Theoretical Study on Photocatalytic Reduction of CO2 on Anatase/Rutile Mixed-Phase TiO2

The construction of anatase/rutile heterojunctions in TiO2 is an effective way of improving the CO2 photoreduction activity. Yet, the origin of the superior photocatalytic performance is still unclear. To solve this issue, the band edges between anatase and rutile phases were theoretically determined based on the three-phase atomic model of (112)A/II/(101)R, and simultaneously the CO2 reduction processes were meticulously investigated. Our calculations show that photogenerated holes can move readily from anatase to rutile via the thin intermediated II phase, while photoelectrons flowing in the opposite direction may be impeded due to the electron trapping sites at the II phase. However, the large potential drop across the anatase/rutile interface and the strong built-in electric field can provide an effective driving force for photoelectrons’ migration to anatase. In addition, the II phase can better enhance the solar light utilization of (112)A/(100)II, including a wide light response range and an intensive optical absorption coefficient. Meanwhile, the mixed-phase TiO2 possesses negligible hydrogenation energy (CO2 to COOH*) and lower rate-limiting energy (HCOOH* to HCO*), which greatly facilitate CH3OH generation. The efficient charge separation, strengthened light absorption, and facile CO2 reduction successfully demonstrate that the anatase/rutile mixed-phase TiO2 is an efficient photocatalyst utilized for CO2 conversion.


Introduction
The photocatalytic reduction of CO 2 into high-value-added chemicals and fuels on semiconductors is an efficient and clean energy conversion technology which has been considered to be a promising approach to simultaneously solving energy and environmental issues [1][2][3].Among the various semiconductor materials, TiO 2 is usually taken as a prototypical photocatalyst for CO 2 conversion owing to its merits including environmentally friendliness, low cost, and long-term photochemical stability [4][5][6].At present, enormous efforts have been devoted to enhance the photocatalytic activity of CO 2 reduction on TiO 2 [7].For instance, Liu et al. [8] have pointed out that introducing oxygen vacancies, which can act as active sites, is beneficial to CO 2 binding, activation, and dissociation.In addition, Umezawa et al. [9] have demonstrated that loading Pt clusters on TiO 2 's surface can promote the photocatalytic performance of CO 2 reduction by facilitating the ionization of HCOO -and OH -on the surface.In addition, fabrication of heterogeneous semiconductors is also regarded as an effective strategy to increase the photocatalytic activity due to the efficient charge separation and migration across the junction interface, such as the design of anatase (100)/(001) surface heterojunctions [10] and TiO 2 /ZnIn 2 S 4 phase heterojunctions [11].Alternatively, anatase/rutile mixed-phase TiO 2 has been demonstrated to be a good photocatalyst with remarkable photocatalytic CO 2 reduction capabilities due to the synergistic effect between anatase and rutile phases [12][13][14].
Although the anatase/rutile mixed-phase TiO 2 as a photocatalyst for CO 2 reduction has been extensively studied, a profound understanding of the detailed reaction pathways from CO 2 to the reduced products is lacking, both experimentally and theoretically.Consequently, the origin of the superior photocatalytic performance on mixed-phase TiO 2 is still obscure.This is largely attributed to the fact that the fundamental mechanism of charge separation and transport, i.e., how the photogenerated electrons and holes transfer across the anatase/rutile phase junctions, is still in dispute.Some hold the view that the photogenerated electrons preferentially move from anatase to rutile [15,16].Meanwhile, Li et al. found a built-in electric field across the anatase/rutile interface with a upward band bending from anatase to rutile, which can facilitate the photogenerated electrons' transport from rutile to anatase [17].These inconsistent results cause the crystal phase for the CO 2 reduction reaction being confusing.Generally, the charge migration direction across the interface is closely related to the band alignment between phases.Therefore, clarifying the band edge positions of anatase and rutile in mixed-phase TiO 2 is helpful to understanding the charge migration mechanism.Theoretical simulations can provide valuable insights into the electronic band structures of photocatalysts at the atomic level.However, because no atom-resolved anatase/rutile phase junctions have been reported experimentally, constructing a realistic structural model for anatase/rutile TiO 2 heterophase junctions is a challenging task.
At present, the commonly used theoretical models of the anatase/rutile interface are direct interface models with a two-phase junction, i.e., direct contact between anatase and rutile atomic surfaces.For instance, Deskins et al. established the anatase/rutile interface by connecting the anatase (101) with rutile (110) [18], which are the thermodynamically most stable surfaces for anatase and rutile, respectively.However, the combination of (101) A /(110) R may generate a large interfacial strain and induce a disordered interfacial structure, which is unfavorable for the transport of photogenerated charge carriers at the interface.Instead, some researchers have proposed constructing interfacial models using TiO 2 surfaces with relatively high energies.These researchers believed that the highly active surfaces may have a stronger tendency to form the heterojunction interfaces than the stable surfaces.However, a variety of combinations have been reported, including (001) A /(101) R [19], (100) A /(100) R [20] and (101) A /(111) R [21].Later, Liu et al. built an indirect interface model for anatase/rutile with a structurally ordered three-phase junction, i.e., involving an intermediate phase (TiO 2 -II (α-PbO 2 -like form)) between anatase and rutile ((112) A /II/(101) R ) [22].The intermediate II phase, despite having thin atomic layers, is essential to alleviate the interfacial strain energy and stabilize the anatase/rutile interface, thus promoting the electron and hole migration and separation and enhancing the photoactivity.Importantly, this indirect interface model is consistent with the macroscopic structure of anatase/rutile crystals synthesized by Hosono et al. [23].Although Liu et al. have predicted the charge migration direction across the anatase/rutile heterophase junction, the transport mechanism is a rough estimation, which is obtained on the basis of the computed energetics of charge carriers and the experimental band gaps for anatase and rutile.
Hence, to unravel the mechanism of charge separation and transport across the anatase/rutile interface and explore the influence of the phase junction on the electron-hole migration, in this study we presented an ab initio calculation on the band edge positions of the indirect three-phase junction model of (112) A /II/(101) R .In addition, the detailed mechanistic pathways of CO 2 photoreduction on the anatase/rutile mixed-phase TiO 2 were meticulously investigated to propose an optimal reduction reaction route.It is anticipated that this work can help us to deeply understand the role of phase junctions in semiconductor photocatalysis and provide a theoretical guidance for experimental researchers to design efficient TiO 2 -based heterostructures.

Structural Modeling
To clarify the charge migration mechanism in anatase/rutile mixed-phase TiO 2 , a reasonable structural model of the heterophase junction is initially required.According to Liu et al.'s work [22], the three-phase junction model of (112) A /II/(101) R is a nanopin-like structure, i.e., an aperiodic system.Due to the limitations of periodic boundary conditions, this indirect model could not be constructed directly.Therefore, we divided the entire threephase model ((112) A /II/(101) R ) into two separate biphase models, namely (112) A /II and II/(101) R .The indirect three-phase junction model can be obtained by rotating the II/(101) R junction by 90 • with respect to the (112) A /II junction and then attaching it to the (112) A /II structure via the intermediate II phase.Based on the structural information from SSW sampling pathways [24][25][26], the intermediate phases in the (112) A /II and II/(101) R models correspond to two different crystal facets, namely the (100) surface (i.e., (112) A /(100) II ) and the (001) surface (i.e., (001) II /(101) R ).
Prior to the contact, the lattice parameters of anatase (112) and II (100  001)).It can be seen that there is a lattice mismatch between anatase (or rutile) and the intermediate II phases, especially between anatase (112) and II (100) (9.4% and 4.9% along a and b directions, respectively).This large lattice mismatch (>3.0%) will lead to a significant strain and a poor Ti-O match at the interface.Liu et al. suggested that the lattice-misfit strain can be released by reducing the number of atomic layers in the intermediate II phase [22], contributing to a good cation-anion match in the contact region.Therefore, we assume that the lattice parameters of II (100) and II (001) in the biphase models are determined by anatase and rutile phases, respectively, which are consistent with those of anatase (112) and rutile (101).Meanwhile, because II (001) attaches to II (100) by rotating 90 • , the lattice of II (001) in the c direction corresponds to that of II (100) in the a direction.Similarly for II (100), its lattice parameter in the c axis is equal to that of II (001) in the a axis.
In addition to the lattice parameters, another important aspect to be taken into account in the construction of interfacial structures is the thickness of TiO 2 slabs.We first studied the pure-phase TiO 2 of anatase (112) and rutile (101) in vacuum, which were both modeled with 2 × 2 supercells in the xy dimensions.Then, the electrostatic potentials of these two TiO 2 surfaces with different atomic layers were calculated (see Tables S1 and S2).By analyzing the convergence of electrostatic potential difference (∆V, the difference in average electrostatic potentials between TiO 2 and vacuum phases) with the slab thickness (see Figure 1), it is found that the ∆V of both anatase (112) and rutile (101) displays fast convergence at six atomic layers with small oscillations not exceeding 0.02 eV from six-to eight-layer slabs.Therefore, we deemed that the appropriate TiO 2 slabs for anatase (112) and rutile (101) are both six atomic layers thick.Regarding the intermediate phases of II (100) and II (001), we evaluated their atomic thickness using the biphase junction models of (112) A /(100) II and (001) II /(101) R .Based on the computed electrostatic potentials (see Tables S3 and S4) and the dependence of ∆V (the difference in average electrostatic potentials between anatase (or rutile) and intermediate II phases) on slab thickness (see Figure 1), a six-layer slab was also chosen for both II (100) and II (001) to ensure the convergence of the TiO 2 slab.Following the above analysis, the reasonable heterojunction models of (112) A /(100) II and (001) II /(101) R were established, as illustrated in Figure 2.

Electronic Properties
Due to the disequilibrium in the electrochemical potentials of electrons, when two semiconductors are in contact, charge transfer will occur at the interface until a unified Fermi level is reached.Work function () is a key quantity for determining the behavior of charge transfer and can be defined as [27]  =  vac −  F (1 where  vac and  F are the vacuum level and Fermi level, respectively.Figure 3 displays the profiles of electrostatic potential along the Z direction normal to the TiO2 surfaces.As shown in Figure 3a,b

Electronic Properties
Due to the disequilibrium in the electrochemical potentials of electrons, when two semiconductors are in contact, charge transfer will occur at the interface until a unified Fermi level is reached.Work function () is a key quantity for determining the behavio of charge transfer and can be defined as [27]  =  vac −  F (1 where  vac and  F are the vacuum level and Fermi level, respectively.Figure 3 display the profiles of electrostatic potential along the Z direction normal to the TiO2 surfaces.A shown in Figure 3a,b

Electronic Properties
Due to the disequilibrium in the electrochemical potentials of electrons, when two semiconductors are in contact, charge transfer will occur at the interface until a unified Fermi level is reached.Work function (ϕ) is a key quantity for determining the behavior of charge transfer and can be defined as [27] ϕ = E vac − E F (1) where E vac and E F are the vacuum level and Fermi level, respectively.Figure 3 displays the profiles of electrostatic potential along the Z direction normal to the TiO 2 surfaces.As shown in Figure 3a,b, the work function of II (100) is 7.77 eV, which is higher than that of anatase (112), with 6.72 eV.This indicates that electrons will transfer from anatase (112) to II (100) until the Fermi levels achieve equilibrium.Meanwhile, rutile (101) and II (001) have approximately equivalent work functions (5.64 eV for rutile (101) and 5.69 eV for II (001), see Figure 3c,d).The comparable ϕ values will provide a weak driving force for electron transfer.
Molecules 2024, 29, x FOR PEER REVIEW 5 of 16 (001), see Figure 3c,d).The comparable  values will provide a weak driving force for electron transfer.To gain a clear understanding of the charge transfer process at the phase junction, the charge density difference (∆  ) was further calculated as follows: where   (i/ii) ,   (i) , and   (ii) are the electron densities of the i/ii biphase junction, pure phase i, and pure phase ii, respectively.The three-dimensional charge density difference maps for (112)A/(100)II and (001)II/(101)R are plotted in Figure 4.The pink-and bluecolored isosurfaces represent the charge depletion and accumulation regions, respectively.It can clearly be seen that the main charge density changes are localized at the interface.For (112)A/(100)II, the pink isosurfaces appear around the Ti atoms in the anatase phase, while the blue isosurfaces distribute in the O atoms in the intermediate II phase (see Figure 4a).This suggests that there is a charge transfer from anatase (112) to II (100), which is in accordance with the results for the work functions.In the case of (001)II/(101)R, although the charge transfer also occurs between Ti and O atoms, it happens within the respective phase of rutile (101) and II (001) rather than between the two phases (see Figure 4b).This observation provides direct evidence for the aforementioned conclusion that there is less charge transfer across the (001)II/(101)R interface when they are in contact.To gain a clear understanding of the charge transfer process at the phase junction, the charge density difference (∆ρ e ) was further calculated as follows: where ρ e (i/ii), ρ e (i), and ρ e (ii) are the electron densities of the i/ii biphase junction, pure phase i, and pure phase ii, respectively.The three-dimensional charge density difference maps for (112) A /(100) II and (001) II /(101) R are plotted in Figure 4.The pink-and bluecolored isosurfaces represent the charge depletion and accumulation regions, respectively.It can clearly be seen that the main charge density changes are localized at the interface.For (112) A /(100) II , the pink isosurfaces appear around the Ti atoms in the anatase phase, while the blue isosurfaces distribute in the O atoms in the intermediate II phase (see Figure 4a).This suggests that there is a charge transfer from anatase (112) to II (100), which is in accordance with the results for the work functions.In the case of (001) II /(101) R , although the charge transfer also occurs between Ti and O atoms, it happens within the respective phase of rutile (101) and II (001) rather than between the two phases (see Figure 4b).This observation provides direct evidence for the aforementioned conclusion that there is less charge transfer across the (001) II /(101) R interface when they are in contact.The strong charge transfer can cause a distinct charge redistribution at the (112)A/(100)II interface, leading to the creation of an internal built-in electric field and an upward band bending from anatase (112) to II (100) across the phase junction.Upon light illumination, the built-in electric field can provide a direct driving force for the photoelectrons' transfer from II (100) to anatase (112).However, almost no charge transfer between rutile (101) and II (001) may induce a weak built-in electric field and a negligible band bending.These deductions offer a good explanation for the experimental finding that to achieve good photocatalytic performance for water oxidation, the concentration of the anatase phase in an anatase/rutile heterostructure catalyst should be much higher than that of rutile, i.e., anatase (80%)/rutile (20%) [28,29].The abundance of the anatase phase is required to form a high concentration of the (112)A/(100)II interface, which is responsible for creating a strong built-in electric field, thereby accelerating the separation and transport of photogenerated charge carriers.

Charge Migration Mechanism
Based on the optimized biphase junction models, the projected density of states (PDOS) and the band edge positions of (112)A/(100)II and (001)II/(101)R with respect to the vacuum level were calculated using the hybrid HSE06 functional, as shown in Figures 5  and 6, respectively.It is noteworthy that for both pure-phase TiO2 (anatase (112), II (100), II (001), and rutile (101)) and mixed-phase TiO2 ((112)A/(100)II and (001)II/(101)R), the CBM positions are primarily derived from the Ti-3d orbitals, while the VBM positions are mainly contributed by the O-2p orbitals.Additionally, the formation of (112)A/(100)II heterojunctions moves the CBM to a lower-energy position, resulting in an obvious reduction in the band gap compared to those of anatase (112) and II (100) (see Figure 5a).Meanwhile, the band gap of the (001)II/(101)R heterojunction remains almost unchanged (see Figure 5b).In Figure 6a, it can be seen that for (112)A/(100)II, the valence and conduction band edges of anatase (112) straddle those of II (100), which is unfavorable for the separation of electron-hole pairs.For (001)II/(101)R, the VBM positions of rutile (101) and II (001) are −6.71 and −7.69 eV, respectively, while the CBM positions are −3.65 and −4.64 eV, respectively.Both the VBM and CBM positions of rutile (101) are obviously higher than those of II (001), leading to a staggered type II heterojunction.Accordingly, the (001)II/(101)R interface is beneficial for electron and hole accumulation on II (001) and rutile (101), respectively.The relative band levels are in agreement with Liu et al.'s results obtained by calculating the energy difference for the electrons and holes [22].The strong charge transfer can cause a distinct charge redistribution at the (112) A /(100) II interface, leading to the creation of an internal built-in electric field and an upward band bending from anatase (112) to II (100) across the phase junction.Upon light illumination, the built-in electric field can provide a direct driving force for the photoelectrons' transfer from II (100) to anatase (112).However, almost no charge transfer between rutile (101) and II (001) may induce a weak built-in electric field and a negligible band bending.These deductions offer a good explanation for the experimental finding that to achieve good photocatalytic performance for water oxidation, the concentration of the anatase phase in an anatase/rutile heterostructure catalyst should be much higher than that of rutile, i.e., anatase (80%)/rutile (20%) [28,29].The abundance of the anatase phase is required to form a high concentration of the (112) A /(100) II interface, which is responsible for creating a strong built-in electric field, thereby accelerating the separation and transport of photogenerated charge carriers.

Charge Migration Mechanism
Based on the optimized biphase junction models, the projected density of states (PDOS) and the band edge positions of (112) A /(100) II and (001) II /(101) R with respect to the vacuum level were calculated using the hybrid HSE06 functional, as shown in Figures 5 and 6, respectively.It is noteworthy that for both pure-phase TiO 2 (anatase (112), II (100), II (001), and rutile (101)) and mixed-phase TiO 2 ((112) A /(100) II and (001) II /(101) R ), the CBM positions are primarily derived from the Ti-3d orbitals, while the VBM positions are mainly contributed by the O-2p orbitals.Additionally, the formation of (112) A /(100) II heterojunctions moves the CBM to a lower-energy position, resulting in an obvious reduction in the band gap compared to those of anatase (112) and II (100) (see Figure 5a).Meanwhile, the band gap of the (001) II /(101) R heterojunction remains almost unchanged (see Figure 5b).In Figure 6a, it can be seen that for (112) A /(100) II , the valence and conduction band edges of anatase (112) straddle those of II (100), which is unfavorable for the separation of electron-hole pairs.For (001) II /(101) R , the VBM positions of rutile (101) and II (001) are −6.71 and −7.69 eV, respectively, while the CBM positions are −3.65 and −4.64 eV, respectively.Both the VBM and CBM positions of rutile (101) are obviously higher than those of II (001), leading to a staggered type II heterojunction.Accordingly, the (001) II /(101) R interface is beneficial for electron and hole accumulation on II (001) and rutile (101), respectively.The relative band levels are in agreement with Liu et al.'s results obtained by calculating the energy difference for the electrons and holes [22].Arranging the band edge positions of (112)A/(100)II and (001)II/(101)R together, we can summarize the overall band alignment of the indirect three-phase junction in anatase/rutile mixed-phase TiO2 (see Figure 6b).This figure shows that the VBM positions of the three phases decrease following the order of rutile > II > anatase.The VBM of rutile is much higher than that of anatase, by 1.24 eV.Consequently, the photogenerated holes can transfer easily from anatase to rutile via the intermediate II phase without a barrier.By contrast, due to the slightly higher conduction band edge of anatase than II, after the photogenerated electrons flow from rutile to II, the electrons may be trapped at the intermediate phase.However, the CBO between the anatase and II phases is only 0.09 eV.Taking into account the computational errors, such a small energy difference can almost be ignored.In addition, the thickness of the intermediate II phase is relatively thin.Thus, the trapped electrons can readily reach saturation and then be driven to the anatase side by the large potential drop between the anatase and rutile phases (0.90 eV).Furthermore, as mentioned above, there is a built-in electric field at the (112)A/(100)II interface directed from anatase (112) to II (100), which is conducive to the photogenerated electrons' transfer from intermediate II to the anatase phase.To give an intuitive picture about the charge migra-  Arranging the band edge positions of (112)A/(100)II and (001)II/(101)R together, we can summarize the overall band alignment of the indirect three-phase junction in anatase/rutile mixed-phase TiO2 (see Figure 6b).This figure shows that the VBM positions of the three phases decrease following the order of rutile > II > anatase.The VBM of rutile is much higher than that of anatase, by 1.24 eV.Consequently, the photogenerated holes can transfer easily from anatase to rutile via the intermediate II phase without a barrier.By contrast, due to the slightly higher conduction band edge of anatase than II, after the photogenerated electrons flow from rutile to II, the electrons may be trapped at the intermediate phase.However, the CBO between the anatase and II phases is only 0.09 eV.Taking into account the computational errors, such a small energy difference can almost Arranging the band edge positions of (112) A /(100) II and (001) II /(101) R together, we can summarize the overall band alignment of the indirect three-phase junction in anatase/rutile mixed-phase TiO 2 (see Figure 6b).This figure shows that the VBM positions of the three phases decrease following the order of rutile > II > anatase.The VBM of rutile is much higher than that of anatase, by 1.24 eV.Consequently, the photogenerated holes can transfer easily from anatase to rutile via the intermediate II phase without a barrier.By contrast, due to the slightly higher conduction band edge of anatase than II, after the photogenerated electrons flow from rutile to II, the electrons may be trapped at the intermediate phase.However, the CBO between the anatase and II phases is only 0.09 eV.Taking into account the computational errors, such a small energy difference can almost be ignored.In addition, the thickness of the intermediate II phase is relatively thin.Thus, the trapped electrons can readily reach saturation and then be driven to the anatase side by the large potential drop between the anatase and rutile phases (0.90 eV).Furthermore, as mentioned above, there is a built-in electric field at the (112) A /(100) II interface directed from anatase (112) to II (100), which is conducive to the photogenerated electrons' transfer from intermediate II to the anatase phase.To give an intuitive picture about the charge migration direction upon light excitation, the spatial distributions of electrons and holes (gray and orange, respectively) corresponding to the strongest absorptions of (112) A /(100) II (580 nm) and (001) II /(101) R (614 nm) are depicted in Figure 7, which originate from the S 0 → S 40 and S 0 → S 41 excitations, respectively.The electron-hole analysis was performed using the Multiwfn software package (version 3.7) [30].It can clearly be seen that for (112) A /(100) II , the electrons and holes generated upon photoexcitation are mainly localized at the anatase and intermediate II phases, respectively, while for (001) II /(101) R , the photogenerated electrons and holes are distributed in the intermediate II and rutile phases, respectively.Driven by the combined effect of various factors, it can be concluded that in anatase/rutile mixed-phase TiO 2 , the three-phase junction can prompt the photogenerated electrons to flow to the anatase phase while the holes transfer to the rutile phase, leading to an efficient spatial separation of electron-hole pairs.This charge migration mechanism is consistent with the observation by Li et al. [31].Experimentally, they showed that the mixed-phase TiO 2 exhibiting superior photoelectrochemical water splitting is the TiO 2 -AR electrode with rutile as the external layer, which possesses an appropriate phase alignment for forward electron migration from rutile to anatase.
Molecules 2024, 29, x FOR PEER REVIEW 8 of 1 and orange, respectively) corresponding to the strongest absorptions of (112)A/(100)II (580 nm) and (001)II/(101)R (614 nm) are depicted in Figure 7, which originate from the S0 → S4 and S0 → S41 excitations, respectively.The electron-hole analysis was performed using the Multiwfn software package (version 3.7) [30].It can clearly be seen that for (112)A/(100)II the electrons and holes generated upon photoexcitation are mainly localized at the anatase and intermediate II phases, respectively, while for (001)II/(101)R, the photogenerated elec trons and holes are distributed in the intermediate II and rutile phases, respectively Driven by the combined effect of various factors, it can be concluded that in anatase/rutile mixed-phase TiO2, the three-phase junction can prompt the photogenerated electrons to flow to the anatase phase while the holes transfer to the rutile phase, leading to an efficien spatial separation of electron-hole pairs.This charge migration mechanism is consisten with the observation by Li et al. [31].Experimentally, they showed that the mixed-phase TiO2 exhibiting superior photoelectrochemical water splitting is the TiO2-AR electrode with rutile as the external layer, which possesses an appropriate phase alignment for for ward electron migration from rutile to anatase.In addition to the efficient charge separation and transfer, high-performance semi conductor photocatalysts also require effective solar light utilization.Therefore, the opti cal absorption spectra of biphase TiO2 ((112)A/(100)II and (001)II/(101)R) were investigated as illustrated in Figure 8.For comparison, the optical absorption properties for pure-phase TiO2 (anatase (112), II (100), II (001) and rutile (101)) were also included.One can see tha the maximum absorption peaks for pure anatase (112) and II (100) are both located a about 500 nm.After the formation of heterojunctions, the (112)A/(100)II heterostructure shows an obvious redshift (about 800 nm) and possesses a larger optical absorption coef ficient (see Figure 8a).The redshift is attributed to its reduced band gap (see Figure 5a) The broad and strong optical absorption can promote the photoexcitation of electrons and holes.For (001)II/(101)R, the maximum absorption peak slightly shifts to the red light re gion and the optical absorption coefficient mildly increases in comparison with those o rutile (101) and II (001) (see Figure 8b).The above findings indicate that the interfacia interaction between anatase (112) and II (100) plays a more significant role in the ligh absorption than that between rutile (101) and II (001).In addition, in anatase/rutile mixed phase TiO2, anatase phase should act as a photon adsorption agent, which is in accordance with previous experimental and theoretical studies [22,32].In addition to the efficient charge separation and transfer, high-performance semiconductor photocatalysts also require effective solar light utilization.Therefore, the optical absorption spectra of biphase TiO 2 ((112) A /(100) II and (001) II /(101) R ) were investigated, as illustrated in Figure 8.For comparison, the optical absorption properties for pure-phase TiO 2 (anatase (112), II (100), II (001) and rutile (101)) were also included.One can see that the maximum absorption peaks for pure anatase (112) and II (100) are both located at about 500 nm.After the formation of heterojunctions, the (112) A /(100) II heterostructure shows an obvious redshift (about 800 nm) and possesses a larger optical absorption coefficient (see Figure 8a).The redshift is attributed to its reduced band gap (see Figure 5a).The broad and strong optical absorption can promote the photoexcitation of electrons and holes.For (001) II /(101) R , the maximum absorption peak slightly shifts to the red light region and the optical absorption coefficient mildly increases in comparison with those of rutile (101) and II (001) (see Figure 8b).The above findings indicate that the interfacial interaction between anatase (112) and II (100) plays a more significant role in the light absorption than that between rutile (101) and II (001).In addition, in anatase/rutile mixed-phase TiO 2 , anatase phase should act as a photon adsorption agent, which is in accordance with previous experimental and theoretical studies [22,32].

CO2 Photoreduction Mechanism
Driven by the spatial charge separation, the photogenerated holes and electrons will preferentially accumulate on rutile and anatase phases, respectively.The photogenerated electrons in the conduction band of anatase can trigger CO2 conversion.Therefore, the CO2 reduction reaction prefers to proceed on the anatase phase.Moreover, (112)A/(100)II heterostructure possesses superior light absorption ability, which is conductive to enhancing its photocatalytic activity.Therefore, the anatase/rutile mixed-phase TiO2 is regarded as a preferable photocatalyst for CO2 conversion.Next, the CO2 reaction processes on the anatase side of (112)A/(100)II heterostructure were systematically explored.In order to reveal the influence of heterojunctions on CO2 reduction, we also took into account the reaction pathways on pure-phase anatase for comparison.
The adsorption of CO2 on catalyst surface is the initial and most vital step in the CO2 reduction reaction [7].The CO2 adsorption configurations have a significant influence on the selectivity of catalytic reactions in the following steps [33,34].Therefore, our study started by investigating the adsorption behaviors of CO2 on the anatase surface.In this simulation, four possible configurations for the CO2 adsorption were explored and the corresponding optimized geometries are shown in Figure 9.According to the calculated adsorption energies ( ad = (TiO 2 /CO 2 ) − (TiO 2 ) − (CO 2 )) (see Table 1), it is found that in all adsorption configurations, the Ead,A/II values are more positive than Ead,A, indicating a weaker adsorption capacity of CO2 adsorbed on the (112)A/(100)II heterostructure compared to that on the pure-phase anatase surface.This may be attributed to the fact that the formation of a (112)A/(100)II heterostructure can induce the charge transfer between anatase (112) and II (100) surfaces.The charge redistribution may break the original stability of the anatase (112) surface and thus cause a slight local deformation on the anatase surface, which is unfavorable for CO2 adsorption on the (112)A/(100)II heterostructure.In addition, the most stable adsorption configuration of CO2 on both pure-phase anatase and the (112)A/(100)II heterojunction is a nearly linear configuration (L1), slightly tilted relative to the surface normal through the interaction of the O atom in CO2 with surface five-foldcoordinated Ti5c (d(Ti5cO) = 2.62 and 2.71 Å, respectively) and the C atom in CO2 with surface-bridging O2c (d(O2cC) = 2.70 and 2.78 Å, respectively).The metastable structure also displays a linear configuration (L2), in which the CO2 molecule is nearly vertically adsorbed on the top of surface Ti5c atoms through relatively weak interactions with an adsorption energy of −0.02 and 0.21 eV, respectively.In bidentate carbonate (B1, one side of CO2 laying along the Ti5c-O2c bond) and bridged carbonate (B2, two O atoms in CO2 bridging two surface Ti5c and the C atom in CO2 pointing downward) adsorption configurations, the CO2 molecules are largely deformed with respect to the linear shape and exhibit bent structures.Both of these configurations are unstable and the energy of the B2 structure is even higher than that of B1 by 0.53 and 0.30 eV, respectively.The stability order of the adsorption structures, L1 > L2 > B1 > B2, is similar to the CO2 adsorption on anatase

CO 2 Photoreduction Mechanism
Driven by the spatial charge separation, the photogenerated holes and electrons will preferentially accumulate on rutile and anatase phases, respectively.The photogenerated electrons in the conduction band of anatase can trigger CO 2 conversion.Therefore, the CO 2 reduction reaction prefers to proceed on the anatase phase.Moreover, (112) A /(100) II heterostructure possesses superior light absorption ability, which is conductive to enhancing its photocatalytic activity.Therefore, the anatase/rutile mixed-phase TiO 2 is regarded as a preferable photocatalyst for CO 2 conversion.Next, the CO 2 reaction processes on the anatase side of (112) A /(100) II heterostructure were systematically explored.In order to reveal the influence of heterojunctions on CO 2 reduction, we also took into account the reaction pathways on pure-phase anatase for comparison.
The adsorption of CO 2 on the catalyst surface is the initial and most vital step in the CO 2 reduction reaction [7].The CO 2 adsorption configurations have a significant influence on the selectivity of catalytic reactions in the following steps [33,34].Therefore, our study started by investigating the adsorption behaviors of CO 2 on the anatase surface.In this simulation, four possible configurations for the CO 2 adsorption were explored and the corresponding optimized geometries are shown in Figure 9.According to the calculated adsorption energies (E ad = E(TiO 2 /CO 2 ) − E(TiO 2 ) − E(CO 2 )) (see Table 1), it is found that in all adsorption configurations, the E ad,A/II values are more positive than E ad,A , indicating a weaker adsorption capacity of CO 2 adsorbed on the (112) A /(100) II heterostructure compared to that on the pure-phase anatase surface.This may be attributed to the fact that the formation of a (112) A /(100) II heterostructure can induce the charge transfer between anatase (112) and II (100) surfaces.The charge redistribution may break the original stability of the anatase (112) surface and thus cause a slight local deformation on the anatase surface, which is unfavorable for CO 2 adsorption on the (112) A /(100) II heterostructure.In addition, the most stable adsorption configuration of CO 2 on both pure-phase anatase and the (112) A /(100) II heterojunction is a nearly linear configuration (L1), slightly tilted relative to the surface normal through the interaction of the O atom in CO 2 with surface five-fold-coordinated Ti 5c (d(Ti 5c O) = 2.62 and 2.71 Å, respectively) and the C atom in CO 2 with surface-bridging O 2c (d(O 2c C) = 2.70 and 2.78 Å, respectively).The metastable structure also displays a linear configuration (L2), in which the CO 2 molecule is nearly vertically adsorbed on the top of surface Ti 5c atoms through relatively weak interactions with an adsorption energy of −0.02 and 0.21 eV, respectively.In bidentate carbonate (B1, one side of CO 2 laying along the Ti 5c -O 2c bond) and bridged carbonate (B2, two O atoms in CO 2 bridging two surface Ti 5c and the C atom in CO 2 pointing downward) adsorption configurations, the CO 2 molecules are largely deformed with respect to the linear shape and exhibit bent structures.Both of these configurations are unstable and the energy of the B2 structure is even higher than that of B1 by 0.53 and 0.30 eV, respectively.The stability order of the adsorption structures, L1 > L2 > B1 > B2, is similar to the CO 2 adsorption on anatase (101) surfaces [35][36][37].Meanwhile, on anatase (001) [33] and rutile (001) surfaces [38], the most stable CO 2 adsorption structure displays a bent configuration, suggesting that the CO 2 adsorption behavior is related to both the adsorbed crystal phases and the crystal facets.Based on the above analyses, the L1 configuration is chosen for the following mechanism study of CO 2 photoreduction on both pure-phase anatase and a (112) A /(100) II heterostructure.
Molecules 2024, 29, x FOR PEER REVIEW 10 of 16 (101) surfaces [35][36][37].Meanwhile, on anatase (001) [33] and rutile (001) surfaces [38], the most stable CO2 adsorption structure displays a bent configuration, suggesting that the CO2 adsorption behavior is related to both the adsorbed crystal phases and the crystal facets.Based on the above analyses, the L1 configuration is chosen for the following mechanism study of CO2 photoreduction on both pure-phase anatase and a (112)A/(100)II heterostructure.Table 1.Calculated adsorption energies (eV) of CO2 on the pure-phase anatase (Ead,A) and the (112)A/(100)II heterostructure (Ead,A/II).Possible reaction pathways and intermediates of CO2 reduction are listed in Scheme 1 and the potential-energy-change profiles of various possible reaction pathways are displayed in Figure 10.Our investigations show that for the first hydrogenation step on purephase anatase, the reaction energy of the formation of COOH* by connecting the H atom to the O atom of CO2 is 0.62 eV, which is more thermodynamically favorable by 0.87 eV than the generation of HCOO* through the H atom's addition to the C atom (see Figure 10a).This is mainly because due to the higher electronegativity of the O atom, as the C and O atoms of CO2 are positively and negatively charged, respectively.Hence, the O atom of CO2 is more easily hydrogenated to COOH*.COOH* subsequently undergoes hydrogenation to HCOOH or dehydroxylation to CO.The acquisition of HCOOH is an exothermic reaction with an energy decrease of −1.81 eV, whereas the transformation to CO is an endothermic process (0.42 eV).Therefore, CO2 is more likely to undergo a twostep hydrogenation mechanism to HCOOH.In addition, the adsorption energy for HCOOH and CO are −1.57and −0.33 eV, respectively.This suggests that the interaction between HCOOH and anatase is stronger than that of CO, which further confirms that  Possible reaction pathways and intermediates of CO 2 reduction are listed in Scheme 1 and the potential-energy-change profiles of various possible reaction pathways are displayed in Figure 10.Our investigations show that for the first hydrogenation step on pure-phase anatase, the reaction energy of the formation of COOH* by connecting the H atom to the O atom of CO 2 is 0.62 eV, which is more thermodynamically favorable by 0.87 eV than the generation of HCOO* through the H atom's addition to the C atom (see Figure 10a).This is mainly because due to the higher electronegativity of the O atom, as the C and O atoms of CO 2 are positively and negatively charged, respectively.Hence, the O atom of CO 2 is more easily hydrogenated to COOH*.COOH* subsequently undergoes hydrogenation to HCOOH or dehydroxylation to CO.The acquisition of HCOOH is an exothermic reaction with an energy decrease of −1.81 eV, whereas the transformation to CO is an endothermic process (0.42 eV).Therefore, CO 2 is more likely to undergo a two-step hydrogenation mechanism to HCOOH.In addition, the adsorption energy for HCOOH and CO are −1.57and −0.33 eV, respectively.This suggests that the interaction between HCOOH and anatase is stronger than that of CO, which further confirms that HCOOH is the preferential intermediate product.Then, HCOOH* is hydrogenated and dehydrated to form HCO*, and this step is considered to be the rate-limiting step with the highest energy barrier of 0.80 eV.The next step of HCO* hydrogenation contains two possible pathways-one to H 2 CO* and the other one to CHOH*.The production of H 2 CO* has an exothermic reaction energy of −0.23 eV, while the formation of CHOH* is an endothermic process with a distinct energy increase of 1.39 eV, indicating that the generation of H 2 CO* is more favorable than CHOH*.Subsequently, H 2 CO is more easily reduced to CH 2 OH* intermediate (−0.40 eV), rather than undergoing hydrogenation to form CH 3 O* (1.04 eV).In the following step, there are considerable differences in the reaction energies for the formation of CH 3 OH (−1.48 eV) and CH 2 * (1.31 eV).The significantly negative energy barrier implies that CH 2 OH*'s reduction to CH 3 OH is more competitive relative to CH 2 *.In addition, it is noted that CH 2 OH* → CH 2 * is the rate-limiting step for CH 4 formation, and its corresponding energy barrier (1.31 eV) is much higher than the rate-limiting energy for CH 3 OH generation (HCOOH* → HCO* with 0.80 eV).Therefore, the final product is more likely to be CH 3 OH.In brief, the optimal route of CO 2 reduction on pure-phase anatase is CO 2 → COOH* → HCOOH* → HCO* → H 2 CO* → CH 2 OH* → CH 3 OH, which is similar to the reaction mechanism of CO 2 reduction on g-C 3 N 4 -based photocatalysts [39,40].Figure 10b presents the potential energy diagram of CO 2 reduction reaction pathways on the (112) A /(100) II heterostructure.It can be seen that the reaction pathways of CO 2 's transformation to CO, CH 3 OH, and CH 4 on the (112) A /(100) II heterostructure are the same as those on pure-phase anatase, but the corresponding reaction energy for each step is quite different.On the (112) A /(100) II heterostructure, the calculated reaction energy of the initial step of CO 2 's hydrogenation to the COOH* intermediate is 0.09 eV, which is much smaller than that on pure-phase anatase, at 0.62 eV, indicating that the (112) A /(100) II heterostructure is more conductive to the formation of COOH* through a barrierless pathway.This is mainly because when anatase (112) and II (100) surfaces are in contact, there will be charge transfer between the two phases.The charge rearrangement may induce more negative charges around the O atoms of CO 2 on the (112) A /(100) II heterostructure (−0.19 and −0.27 e) compared to those on pure-phase anatase (−0.14 and −0.20 e).Consequently, the H atom is preferably bound to the O atom of CO 2 on the (112) A /(100) II heterostructure to generate the COOH* intermediate.In addition, although the rate-limiting step of generating CH 3 OH on the (112) A /(100) II heterostructure is also the hydrogenation and dehydration of HCOOH* to HCO*, it possesses a lower energy barrier than the pure-phase anatase by 0.42 eV.Moreover, the reaction energy of CH 2 OH*'s reduction to CH 2 * on the (112) A /(100) II heterostructure is 1.64 eV, much higher than that on pure-phase anatase (1.31 eV), which suggests that the selectivity of CO 2 reduction to form CH 3 OH might be enhanced on mixed-phase TiO 2 .In summary, the (112) A /(100) II heterostructure is more favorable for the generation of CH 3 OH compared to pure-phase anatase.It is known that commercial P25 is also a mixed-phase TiO 2 .However, many experimental studies have shown that the P25 photocatalyst exhibited excellent photoreduction activity in reducing CO 2 into CH 4 [41][42][43], which is different from the main product generated by our constructed anatase/rutile heterostructure model.This distinction may originate from the differences in the exposed surface for the CO 2 reaction process, proceeding on the anatase (112) surface in our model and the anatase (101) surface in P25 [41][42][43].

Calculations of Band Edges
In the heterojunction model, the band information that we could directly obtain was the valence band maximum (VBM) and the conduction band minimum (CBM) positions of the overall system.Then, the valence band offset (VBO) and conduction band offset (CBO) at the mixed-phase junctions were calculated to evaluate how the remaining two band edges were shifted relative to the VBM and CBM.Based on the viewpoint proposed by Ceder et al. that the difference between energy level and Hartree potential remains unchanged everywhere in space [44], the valence band offset value (E VBO ) can be computed as ii where i and ii stand for the semiconductors of phase i and phase ii, respectively.HOMO bulk sc is the highest occupied molecular orbital (HOMO) energy of the bulk semiconductor.V bulk sc is the electrostatic potential of the bulk semiconductor.Under the periodic boundary condition (PBC), the V bulk sc value is zero.V int sc is the averaged electrostatic potential in the bulk-like region of the heterojunction interface for a semiconductor, which is obtained by nanosmoothing the original electrostatic potential profile with the MACROAVE code [45].E VBO > 0 suggests that the photogenerated holes tend to flow from phase ii to phase i.
In the same way, the conduction band offset value (E CBO ) is given by where LUMO bulk sc is the lowest unoccupied molecular orbital (LUMO) energy of the bulk semiconductor.E CBO > 0 indicates that the photogenerated electrons are likely to transfer from phase i to phase ii.

Computational Setup
All density functional theory (DFT) simulations were performed using the freely available program package CP2K/Quickstep [46].The Perdew-Burke-Ernzerhof (PBE) functional [47] was employed for ab initio calculations.The basis sets for valence electrons were double-ζ basis functions with one set of polarization functions (DZVP) [48].The core electrons were represented using analytic Goedecker-Teter-Hutter (GTH) pseudopotentials [49].The dispersion correction of the Grimme method D3 [50] was adopted to describe the van der Waals interactions.For geometry optimizations, the wave function optimization was carried out using an orbital transformation minimizer, which can give the optimal convergence control [51].Meanwhile, for absorption spectra calculations, the matrix diagonalization method was applied to obtain the wave function information of unoccupied molecular orbitals for data analysis.The convergence criterion for wave function optimization was set at a maximum electronic gradient of 3 × 10 −7 a.u. and the plane wave cutoff for the electron density expansion was 400 Ry.It is known that when employing the pure generalized gradient approximation (GGA) functional to estimate the solid electronic structures, there is a delocalization error leading to an underestimation of the band gap.Therefore, to more accurately describe the alignment of electronic energy levels across the heterojunction interface, the band edge positions were computed using the Heyd-Scuseria-Ernzerhof (HSE06) screened hybrid functional [52,53] based on the structures from the PBE functional calculations.

Conclusions
In this work, the band edges of three-phase junctions in the anatase/rutile mixedphase TiO 2 were successfully determined and the mechanism of charge separation and transport across the anatase/rutile interface was revealed based on ab initio simulations.Our results show that the VBM positions decrease in the order of rutile > II > anatase, facilitating the holes' transfer from anatase to rutile phases under sunlight irradiation.Meanwhile, the CBM position of anatase is slightly higher than that of intermediate II phase, and thus the II will act as an electron trapping site and impede the electrons' flow from rutile to anatase.However, the potential drop across the anatase/rutile interface is so large that it can provide a relatively high driving force for the photoelectrons' migration to anatase via the very thin layer of II.Moreover, the work function of II is higher than that of anatase, leading to the formation of a built-in electric field and an upward band bending from anatase to II, which is also favorable for the electrons' accumulation on the anatase phase.Briefly, electron transfer from rutile to anatase is energetically permitted, as indicated experimentally [17,31].In addition, it is found that after the construction of the (112) A /(100) II heterostructure, its optical absorption capacity is significantly enhanced compared to the pure-phase anatase.The effective utilization of solar light is conductive to promoting the photocatalytic activity.
Simultaneously, the CO 2 photoreduction mechanism on an anatase (112) surface was systematically investigated.It is confirmed that the most stable CO 2 adsorption configuration is a nearly linear configuration (L1), slightly tilted with respect to the surface normal, which is similar to the adsorption behavior on an anatase (101) surface [35].The calculated potential energies suggest that on both pure-phase anatase and the (112) A /(100) II het-erostructure, CH 3 OH is more liable to be the final product and the corresponding optimal route is CO 2 → COOH* → HCOOH* → HCO* → H 2 CO* → CH 2 OH* → CH 3 OH.During the whole reaction process, the rate-limiting step is the hydrogenation and dehydration of HCOOH to HCO*.The rate-limiting energy on the (112) A /(100) II heterostructure is obviously lower than that on pure-phase anatase, and the first hydrogenation step of CO 2 to COOH* on the (112) A /(100) II heterostructure is thermodynamically spontaneous with a barrierless pathway, demonstrating that anatase/rutile mixed-phase TiO 2 is an excellent photocatalyst for CO 2 reduction.

Figure 4 .
Figure 4. Planar-averaged electron density difference in the Z direction for (a) (112)A/(100)II and (b) (001)II/(101)R heterostructures.The pink and blue isosurfaces represent the electron depletion and accumulation, respectively.The "II" stands for the intermediate phase (TiO2-II).

Figure 4 .
Figure 4. Planar-averaged electron density difference in the Z direction for (a) (112) A /(100) II and (b) (001) II /(101) R heterostructures.The pink and blue isosurfaces represent the electron depletion and accumulation, respectively.The "II" stands for the intermediate phase (TiO 2 -II).

Figure 6 .
Figure 6.(a) Band edge positions relative to the vacuum level of (112)A/(100)II and (001)II/(101)R heterostructures.(b) Illustrations of the proposed band alignment and the charge transfer mechanism in anatase/rutile mixed-phase TiO2.The "II" stands for the intermediate phase (TiO2-II).

Figure 6 .
Figure 6.(a) Band edge positions relative to the vacuum level of (112)A/(100)II and (001)II/(101)R heterostructures.(b) Illustrations of the proposed band alignment and the charge transfer mechanism in anatase/rutile mixed-phase TiO2.The "II" stands for the intermediate phase (TiO2-II).

Figure 6 .
Figure 6.(a) Band edge positions relative to the vacuum level of (112) A /(100) II and (001) II /(101) R heterostructures.(b) Illustrations of the proposed band alignment and the charge transfer mechanism in anatase/rutile mixed-phase TiO 2 .The "II" stands for the intermediate phase (TiO 2 -II).

Figure 7 .
Figure 7. Spatial representations of electron and hole distributions of (a) (112)A/(100)II and (b (001)II/(101)R heterostructures.Gray and orange areas represent the electron and hole distributions respectively.The "II" stands for the intermediate phase (TiO2-II).

Scheme 1 .Scheme 1 .
Scheme 1. Possible reaction pathways and intermediates of the CO2 reduction reaction.The asterisk (*) indicates that the intermediate is adsorbed on the active site.The red parts correspond to the optimal reaction pathways.

Scheme 1 .Figure 10 .
Scheme 1. Possible reaction pathways and intermediates of the CO2 reduction reaction.The asterisk (*) indicates that the intermediate is adsorbed on the active site.The red parts correspond to the optimal reaction pathways.

Configuration E ad,A E ad,A/II
[39,40]s the preferential intermediate product.Then, HCOOH* is hydrogenated and dehydrated to form HCO*, and this step is considered to be the rate-limiting step with the highest energy barrier of 0.80 eV.The next step of HCO* hydrogenation contains two pos sible pathways-one to H2CO* and the other one to CHOH*.The production of H2CO* has an exothermic reaction energy of −0.23 eV, while the formation of CHOH* is an endo thermic process with a distinct energy increase of 1.39 eV, indicating that the generation of H2CO* is more favorable than CHOH*.Subsequently, H2CO is more easily reduced to CH2OH* intermediate (−0.40 eV), rather than undergoing hydrogenation to form CH3O* (1.04 eV).In the following step, there are considerable differences in the reaction energies for the formation of CH3OH (−1.48 eV) and CH2* (1.31 eV).The significantly negative en ergy barrier implies that CH2OH*'s reduction to CH3OH is more competitive relative to CH2*.In addition, it is noted that CH2OH* → CH2* is the rate-limiting step for CH4 for mation, and its corresponding energy barrier (1.31 eV) is much higher than the rate-limit ing energy for CH3OH generation (HCOOH* → HCO* with 0.80 eV).Therefore, the fina product is more likely to be CH3OH.In brief, the optimal route of CO2 reduction on pure phase anatase is CO2 → COOH* → HCOOH* → HCO* → H2CO* → CH2OH* → CH3OH, which is similar to the reaction mechanism of CO2 reduction on g-C3N4-based photocatalysts[39,40].