{'fraction_non_alphanumeric': 0.03115443924622984, 'fraction_numerical': 0.022973785316640967, 'mean_word_length': 4.6550399054094, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 1, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Exploring the Catalytic Properties of Unsupported and TiO2-Supported Cu5 Clusters: CO2 Decomposition to CO and CO2 Photoactivation

In this work, we explore the decomposition of CO2 on unsupported and TiO2-supported Cu5 clusters via computational modeling, using both finite cluster and periodic slab structures of the rutile TiO2(110) surface. While the energy needed for C=O bond breaking is already significantly reduced upon adsorption onto the unsupported metal catalyst (it drops from 7.8 to 1.3 eV), gas desorption before bond activation is still the inevitable outcome due to the remaining barrier height even at 0 K. However, when the Cu5 cluster itself is supported on TiO2, reactant and product adsorption is strongly enhanced, the barrier for bond breaking is further reduced, and a spontaneous decomposition of the molecule is predicted. This finding is linked to our previous work on charge-transfer processes in the Cu5–TiO2 system triggered by solar photons, since a combination of both phenomena at suitable temperatures would allow for a photoinduced activation of CO2 by sunlight.


INTRODUCTION
During the past few years, highly stable metal clusters of subnanometer size, as required in industrial applications, have emerged as a new generation of catalysts and photocatalysts with appealing properties arising from their molecule-like electronic structures. As opposed to metal nanoparticles in the visible region, 1 these "atomic" or subnanometer-sized clusters do not sustain their metallicity and do not show plasmonic behavior. Instead, the presence of a molecule-like HOMO− LUMO gap impacts their chemical and physical properties, making them innovative materials for applications including luminescence, 2 sensing, 3 therapeutics, 4 energy conversion, 5 catalysis, 6 and electrochemical applications. 7,8 In particular, Cu 5 clusters have been shown to be less susceptible to oxidation than larger systems like Cu 8 or Cu 20 and have therefore been proposed as promising catalysts. 9,10 Moreover, it has been observed that Cu 5 clusters are stable against oxidation up to a temperature as high as 423 K. 10 These clusters can be synthesized by kinetic control using electrochemical methods, 11 showing an exceptional chemical and thermodynamical stability in solution over the whole pH range. 11 As discussed in ref 10, high monodispersity of synthesized Cu 5 clusters has been shown since the method of cluster synthesis was extremely size-selective. As compared with closed-shell cases, the outer unpaired electrons of openshell clusters such as the Cu 5 cluster are expected to be more active in chemical reactivity either by sharing or transferring them. For all these reasons, we have chosen the Cu 5 as the potential catalysts in this work.
This article addresses the decomposition of CO 2 over Cu 5 into CO due to its potential relevance in the context of climate change and global warming (see ref 12 for a very recent and comprehensive review on heterogeneous CO 2 reduction). The CO 2 transformation onto copper clusters into methanol has recently attracted much attention. 13,14 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 15 in order for it to be broken in the gas phase. The catalytic properties of metal clusters can be optimized through suitable supporting materials, which affect their geometry and electronic structure as desired. 16 For instance, the electronic structure of Au 8 clusters is strongly influenced by the MgO support which increases its CO oxidation reactivity. 17 For Cu 4 clusters, it could be shown that the Al 2 O 3 support is lowering the energetic barrier for CO bond-breaking to less than 1 eV due to the strong interaction of the CO 2 molecule with the copper cluster. 18 Hence, similar effects are expected for a metal-oxide support of Cu 5 clusters.
In this work, the TiO 2 surface has been selected as the support due to its abundance, nontoxicity, biological inertness, and chemical stability. In fact, it is one of the most popular materials for (photo)catalytic applications and solar energy conversion. Moreover, we have recently shown that the deposition of a single monolayer of Cu 5 clusters on a TiO 2 surface improves its optical properties significantly, 19 making it a visible-light photoactive material. More specifically, we demonstrate that, when deposited on the surface of titanium dioxide, the copper clusters are able to shift the adsorption from the high energy range, i.e. the UV spectrum, toward the visible light, where the sun has its maximum energy output. As a consequence, 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 for follow-up chemistry.
The CO 2 activation and dissociation on TiO 2 -supported Cu n (n < 5) 20 and Cu 5 clusters 21 has been addressed in previous works, 20,21 with the specific surface being rutile TiO 2 (110) in ref 20 and anatase TiO 2 (101) in ref 21. Thus, Iyempeurumal and Deskins 20 found that clusters of 1−4 copper atoms supported on the rutile TiO 2 (110) surface stabilize a bent CO 2 molecule (i.e., the precursors for CO 2 decomposition), especially the Cu 2 dimer. More recently, Jafarzadeh et al. 21 considered, besides the CO 2 activation, its dissociation into CO and O fragments attached to Cu 5 -and Ni 5 -modified anatase TiO 2 surfaces, addressing also the impact of plasmainduced surface charging. The authors found that adding plasma-induced excess electrons stabilize further bent CO 2 structures. 21 Moreover, it was found that the dissociation of CO 2 on charged clusters is energetically more favorable than that on neutral clusters. 21 However, actual reaction paths to CO 2 dissociation were not considered.
Applying density functional theory (DFT), time-dependent DFT, and an approach combining DFT with reduced density matrix theory, we focus on exploring the following aspects: (1) possible reaction energy pathways to both CO 2 activation and dissociation on unsupported as well as TiO 2 -supported Cu 5 clusters; (2) the optical response of the system under solar irradiation. Thus, in section 2, the computational approach and the details of our calculations are presented. Section 3 focuses on analyzing the reaction energy pathways as well as the UV− vis absorption spectra of unsupported and supporteed Cu 5 clusters. Finally, section 4 closes with the concluding remarks.

METHODS
Density functional theory (DFT) is applied to shed light on the catalytic mechanism for CO 2 decomposition to CO on unsupported and TiO 2 -supported Cu 5 clusters. We employ a dispersion-corrected DFT-D3 ansatz, 22,23 given its excellent performance in describing the adsorption of small silver clusters on the same surface. 24 Structural optimizations and the calculation of interaction energies are performed with the Perdew−Burke−Ernzerhof (PBE) density functional and the Becke−Johnson (BJ) damping 22 for the D3 dispersion correction. We will refer to this combination as the PBE-D3(BJ) scheme. Both finite cluster and periodic slab models (see Figure 1) have been used to account for TiO 2 (110) rutile surface effects. We first explore minimum energy pathways for both physisorption and chemisorption of the CO 2 molecule on supported and unsupported Cu 5 clusters. Next, we seek for possible reaction pathways leading to CO bond breaking, starting with the lowest-energy chemisorption states found for the attached CO 2 molecule. Additionally, time-dependent density functional calculations of the UV−vis spectra are carried out to explore the possibility that a photoinduced activation of physisorbed CO 2 occurs via electron transfer from TiO 2 -supported Cu 5 clusters to the attached CO 2 molecule. Finally, as a second route to obtain the UV−vis spectra, a reduced density matrix (RDM) approach in the Redfield approximation 25 is employed, with the orbitals generated from periodic DFT calculations. In particular, we employed the HES06 hybrid functional of Heyd, Scuseria, and Ernzerhof, 26,27 a well-established treatment for the band gap analysis of semiconductors including TiO 2 . 28 This combined RDM-DFT treatment 29,30 has provided UV−vis absorption spectra in very good agreement with the experiment for the Cu 5 -decorated rutile TiO 2 (110) surface. 19 If not explicitly mentioned otherwise, distances and energies are given in angstrom (1 = 10 10 m) and electronvolt (1 eV = 1.602176565(35) 10 −19 m 2 kg s 2 ) units, respectively.  The Journal of Physical Chemistry C Article with the ORCA 31 suite of programs (version 4.0.1.2). For this purpose, an atom-centered def2-TZVPP 32 basis set was used for copper and carbon atoms while the (augmented) polarized correlation-consistent triple-ζ (aug-cc-pVTZ) basis of Woon and Dunning, Jr., 33 as reported in ref 34, was employed for oxygen and titanium atoms. As can be seen from Figure 1 (lefthand panel), a hydrogen-saturated cluster model of stoichiometry (TiO 2 ) 13 (H 2 O) 14 was employed to model the rutile TiO 2 (110) surface, in which the number of hydrogen atoms are chosen so that the whole cluster remains electrically neutral. As mentioned in ref 19, this cluster model provides a very similar description of the Cu 5 −TiO 2 (110) system to that obtained via periodic calculations. For the sake of accuracy, we have also realized state-of-the-art periodic model calculations in this work (see section 2.2). In fact, the periodic model provides a better account of the extended nature of the surface and, particularly, of (long-range) dispersion corrections. However, the cluster model has allowed a vis-a-vis comparison of CO 2 adsorption properties on supported and unsupported Cu 5 clusters, as well as the application of more expensive ab initio methods. We assume the system to be in a doublet spin state since the quartet spin state is higher in energy for the free Cu 5 cluster (by 0.64 eV at PBE-D3(BJ) level). PBE-D3(BJ) interaction energies were found to agree within 10% with reference values obtained with the domain-based pair natural orbital correlation approach DLPNO−CCSD(T) 35 as well as the symmetryadapted perturbation theory [SAPT(DFT)] method 36,37 (see ref 24) for the related Ag 2 /TiO 2 (110) system.
When optimizing the geometries in the cluster model, the atoms of both CO 2 and Cu 5 subsystems were allowed to relax, while the atoms of the support were kept fixed to experimentally determined values of the TiO 2 (110)-(1 × 1) surface. 38 Using this computational protocol, the adsorption energies were found to agree rather well with those obtained using the periodic slab model (see below), in which all the atoms were allowed to relax. Moreover, the employment of the ORCA suite of programs allowed us to obtain relaxed surface scans in constrained optimizations for which specific internal coordinates are kept frozen (i.e., the value of the C−O bond length). The modeling through a finite cluster was also used to test the performance of the PBE-D3(BJ) approach against higher levels of ab initio theory such as second-order Moller− Plesset perturbation theory (MP2) level. This way, additional calculations on the physisorption interaction energies of CO 2 on TiO 2 -supported Cu 5 clusters showed that the PBE-D3(BJ) approach provides values agreeing to within 10% with those obtained at MP2 level with the same basis set, and within 4% with those calculated using the larger def2-QZVPP 32 basis set and the same PBE-D3(BJ) scheme.
Time-dependent DFT (TDDFT) calculations of the UV− vis spectra were also performed using the PBE-D3(BJ) scheme and the cluster model. The number of roots were limited to 110 for the TiO 2 -supported Cu 5 cluster, with a focus on the first transition involving the "jump" of an electron from the highest-energy "doubled-occupied" molecular orbital (referred to as HOMO) of the complete system to an unoccupied molecular orbital with high density around the attached CO 2 molecule.
2.2. Periodic Calculations. Periodic electronic structure calculations are performed with the Vienna ab initio simulation package (VASP 5.4.4), 39,40 following a similar computational approach to that reported in previous work on He-, Ag 5 -, and Cu 5 −TiO 2 (110) interactions 19,24,41 as well as a systematic analysis of noble-gas atoms on the same surface. 42 Electron− ion interactions are described by the projector augmentedwave method, 40,43 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 Cu(3d, 4s) 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 is sampled at the Γ point. Test calculations showed that interaction energies at the potential minimum, using a 5 × 5 × 1 Monkhorst−Pack 44 kpoint mesh, are similar (within ca. 0.01 eV) to those calculated at the Γ point. By shifting the kinetic energy cutoff from 700 to 1000 eV, the interaction energies were found to vary by less than 1 meV. The convergence criterion was 10 −4 eV for the self-consistent electronic minimization. Geometries were relaxed with a force threshold of 0.02 eV/Å.
The Cu 5 -decorated surface was modeled via periodic slabs, using a 4 × 2 supercell (four TiO 2 trilayers giving ca. 13 Å slab width). Adsorption was modeled on one side of the slab, with 38 Å of vacuum above it. This large vacuum region allowed the description of long-range tails of the interaction potentials while avoiding unphysical overlaps of electronic densities. Interaction energies are derived via with E Cu 5 /Cu 5 −TiO 2 (110) as the total energy of the system, E Cu 5 −ETiO 2 (110) as the energy of the supported-TiO 2 Cu 5 cluster, and E CO 2 denoting the energy of the free (gas-phase) CO 2 molecule, all calculated in the same supercell slab for the sake of consistency. Adsorption energies are calculated with the PBE-D3(BJ) scheme with the Hubbard term (DFT+U) added and including spin-polarization. The values of U reported in previous studies of Cu n clusters (n ≤ 5) on the (101) and (100) surfaces of anatase 45 and rutile 19 were used (4.2 eV for titanium and 5.2 eV for copper). Due to the known underestimation of the band gap with the PBE functional, the photoabsorption spectra are calculated with the HSE06 exchange-correlation functional instead, which uses a screened Coulomb potential for increased efficiency on metallic systems. 26,27 This approach was applied using a HF/GGA mixing ratio of 25:75 with the screening parameter of 0.11 bohr, −1 as recommended in ref 27. All the surface ions and atoms from both the Cu 5 cluster and the attached CO 2 molecule were relaxed using the PBE-D3(BJ) method but with the Hubbard term (DFT+U) added. Finally, the optimized geometries, obtained at the PBE+U/D3 level, were used in final HSE06 calculations of the electronic structures. This computational protocol is the same as in our previous calculations of the UV−vis spectra for the Cu 5 − TiO 2 (110) system. 19 2.2.1. Reduced Density Matrix Treatment. Photoabsorption spectra are calculated using the computational approach previously applied to the Ag 5 /TiO 2 and Cu 5 /TiO 2 systems in refs 19 and 24. The relaxation processes involved are described by the reduced density matrix (RDM) approach in the Redfield approximation, 25 based on orbitals taken from calculations employing the HSE06 hybrid functional. This combination of RDM and DFT, proposed by Micha and The Journal of Physical Chemistry C Article collaborators, 29,30 has been successfully applied to silver 24,46−48 and copper 19 clusters on semiconductor surfaces. 49 Very briefly, in the presence of a monochromatic electromagnetic field of frequency Ω, the evolution equation for the reduced density ρ in the Schrodinger picture takes the form  Within the Redfield approximation, the relaxation tensor incorporates not only fast electronic dissipation due to electronic fluctuations in the medium but also the relatively slow relaxation due to vibrations of the atomic lattice. It is convenient to perform a coordinate transformation into a rotating frame accounting for the electromagnetic field oscillation. This is described by the equations where ε i is the energy of the ith Kohn−Sham orbital. Time averaging over the fast terms in the equation of motion for the RDM yields as stationary-state solutions for the diagonal elements. 29 In it, HOMO and LUMO denote the lowest-energy unoccupied and the highest-energy occupied molecular orbital, respectively. Γ j is a depopulation rate, and the sum terms g jk are given by with γ denoting the decoherence rate, Ω jk as the Rabi frequencies given by Ω = − · ℏ D / In terms of the stationary populations, the absorbance is given by 18,24,47,48,51  where f̅ jk is an oscillator strength per active electron. 52 The solar flux absorption spectrum is then expressed as where the solar flux is approximated by the blackbody flux distribution, normalized to an incident photon flux of 1 kW/ m 2 , with C T the flux normalization constant and the temperature T set to 5800 K.

RESULTS AND DISCUSSION
3.1. Reaction Pathways: CO 2 Interaction with Unsupported Cu 5 Clusters. Let us first analyze the interaction of CO 2 with unsupported Cu 5 clusters. Our results have indicated that a planar trapezoidal structure of Cu 5 is only slightly energetically favored (by 0.13 eV when the energy difference is calculated with the PBE-D3(BJ) scheme) over a trigonal bipyramidal structure so that we have considered both. By relaxing the geometries of the Cu 5 and CO 2 reactants at each intermolecular Cu 5 −CO 2 distance, defined here as the distance between the carbon atom and the central atom of the Cu 5 cluster, we obtain the interaction energies shown in the upper panel of Figure 2. Zero energy is set to having CO 2 at infinite distance from the cluster. The energy pathway is characterized by a very shallow minimum of about −0.15 eV at a long Cu 5 −CO 2 distance (about 5 Å) and a relatively deep potential minimum of about −0.6 eV at a shorter distance (∼3.9 Å), with a very low energy barrier in between. The shallow energy minimum emerges from a weak dispersiondominated interaction between the two reactant species. Note that the barrier is appearing only if a bending of the CO 2 molecule is allowed. Preliminary calculations of the same reaction pathway at the MP2 level of theory yield a slightly higher energy barrier (about 0.2 eV). Work is in progress to get a better estimate of the barrier to chemisorption using multireference perturbation theory, allowing us to better characterize the mixing between covalent and ionic contributions (see, for example, ref 53).An analysis of Loẅdin reduced orbital charges reveals no net charge transfer between the Cu 5 and CO 2 species but a strong polarization of both reactant species at the energy minimum configuration. The CO 2 bending gives rise to the formation of a dipole moment that interacts attractively with induced dipole and quadrupole moments formed in the polarized Cu 5 cluster. From the Gibbs energies at the right-hand panel, it can be seen that the energy minimum is deep enough to "survive" at room temperature but not at temperatures higher than 100°C.
The middle panel of Figure 2 illustrates how the adsorbed CO 2 molecule, starting from its energy minimum configuration as shown in the upper panel, becomes decomposed by increasing one of the CO distances. The planar Cu 5 cluster catalyzes the CO 2 decomposition, but the energetic barrier to break the CO bond is still too high (∼1.3 eV) to provide a reasonable reaction rate at room temperature. The final configuration with the CO fragment attached to Cu 5 is rather unstable: At about 200°C, the asymptote for CO desorption from Cu 5 −O lies approximately at the same energy as the transition state for CO bond breaking and reduces significantly at higher temperatures due to increasing entropy.
This picture changes remarkably when considering the bipyramidal trigonal structure of Cu 5 (bottom panel). Not only the energetic barrier of the rate-limiting step (CO breaking) is clearly lower (∼0.8 eV) but also the complex formed upon CO breaking are very stable, as both fragments remain adsorbed at ambient temperature. Also, in contrast with the planar Cu 5 counterpart, the entrance channel is characterized by a very weak interaction of the CO 2 molecule with the bipyramidal-shaped Cu 5 cluster (about −0.3 eV). This finding once again illustrates the extreme sensitivity of atomic cluster properties with respect to structural reconfigurations, and it brings us straight to a final but crucial extension of our model with respect to the cluster support.
The Journal of Physical Chemistry C Article 3.2. Reaction Pathways: CO 2 Interaction with TiO 2 − Supported Cu 5 Clusters. In this section, we focus on how the CO 2 −Cu 5 interaction is modified when the Cu 5 atomic cluster is supported on the rutile TiO 2 (110) surface. Figure 3 summarizes the main adsorption geometries found using both the nonperiodic (left-hand panel) and periodic (right-hand panel) approaches, with the corresponding adsorption energies and main geometrical parameters summarized in Table 1. It can be seen that, with the exception of the adsorption energy for the most attractive chemisorption configuration (labeled as "4" in Table 1 and Figure 3), nonperiodic and periodic calculations provide rather similar results. The larger discrepancies in the latter case might be ascribed to the fact that the copper cluster is lying flat on the surface and therefore too close to the boundaries of the actual cluster model. This is also reflected in the larger d(Cu−Cu middle ) distance obtained in the periodic calculation for the physisorption configuration labeled as "2" (see Table 1) since the Ti atom becomes located close to the cluster model boundaries (see Figure 3). The discrepancies in structural parameters should be reduced upon enlargement of the cluster model. However, the next cluster size was too large for a TDDFT treatment.
When considering chemisorption configurations (labeled as "3" and "4" in Figure 3), a Bader decomposition 53 shows that the Cu 5 cluster donates about 0.5 and 0.7 |e| of electronic charge to the attached CO 2 molecule, while the charge donation is almost negligible (below 0.02 |e|) when physisorption configurations are analyzed instead (labeled as "1" and "2" in Figure 3). There is a direct correlation between how much the CO 2 molecule becomes bent and how much electronic charge it accumulates from the Cu 5 cluster. In fact, upon bending, the energy of the antibonding LUMO orbital of the CO 2 orbital becomes lower and thus closer to that of the HOMO of the Cu 5 cluster, enhancing the probability of electron-transfer.
Using the finite cluster model, the upper panel of Figure 4 shows the interaction energies as a function of the intermolecular distance between the carbon atom and the central Cu atom. It can be readily observed that the interaction is strongly influenced by the support: the potential energy minimum from the surface scan is now located at a configuration with the CO 2 molecule physisorbed on top of one 5-fold Ti atom. As expected, with a well-depth of −0.33 eV, the physisorption minimum is dominated by the dispersion component of the interaction (−0.24 eV). There is almost zero net charge transfer to the CO 2 molecule (less than 0.02 |e|) but a slight polarization is occurring at the C atom. At this physisorption configuration, there is almost no bending of the CO 2 molecule (see Table 1). Also, a very good agreement is found between the adsorption energies and adsorption geometries obtained for the cluster and the periodic slab models of the rutile TiO 2 (110) surface (see Table 1 and Figure  3). As can be seen in Figure 3, the physisorption nature of this configuration is also reflected in the shape of the HOMO. It is very similar to that obtained without the attached CO 2   Figure 1 for the Labeling of the Oxygen and Copper Atoms) Corresponding to the Adsorption Configurations Presented in Figure 3 for the Non-Periodic Cluster and Periodic Slab Models Shown in Figure 1 d It is interesting to analyze the reasons for the adsorption energy differences which occur for the CO 2 molecule adsorbed on top of unsupported and supported Cu 5 clusters (−0.61 vs −0.22 eV). The free Cu 5 cluster is highly polarizable and the electronic charge becomes pushed toward the two terminal copper atoms upon the approach of the CO 2 molecule so that the electrostatic interaction is optimized. This polarization effect is somewhat constrained in the TiO 2 -supported Cu 5 cluster since the support causes a marked redistribution of the charge (see ref 19), with the two terminal copper atoms already being negatively charged. This redistribution is only slightly modified when the CO 2 molecule approaches the cluster in the symmetric "on top"-configuration. A very different picture emerges if the CO 2 molecule is approaching from a lateral side of the Cu 5 cluster (see middle panel of Figure 4 and configuration labeled as "3" in Figure 3 and Table  1): in this scenario, the charge distribution on copper atoms becomes polarized toward the opposite side from the attachment of the CO 2 molecule. This redistribution eases the bending of the CO 2 molecule (even without a barrier), with the carbon atom becoming negatively charged by about −0.5 |e| according to a Bader decomposition applied to the periodic model (configuration labeled as "3" in a right-hand panel of Figure 4). As a result, the adsorption energy becomes significantly lower (−0.5 eV). This adsorption energy is slightly below to that obtained considering a periodic slab model of the TiO 2 (110) surface (−0.4 eV, see Table 1). As can be seen in Figure 3, the HOMO isodensity profile is very different from those obtained in physisorption scenarios: there is a clear mixing of orbitals of the Cu 5 cluster with the lowest-energy unoccupied molecular orbital (LUMO) of the free CO 2 molecule (i.e., the antibonding π* orbital). It is dominated by 3d components from the copper atoms, bearing also important 4s-type contributions, while carbon and oxygen atoms provide 2s-and 3d-type (carbon) and 2p-type (oxygen) contributions.
Interestingly, the charge transfer to CO 2 in chemisorption configurations comes from the HOMO of TiO 2 -supported Cu 5 and not the lowest-energy single-occupied molecular orbital (referred to as SOMO). This holds true for nonperiodic as well as periodic calculations. In fact, as analyzed in ref 19., the energy of the HOMO is very close to the bottom of the conduction band while the energy of the SOMO is about 1 eV lower (i.e., too far away from the LUMO orbital of the CO 2 molecule). When the system is modeled by a periodic slab, the unpaired electron from the SOMO orbital becomes localized at a 5-fold Ti ion (i.e., characterizing a small polaron Ti 3+ state). In fact, the SOMO is localized in a Ti(3d) orbital lying in the surface plane, showing no overlap with frontier orbitals of the approaching CO 2 molecule. This is illustrated in Figure 5,  The Journal of Physical Chemistry C Article presenting the electronic density of states (EDOS) together with isodensity profiles of the SOMO and HOMO. As mentioned in the introduction, as compared with closed-shell cases, the outer unpaired electrons of open-shell clusters such as the bare Cu 5 cluster are expected to be the ones shared and/ or transferred to a molecular adsorbate such as CO 2 . Our results clearly show that the open-shell TiO 2 -supported Cu 5 cluster is a different case since the unpaired electron is localized at the small polaron Ti 3+ state so that one of the paired electrons occupying HOMO orbitals is mainly responsible for the chemical bonding with CO 2 .
Finally, the bottom panel of Figure 4 shows how the adsorption complex with a bent CO 2 molecule attached to the lateral side of the Cu 5 cluster (middle panel) evolves upon increasing of one of the CO distances. Very remarkably, the Cu 5 cluster then prefers to lie flat on the TiO 2 support, and a rather stable adsorption CO 2 /Cu 5 complex is obtained for an elongated C−O distance of about 1.4 Å. This is also clearly reflected in the mixing between Cu 5 and CO 2 orbitals, as can be observed in the HOMO isodensity profile (see the bottom panel of Figure 3). At a variance with the chemisorption state labeled as "3" in Figure 3, the carbon atom provides mostly 2sand 2p-type orbital contributions for CO 2 /Cu 5 bond formation rather than 2s-and 3d-type contributions (see above). Essentially, when the Cu 5 cluster is lying flat on the surface, the two terminal Cu atoms become bonded to in-plane oxygen ions. This feature favors the charge-transfer from the Cu 5 cluster to the attached CO 2 molecule so that the net donation becomes significantly larger (0.7 |e|). In turn, the CO 2 molecule becomes more bent than when attached to the Cu 5 cluster at the "raised" configuration (labeled as "3" in Figure  3). Notice also that the HOMO expands around the carbon atom and both copper and titanium atoms and not only the former, resulting in a stronger CO 2 −Cu 5 interaction. It should be noticed that the adsorption energies calculated for the CO 2 molecule on the supported Cu 5 −TiO 2 cluster are consistent with those reported by Afarzadeh et al. but considering the anatase TiO 2 (010) surface and, as large as −0.64 eV 20 with the CO 2 molecule becoming also strongly bent (O−C−O angle of 129.5 deg).
Upon further increase of the C−O distance by about 2.0 Å, an energy barrier of about 0.4 eV has to be overcome. As a consequence, CO 2 decomposes into an adsorbed CO fragment, which, at longer C−O distances, eventually desorbs from the catalyst, leaving behind a single oxygen atom which remains attached to the Cu 5 cluster.
Starting with the structures of the complex in the bottom panel of Figure 4, we have realized a reoptimization using the periodic slab model of the rutile TiO 2 (110) surface, allowing the atoms from the support also to relax. This way, we obtain a reaction pathway for CO 2 decomposition as shown in Figure 6.
Although the values of the adsorption energies are below those obtained for the finite cluster model, the energy necessary for breaking the CO bond is very similar (0.42 eV). The reaction pathway shown in Figure 6 highlights the occurrence of a spontaneous activation and decomposition of CO 2 on Cu 5 −TiO 2 . This outcome, along with the lower energy penalty (by about a factor of 3) in the rate-limiting step (CO bond breaking), are in fact the most relevant differences when compared to the case of the unsupported Cu 5 cluster scenario.
A reaction pathway leading to CO 2 dissociation to CO has also been found for the anatase TiO 2 -supported Pt 8 cluster with an energy barrier of 1.01 eV. 54 The enhanced catalytic activity of the Pt 8 -modified TiO 2 support was also rationalized in terms of the fluxional nature of the subnanometer-sized cluster. Similarly, a reconstruction of the Pt 8 cluster was found upon CO 2 adsorption. In our case, the C−O bond is even weaker if Cu 5 cluster reconstruction is allowed. Another, very recent study investigated the nature of CO 2 adsorption on Pt n − atomic clusters (n = 4−7) as a function of cluster size. 55 The authors found the molecule to be highly activated yet still molecularly bound, but assume dissociative adsorption for larger cluster species.
3.3. UV−Vis Absorption Spectra. 3.3.1. Cluster Model Calculations of the UV−Vis Absorption Spectra. Having analyzed the CO 2 /Cu 5 and CO 2 /Cu 5 −TiO 2 systems in the ground electronic state we focus now on its optical excitation. To this end, we have chosen the global minimum configuration of the unsupported CO 2 /Cu 5 system (see section 3.1), with the CO 2 molecule adsorbed on top of the Cu 5 cluster (adsorption energy of about 0.6 eV). Using the cluster model of the TiO 2 surface shown in Figure 1 (left-hand panel), we first compare the TDDFT spectra for CO 2 adsorbed on unsupported and supported Cu 5 clusters. Figure 7 (upper panel) illustrates how the irradiation of UV light onto the Cu 5 cluster (photon energies from 3.5 to 4.3 eV) is driving an electron transfer from orbitals having the higher densities on copper atoms to orbitals bearing the higher densities centered on carbon atoms. Specifically, the electron transfer process gives rise to the formation of a complex that is better characterized as the CO 2 •− radical ion attached to the copper cluster. Preliminary calculations using the multistate complete-active-space second-order perturbation theory (CASPT2) method indicate that the well-depth of the PES in the corresponding excited ionic state is larger than 0.5 eV. As expected from the population of an orbital correlating to the SOMO antibonding orbital of the CO 2 − fragment at the asymptotic region, the CO bond becomes weaker than in the ground electronic state. Therefore, a higher activity for CO 2 reduction is expected upon photoexcitation.
The bottom panel of Figure 7 shows the absorption spectra of CO 2 adsorbed on the Cu 5 -modified TiO 2 surface. The electron "jump" from the HOMO to an orbital with density projection on the carbon atom is evident, with the responsible peaks located at about 0.8 eV, i.e., in the infrared spectral The Journal of Physical Chemistry C Article region. As discussed in ref 19, the HOMO of the Cu 5 −TiO 2 system is dominated by 4s contributions from the copper atoms, bearing also 3p and 3d components. Essentially, the Cu 5 cluster donates electronic charge so that a CO 2 •− radical attached to the Cu 5 −TiO 2 composite is formed, similar to the unsupported case (see upper panel). However, as the main effect of the support, the photon energy necessary for the electronic transition is reduced by approximately 3 eV.
3.3.2. Periodic Calculations of the UV−Vis Absorption Spectra. In order to obtain a most accurate UV−vis absorption spectrum, we have used the periodic slab model of the rutile TiO 2 (110) surface shown in Figure 1 (right-hand panel) and the RDM-DFT method as outlined in section 2.2.1, which employs the hybrid HSE06 functional. The accuracy of this methodological protocol was assessed in ref 19 for the Cu 5 − TiO 2 (110) system, where the theoretical photoabsorption spectra agreed very well with the experimental spectra recorded using diffuse reflectance measurements.
As shown in Figure 8, after depositing the Cu 5 cluster on the TiO 2 (110) surface, the composite system presents absorption in the visible region. Furthermore, a strong enhancement of the absorption in the UV region is observed as compared with the unmodified material. 19 The physisorption of the CO 2 molecule on top of the Cu 5 clusters modifies the spectrum profile only slightly. The major modification is observed at about 2.1 eV (blue arrows in Figure 8). As already described using the cluster approach, the transition responsible for the two additional peaks involves an electron "jump" from the HOMO so that the final state can be characterized as the CO 2 •− radical attached to the Cu 5 -modified surface.

CONCLUSIONS
In this article, we have explored the energy landscape characterizing the interaction of a CO 2 molecule with an unsupported or TiO 2 -supported Cu 5 cluster. We further investigated the occurrence of a photoinduced charge-transfer process between the cluster and the CO 2 molecule. Thus, via computational modeling, we have shown how Cu 5 clusters catalyze the CO 2 decomposition by CO bond activation and a reduction of the barrier for bond breaking. Dissociation often represents the rate-determining step in reactions involving metallic nanoparticles. 56 When supported on TiO 2 , CO splitting becomes more favorable than spontaneous desorption of CO 2 . Moreover, time-dependent DFT and RDM-DFT calculations of the UV−vis spectra indicate that the TiO 2supported Cu 5 cluster donates electron charge to a physisorbed CO 2 molecule when illuminated with visible light, which is further beneficial for CO 2 activation. We point out two important findings: (1) CO 2 can be trapped in a dispersion-dominated physisorption state and, when irradiated with visible light, is transformed into a radical CO 2 •− . This radical is a clear precursor-state for dissociation due to its weakened CO bond. (2) The fluxionality of the subnanometric Cu 5 cluster makes it an efficient functional environment (isomer lying flat to the surface) for the bending of the CO 2 molecule. It is this enforced deformation that makes the adsorbed molecule more prone to accept electronic charge from the cluster, which in turn leads to a weaker CO bond.  The Journal of Physical Chemistry C Article Altogether, our results, along with those presented in our previous work, 19 point out that TiO 2 -supported Cu 5 clusters are not only innovative visible-light photoactive materials but also potential catalysts for CO 2 reduction, highlighting how new catalytic and optical properties are acquired by subnanometer-sized metal clusters when deposited on technologically relevant materials. More generally, our work shows how the first-principles modeling of this new generation of angstrom-sized catalysts and photocatalysts allows to understand them and, then, better control their properties. In particular, when both reactants, the metal cluster and the gas-phase molecule attached to it, are open-shell species, characterizations at a higher level of theory will become necessary, such as, e.g., those recently established by Aoiz and collaborators. 57−59 According to our results, experimental measurements capable of detecting CO desorption from Cu 5 −TiO 2 supported clusters as a function of temperature, with and without visible-light, would provide very useful insights regarding the conditions under which Cu 5 clusters could become efficient catalysts for the removal of CO 2 from the atmosphere.