accompanying the formation of surface polarons (along with the well-known structural distortion of the crystal lattice). This phenomenon has been manifested as a depopulation of titanium 3d orbitals favouring oxygen 2p orbitals, as experimentally observed through X-ray absorption spectroscopy at the Ti K-edge and theoretically predicted by applying state-of-the-art computational modelling. The self-trapped Ti 3+ 3d 1 electron repels nearby oxygen ions and attracts nearby titanium cations which, in turn, affects their electronic structure, causing the transfer of electronic charge from Ti 4+ cations to O 2À ions. On the other hand, our results point out that TiO 2 -supported Ag 5 clusters are not only visiblelight photo-active materials but are also potential photocatalysts for CO 2 reduction.
From a practical perspective, the modication of TiO 2 surfaces with subnanometer Ag 5 clusters has revealed a new way of stabilizing surface polarons and producing at the surface a kind of polaronic 2D material, which could be used for further experimental and theoretical studies of polaron interactions, currently a matter of high relevance. 64 From a broader perspective, the main novelty of our present work is that we revealed theoretically and conrmed experimentally an electron polarization phenomenon associated with a surface polaron formation for the rst time. At present, the experimental observation along with the theoretical interpretation suggests an important step for the fundamental understanding of surface polarons and photoexcitation.

Materials
Ag 5 clusters were synthesized and characterized according to a previously developed electrochemical method, 10,11 using a Ag electrode. 11 The experimental method for Ag 5 cluster synthesis and full characterization has been described in ref. 65. TiO 2 titanium dioxide nanoparticles were purchased from GetNa-noMaterials, 66 in the form of nanopowders, which according to the supplier are composed of particles with a primary particle size (99.9%) of 5 nm.

Experimental methods
We carried out X-ray absorption spectroscopy measurements (XAS) in the XANES (X-ray absorption near edge structure) regions at the XAFS2 beamline 67 of the Laboratório Nacional de Luz Síncrotron (LNLS), Campinas, Brazil. These XANES measurements were performed in transmission mode using a Si(111) crystal monochromator around the Ti K-edge (4966 eV) at ambient temperature using three ion chambers as detectors. Harmonics were attenuated by detuning to 50% of the peak intensity. We determined the sample absorption between the rst two chambers. For calibration purposes, the third chamber was used to measure a metallic Ti reference. In order to achieve an edge-step close to unity in the XAS measurements, we calculated the optimum amount of material. Powdered samples were dispersed in 10 ml of isopropyl alcohol and then ltered through a 0.45 mm pore size MF-Millipore™ membrane lter. We normalized XANES data by standard methods using ATHENA soware which is part of the IFEFFIT package. 68 We obtained the optical absorption spectra through diffuse reectance spectroscopy (DRS) using a Shimadzu ISR-2600 Plus spectrophotometer. The setup includes an integrating sphere with two detectors, a photomultiplier and an InGaAs detector. The DRS spectra were collected at room temperature in the range between 200 and 700 nm with a step of 1.0 nm using standard BaSO 4 (Nacalai Tesque) as a reference. DRS was obtained by determining the ratio of intensities of diffusely re-ected radiation from the sample and from the standard.  15,19 Electron-ion interactions are described by the projector augmented-wave method, 70,71 using PAW-PBE pseudopotentials as implemented in the program. The electrons of the O(2s, 2p), C(2s, 2p), Ti(3s, 4s, 3p, 3d) and Ag(4d, 5s) orbitals are treated explicitly as valence electrons. A plane wave basis set with a kinetic energy cutoff of 700 eV is used. A Gaussian smearing of 0.05 eV is employed to account for partial occupancies, and the Brillouin zone sampled at the G point. 72 The convergence criterion was 10 À4 eV for the self-consistent electronic minimization. Geometries were relaxed with a force threshold of 0.02 eVÅ À1 .
The TiO 2 surface is modelled via periodic slabs, using a 4 Â 2 supercell (four TiO 2 trilayers giving ca. 13Å slab width). Ag 5 adsorption and CO 2 physisorption are assumed on one side of the slab, with 38Å of vacuum above it. 73 Adsorption energies of the Ag 5 cluster on the surface are derived via where E Ag 5 /TiO 2 (110) is the total energy of the system, E TiO 2 (110) is the energy of the substrate, and E Ag 5 denotes the energy of the bare silver cluster. When considering the adsorption of CO 2 on TiO 2 -supported Ag 5 clusters, the interaction energies are derived via E int ¼ E CO 2 /Ag 5 -TiO 2 (110) À E CO 2 À E Ag 5 -TiO 2 (110) with E CO 2 /Ag 5 -TiO 2 (110) as the total energy of the system, E Ag 5 À E TiO 2 (110) as the energy of the supported-TiO 2 -Ag 5 cluster, and E CO 2 stands for the energy of the free (gas-phase) CO 2 molecule. All these values were calculated in the same supercell slab for the sake of consistency.
The geometries were optimized with the PBE-D3(BJ) scheme with the Hubbard term (DFT+U) added and including spinpolarization. We used the same value of U (4.2 eV) reported in previous studies of TiO 2 -modied copper clusters. 15,37 For the dispersion-dominated Ag 2 /TiO 2 interaction, 20 the PBE-D3(BJ) interaction energies agreed to within 10% with reference values obtained with the domain-based pair natural orbital correlation approach DLPNO-CCSD(T) 74 as well as the symmetry-adapted perturbation theory [SAPT(DFT)] method. 75,76 The performance of the PBE-D3(BJ) approach against higher levels of ab initio theory has also been tested for the estimation of the CO 2 physisorption energy on TiO 2 -supported Cu 5 clusters. 19 An agreement to within 10% was found between PBE-D3(BJ) and second-order Möller-Plesset perturbation theory (MP2) levels.
We used the optimized geometries, obtained at the PBE+U/ D3 level in nal HSE06 calculations. The HSE06 exchangecorrelation functional uses a screened Coulomb potential for increased efficiency on metallic systems. 43,44 It has been the preferred approach in previous studies of optical and other electronic properties of TiO 2 . [77][78][79] We applied the HSE06 approach using a HF/GGA mixing ratio of 25 : 75 with a screening parameter of 0.11 bohr À1 , as recommended in ref. 44. At a variance with our previous study of TiO 2 -supported Ag n clusters (n < 5), 20 all calculations are spin-polarized and all atoms and ions from the supercell models were relaxed.
4.3.2 Reduced density matrix treatment. We calculated the UV-Vis absorption spectra using the computational approach previously applied to TiO 2 -supported Cu 5 clusters. 15 The relaxation processes involved are described by the reduced density matrix (RDM) approach in the Redeld approximation, 46 based on orbitals taken from calculations employing the HSE06 hybrid functional. This combined RDM-DFT treatment developed by Micha and Kilin 47,48 is already a well-established tool in describing the optical spectra of subnano metal clusters adsorbed on semiconductor surfaces 80 (see, e.g., ref. 20 and 50-52).
Very briey, in the presence of a monochromatic electromagnetic eld E of frequency U, the evolution equation for the reduced density r in the Schrödinger picture takes the form whereF KS denotes the effective Kohn-Sham Hamiltonian (the indices refer to its representation in the Kohn-Sham basis set), D is the electric dipole moment operator, and R jklm stands for the Redeld coefficients, i.e. the Kohn-Sham components of the relaxation tensor. The latter is dened as in ref. 46 and is implemented as described in ref. 47. Within the Redeld approximation, the relaxation tensor incorporates not only fast electronic dissipation due to electronic uctuations in the medium, but also the relatively slow relaxation due to vibrations of the atomic lattice. It is convenient to perform coordinate transformation into a rotating frame accounting for the electromagnetic eld oscillation. This is described by the equations rĩ j (t) ¼ r ij (t)exp(iUt), 3 i > 3 j rĩ j (t) ¼ r ij (t)exp(ÀiUt), 3 i < 3 j where 3 i is the energy of the i-th Kohn-Sham orbital. Time averaging over the fast terms in the equation of motion for the RDM yieldsr SS jj ¼ G j À1 X HOMO k¼0 g jk ðUÞ; j $ LUMÕ r SS jj ¼ 1 À G j À1 X N k¼LUMO g jk ðUÞ; j # HOMO as stationary-state solutions for the diagonal elements. 47 In this, HOMO and LUMO denote the lowest-energy unoccupied and the highest-energy occupied molecular orbital, respectively. G j is a depopulation rate, and the sum terms g jk are given by g jk ðUÞ ¼ gU jk g 2 þ D jk ðUÞ 2 ; with g denoting the decoherence rate, U jk as the Rabi frequencies given by U jk ¼ ÀD jk $E 0 =ħ, and D jk (U) ¼ U À (3 j À 3 k ) as detunings. The diagonal elements provide the populations of the KS orbitals. The population relaxation rate ħG and the decoherence rate ħg are kept xed to values of 0.15 meV and 150 meV (27 ps and 27 fs). These values have been chosen according to known rates for phonon decay and electronic density excitations in semiconductors (see, e.g., ref. 81).
In terms of the stationary populations, the absorbance is given by 20,51,52,82,83 aðUÞ ¼ X where f jk is an oscillator strength per active electron. 84 The solar ux absorption spectrum is then expressed as where the solar ux is approximated by the black body ux distribution, normalized to an incident photon ux of 1 kW m À2 , F solar ðħUÞ ¼ ðħUÞ 3 p 3 ħ 3 c 3 C T expðħU=k B TÞ À 1 ; with C T the ux normalization constant and the temperature T set to 5800 K.

Cluster model calculations.
Cluster model calculations were performed for the interaction between CO 2 and the bare Ag 5 cluster by applying the PBE-D3(BJ) scheme and the MP2 method with the ORCA 85 suite of programs (version 4.0.1.2). For this purpose, we used an atom-centered def2-TZVPP 86 basis set for carbon, oxygen, and silver atoms. When optimizing the geometries in the CO 2 -Ag 5 cluster, the atoms of both CO 2 and Cu 5 sub-systems were allowed to relax. We also calculated Helmholtz free energies of formation 62,87 using the thermochemistry output of ORCA. 85 Next, we carried out timedependent DFT (TDDFT) calculations of the UV-Vis spectra using the PBE-D3(BJ) scheme.