Understanding and Optimizing the Sensitization of Anatase Titanium Dioxide Surface with Hematite Clusters

The presence of small hematite (Fe2O3) clusters at low coverage on titanium dioxide (TiO2) surface has been observed to enhance photocatalytic activity, while excess loading of hematite is detrimental. We conduct a comprehensive density functional theory study of Fe2O3 clusters adsorbed on the anatase TiO2 (101) surface to investigate the effect of Fe2O3 on TiO2. Our study shows that TiO2 exhibits improved photocatalytic properties with hematite clusters at low coverage, as evidenced by a systematic study conducted by increasing the number of cluster adsorbates. The adsorption of the clusters generates impurity states in the band gap improving light absorption and consequently affecting the charge transfer dynamics. Furthermore, the presence of hematite clusters enhances the activity of TiO2 in the hydrogen evolution reaction. The Fe valence mixing present in some clusters leads to a significant increase in H2 evolution rate compared with the fixed +3 valence of Fe in hematite. We also investigate the effect of oxygen defects and find extensive modifications in the electronic properties and local magnetism of the TiO2 - Fe2O3 system, demonstrating the wide-ranging effect of oxygen defects in the combined system.


Introduction
Photocatalysis emerges as a promising technique to address contemporary energy challenges.In particular, photocatalytic water splitting represents a highly sustainable approach to produce green hydrogen and oxygen by dissociating water using natural light.This environmentally friendly method enables the conversion of solar energy into chemical energy without contributing to pollution.Semiconductors with band gaps ranging from 2.5 to 3.4 eV are favorable photocatalysts covering visible to ultraviolet (UV) spectra [1].Consequently, incident photons with energies greater than or equal to the band gap of the material liberate electrons to the conduction band (CB) and holes to the valence band (VB).These photogenerated charge carriers can migrate to the surface of the material participating in oxidation and reduction reactions.Amongst the semiconductors suitable for these purposes, TiO 2 has been considered as a premier material since its discovery in 1972 by Fujishima and Honda [2].It possesses exceptional properties that make it attractive for photocatalysis.These properties include oxidation properties, physical and chemical stability, non-toxicity and abundance [3][4][5][6].Moreover, TiO 2 possesses a band structure suitable for efficient water splitting, as it straddles the reduction (-4.44 eV) and oxidation potentials (-5.67 eV) of water [6].However, despite the favorable attributes, a large band gap, quick recombination of the electron-hole pairs and being inactive for overall water splitting in the absence of sacrificial reagents leads to a performance degradation of TiO 2 [5,7,8].These factors limit the widespread utilization of TiO 2 in photocatalytic applications.Therefore, attempts are made to overcome the shortcomings and enhance the performance of TiO 2 .TiO 2 exhibits three phases at atmospheric pressure: stable rutile, metastable anatase and brookite.The crystalline structure can strongly affect the photocatalytic activity of a material.
Since the synthesis of pure brookite is difficult [9], extant investigations have mainly focused on rutile and anatase phases.Even though anatase possesses a larger band gap than rutile, anatase has been considered to have a superior photocatalytic performance [10][11][12][13][14].The better performance is generally attributed to indirect band gap and lower effective mass of photogenerated electrons and holes, increasing the lifetime of electron-hole pairs and lowering their recombination rate [15].However, researchers have also reported a good performance of rutile in special experimental synthesis conditions [16,17].Moreover, mixing anatase and rutile phase structures have shown even better activity than pure anatase, attributed to interfacial charge transfer occurring between the two phases [17,18].
A variety of strategies have been proposed to modify both chemical and physical properties of pure TiO 2 , and the construction of heterostructure systems has shown improvements in photocatalytic performance [19].It is recognized that by combining appropriate photocatalytic materials, heterojunction structures with matching band alignments can be formed.One promising candidate for combination with TiO 2 is hematite (α-Fe 2 O 3 , hereafter referred to as Fe 2 O 3 ).It is the most stable phase of iron (III) oxide, possessing a narrow band gap of 2.0-2.2eV [20,21].Several studies on TiO 2 -Fe 2 O 3 interface have been carried out earlier.For instance Mei et al. [22] and Singh et al. [23] have synthesized TiO 2 -Fe 2 O 3 heterostructure using deposition methods, where the TiO 2 (Fe 2 O 3 ) surface was fully covered and Fe 2 O 3 and TiO 2 are in direct contact.The results of Mei et al. suggested that Fe 2 O 3 concentration plays a key role in light adsorption, and the photoresponse could be engineered by the amount of surface Fe 2 O 3 in TiO 2 .However, many studies have found that the increased amount of Fe 2 O 3 content is not leading to a superior photocatalytic activity.For instance, in the study of Mei et al., using the photoluminescence spectroscopy (PL), the PL intensity of TH0.5 sample was found to be the lowest, indicating the most efficient charge separation compared to the samples with lower or higher Fe 2 O 3 content.Cao et al. [24] have the same conclusion on Fe 2 O 3 coated TiO 2 using atomic layer deposition (ALD) methods.They reported that 400 cycles of Fe 2 O 3 coating led to better photocatalytic activity than 200, 600 and/or 800 cycles.In general, at high Fe 2 O 3 content iron has been proposed to become a recombination center for the charge carriers, having a negative impact on catalytic activity [25,26].Singh et al. [23] studied TiO 2 -Fe 2 O 3 heterostructure over pure Fe 2 O 3 surface and a low performance in photoelectrochemical cells (PEC) was attributed to inefficient charge separation in the heterostructure.It is also worth noticing that in their computational investigation, they highlighted that anatase TiO 2 (101) surface placed on top of the Fe 2 O 3 surface was reconstructed during the geometry optimization.TiO 2 was reported to exhibit an "amorphous" structure that resembled none of the stable crystal structures of TiO 2 .The notable reconstruction may be attributed to the large lattice mismatch of the two surfaces.Further, investigations focusing on heterostructures with various Fe 2 O 3 coverage and content on TiO 2 , have shown that finding an optimal Fe 2 O 3 content is essential in order to maximize the photocatalytic activity [22,[24][25][26][27][28][29].For instance, Sun et al. [26] conducted an experimental study on anatase TiO 2 surface modified with the hematite cluster for phenol degradation.They reported that small clusters enhanced the photocatalytic activity of TiO 2 by improving its response to visible light, and charge carrier transfer and separation.In general, the observed enhancement in catalytic activity has been attributed to the formation of a heterojunction between TiO 2 and Fe 2 O 3 [24][25][26][27][30][31][32].Based on a thorough literature search, we can conclude that increased coverage of Fe 2 O 3 is detrimental to photocatalytic performance of the material.
Defect engineering emerges as another effective method to modify the catalytic properties and mechanisms.In metal oxides, including TiO 2 , oxygen vacancies are common defects [33].Resulting from an oxygen vacancy, impurity states are generally observed in the band gap of TiO 2 , often manifested as Ti 3+ species.These impurity states contribute to a shift in the absorption spectrum and increased conductivity of TiO 2 [34,35].Consequently, these can lead to enhanced photocatalytic activity, demonstrated by Sheiber et al. [36] for example.They reported that oxygen vacancies improved the photocatalytic activity of anatase TiO 2 in water adsorption.Several experiments have also demonstrated an existence of oxygen defect states in Fe 2 O 3 -TiO 2 and Fe-TiO 2 systems, and the states have been attributed to oxygen vacancies in the TiO 2 lattice [37][38][39][40].Spectroscopy techniques, such as X-ray photoelectron spectroscopy (XPS), have been used to confirm oxygen vacancy defects in the systems.The studies have reported a successful incorporation of Fe 3+ into the TiO 2 lattice, and due to the charge compensation mechanism, Fe 3+ species results in the formation of oxygen vacancies.For instance, Zhu et al. [40] proposed that the oxygen vacancies could contribute to a reduction in recombination rate.Correspondingly, Bootluck et al. [27] suggested that oxygen vacancies contribute to enhanced photocatalytic activity.They reported that resulting from the Arplasma treatment, oxygen vacancies were produced in the Fe 2 O 3 -TiO 2 nanocomposites, contributing to improved photocatalytic activity compared to untreated Fe 2 O 3 -TiO 2 .It is also demonstrated that Fe 2 O 3 -TiO 2 may be suitable material for hydrogen evolution reaction (HER).The improved photocatalytic activity of Fe 2 O 3 -TiO 2 nanocomposites was attributed to a lower charge transfer resistance, which has led to better charge separation and reduced recombination rate of electron-hole pairs compared to bare TiO 2 .It is worth noting that the study did not provide direct comparison between the HER activity of Fe 2 O 3 -TiO 2 and bare TiO 2 .
Inspired by the investigations of Sun et al. [25], we employ first principles calculations to inves-tigate the adsorption of hematite clusters on anatase TiO 2 (101) surfaces and its effect on photocatalytic properties.The choice of the anatase phase was motivated by its superior photocatalytic activity compared to other polymorphs, as discussed earlier.Moreover, studies have reported that the (101) plane of anatase possesses the highest photocatalytic activity than other crystal orientations [41,42].In order to improve the photocatalytic properties of TiO 2 Sun et al. [26] highlighted the advantage of small Fe 2 O 3 cluster size and low Fe 2 O 3 coverage on anatase TiO 2 .Building upon this, we introduce small hematite clusters, (Fe 2 O 3 ) n with n = 1,2,3 at the TiO 2 surface.We also delve into defect engineering as another effective method to modify the properties of the heterostructures.More precisely, we introduce an oxygen defect in the heterostructure of TiO 2 and (Fe Finally, to assess the photocatalytic performance, we focus on evaluating the suitability of the investigated heterostructures for HER.Our aim is to understand the effects brought about by the hematite clusters and further oxygen defect towards the electronic properties of TiO 2 , due to the change in carrier concentration compared to the pristine surface.We also demonstrate that coating the anatase titanium dioxide with mixed-valence iron containing O-ligands using various hematite cluster coverings represents an effective approach to enhance photocatalytic hydrogen production.

Computational methodology
First principles calculations based on density functional theory (DFT) were performed using Vienna Ab initio Simulation Package (VASP) [43][44][45] including the spin polarization.The exchangecorrelation potential was described by generalized gradient approximation (GGA) parameterized by Perdew-Burke-Ernzerhof (PBE) functional [46].The Hubbard correction was employed according to Dudarev et al. [47] to describe localized d electrons of titanium and iron in order to obtain more realistic electronic and magnetic properties.Within the GGA+U method we adopted the corrections of U eff = 4.5 eV (U= 4.5 eV and J= 0 eV) [48] for the Ti (table S1) and U eff = 4.0 eV (U= 4.0 eV and J= 0 eV) [49] for the Fe.In some studies the Hubbard correction has also been applied to O 2p states to further improve the description of Ti-O bonds and obtain a larger opening of the band gap for TiO 2 [50].Based on our results, in bulk TiO 2 , applying the U correction to the O 2p states did not provide a significant improvement in the band gap (table S1), and therefore we chose to consider the Hubbard correction only for Ti 3d states.The 1st Brillouin zone was sampled according to the Monkhorst-Pack scheme [51].The Projector augmented wave (PAW) method [52] was employed to describe the electron-ion potential with the plane wave energy cutoff of 650 eV (figure S1).The atomic relaxations were performed until the forces and energies were less than 0.001 eV/ Å and 10 −6 eV, respectively.We used VESTA [53] for visualization and VASPKIT [54] for post-processing of the data from the VASP calculations.
To simulate the pristine anatase TiO  2).To prevent interaction between periodic images, a vacuum space of 20 Å was applied along the c-axis.The heterostructures were formed by placing the hematite clusters (Fe 2 O 3 ) 1,2,3 on the TiO 2 surface.The models were denoted as (Fe 2 O 3 ) 1 /TiO 2 , (Fe 2 O 3 ) 2 /TiO 2 and (Fe 2 O 3 ) 3 /TiO 2 , and only these three heterostructures were considered in this study.K-point sampling of 3 × 2 × 1 and Gaussian smearing of 0.05 eV were used for the TiO 2 surface and heterostructures.To investigate the effect of an oxygen defect, several defect sites, shown in figure 7, were created in the (Fe 2 O 3 ) 1 /TiO 2 .An oxygen atom was removed either from the TiO 2 (surface or subsurface vacancy) or from the (Fe 2 O 3 ) 1 cluster.We created an oxygen vacancy in the surface layer of TiO 2 by removing a twofold-coordinated O atom, not forming a bond with the cluster.Three subsurface oxygen atoms were removed at different distances from the cluster in the first subsurface layer.Lastly, two different oxygen defects were created in (Fe 2 O 3 ) 1 cluster.
The surface vacancy was labeled as O v , the subsurface vacancies as O sv1 , O sv2 and O sv3 , and the oxygen defects located in the (Fe 2 O 3 ) 1 cluster as O c1 and O c2 .The defective heterostructures were further denoted as (Fe 2 O 3 ) 1 /TiO 2 -O vac where O vac specifies the oxygen defect.In addition, to comprehensively investigate the effect of hematite clusters on the HER activity, we also considered the Fe 2 O 3 surface in our calculations (figure S2).Thus, the HER activity of heterostructures was compared with both pristine TiO 2 and Fe 2 O 3 surfaces.For hydrogen adsorption a supercell of (2 × 2 × 1) of Fe 2 O 3 (0001) surface with a single Fe-termination with a vacuum thickness of around 20 Å was taken, and k-point sampling of 3 × 3 × 1 was used in the calculations.
The adsorption energy of the (Fe 2 O 3 ) n cluster at the TiO 2 surface was calculated from the formula where E((Fe 2 O 3 ) n /TiO 2 ) is the total energy of the heterostructures and E(TiO 2 ) and E(( are the total energies of the pristine TiO 2 surface and (Fe 2 O 3 ) n cluster, respectively.To investigate the stability of oxygen defects, we calculated the formation energy of the defects using the equation where the first term is the total energy of the defective heterostructure, in which the O vac specifies the investigated oxygen defect. 1 2 E(O 2 ) is the chemical potential of an oxygen atom that is half of the total energy of an isolated oxygen molecule O 2 .To evaluate the HER activity, we attached a hydrogen atom on the pristine TiO 2 and Fe 2 O 3 surfaces, and also on defect-free and defective heterostructures (figure S3 and S4), and calculated the adsorption energy of hydrogen.In general, the free energy of hydrogen adsorption is accepted to be a descriptor for hydrogen-evolving catalysts.
We also calculated the work function for the heterostructures.Work function is essentially the energy needed to introduce carriers to the surface and will be affected by doping and the presence of adsorbates.It is an essential parameter in understanding the interaction between the hematite clusters and TiO 2 and the effect of oxygen defect on the surface properties, and it is calculated by subtracting the Fermi energy E F from the vacuum energy The electronic structure of the systems investigated was examined through the density of states (DOS).To analyze the charge distribution and charge transfer quantitatively, we performed the Bader analysis [55][56][57][58].A negative Bader charge on an atom refers to electron gain and positive value to electron loss.The charge density differences are also calculated as where ρ AB (r) is the total charge density of the heterostructure, and ρ A (r) and ρ B (r) are the total charge densities of the TiO 2 surface and the (Fe 2 O 3 ) n cluster with atoms in exactly the same sites as they occupy in the heterostructure.Since Fe 2 O 3 is a magnetic material, we also calculated the spin density difference.It is calculated from the same equation as charge density difference by replacing charge density ρ(r) by spin density s(r).In the charge density difference (CDD) plots yellow refers to charge accumulation and cyan refers to charge depletion while in the spin density difference (SDD) plot the orange shows excess spin up polarization and turquoise shows excess spin down polarization.We set the isosurface value of 0.005 e Å−1 in all CDD and SDD plots.

Bulk parameters
Initially, we calculated the bulk parameters of Fe This is a well-known issue in predicting the electronic structure of transition metals oxides [61][62][63][64][65].
Previously, for instance, using the HSE functional with mixing parameter of a = 0.15, and Yamamoto et al. [72] and Deák et al. [74] have reported a band gap of 3.37 eV and 3.58 eV using the HSE06 functional.Even though hybrid functionals are generally more accurate for semiconductors, the GGA+U provides a reasonable compromise between the accuracy and computational cost in band gap calculations.
Therefore, based on the results, we conclude that the selected methods are sufficient for describing the electronic properties of both materials.S2).These geometries and Fe-O distances compared well with previous works [75][76][77][78][79], providing a good starting point for the rest of the calculations.Furthermore, we evaluated the oxidation state of iron in the free-standing clusters.
Details of Bader charges and magnetic moments of atoms in the clusters are provided in table S3.
According to the Bader analysis, Fe atoms exhibited a gain of charge which was depleted from O atoms.Ferromagnetic configuration was indicated for all the three clusters.showing the cluster-surface interaction to be energetically favourable.More negative adsorption energy indicates stronger interaction with TiO 2 , and which, in this case, correlates with the number of newly formed bonds between the clusters and TiO 2 .

Electronic structure analysis
The electronic structure of the (Fe

Charge transfer analysis
Efficient charge separation and transfer are essential factors affecting the photocatalytic activity.
To gain further insight into the charge transfer properties in the heterostructures we calculated the CDD, shown in figures 5, and performed the Bader analysis.The Bader charge and magnetic moment of selected atoms are listed in table S3.       was found to be the most stable, located underneath the cluster, with a formation energy of 2.71

Hydrogen evolution reaction activity
eV.The formation energy of the O sv1 and O sv2 were 0.41 eV and 0.79 eV larger than that of O sv3 , and their transverse distance, perpendicular to the b-axis, from the cluster were around 11 Å and 4 Å, respectively.This suggests that the cluster introduces a dependence of the formation energy on the distance from the cluster in the subsurface layer.Previously, Hoh et al. [87] have reported a distance dependence of oxygen vacancy formation energy from the Au-clusters on hematite surface, proposing that the cluster stabilizes the region underneath and near to it, making it more stable against reduction.We also observed the cluster to enhance the oxygen defect formation at the surface.In the pristine TiO 2 surface the formation energies of the O v , O sv1 , O sv2 and O sv3 were 5.47 eV, 5.46 eV, 5.12 eV, 5.46 eV, showing that the presence of the cluster can decrease the formation energy even by 50%.A similar observation has been reported in previous studies [88,89].
Among the modeled defect sites, we chose to further investigate the effect of the O v , O sv3 , and O c1 and O c2 on the properties of the (Fe 2 O 3 ) 1 /TiO 2 heterostructure.We employed the same methods to investigate these defective heterostructures as for the defect-free heterostructures.surface, preserving the coordination number of five.narrower band gap than the pristine TiO 2 surface.Interestingly, a localized Ti 3d peak was observed at -0.57 eV, arising from the Ti3 atom (figure 8).This can be evidence of formation of Ti 3+ species at the TiO 2 surface, which is common phenomenon in TiO 2 in the presence of oxygen vacancies.

Charge density analysis
As previously, we investigated the changes in the charge transfer properties via the CDD and Bader analysis, supported by the SDD.The Bader charges and magnetic moments are listed in table S7 for selected atoms.The CDD plots, shown in figure (figures 10), showed that the main charge redistribution occurred in the cluster and at the interface in the defective heterostructures as well.
When a neutral oxygen defect is formed it releases effective excess charge which can generally be transferred either to Fe or Ti.The Bader analysis confirmed the charge gain of Fe, with a yellow isosurface observed around Fe atoms in the CDD plots.The calculated Bader charge of the Fe1 and A lower magnetic moment supports a charge gain for Fe.To confirm lower spin magnetization of some Fe atoms, we calculated the SDD which showed a larger probability for spin down density (turquoise isosurface) around Fe (figure 10).In the (Fe 2 O 3 ) 1 /TiO  [80,84,85].This was supported by the lower Bader charges and even

Effect on hydrogen evolution
The results show that oxygen defects enable the engineering of electronic properties of the (Fe

Conclusions
First principles DFT calculations were employed to investigate the heterostructure of the TiO 2 surface and (Fe 2 O 3 ) n (n = 1,2,3) clusters, and superior catalytic performance was indicated for the heterostructures.The adsorption of the clusters on the surface was exothermic, thus enabling the modification of the surface properties of TiO 2 .The formation of a heterojunction between TiO 2 and Fe 2 O 3 was identified to affect band gap energy, charge transfer and charge separation in the heterostructures, leading to enhanced photocatalytic properties.The clusters were observed to improve the HER activity of TiO 2 .The existence of mixed-valence Fe (Fe 2+ /Fe 3+ ) led to greater enhancement in the HER activity.We also incorporated oxygen defects on the (Fe 2 O 3 ) 1 /TiO 2 , and the defect formation was found to be endothermic.The presence of the (Fe 2 O 3 ) 1 cluster substantially enhanced the oxygen defect formation at TiO 2 compared to the pristine surface.We found that electronic structure and charge transfer and the local magnetism can be tuned by oxygen defects, which can indirectly affect the oxidation state of Fe.However, it was observed that an oxygen defect was not beneficial in order to improve the HER activity.
Our investigation also suggests variations of the dye-sensitized solar cells originally proposed by Grätzel [6].Here, hematite nanoparticles play the role of dyes used to sensitize TiO 2 in order to produce H 2 /O 2 by water photoelectrolysis.The hematite nanoparticles are bound to the nanostructured wide-band-gap TiO 2 semiconductor and can be used as photosensitizers to harvest solar energy and generate excitons needed to fulfill the requirements for a photovoltaic scheme.
In summary, the results of our work reveal three important points.The first point is that +2 and +3 valence-state mixing offers a lot of potential to control the electronic structure of hematite clusters.The second point is that further electronic structure optimization could be achieved by engineering these clusters with various oxygen defects.The third point is that the presence of Fe 2+ -Fe 3+ intervalence charge transfer implies charge transfer between these non-equivalent Fe sites and could result in broad absorption in the visible or IR region of the electromagnetic spectrum.To calculate the electronic structure, we used the k-point sampling of 9 × 9 × 4 for bulk TiO 2 .To obtain better quality for the DOS of hematite we increased the k-point sampling symmetrically from 4 × 4 × 1 to 8 × 8 × 3 and smearing width from 0.05 eV to 0.1 eV.Using the GGA functional Fe 2 O 3 was predicted to be metallic and for TiO 2 we found a band gap of 1.7 eV.After employing the Hubbard correction we found a band gap of 1.16 eV for Fe 2 O 3 and 2.3 eV for TiO 2 .Besides, we found a magnetic moment of 4.328 µ B for Fe in the Fe 2 O 3 which is also comparable to the experimental value of 4.9 µ B [8]. TiO 2 was correctly predicted to be non-magnetic.At the surface, near the clusters, the spin magnetization of atoms was generally between 0.020 and 0.060 µ B .The amount of magnetization spread around the rest of the atoms of TiO 2 was negligible.The Bader charges of Ti atoms were around 2.0 e.This most probably indicates the oxidation state of Ti to be +4 [9].When forming bonds with the Fe 2 O 3 clusters, Ti atoms tend to lose 2 electrons while the rest are involved in the covalent bonding.The charge redistribution of oxygen was generally around -1.0 e which can be identified as oxidation state of -2 for oxygen [9].
2 (101) surface we constructed a slab of 4 layers containing 192 atoms (64 Ti atoms and 128 O atoms) with lattice parameters of 10.32 Å 15.25 Å and 35.68 Å in a, b and c directions (figure

2 O 3
and TiO 2 (figure S5).The lattice constants were determined to be a = b = 4.780 Å and c = 13.323Å and a = b = 3.98 Å and c = 9.56 Å for Fe 2 O 3 and TiO 2 , respectively.These results are consistent with experimental measurements [59,60].The DOS of the bulk Fe 2 O 3 and bulk TiO 2 are in figure S6, showing the electronic structure of the materials.Using the GGA functional Fe 2 O 3 was predicted to exhibit metallic behaviour whereas TiO 2 possessed a band gap of 1.7 eV.The results demonstrate that the standard GGA functional is incapable of accurately describing both Fe 2 O 3 and TiO 2 because of the localized d electrons.

Figure 2 :
Figure 2: The surface model and computed DOS of anatase TiO 2 .A reasonable band gap of approximately 2.5 eV was found for the TiO 2 surface.Fermi level is set to zero energy.

3. 2
Freestanding clusters and TiO 2 surface Before investigating the heterostructures, we simulated the freestanding hematite clusters and pristine TiO 2 surface.The relaxed structures of (Fe 2 O 3 ) 1 , (Fe 2 O 3 ) 2 and (Fe 2 O 3 ) 3 are shown in figure 1.The (Fe 2 O 3 ) 1 showed a planar structure whereas the (Fe 2 O 3 ) 2 and (Fe 2 O 3 ) 3 had a cage-like structure.The Fe-O distances were ranging from 1.65 to 1.87 Å in the (Fe 2 O 3 ) 1 , from 1.73 to 1.83 Å in the (Fe 2 O 3 ) 2 and from 1.69 to 1.99 Å in the (Fe 2 O 3 ) 3 (table photoactivation of anatase surface could be achieved by visible light radiation with wavelength up to 500 nm.Due to the dangling bonds the surface band gap of TiO 2 is generally lower than the bulk band gap (3.0-3.3 eV).Moreover, the work function of the surface was calculated to be 7.23 eV.In general, TiO 2 possesses a high work function of 5-6 eV [82, 83].Compared to this our calculations moderately overestimated the work function.

3. 3
Structural and electronic properties of the (Fe 2 O 3 ) n /TiO 2 heterostructures 3.3.1 Structural optimization The optimized structures of the (Fe 2 O 3 ) n /TiO 2 heterostructures are shown in figure 3. Importantly, the results showed that Fe 2 O 3 clusters remained stable on the TiO 2 surface without breaking down.For the (Fe 2 O 3 ) 1 the optimization yielded a closed cage-like structure on the surface that resembles a pyramid with a parallelogram shaped base.The (Fe 2 O 3 ) 2 and (Fe 2 O 3 ) 2 maintained a cage-like structure at the TiO 2 surface after the adsorption.The coordination number of the (Fe 2 O 3 ) 1 and (Fe 2 O 3 ) 3 were found to be five and nine, respectively, while the coordination number of the (Fe 2 O 3 ) 2 was only two.The adsorption of the clusters resulted in some lattice distortion at the TiO 2 surface primarily limited to the top layer of the surface.The nearest Ti and O atoms at the surface are generally shifted toward the clusters to form new Ti-O and Fe-O bonds between the surface and clusters.The surface Ti -O distances were 1.88 Å, 1.98 Å and in the range of 1.94 to 2.12 Å, and Fe -surface O distances in the range of 2.04 to 2.14 Å, 1.95 Å and in the range of 1.87 to 2.02 Å in the (Fe 2 O 3 ) 1 /TiO 2 , (Fe 2 O 3 ) 2 /TiO 2 and (Fe 2 O 3 ) 3 /TiO 2 , respectively.We also investigated the structure of the clusters after the adsorption.In the adsorbed (Fe 2 O 3 ) 1 cluster the Fe-O bond lengths varied from 1.84 to 2.14 Å, showing significant change in the bond lengths when compared with the freestanding (Fe 2 O 3 ) 1 cluster.In the adsorbed (Fe 2 O 3 ) 2 and (Fe 2 O 3 ) 3 clusters the distances lied in the range of 1.69 to 1.91 Å, and 1.69 to 1.94 Å, respectively.These are similar to that of freestanding (Fe 2 O 3 ) 2 and (Fe 2 O 3 ) 3 clusters.Detailed information on structural parameters are listed in table S4.The energetic stability was checked by calculating the adsorption energies of the (Fe 2 O 3 ) 1 , (Fe 2 O 3 ) 1 and (Fe 2 O 3 ) 3 .The energies were -2.28 eV, -1.72 eV and -3.24 eV, respectively,
The results indicated a charge redistribution in the systems after the adsorption of the clusters, localized on the cluster and the top layer of the TiO 2 surface.At the interface the electron accumulation and depletion regions were aligned in the direction of the formed bonds between TiO 2 and Fe 2 O 3 .This suggests that the bonds can be considered covalent with a polar feature.The blue isosurface around Fe showed charge depletion from Fe, indicating electron donor nature for the clusters.Increased amount of charge accumulation was observed around Fe atoms in case of larger Fe 2 O 3 clusters.The work function of TiO 2 was observed to be affected by the clusters.The work function decreased from 7.23 eV to 6.70 eV, 5.90 eV and 6.18 eV in the (Fe 2 O 3 ) 1 /TiO 2 , (Fe 2 O 3 ) 2 /TiO 2 and (Fe 2 O 3 ) 3 /TiO 2 , respectively, supporting donor nature for Fe 2 O 3 clusters.The lower work function can also facilitate electron injection from the TiO 2 surface.The Bader charge of the (Fe 2 O 3 ) 1 , (Fe 2 O 3 ) 2 and (Fe 2 O 3 ) 3 were 0.32 e, 0.036 e and 0.42 e, suggesting an electron transfer from Fe 2 O 3 clusters to TiO 2 .Bader charges indicated an occurrence of notable charge transfer in the presence of (Fe 2 O 3 ) 1 and (Fe 2 O 3 ) 3 whereas the adsorption of the (Fe 2 O 3 ) 2 induced only a small charge displacement.Nearly 90% of the transferred charge was redistributed to the surface layer of TiO 2 .Neither the CDD plots nor Bader charges showed charge localization at the surface, indicating even distribution of charge among surface layer atoms.It should be noted that our results are in conflict with Moniz et al. [75] who proposed an electron transfer from TiO 2 to Fe 2 O 3 based on their theoretical study on the combined system of TiO 2 and Fe 2 O 3 clusters.The difference in the results may result from the use of different methods.Donor nature of Fe atoms was confirmed by the Bader charges.The Bader charges of the Fe1 and Fe2 atoms were 1.61 e and 1.52 e in the (Fe 2 O 3 ) 1 /TiO 2 .The correlation between the Bader charges and oxidation state is still somewhat debuted.However, according to Posysaev et al. [80] the particular values suggested Fe 3+ oxidation state for Fe in the (Fe 2 O 3 ) 1 /TiO 2 .Larger variation in the Bader charge of Fe atoms was observed in the adsorbed (Fe 2 O 3 ) 2 and (Fe 2 O 3 ) 3 .In the (Fe 2 O 3 ) 2 /TiO 2

Figure 4 :
Figure 4: The computed DOS of (Fe 2 O 3 ) 1 /TiO 2 (a and b), (Fe 2 O 3 ) 2 /TiO 2 (c and d) and (Fe 2 O 3 ) 3 /TiO 2 (e and f).Projected DOSs and band gap regions are shown in the left and right, respectively.Fermi level is set to zero energy.
parallel spin orientation with a magnetic moment of -0.842 µ B .The SDD plot of (Fe 2 O 3 ) 3 /TiO 2 also showed an increased amount of spin down components in the cluster.Thus, ferrimagnetism occurred in the (Fe 2 O 3 ) 3 /TiO 2 .With the varying Bader charges, the results can highly suggest mixed-valence state (Fe 2+ /Fe 3+ ) for Fe in the (Fe 2 O 3 ) 2 /TiO 2 .It is worth noticing that magnetic moments do not directly correlate with the Bader charges.Due to the charge transfer, spin magnetization was also transferred to the atoms nearby Fe.Bader charge and magnetic moment of selected atoms are listed in tableS5.

Figure 6 :
Figure 6: Free energy diagram for hydrogen evolution reaction on the pristine TiO 2 and Fe 2 O 3 surfaces and (Fe 2 O 3 ) n /TiO 2 heterostructures.

3. 4 Figure 7 :
Figure 7: The modeled defect sites in the (Fe 2 O 3 ) 1 /TiO 2 and their formation energies, E Form .(a) Surface vacancy O v and subsurface vacancies (b) O sv1 , (c) O sv2 , and (d) O sv3 .The defects (e) O c1 and (f) O c2 are located in the (Fe 2 O 3 ) 1 cluster.The defect sites are coloured yellow.The modeled defect sites and their formation energies are shown in figure 7. Positive formation energies showed that the defect formation is endothermic.The formation energy of the O c1 and O c2 was the lowest, only 1.59 eV, indicating that the removal of oxygen is easier from the cluster than from the TiO 2 surface.This can be explained by the weaker bonding of oxygen in the adsorbed cluster than at the TiO 2 surface.Considering the relatively high formation energy of 3.41 eV of the surface vacancy O v , we decided to introduce several subsurface vacancy sites.Based on our findings, a subsurface vacancy is generally more stable in the (Fe 2 O 3 ) 1 /TiO 2 than a surface vacancy.The O sv3

Figure 9
Figure 9 represents the calculated DOS of the (Fe 2 O 3 ) 1 /TiO 2 -O v , (Fe 2 O 3 ) 1 /TiO 2 -O sv3 and (Fe 2 O 3 ) 1 /TiO 2 -O c , showing changes in the band gap region.The valence band was further upwardshifted due to the oxygen defects.The VBM positions of TiO 2 were found to be at -0.96 eV in the (Fe 2 O 3 ) 1 /TiO 2 -O v , -1.8 eV in the (Fe 2 O 3 ) 1 /TiO 2 -O sv3 , and -0.93 eV in the (Fe 2 O 3 ) 1 /TiO 2 -O c , respectively.The properties of primitive TiO 2 remained still unchanged.The presence of defects altered the band gap of the heterostructure.The (Fe 2 O 3 ) 1 /TiO 2 -O sv3 showed a narrow band gap of 0.75 eV.Inversely, the O v and O c resulted in an increase in the band gap energy compared to the defect-free (Fe 2 O 3 ) 1 /TiO 2 .We found a band gap of 1.45 eV for the (Fe 2 O 3 ) 1 /TiO 2 -O v and 1.80 eV for the (Fe 2 O 3 ) 1 /TiO 2 -O c .Nevertheless, all the three defective heterostructures possessed a

Figure S1 :
Figure S1: The convergence of the total energy with respect to k-point sampling (on the left) and energy cutoff (on the right) was performed for the bulk Fe 2 O 3 , the unit cell of which is shown in figure S5.Based on the results the optimal energy cutoff and k-point sampling were found to be 650 eV and 4 × 4 × 1.The chosen energy cutoff was employed for the rest of the calculations.For modeling the bulk Fe 2 O 3 , a k-point sampling of 4 × 4 × 1 was used.

Figure S2 :
Figure S2: (a) Top view and (b) side view of the Fe 2 O 3 (0001) surface with Fe-O 3 -Fe-R termination.Besides the pristine TiO 2 surface, we also included the Fe 2 O 3 surface into our investigations.According to previous studies (0001)-surface is the most stable and dominant facet in natural and synthesized Fe 2 O 3 , and thus intensively studied[3, 4, 5].Pristine Fe 2 O 3 (0001) has three possible surface terminations: Fe-O 3 -Fe-R (single iron layer), Fe-Fe-O 3 -R (double iron layer), and O 3 -Fe-Fe-R (oxygen layer)[3].Of the different terminations, Fe-O 3 -Fe-R has been reported to be energetically the most favorable at room temperature and over the wide range of oxygen chemical potential[4, 5, 6], and therefore, we decided to model the Fe 2 O 3 (0001) surface with a single Fe layer (a and b).The (0001) surface was created by taking the bulk structure of Fe 2 O 3 (figureS4a) and adding a vacuum with a thickness of around 20 Å along the z-direction.After the relaxation, the optimized structure with (2 × 2 × 1) supercell of Fe 2 O 3 (0001) surface was taken in order to investigate the hydrogen adsorption.

Figure S3 :
Figure S3: Hydrogen adsorption on the (a) TiO 2 and Fe 2 O 3 surfaces (side and top view).Adsorption site is highlighted with a green circle.

Figure S5 :
Figure S5: Schematic illustration of the crystal structure of the (a) bulk Fe 2 O 3 and (b) tetragonal anatase TiO 2 .We used the hexagonal representation for the unit cell of Fe 2 O 3 , containing 30 atoms in total (12 Fe and 18 O atoms), and tetragonal unit cell for anatase TiO 2 , containing 12 atoms in total (4 Ti and 8 O atoms) [7].

Figure S6 :
Figure S6: The computed density of states of the (a) bulk Fe 2 O 3 and (b) bulk TiO 2 using the GGA+U functional.
[79]total magnetic moment of the (Fe 2 O 3 ) 1 was 9.28 µ B , and spin magnetic moments of Fe atoms were 3.32 µ B and 3.60 µ B , suggesting co-existence of Fe 2+ and Fe 3+ oxidation states[79].Bader charges of 1.08 e and the range of 1.03 to 1.53 e, and 2.97 to 4.04 µ B .The reduction in magnetic moment may imply lower oxidation state than Fe 3+ for Fe in these clusters.We proceeded with the optimization of anatase TiO 2 (101) surface.There are four types of atoms at the surface: two-and threefold coordinated oxygen atoms (O 2c and O 3c [80] e supported the presence of mixed-valence Fe[80].In the (Fe 2 O 3 ) 2 Bader charges of Fe atoms were around 1.30 e for all four Fe atoms whereas magnetic moments of the Fe atoms were 3.70 µ B , 3.32 µ B , 2.89 µ B and 2.85 µ B .In the (Fe 2 O 3 ) 3 the Bader charge and magnetic moment of Fe atoms varied in [84,85]er charges of Fe1, Fe2, Fe3 ad Fe4 were 1.37 e, 1.39 e, 1.61 e and 1.45 e while in the (Fe 2 O 3 ) 3 /TiO 2 the values were 1.63 e, 1.51 e, 1.32 e, 1.20 e, 1.56 e and 1.30 e for Fe1, Fe2, Fe3, Fe4, Fe5 and Fe6, respectively.Reduction in Bader charge could indicate an emergence of Fe 2+ species[80]and therefore, existence of different valences, Fe 2+ and Fe 3+ , in these heterostructures.Increased amount of charge accumulation indicated by the CDD plot can support the conclusion.We were also interested in the magnetism brought by Fe 2 O 3 in order to evaluate the oxidation state of Fe.In general, Fe introduces ferromagnetism in the heterostructures which is supported by the positive spin density around Fe in the SDD plots (figures 5).We found a total magnetic moment of 9.61 µ B , 17.2 µ B and 17.8 µ B per unit cell for the (Fe2 O 3 ) 1 /TiO 2 , (Fe 2 O 3 ) 2 /TiO 2 and(Fe 2 O 3 ) 3 /TiO 2 .In the (Fe 2 O 3 ) 1 /TiO 2 the magnetic moments of the Fe1 and Fe2 were 4.11 µ B and 4.06 µ B , respectively, indicating high spin configuration and 3d 5 occupation[84,85], that is, Fe 3+ oxidation state.In the (Fe 2 O 3 ) 2 /TiO 2 the Fe atoms had an odd contribution to the total magnetic moment.We found a large magnetic moment of 4.02 µ B and 4.13 µ B for the Fe2 and Fe3, whereas a reduced magnetic moment of around 3.26 µ B and 3.36 µ B for the Fe1 and Fe4, respectively.In the adsorbed (Fe 2 O 3 ) 3 , Fe1, Fe2 and Fe5 exhibited a magnetic moment of 4.10 µ B , 3.67 µ B and 3.96 µ B , respectively.The magnetic moment of Fe3 and Fe4 were only around 2.90 µ B , and Fe6 showed anti- [80,84,85] total magnetic moment was still 9.66 µ B per unit cell whereas in the (Fe 2 O 3 ) 1 /TiO 2 -O c the total magnetic moment decreased to 7.79 µ B .Surprisingly, the Fe2 atom in the (Fe 2 O 3 ) 1 /TiO 2 -O sv3 experienced a magnetic phase transition.This resulted in a total magnetic moment of 0.09 µ B .Due to the anti-parallel but unequal magnetic moment of Fe atoms, the (Fe 2 O 3 ) 1 /TiO 2 -O sv3 exhibits weak ferrimagnetic behaviour.The magnetic phase transition was attributed to be to the notable lattice distortion at the TiO 2 surface caused by the O sv3 .For instance, in their study, Menéndez et al.[91]have reported that the lattice distortion caused by oxygen defect can correlate with magnetic behavior and induce a magnetic phase transition.Our findings suggest that Fe can have the mixed valence state (Fe 2+ /Fe 3+ ) in the (Fe2 O 3 ) 1 /TiO 2 -O v[80,84,85].We also observed localized spin density between the Fe atoms (figure10d).This can indicate magnetic coupling between the cations with different oxidation states, supporting the mixed-valence state for Fe.In the (Fe 2 O 3 ) 1 /TiO 2 -O sv3 and (Fe 2 O 3 ) 1 /TiO 2 -O c the results indicates the Fe 2+ oxidation state for Fe 2 O 3 ) 1 / TiO 2 .Finally, we evaluate the HER activity of the defective heterostructures.H-containing structures are shown in figure S4.Based on the results, oxygen defects have a detrimental effect on the HER activity of the (Fe 2 O 3 ) 1 /TiO 2 .The O v , O sv3 and O c increased the adsorption energy of hydrogen from 0.43 eV to 0.71 eV, 0.61 eV and 0.60 eV, respectively.Thus, the interaction with hydrogen becomes weaker again, indicating decrease in HER activity.The HER activity of the defective heterostructures is comparable with the pristine TiO 2 surface.